2. Philosophy - Stefano Franchi

ENDGAMES
Game and Play at the End of Philosophy
Stefano Franchi

ii
E NDGAMES
Copyright © Stefano Franchi 1999

I. Prelude
1. Mr. Palomar 3
2. Mr. Palomar’s checkmates 5
3. The World of Candrakirti 12
4. The irreparable light of dawn 26
CONTENTS
II. The End of Philosophy
1. Truth 30
2. Philosophy 31
3. Hegel’s paradox 36
4. Philosophy’s ends 48
5. Of lines, circles, and spheres. 62
6. “Ein Spielen der Liebe mit sich selbst…” 69
III. Absolute(s) Spielen
1. “to die game” 80
2. Absolute(s) Spielen 87
3. Bordering philosophy 96
4. Spielen, the Abyss, and the Child 106
5. The great beyond 118
IV. Philosophy, Non-Philosophy, and Science
1. Non-Philosophy 126
2. On the various meanings of “X is not a science” 133
3. Between engineering, science, and philosophy. 145
4. Artificial Intelligence as a non-philosophical project 162
5. Structuralism and philosophy 168
6. AI, Structuralism, and Spiel 175
V. Chess, games, and flies
1. The Drosophila of AI. 178
2. Game theoretic games 187
3. Combinatorial explosions 197
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VI. Structures (and spaces)
1. Games and Structures 212
2. From language to myth 216
3. Search-spaces and structures 234
VII. Anaclastic Supplements
1. Game, Spiel, and the End 240
2. The supplement 241
3. Form and content 250
4. Structure and Substance 259
5. Structuralism, Philosophy, and AI 266
6. The challenge of closure 278
7. The anaclastic illusion of a transcendental unity 285
VIII. A Movable Conclusion
1. After game-based Spielen 308
References 311
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PRELUDE

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Jeu est la cyphre de l’ouverture anti-dialectique par excellence
Jacques Derrida
This book explores the relationship between the end of philosophy and the concepts of
game and play that have very often been associated with it. In the course of the following
chapters, I will transverse a considerable amount of philosophical and scientific texts in or-
der to clarify the variegated meaning of the word “end” when used in conjunction with phi-
losophy, and I will try to explain why it happens that the concepts of game and play (or
Spiel,
as I will call the common concept underlying the two terms) seems to appear every
time philosophy’s end is announced or proclaimed. However, one of the risks of any inves-
tigation that claims its validity from a patient textual reading is that the overall significance
of the problems at issue may be easily lost in the intricacies of the arguments and in the
detail of the textual and conceptual exegesis. I offer this prelude as a remedy to the prob-
lem: it presents an overall view of the same problems I deal with in the following chapters,
but in a very different, and much more succinct form.
It has often been said that art, and literature in particular, is capable of achieving a den-
sity of expression unparalleled in any other form of communication. Regardless of its gen-
eral validity, the statement seems certainly to be valid in the case of Italo Calvino’s novel
Mr. Palomar,
a short book of 100 pages whose scope, if not its ambition, is perhaps com-
parable to the Hegelian Logic. The next few pages will provide a reading of the novel that

M R . PALOMAR
will make clear, hopefully, why game and play seem to be summoned so often in this age
of the end of philosophy, and why, I believe, it is incumbent upon us to answer their perhaps
misplaced call.
The first section will briefly introduce the novel and its particular way of addressing
philosophy’s concerns. Then, the section called “Mr. Palomar’s checkmates” corresponds,
roughly, to the first two chapters: it explain why philosophy has to reach an end if human
existence is to gain any significance. In other words, the section presents, on the basis of
Calvino’s short proses, the existential import of the end of philosophy—it claims to answer
the question: why does it matter to us that philosophy be achieved?
The next section, “The world of Candrakirti,” illustrates one possible, and I believe
very common, solution to the problem of the end of philosophy in our postmodern era. It is
the combinatorial view, as I call it, that interprets the world as a a game, sometimes a cos-
mic game, sometimes a power game. The content of this section corresponds, approximate-
ly, to the last three chapters ( IV-VI)
of the book , i.e. to the chapters in which I explore the
solutions provided by Artificial Intelligence and Structuralism, the two disciplines that, I
believe, have better probed the depths of the combinatorial view and have provided a fine
articulation of the formal concept of game that underlies it.
The last, very brief section, “The irreparable light of dawn,” is a pointer to what, with
a bit of luck, I hope I will be working on next. It illustrates the reasons why, I believe, Spiel,
both under the guises of game and of play, cannot represent a solution to the existential
abyss that the philosophical end opens up before, or rather under, us. What may lie on the
bottomless surface of that
1. Mr. Palomar
Ab-grund,
however, I will not try to tell here.
A few years ago, in a conference devoted to Italo Calvino’s work, Giorgio Agamben
pointed out that the existence of the unrepresentable, the implications of quantum physics,
Heisenberg’s indeterminacy principle etc. are issues so commonly debated in the present
intellectual discussions that they have become utterly meaningless. He went on to affirm
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that a writer’s or scientist’s work becomes interesting when it goes beyond such a common
situation rather than when it presents yet another exposition of the unavoidable limits of
representation. Such a theme, he concluded, is so banal that it might be rightly called the
“triviality of modernity.” In a text written around the same time that treats of the difficulties
encountered by the Indian philosopher Nagarjuna in his teaching of the doctrine of the void,
1
Agamben describes more precisely what he means by such a term. Indeed, several among
Nagarjuna’s disciples—even Candrakirti, the most faithful—misunderstood his doctrine on
an essential point, a point so subtle that even he, at times, could not grasp it. The difference
between the two interpretations was infinitesimal, but incommensurable: his doctrine
taught the vacuity of representation whereas his disciples “treated the void as a thing, they
would form a representation of the vacuity of representation. But the realization of the void-
ness of representation—continued Nagarjuna—is not, in turn, a representation: it is the end
of representation.” Those who believe that “even the void is an opinion and that the irrep-
resentable is a representation” fall into the trap of nihilism and miss the most important
point of his teachings: “that the empty image is not an image of anything. The word, of its
2
vacuity, is perfectly full.”
The following pages explore a possible interpretation of the difference between the
doctrine of Nagarjuna and the misunderstanding of Candrakirti, between the doctrine of the
void and the triviality of modernity, by reading a text by Italo Calvino, the author Agamben
was referring to on both occasions. In the first section I will show that the unity and differ-
ence of the two doctrines are portrayed by Mr. Palomar with a rare rigor and clarity and I
will show how the enigmatic conclusion of the book is ideally suited to reflection. In short,
1. See, respectively, Beppe Cottafavi, Maurizio Magri, eds., I narratori dell’invisibile (Modena: Mucchi,
1987) 156 and Giorgio Agamben, Idea della Prosa (Milano: Feltrinelli, 1985) 98-101. Engl. tr. Idea of
the Prose (Minneapolis: Minnesota UP, 1995)131-133. The latter text—’Idea del risveglio’ or “The
idea of awakening—proposes a short but extremely interesting interpretation of the doctrine of voidness.
The doctrine was developed by the Indian philosopher Nagarjuna in the second century A.D. and
reinterpreted four centuries later by the philosopher Candrakirti in the school founded by Nagarjuna.
The text is dedicated to Italo Calvino. It may be worth noting that every reference to the doctrines of
Nagarjuna and Candrakirti in what follows is to be intended as a reference to Agamben’s text and not
as a reference to the historical thinkers without which, perhaps, it cannot be understood.
2. Giorgio Agamben, Idea della Prosa…,
100; Engl tr. 133, Translation modified.

M R . PALOMAR’
S CHECKMATES
I will show that the doctrine of the void and the vacuity of representation are what Mr. Pal-
omar forces us to think.
2. Mr. Palomar’s checkmates
Calvino seems certainly intent to play with the representation of the irrepresentable:
the 27 texts in the book describe as many efforts to find an ultimate meaning in the every-
day interactions with the world and they all end up in failure and disarray. Twenty-even ef-
forts result in 27 defeats that document the inability of Mr. Palomar, the main character, to
enter in a meaningful relationship with the world, and bridge the abyss that separates him
3
from reality and his fellow men. Mr. Palomar’s experience is all in the negative. He search-
es a more equilibrated and less painful relationship with the world as it can arise on the ba-
sis of a newly found harmony, a new and fully organic way to be amidst things and people.
What exactly is to be understood by ‘harmony’ Mr. Palomar doesn’t say—most likely be-
cause if he were in the position to do so his tribulations would be over. Guided in all its
steps by what precedes and anticipates it, the search itself would be already over because it
would be reduced to a mere technique which, as such, would be an integral part of the goal
to be attained. Mr. Palomar can, at most, sense harmony in the subtle movements of the af-
ternoon moon, or in the delicate geometries of the sidereal spaces which, he feels, are based
on a regularity much deeper than the disordered succession underlying human events. Mr.
Palomar intimates the existence of a just order, possibly independent from the human. A
total order that encompasses everything, opposing and negating division, laceration and
4
fracture. Harmony—in the musical sense, at least—is given only in a concert, i.e., by in-
3.
Mr. Palomar includes three parts: “Mr. Palomar’s vacation,” “Mr. Palomar in the City,” “The silences
of Mr. Palomar.” Each of them, in turn, is subdivided in three sections including three texts each, for
a total of 27 very short ‘chapters’. Each text contain a meditation on a particular aspect of reality Mr.
Palomar has run into: a wave, a charcuterie, death, the Jardin des Plantes, etc.
Some of the texts collected
in the book had previously appeared on newspapers—first Il Corriere della Sera and then La
Repubblica—but
were substantially revised for the publication in book form. See Italo Calvino, Palomar
(Torino: Einaudi, 1983) and the English translation by William Weaver, Mr. Palomar (New York:
Harcourt Brace Jovanovich, 1985). For a discussion of the differences between the newspaper and
book form of the texts see Gian Carlo Ferretti, Le capre di Bikini (Roma: Editori Riuniti, 1989).
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dividual voices singing different melodies and composing, while unfolding them, a broader
all-encompassing texture. The main feature of the intimated harmony is the movement of
a completely given whole whose single parts enjoy their relative positions. Harmony is pos-
sibly the name of the opposition between man and world when such an opposition, instead
5
of being a discordant fracture, is recomposed in a chord, as Heraclitus reminds us. Be that
as it may, such an order, even if exists, must be found. And it is in the everyday world pop-
ulated by things, animals and plants, characterized by ongoing social interactions, enriched
by the fruits of human labor where Mr. Palomar seeks it.
However, he does not find any identifiable rhythm or pattern in reality, only chaos and
disorder. But in fact it would take little to meet the challenge of such complexities: it would
suffice to fix one’s gaze on any phenomenon whatever—on a wave, for example—and to
find in its motions what distinguishes it from the other waves while keeping it identical to
itself. It would be enough to identify what makes it a wave—as opposed to a ripple, crest,
or billow—and what distinguishes it from all the other similar but different waves. The
form of a wave might then appear to the intent observation of Mr. Palomar and from this
humble shadow of a broader harmony he might be able to broaden his field of observation
and eventually find the harmony of the whole universe. Or perhaps Mr. Palomar could hope
to find a wave, at least, a wave itself, with all its particularities, regularities and idiosyncra-
sies. In short, he might be able to grasp a thing, no matter how humble, in its wholeness.
But his attempt fails.
Far from unraveling themselves, from exposing their nude identity to his gaze, the
waves—when observed at length—start to sink into confusion. They even lose what
seemed to be most characteristic of them, to the point that they seem to move from the shore
to the open sea:
4. Concerto comes from concertare,
a contraption of cum certamen,
literally “fighting together.” Late
Latin has also another form, however, concento,
from cum cantus.
“Harmonia” is defined as the “tuning
of the instrument of the soul” by Plato. See Phaedrus,
86b7-c2
5. See Heraclitus, fragment 8 (Diels): “The opposites in agreement and from the disagreement a beautiful
harmony.” In the last pages of Stanze (Torino: Einaudi, 1977); Engl tr. Stanzas (Minneapolis: Minnesota
UP, 1993) Giorgio Agamben, commenting upon this fragment, insists that armonia is inseparable
from the idea of a juncture and an articulation: “the ‘perfect jewel of the cosmos’ implies for the
Greeks the idea of a laceration which is, at the same time, a suture” (188).

M R . PALOMAR’
S CHECKMATES
Concentrating the attention on one aspect makes it leap into foreground
and occupy the square, just as, with certain drawings, you have only to close
your eyes and when you open them the perspective has changed. Now, in
the overlapping of crests moving in various directions, the general pattern
seems broken down into sections that rise and vanish. In addition, the reflux
of every wave also has a power of its own that hinders the oncoming waves.
And if you concentrate your attention on these backward thrusts, it seems
that the true movement is the one that begins from the shore and goes out to
the sea.
The observation does not find a renewed harmony: it discovers the fracture between the ob-
server and the observed, the abyss of the distance. Or even worse, it discovers that order
and lawfulness exist in nature, but are inaccessible to human understanding and even less
to human language and its power of description. Indeed language, in order to function prop-
erly, should reach things in their singularity, in their being themselves and nothing else.
Such a goal is not reached. Names fail: in spite of Mr. Palomar’s efforts, in spite of all the
care he puts in his observations, in spite of his attempts to be precise in his descriptions and
adequately informed on the cultural and historical precedents, in spite of all this, things es-
cape him, by not answering the names that should evoke them. Instead of the things them-
selves, names find only other names. Language refers only to itself and its own history.
This is borne out in the episode in Mr. Palomar entitled “Two pounds of goose fat.”
While waiting in line in a charcuterie in Paris, Mr. Palomar is overwhelmed by the abun-
dance of smells, colors and images emanating by the patés and galantines and he would
like to find a deeper union with them. He would like to find once again the deep link be-
tween himself and this part of the world, between himself and these gifts that “nature and
culture have handed down for millennia” (69). He would like to feel immersed in a secret
harmony generated by the concert of flavors vibrating all around. In vain. Beyond the
paté,
Mr. Palomar finds only the , the name reveals only the name itself: “his imagination
does not instinctively associate the flavors with the images and names” ( ib. ). His honest ef-
fort to read into the delicacies the nature and culture that made them is even more frustrat-
ing, even deadly: “his gaze transform every food into a document of the history of
civilization, a museum item”(70). Instead of cheese, of the thing itself, “he sees names of
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cheeses, concepts of cheeses, meanings of cheeses, contexts of cheeses, psychologies of
cheeses...”(73). Far from calling things up and bringing them to us, names seem to alienate
them from us, by negating their singularity. Name only repeat the irreducible fracture, the
laceration, the death that separates us from the world. Indeed, could they be the cause of
death itself?
The primary fracture is not just between the self and the world, it also comes between
fellow human beings. In Mr. Palomar communication—and not only denomination—ap-
pears to be impossible. In one of the most beautiful texts of the book, The blackbird’s whis-
tle, Mr. Palomar compares the infinitely monotonous language of the bird—always the
same whistle, identical, rhythmical, unmistakable—with the infinite variety of human lan-
guage. He doubts that any communication between the blackbirds may be established on
such a slim informational basis. At most, the whistle of the bird stands for an existential
affirmation, an “I am here” obstinately repeated. Or perhaps it is just an illusion, the inane
effort to compress into the same sound a whole series of meanings to which the other cannot
but answer—in order to assent, negate, disagree or whatever—with the same identical
sound. It would seem to be a dialogue well below the expressive capacities of human lan-
guage, but a short interaction between Mr. Palomar and his wife, who comes into the garden
to water the flowers, dispels very soon such a comfortable delusion. The dialogue is ex-
tremely short, only a few words—”there they are” “shhh” “it is dry again, since yesterday”
“crooked...for all that, yes, my foot...“ “shhh, you scare them.” Yet, the analytical reflection
of Mr. Palomar does not fail to recognize the unexpressed elements that underlies it, the im-
plicit reproaches and the silent excuses. “It is dry again, since yesterday” means at bottom
“you could take care of the garden as well,” while the grumbles uttered by Mr. Palomar as
an answer are just the usual masculine strategy that opposes its omnipresent activities to
feminine garrulous talk. Deceptive as well is the objectivity of the deixis, of the impera-
tives, of the simplest interjections; those little words almost at the limit of communication
appear overburdened by meaning since they purport to show the proprietary relationship
with nature of each of the conversants. “There they are” means therefore “I was waiting for
them, I know them better than you who only now see and are amazed by them.”The lean

M R . PALOMAR’
S CHECKMATES
“shh” obtained as an answer expresses a resolute negation, since it means “don’t interrupt
them because I am listening to them; don’t you see I’m trying to understand them, and may-
be I can; at any rate I understand them better than you” (26-28).
On the other hand, if language is so inefficient, or perhaps too efficient, in carrying out
communication, silence is certainly not a better solution, simply because it does not exist.
In a universe as saturated by communication as ours, silence is nothing but a different form
of communication. Silence communicates as effectively as speech. Mr. Palomar—who has
made a habit to bite his tongue three times before speaking, as a healthy antidote to the
flood of opinions and judgments that surrounds him—soon realizes the futility of his
pledge. In the universe of communication, not to speak means to let the others speak, to
conform to their opinions and to implicitly justify their glib words. Methodical silence
seems only to help increasing the amount of words in circulation—an unsurprising result
since “even silence can be considered a kind of speech, since it is a rejection of the use to
which others put words”(103). True silence, like things, keeps escaping beyond words and
their absence.
If names refer only to themselves, if speech serves only to misunderstand each other
even too well, if things disappear continuously beside and beyond word and silence—what
is left is chaos, disorder and isolation. What is left is the incommunicability of experience,
even of the ultimate and most proper experience: death.
Death bears witness to the last phase of the tormented search for harmony we are fol-
lowing, in which Mr. Palomar tries to learn how to be dead. This indeed seems to him the
only possible way to free himself from his constant anxiety. Death, as end, conclusion, an-
nihilation of his life, should finally free Mr. Palomar from his inability to connect to the
world. Learning to be dead seems to be the only way out. But the feat is much more difficult
than expected. Being dead should mean that the world goes on without him,
a world in which things happen independently of his presence and his reactions,
following a law of their own or a necessity or rationale that does not
involve him? The wave strikes the cliff and hollows out the rock, another
wave arrives, another, and still another; whether he is or is not, everything
goes on happening. The relief in being dead should be this: having eliminat-
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ed that patch of uneasiness that is our presence, the only thing that matters
is extension and succession of things under the sun, in their impassive serenity.
(122)
But this does not resolve the dilemma, since the world has always excluded him from the
beginning. Now death, instead of being the final experience, the last act that terminates the
series of human events by making them a closed set, becomes the sentence to remain al-
ways the same in one’s own futility. Even suffering is denied to the dead. Death should ar-
rive at the supreme moment, as to the condemned of Kafka’s
Penal Colony,
when the
victim, after hours of torture, begins to decipher on his own body the meaning of the sen-
tence and in the flash that separates him from the end of existence understands its intimate
meaning. The fate that awaits M. Palomar looks more like the fate of the officer of the story,
deprived of the quasi-mystical experience that he had managed to provide to all the con-
demned by the breakdown that kills the infernal machine while it works on its own tutor.
Mr. Palomar realizes that being dead means “resigning himself to remaining the same in a
definitive state that he can no longer hope to change” (126). Then he reflects that death, if
it cannot be lived, can at least be overcome, since one can rely
on the biological mechanism, which allows leaving to descendants that
part of the self known as the genetic heritage; and the historical mechanism,
which grants a continuance in the memory and language of those who go on
living and inherit that portion, large or small, of experience that even the
most inept man gathers and stores up. These mechanisms can also be seen
as a single one, considering the succession of generations like the stages in
the life of a single person, which goes on for centuries and millennia (125)
It may seem that the problem of death is only postponed by such a thought since it has been
shifted from the death of the individual to the extinction of human race. Further reflection
convinces Mr. Palomar of the contrary. Indeed, after the human race has long been extinct,
explorers from another planet might land on earth and retrieve the traces oh human civili-
zation, deciphers its pyramids and uncover its computers. Humanity will be reborn ‘from
its ashes’ and will continue to spread in the universe. It is easy to see that there is no end to
the process, or almost:

M R . PALOMAR’
S CHECKMATES
after one postponement or another, the moment comes when it is time to
wear out and be extinguished in an empty sky, when the last material evidence
of the memory of the living will degenerate in a flash of heat, or will
crystallize its atoms in the chill of an immobile order (ib.)
Death can be postponed indefinitely from one generation to the other until the end of time,
until not even one atom in the universe will be left to support the memory of living. The
last consideration forces Mr. Palomar to think of time itself and of the relationship between
time, its end, and death. He suddenly realizes that to differ death to and beyond the end of
time means to defeat it:
‘If time has to end, it can be described, instant by instant,” Mr. Palomar
thinks, “and each instant, when described, expands so much that its end can
no longer be seen.” He decided that he will set himself to describing every
instant of his life, and until he has described them all he will no longer think
of being dead.
It is precisely when he talks himself into this supreme deceit that Mr. Palomar dies.
At that moment he dies. With these words Mr. Palomar’s search ends, and the book
with it. His search, in other words, ends at the same moment his life ends. The strange co-
incidence is quite remarkable and calls for a closer look. In fact, there are two different
“movements” in the text which should be considered separately. First, Mr. Palomar’s
search: it can be considered terminated when death—both the symbol and ultimate mean-
ing of the fracture that opposes him to the world—is neutralized by means of an indefinite
deferral that brings it to coincide with the end of the ages and the universe, when the latter
will disappear in a “flash of heat.” This sudden realization marks the end of Mr. Palomar’s
thoughts and is immediately followed, in the text, by the termination of the second, parallel,
process: his biological life. A more appropriate conclusion to Mr. Palomar’s search could
not be imagined: death intervenes to interrupt his search when the latter has reached its end.
Death undergoes here a peculiar transmutation. The limit as impossibility to reach the
outside, as border that marks an ineluctable division between what it separates, such a
boundary is transformed,
à la Kant,
into a horizon which renders that which lies within it
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fully attainable and masterable. If the irrepresentable lies beyond this limit, then the impos-
sibility of full representation becomes the possibility of impossibility, that is, it becomes
the affirmation or the vindication of the impossibility of the plenitude of representation.
The existence of the irrepresentable—to use Agamben’s terminology—becomes a full,
completely given representation. Indeed although being cannot be reached, since it is never
given but in a fracture, this ‘not being given’, this fracture as such, is nonetheless complete-
ly accessible. The representation of the irrepresentable, or rather the representation of the
existence of the irrepresentable can be reached and mastered in its wholeness. The division
inscribed into signification can therefore be neutralized. It can be forgotten as if it never
existed, since the representation of the irrepresentable implicitly recuperates the totality
that it pretends to reject as a deception. It is important to understand that the effect of the
separation is total and, in fact, totalizing. In other words, the existence of a fracture so com-
plete as to be recognizable everywhere entails the delimitation of a perfectly closed domain
6
from which nothing can escape .
Let me summarize. We have seen that nothing can reach the fullness of representation.
This means that nothingness comes to representation. It can reach it only if it is thematized
and explored in its integrity. It follows that the search itself must completed, that it must
come back to itself and that nothing escapes it. This, in turn, means that the doctrine of the
existence of the irrepresentable, if it hopes to recuperate the harmony that it negates in its
descriptive phase, must be able to describe a closed, consistent system. A system bent back
onto itself, where every sign points to the inside, where the outside exists only as intangible
limit because every possible operation, combination or process on whatever element of the
system is by definition incapable of transcending itself or referring to something else.
Names, the emblematic symbol of all this, can only reach other names, and never things, as
6. It is of little importance, then, that the fracture be so deep as to split the subject itself. Against another
thought on being and nothingness, what is questioned here, and in Palomar as well, is the possibility
of the unity of the human subject delivered to its freedom by the experience of the limit. That impossibility
does not bar that a lacerated subjectivity, although intimately divided, could eventually be recuperated.
Or rather, it does not forbid that the pieces into which such a subjectivity is shattered could
eventually be recuperated in the broader order of a harmonic world. A clear illustration of this point
can be seen in the debate on subjectivity and the origin of sense that took place between Claude Lévi-
Strauss and Paul Ricoeur. See Chapter VI below.

T HE WORLD OF CANDRAKIRTI
we have seen. At most, they can refer to history, to culture, but never beyond them. The
doctrine of the irrepresentable discovers the world as a closed, self-referential, combinato-
rial system. As a game. The interpretation of the world as a game, or more precisely as an
immense sequence of chess games, is the emblem of the representation of the irrepresent-
able, or of what Agamben called, in the above mentioned text, the “triviality of the mod-
ern.”
3. The World of Candrakirti
At that moment he dies. It is not simply the death of the protagonist that represents a
triumph over the death that pervades existence and manifests itself in everyday life as the
impossibility of having a full experience of the world, things, or people, but rather the co-
incidence between his death and the end of his search. In fact, Mr. Palomar has discovered
that among the people, things and events that language and observation cannot reach lies
the most important event—his own death.
The division that separates him from the world—the restlessness that had pushed him
to try to learn to be dead—is discovered to be total: nothing can be reached. In a sudden
flash, Mr. Palomar realizes he has attained his goal: if there is nothing beyond experience
then there is nothing to be separated from and nothing to be afraid of. The world is void—
this is what Mr. Palomar senses—but the voidness of the world is completely given in his
experience. The organized and harmonic whole whose presence he thought to glimpse in
the celestial spheres is fully given: this whole is nothingness, the vacuity of which everyday
experience is but a representation. What is left is the minute description of the experience:
an analysis of its completeness and of the ways in which it is organized. This is precisely
what Mr. Palomar sets out to do: he decides to describe every single instant of his life and
discovers that the incompleteness that seemed to characterize it disappears as soon as all
the fragments are recomposed into a system. The system cannot mean anything because it
is totally closed upon itself and therefore it cannot refer to nothing outside itself. Howev-
er—and this is the decisive step—precisely because it means nothing, the system into
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which experience is organized expresses nothingness itself—it expresses the voidness of
every possible experience. This, at least, is what Mr. Palomar seems to intuitively perceive
when he decides to compile the catalog of his past experiences with the intention to grasp
their intrinsic systematicity. The death that seizes him in the midst of such a resolution is
then a secondary accident that cannot really touch him. Degraded to a mere demise, his own
death completes a wisdom that has already been attained, the absolute wisdom that comes
after the end of time and history. Two conditions have to be met, however, to make the neu-
tralization of nothingness really work: the separation from the world must truly be total and
the total separation must be fully recognized and accepted. Both conditions are less simple
than it may at first appear and they turn out to be ultimately incompatible. If taken together,
they define the philosophical position that we have referred above as the doctrine of the
world as game. Or better, the doctrine of the world as a chess game. For chess is considered
a perfect example of a structure that satisfies both requirements: on the one hand an orga-
nized and dynamic totality that refers only to itself; on the other, a structure encompassing
a finite number of possibilities that can be exhaustively described. In short, chess is a com-
plex structure that can be mastered (at least intellectually) in its entireness.
Calvino himself recurs very often to the metaphor of play in general and chess in par-
ticular, sometimes absorbing the game into the very narrative structure of his works 7 . To
understand why he was fascinated by he metaphor of chess, is necessary to examine the
game’s structure. In so doing, we will be able to discuss the doctrine it metaphorizes and
its importance for the book we are reading.
First, it is necessary to focus on the game itself regardless of the players and the situa-
tions in which it may take place as an event. Let us think of chess as it might be described
7. Many works by Calvino are inspired by games and chess. The narrative structure of Il Castello dei destini
incrociati (Torino: Einaudi, 1973); Engl tr. The castle of crossed destinies (New York: Harcourt
Brace Jovanovich, 1977) is built around the disposition of playing cards (tarots, to be precise) on the
table.Città Invisibili (Torino: Einaudi, 1971); Engl. tr. Invisible cities (New York: Harcourt Brace Jovanovich,
1974) contains long discussions on chess and chess playing (one of which will be quoted
later). Game-related themes are contained also in t con zero and Se una notte d’inverno un viaggiatore...
(respectively, t con zero (Torino: Einaudi, 1967); Engl. tr. t zero (New York: Harcourt Brace Jovanovich,
1969) and Se una notte d’inverno un viaggiatore... (Torino: Einaudi, 1979); Engl. tr. If on a
winter’s night a traveler.... (New York: Harcourt Brace Jovanovich, 1981).

T HE WORLD OF CANDRAKIRTI
in a manual for beginners. Once such an epoché is done, the game discloses an extremely
simple structure. It is possible to define in an univocal way its basic elements: a chessboard
plus a certain number of pieces moving over it. There may be some uncertainty concerning
the material substrates of the former as well as of the latter, but that is irrelevant for the
game itself: what matters is that the playing ground presents a determined and precise con-
figuration and that a determined and immutable number of pieces are placed on it. Second,
it is clear that there are rules governing the movement of the pieces on the chessboard, i.e.
operations that can be performed on the pieces whose effect is to alter their position. Even
in this case it is important to underline, in spite of the apparent triviality of the observation,
that such rules are univocally and absolutely defined: each piece has its own rules that apply
from the beginning to the end of the game. There is no room for uncertainty, ambiguity or
negotiation. To be more precise, we should say that the pieces themselves—and their com-
plex and misleading iconography— are just a heuristic device for the players. Knights and
queens, in this sense, are in a certain sense like the apples and oranges we have all been
taught arithmetic with: a teacher’s trick to be forgotten once in possession of the real thing.
What count are the rules of placement: the carved shape of the piece is just an aid to the
player’s memory to help him retrieve the proper rule to apply. The name itself, “rules,” is
slightly misleading since they are so fixed as to be very different from what we normally
intend by the word “rules.” They are not prescriptions to be followed—and which can be
disobeyed—but rather mathematical operations: perfectly definable, immutable, and pre-
dictable. Furthermore, the rules of placement make up a closed system: every application
will produce another instance of the game itself. The set including the possible configura-
tions of the game, moreover, is discrete: between two successive configurations of the
chessboard there is no middle ground—just the intangible flash of a move that instanta-
neously changes the playing situation. The application of a rule will always result in an an-
other possible configuration of the chessboard, in the same sense in which the application
of the operation of addition to two numbers will always give another possible number.
Chess, however, enjoys an advantage over numbers. The number of possible configu-
rations on a chessboard, although very large, is still finite. If we consider that each specific
15

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position on the chessboard is determined by an application of the rules, it follows that every
possible configurations is generated by them. The rules of the game make up an exhaustive
combinatorics, i.e. they make possible the generation of the totality of the game. The latter
term is to be understood in a broad sense: the totality of the game includes all the possible
configurations of the chessboard, which means that it includes all the possible past, present,
and future games that may be played on it. Such a number is in fact barely thinkable, but
what matters here is that it can be obtained. In short: consider the initial position of the piec-
es on the board and consider then all the possible moves (there are just 20 of them). For
each of them, consider all the possible answers, or countermoves, available to the other
player. It is enough to proceed for a while on this path and the whole game will be gener-
ated.
We begin, perhaps, to see the source of the fascination that chess—when considered
from this narrow standpoint—can engender: chess is endowed with an extremely complex
structure—a complexity difficult to imagine in fact— but a structure that can be fully given
and concretely, effectively obtained. Moreover, chess is completely self-referential: con-
trary to some knaves and queens of hearts, pawns and bishops cannot harass sweet little
girls. Chess pieces enjoy an independent existence: outside the chessboard they are only
pieces of wood or jade. On the other hand, once in play they enjoy a full and undivided ex-
istence, since what lies outside the chessboard can never touch them: the inside and the out-
side of the game are marked by impassable border, an irreparable gap.
Moreover, chess has something else beyond the outlined combinatorics which guaran-
tees its success as an explanatory paradigm: a telos that secures the internal movement by
putting the whole structure into motion, thereby assuring the perpetual dance of the pieces
on the board, a dance as precise as the movements of the pieces of a clock—an implacable,
predictable and therefore harmonious dance. The telos is nothing else than the agonistic el-
ement implicit in the game, the effort to overcome the antagonist, be it real or virtual. It is
because the agon enters inevitably in every ludic phenomenon that it is essential that chess
be a game. A discrete, closed, combinatorial structure is certainly necessary, but it is not
sufficient, by itself, to attain the desired harmony: it is also necessary to provide a principle

T HE WORLD OF CANDRAKIRTI
securing movement, a principle capable to put the combinatorics in motion. Moreover, this
principle must be internal to the structure itself, lest the border between the inside and the
outside of the game be lost. The agon, if considered from the standpoint of the structure and
not of the players, is a goal completely internal to the structure. The end of the game, if seen
from the perspective we are exploring, is merely a possible configuration of its basic ele-
ments: a certain position of the king, of the ball, of the rope, etc. A position that, once at-
tained, has the only effect to efface the final position and to bring back the beginning, ready
for another game of an infinite series 8 . A pure dynamic principle then, an attractor for other
configurations that secures the perpetual, immutable and harmonic movement. It is precise-
ly such a movement inside a completely closed system that engenders what I might call the
‘ecstatic’ dimension of the game. By that word I mean to denote the rapture or vertigo pro-
cured in the player by the fullness finally attained, the ecstasy deriving from the total iden-
tity with a broader system. More precisely, I mean to underline—by recalling the ek-stasis,
the standing out—the result of a union with a system essentially external and foreign to the
player, a system the player can lose himself in. It is in this sense, I believe, that the ecstatic
union of play can free the player from the sheer weight of existence: precisely by inserting
him or her into the harmonic motion of a system that—because essentially other—does not
require its active participation, engagement and choices 9 . Such an ‘ecstatic’ dimension is
essentially present in every ludic phenomenon and if it has a preeminent part in events like
gambling and roller coasters—as well as in innumerable infant games—it is easily found
even in the most sophisticated and intellectual games 10 . An extremely pregnant description
8. Remember that the total set generated by the previous description of chess contains all possible games.
This entails that many configurations will be repeated and the redundancy of the system is incredibly
high. But the heavens as well, in an interpretation similar to ours, come periodically back to identical
configurations. That is precisely what makes them part of the cosmic “jewel.”
9. I rely here on the analysis of play put forth by Hans Georg Gadamer in Truth and Method. Gadamer
points out that the family of terms connected to Spiel (which encompasses both the English play and
game as in all the Romance languages) have all a common semantic component: freedom of movement.
Play is the performance of the movement as such. [...] The most original sense of playing is the
medial one.” The originary meaning of play is thus a “natural to-and-fro motion which goes all by itself,
with no strain. It follows that the “structure of play absorbs the player into itself and thus takes
from him the burden of initiative, which constitutes the actual strain of existence.” See Hans Georg
Gadamer, Truth and Method (New York: Crossroad, 1985) 91 and 94.
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of the deep interpenetration between games, the agon and the ecstasy is given by Georges
Perec with regard to a game whose purely intellectual dimension would seem to make it
alien to any rapture: the jigsaw puzzle.
[Bartlebooth,] having gone through every stage of controlled anxiety and
exasperation, reached a kind of ecstasy, a stasis, a sort of utterly oriental stupor,
akin, perhaps, to the state archers strive to reach: profound oblivion of
the body and the target, a mental void, a completely blank, receptive, and
flexible mind, an attentiveness that remained total, but which was disengaged
from the vicissitudes of being, from the contingent details of the puzzle
and its maker’s snares. In moments like that Bartlebooth could see
without looking how the delicate outlines of the jigsawed wood slotted very
precisely into each other, and taking to pieces he had ignored until then or
which perhaps he had sworn could not possibly join, he was able to fit them
together in one go.
This intimation of grace would sometimes last for several minutes, which
made Bartlebooth feel as if he had second sight: he could perceive everything,
understand everything, he could have seen grass grow, lightning
strike a tree, erosion grind down a mountain like a pyramid very gradually
worn away by the very gentle brushing of a bird’s wing: he would juxtapose
the pieces at full speed, without error, espying, beneath all the details and
subterfuges intended to obscure them, this minute claw or that imperceptible
red thread or a black-edged notch, which all ought to have indicated the
solution from the start, had he but had eyes to see [...] These privileged instants
were as rare as they were intoxicating, as fleeting as they were seemingly
effective. Bartlebooth would soon revert to being a sandbag, a lifeless
lump chained to his worktable, a blind-eyed subnormal, unable to see, waiting
hours without knowing what he was waiting for. 11
The gloire experienced by Bartlebooth is the symptom of the attained identity with the
world that the game makes possible once the threshold that separates it from reality has
been crossed. It follows that what is essential to the game is its combinatorial dimension
10. Here, I am partially following the phenomenology of play proposed by Roger Caillois in his classic
work, Les jeux et les hommes (Paris: Gallimard, 1958). Caillois underlines, without actually explaining
it, that vertigo (or ilynx, in his terms) is one of the four basic components of every ludic activity.
11. Georges Perec, La Vie mode d’emploi (Paris: Hachette, 1978); Engl. tr. Life A user’s manual (Boston:
Godine, 1987) 338.

T HE WORLD OF CANDRAKIRTI
and combinatorics’ intrinsic possibility to generate harmony. For these reasons, i.e., that
chess exhibits this combinatorial dimension and that it is a game that it has become an em-
blematic example of a perfectly closed, dynamic and harmonic structure. Not every game,
in this sense, would do. What matters is the combination of discreteness and closure, be-
cause a combinatorics can only be obtained over a discrete set of separable and composable
elements; a set, moreover, totally closed upon itself. Furthermore, an internal finality is
needed and provided by chess, whose agonistic dimension, paradoxically, generates the
harmony defined as the just order of a closed and separated system. In other words, the
game in itself is not important: what is important is the dynamic combinatorial structure
that chess happens to embody. 12
Let us now proceed from the analysis of the combinatorial structure toward and be-
yond Calvino, where the theme is extremely pervasive. I am thinking of The Castle Of The
Crossed Destinies, for example, or Invisible Cities, where the intimate connection between
chess, harmony and nothingness reaches an dazzling clarity. Invisible Cities tells the story
of Kublai Khan, emperors of the Tartars, who wants to know about the territories he has
conquered. Marco Polo is sent to explore the borderless empire Kublai Khan commands.
The young Venetian wanders across the plains, visits cities, meets people and eventually
comes back to the royal palace to inform Kublai of his findings. Their conversation is
marked, once again, by the impossibility to communicate, since Marco does not speak the
languages of the East and can only express his thoughts with gestures, occasionally helping
himself with the objects he brought back in his bags. Marco set these objects on the black
12. To put it differently: what really matters here is to understand the internal articulation and the philosophical
import of a representation of the game that has first been produced (through a historical process
too long to retrace), then imported into the intellectual realm as a ‘natural’ explanation of the game
and finally used in the philosophical discourse. Each step of process would deserve careful analysis,
something I attempt in chapter 4 below. My concerns here, are wholly contained in the last phase of
the process.
Alan Aycock, “Derrida/Fort-da: deconstructing play,” in Postmodern Culture, v.3, n.2, January 1993,
contains one of the few analysis of chess that examines the concrete event of chess playing and offers
a very different perspective on rules perfect closure, etc. More general critiques of the conception of
rule outlined above can be found in the present debate on Artificial Intelligence, its ambitions and
shortcomings. See for example H.M. Collins, Artificial Experts, Social Knowledge and Intelligent Machines
(Cambridge: MIT UP, 1990).
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and white ceramic tiles of the floor of the palace. He tries to represent the characteristics of
each city he visited, their citizens and their civilizations. The emperor, being a good chess
player, realizes very soon that a regular chessboard with the usual pieces is far superior to
Marco’s gimcracks since a knight can represent an army as well as a horse, a queen can
stand for a lady at the window, etc. Moreover, the movement of the pieces according to the
rules is more faithful to Marco’s expressive intentions: each of the innumerable configura-
tions of the chessboard can indeed represent one of the cities Marco visited, its inhabitants
and its conflicts. Each state of the chessboard, in fact, represents “one of the forms that the
system of forms pools together and destroys,” and the game itself, since it includes all the
possible forms, comprehends the whole spatio-temporal universe. Endless games of chess
take soon the place of the experiences of the journeys, of the discussions about the objects
retrieved, of speech itself. Completely absorbed by the effort to grasp the hidden essence
of his empire, Kublai loses himself in the movements of kings and pawns until he reduces
his actions to the contemplation of what is left of every game: the black or white square
underneath the murdered king: “by disembodying his conquests to reduce them to the es-
sential, Kublai had arrived at the extreme operation: the definitive conquest, of which the
empire’s multiform treasures were only illusory envelopes: it was reduced to a square of
planed wood: nothingness...” 13 .
The most convincing clue indicating the centrality of combinatorial themes in Palomar
is to be found in its most enigmatic page, the page following the last. While the single texts
composing the book are simply introduced by the title (Reading a wave, The naked bosom,
etc.), in the index all the twenty-seven texts are reorganized in a totalizing and systematic
way. The index is composed of two distinct section: the list of chapters, where each of one
labeled by a triplet of digits, and an explanatory note. The former looks as follows:
13. Italo Calvino, Invisible cities…, 131. Translation slightly adapted.

tion:
T HE WORLD OF CANDRAKIRTI
1. Mr. Palomar’s Vacation
1.1. MR. PALOMAR ON THE BEACH
3 1.1.1. Reading a wave
9 1.1.2. The naked bosom
13 1.1.3. The sword of the sun
1.2. MR. PALOMAR IN THE GARDEN
19 1.2.1 The love of the tortoises
[.............. ............ ..........................................................]
...
3. The silences of Mr. Palomar
[.............. ............ ...........................................................]
...
3.3. THE MEDITATIONS OF MR. PALOMAR
113 3.3.1. The world looks at the world
116 3.3.2. The universe as a mirror
121 3.3.3. Learning to be dead
A brief note preceding the chapters’ list discloses the meaning of the strange numera-
The numbers 1,2,3 that mark the titles of the index, whether they are in
the first, second, or third position, besides having a purely ordinal value,
correspond also to three thematic areas, three kinds of experience and inquiry
that, in varying proportions, are present in every part of the book.
Those marked “1” generally correspond to a visual experience, whose object
is almost always some natural form; the text tends to be descriptive.
Those marked “2” contain elements that are anthropological, or cultural
in the broad sense; and the experience involves, besides visual data, also
language, meaning, history. The text tends to take the form of a story.
Those marked “3” involve more speculative experience, concerning the
cosmos, time, infinity, the relationship between the self and the world, the
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dimensions of the mind. From description and narrative we move into meditation.
The Book reflects then the conclusions of its protagonist in the narrative structure itself.
The total combinatorial structure that is needed, as we saw, for the final triumph over the
anxiety of death and the transfiguration into the harmonic world of play is exhibited by the
text itself as its raison d’être. The whole range of possible experiences is carefully subdi-
vided and totally covered by the exemplary texts included in the book. We must not be de-
ceived by the extreme narrative focalization of the single texts and recall instead how the
knight pawn was employed by Kublai to represent a marching army as well as a equestrian
statue precisely because of its intrinsic plurivocity. The carved piece of wood assumes a
universal meaning because it comes to represent, inside the closed world of chess, one of
the (few) possibilities of movement, i.e. one of the possible interactions with the world. In
other words, one of the possible experiences. Similarly, the reading of a wave that opens
the book is much more than the faithful transcription of the obsessive musings of a middle-
aged character: once assumed inside the closed world of Mr. Palomar’s experience as strat-
egy 1.1.1, it becomes the universal signifier of the indirect and im-mediate interaction with
the world, in whatever form, time, or occasion it happens to occur. Thus, Mr. Palomar’s
meditations are necessarily written a posteriori, after the experience of the failed death.
They must be interpreted as a total systematization of experience into a system of equiva-
lent strategies. This system is necessarily written after, After the end of an essentially his-
torical ‘world’ like ours: it can be written only after having entered that ‘Sunday of Life’,
to repeat Hegel’s and Queneau’s expression, that follows the end of history. If we leave
aside the secondary difference between the number of possible experiences in the chess
world—6, since there are as many pieces—and those presented in the index, then the ho-
mology between the two universes is complete. Such homology is, furthermore, certified
by the author himself in the authoritative modality of paratext. Thus, the index is the true
explication du texte providing the ‘truth’ of the work to the reader by justifying and autho-
rizing one among the possible interpretations of its last words. The place of the index—ex-
ternal with regard to the text—gives it the necessary authority to put an end to the

T HE WORLD OF CANDRAKIRTI
interpretative squabbles, since, coming after the end of the book, it automatically enjoys the
distance necessary to judge the work in its entirety. Or so it seems.
The relative exteriority of paratext, in fact, raises a crucial theoretical issue: it is not
possible to decide whether the index itself is inside or outside the text; in other words,
whether it is or is not part of Mr. Palomar’s reflections. The index is both inside and outside,
this is the most that we can say: inside because its content is an integral part of the text itself,
but inevitably outside because it belongs to a level of discourse that has the text as its own
object. The logical location of the index is undecidable, as undecidable—because essential-
ly ambiguous—as the position of the player with respect to the game played. When the
player participates in the game, when he lets himself be completely absorbed by the inex-
orable combinatorics of the game, he is totally dissolved into the game. Consequently, he
annihilates himself through an identification with the game that is so total to enable the ec-
stasy of complete communion. As a matter of fact, however, the participant to the game
must paradoxically distance himself from the game in order to accept it as such. He must
be able to decide to start playing. The total combinatorial system is never simply given, but
always recognized first and eventually accepted 14 . This entails a distance between player
and game that is fatal to the functioning of the latter as a mechanism capable of solving the
impossibility of experience. Or, to be more precise, it is fatal to the success of the philo-
sophical position that assumes a certain reading of game as its guiding paradigm. Indeed,
we have seen how the doctrine of the world as play finds its ground in the resolution of the
voidness of experience into a close and organized system that must be able to radically sep-
arate its inside from its outside in order to function. The world of chess, in order to provide
an access to harmony, must be completely separated from everything surrounding it, it must
have nothing outside itself. The combinatorial structure I have described above is just the
14. Why? Because the combinatorial system is a system of differences, i.e., is a system made of differentiated
elements interacting with each other. A total unity given from the outset would be an essentially
undifferentiated unity. This is, of course, a basic Hegelian point I am relying on here, while disregarding,
however, the issue of the possibility of a whole beyond difference, fracture and master-slave dialectics,
as Kojève’s interpretation of Hegel that I am following here, would want it. See Alexandre
Kojève, Introduction à la lecture de Hegel (Paris: Gallimard, 1947), partial Engl. translation id. Introduction
to the Reading of Hegel (New York: Basic Books, 1969) lecture 12 of year 1938-39.
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concrete realization of such a theoretical imperative: a system that is complex enough to be
interesting but is fully bent upon itself. However, the dialectics between the open and the
closed that is essential to the world of game finds a last but decisive resistance in the ne-
cessity of the acceptance of the game by the player. The game must be recognized as such
and then accepted, but recognition implies an ineliminable distance between the player and
the play that is fatal to the whole operation because it necessarily entails the existence of
something external to the game itself. Something that nullifies the whole effort. Or, to be
more precise, something that changes its import, since ‘the’ game of existence becomes
‘just’ a game. It was the final solution to the voidness of experience—now it has been de-
graded to being just another, unsatisfactory experience. The characteristic vacuity it derives
from self-referentiality becomes now the mark of the ultimate meaninglessness of the
world. Even death, when considered from this perspective, changes its value. In fact, let us
go back once again to the last page of Mr. Palomar and take another look at the coincidence
between the end of the protagonist’s search and his death.
If, on the one hand, the coincidence between the end of the intellectual exploration and
the biological end can make up a true chord concluding on a restful harmony Mr. Palomar’s
existence, on the other hand it is not difficult to hear, in that same final clause, a dissonant
contrast. If we think it through, death reaches Mr. Palomar exactly at the moment when his
reflection has brought him to doubt of the possibility of death. Indeed, it is precisely be-
cause time has to come to an end, because its end can be imagined, it is precisely because
death exists and pervades existence that its reality begins to fade away. If the only place
where death can be met coincides with the end of time and space, it is clear that the uncer-
tain ontological status of such place cannot but weaken and almost annihilate the reality of
death itself. And yet, no rebuke was ever sharper: At that moment he dies. Far from being
the crowning of existence, Mr. Palomar’s death marks his life as a total failure. Not just the
single events, but also the will itself that animated them and his whole existential project
result in a failure. At that moment he dies. What is astonishing in that last enigmatic clause
is not only the possibility of the two conflicting interpretations I have just delineated, but
the contemporary presence of both of them in spite of their total incompatibility. The am-

T HE WORLD OF CANDRAKIRTI
biguity, in other words, is structural, because it is impossible, on the basis of the text, to
decide for one or for the other; that is, it is impossible to decide whether Mr. Palomar’s fate
is a triumph or a rout.
Paradoxically enough, the last remark makes even more enigmatic the status of the in-
dex. In fact, it seems to oscillate between two opposite and irreconcilable extremes. On the
one hand, it can be read as the exemplification of the combinatorial structure that pervades
the whole work. In this sense, and in virtue of its privileged textual position, the index can
be interpreted as the reason and ground of Mr. Palomar. On the other hand, the very expo-
sition of such an interpretation makes it unacceptable. The paratextual position of the index
implies a distance between its content and the text that makes the whole combinatorial con-
struction vain, since its content—the thematization of the combinatorial game—should be
present within the text as one of the possible experiences. The perfect language capable of
expressing every possible experience cannot tolerate any meta-linguistic reflection, lest its
perfection be lost 15 . The contradiction between these two aspects of the index, the contra-
diction between what the index says of the text and what it does to it in virtue of its external
location, the contradiction between its constative and performative dimensions is ultimate-
ly unsolvable. Its logical status, even its very existence contradict what it says.
This has some broader implications for the interpretation of Mr. Palomar at large. The
reading offered by the index succeeds in the difficult task of enclosing in a single gesture
the essential duplicity of the text that we have I have shown is condensed in its last sen-
tence. In the index—and in the whole text—both irreconcilable dimensions of triumph and
defeat are simultaneously present. Mr. Palomar, to put it differently, brings to view the ir-
reducible antinomy generated by the fracture of presence, by the original division from the
world of things and of the others, an antinomy that I have tried to retrace in the paradigmatic
form it assumes in the death of Mr. Palomar and particularly in the double dimension of
triumph and defeat that distinguishes it. The triumph that abolishes the original division in
a total communion with the world of pure appearance under the aegis of combinatorics and
15. See Maurice Merleau-Ponty’s characterization of the perfect language in Maurice Merleau-Ponty,
The Prose of the World (Evanston: Northwestern UP, 1973) 3-8.
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the rout that derives from the recognition of the impossibility to surpass such a fracture and
the resignation to the distance. However, to illustrate such an antinomy, to explain it in the
language of the reader is altogether impossible, I believe, since what Mr. Palomar makes
clear without saying is how the two dimensions are inextricably connected. It is impossible
to choose between one or the other because both are always simultaneously present. Or
rather, because any effort to isolate one of them immediately converts it into the opposite.
This is why we can define as a dialectic what Mr. Palomar brings to light. We have seen
exemplified this dialectic in the index: the death of Mr. Palomar, as well as each one of the
experiences he narrates, is always and at the same time inside and outside the structure that
might give it a meaning. It is always inside a determined game, within a specific signifying
chain. It has always a sense but a sense that is always ‘partial’, never fully given and never
fully masterable 16 . The chess game has always already started and death (be it real or not,
i.e. the end of the individual or collective experience) always occurs before the game is
over. This, nonetheless, does not mean that the game cannot be played. The sudden shift
from one of the dimensions to its opposite happens only when one tries to isolate and de-
limit any experience whatsoever in its absolute identity. It happens when one tries to sepa-
rate completely what is inside the individual experience from what lies outside it.
I have tried to show that any experience can be made significant through its insertion
in a complex, dynamic, and completely closed combinatorial system. However, the con-
struction of such a cathedral of the spirit, once terminated, misses its goal insofar as it im-
mediately expresses its own incompleteness by the reference to its builder. The effort to
reach a total transparency of experience turns, then, into its opposite: in the total vacuity of
any possible experience. Conversely, the “annihilation” of experience—the effort to negate
16. A full explanation of this term would require more space than I can afford here. The essential reference
is to Derrida’s work, and in particular to Limited Inc., where, while discussing speech act theory, he
challenges the possibility to close a set of utterances against any possible intrusion from the outside.
He denies that a definite and absolute meaning can be assigned, and underlines that any analysis trying
to retrieve a fixed meaning “will still form part of the ensemble and will therefore raise the same questions.
It will necessarily be what I will here call a prise de partie, that is: partial. It will be always be
lacking the completeness of a set.” The next few pages of this essay can be seen as a tentative application
of the preceding discussion of the concept of play to Derrida’s thought. See Jacques Derrida,
Limited Inc. (Evanston: Northwestern UP, 1977) 39 and following.

T HE IRREPARABLE LIGHT OF DAWN
the possibility of the meaningfulness of any experience by the recognition of the subject’s
failure to transcend the limits of its own language and its own history—produces exactly
the opposite effect. As we seen above, it is precisely at the moment when even the ultimate
experience, death itself, becomes an empty simulacrum that the final transfiguration takes
place: to expose the purely positional nature of any possible experience, to show its essen-
tial voidness, means to bring about the total combinatorial system in which everything
means because it refers to everything else.
If the intrinsic and inevitable duplicity of Mr. Palomar’s death arches back from the
end of the book to its beginning and to the whole novel, then how should we read in Mr.
Palomar? The book seems to end on a tragic note: not even defeat is possible, not even
death. Mr. Palomar is forever condemned to play games others have started, prisoner of the
most original inauthenticity. He had begun his search from in anxious consciousness of a
separation from the world. Once the search is over, he cannot but recognize the inevitability
of the original fracture. His meager and sole consolation is that he can enjoy his understand-
ing of its inexorable internal dynamics.
But is such a consolation really meager or is it more than is ordinarily given to think?
4. The irreparable light of dawn
The reading of Mr. Palomar I attempted in the preceding pages has shown that the im-
possibility to reach a full experience of the worlds and things and the consequent search for
harmony—i.e. the search for an organic relationship with the world in which the subject is
completely absorbed by the system outside him—generates what I called the “dialectic of
partiality.” “Partial” because the connection of the subject of experience with the world is
always imperfect insofar as it is always marked by a fracture impossible to transcend with-
out the generation of a dialectic that produces a recurring transmutation of one of its mo-
ments into its opposite.
Mr. Palomar is able to carry out his everyday affairs, he can buy his cheese and he can
hear the blackbirds, although in an inauthentic way; when he tries to overcome such inau-
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P RELUDE
thenticity, however, he is projected onto a metaphysical seesaw that bumps him alternative-
ly from a cosmos where everything is ordered but from which he is excluded, to a
disordered universe where every experience means nothing.
According to Agamben, this unsurpassable dialectic lies at the root of all metaphysics.
The form it assumes in Mr. Palomar represents with particular efficacy, I believe, its last
reincarnation. It is such a negative ground, such a primitive fracture that unfetters the dia-
lectics that must be identified at the origin of metaphysics and not the overvaluation of truth
over appearance (or vice versa) that can be obtained if the dialectics is temporarily (and im-
possibly) frozen into one of its moments. To quote Agamben from Stanzas
metaphysics is not, in fact, simply the interpretation of the fracture of
presence as a duality of appearance and essence, of signifier and signified,
of sensible and intelligible; rather, that the original experience be always already
caught in a fold, be already simple in the etymological sense
(sim--plex, “once pleated”), that presence be always already caught in a signification:
this is precisely the origin of Western metaphysics. 17
What I have been trying to show through my reading of Mr. Palomar is perhaps only this
simple fold that cuts through experience. I have tried to underline how harmony—seem-
ingly the positive solution of such a fold—is indeed only its flip side. Indeed, as Agamben
writes elsewhere, the transition between man and world that the concept of harmony is
called to resolve by unfolding its inherent contrast
is always already conceived as an arthron, an articulation; or rather, as a
discontinuity that is also a continuity, a removal that is also a preservation
(arthron, like armonia, originally derives from the language of woodworking;
armotto signifies to conjoin, to unite, as the woodworker does with two
pieces of wood).In this sense, the Voice is truly the invisible harmony, which
Heraclitus says was stronger than visible harmony (armonie aphanes phaneres
kreitton; fr. 54 Diels), because in its double negativity, it enacts the
conjoinment that constitutes the essence of that zoon logou echon that is
man. 18
17. Giorgio Agamben, Stanzas…, 156.
18. Giorgio Agamben, Language and Death (Minneapolis: Minnesota UP, 1991) 85.

T HE IRREPARABLE LIGHT OF DAWN
In Mr. Palomar the connection between the negative ground of the human condition and
harmony is shown with exemplary rigor and it is developed in all its consequences. The es-
sential undecidability between the ecstasy of total communion and the anxiety deriving
from the definitive separation from the world—as well as their mutual convertibility—are
‘deduced’ as necessary consequences of the protagonist’s search for the harmony that
would heal the basic scission. What Mr. Palomar shows is that such an opposition is falla-
cious. It is harmony itself that generates a mortal dialectics—and precisely because harmo-
ny is always thought as an articulation that joins only by keeping at a distance the human
and the non-human. On the basis of Mr. Palomar ‘s mise en scène we can the ask the fol-
lowing questions: is there a possible way to be human which is not always already captured
in the dialectic generated by the fracture and the search for harmony? Is there an access to
experience not marked from the beginning by the fracture of presence, not caught in that
fold that separates signifier and signified in a mortal embrace? Is it possible to escape such
a dialectic? Diversions, refusals and denials are poor strategies in fact, if we consider that
what Mr. Palomar exposes is precisely the structure of negativity, the structure of that orig-
inal negativity that make negation possible.
What is needed, and what seems impossible, is instead a thought thinking the purest
affirmation; a thought that thinks a wholeness which is not found or built at the end of a
process but simply given. Or rather an wholeness that has always been had. The thought
that manages to think such an wholeness, to think “a presence that, free at last from differ-
ence, would be a pure and undivided station in the open” (Stanzas, p. 157) might perhaps
inaugurate the age of the end of difference. The age of those who,
like the freed convict in Kafka’s Penal Colony, who has survived the destruction
of the machine that was to have executed him, these beings have
left the world of guilt and justice behind them: the light that rains down on
their foreheads is the irreparable light of the dawn following the novissima
dies of judgment. But the life that begins on earth after the last day is simply
human life19 .
19. Giorgio Agamben, The Coming Community (Minneapolis: Minnesota UP, 1993) 7.
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CHAPTER I
THE END OF
PHILOSOPHY
in which it is shown, with the help of Hegel, that philosophy must
come to an end, and what it looks like.

1. Truth
30
T HE END OF PHILOSOPHY
La vérité est dans ces pages. Elle doit y être. Mais où? Parmi les
innombrables chemins possibles, lequel m'y conduira? J'ai la sensation un
peu étouffante d'être au coeur d'un de ces problèmes de logique oú l'on doit,
avec une seule question, désigner l'eternel diseur de vérité et le total
menteur. Mais ici ne sont pas deux hommes qui sont postés au carrefour,
mais dix ou quinze, et ils n'ont rien de ces entités abstraites et sans failles:
l'un dit parfois ce qu'il croit être la vérité, mais il arrive encore assez souvent
qu'il se trompe; l'autre dit le contraire de ce que dit un troisième qui dit
n'importe quoi; un quatrième dit quelque chose que l'on n'entend pas et qui
est répeté par un cinquième dont on sait qu'il faut se méfier; un sixième, qui
se proclame Fébruariste dissident, déclare avoir reçu de Dieu une vérité qu'il
transmettra le jour où tous les mois de février auront enfin trente jours; le
septième se tait obstinément. 1
1. Georges Perec, La Vie. Mode d’emploi

2. Philosophy
P HILOSOPHY
Discourse about the end of philosophy has never thrived more than lately. Not so long
ago the reserved hunting ground of Heideggerian and post-Heideggerian philosophers, it
has diffused, in subtly different forms, to both sides of the Atlantic. Indeed, if we only con-
sider that much of the work done in analytic philosophy is conducted under the banner of
different forms of naturalization, e.g. of ontological or epistemological forms of reduction-
ism, we might want to apply to “eliminativism,” “epiphenomenalism,” and all the other
various “isms” what Habermas once said à propos of the continental philosophical tradi-
tion:
these pseudonyms are by no means disguises under which the traditional
form of philosophy lies hidden; the drapery of philosophical concepts more
likely serves as a cloak for a scantly concealed end of philosophy. 2
Habermas’s view on the positive role philosophy that can assume as “interpretative medi-
ator” is well known. He sums it up as follows: “What remains for philosophy and what is
within its capabilities is to mediate interpretively between expert knowledge and an every-
day practice in need of orientation. What remains for philosophy is an illuminating further-
ance of lifeworld processes of achieving self-understanding, processes that are related to
totality.” 3 As for the various “isms” alluded to in the text, consider that native (and even
more so adopted) analytically minded thinkers have been busy for a long time compiling
positivistically accurate death certificates on behalf of the empirical sciences (or, in certain
cases, mathematics) that will soon come up with definite answer to close off century-long
“pseudo-problems.” W. V. O. Quine’s “naturalization” of epistemology can be considered
the most recent ancestor (but by no means the absolute starting point) of the effort to “ex-
plain away” age-old unresolved issues like the mind-body problem by grounding (and ac-
tually reducing) philosophy to either psychology or biology. As for a few contemporary
examples, it will be sufficient to mention the well-known works by Patricia Churchland,
2. Jürgen Habermas, The Philosophical Discourse of Modernity (Cambridge: MIT Press, 1987) 53.
3. Jürgen Habermas, Postmetaphysical thinking (Cambridge: MIT Press, 1992) 17.
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T HE END OF PHILOSOPHY
John Searle, and Fred Dretske, among others 4 .
In contrast, more or less mournful (but always angered) memories that prelude at a re-
construction of philosophy’s ever-lasting goals on a different “non-metaphysical” basis
seem to be one of the hallmarks of the Franco-Germanic scene. The publication of Philos-
ophie ‘68. Essai sur l’antihumanisme contemporaine 5 (Paris: Gallimard, 1985) by Luc Fer-
ry and Alain Renaut has been the first act of the passionate and at times heated debate
currently underway in France between the “old” anti-humanist school and what Renaut
himself calls—in a recent book devoted to “the last philosopher”, e.g. Sartre—”un human-
isme non-métaphysique.” His previous work, he claims, opened the way by striving to de-
termine “dans quelle mesure et sur la base de quels réamégenaments le projet de
l’humanisme moderne (savoir: désigner dans une certaine idée de l’homme et de sa dignité
un terme de réferénce irréductible aux conditions historique de son émergence et, comme
tel, ouvrant une dimension d’universalité) [peut] encore constituer un programme
philosophique susceptible de se laisser assumer.” 6 The obvious antagonist of so much re-
cent French philosophy is Jacques Derrida’s work and more particularly his distinction be-
tween the “end” and the “closure” of metaphysics. 7
In order to assess the alleged “actuality” of the question about the end of philosophy I
will start by reading a few texts from the Western philosophical tradition that deal with the
relationship between philosophy and its end. I will argue, that the analysis of an argument
Hegel presents in the opening pages of the Lectures on the History of Philosophy shows
that philosophy has always dealt with its end, in all the various meanings of the term (telos,
terminus, Vollendung, etc.). In fact, the meanings of “end” and “philosophy” are so inextri-
4. See Patricia Churchland, Neurophilosophy (Cambridge: MIT Press, 1986); John Searle, The Rediscovery
of the Mind (Cambridge: MIT Press, 1992); Fred Dretske Naturalizing the mind (Cambridge:
MIT Press, 1995).
5. Luc Ferry and Alain Renaut, Philosophie ‘68. Essai sur l’antihumanisme contemporaine (Paris: Gallimard,
1985).
6. Alain Renaut, Sartre, le dernier philosophe (Paris: Grasset, 1993) 15. Renaut explicitly mentions the
work of Paul Ricoeur, Emmanuel Lévinas and Jürgen Habermas as going in such a direction. He might
have also mentioned Dieter Henrich’s project as substantially coherent with his overall plan.
7. See, among many occurrences, Jacques Derrida, D’un ton apocalyptique adopté naguère en philosophie,
(Paris: Galilée, 1983) 80 ff.

P HILOSOPHY
cably intertwined that any interrogation about the end of philosophy may be better off by
starting to bring the senses of ‘end’ into question. Before I begin what will turn out to be a
long trip, I would like to stress, however, that my analysis is not an attempt to dismiss or
debunk contemporary discourse about the end of philosophy. 8 Even if it turns out, as I hope
to show, that philosophy has always, and already, been deeply involved with its own end,
this does not mean that we can dispense with it. Just the contrary. It means that we philos-
ophers have to be even more careful when dealing with an issue that is intrinsically un-
avoidable. To put it differently, and more bluntly, the goal of what follows is to try to add
further depth, and to broaden the scope, of a debate that, I believe, cannot but concern us.
Let us begin, then, with a first recognition of the various meanings of “end” in clauses
like “end of philosophy.” No doubt, the first interpretation that comes to mind has to do
with the ‘end’ in the sense of ‘termination’, the ‘end’ as used in the expression ‘coming to
an end’: in the purely temporal sense of ceasing to exist. From this first, non-evaluative
meaning, it is easy to be carried over to more pejorative interpretations: the ‘end’, in this
sense, is what happens when something ceases to exists because no longer pursued. The
‘end of philosophy,’ therefore, becomes something very close to ‘the failure of philosophy.’
Opposed to this first meaning of ‘end’ stands another prominent sense: ‘end’ as the goal to
be pursued or the task to be accomplished. Although such meaning is more often conveyed
by the plural form (the “ends,” “les fins,” etc.) is undoubtedly present in the singular as
well. In order to get a better grip on the relationship among the meanings I have just men-
tioned, I will rather freely borrow the Kantian distinction between questions asked in the
de jure and in the de facto mode, i.e. the distinction between the legitimacy and rightfulness
of the question about the end of philosophy and its factual content (things turn out to be not
so simply clear-cut. But let us assume the validity of the classification for a while and see
where it brings us).
8. See for example the recent contribution by John Passmore, “The End of Philosophy? The “End of”
Syndrome,” Australasian Journal of Philosophy, 74, 1 (March 1996).
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T HE END OF PHILOSOPHY
Properly (de jure) speaking, the question about philosophy reaching (or not) its end
concerns philosophy as a whole: it questions the possibility of accomplishing its own goal,
however that is defined. It is, therefore, a question about the end of philosophy as telos, a
question about its validity. On the other hand, to ask the question de facto is to ask whether
philosophy has effectively reached its end because it has failed its goal, and brings in the
different meaning of ‘end’ as terminus, as failure. If a positive answer to the former inter-
rogation seems, most often, to entail an analogous result for the latter, the converse is ob-
viously not always true. One can point to the failures of a quest that degenerated into a
“battlefield of endless controversies” without relinquishing the goal of philosophy as such,
and remarking instead the basic faux pas that took past philosophers astray. In this respect,
Kant’s prefaces to the first Critique provides an example of a classic argumentative line that
can be easily found elsewhere in modern philosophy, for example in Descartes or in Hus-
serl. 9 After the customary remarks about the situation of total disarray into which metaphys-
ics has fallen, Kant points to its basic mistake: previous philosophies have missed the goal
because of an improper extension of rational procedures to objects lying beyond the realm
of possible experience.
Failures in the past, however, do not necessarily spell ill for the future. Philosophy’s
mission can be saved from the ruins of crumbled systems to be delivered intact as ever to
the future, once the proper path has been found. Such a future can indeed be very near, Kant
thinks, as he makes clear in the final words of his first major work, published in 1781:
If the reader has the courtesy and patience to accompany me along this
[critical] path, he may now judge for himself whether […] it may not be possible
to achieve before the end of the present century what many centuries
have not been able to accomplish; namely, to secure for human reason complete
satisfaction in regard to that which it has all along so eagerly occupied
itself, though hitherto in vain. 10
9. See for example Descartes’s Discourse on Method in Descartes, Philosophical Writings (Cambridge:
Cambridge UP, 1988), 23 (=AT VI, 8) First meditation and Edmund Husserl, “Philosophie als strenge
Wissenschaft,” Logos, I (1910,1911)) Engl. Tr. “Philosophy as a Strict Science,” Cross Currents, Summer
Issue (1956).

P HILOSOPHY
As this passage shows, the Kantian distinction we have been using so far begins to gain
some complexity, since upholding the de jure validity of philosophy seems to entail that its
end can be reached de facto. In other words, we have a partial reversal of the position pre-
viously discussed by Kant in the preface: the validity and possibility of philosophy as such
authorizes the philosopher to diagnosticate the end—interpreted now as completion and
fulfillment—of the whole enterprise.
What I would like to stress, in this context, is that the position Kant is upholding suffers
from an asymmetry with respect to the past. The argument is not reflective, we might say,
since it relies on an assessment of the past that excludes the possibility that Kant’s philos-
ophy itself might become part of it. On the one hand, it secures a vantage point for philos-
ophy (in Kant’s case, the impossibility of extending theoretical knowledge beyond possible
experience, with all that follows) by—partially, at least—taking a distance from the past.
The gesture that accomplishes it, however, puts philosophy out of time, in the realm of the
eternal a-temporal truth. By not being part of the past it claims to assess, Kant’s gesture im-
poses a radical break between itself and philosophy’s history that casts doubts on its ability
to provide a proper judgment. We see here a tension arising between philosophy as happen-
ing in time and its atemporal character, a tension between the historical failures of past phi-
losophies and the eternal validity of the truth gained by a philosophy that is explicitly
declared as completed in time.
The tension arises because Kant is not radical enough. He forces his own philosophy
to be reflexive, so to speak, since it forces it to question its own possibility, but he does not
ask how philosophy as a whole, including past philosophies, can be possible. In other
words, he does not ask how it is possible that philosophy can (and must) be reflexive, or
how it is possible that philosophy is (and has been) possible. By foregoing this kind of sec-
ond-order reflexivity, Kant introduces a cut between the past and the present, i.e. between
the previous, misguided systems and the critical path attempted by his own philosophy, that
cannot but disqualify the former in favor of the latter while at the same time relying upon it.
10. Immanuel Kant, Critique of Pure Reason, trans. by Norman Kemp Smith, (New York: St. Martin’s
Press, 1965) 668 (A856/B884).
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T HE END OF PHILOSOPHY
Hegel, in the text I will be dealing with shortly, begins his reflection on philosophy pre-
cisely from this point of tension: he faces the fact that philosophy happens in time and
draws the consequences by bringing philosophy face to face with its history. The most well-
known text in which Hegel presents his view on philosophy and its end is the dense final
chapter of the Phenomenology on Absolute Knowing. However, I believe that the different
path taken up in the Introduction(s) to the Lectures on History of Philosophy can perhaps
be considered more illuminating for a discourse on philosophy and its end. In the Lectures,
in fact, Hegel develops an argument that takes the reader from an analysis of the paradox-
ical relationship between philosophy, history, and end, and shows the way that leads—nec-
essarily, according to him—to the interpretation of philosophy as Absolute Wissen. The
next few sections are devoted to an analysis of that text, i.e. to an analysis of the preliminary
work Hegel performs in order to introduce his view of philosophy as an all-encompassing,
necessarily completed theoretical effort. I will try to show how that conclusion is forced
upon us by a much simpler argument than what constitutes chapters I-VII of the Phenom-
enology. The conclusion to draw from Hegel’s text are refreshing, or perhaps disparaging,
for any discourse on the end of philosophy. According to Hegel, in fact, a strong relation-
ship with its end has always been a constitutive part of philosophy ‘s nature.
Does that mean that we cannot help being Hegelians and have to merrily embrace the
supreme wisdom that was born under the cannons of Jena, as Kojève once suggested? Yes,
would go the answer, but only if the concept of Absolute Knowing itself would be proved
to live up to the demands imposed by the Hegelian argument. Consequently, I will proceed
to an analysis of the result of Hegel’s argument—namely the concept of Absolute Know-
ing—and try to uncover the main features of the form of knowing that can (or must, accord-
ing to Hegel) take place at the end of philosophy.
3. Hegel’s paradox
Hegel lectured on the history of philosophy several times in his academic career, first
at Heidelberg and then in Berlin. Every time he began his course from what he called “the

H EGEL’ S PARADOX
inner contradiction” seemingly entailed by the discipline itself: how can philosophy have a
history? Philosophy aims at truth, at what “is eternal and imperishable” and cannot there-
fore change over time. Yet history’s aim is to report what once existed (gewesen) and then
perished (verschwunden, disappeared) or was superseded (verdrängt). 11 A history of phi-
losophy, being a narration of the different and often mutually contradictory truths held in
the past, would therefore constitute a true oxymoron. Hegel expresses it succinctly as fol-
lows:
If we start from the fact that truth is eternal, then it cannot fall into the
sphere of the transient and it has no history. But if it has a history, and history
is only a display of a series of past forms of knowledge, then truth is not to
be found in it, since truth is not something past. (11/9)
In order to understand this position, we of course have to read “truth” in a strong, ontolog-
ical sense.As Hegel explicitly says, the truth aimed at by philosophy is “what exists in and
for itself”, i.e. the true, das Wahre. Nowadays, it is more common to give a linguistic inter-
pretation of truth, and to take the term as referring to a relationship between linguistic ob-
jects such as statements and states of affairs. An ontological reading may seem so
hopelessly disqualified to our modern or postmodern eyes, to preempt the whole argument
that is about to come. It should be remarked, however, that in the present context Hegel is
not putting forth any claim about the nature of such a truth. In other words, he is not assum-
ing anything about the ontological status of the “truth” nor is he relying on any epistemo-
logical claim about the accessibility of such a truth to human knowledge. Later on, he will
introduce and defend a substantial thesis on this topic, but at this point he is only presenting
an extremely general characterization of philosophy as a “science,” and he is taking the
11. “die Geschichte aber erzählt solches, was zu einer Zeit gewesen, zu einer andern aber verschwunden
and durch anderes verdrängt worden ist.” See Georg Wilhelm Friedrich Hegel, Introduction to the Lectures
on the History of Philosophy, translated by T. M. Knox and A. V. Miller on the basis of the 1944
edition by Hoffmeister and Nicolin, (Oxford: Clarendon Press, 1985) 11. See the latest German critical
edition: Georg W. F. Hegel, Vorlesungen über die Geschichte der Philosophie, herausg. v. Pierre Garniron
und Peter Jaeschke, Teil 1, Einleitung in die Geschichte der Philosophie; Orientalische Philosophie
(Hamburg: Felix Meiner Verlag, 1994) 9. The last volume of the German edition, dedicated to
the philosophy of modern times, has been translated into English: G.W.F. Hegel, Lectures on the history
of philosophy (Berkeley: California UP, 1993), v.3. Hereafter all references will be given in parenthesis
in the text, followed by the page reference to the German critical edition.
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T HE END OF PHILOSOPHY
most general characterization of science itself: any discipline that aims at knowing how
matters really stand, e.g. that aims at knowing the truth about a particular domain. Howev-
er, according to Hegel, this characterization, no matter how general, leads philosophy as
such into trouble when it is confronted with its past history.
The Hegelian statement of philosophy’s “inner contradiction” may prompt some skep-
tical reactions. How come, we might ask, that other well-established scientific enterprises
do not seem to suffer from the same problem? Physics, for example, or mathematics, have
a long-standing history that is similarly dotted by “errors” and “faux pas”, but their devel-
opment do not seem to present particularly intractable problems. Moreover, they are “after
truth” as much as philosophy is. It seems to follow that either the Hegelian formulation of
the problem is vacuous—since it covers more than philosophy and cannot, therefore, be
used to say anything relevant to it—or that his assumptions about truth and history are so
strong to lead him into trouble at a very early stage of the analysis. Or perhaps both.
In fact, Hegel is well aware of the similarities and differences between philosophy and
other scientific disciplines. However, a discussion of this difference will be more fruitful
after we have gained some clarity on the form of this problem specific to philosophy. I will
therefore postpone it to the next section. Let me focus, first, on the form taken by the prob-
lem when applied to philosophy.
If philosophy is a science, i.e. a discipline of “objective, conceptual knowing”, then
Hegel claims that it cannot have a history since its past would simply amount to an indefi-
nitely long collection of the former errors of the discipline. History, for Hegel, at least, can-
not be just a collection of more or less amusing anecdotes. Rather, it is the reconstruction
and narration of what was true and real in the past. “A science of men in time”, as it has
been defined, whose purpose is the reconstruction—always guided by the present, to be
sure—but nonetheless striving to grasp the objective reality of what happened, of what was
the meaning of its inner reasons. A history of peasantry in the middle ages, for example,
aims at the reconstruction of that world that once was, and, by being real, had its validity.
No one would deem such a world an ‘error’, no matter how painful and labor-laden its
dwellers might have been. Such a world was true, although it was eventually superseded,

H EGEL’ S PARADOX
for better or for worse, by a different one. 12 But a history, in this sense, of past philosophies
seems to make little sense, since, once again, on the one hand it would have to grant validity
to different, successive philosophies, and on the other it would allow one truth to suppress
another. A superseded truth is not very different from a mistake, being what has been rec-
ognized as such. Furthermore, such a narration would be totally irrelevant to philosophy
and philosophizing, given the necessity to start ex-novo every time.
Conversely, if philosophy has a history then it cannot be a science, i.e. it cannot be phi-
losophy, since there would have been truths objectively valid in the past. But again, multi-
ple truths do not add up to a greater truth but constitute rather a series of opinions. Unless,
of course, one is willing to abandon philosophy’s aspiration to be a science and set a more
modest goal for it: to provide a general world-view compatible with the time in which it is
developed. 13
We face a classic dilemma, a proposition that opens up to two incompatible and equal-
ly unsatisfactory consequences. Before we begin to explore it in further details, we may
start by appreciating its real scope. It would be easy to dismiss the contradiction by relegat-
ing it to the characteristic quagmires of a discipline, history of philosophy, which can serve
useful purposes but is nevertheless distinct from philosophy proper. Easy—but wrong. The
issue Hegel is trying to bring forth by pointing at the problematic relation between philos-
ophy and its own history does not concern primarily historians—rather, it concerns philos-
ophy itself (although it is well known that his solution of the problem will radically
undermine the very possibility of such a distinction between theory and history). Hegel’s
12. There is another possibility I am not exploring here: namely, that philosophy’s history be envisioned
as a continuous progress toward richer and richer theories. We are all familiar with this model of monotonic
growth, since it corresponds to the received view about science’s progress. Hegel deals with it
explicitly in the Lectures and I will discuss his position at length in section 4 below.
13. In fact Husserl, in his polemic against Dilthey, traces back to Hegel the origin of such a view of philosophy.
Husserl acknowledges that Hegel’s philosophy rejects such a view, but he claims that Hegel’s
strong conception of history allows such a possibility, once the concept of absolute Wissen is relinquished:
“Hegelian philosophy produced lasting effects by its doctrine on the relative justification of
every philosophy by its own time—a doctrine, it is true, which in Hegel’s system, pretending to absolute
validity, had an entirely different sense from the historistic one attributed to him by those generations
which had lost, along with their belief in Hegelian philosophy, any belief whatsoever in absolute
philosophy.” See Edmund Husserl, “Philosophy as a Strict Science…,” 229-30.
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T HE END OF PHILOSOPHY
question—”How can philosophy have a history?”— is addressed to philosophers and ques-
tions their own theoretical activity. To see how this is possible is sufficient to rephrase He-
gel’s question—which, as we may remember, occurs at the beginning of a lecture course
devoted to the history of philosophy—as follows:
‘If philosophy is a truly scientific, objective form of knowledge, then it cannot have a
history. But since it seems to have one, it follows that philosophy cannot, in principle, live
up to its ambition.’
This conclusion is certainly not an undisputed philosophical thesis. As it stands, it is
just a beginning, and it is not by chance that its formulation occurs on the very first page of
a long work covering the whole history of Western philosophy. It is the starting point of an
inquiry that strives to force philosophy—and we might want to read ‘philosophers’ into the
abstract Philosophie in order to capture the concreteness of the activity Hegel has in sight
with his questioning—to think about its own goal and its own end, in all the meanings of
these terms.
What happens if we consider in more detail the first branch of the opposition set up by
Hegel, if we concentrate on the possibility of a philosophy with no history? If philosophy
aims at truth, then there can be only one true philosophy, and it follows that all other phi-
losophies must be errors. Moreover, as Hegel says, “of being that one is assured, grounded
and proved by anyone of himself” (17/15). In other words, the philosopher whose end is
truth, or at least a certain truth, the kind of truth that can be said to be objective, such a phi-
losopher has to keep (at least) two ends in sight: the end of all other philosophies, past and
present, and the end of his own philosophy. The two ends are substantially different, how-
ever. Past philosophies have ended their dominion: insofar as they are wrong there is no
place for them in the realm of truth. Or rather, they have been ended by true philosophy.
They are no longer true, nor alive. The latter, present day philosopher’s philosophy, enjoys
a different status: if it is a (i.e. the) true philosophy, then it has achieved (in principle, at
least) the intrinsic goal of philosophy. After it, after the last and finally only true philosophy,
philosophy itself, as an effort, as a research, and as a science comes to an end. A different
meaning of the word ‘end’ comes into play here: ‘end’ as completion, as the final result of

H EGEL’ S PARADOX
a series of events (what the Latin calls exitus and Hegel preferably expresses with the word
Vollendung). The true philosophy, having finally reached Truth, constitutes an end of this
sort, since it brings a long series of failed attempts to its logical conclusion. By accomplish-
ing such a feat it would have also fulfilled philosophy’s task, since it would have finally
reached the goal it had always aspired to, its telos. Hegel says that philosophy’s life-long
goal is to bring itself to completion by carrying all the other philosophies to their end. Or,
shortly, although more cryptically: philosophy’s end (as telos) is to come to an end (as com-
pletion) by implicitly bringing all other philosophies to an end (as terminus).
It might be worth stressing that this definition does not apply to Hegel's characteriza-
tion of his own philosophy. Or rather, it would apply only if we read the last ‘end,’ in the
previous definition, in the sense of completion, of Vollendung: Hegel's philosophy brings
all other philosophies to their end only insofar as it accomplishes them by bringing out their
inner truth. In short, Hegel's philosophy “sublates” them, as we say, in a higher unity, in the
unity of the system encompassing the whole history of philosophy. Instead, Kant’s concep-
tion of philosophy mentioned above satisfies quite well the definition. Its stated goal, as
Kant says, is to reach the result that has always eluded past philosophers and, by doing so,
to complete philosophy itself. Hegel wants to show that this view (which, let me remark in
passing, is already more sophisticated than most of what we encounter today, since it asks
explicitly about philosophy’s role, failures, and future) leads into a contradiction whose
only solution is represented by his dialectical view. The path toward Aufhebung takes off,
in the Lectures, from the ‘common view’ about philosophy and its history (15/15) and
brings forth what Hegel calls its inner contradiction. This contradiction is actually even
stronger than the Hegelian text might suggest and it affects deeply both Hegel’s conception
of philosophy and, indirectly, our own. To be more precise, the clash between truth and his-
tory that comes together around the notion of ‘end’ is more than a contradiction: it is actu-
ally a paradox, in the technical, logical sense of the word. This paradox is thoroughly
‘Hegelian’ in the sense that Hegel sees it as the basic problem (or ‘intrinsic contradiction’,
in Hegel’s words) pervading philosophy and threatening its survival. It is the paradox that,
according to Hegel, remains hidden and unsolved in previous philosophies, and especially
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in Kant’s, and makes them vulnerable. The path to a true philosophy, e.g. to philosophy tout
court, passes necessarily through its resolution.
We can get a grip on this paradox—whose Hegelian solution will involve the develop-
ment of the concepts of Aufhebung and absolute Wissen, which he briefly recalls in the text
we are dealing with—by focusing on the concept of telos that underlies the definition of
philosophy given above. Let me recall it here, verbatim: philosophy’s end (as telos) is to
come to an end (as completion) by implicitly bringing all other philosophies to an end (as
terminus).
This telos, as provisionally defined by Hegel, hides an essential instability. On the one
hand, it contains an implicit reference to history that comes forth through the necessity to
bring to an end all past philosophies. On the other hand, it lacks an explicit acknowledg-
ment of history’s role within philosophy. Let me introduce a distinction often used to clarify
the meaning of the word ‘history’ in order to get a clearer sense of this instability. By ‘his-
tory’ we may refer either to the series of events that make up the past, to what is sometimes
called res gestae (the ‘accomplished feats’), or to the later analysis of the past events, to the
historia rerum gestarum (the “history of those accomplished feats’). Although the distinc-
tion is obviously highly idealized—historical facts are not presented to us in their bare
givenness, but rather reached through historical analysis, to name just one possible relation-
ship between the two meanings—it can still be helpful in the present context. In our previ-
ous characterization, history as res gestae (or should we say as res philosophatae) has a
place: it has to be negated. Yet, the history of past philosophies, the historia rerum
philosopharum is excluded by the interpretation Hegel is considering: the new philosophy
coming onto the scene looks only ahead and considers its past as an error to suppress. In
other words, history is and at the same time is not present: this philosophy depends, in some
crucial way on its history (as res gestae), since it has to negate it, but on the other hand is
never allowed to look back to it, since history (as H. rerum gestarum) is by definition out-
side its scope. Hegel’s strategy, at this point, is to proceed to unfold the truly paradoxical
nature of this double relationship and to examine the consequences for philosophy as a
whole.

H EGEL’ S PARADOX
Let us go back to our previous reformulation of the telos of philosophy: ‘its task (as
telos) is to come to an end (as completion) by implicitly bringing all other philosophies to
an end (as terminus).’ Notice that the grandiosity of the effort lying ahead of the philoso-
pher begins to cast doubts on the feasibility of an enterprise that strives to bring philosophy
to an end. As soon as the philosopher starts to consider that in order to reach science he has
to succeed where great minds have failed, his resoluteness may begin to waver and, with it,
his belief in truth. If philosophy cannot achieve such lofty goals, perhaps it can offer a col-
lection of Weltanschauungen, among which the learned man can pick the most suitable to
his taste. Hegel is fully aware of this possibility, when he writes:
We see that in the great matters to which we [e.g. the philosophers] are
attracted […] the greatest minds have erred because they have been refuted
by others. Since this has happened to great minds, how am I, ego homuncio,
to attempt a decision? […] If it be granted that philosophy is to be a real science
and that one philosophy is a true one, the question is ‘Which one?’
‘How on earth is it to be recognized? Every philosophy asserts that it is the
true one; everyone cites different signs and criteria whereby the truth is to
be recognized. Therefore a prudent and circumspect way of thinking (Denken)
must hesitate to decide among them.’ (16/13, last italics are mine. Tr.
modified)
Hegel not only stresses, once again, that philosophy has decayed from the search for truth
to a stock of world-views, he also points out how and why such a shift occurs: it is precisely
because past philosophies have been reduced to a series of errors that the philosopher’s re-
solve begins to waver. The shift happens when a certain a-historical view of philosophy’s
end is pushed to the limit and—after having reduced past doctrines to mistakes—the phi-
losopher thinks of his own experience (and silently utters: memento mori). Yet another
meaning of “end” comes into play: end as limitation and, more specifically, as a limitation
of possibilities. End as the root of endlich, “limited,” more specifically in the Kantian sense
of being limited to (by) some external contingency. A human being, in this sense, is a finite
thinker since its knowledge is limited by sensible intuition and it is thereby restricted to the
objects presented to such an intuition. A “circumspect thinker,” a thinker who takes circum-
stances into account, and is therefore limited by them, cannot but hesitate among the dif-
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ferent world-views. He is bounded by them, in fact, his philosophizing being reduced to the
mere power of choice. Indeed, the whole structure of the “call to history” that opens Hegel’s
lectures may be interpreted as a reminder of the necessity to assume philosophy’s (and phi-
losophers’) intrinsic finitude as a starting point. By calling up history, Hegel underlines that
philosophy and philosophers cannot be a-temporal. They are in time and, as such, subject
to falsification, evolution, development and similar phenomena. It is precisely this possi-
bility that makes the philosopher (more properly, the activity of thinking, das Denken) balk
and retract even before the mere choice: “since this has happened to such great minds, how
should I, ego homuncio, want to decide?”
What is more important, the limitations of past philosophies cannot be exploited: since
history as a recollection of the past is excluded by the ‘common wisdom’ about philosophy,
any true relationship with the past is severed. At most, and that task would already be prob-
lematic, past philosophies can be juxtaposed next to each other in a stockpile from which
to choose. To see how this is possible, consider that the limit encountered by past philoso-
phers, e.g. their work being no longer true, proves that they are limited and subject to error.
Such a limit would have to be transcended, in order to turn it into a positive experience.
However, the philosopher who, wanting to abandon the love of science for science itself,
claims the a-historicity and a-temporality of philosophy, finds no positive side, no uplifting
into a higher level into such an experience. Inevitably, since history has been banned in the
name of science, and, with it, the very idea of a development intrinsic to the notion of truth,
the experience of the past is inevitably bound to happen again, since nothing has changed.
And the experience of being refuted marks much more than the error of such and such a
philosopher, it marks the error of philosophy itself and its fall into a history of conflicting
opinions.
The net result of this movement is that Hegel’s question about the possibility of a his-
tory of philosophy appears as a paradox in the strict logical sense: a sentence which is nei-
ther true nor false, since it is true when it is false and vice versa. Think, as a comparison,
of the ancestor of all logical paradoxes, the paradox of the liar—the sentence “Now I lie”.
This proposition is true when it is false and vice versa because if I lie when I say I am lying

H EGEL’ S PARADOX
then I am clearly telling the truth. But if I tell the truth when I say I am lying, then I am
clearly lying and I am not telling the truth, and so on. Similarly, Hegel’s question about phi-
losophy and history exhibits the same behavior, flip-flopping as it does from one extreme
to its incompatible opposite.
Indeed, we see that if philosophy is a science, and therefore has no history, it follows
that all (and especially the current, actual, present-day) philosophers are always on the
verge of being in error. But if they are in error then, ironically, they literally are history and
it follows that philosophy as a science has never nor will it ever exist. Thus, the most glar-
ing contradiction follows: if philosophy is a science then it is not a science. Or, to put it
more dramatically, philosophy is and is not a science. Conversely, if philosophy is not a sci-
ence then it can have a history, although only a history of conflicting opinions. But if its
past is only a succession of mistakes, then philosophy can be a science if it only corrects
the basic faux pas. Then it will be a science. But note that we have reached this conclusion
only by assuming that philosophy was not a science. In short, both branches of the paradox
lead to the same conclusion: philosophy is and is not a science. Or better: it is one when it
is not. And vice versa. Philosophy, it seems, cannot and perhaps should not exist, and re-
gardless of its scientific status, if it falls prey to such fundamental contradictions.
It might seem misleading to compare logical contradictions like those presented by the
Liar’s paradox with the dialectical contradictions presented by Hegel because a logical an-
tinomy has no solution other that its dissolution (by removal of the difficulty, like the Liar’s
paradox self-referentiality, that caused it), whereas a dialectical contradiction admits a so-
lution into the higher unity that preserves and sublates the opposites. I certainly do not wish
to deny this difference, but rather to argue that the first presentation of the paradox in the
text can be read as a logic-like antinomy and what follows it is precisely a re-interpretation
of the antinomy by dialectical means (which depends on a very different interpretation of
contradictions) that makes a solution, instead of a dissolution, possible. In other words: if,
as I believe it is the case in the Hegelian text, the contrast of truth and history that crystal-
lizes around the concept of end (of philosophy) can be read as a classical logic-like antino-
my then the only classical way out is to dissolve the antinomy by abolishing the source of
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the paradox—e.g. the possibility of philosophy. The Hegelian solution, instead, is to rein-
terpret the antinomy by substituting a different reading of contradiction fro the classical
one—e.g. by introducing dialectics. 14
More generally, Hegel shows that if the notions of truth and history are taken seriously,
then the very, undeniable fact that philosophy, e.g. the search for truth, might have a history
brings about a paradox that casts a spell on philosophy itself and threatens to destroy its
very possibility. This paradox, it may be worth remembering, arises when the implicit and
deeply a-historical relationship of philosophy with its end is brought to the fore. The first
conclusion to be drawn from it, then, is that unless philosophy takes an explicit stance to-
wards its end, it can never exist, since it bounces from a series of historical temporal opin-
ions to an a-historical truth that mutually converts into one another.
But Hegel’s point can also be read from the conclusion to the premises, or, as the logi-
cians say, by contraposition. Since it is a fact, contrary to the previous alleged conclusion,
that philosophy has existed and does exist (and Hegel would be the last one to contest such
a fact) it follows that it has, always, and more or less explicitly, taken a stance towards its
end. In fact, we might say that what Hegel’s paradox does is to show how philosophy—
Hegel’s philosophy first and foremost, and ours as well insofar as it might share some of
Hegel’s assumptions on truth and history that bear the weight of the paradox—is tied to its
ends. We might even say—but it would be too strong, since such a privilege is shared by
other words—that what the paradox shows is that ‘end’ is the philosophical word par ex-
cellence, since it is impossible to speak about or do philosophy without being drawn into
thinking about the end and the ends, of philosophy and of philosophers. (Anyone existen-
tially minded might want to push this thought a bit further and claim that philosophy, in the
end, has just one concern: the end with a capital E, i.e. “the most extreme possibility”
14. Removing the possibility of self-referential sentences is the classical, Russellian solution to the Liar
paradox as it arises in set-theory. Although other non-Russellian alternatives are in fact possible, the
difference between a logical “dis-solution” and the Hegelian “re-solution” of the antinomy remains unchanged,
insofar as it involves a deeply different treatment of contradiction and a different concept of
“solution.” For a detailed discussion of the Liar paradox see Jon Barwise and John Etchemendy, The
Liar (Oxford: Oxford UP, 1987) and, more recently, Jon Barwise and Lawrence Moss, Vicious Circles
(Stanford, CA: CSLI Publications, 1996), p. 177-197.

H EGEL’ S PARADOX
opened up for us, the end of all possibilities—death. It concerns nothing but death, it deals
with that limit that defines our finitude and all the possible ways to defy it, from simple de-
nial to utterly acceptance to dialectical overcoming. But we will leave this aside).
If speaking about philosophy as such brings up the issue of its end, the converse is as
much true although usually more readily acknowledged. Any reflection on the end brings
immediately up philosophy, since the attempt to disentangle the multitude of aspects that
‘end’ covers cannot but use the most traditional vocabulary of philosophy: telos, finis, ter-
minus, peras, etc., as we have witnessed in the previous exposition. Such meanings have
received their definition within the discourse of philosophy and it would be naive (and,
properly speaking, non-sensical in the strict sense of the term) to use them to position one-
self ‘outside,’ as it were, the philosophical discourse. Nonsensical, because if ‘end’ re-
ceives its meaning within the discourse of philosophy, then of what use can it be outside
such a realm? This is, or can be read as, an indictment of the possibility of speaking of the
end of philosophy—but only if such a task is joined (accompanied) by the pretension of
thereby stepping out of it. In other words, the strict relationship existing between ‘end’ and
‘philosophy’ means that any effort to think ‘the end of philosophy,’ in these terms, is there-
by totally within the scope of philosophy while striving to ‘step out’ of it. As the fly caught
in the spider web, its efforts only make the situation worse. Should we therefore declare
“over” any effort to investigate the end of philosophy? (While acknowledging that such a
gesture, paradoxically enough, is nothing but classical philosophy?) A clear example of the
difficulty involved in detaching the meaning of ‘end’ from ‘philosophy’ is shown by a pas-
sage in the lecture course Heidegger gave on Hegel’s Phenomenology in 1930, where he
refers to Nietzsche and Kierkegaard as non-philosophers. Or, more precisely, he says that
we should not say offhand that they are not philosophers. Much less
should we hurriedly say that they are philosophers and thus part of the genuine
history of philosophy. Perhaps in both Kierkegaard and Nietzsche—
and we cannot take them seriously enough—something has been realized
which is in fact not philosophy, something for which we have as yet no concept.
Therefore, in order to understand them and their influence, it is crucial
that we search for that concept instead of pitting them against philosophy.
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We must keep the possibility open that the time to come, as well as our own
time, remains with no real philosophy. That would not be at all bad. 15
Heidegger does not make any reference to the ‘end of philosophy’, when he points to Ni-
etzsche and Kierkegaard, since any such use would either (1) put them immediately back
within the scope of that same philosophy they have allegedly broken free from, or (2) force
him to stake out a somehow more original, more basic, and in a certain sense archetypal
sense of end that would come before philosophy’s appropriation of the term, with the only
result that philosophy’s scope would be wider in scope but not qualitatively different.
Heidegger advances a suggestion, however, when he hints at the lack of an adequate con-
cept for the work of non-philosophers as Kierkegaard and Nietzsche. How do we search for
it, so that “our own time remains with no real philosophy”, but comes instead to non-phi-
losophy? Perhaps, we might find an opening if we keep looking into the “end of philoso-
phy” as an integral part of philosophy’s endeavor. Instead of assuming that talk about the
end would bring us out of it, we should perhaps try to see better to which end philosophy
bring us. The clause “end of philosophy” should, consequently, be read in the subjective
sense of the genitive: as the particular end that philosophy owns, or claims to own, as its
most proper place. The end as a place toward which philosophy strives should perhaps be-
come the focus of our efforts. If the previous analysis of the relationship between ‘end’ and
‘philosophy’ has proved successful, then it will have demonstrated the existence of a dou-
ble, inextricable correspondence between the two terms, between the project of philosophy
and the meanings of ‘end.’ Such a conclusion allows us to reverse the previous statement:
if the end of philosophy brings the very meaning of end into question then bringing the
sense(s) of end into question is tantamount to question philosophy to the end. As it has al-
ready been noticed, the strict relationship between philosophy and end entails that the end
(as terminus and completion but no longer telos) if reached, would bring the very sense of
end into question. 16
15. Martin Heidegger, Hegel’s Phenomenology of Spirit (Bloomington: Indiana University Press, 1988)
13.
16. I am borrowing a suggestion advanced by John Sallis in Delimitations (Bloomington: Indiana University
Press, 1986) 17.

P HILOSOPHY’ S ENDS
Therefore, our own, more limited telos becomes to come closer to that place where
ends meet and try to see what happens “there.” The Hegelian text is helpful, in this respect,
since, after the first formulation of the paradoxical relation between philosophy and history,
the text its analysis proceeds to an examination of the different relationships that a disci-
pline may entertain with its history, and therefore with its end. In other words, Hegel pro-
vides an analysis of the different encounters that philosophy has always had with its own
end, conducted by comparison with the models offered by other, related disciplines, where
different types of truth and different types of end come to meet.
4. Philosophy’s ends
In which ways can a discipline relate to its history and, therefore, to its possible end?
In the Lectures, Hegel compares philosophy to the other sciences and to religion and claims
that their model cannot be adopted by philosophy although they both share important sim-
ilarities with it. Hegel conducts his discussion on the possibility of philosophy by assuming
that philosophy is (or has to become) a science. This assumption looks so outdated that it
seems to cast a very dark shadow on the relevance of the Hegelian argument for contem-
porary philosophy. However, a brief discussion will show that, once terminology has been
clarified, the disagreement is more apparent than real.
In its current most common uses, “science” generally denotes the body of knowledge
provided by the natural and physical sciences. In other words, it denotes the “connected
body of either demonstrated truth or systematically classified facts brought under general
laws that can be found in the study of the material universe,” as the dictionary has it. The
German word used by Hegel, Wissenschaft, has a broader denotation and refers, to use He-
gel’s own words, to any discipline capable of providing an “objective, discursive knowl-
edge.” The Hegelian accent is on a discipline capable of exhibiting objective truths that can
be expressed discursively, i.e. in concepts and not, for example, in some intuitive feeling.
“Philology,” then, is as much a science as physics, insofar as its methods can establish a
(perhaps limited, but nonetheless valid) set of truths about a text handed down by the tra-
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dition. However, Wissenschaft is not, by and large, qualitatively different from the current
English word “science,” the main difference being one of scope, at least if one allows that
different disciplines may have different methods to ascertain the objective validity of their
truths. Far from being tainted by an old-fashioned conception of science, Wissenschaft is
instead more general in scope and more epistemologically neutral than the current use of
the term “science,” because it does not assume a built-in preference for the mathematical-
physical paradigm as the standard of validity. When Hegel asserts that philosophy has to
become a “science,” then, he is stating that the truths provided by philosophy must be as
epistemologically valid as those provided by, say, physics or philology, but he is not assum-
ing that there must me one preferred epistemological standard provided by a specific dis-
cipline. To put it differently, there are no substantive claims hidden behind the use of the
term Wissenschaft (which was in fact quite common at the time), but rather the effort to use
a term broad enough to cover disciplines across the board with no special epistemological
preferences. The use of the term Wissenschaft makes in fact Hegel closer to philosophers
like Carnap and Russell than to what we ordinarily design with the umbrella term “Conti-
nental” philosophy. The difference lies in the kind of truths (and therefore the kind of meth-
ods) that philosophy can reach. There is little doubt that the Russellian analysis of
propositions is far different from Hegel’s dialectical progression of concepts in the Wissen-
schaft der Logik, but the epistemological goal that philosophy must attain is the same. 17
It might be contended, however, that it is precisely this overvaluation of theory that
makes Hegel’s argument for the end of philosophy suspicious. It might be said, in other
words, that philosophy is, and perhaps has always been, engaged in the search for “Sophia”,
the latter term to be reinterpreted as a form of practical wisdom and not as a science-like
form of knowledge. The issue becomes whether such a (very broadly construed) “ethical”
wisdom can stand on its own without a metaphysics to support it. As a matter of fact, in our
17. More precisely, it may be said that it was as a reaction against the “metaphysics way of attaining truth”
that the logical analysis was devised (see, for example, Carnap’s violent critique of Heidegger’s inaugural
lecture on “What is metaphysics?” as a mere word-play that is meaningless because it just confounds
the various meanings of “nicht.”). In other words: the path had to change so that the destination
could be reached.

P HILOSOPHY’ S ENDS
Western tradition, this has never been the case. That is, it is precisely the point of our tra-
dition to base the former on the latter, whether implicitly or explicitly. “What I ought to do”
depends on “what I can know” to use the Kantian terminology, with very few, unorthodox
exception, in the period preceding Hegel. Sophists come to mind as one example, and the
debate between Gorgias and Plato as the relevant evidence. Notice, for example, that Pla-
to’s Socrates is fully within this model. Post-Hegelian philosophy’s privilege of “ethics,”
see Nietzsche and Kierkegaard, disputes precisely this point, the dependence of ethics on
metaphysics, and that’s why we are reluctant to position these latter philosophers within the
orbit of Western Metaphysics. When dealing with these alternative readings of Sophia in
philosophy, however, the real issue at stake is to understand how to reject the classical goal
of philosophy as science. By and large, the only way out is by arguing against the Hegelian
“solution” to the problem of the end of philosophy in favor of a different “end” and a dif-
ferent (non)-philosophy. Once again, a discussion of Hegel represents a crucial carrefour
that cannot be avoided even, and especially, by a non-metaphysical reading of philosophy.
Alternatively, one may accept the hierarchical relationship between metaphysics and
ethics or, more precisely, between theoretical knowledge and practical wisdom and dispute
whether (a) philosophy as metaphysics can supply the necessary theoretical knowledge re-
quired to ground a wisdom and (b) whether this metaphysics can have a “scientific”, e.g.
“discursive, objective” form. Hegel wants to argue for a positive answer to both (a) and (b).
Other options would prescribe, respectively, that the goal (telos) of philosophy may be pre-
served but put outside of philosophy’s scope (and then assigned to another discipline, usu-
ally religion or empirical science) or that only a non-discursive form of knowledge can be
up to the task. 18 I will discuss both options at length in the following section.
In short, it may seem that this Hegelian argument is of little relevance given its reliance
upon such a strong notion of philosophy as science. But, once the terminological issue is
settled, we can see that the alternative options are either to argue against the predominance
18. The former option is discussed at length by Alexandre Kojève in his well-known interpretation of the
chapter VII of the Phenomenology of Spirit as a the alternative between Plato and Hegel, while the latter
is represented, in the context of German Idealism, by the positions defended by both Hölderlin and
Schelling. I will come back to Kojève’s interpretation of Absolute knowing below.
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of metaphysics over ethics that is typical of the Western tradition (which entails arguing
against the whole tradition, and Hegel in primis), or to try to put an end to philosophy as
the bearer of the necessary theoretical knowledge. And Hegel’s argument sits squarely at
the center of this debate. Either way, then, we have to deal with him. Let us go back to the
text of the Lectures on the History of Philosophy and see how Hegel proceed to establish
philosophy’s possible end.
Philosophy is similar to the other sciences in form, Hegel says, and to religion in con-
tent. It is similar to the other, empirical sciences, because “they have thinking in common
with philosophy. Experience is their element, but they do have thinking too because they
strive to discover the universal in it” (116/241-2). 19 On the other hand, philosophy is sub-
stantially similar to religion, since they share the same subject-matter: “Religion has the
substantial (content) in common with Philosophy—namely God, the Absolute, what is in
and for itself. This is the content of Religion and of Philosophy, the essence of the world;
the relationship to truth, to the absolute idea is their common ground.” (ib.)
In spite of these important affinities, both science and religion cannot be said to have
a history, Hegel claims, in the proper sense of the word. Every discipline has clearly an “ex-
ternal history” (außere Geschichte), a history of its diffusion, of its teachers, of its recep-
tion, etc. But what is at stake here is the history of the internal content, of “the subject
itself,” of their truths. Sciences, in this respect, exhibits a history of this kind insofar as what
they hold true has changed over time, insofar as findings which had been held good have
been rejected and new results have been secured. By and large, however,
a great, perhaps a greater part of their contents consists of what has been
retained. New things that have arisen are not alterations of earlier gains, but
an addition and increase of them. These sciences advance by a juxtaposition.
[…] there have been many corrections of earlier mistakes. But by far the
greatest part of them still stands and, without alterations, is enriched by new
discoveries. In a science like mathematics, its history, so far as its content
19. e.g. 1825-26 More precisely: Das wissenschaftliche Bemühen, Treiben hat das Formelle mit ihr gemein,
das Denken; es geht von der Erfahrung aus, aber die Wissenschaft denkt über die Erfahrung,
sucht das Allgemeine in dem, was es betrachtet. Diese Seite hat also das Formelle gemeinschaftlich
mit der Philosophie]

P HILOSOPHY’ S ENDS
goes, has chiefly only the pleasing business of relating amplifications. Elementary
geometry, for example, in its scope as expounded by Euclid, can
from them on be regarded as having no further history. (13/12. My emphasis.)
The relationship between the empirical as well as the formal sciences and their own end is
then quite simple, according to Hegel, because of the very limited role played by history in
their development. Sciences grow by accumulating results, by juxtaposing them, until they
exhaust the field of experience they deal with. At which point, they reach their end, in the
two senses of terminus and telos: they have fulfilled their goal by coming to an end. This,
Hegel says, is what happened to elementary geometry with Euclid: it came to its end by be-
ing completed. Before Euclid, it is reasonable to suppose, there must have been a history
of errors and corrections that led up to the final systematization in the Elements. What is
characteristic of science, stresses Hegel, is the linearity of the process, or, to be more pre-
cise, the monotonic character of the curve describing its process in time. 20
This view of science may strike us as extremely unfashionable and outdated. Who still
believes in the linear progress of the scientific acquisitions of mankind? Hegel seems irrep-
arably off-track in his scientific examples. However, we might begin by pointing out that
Hegel’s view, however unfashionable, is far from dead. As recently as 1980, Stephen
Hawking discussed a very similar position in the inaugural lecture as Lucasian Professor of
Mathematics at Cambridge, which he significantly titled, “Is the end in sight for theoretical
physics?” 21 Hawking discusses the possibility that physics, as a science, can be “achieved”
in the near future (before the end of the century, he says, or 20 years down the line.
20. A monotonic curve is a curve whose slope does not change sign, or direction: it is either always growing
or always decreasing, e.g. it has either one of the two following shapes:
A non-monotonic curve presents peaks or depressions, and the kind of curve that may represent philosophy’s
historical development with respect to truth that falls prey of the paradox is probably, in Hegel’s
view, of the form:
21. Stephen Hawking, Is the end in sight for theoretical physics? (Cambridge: Cambridge University
Press, 1980).
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The goal to be reached is clearly set: physics will have to provide “a complete, consis-
tent and unified theory of the physical interactions which would describe all possible ob-
servations” (1). Hawking is quite confident that such a theory might be found and actually
reviews the possible candidates pointing his attention on a specific supergravity theory as
the most likely one. More calculations are needed in order to test the theory, he affirms, and
if it “survives these tests, it will probably be some more years before we develop computa-
tional methods that will enable us to make predictions and before we can account for the
initial conditions of the universe as well as the local physical laws”(24). But once these two
last tasks have been taken care of, physics can well be considered closed.
Of course, the similarity between Hegel's and Hawking's epistemologies, proves very
little, since nothing excludes that they both be wrong. My previous quotation from the
opening lecture of the distinguished Cambridge professor serves a rather different purpose:
it points to the “plausibility” of Hegel's view of science. In other words, it shows that He-
gel's view of scientific progress, although couched in rather unfashionable terms, is actually
quite close to science’s self-understanding. More generally, this common and shared view
of science’s progress serves a broader goal: it points to a possible interpretation of the re-
lationship between a discipline and its end that could solve—or rather dissolve— the par-
adoxical relation between philosophy, history and truth. We understand, therefore, how this
view of science might become an attractive model that anyone wishing to carry philosophy
beyond the Scyllas and Carybdis of truth and history may want to adopt.
This remark was necessary in order to get some clarity on what is at stake in the He-
gelian discussion of “science’s progress.” In the present context of the Lectures, Hegel’s fo-
cus is philosophy, and philosophy's problems, only. If his argument brings in science it is
only because he wants to discuss a possible solution of the paradox that would consist in
pulling philosophy toward this scientific model of progress. Hegel’s science, we might say,
is philosophy in disguise: it is a certain view of philosophy as a scientific discipline that
comes to the fore under the clothes of Euclidean geometry. What we have to discuss, then,
is not the intrinsic value of the philosophy of science that can be extracted from Hegel's cur-
sory remarks in the Introduction. The issue is the role played by this view of science within

P HILOSOPHY’ S ENDS
his argument. Hegel mentions science because he wants to stress that in its case there is a
possible simple solution to the problem of the relationship of a discipline with its end: linear
progress culminating in the end as fulfillment of the goal. This possibility depends crucially
on two factors: the monotonic advancement of scientific knowledge (what Hegel calls the
juxtaposition of results) and the existence of a criterion to determine whether the end has
been reached or not, which, in the examples he mentions, seem to be constituted by the sim-
ple exhaustion of the phenomenal domain the discipline sets out to explore. In other words,
an external, finite criterion has to be in place to measure the distance between the current
state of the discipline and its end. This criterion is, quite simply, constituted by the initial
definitions of the phenomena to investigate. Hawking’s formulation —”a complete, consis-
tent and unified theory of the physical interactions which would describe all possible ob-
servations”— although certainly more modern seems perfectly consistent with Hegel’s old-
fashioned version. Both conditions, the linear progress and the external criterion, have to
be present for the simple relation to obtain. In the case of philosophy, Hegel claims that the
first condition, at the very least, does not hold since philosophers have not only contradict-
ed but refuted each other.
It would not constitute an objection to Hegel’s point to claim that his model of science
is inadequate for his point was ultimately not about science but about philosophy modeling
itself after (a possibly inadequate model of) science. In other words, an analysis showing
that science’s way of proceeding is more sophisticated than the simple juxtaposition of re-
sults Hegel speaks about, would not constitute a valid objection, since it would only prove
that science itself needs to entertain a more sophisticate relationship with its own end. He-
gel’s point, in the present context, is that philosophy cannot avail itself of such a simple so-
lution unless it proves to proceed more or less linearly toward the fulfillment of a task
measured by an independently established criterion. And both conditions seem, to Hegel at
least, quite unlikely to be met. It should be remarked that the various programs of scientific
reformation of philosophy, have tried to pick up precisely this model, by defining a phe-
nomenal field and a task to achieve which can be measured by an external criterion. The
shift to linguistic investigation so characteristic of contemporary philosophy can, in several
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cases, be seen precisely as the attempt to secure such a field in order to leave the quagmires
of metaphysics. Certainly, many strategic gestures by the so-called analytic tradition in
contemporary philosophy can be read along these lines.
A similar verdict applies to religion, the other sister discipline of philosophy. Again,
Hegel claims that philosophy—in spite of the deeper affinity it shares with religion than
with the other sciences—has to have a substantially different relationship with the end. Re-
ligion is in a totally different situation, he says, since the only history it knows relates its
spread, the fates of its adherents, etc., and that is irrelevant to the issue at hand. Insofar as
the ‘inner content” goes, Hegel remarks that
Christian doctrine as such is also not without a history, although of necessity
it soon finished its development and achieved its settled form. […] But
the content of Christianity, i.e. the truth, has as such remained unaltered and
has therefore no history, or as good as none. (12/10)
The content, what Hegel in this context calls the doctrine, is granted to religion from the
beginning, and, therefore, is excluded from history. The text does not give further elucida-
tions about the “necessity” that soon brings the doctrine’s development to an end [aber sie
hat notwendig bald ihre Entwicklung erreicht]. And in fact this argumentative line—which
we are now quoting from Hegel’s 1818 lecture course on the history of philosophy—is ab-
sent from the later versions of the Lectures. The passage might be interpreted, in a first ap-
proximation, as an implicit reference to the written form in which the content of many
religions (and the Christian among them) is handed down. But it is not the mere presence
of the sacred scriptures that contains religion’s doctrinal development to a rather limited
lapse of time. Rather, the possibility of a sacred scripture as such, i.e. the possible existence
of an external source in which the truth about the essence of the world, to use Hegel’s terms,
is deposited for man to retrieve, depends, it seems, on the distinctive character of religion.
In it, Hegel says, the Absolute comes to consciousness from the outside, is perceived and
recognized, at least at the beginning, as totally exterior to consciousness. Later on, when he
comes to a more detailed discussion of the differences between religion and philosophy,
Hegel remarks that the former’s essential character lies in the fact that the Absolute, is pre-

P HILOSOPHY’ S ENDS
sented as separate from the religious consciousness, “it comes from without.” More pre-
cisely,
In religion, two factors are present: (1) An objective form, or kind, of consciousness
(wherein the essential spirit, the Absolute, appears as outside the
subjective spirit and so as its object) comes to image the spirit historically
or in the shape of art, removed in time and space. (2) The character or phase
of devotion and fervor; here this removal is discarded, and the separation is
superseded; here the spirit is one with the object, the individual is filled with
the spirit. (137/252)
The truth of religion is constituted by the sensible revelation of the divine through art, wor-
ship and cult, while in philosophy there is no external source of objectivity. Even in its sec-
ond phase, in the unity reached through devotion, the spirit comes from the outside, and
always stands out and against consciousness, although the latter has to bear witness to it.
This is what guarantees, it seems, that the development of religion’s inner content can be
settled rather rapidly, so that the relationship between it and its end can achieve the simpler
form we have already witnessed with respect to the sciences. What matters, in this context,
is the external source of authority: both science and religion possess an intrinsic openness
to the outside since the former relies ultimately on empirical experience, according to He-
gel, and the latter is based on the consciousness of the divine substance that comes through
an ultimately sensuous perception— the religious feeling, as it were.
This intrinsic openness ultimately means that science and religion are essentially “lim-
ited,” in the technical sense of being bounded in their aspirations by a horizon, by a limit
over which they have no control. Experience is, by definition, precisely what, being outside
science’s control, warrants its objectivity. Analogously, in religion, the religious conscious-
ness finds its truth outside itself. Science and religion are therefore immune, according to
Hegel, from the characteristic oscillations that he has described with respect to philosophy.
We might say that the presence of an external horizon, of a boundary condition of sorts, is
what limits the amplitude of such oscillations and, eventually, reduces them to nothing
(whether in time or asymptotically, it is a separate issue whose relevance is minimal in this
context). This is why the end of science and religion is so relatively unproblematic. The
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presence of the horizon, of the limit that bounds them has an extremely positive effect: it
de-limits from the outset a realm which can and will (in the case of science) or has been
(for religion) be filled in time. Science can proceed therefore by addition—by juxtaposi-
tion, as he puts it—and religion can stop after a relatively short time its development. Both
are almost totally free from all the nuances and sophistications of the concept of end we
have explored above, because one of the many meanings of end, the end as limit, over-
whelms all the others and predetermines their (limited) scope. In other words, science and
religion have always their end in sight because their essential limitation make them over,
so to speak, from their inception.
Philosophy, however, has to transcend this limit—or rather this one-sided reading of
‘end’ as limit—if it is to remain faithful to its ambitions. In fact, the preceding discussion
makes clear, I think, that science and religion, although similar to philosophy in Hegel’s
conception, will never be able to fulfill philosophy’s goal. Philosophy’s aspiration is to tell
the truth about the world, or as Hegel puts it, to explain by means of concepts the essence
of the world. This goal is beyond science’s and religion’s scope because there will always
be something beyond their reach, something lying beyond the limit—beyond, respectively,
the realm of possible experience or beyond the religious feeling—that assures their stability
and their raison d’être. Both will always be limited, now in the negative sense of the word:
their truth has its ground in something external to them. Philosophy, in Hegel’s reading at
least, cannot rest content with such a limitation without admitting defeat.
The confrontation with science and religion, therefore, allows Hegel to establish a fur-
ther point: philosophy lacks an external limit bounding the scope and method of its re-
search. This conclusion can be interpreted, however, in three different ways since the lack
of such a limit can be taken: (a) as evidence that philosophy can be useful in setting goals
and clarifying concepts whose realization will be achieved elsewhere; (b) as a proof, by re-
ductio ad absurdum, that philosophy’s very task is bound to fail and its discourse doomed
to collapse in a sequence of ‘conflicting opinions’; (c) as the demonstration that philosophy
has to find a different kind of limit, internal to itself, in order to escape such a collapse.

P HILOSOPHY’ S ENDS
The first option can be seen as a surrender of philosophy to either science or religion;
or, to put it differently, as a transfiguration of philosophy into either epistemology or theol-
ogy. Alexandre Kojève illustrates the latter possibility in his analysis of the final chapter of
Hegel's Phenomenology (i.e. the chapter on “Absolute Knowledge” which he renders as
wisdom, sagesse, as opposed to philosophy, philosophie). Kojève draws a comparison be-
tween Plato and Hegel and sees both as setting the same project for philosophy: the defini-
tion of the Wise man, that is, the man who is no longer a philos-of-sophia, a lover of
knowledge who asks questions, but rather the man who has reached knowledge and pos-
sesses all the answers: “a perfectly self-conscious man, fully satisfied by this coming to
consciousness, and thus serving as a model for all his ‘colleagues’.” 22 The fundamental dif-
ference between the two thinkers lies in the fact that Plato “denies [and Hegel affirms] that
this ideal can be realized by man. (that is, by real man, living in a real World, during the
length of time delimited by his birth and his death)”(83/278). The consequence is that for
Plato, according to Kojève, the ideal of philosophy, Wisdom, lies outside philosophy’s
scope since it can only by realized “by a being other than man, outside of time. We all know
that such a being is called God” (89/283). Philosophy, then, sets the goal that only theology
can realize. For Hegel, on the other hand, the ideal is realizable in time and by man.
In Hegel’s times the confrontation between philosophy and religion was particularly
pressing and especially so in Berlin during the years in which he was giving the lectures on
the history of philosophy. In our day and age—and especially in the countries where the
empiricist and positivist traditions are stronger—we are perhaps more familiar with the
similar confrontation that philosophy has to sustain, at the intellectual and institutional lev-
22. Alexandre Kojève, Introduction à la lecture de Hegel…, 88; Engl. tr. 282. Kojève is referring to (and
partially retranslating into his own language) the celebrated passage in the Preface to the Phenomenology
of Spirit: “Die wahre Gestalt, in welcher die Warheit existiert, kann die allein die wissenschaftlichene
System derselben sein. Daran mitzuarbeiten, daß die Philosophie der Form der Wissenschaft
näherkomme,—dem Ziele, ihren Namen der Liebe zum Wissen ablegen zu kommen und wirkliches
Wissen zu sein,—ist es, was ich mir vorgesetzt.” (Engl. Tr. 3). The first formulation of this opposition
(e.g. science vs. love of Knowledge) is perhaps to be found in Fichte’s Letter to Böttinger, March 1,
1794.The very title of Fichte’s system, Wissenschaftslehre, is motivated by this opposition between
knowledge and love of knowledge. See also Fichte’s “On the concept of the Wissenschaftslehre,” and
the “Comparison between Prof. Schmid’s System and the Wissenschaftslehre” in Early Philosophical
Writings, (Ithaca: Cornell University Press, 1988).
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els, with science. Since the (neo)Positivist reaction turned metaphysics into a field of pseu-
do-problems, it is been quite common to assign to philosophy the role to unify— chiefly,
by linguistic analysis— the empirical results reached by the empirical sciences in a meth-
odologically consistent view.
Hegel emphasizes science much less than religion, but he is so aware that either of
them can become all too powerful rivals for philosophy that he does not hesitate to call
them the two “antagonists” that it has to meet.” 23 These two antagonists may be seen as
striving to replace philosophy altogether, without even needing its help to set goals or to
clarify their methodologies.
The second option sketched above represents just a radicalization of this view: philos-
ophy has to be suppressed as a misguided attempt. At most, its goal and worries can be re-
constructed within the framework of an empirical discipline, bringing effectively about a
death penalty that cannot be appealed. Quine's well-known project of an “epistemology
naturalized” can be seen as an exploration of this route: philosophy is first reduced to a re-
flection on science, following the neo-Positivist lead, and then reduced to a branch of a par-
ticular empirical science (in his case psychology).
By resolutely choosing the third option, Hegel makes clear what is involved in philos-
ophy as he conceives it: a search for truth which cannot find an exterior limit. This means
that since the positive effects of being limited, i.e. stability, cannot be exploited, philosophy
is prone to becoming “a spectacle of ever innovating changes of the whole thing and these
at the end (zuletz, eventually) no longer have even the mere aim of having a common bond”
(13/12). Ziel, the word Hegel uses here, can be read as goal, telos. The common bond is no
longer present even as a telos then, and philosophy is prone to dissolving, or risks contin-
uously to do so, unless the goal is preserved. On the other hand, its total “inwardness”
makes that goal even more difficult to secure. In fact what happens to philosophy is that
any allegedly “new” system claiming to bring philosophy to an end (as we have seen it is
necessary) has no more authority than the antagonists it tries to unseat. As a consequence,
says Hegel
23. Knox 58. Note that in this passage Hegel speaks, more accurately, of piety and Reason.

P HILOSOPHY’ S ENDS
to philosophy we can apply the words of the Apostle Paul to Ananias: ‘See
the feet of those who will carry thee out are already at the door.’ (61/143)
However, it should now be clearer, after the previous discussion of science and religion,
why this refrain to which Hegel is constantly coming to is no idle talk. The depiction of
philosophy as a succession of opinions can in fact be used, in the present context of the dis-
cussion of science and religion, as a very effective weapon toward its dismissal in favor of
theology or (nowadays) science. Hegel thinks that philosophy’s chances of survival are in-
trinsically related to its ability to take up the challenge represented by the paradox of the
end. The problem the latter presents can therefore be restated as follows: how and where
can philosophy find a limit—in a positive sense of a totally intrinsic (internal) constraint—
that would rein in its course and keep it from going astray into a sea of conflicting opinions?
Hegel's answer is that a solution to the problem can only be found by accepting the
contradiction between one truth and many philosophies and by showing its necessity. What
this means, simply stated, is that philosophy's inner limit cannot be anything else than phi-
losophy's development itself, its past history. This entails that we—that is, us philosophers
who have appreciated and felt the power of the contradiction—we have to shift to a higher
level of understanding and reconsider our naive view of philosophy and philosophies.
Since the existence of conflicting philosophies is a contradiction, we have to abandon the
idea that any single philosophical “system” can really be considered Philosophy in the
proper sense of the word. Instead, we must broaden our view of what a concrete philosophy
is, and a real philosophical system consists of. It cannot be an intellectual construction built
“on a one-sided principle” but a “true totality” that, as such, encompasses all philosophy. 24
A totality within which the different competing (and improperly called) “systems” can be
recomposed as parts of a higher and harmonious whole. In other words, philosophy has to
be considered as a whole system that encompasses its whole history and strives to close up
upon its own end as telos.
We better pause for a second on this conclusion, in order to appreciate its magnitude.
Hegel is saying that there is no essential difference between (a) philosophy as a science,
24. Knox 87.
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(which he calls the Logic) i.e. as a conceptual discipline aiming at understanding the truth
of the world and (b) philosophy as history, e.g. as the sequence of the past efforts towards
such an understanding. This does not mean that the two are the same; rather, they are to be
considered as two sides of the same effort, two different paths that can be taken to study
philosophy.
This conclusion entails an immediate reversal of Hegel's and “our” consideration of
philosophy's past history. So far, we have always been confronted with an opposition, or
rather an “intrinsic contradiction,” between Truth and History in the particular form of a
contradiction between the atemporal and unique character of Truth and the conflicting
opinions of past philosophers. Now, however, at the end of this argument that takes the
form of a journey through philosophy's end, ends, and limits, things start to appear in a quite
different light. The analysis of the concept of philosophy shows that it is only to the non-
enlightened, non philosophical eye that philosophy's history seemed like a series of un-
grounded opinions. The apparent but nonetheless real contradiction is removed (that is, auf-
gehoben) once we broaden—as we are forced to do, according to Hegel—the concept of
philosophy to encompass its whole historical range. From this higher standpoint, history
will show itself, to us philosophers, as a coherent system which has always had its internal
limit and whose wanderings into apparently conflicting “systems” had its inner raison
d'être. This means that the “inner contradiction” between opinions and truth, or between
opinions in history and truth as eternal with which Hegel opened his lectures has to be
shown to be necessary, and does not descend from a superficial understanding of philoso-
phy and its history. 25 Rather it is a real contradiction in the things themselves, so to speak,
which has to be understood as an integral part of philosophy itself:
25. For a perhaps clearer example of a “philosophical contradiction,” see the following passage by Fichte
from the first introduction to the Wissenschaftslehre: “Neither of these two systems [e.g. idealism and
dogmatism, as previously defined by Fichte on the basis of the Kantian system] can directly refute its
opposite, for their quarrel is about the first principle, which admits of no derivation from anything beyond
it; each of the two, if only its first principle is granted, refutes that of the other; each denies everything
in its opposite, and they have no point at all in common from which they could arrive at
mutual understanding and unity. Even if they appear to agree about the words in a sentence, each take
them in a different sense.”See Johann G. Fichte, Wissenschaftslehre; Engl. Tr. The Science of Knowledge
(Cambridge: Cambridge UP, 1982) 12 ff.

P HILOSOPHY’ S ENDS
This multiplicity of philosophies, this contradiction I want to illuminate
and make intelligible. I want thus to provide an introduction to the relation
of the many philosophies to the one philosophy, and this will make clear at
all events the difference between the history of philosophy and philosophy
itself. (K 62)
Furthermore, it is not an epistemological contradiction between false and real truths, rather
it is a contradiction between different truths that has to be “removed” as soon as the differ-
ent competing truths are considered as parts of a higher totality. The removal, however,
does not mean that their presence has been accidental. Once again, if the development of
philosophy has been faithful to itself then it follows that the different philosophies must all
have been necessary, as Hegel stress immediately:
In this way we will see that this multiplicity of philosophies not only does
no damage to philosophy itself and its possibility, but is and has been downright
necessary for the very existence of philosophy. (ib.)
Hegel’s conclusion is that the real issue confronting both the historian and the philosopher
does not concern at all the presence of false philosophies, the existence of philosophical
“opinions.” The real issue is to understand the contradictory existence of conflicting phi-
losophies that must all be considered true unless the very existence of philosophy in the
general sense is jeopardized. “Thus we will have nothing to do with opinions,” Hegel con-
cludes at the end of the passage previously quoted, “we have to do with philosophical
Ideas.” More accurately, he will have to do with the whole history of philosophy as a system
guided by its own internal goal, and striving to reach it.
At this point in the analysis, we might remark that Hegel has not shown has yet any
characteristics of the end of philosophy. Rather, he has been involved with the features of
the path that would take us there. He has determined that the road towards the end is not
straight: it is not a simple line but a bumpy road marked by contradictions. Second, he has
claimed that the road to the end risks getting out of control and take nowhere unless philos-
ophy finds an internal limit to constraint its course and force to end somewhere. Third, un-
less such a limit is found, philosophy will disappear, possibly in favor of science or religion.
And last but by no means least, he claims that the only way to find a limit is to use philos-
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ophy’s history as the limit itself. Let us now trod a bit further the path that philosophy’s his-
tory opens up.
5. Of lines, circles, and spheres.
Philosophy can reach the end that necessarily awaits it only if it is considered as a sys-
tem moved by its own, totally internal necessity that encompasses its whole past history.
This is why Hegel deems philosophy inherently free and actually considers it the freest ac-
tivity: because its necessity springs only from itself. Philosophy is, and must be, a system
that is continuously in motion by developing itself from itself. In this form, however, the
statement is just a prescription for philosophy: it sets the goal that the latter must accom-
plish if it is to live up to its ambition. It does not yet say that such a goal is at hand, or even
that it is possible. More importantly, it does not say how the goal can be reached, that is,
how the history of philosophy preceding Hegel's has to be considered in order to transform
it from a chaotic succession of systems that “no longer have even the aim of having a com-
mon bond” to a consistent, all-encompassing system striving to reach its completion. There
is actually an ambiguity, or rather a productive uncertainty in the Hegelian text between the
two similar expression for such a completion: Vollendung, which points more toward the
fullness of the process coming to an end, and Vollkommenheit, which is the perfection
reached at the end of a process where everything, literally, comes together. But of course
the very same term “perfection” comes from perficio, e.g. from the Latin expression for
“having reached an end” (cf. the “perfect” tense of a verb, an expression that preserves the
Latin meaning). All this seems to say that the “ambiguity” is not so much in the word as in
the concept of end as completion itself, as I have been trying to articulate.
This uncertainty may prove to be important when discussing the structure of the end-
point of philosophy. For now, it is important to continue the analysis of the path itself and
to remark that nothing, in what Hegel has said so far, precludes the other two options de-
lineated above: philosophy’s rejection or philosophy’s essentially helping role to either sci-
ence or religion. What Hegel has established, in these introductory pages, is a strong

O F LINES, CIRCLES, AND SPHERES.
conclusion about the general shape that philosophy must assume if it has to be true to itself
and, therefore, capable to survive the challenge moved by both religion and science. In oth-
er words, the result Hegel has reached is nothing more than a deepening of the previous
conclusion about the relationship between philosophy and its end, and a much sharper de-
limitation of what is at stake. Two important points must be established in order to turn this
prescriptive statement into a result. First, it must be specified how philosophy develops,
how it can proceed from one “system” to the next. Furthermore, the process governing its
movement must be shown at work both in abstracto and in concreto, that is, the ruling prin-
ciple must be exhibited and the historical, actual development of philosophy must be
proved to follow it. Second, it must be clarified where this developing movement leads to.
Is it an infinite development? Does it reach an end? If so, what happens at the end? Further-
more, how can we tell if such an end has been reached?
Let us begin by examining the how of the philosophical development, since its expla-
nation will shed quite some light on its where. Hegel starts by distinguishing between the
form and the content of the individual philosophical systems. The content is the same for
each, since it is just what philosophy, generally considered, is about: truth, and more spe-
cifically the truth of the world. The content of philosophy, in other words, is what I have
been trying to elucidate in the previous pages when discussing what, according to Hegel,
philosophy is, or rather cannot but be. Hegel calls such a content the Idea. The form of a
specific philosophical system, on the other hand, is the particular shape that the latter as-
sumes at the hands of a specific thinker in a determinate time. Between form and content,
Hegel contends, there is an intrinsic contrast because the content is necessarily infinite,
while the specific shapes are necessarily finite. Something is finite when it has a limit, when
something else bounds it from the outside and therefore gives it its finitude. Truth cannot
be finite in this sense since otherwise it would have to be limited and partial and would gain
its determinatedness from what lies outside itself. Truth in the true sense of the word can
only be infinite.
This contrast originate a dialectic movement that puts the history of philosophy in mo-
tion. Here is how Hegel puts it:
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This progress is more precisely defined as proceeding in accordance with
the contrast of content and form. What conducts the forward development
is the inner dialectic of the thought-formations. I mean that what is shaped
is something determinate. It must have a character; determinacy is necessary
to its being and existing. But, if so, it is something finite and the finite
is not the truth; it is not what it ought to be. It contradicts its content, i.e. the
Idea, and must perish. [...] What conducts the development lies in this dialectic
of the inherent infinity of the Idea which exists in a one-sided form
and must cancel this one-sidedness.(94.)
Each single philosophical system must assume a determinate form in order to acquire de-
terminacy, or to exist: it must assume a specific principle, or set of principles, and work
them into a philosophical construction. That’s what gives it its determinate shape or char-
acter, what sets it apart from the others. Atomism, for example, takes the atom as the abso-
lute, Stoicism assumes thinking as its principle, Epicureanism defines feeling and pleasure
as the true (98). The contrast is bound to arise because these philosophies (as all the others)
suffer from the intrinsic contradiction between, on the one hand, the limitedness of their
principle, their one-sided form as determined by their guiding principle, and, on the other,
their common aspiration to be philosophies tout-court, that is, their striving to comprehend
the truth as a totality. In other words, each single philosophy, in virtue of its adherence to a
single principle, offers a knowledge that is relative to that principle and bound by it. But
philosophy in general cannot be relative to anything, since, as we have seen, philosophy’s
intrinsic goal is to be ultimate, to achieve its end by putting an end to all determinatedness
and one-sidedness. Of course, the limitations of a specific system cannot be seen from with-
in it, but only from the outside, as it were, from another philosophical system that opposes
a new principle to the preceding one and thus refutes the prior philosophy while, at the same
time, keeping the whole process in motion. Refutations of this kind have a double character,
Hegel points out immediately, since they are both negative and positive at the same time.
In fact, what is refuted is only the form of the specific system, not its philosophical content.
In other words, what is refuted is the claim to absoluteness grounded on a specific principle,
not the principle itself: “what is refuted is not the principle of a philosophy, but only the
claim of one principle to be final and absolute and, as such, to have absolute validity” (95/

O F LINES, CIRCLES, AND SPHERES.
128). The content must be retained, then, while its form must be suppressed: “the refutation
is the reduction of one principle to be a specific factor in the whole.” The double movement
of negation and conservation at the same time makes the whole process a dialectic progres-
sion where nothing, content-wise, is ever lost. Each single philosophy is conserved and re-
tained in the next one (Aufhebung is the typical Hegelian term for this process) so that the
latest philosophy “must contain it itself the principles of all the previous philosophies and
consequently is the highest one”(95); at the same time it will be the deepest and most con-
crete one, since it has absorbed all the determinations of the previous systems. It follows
that “the essence of the history of philosophy is that one-sided principles are made into fac-
tors, concrete elements, and preserved, as it were, in an amalgam” (98). It could not be oth-
erwise: a simple negation with no positive and conservative moment would mean that the
single philosophies are bound to fight each other in an endless battle with no real progress.
We have already seen that such a conception would entail the degradation of philosophy to
a battlefield of opinions and require its surrender to other disciplines. Dialectic mediation,
then, is required by the intrinsic necessity of Hegel’s conception as the only process that
can resolve the contradiction between truth and history or, which is the same, between phi-
losophy and its end. Hegel can therefore call the dialectic that governs historical develop-
ment an a priori: “the history of philosophy has simply to confirm this a priori, this heart
of the nature of the Idea; of this nature it is simply an example.”(94) The example has to be
shown to be such, of course, which is no small feat. The three volumes of historical analysis
following the introduction are devoted to prove in concreto what the introduction has es-
tablished in the abstract: that the historical succession of philosophical systems is in fact a
development governed by dialectical mediation.
Where does the process lead to? Is it going to continue forever toward more and more
inclusive and sophisticated form of philosophical knowledge? In geometrical terms: can we
envisage philosophy’s progress as a straight, slanted line that goes on to infinity without
ever reaching an endpoint? Note that the issue here is essentially different from the previous
discussion of the “scientific” model of progress, although the outcome turns out to be sim-
ilar. In that case, the temporal increase of knowledge proceeded by juxtaposition, e.g. by
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the securing of new provinces of the phenomenal domain to the scientific understanding.
The progress, then, was measured by the breadth, so to speak, of the system, by its ever-
increasing content. (While the form, e.g. the structure of the scientific theories, remained
substantially similar). The problem under scrutiny here is in a certain sense the reverse of
the previous one. Can we imagine a monotonic progression of different and ever more in-
clusive philosophical forms?
It is easy to see that the answer is negative if the constraints laid on philosophy’s ends
are to be respected. The contradiction between the form and the content of philosophical
formations cannot continue forever because, in that case, philosophy would be in principle
incapable to give an adequate expression to its philosophical content. Philosophy would be
doomed to present partial and incomplete—albeit more and more complex— versions of
truth, and it would be forced to admit that either truth in its entirety is beyond knowledge
or that others, non-philosophical forms of thinking are more apt to grasp it. The end of phi-
losophy would therefore be forced to remain an unattainable telos which, at most, can be
asymptotically approximated by an ever increasing amount of knowledge. Hegel’s discus-
sion of the difference between philosophy and science already ruled out this possibility. The
necessary lack of any external criterion that is intrinsic to philosophy entails that it
“progress” cannot be represented by a monotonic line. Philosophy does not proceed by jux-
taposition: it advances by contradictions. And if the contradictions do not reach an end, the
reassuring straight line turns itself into a bumpy sequence of ups and downs that is nowhere
closer to the limit. The end as telos —for philosophy, at least—does not constitute a proper
end. Or, rather, the telos is a paradoxical construction of the end since it is always on the
verge of collapsing either into the positive or the negative reading of “end”—making there-
fore the process it rules either a success or a failure—depending on whether the process it-
self can attain the goal or not. Obviously, if the historical process can reach its end as telos
then the telos itself, in that precise moment, ceases to be one to become a result. On the
other hand, if the telos is in principle unattainable by the process it directs, it follows that
the process itself can be very easily considered as failed; a consideration that will very soon
bring about a new, and more easily reachable telos. If all this seems a bit implausible, it is

O F LINES, CIRCLES, AND SPHERES.
only because we often think we are assuming unreachable ends as goal of our behavior
when in reality we are dealing with a totally different situation. “To be the best writer in the
world” may be an unreachable goal but to be a better writer is so much a goal at hand that
hardly anyone would try to improve his writing if he or she didn’t believe it reachable. “To
become a slightly better writer,” then, far from being the by-product of an asymptotic pro-
cess is the real goal that rules one’s self-improvement. This means that if philosophy’s di-
alectical progression could never reach its end, philosophy itself would be forced to change
its telos. But since such a telos was, in Hegel’s discussion, only derived from the definition
of truth, such a possibility entails that truth itself has to be put under discussion. Or rather
the truth of truth, its structure and inner being. The only way to escape such a possibility is
to accept that the dialectical process can reach its end. In other words, the development can
stop because the contrast between the form and content of philosophical systems has dis-
appeared: the form of the system has reached the ability to give expression to the absolute
Idea. The system in question here is not, we may recall, any single thought formation, but
rather the entirety of philosophy’s development.
On the other hand, reaching the telos in the usual sense comports the end, in the sense
of termination, of the correlated process. Philosophy’s reaching the end, in the positive
sense of the terms, entails that philosophy itself, as a process, ceases to exist because it has
attained its goal. But how can philosophy’s end be a disappearing of this sort? If we are to
remain faithful to Hegel’s argument, such an ending cannot be an interruption but rather a
completion that gathers up all and the whole of philosophy in its final and utmost perfec-
tion. History of philosophy cannot reach its terminus by a simple coming to an end that in-
terrupts it, because the consistency of the process—e.g. dialectics—requires that nothing
will be lost. Therefore, philosophy cannot annul itself with a self-effacing gesture that
would bring about something “else.” Or, even worse, by a gesture that would point to some-
thing other than philosophy, to some different form of knowledge perhaps, lying outside
and beyond philosophy itself. The line representing the philosophical development must
reach an end, but it cannot obviously terminate by leaving anything beyond and beside it-
self, both in space and in time, as if something would be left to explain or as if something
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else will substitute it. If philosophy’s progression reaches its end this does not, cannot mean
that philosophy goes away but rather that philosophy has finally reached its fullness, its fi-
nal state of completion (Vollendung or rather, Vollkommenheit) in which it will persist. The
end of philosophy must be a terminus that achieves philosophy’s goal and keeps it in there,
in that place where everything does come together. The line must not be a line or rather
must be a line that reaches the end by reaching no end, a line that will not encounter a limit
but will nonetheless end its course. In other words, philosophical progress must achieve in-
finity without going on ad infinitum. This can only be done if the straight line turns back
into itself and revert into a circle, or even a circle or circles, since each single step of phi-
losophy’s overall development can be considered, in turn, as consisting of many steps:
This series [of formations of the spirit] is not to be envisaged as a straight
line, but as a circle returning into itself. This circle has for its circumference
a great number of circles; one development is always a movement through
many developments; the entirety of this series is a succession of developments
retiring into itself; and each particular development is one stage in the
whole. In development there is an advance, not into the abstract infinite, but
returning back into itself. (80, my emphasis).
The circle points to philosophy completing its course and reaching true (vs. Abstract) in-
finity, leaving nothing behind. The circle stresses the total closure of both philosophy and
the Idea. Nothing is left outside, so to speak, since the circle has no boundary. Only at the
end of its development, that is, at the closure of the circle, truth is finally attained. Or rather,
more than of a circle—whose image may suggest a plane circumscribing it—we should
think of a sphere on whose unbounded surface philosophy, and us with it, roam freely with-
out ever encountering a limit.

“EIN SPIELEN DER LIEBE MIT SICH SELBST…”
6. “Ein Spielen der Liebe mit sich
selbst…”
A truly scientific knowledge will be reached only when the circle is closed and all the
single-standing “systems” will have found their places in the harmonious whole thereby
transfiguring philosophy, the love of knowledge, into the proper Wissenschaft that awaits it
at the end of its development. By looking into it we will have a first prefiguration of the end
that begins, slowly, to take shape.
This circular, all-encompassing form that philosophy will assume has an immediate
and all too important consequence on its content, e.g. on what philosophy can be about. In-
deed, the very status of that word, “about,” is precisely what is at issue here. If philosophy
is, or will be, a totally closed system, then it cannot be about anything, properly speaking,
since its “aboutness” would imply the existence of something external to philosophy and
therefore outside its allegedly all-encompassing circle. Philosophy is a cognitive activity,
to put it in a very abrupt form, which can assume a circular shape only if the object of the
knowing act is not outside it. Since, on the other hand, to be an object, in a first approxima-
tion, means precisely to be standing over the subject in an act of reciprocal self-delimita-
tion, it seems to follow that the object cannot be inside it as well. In other words, the
circularity of philosophy breaks any characterization of knowledge implying a simple op-
position between a subject and a object standing opposed to each other and belonging to
two different and reciprocally external spheres. The circle can be a circle only if no “part”
of the subject is totally and ultimately outside of the object and, conversely, no “part” of the
object is totally and ultimately outside of the subject.
However, such a mode of expression is still radically inadequate, since it pays a heavy
linguistic tribute to an understanding of knowledge incompatible with the Hegelian char-
acterization. Words like “part of,” “inside,” “outside,” and “about” already presuppose in
their meaning a non-circular form: they become understandable only if the subject and the
object are reciprocally external. On the contrary, the circular shape of knowledge intimates
that the relationship between subject and object preserve the fundamental character of an
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opposition that makes knowledge possible while, at the same time, abandoning the tradi-
tional gap between subject and object that makes that same opposition understandable.
An opposition between subject and object is necessary, but the circular shape intimated
by philosophy’s end demands that its content express the unity of that opposition. The prob-
lem becomes how to think this unity that must preserve the opposition while at the same
time negating the reciprocal externality of the opposed terms. It is clear that such a unity
cannot be a reduction of one term to the other. Neither the world can disappear into a fig-
ment of the subject’s imagination nor the subject of the knowing process can be absorbed-
nullified into an impersonal, external substance. The latter option is not viable because the
cognitive process itself, in that case, would become impossible, producing a non sequitur.
To use Hegel’s celebrated expression, such an “intuition” that nullifies the subject into the
vision of the undifferentiated unity of an all-encompassing external substance can only lead
to a “night where all cows are black”, i.e. to an “immediate intuition of the divine and the
eternal that is not an act of knowing.” 26 The first option isn’t any better, since a finite sub-
jectivity can never be totally self-enclosed, being irremediably empirical and therefore en-
tangled in its empirical “other,” in a concrete material base that lies necessarily outside its
scope. In such a form of idealism “the content of knowledge is determined merely by the
self or has subjective validation enclosed within self-consciousness.” But the subjectivity
of the self that, in order to be such, “see itself as something particular in contrast to objects
and can distinguish its own determinations in itself as different from others outside itself
and over against itself” has to be abandoned. 27
The unity is a unity of the opposition itself, of the relation opposing the two terms of the
cognitive act. In other words, the “unity of the opposition” should not be thought as a static
coincidence flattened onto one of its terms but rather as a process that continuously opposes
and recovers the “subject” (or the agent, individual or collective as it may be) of the know-
26. The first expression is from the Vorrede to the Phenomenology (17/67), while the second comes form
the Vorlesungen, 415. It is precisely the task of the Phenomenology to spell out how and why either
reduction is impossible by taking off from the Sense certainty, e.g. from the alleged certainty of the
knowledge of an object opposed to a consciousness. As we will see shortly, the endpoint of that book
coincides with the endpoint of the Vorlesungen.
27. See Encyclopedia. §5. My emphasis.

“EIN SPIELEN DER LIEBE MIT SICH SELBST…”
ing process and its object to such a point that our common view of their self-standing iden-
tity and reciprocal independence is shattered. In Adorno’s words, Hegel does not “set up an
irrational unity of subject and object but instead preserves the distinctive moment of the
subjective and of the objective while at the same time grasping them as mediated by one
another.” 28
Hegel calls Absolute Wissen, absolute knowing, the understanding of the unity, or the
reciprocal mediation between the subjective and objective moments. The last chapter of
Phenomenology of Spirit is explicitly devoted to the exposition of the concept, but he re-
calls it also at the end of Lectures on History of Philosophy, when he comes to the exposi-
tion of his own philosophy after the long journey through the whole efforts of Western
thought:
To know the opposition in the unity, and the unity in the opposition, this
is absolute knowing; and science consists in knowing this unity in all its unfolding
for and by itself. 29
Absolute knowing can be totally self-enclosed because there is no “other” to know from the
standpoint of the knowing agent. To put it more accurately, there is nothing to know outside
the process itself. The True, das Wahre, is nothing else but the process that perpetually ne-
gates itself only to recover itself. Knowledge of the true, absolute knowing, that is, is this
agonistic but harmonious process in its very being process in action. The process is absolute
because it does not need any more reference to anything outside itself. “Absolute,” here,
should not be primarily interpreted as a synonym of “supreme,” “perfect,” or “highest”;
rather, we should recall the root of “absolute” in the Latin “absolvere” “to free (or relin-
quish) from” as in the canonical formula uttered by the confessor in the Catholic rite: “ego
28. Theodor Adorno, Hegel: Three Studies (Cambridge: MIT UP, 1993) 7. It should be noted, at this point,
that such an act of knowing cannot be considered just a cognitive activity. Rather it is a form of living
as well, since, if there is no ontological difference between thought and being, between “thinking about
something” and the “something” about which one thinks, it follows that being is a way of thinking and
thinking is a way of being
29. My very literal translation. Haldane has “to know opposition in unity, and unity in opposition—this is
absolute knowledge; and science is the knowledge of this unity in its whole development by means of
itself.” (3, 551)
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te absolvo peccatiis tuis.” Absolute knowing stands in opposition to any form of knowledge
that is relative to something external to itself and to its own act of knowing. Absolute know-
ing is also, indirectly, a “perfect” knowing, but only in the sense of the perfection and com-
pletion (Vollkommenheit and Vollendung, respectively) that philosophy reaches, inevitably,
at the end of its development.
It is important, however, not to interpret this “perfection” as a state, or as a station out-
side of time and space where knowing comes to an end in a post-historical transfiguration.
Hegel speaks of “absolute Wissen”, not of “absolute Wissenschaft” or “absolute Erkennt-
nis”, which would be a contradiction, since he is claiming that Wissenschaft, scientia, sci-
ence, can exist only if and when knowledge ceases to be derived from particular principles
and reaches the level of an absolute knowing, of absolutes Wissen. In other words, we
should pay attention to the fact that “Wissen” is the nominal form of a verb, and strive to
hear the reference to the action that the latter expresses. Absolute knowing is the way in
which the act of knowing continues to be performed after the closure of the dialectical de-
velopment—and finally in the form of a scientific knowledge of the whole production of
the Spirit in both time (history) and space (Nature).
Absolute Wissen represents the closure of the continuous motion that is characteristic
of all the aspects of the Spirit and that Hegel expresses as a duplicity of estraniation/nega-
tion and interiorization/remembering, that is, Entäußerung and Erinnerung. The closure
means that this continuous motion keeps coming back to itself, in the simple sense that
there is no “other” to which it would go. The circle has no outside to which it may point to,
it is totally self-contained. As Hegel explicitly remarks in the final chapter of the Phenom-
enology, the circle is nothing else that this movement:
This movement [that constitutes knowing] is the circle that keeps coming
back to itself, the circle that presupposes its beginning and reaches it only at
the end. 30
30. Georg Wilhelm Friedrich Hegel, The Phenomenology of Spirit, A. V. Miller, tr. (Oxford: Oxford University
Press, 1977) 429. The German text is “Sie [die Bewegung, die das Erkennen] ist der in sich
zurückgehende Kreis, der seinen Anfang voraussetzt, und ihn nur im Ende erreicht” (1053/429). Note
that knowing is, here, Erkennen, another substantivized verb, not Erkenntnis.

“EIN SPIELEN DER LIEBE MIT SICH SELBST…”
The circle is such only at the end, after its closure has been reached, and it is possible
to live in it and reach the form of knowing that will inaugurate science only when its end
will have joined its beginning. This means that no immediate knowledge of the Absolute is
possible, as Hegel stresses over and over again. First, because it would not constitute a
knowledge at all, and therefore it would not be philosophy. Rather, it would be an intuition,
a feeling of an indistinct unity of and with an Absolute that “is not supposed to be compre-
hended, [but] felt and intuited. Not the concept of the Absolute, but the feeling and intuition
of it must govern what is said and must be expressed by it.”(4) Furthermore, and more im-
portantly, such a self-contradictory philosophy cannot get to the absolute at all, since it re-
duces it to an empty, contentless entity. The intuition of God and God’s Love become the
slogans of a position that refuses to provide penetration and comprehension by reducing
philosophy to a mere edification that “shrouds in fog the manifold variety of its earthly ex-
istence its thought”, and “pursues the indeterminate enjoyment of this indeterminate divin-
ity.”(5) But such a position is so vacuous it can find anywhere the “ghosts” it has allegedly
discovered.
Hegel, instead, wants to recover the concept of God and the Absolute as Substance that
Spinoza had already put forward and that inspired so much debate in Germany around the
turn of the century. To think the true as substance comports to think it in both its universality
as well as in its concreteness, that is, in the multiplicity of forms in which it develops. The
Substance, however, cannot be external to the subject, as it still is in Spinoza, lest the whole
characterization of philosophy as a circular structure that reaches its beginning at the end
collapses in the reciprocal externality of subject and substance. The substance has to be
thought as subject—this, Hegel claims, is the basic insight from which everything else fol-
lows.
This is the basic, and only, difference that Hegel acknowledges between the “highest
point of philosophy’s development” and the Spinozian characterization of the Substance.
As he says in the final pages of the Vorlesungen, while summing up the principal phases of
philosophy’s history:
Being and thought are opposed and identical in Spinoza, who has the fun-
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damental intuition, but knowing is external to substance. (It. 414)
In the section of the Lectures devoted to the Dutch philosophers he further specifies his
thoughts by adding:
This Spinozian idea has to be considered true and grounded. It is an absolute
Substance; this is the True. But this is not the whole True; the substance
must also be thought as active and living in itself and consequently self-determining
as Spirit. The Spinozian substance is the general and therefore abstract
determination [of the Spirit].(105)
What matters is the total harmony of the subject with the world that he has discovered as
his and in which he can (and must) lose himself in order to come back to himself. The har-
mony does not exclude, rather it requires, the alienation, the Entäußerung, the work of the
negative. Harmony can exist, in this context, only in what we may call an agonistic mode:
as a confrontation with the other that is required by mediation itself. But the true meaning
of this agonistic moment, the reason why it really constitutes an agon, is that the subject is
such only in the confrontation: he will be himself only by losing and finding himself again.
The process, the agonistic process, is logically and ontologically prior. We are not faced
with a subject who “proves” himself, who start from an identity of some sort to “try it out”
and see his worth with or against the other who faces him. As in the master/slave dialectic,
the subject finds such an identity after the confrontation, on the rebound, after having lost
or having been ready to lose everything that mattered—life itself. And this is true in both
cases: for the master-to-be, who is ready to die in the fight for recognition and achieves it,
although in an imperfect form, at the precise moment in which everything is lost; and for
the slave as well, who begins to realize his truly “subjective” identity only after he has been
reduced to a totally subjugated entity who is literally nothing since his life is wholly for the
other and nothing for himself.
If the Absolute is expressed in terms of God and God’s Love, as Hegel contemporaries
loved to do, then the word “God” has to be more than a mere name pointing to a simply felt
but empty communion as the only possible exitus. Rather, the Absolute has to be under-
stood and comprehended in its determinations and this can only be done by focusing on the

“EIN SPIELEN DER LIEBE MIT SICH SELBST…”
dialectic of reciprocal mediations. Only then, and for the first time, the Absolute becomes
really expressible, or rather comes to the expression that marks the sign of true comprehen-
sion. Once the concreteness of the Substance as explicated in the multiplicity of its deter-
minations has been recovered, then God and God’s love acquire their full meaning because
they are no longer the vacuous objects of an intuition but rather the process itself of recip-
rocal self-determination. The absolute is the circle itself.
In the passage of the Vorrede that follows immediately the famous polemic with Schelling
culminating in the “nights in which all cows are black”, Hegel claims for himself the right
to use, and in a different and richer sense, such “trite” words as “God” and “Love.” After a
description of the circle of absolute knowing expressed in terms almost identical to those
of the previous quotation from the final chapter, 31 he goes on to say:
Das Leben Gottes und das Göttliche Erkennen mag also ein Spielen der
Liebe mit sich selbst ausgesprochen werden (68/18)
Literally translated,
the life of God and the divine knowing may thus be expressed as a
play(ing) of Love with itself. 32
The reference to love, and God’s Love in particular, is not casual. The young Hegel had al-
ready stressed the particular status of the members of a love relationship: they are in oppo-
sition but, in that opposition, united. In a fragment from the early theological writings, we
found a quite clear statement of the reasons why love is so important: on the one hand the
union of the lovers in love is radically and qualitatively different from the oppositions we
31. “[Das Wahre] ist das Werden seiner selbst, der Kreis, der sein Ende als seinen Zweck voraussetzt und
zum Anfang hat, und nur durch die Ausführung und sein Ende wirklich ist” (68/18).
32. The different semantic scope of “Spiel” and “Play” constitutes a major obstacle to the understanding
of all the passages in which Hegel uses Spiel and its cognates. In particular, what seems more troublesome
is the breadth of the German term, that covers both the relatively “unstructured” meaning of
“play” as well as the more regulated activities that the English language denotes by “game,” not to
speak of the area covered by all the cognates of “sport.” The English translator of the Phenomenology
has in fact opted for the latter (and quite narrow) meaning by rendering “Spielen” as a “disporting”
(Eng. tr. 10) Although clearly correct, this perhaps unavoidable choice narrows the semantic richness
of the German term to just one of its component. In order to limit the possibility of misunderstandings,
I have tried, in the following, to use the German term “Spiel” as a kind of technical term that covers
the three distinct areas covered by “play”, “game,” and (partially) “sport” in English.
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T HE END OF PHILOSOPHY
it is not intellect whose relationships always leave the manifold as manifold
and whose unity itself are oppositions; it is not reason, which opposes
its own determining to the determined; love is not determining, nor it is determined
nor finite. [529/379] 33
On the other hand, love provides a form of union which is truer than those afforded by in-
tellect and reason because
true unification, true love, exists only between living beings who are the
same in power, and who therefore live for each other in the most complete
way; and from no side one is dead for the other. […] In love the separated
still exists but not as separated anymore, rather as united; and the living feels
the living.[529/379] 34
In love, however, and in earthly love above all, the unification finds an ultimate resistance,
as Hegel notes, in the properties of the lovers and in their mortality. True unification would
require a total communion, while in love the lovers have also something else beyond the
love for their lovers: they have goods to take care of, their thoughts, and ultimately bodies
that resist total unification. This form of love must therefore be superseded by a more com-
plete one. In the Phenomenology this transformation seems to have taken place: Love,
God’s love now, is still at the center of the speculation, but the focus has shifted from the
unification of the lovers through love to love itself and its playing with itself. The process
continuously posits and surpasses the “agents” that are secondary with respect to love itself.
Love is playing with itself because it is constantly engaged in an action that opposes the
players but only within the limited scope of the game being played, an infinite game that,
having come full circle, finds an end only to start all over again.
33. G. F. W. Hegel, Early Theological Writings (Chicago: Chicago UP, 1948): “It is not the understanding,
whose relations always leave the manifold of related terms as a manifold and whose unity is always a
unity of opposites [left as opposites]. It is not reason either, because reason sharply opposes its determining
power to what is determined. Love neither restricts nor is restricted; it is not finite at all.” (304)
34. Engl ed.: “True union, or love proper, exists only between living beings who are alike in power and
thus in one another’s eyes living beings from every point of view; in no respect is either dead for the
other. […] In love the separate still remain, but as something united and no longer as something separate;
life [in the subject] senses life [in the object].” (304/305).

“EIN SPIELEN DER LIEBE MIT SICH SELBST…”
The action is intrinsically agonistic, since it is always a confrontation that searches for
itself in the other (e.g. the opponent) but it is, at same time harmonious, since no action is
lost and all of them come together to make up the whole of the game being played. The
meaning lies in the result, i.e. in the shape of the actions (e.g. the moves) as considered from
an endpoint that is nothing but the realization of the beginning. The game itself, in fact, is
this movement, this continuous going back-and-fro within the enclosed space delimited by
the rules of the game. The game is, or rather has as its basic characteristic the freedom of
movement, the lightness that permeates the players while they are carried by the game and
fully absorbed by it.
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T HE END OF PHILOSOPHY

CHAPTER II
ABSOLUTE(S)
SPIELEN
in which the concept of Spiel is introduced, and why it is so difficult
to handle.

1. “to die game”
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A BSOLUTE( S ) SPIELEN
Solo a chi ama il Diverso accende i suoi
splendori
e gli si apre la casa dei due misteri:
il mistero doloroso ed il mistero gaudioso.
Elsa Morante
We have seen Hegel suggesting the image of Spiel, and Love’s Spiel in particular, as a
characterization of the completion of the circle of circles that would bring about the end of
philosophy. The concept of Spiel itself, however, is far from transparent. Even in common
speech, Spiel denotes a broad range of phenomena, with vastly and sometimes conflicting
features. First of all, it has a broader semantic spectrum than its English counterpart since
it covers both the areas of “play” and “game.” The game of chess, the game of tennis, and
child’s play, (not to speak of the actors’ and musicians’ activities), are all covered by the
term Spiel. In this respect, German is closer to other Western European languages than En-
glish: jeu, gioco and juego, for example, all behave quite similarly to Spiel.
In the context of our present discussion, the semantic breadth of Spiel and its Western
relatives is not quite an advantage because it apparently collapses into one word wildly dif-
ferent activities. We might take the situation in English to be clearer and perhaps try to ex-
ploit its richer lexical articulation to clarify the connection between Spiel and the end of
philosophy. In English, although we say that someone plays chess, chess itself is certainly
a game and not a play. The unqualified form of “play” seems to be used only in the context
of children’s activity: adults may play all sort of games, and even quite silly ones at that,
but only children play without further qualification. This may suggest that the concept of

“ TO DIE GAME”
Spiel is actually an historically contingent juxtaposition of two quite different ranges of
phenomena which are polarized around the free, self-fulfilling “play” and the engaged, se-
rious “game.” In fact, we tend to associate all the derivatives of “play” with a certain light-
heartedness, with a lack of seriousness, and more particularly the lack of the seriousness
required to work, to do something “serious” in the sense of important, worthwhile, etc.
Playing is, or can be, “amusing,” “entertaining,” and, often “time wasting” while working
is “serious,” “productive,” and, most appropriately, “laborious.” We might add the men-
tioned opposition, namely that “play” is usually children’s most prominent activity, while
“work” is the adults’ domain. The passage from childhood to adulthood, is also, and per-
haps mostly, a passage from a play-oriented to a work-oriented world. The opposition play/
work, built along the axis serious/playful and adult/child, seems to be constitutive of our
understanding of the concept. Moreover, “playing”, as in “children play” is generally an ac-
tivity featuring very loose rules if it requires any rule at all. Think, for example, of the series
of activities children perform on a playground: swinging, sliding, running, chasing, tag-
ging, etc. “Play,” in short, seems to epitomize the free, spontaneous, self-rewarding, and
free-flowing activity most typical of childhood and most opposed to adult work and wor-
ries.
“Game,” on the other hand, usually denotes an activity regulated by more or less strin-
gent rules and that usually requires a quite serious engagement on the part of the actors.
Boardgames, and chess over all, offer the prototypical image of an activity that requires to-
tal devotion from their adepts and that often strains their resources to the limit. Resources
that are not only intellectual, but often quite material: in pre-television times “playing” was
in fact a favorite pastime and it meant first and foremost playing cards for monetary re-
wards. 1 It is difficult to think of gambling in the same category as playing tag, and yet this
is what Spiel would encourage us to do. Not only, but the co-existence of the strenuous,
confrontational antagonism required by most games and the spontaneous, self-rewarding
1. Most reference to “play” (e.g. Spielen) in classic philosophical texts have such an implicit reference.
See, for example, Kant’s Anthropology from a Pragmatic Point of View (Carbondale: Southern Illinois
UP, 1978) , sec 88 (B243 ff): “the game that—it is said— has the only function to fill the void of conversation
after dinner....”
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features of play are what Hegel seems to need, as we have seen, in his concept of Play and
God’s Love playing with itself that may bring philosophy to an end. This may suggest, in
other words, that Hegel’s speculation rests on a linguistically infelicitous contingence of
the German language. Once clarified with the help of some English savvy, the word Spiel
would appear to be just an ambiguous term referring to different and unrelated activities, a
word no more puzzling than any of the innumerous homonyms that any language has to of-
fer.
However, a moment of reflection on the uses of “play” and “game” is enough to realize
that the situation is not so simple. In fact, the oppositions “serious vs. non-serious”, “child-
ish vs. adult”, etc., play their role within the very concept of Spiel and within Spiel’s com-
ponents of “game” and “play.” Even the most serious game cannot be totally “serious” if it
is still to be considered a game in the proper and non-metaphorical sense. For example: the
game of chess, even when played by world-class masters for substantial monetary rewards
is a game because it is not considered part of the normal productive activities. It is not
“work,” although the players work as hard as most workers, because playing chess is not a
productive activity. In this sense, the chess player, in spite of all of the game’s seriousness
and brainy reputation, is closer to the child’s swinging in the playground than to the worker
in a factory. On the contrary, when we speak of the “game of love”, or the “game of war,”
we are leveraging on one component of game, e.g. the strict, rule-based, regulated structure,
but we are leaving aside the playful, non-serious engagement. And it is precisely for this
reason that we may say that war and love are “like” a game: although they are not games
at all, with such an expression we want to stress their formal, well-regulated character
while—at the same time— holding fix their distance from real games.
Conversely, even when we say, as we often do, that love, for example, is “just” a game,
we do not generally mean to identify love with a game. We are not saying that love is eq-
uiparable to chess. Rather, we are saying, in an almost prescriptive mode, that love should
not be considered such a serious affaire because, after all, it might be considered as point-
less as a game of chess, where the winner and the loser, once the game is over, are neither
better nor worse off than when they started. In other words, whenever we use “game” in the

“ TO DIE GAME”
context of a “serious” activity we either presuppose a fundamental difference between se-
rious and non serious business in order to stress the well regulated character of both, or we
leverage on the non-serious, e.g. the playful, character of game in order to exhort people to
take the serious businesses of life in a ligher manner. In either case, we rely heavily on the
playful component of “game.”
In short, “games” can be seen as representing the most serious, well-regulated com-
ponent of Spiel, but they are dependent on the opposite, “playful” component to be regard-
ed as such. No matter how well an activity is constrained by rules, only if it is separated by
“normal,” “adult,” “productive” life, it is considered a game in the proper sense. Notice that
this does not mean that an activity must belong or be derived from the realm of childhood
to be considered a game. In fact, in many societies, “games” traditionally belonged to the
realm of the sacred life, the most notable example being the Olympic games. In that case
as well, though, what is most important is the separation between “normal” everyday life,
between the life of labor and pain, and the separated, sacred space in which games can take
place.
A similar point can be made for “play,” the component of Spiel that stands for the free,
spontaneous, and self-renewing activity. One of the most disconcerting aspects of play,
even in its most common, everyday uses, is the co-existence of the serious aspect in a con-
cept that derives most of its meaning from the opposition to seriousness itself. 2 Children’s
play is supposedly the mark of such a free activity. But any observation of children “at
work” will quickly reveal that they are as inflexible about the rules of their playing as the
most consummated chess master. In fact, children can even spend a substantial part of their
playing time negotiating over the rules presiding their games and any player not observing
them is very often severely reprimanded. The only difference with chess is that children’s
2. The serious side of play has been emphasized over and over by scholars of play. Most often, however,
this emphasis has been translated into a reduction of the playful to the serious that goes hand in hand
with the reduction of the whole universe of play—from child’s play to chess—to the serious games
played in social occasions. Huizinga, for example, stresses the serious element so much that he decides
(but actually he is forced) to limit his investigation in Homo ludens to the “higher forms of play”. As
a consequence, everything having to do with “fun”, enjoyment, “merriment” etc., is left out of play and
judged inessential. But the problem, as I will show, is precisely the analysis of their interrelationship.
Flattening one element upon the other does not take us very far.
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playing rules are not codified in advance: rather, they are rectified every time a group of
children gather together to play and often during playing time as well. But the role of the
rules within the activity is exactly the same.
In fact, play is an activity that seems to require the most extreme seriousness. Play can
happen only when the players adhere totally to the rules of what they play and even submit
their being—by forgetting it and leaving it aside, in most instances—to the being of play
and to its absolute rule. The rules of the game, to put it differently, know no exceptions:
when a player stops following them the “playing” itself is thereby concluded. 3 The serious-
ness derives from the total immersion and unchallenged attention that the participation in
a game, and especially the confrontation with the other, with the antagonist, requires from
the player. The playfulness of play—the element that risks transforming any thinking of
play into an “edifying thought,” as Hegel notes—derives instead from the total self-enclos-
edness of any game. Being totally separate from any other activity, the phenomenon of play
extracts the players from their normal and usually burdensome activities to immerse them
in a different and totally other medium where they can forget themselves to be only what
the game makes them be. But playfulness and lightness so understood are just the opposite
of a lack of seriousness. We might even say that play requires a total seriousness in order
to be playful: only if “playing” is closed upon itself because the devotion to its rules is ab-
solute, can the players renounce their being and be carried away by the game itself.
Therefore, it is impossible to get rid of the complexity or even of the apparently apo-
retic character of Spiel by neatly splitting the concept into the play- and game- components.
In fact, the mutual solidarity shown by “play” and “game” points to on opposition between
playful and serious, productive and wasteful, etc., that lies within the semantic content of
Spiel and that cuts across “play” and “game” respectively. There is little to be gained, if
anything at all, in the effort to clarify Spiel through the apparently neat English distinction
of Play vs. Game since the same basic opposition at work within Spiel represents itself
within each component. In fact, there is some etymological evidence to support the conten-
3. I am relying quite heavily on Gadamer’s analysis of Spiel in this characterization of its play-like component.See
Hans-Georg Gadamer, Truth and Method…, 90ff.

“ TO DIE GAME”
tion that is the English classification that may be linguistically contingent. Or, to be more
precise, there is some evidence suggesting that the semantic area of Spiel, in virtue of the
opposition playful/serious, provides an extended leeway whereby “play” and “game”can
move, and have in fact moved, quite considerably.
The linguistic history of the English words “play” and “game” provides some interest-
ing confirmations of the existence of an intrinsic leeway within the concept of Spiel. “Play”
for example, according to the Oxford English Dictionary, derives most likely from an Old
Saxon word, plagan, meaning “‘to have the care of, take charge of, attend to, cultivate’, ‘to
be in the habit of, to be wont or accustomed to’. The origin of the term, in other words,
comes from the opposite pole of the current uses of “play,” since it used to denote an activ-
ity tied to the sphere of work and physical labor. In Old English “play” can be applied to
the activity of plowing a field, as in the following example: “Eche man to pleye with a plow
pykoys or spade.” 4 The evolution of the word, or at least one of the lines of evolution, in-
creasingly privileges the process itself and tends to disregard the purpose of the action, so
that the term comes to mean “being idle,” in the sense of being actively engaged in some-
thing not useful, e.g. being busy not working. The current meaning of “playing” as “amus-
ing oneself”, “recreating”, seems to derive from this privilege of an activity that bends back
upon itself and has no longer an outwardly directed purpose. When considered along its
whole history, “play” seems to have covered quite a long path. From an original use in
which it can be applied to an activity as productive and as socially engaged as plowing a
field it comes to signify what may perhaps be considered the most unproductive and most
solitary activity of all. 5
The opposite movement is exemplified by the linguistic evolution of “game.” Origi-
nally derived, most likely, by ga, “together” + man, “human being”(cf. Were-man/Wo-
man) it takes the meaning of joy and merriment found in communion (Cf. German Gemein,
4. 1377 Langl. P. Pl. B. iii. 307
5. This meaning of “play” as the intrinsically wasteful activity best exemplified by the English phrase
“playing with oneself” is actually crucial to the contemporary philosopher who has is perhaps best
known for his use of jeu: Jacques Derrida. See, for example, La Dissémination. I will come back, partially
at least, to Derrida’s use of jeu in the last section of chapter VI below.
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Gemeinheit). In other words, the original, pre-English meaning comes from the opposite
pole of the current use, in fact from a pole very close to the current use of “play” in its re-
liance on the “non-serious”, merry aspect of life. “Game” gradually picks up, during its
evolution, the characteristic of a well-regulated and serious activity and ends up as a pos-
sible predicate of the most serious affair man can encounter in life. It is speculative how
this evolution took place. One possibility is that from the original meaning of social com-
munion, “game” has been applied to a prototypical case of such a social communion: the
organized and socially well structured chase hunt. From there, the word shifts to cover not
just the act but the object as well: game as fowl, as the animals being hunted. Then, “game”
starts signifying the characteristics of the hunted animal, at least in the perception of the
hunter: namely, its fierceness and spirit for fighting and endurance. With a last metonymic
act, “game” takes up the meaning of “as brave and independent as a hunted animal”. “Are
you game?” is the prototypical expression at this stage of evolution, and it means the will-
ingness to be taken in by the process and play, e.g. fight , as bravely as possible. “Game”
becomes the mark of courage, and especially the courage to be shown in the harshest occa-
sion: death. “To die game,” an expression found already in Gay’s Beggar’s Opera and used
by Byron and Spencer, stands for the courage and resolution that may be shown in front of
death by the bravest souls. As the OED defines it, “to die game” is “to maintain one’s spirit
and endurance to the last”: “to die game” means to be able, to use Hegel’s expression, “to
look death in the face.”
The conclusion to be drawn from this brief linguistic excursion is that the oppositions
between serious and non-serious, merriment and resoluteness unto death, labor and recre-
ation, productive and wasteful, etc. all cut through the phenomena of game and play. Game/
play, or Spiel as I will call it hereafter for short, displays a complex network of components
with at least three main elements: (a) movement (and freedom thereof), (b) commitment
and especially the commitment to rules that can be found in a social communion (e.g. a Ge-
meinheit), and (c) self-fulfillment and recreation in all the possible senses.
Hegel’s conjunction of the the end of philosophy and Spiel relies, in fact, on all the
components of this complex network. On the one hand, Spielen can be so serious as to be

A BSOLUTE( S ) SPIELEN
tragic: this is appropriate, in a certain sense, to an understanding of the Absolute that does
not refrain in the face of death and holds on the contrary that the “true life of the Spirit is
that life that bears death and stations in it.” In such a “play,” the rule is to look death in the
face and be transformed by it.
On the other hand, the reference to Spielen is essential in order to understand how the
dialectical movement can continue once the process that dialectics rules (or used to rule)
has reached its end. What happens in and at that end is a transfiguration of life into a form
of playing that preserves the agonistic character proper to it, while at the same time being
worth of the name of intellectual intuition or of amor Dei intellectualis. Let us now go back
to the Hegelian text and see, in more details, how this complex interaction takes place.
2. Absolute(s) Spielen
Let me retrace my steps. I started from Hegel’s argument about the end of philosophy,
and from his insistence that philosophy, if it wants to be true to its vocation, has to be com-
pleted and turned into a science that will be able to tell the truth about the world. I then fol-
lowed Hegel’s search for the concept of this science and found it in the exposition of
Absolute Knowing put forward at the end of the Phenomenology of Spirit. Finally, I fo-
cussed on the characterization of Absolute Knowing by the ludic metaphor of “God’s Love
playing with itself.”
Absolute Knowing, as the “beyond” of philosophy to be reached through the latter’s
completion, is therefore characterized as a form of playing. Even if I believe that the ludic
formulation can help shed some light on Absolute knowing, it by no means explains it. That
is, the concept of Spiel, and Love’s Spielen in particular, does not represent the end to the
quest for the end of philosophy because the concept of Spiel itself is far from transparent,
as I have explained above, and even if it were, it would still remain unclear how to apply
the image of play to the full circle finally reached by Absolute Knowing. Who plays the
absolute game? What happens during the game being played? Can the game ever be over?
Or is it already over?
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The question about the players—or, to put it differently, about the actors of the playing
process—is particularly crucial. If Absolute Knowing is characterized as “Love’s playing
with itself,” then a possible interpretation is to attribute to God’s Love the role of a player
whose game in time and space is nothing else than the history of the world as we know it.
This form of divine playing seems to reduce the human actors to the role of mere pawns in
a game that the divine Love is eternally playing. Absolute Knowing would therefore be a
cosmic chess game having Love vs. Love behind the board and the whole world (or, to be
precise, the whole history of the world) as both battleground and pieces of the game. This
“panlogistic” interpretation represents, basically, the philosophy of the substance that He-
gel attributes to Spinoza. The subject is missing from the substance and, as a consequence,
the Absolute is external to the substance. It is a totally deterministic system that offers no
point of access, no entry into it except a blind intuition of the Absolute. In other words, this
is the vision of the Absolute that Hegel refers to Schelling and that he attacks vehemently
in the passage immediately preceding the ludic metaphor of the Absolute.
Regardless of whether this interpretation adequately explains Hegel’s position in the
Phenomenology, it must be noted that it runs quickly into troubles of its own, because it
requires Love being external to the game, while it clearly cannot be, since the process Hegel
is describing must be totally immanent to itself. Or, to put it differently, it is impossible to
see how such a depiction could be a form of “knowing.” It might represent a characteriza-
tion of the Absolute, but it cannot represent any cognitive activity. Given the absolute dif-
ference between the players and the pawns being played, their total incommensurability, so
to speak, there is no path, or at least no cognitive path, leading from the latter to the former.
At most, there may be an utterly “irrational” semi-mystical leap that force forward to an
almost impossible identification with the absolutely Other lying beyond everything we
know or will ever be able to know. The pawns of a chess game, in other words, might even
be able to forgo their wooden status and rise—through an Herculean feat of self-transcen-
dence—to an understanding of their position in the immensity of the world lying beyond
the chessboard. But can they start discussing the fine details of the Sicilian opening with

A BSOLUTE( S ) SPIELEN
the player moving them up and down the black and white squares? And yet, this is what
Hegel’s prescription would require to be meaningful.
To put it more soberly, the playing process, if considered from the “earthly” point of
view of consciousness, can neither (a) admit something outside itself nor (b) can it locate
the subject in any position except that of the main player. Moreover, as I have stressed over
and over, it must (c) admit of an end, that is, it must be closed upon itself. Hegel tries to
capture all three requirements in the image of Love playing with itself. But can we think
play in such a way to satisfy the constraints that Hegel seems to be placing upon it? In other
words, is it possible to think a concept of Spiel that does justice to what Hegel portends?
Let us begin by noticing that Hegel seems to be well-aware of the complexity of the
concept of the Spiel and of its subtle inner articulation. In fact, in the sentences following
the characterization of the Absolute as Love’s Spiel he goes on to say:
this idea [of divine Love playing with itself] sinks into mere edification,
and even insipidity, if it lacks the seriousness, the sorrow, the patience and
the work of the negative. [ib. my emphasis]
Hegel opposes playfulness to seriousness and, as noticed above, reinforces the oppo-
sition by bringing forth the conflict between Spiel and Arbeit, play and work, and more spe-
cifically the work of the negative, that is the process of negation of and into the other. He
then proceeds to set up the opposition in even stronger terms, again stressing the motif of
playfulness (here colored by another typical characteristic of play—transparency vs. seri-
ousness:
In itself, this life [e.g. God’s] is indeed one of untroubled equality and unity
with itself, which is not serious with the otherness (Anderssein/being-other)
and with the alienation nor with the overcoming of this alienation.
(Überwinden and Entfremdung) (10, tr. slightly altered).
This characterization, however, is problematic: if play is taken to be opposed to work
(Spiel vs. Arbeit), how can the previous description of the absolute be adequate? “Divine
knowledge” is a form of playing, Hegel says, but this play must be considered as deeply
serious lest the thought itself falls into a merely edifying proposition.
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According to Hegel, play is both opposed to work and must include it. It follows that,
as we have seen above, the only possibility to make sense of what Hegel is saying is to as-
sume that the division between play and work, or rather between playfulness and serious-
ness is internal to Spiel itself. He would then not be proposing a contradictory definition
but rather drawing our attention to the complexity of the concept of Spiel—and therefore
to the complexity of the concept that Love’s Spiel expresses. In other words, he would be
saying that the life of the Absolute could be expressed as a form of playing, provided that
we do not forget the seriousness that can be involved in a playful activity.
But what is involved in this act of remembering? Or, to put it differently, what is in-
volved in the fact that the Absolute, and any understanding of the Absolute becomes con-
nected with the understanding of Spiel?
Merely stressing that play must be playful and serious at the same time—or even more,
that it can be playful only if it is serious, and vice versa—is clearly not enough. Once it has
been accepted that the playful and the serious must be considered together and as belonging
to the same concept, one has to show its inner articulation. In other words, one has to show
how is it possible that seriousness (all the way to the determination to die) and playfulness
belong together: why and how is it so? The clues provided by language may force the ur-
gency of the question upon us but cannot pretend to take the place of an answer.
In the Preface to Phenomenology, Hegel points explicitly to this problem and rephrases
it in terms of a difference between the in-itself and the for-itself of the “life of God and di-
vine knowledge”. The passage quoted above, in fact, continues as follows:
In itself, that life is indeed one of untroubled equality and unity with itself
[...]. but this in-itself is abstract universality, in which the nature of the divine
life to be for itself, and so too the self-movement of the form, are altogether
left out of account. [...] Precisely because the form is essential to the
essence as the essence is to itself, the divine essence is not to be conceived
and expressed merely as essence, i.e. as immediate substance or immediate
self-contemplation of the divine, but likewise as form, and in the whole
wealth of its developed form; only then it is conceived and expressed in actuality.
(10-11

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Hegel is then equating the in-itself, or the essence of the divine knowledge to the playful
side of the opposition between the non-serious play and the serious engagement with the
otherness. At the same time, he stresses that the serious, painful, and patient work of the
negative is nothing but its form, its for itself. The two are distinct, but inseparable, and the
latter is essential to the former as this is to itself. The crucial issue, however, is to under-
stand how this work can be comprehended, likewise, as play. Or, to put it differently, how
the work of the negative, e.g. labor, death, etc., can be comprehended as playful from the
inside, as it were, and not just from the superior and detached perspective of the essence,
of the “untroubled equality and unity with itself.”
Roughly speaking, the relation Hegel depicts is between the static essence of divine
life and its dynamic form. Such a form is nothing but the movement of its becoming, the
process of its transformations, and of its confrontation with the other. This movement is
what Geist accomplishes in history, in actual human history. This point is made even more
clearly in the final chapter of the Phenomenology:
Die Bewegung, die Form seines Wissens von sich hervorzutreiben, ist die
Arbeit, die er als wirlkliche Geschichte vollbringt.
The movement that propels forward (moving forward) the form of its
knowledge of itself is the work which it accomplishes as effective history.
The Hegelian distinction of playful and serious along the static/dynamic axis is un-
problematic only if we keep the two sides clearly distinct and totally unrelated. In that case,
we can consider, from a first person point of view, human history as a painful and laborious
process of becoming in which we are always involved and in which we are called to par-
ticipate. We can then understand this process as a continuous, often tragic confrontation, as
a painful work of coming to terms with the other, etc. In fact, we can see human life as a
sequence of “tragedies” that find their resolution only to proceed to the next element of the
series, if we decide to use the term “tragedy” for the typical Hegelian dialectic progression
whose paradigm may be represented by the figure of the master/slave dialectic. We may
then switch to the third person perspective, so to speak, to a God’s eye point of view, and
consider the same process as a playful, self-enclosed activity of the divine life.
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The problem is that we are not allowed that switch. More precisely, Hegel is urging us
to consider all the problems that such a switch would entail for philosophy at large, its end
and its completion. We cannot switch from one perspective to the other because there is one
and only one process and one and only one perspective from which to look at it. We can, of
course, try to imagine that the life of the Spirit “might even be considered” as a form of
play. But that thought is, as Hegel says, just an edifying thought, whose efficacy is nil.
Why? Because we live on this earth and cannot pretend to switch places with God. That is
why such a thought is pure “edification” (Erbaulichkeit): it is a mere construction that may
bring some consolatory psychological benefit but has no efficacy on the real. Such a
thought, therefore, has no philosophical value, if philosophy is to have loftier goals than
consolation.
The difficult and perhaps impossible issue confronting Hegel (and us confronting the
Hegelian text) is to understand how both sides can be thought together. All Hegel’s argu-
ment requires is contained in that “likewise” of the previous quotation:
the divine essence is not to be conceived and expressed merely as essence,
[...] but likewise (ebensosehr) as form.
This “likewise” is an arrow that points in both directions: to the essence of divine life as
play and to its form as the movement carried forward through the work of the negative.
Both dimensions have to be present, and at the same time. 6 To reduce Hegel’s conception
to one of its dimensions does not work: if we forget the side of the negative, then we have
just an edifying thought; that is, we are left with a conception that renounces any effort to
understanding the world, —since it excludes itself from it by looking at it from above, as it
were, from a distance where the concrete struggles disappear in the uniform fog of a mean-
ingless bickering— and substitutes it with the “pleasant” image of a divine play. Such a
thought is pure edification in the literal sense of the word: it builds up, it concocts an image
to put in place of concrete work and of knowledge thereof. 7 Such a thought will never be
knowledge, let alone absolute knowing, and philosophy, were it to surrender to this temp-
6. See also Phenomenology VIII: (490) “The spirit cannot be reduced to either moment but has to be considered
as both.”

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tation, would have to abandon its ambitions and be reduced to a void speculation better con-
fined to textbooks.
On the other hand, to renounce the positive side of the essence, the playful dimension
of God’s love playing with itself, is disastrous as well, since it gives up the possibility that
the circle of knowledge will ever close. And this is fatal to the whole argument, since, as
we have seen in detail, the possibility to escape the meaninglessness of philosophy passes
for Hegel necessarily through its closure. The end of philosophy can be reached only if the
two sides of Spiel are kept together. Philosophy itself, therefore, appears as linked to Spiel
and to the possibility of thinking and making sense of a concept of Spiel that recompre-
hends the playful and the serious, the childish and the tragic.
Unfortunately, Hegel’s interpreters are not much help on this point, although their re-
action to the problem I am outlining is quite interesting. In fact, the interpretations of abso-
lute knowing fall in two different camps, each one corresponding to a reduction of the issue
to one side, or moment, to use Hegel’s language. In a somewhat outdated but still useful
terminology, we can call them the “panlogicist” and the “pantragicist” camps, two labels
originally used to refer to different periods in Hegel’s evolution.
The so-called Pantragicist interpretations puts all the stress on the dramatic work of the
negative and emphasizes, as a consequence, the intrinsic “openness” of the Hegelian sys-
tem.
The following programmatic statement by Slavoj Z ˇ izˇek, although possibly not the most
accurate, can be assumed as one of the most salient characterizations of the pantragicist
camp:
the most consistent model of such an acknowledgment of antagonism is
offered by Hegelian dialectics: far from being a story of its progressive
overcoming, dialectics is for Hegel a systematic notation of the failure of all
such attempts—’absolute knowledge’ denotes a subjective position which
finally accepts ‘contradiction’ as an internal condition of every identity. 8
7. This is, again, Schelling’s position, according to Hegel, that reduces everything to an indistinct abyss:
“a Spirit that casts the differences back in the abyss of the Absolute and declares that therein they are
all the same” (490)
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Z ˇ izˇek’s stress on Hegel’s positive consideration of “antagonism” is a significant pointer to
the game-side of the Hegelian process. In other words, stressing the tragic aspect of Hegel’s
dialectics and reducing the concept of Spiel to its serious, game-like component are one and
the same theoretical move. The problem of any interpretation of this kind is how to account
for the closure of the circle of Absolute knowing which will bring philosophy to a close.
The very concept of Absolute knowing, in fact, is quite ill at ease with any pantragicist in-
terpreter who must climb on glass in order to accommodate it, witness this passage by
Z ˇ izˇek: ”The ‘One’ of Hegel’s monism is thus not the One of an Identity encompassing all
differences, but rather a paradoxical “one” of radical negativity which forever blocks the
fulfilment of any positive identity. 9 Z ˇ izˇek, in other words, equates the closure with the emp-
ty void of the most radical negativity: the “positive” side of Spielen consists in the retro-
spective realization of the impossibility of any positivity, on the impossibility of any full
reflection and sublation. The absolute reflection is nothing but the the impossibility of the
total reflection: “Reflection, to be sure, ultimately always fails” but this is” what is, in He-
gel, the very fundamental feature of “absolute” reflection.”(ib. 86) It is indeed difficult to
see how the closure of the Hegelian circle of circles, and therefore the completion of phi-
losophy, can be reached by declaring that the closure itself can never be achieved. However
interesting this reading may be, there seems to be very little Hegel in it, and not just becuase
the philosophical text is stretched so far as to convert closure into its negation. More im-
portantly, it seems to betray the very spirit of the Hegelian project insofar as it foregoes,
and it is forced to forego, all the positive connotations of Spiel in favour of its negative char-
acters.
The dual of the pantragicist is represented by the “panlogist” who stresses the in-itself,
that is the playful, self-concluded and self-contained aspect of absolute knowing and reduc-
es it to a metaphysical pantheist monism of I=I. “This view interprets Hegel as an abstract
metaphysician and absolute knowledge is about a large supersensible entity.” 10 Although
8. Slavoj Zˇ izˇek, The Sublime Object of Ideology (London: Verso, 1989) 6. But see Le plus sublime des
hysteriques (Paris: Point hors ligne, 1988) for a different and more nuanced position.
9. Slavoj Zˇ izˇek, For They Know Not What They Do (London: Verso, 1991) 69.

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the roots of this interpretation go back to Feuerbach, at least, it is alive and well even now-
adays. Jürgen Habermas, for example, comments as follows: “As absolute knowledge, rea-
son assumes a form so overwhelming that it not only solves the initial problem of
reassurance of modernity, but it solves it all too well. [...]reason has now taken over the
place of fate and knows that every event of essential significance has already been decid-
ed.” 11
Both interpretations forget what Hegel understood full well, namely that both aspects
must be present. If one of them is privileged over the other, the whole Hegelian solution to
the end of philosophy problem falls apart. Which means: Hegel is successful in designing
the topography of the ‘beyond’ of philosophy only if he can show that the concept of abso-
lute knowing, interpreted as a form of play, keeps together the work of the negative (e.g.
death) and the superior untroubled unity of this play with itself. Privileging the “negative/
serious” side (and pushing for a “pantragic” and “open” interpretation of Hegel) entails that
the circle cannot close upon itself: like a madly spinning top, philosophy can end up any-
where. Most likely, it will end up in the reassuring inanity of a textbook.
On the other hand, stressing the playful/positive side of the in itself, to use Hegel’s own
terminology (and therefore pushing for a “panlogistic” interpretation) implies that the ab-
solute is deprived of all its real features. It becomes a pure abstraction and its apprehension
can never be a science, since there cannot be any real knowledge of it but just, at most, a
felt intuition. To put it differently, the solution to the problem of the end of philosophy or,
in other words, the very possibility of philosophy’s existence, is contained in what seems
to be a real dilemma. Two conflicting and apparently contradictory constraints must be ful-
filled: first, in order to account for the “work of the negative,” e.g. the reality of human la-
bor, the tragedies and struggles of history, the structure that will account for them must be
necessarily open-ended. It must be and cannot but be a sequence of antagonistic confron-
tations. The game-like side of Spiel, in Hegel’s image, captures precisely this aspect of the
process.
10. Robert Williams’s formulation (who himself does not adhere to this view) in Recognition (Albany, NY:
State University of NY UP, 1992) 253.
11. Jürgen Habermas, The Philosophical Discourse of Modernity (Cambridge: MIT UP, 1987)42.
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Nonetheless, the sequence of confrontations, e.g. the antagonistic, game-like Spiel
cannot go on forever without coming to a close, otherwise there would be no rationale and
its meaning would have to be found outside of it (which means: outside of human history,
outside of this world and this thought, in an otherworldly universe inaccessible to us). This
may well be the case, but philosophy cannot accept an answer that would doom it to the
irrelevance of a consolatory discipline (in the literal sense, also, of being forced to take up
a disciplinary role: how, otherwise, could we control the madness springing forth from an
incomprehensible, non-human world?) Philosophy’s raison d’être is that there must be a
way to make sense—and express in concepts— the true way things are. This translates into
the necessity of a closed system. The concept of Spiel used by Hegel captures the property
of closure in its play-like side. Play is the paradigmatic self-enclosed activity that is totally
bent upon itself and does not need to refer to its outside to be both valuable, meaningful,
and rewarding.
However, if closure is no doubt necessary, it is far from clear what this closure is about,
or, more precisely, what it closes. It is necessary, for example, to transform work, the real
work of the negative in effective history, into a game being played. It is only because the
work, once performed, is recognized as the necessary part of a concluded and self-enclosed
process that the process itself can be understood as a game. The necessity of closure dis-
qualifies any “open,” pantragic solution to the problem of the absolute. Still, it does not
necessarily follow that a closed system has to reduce Reason to Fate, as Habermas con-
tends. To put it differently: closure, the circle of circles, etc., are just the names, the signa-
tures, so to speak, of the Hegelian concept that unites, in my terms, the playful and the
serious, the negative and the affirmative. The necessity that the system be closed reinforces
and repeats the demand—a demand perhaps impossible to satisfy—that Hegel imposes on
the concept. In itself, however, closure does not provide an answer. To uphold the necessi-
ty—totally internal to Hegel’s thought— of a closure as the visible mark of his inevitable
defeat and ultimate surrender to a pantheistic fatalism just misses the point. The issue is to
understand what closure means, what it closes and what comes together in that closure. The
issue is whether that closure is indeed possible, which means: whether Absolute Knowing

B ORDERING PHILOSOPHY
holds itself together and whether it holds itself in front of the negative by transforming it
into a play of divine love—without ever ceasing to stare into the face of death.
The end of philosophy, then, requires the simultaneous presence of these two seeming-
ly contradictory features. Absolute knowing must be both open-ended and closed. This
seems to be an impossible, desperate task to accomplish and Hegel seems to be proclaim-
ing, in fact, the terminus of philosophy: if the task ahead is impossible the completion of
philosophy cannot be reached in principle and philosophy itself is doomed. My suggestion
is that the concept of Spiel is an effort to think such an impossible closure because Spiel
presents us—or so it seems, given its still very imprecise form—with the analogous para-
dox of a closed structure that exhibits freedom and accepts negativity as the mark of its in-
side.
3. Bordering philosophy
Let us now reflect on the status of this tripartite connection between Hegel’s Absolute
Knowing, the end of philosophy, and Spiel that I have been trying to retrace. First, let us
consider the logical level at which this connection is located. It will be seen that it is not
placed, by and large, within the Hegelian system, insofar as such connection determines the
general form that a solution to the problem of the end of philosophy must possess in order
to count as such. In other words, the gesture that brings together the end of philosophy and
Spiel specifies the set of constraints—embodied by the latter—that the accomplishment of
philosophy must satisfy. The Hegelian system, whatever the ultimate truth about it, must
therefore be seen as the effort trying to satisfy the conditions that the concept of Spiel em-
bodies. As such, the system itself is located at what we might perhaps call a logically sub-
ordinate level.
A very important consequence follows from this statement: the validity of the connec-
tion itself is logically independent from the truth of the Hegelian system and rests solely on
the original premisses of his argument about the most general features of philosophy. In
particular, it rests on Hegel’s assumptions about philosophy as a search for truth and about
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the ineludible significance of the past history of philosophy for philosophy’s own activity.
Therefore, relative to those assumptions, the connection is valid. This means that it can be
properly rejected only by either (a) refusing to equate philosophy to the search for the truth
of being or by (b) choosing to ignore the relevance of history for the philosophical activity.
I have dwelt at length, in the previous chapter, on Hegel’s argument for the ineludibility of
history—what I called his second-order reflexivity argument for the possibility of philoso-
phy. I take here for granted that Hegel has established on quite firm grounds that philoso-
phy, if it does not want to collapse into a collection of consolatory opinions, must take its
own history into account.
As for the first premise, the following may be said: it is not as easy as it may perhaps
seems at first glance—which does not mean impossible— to both reject it and exhibit a rea-
son for philosophy’s rights to survival. The first alternative that comes to mind consists in
trying to carve out a specific domain for the philosophical pursuit, and more precisely a
well-defined, rigourously bound range of phenomena. There again, however, the problem
is how to delimit such a terrain from the pursuit of any given empirical science. Think, for
example, of language, or of the range of “mental phenomena,” or of the “epistemological,”
etc. In any specific instance, it is easy to think of an “empiric” scientific discipline that can
lay a legitimate claim on those fields as its most properly own. In the examples mentioned,
linguistics and various brands of psychology have in fact been proposed as legitimate re-
placements of the old-fashioned philosophical enterprise. This alternative, in short, al-
though possible, is not very palatable because it is always on the verge of collapsing into
one of three possible outcomes: either the possibility of a philosophical enterprise, i.e. the
quest for truth independent from science, is negated or it is not. In the latter case, the pos-
sibility of philosophy’s autonomy my be defended on the presumption of a more general
method of looking at phenomena. Philosophy would then become either a general method-
ology for science, or a sort of introductory survey of the a field whose proper study is better
left to the scientific discipline when times will be mature. But then, it is easy to see how
precarious is philosophy’s position, since in both cases it appears that either task would be
better be left to science itself, either as a self-conscious methodological reflection or as an

B ORDERING PHILOSOPHY
informal exploration to be further refined when a proper methodology is conquered. We are
then back to the first branch of the previous alternative, with philosophy being completely
absorbed within a specific scientific discipline like, to mention a well-known example, psy-
chology. Then, a new dichotomy immediately arises: either the telos of philosophy, the
quest for the truth of being as a whole, is picked up by the “substituting” science, or is not.
In the former case, philosophy is replaced by a sort of non-philosophical attempt that
strives, nonetheless, to find out ultimate truths. Let us call these attempts toward the elab-
oration of a scientific metaphysics “non-philosophy,” since they reject parts of philoso-
phy’s while keeping its goal. I will devote quite some space to two of these attempts in the
second part of this work. What I can anticipate right now, is that in these cases as well the
connection with Spiel comes to the fore again.
If, however, after the “absorbtion” of philosophy by a specific science the former’s
goals are not picked up, the questions to be asked are: what takes the place of the void left
by old-fashioned metaphysics? Is there any necessity to fill that void? Or was the very
search for a “truth of being,”metaphysically interpreted, a radically misguided attempt?
Whatever the answers to these questions, they can only come out from a reflection upon the
possibility of philosophy, or rather from a reflection upon philosophy’s radical im-possibil-
ity (or un-necessity, in certain cases). This brings us directly to a different meaning of “non-
philosophy,” one in which we read the effort trying to submit to a radical scrutiny the very
sense of the expression “truth of being,” either by changing the direction of the genitive or,
what often amounts to the same, by trying to provide a radically different interpretation of
“truth.” 12 What is interesting is that in several of the efforts falling under such a label, like,
for example, Derrida’s, Heidegger’s, or Nietzsche’s, a connection with Spiel, and a very im-
portant one, comes up again. In fact, I will provide some evidence in support of this latter
claim in the next two sections. At this stage of the analysis we can just remark, very pre-
12. Here, the implicit reference is obviously to Heidegger’s turning-point lecture “On the essence of truth”
(1929) where the relative equivalence of the expressions “being of truth” and “truth of being” is first
scrutinized and then brought to bear on the history of metaphysics and Heidegger’s own previous attempts
toward a fundamental ontology. However, the exploration of this essay in connection with the
end of philosophy and Spiel exceeds the limit of the present investigation.
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liminarly, that any road departing from the end of philosophy seems to bring us, one way
or another, in close proximity to Spiel. Be it a completion, as in the Hegelian case, a termi-
nus, as in science’s case, or an overcoming, as in Heidegger’s case, in any case the end point
seems to lead to the encounter with the concept of Spiel. The whole path we have traversed
so far under Hegel’s guide might therefore be considered as a straight road that can brings
us all alone, once we have learned the way, from the condition of possibility of philosophy
to the concept of Spiel. 13
Before entering into a closer analysis of the various branches of this path, it seems
however advisable to understand better, taking the Hegelian case as our guiding paradigm,
the relationship between what lies at the end of the road and Spielen. Is the place that is the
end—e.g. either the completion or the terminus of philosophy—literally, a Spielen, a form
of playing? Is there a game, perhaps a cosmic one, lying ahead of philosophy? Or is Spielen
instead to be interpreted in a more metonymical sense as the representative of a set of con-
13. Procedurally minded readers may perhaps appreciate a different rendition of what I have been saying
in the last few pages. It will be seen, in fact, that I have tried to linearize into prose the following diagram
representing the various possibilities, as I see them, opened up by my analysis of the relationship
between the end of philosophy and Spiel.
Non -metaphysics
as radical re-thinking
of Philosophy
SPIEL
NO
Philosophy absorbed
by science
YES
NO
Unstable,
collapses back onto
Philosophy = Truth of Being
Philosophy replaced
by science
NO
YES
Philosophical void
Philosophy's telos
picked up by science
NO
YES
YES
Hegel's case for
Absolute Knowing
SPIEL
Non-Philosophy
as scientific metaphysics
SPIEL

B ORDERING PHILOSOPHY
ditions that must be in place in order for that place to be reached? Both alternatives, in fact,
might be true, since they are not mutually exclusive: it might be that the only example ex-
hibiting the structural constraints that Spiel identifies is, in fact, Spiel itself. To say it a bit
more formally, it might true that Spiel is the only member of a one-element set, a unicum
that exemplifies only itself. Nonetheless, since the second alternative is less stringent, noth-
ing is lost if, at least for now, we decide to follow it and, consequently, we adopt the view
that Spiel has to be provisionally interpreted as a set of conditions to be fulfilled in order to
warrant the existence of an endpoint to the Hegelian path that originates with the reflection
upon the end of philosophy.
However, the distinction between the “proper” and “metonymical” interpretations of
Spiel can also be considered from a different point of view. In fact, it is certainly not granted
that the mapping between Spiel and the constraints outlined above in the context of Hegel’s
discussion is complete and one to one. In other words, there might exist a certain discrep-
ancy between the two, either because what we know, or pretend to know, under the label of
Spiel presents a richer set of features or, conversely, because some of the features required
to either close or terminate philosophy are not quite consistent with Spiel as we “know” it.
We do not have real answers to this point, at this level of the analysis, because we do not
enjoy the comfortable position of someone sitting on the fence and glancing down to both
antagonists in order to dispassionately assess their intrinsic qualities. Nor can we find any
help in empirical investigations or pre-theoretical understandings of play and game, other
than as bare clues toward further progress. The issue is how to think philosophy, or rather
its end, together with play, and how to think both together with their relationship, if any.
Regardless of whether the end of philosophy brings to a Spiel or to a Spiel-like location, are
we sure that what we know about Spiel and Spielen in general is consistent with the fea-
tures—or constraints, as I have I called them—that such a place should and would exhibit?
Unfortunately, there is no readily available touchstone, i.e. a body of knowledge about Spiel
firmly in place and onto- logically independent from philosophy that we may use to settle
the issue. Thus, the only possible way to gain more clarity on it is to conduct the investiga-
tion, as it were, from both sides. That is, on the one hand we are forced to proceed from the
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set of features that the philosophical discourse finds relevant, for its own purposes, within
the complex realm of phenomena that goes under the name of Spiel. On the other hand, we
cannot disregard what other non-philosophical disciplines might have concluded about the
phenomenon of Spiel as it happens in human (and possibly not so human) practices. 14 As
our knowledge progresses from both sides, as it were, we will be in a better position to de-
termine, perhaps, their relative distance. For now, though, it seems better to limit our-
selves to the weakest possible assumptions, and choose therefore to consider Spiel, in the
philosophical context of the end of philosophy, as a set of limitations that must be in place
for the success or the failure of the operation.
What are these constraints? Let me repeat them one last time. Whatever lies at the end
of philosophy must possess the characteristic of a form of playing that is both closed, or
rather self-enclosed, and intrinsically open, as I have insisted. Moreover, the openness con-
sists in the possibility, for the actors involved in the play, to engage in reciprocal, antago-
nistic interactions. This, in turn, involves a freedom of movement that must be present in
order for the interaction to take place.
The first conclusion to be drawn about the connection between the end of philosophy
and Spiel is that its logical independence from Hegel’s system, relative to the assumption
about history and truth, translates into a complex set of relations organized around the con-
cept of Spiel, a set whose observance will qualify “any” (that is, not necessarily Hegelian)
eventual end as a proper place for philosophy to rest.
Let us now turn our attention to another aspect of the complex interrelation between
the end of philosophy, and Spiel: let us consider the respective statuses of the “road” and
the “endplace,” first, and especially their possibly different logical status. Hegel introduces,
in the context of the end of philosophy, the idea of a playful (but deeply serious) terrain that
lies beyond philosophy and represents its beyond while being, at the same time, its most
proper own (since it is its final transfiguration and proper achievement). This idea, howev-
er, is just a glimpse; it is an introduction in the most literal sense of ducere intra, of leading
14. In fact, forms of playing found in animals and machines might be relevant to the analysis, at least because
(a) adding a human-only clause to a very general analysis seems unduly restrictive and, moreover,
because (b) non-human play has been quite extensively studied.

B ORDERING PHILOSOPHY
inside the building of philosophy something (possibly) external to it. Hegel introduces this
idea, most properly, in the Preface to his first major work. He leads this idea into philoso-
phy, or more precisely into his analysis of the conception of the end of philosophy. The He-
gelian gesture, the glimpse of the realm of play lying beyond philosophy, may be
interpreted, at the most general level, in a number of different ways, depending upon how
we read the logical relationship between the path and its destination. It may be the ship tak-
ing us to the promised land of the beyond, or the outside of philosophy that Hegel tries (un-
successfully, perhaps) to domesticate, or even the outside as what underlies philosophy, the
original opening within which philosophy as metaphysics makes, or rather takes, sense.
This gesture must be considered at two different levels. On the one hand, as I have in-
sisted above, it makes more transparent, or so I hope I have shown, what is needed in order
to perform such a closure of philosophy. In the complex dialectical movement which the
Phenomenology, on its path to absolute knowing, will cover, the final point is represented
by an apparently impossible conflation of the most serious commitment to death with the
most lighthearted universe of play. At the same time, Hegel makes also clear that not only
the two aspects must come together, but that they do come together in play, that they do
represent the two sides of the same coin. More precisely, the one cannot exist without the
other. If the weight is then transferred onto the concept of play, the issue is to find out
whether ‘play’ is up to such a task of transfiguration of philosophy. Whether, in other
words, we can think play, game, and their inner articulation in such a way to make sense of
what Hegel is prescribing in order to accomplish the transfer into the ‘beyond’ of philoso-
phy.
The Hegelian gesture becomes even more interesting, and more difficult to think
through, if we are willing to read the Hegelian text literally, if we are willing play along
with his thought. In which case, we are not allowed to consider play and game as useful
“metaphors” or “images” to illustrate absolute knowing, but have to take it, quite literally,
as what the beyond of philosophy is. We should not say, then, that “absolute knowing is a
play”, which can be interpreted as “we can perhaps imagine,” or “it might be useful as a
didactic exercise” to imagine absolute knowing as a form of play. Rather, “absolute know-
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ing is play,” tout court, without further explication. In this case, we might reverse the
former question and ask instead whether philosophy is up to the task that Spiel demands of
it. In other words, we might ask whether Hegel lets philosophy be carried over to the uni-
verse of play or if this cautious introduction of play into the body of philosophy does not
end up forcing play to become something else (by privileging one of its aspects, for exam-
ple).
This points to the possible existence of an important difference between the road that
brings to the end and the end itself, the place the roads leads to. Prima facie, at least, there
seems to be an almost unsurmountable logical difference between the search for the truth
and the truth itself, that is, between the process and the result of that process. In the classical
Hegelian terms we already mentioned above, the difference we are talking above is nothing
but the difference between the mere love for knowledge and the form of knowing that will
finally be able to call itself a science (Wissenschaft). The Hegelian twist on this topic, of
course, is that the process is part of the solution, since the history of philosophy (the path)
is what is necessarily required in order to reach the closure of the circle of circles that marks
the completion of philosophy. In other words, the solution is nothing else than the complet-
ed process. In this case as well, though, it should be remarked that the relationship between
the completed circle, e.g. the reached end, and the path bringing to it, e.g. philosophy, can-
not be totally on a logical par.
Two points must be underlined in connection with this issue. First of all, the present
effort consists precisely in trying to discern the features of the Hegel’s argument that are as
independent as possible from the specific solution given by the Hegelian system. Second,
it should be noted that the necessity that brings from philosophy to absolute knowing is not
necessarily valid in the other sense as well. In other words, even if Hegel shows that the
science of the experience of consciousness must necessarily conclude in a Spiel-like Abso-
lute Knowing, does it follow that the latter is reachable only from the former? Does the ne-
cessity arrow, to put it differently, work in the other sense as well? This does not seem to
be case, within the confines of the Hegelian resources we have exploited so far.

B ORDERING PHILOSOPHY
The existence of a “leeway” between Spiel and philosophy, the presence of a less than
perfect correspondence between the former and the latter leaves open one interesting pos-
sibility. It might be the case that what we have called Spiel stands in relation not only to
philosophy but also to something else. In other words, the existence of a possible distance
between Spiel and philosophy suggests that there might a certain degree of independence,
both at the logical and ontological levels, between the two, and that the promised land of
Spiel might be reachable also from a different starting point. It might be possible that Spiel
actually exceeds philosophy, both in the sense that not all of it is captured by philosophy—
or by the philosophical path reaching to it—and also in the sense that “it” might be reached
from elsewhere. But what do we mean here by “elsewhere”? The term refers, in this context
to whatever can stand in a similar relationship to Spiel as the philosophical path depicted
by Hegel. In other words, we are asking whether it is possible to reach a similar character-
ization of Spiel from a different starting point. The question, first of all, is double: first we
are asking where can we find the starting point of a similar connection to Spiel. Second, we
are asking whether, were we to find it, it would be in any sense relevant to the present dis-
course. Let us try to answer these questions by means a progressive differentiation from the
what we have seen at work in the Hegelian case.
The inquiry that brought to Spiel started from a reflection about the end of philosophy,
in all the complex meaning of this concept, and took his start from within the path of West-
ern philosophy. We should therefore negate this latter term and look outside of that Western
philosophy considered by Hegel for an alternative starting point. For the sake of clarity, we
could rephrase this latter term as the philosophical tradition of Western metaphysics. But
here again we are confronted with two non equivalent and non mutually exclusive qualifi-
cations that define the realm of our previous investigation: the philosophical tradition and
(of) Western Metaphysics. We might therefore look for a significant connection to Spiel ei-
ther in (a) what we might call non-philosophy (regardless of its “Western” affiliation) and
(b) in what we might call non-Metaphysics. The particle “non” should here be taken in the
strong sense of negation (or determinate negation) and not in the blurred sense of a generic
difference. In other words, we should look for, and try to find, one or more inquiries that
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understand themselves as in determinate opposition to either philosophy or to the Western
tradition (or both) and that come up with an essential connection with Spiel.
Let us call what we just stated as the first constraint on the search for an alternative
starting point to be put in relationship with Spiel. It will be immediately seen that it is not
enough to bring about a significant alternative to the Hegelian paradigm. In fact, the other
essential term of the connection previously investigated was a search about the end of phi-
losophy. It follows that what we are looking for as a possible candidate is either a non-
philosophical or a non-metaphysical search about the the end of philosophy that establishes
an essential connection with Spiel. Furthermore, in order to maintain the essential similarity
with the Hegelian connection between the end of philosophy and Spiel, it is important that
the characteristic of the latter I have been insisted upon are respected as well: self-enclos-
edness, essential openness, freedom of movement, etc.
To sum up: the presence of a logical leeway betwen the end of philosophy and Spiel
would leave open the possibility that an analogous relationship might be found that ties to-
gether a structurally similar conception of Spiel with a non-philosophical or non-metaphys-
ical search. What would such a finding entail? The existence of a multifaceted connection
between, on the one hand, the end of philosophy, non-philosophy, and non-metaphysics
and, on the other, Spiel would prompt us to consider the following issues.
First of all, let us examine the sense (in both meanings: the direction and the meaning-
fulness) of such a coupling. We have seen that in the philosophical case, exemplified by
Hegel, it is a completion that takes place, and the direction of such a a completion goes nec-
essarily from philosophy to Spiel. Is this true also in the other, “non-philosophical” instanc-
es as well? What would happen if, instead, we were to find out, as it is likely, a significantly
different sense of this connection? Spiel, for example, can be seen as onto-logically ante-
cedent to philosophy and the latter be interpreted as the consummation of one particular
possibility that the former opens up. We can read along these lines, for example, Heideg-
ger’s, and later Derrida’s, view of play as embodying a larger set of possibilities that West-
ern Metaphisycs can afford to neglect, by and large, through a forcible reduction of the free-
flowing, risky business of jeu to the well-regulated activities embodied by les jeux. 15 A re-

B ORDERING PHILOSOPHY
duction that forces play into game, to say it in the terms of the previous section. In this case,
how is the sense of the coupling to be interpreted? Moreover, how can two or more, possi-
bly confliciting interpretation be reconciled, if at all?
A second strictly related point concerns the inner articulation of Spiel. I have spent
quite some time trying to disentangle the various constraints required by the notion of Spiel
that comes up at the end of philosophy. It is certainly not granted that exactly the same con-
straints must be at work in similar configurations of the concept. In this case, however, we
must first ask what consequences might such a difference have and, moreover, how it is re-
lated to the previous point, namely to the sense of the relationship between the end and
Spiel. For example, it will be seen that in some instances two different aspects of Spiel are
emphasized: sometimes is the play-like that comes to the fore and sometimes is the game-
like side. This difference is accompanied by a diverging intepretation of the sense of the
general relationship between the end and Spiel, which prompts us to ask whether there is a
different interpretation of the inner articulation of Spiel that relocates the sense or it is in-
stead the opposite to be true, namely that a different sense forces a different articulation.
And what would that mean, for the connection as such?
Third, and last, we should ask who is the subject (to use a not too improbable word in
this context) of the Spielen that takes place at and in the end. Who is playing here? A short
list of suggested candidates includes being, Geschick of being, Geist, différance, not to
mention an empirical subject endowed with bounded rationality. It is certainly not easy to
answer this question, especially because it is unavoidably connected to the sense and the
articulation.
15. See, for example, Derrida’s comment on the Rousseauian festival as a festival of full presence, a ball,
a dance, a ring where there is no distinction between players and spectators, voyers and voyants: “there
ary many games (jeux) within the public festival, but no play (jeu) at all, if one understands by that
singular number the substitution of contents, the exchange of presence and absence, chance and absolute
risk. The festival represses the relationship with death...” Jacques Derrida, De la grammatologie,
(Paris: Seuil, 1967) 433. Engl tr. Of Grammatology (Baltimore: Johns Hopkins UP, 1974) 307. Notice
the crucial use of words coming from the three main semantic areas of Spiel—e.g. movement, agonistic
confrontation, and free-flowing activity— organized and organizing an argument about the limit of
metaphysics. See also, in “La pharmacie de Platon,” the programmatic declaration: “Jeu est la cyphre
de l’ouverture anti-dialectique par excellence” (Paris: Seuil 1972) 150.
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These questions cannot be addressed, of course, until the existence of a different path
to Spiel remains a mere hypothesis. To move out of the realm of the possible onto more sol-
id grounds, I will begin by briefly addressing the anti-Hegelian tradition represented by
Heidegger and Nietzsche.
4. Spielen, the Abyss, and the Child
The association between the end of philosophy as completion, as Hegel reads it, and
the idea of the Absolute and of Absolute Knowing as Spielen is bound to raise some ques-
tions if we think about the status of the latter concept in current philosophical discourse. In
fact, the concept of play has been often used in post-Hegelian philosophy as a tool to think
philosophy in a new light and on new grounds, against or beyond Hegel and the whole of
Western metaphysics that he, supposedly, brings to a close. Play becomes, in the reflection
of Heidegger, for example, or of Nietzsche, a key element of a strategy aimed at overturn-
ing philosophy by bringing it to a different kind of end, by taking it to its terminus. The
Heideggerian search for a “concept” for “non-philosophy”, for example, points to Spiel,
and more specifically to the groundlessness of Spiel, as a crucial element.
In other words, play and game have been put forth as the decisive concepts enabling a
transmutation of philosophy into something completely different, something other than
philosophy as metaphysics. It may seems paradoxical, therefore, to see the concept of play
emerging in Hegel, and precisely in conjunction with the thought of the Absolute and of
absolute knowing, the alleged summit of the same metaphysics that the concept wishes to
overcome.
We may of course ask if we are in fact dealing with the same concept at all and whether
there is more than a mere linguistic resemblance between the Hegelian “Love playing with
itself” and, for example, the Heideggerian notion of Spiel. An answer to this question has
to precede any further investigation of the paradox. But, if the answer were to be positive,
another more intriguing question might be asked: how is it possible that when philosophy
comes to its end, both in the sense of completion and in the sense of failure, it reaches the

S PIELEN, THE ABYSS, AND THE CHILD
concept of play? How is it possible that the search for a new concept for non-philosophy—
to use the Heideggerian expression—tries to find an essential leverage on the same concept
reached by philosophy’s end? What is covered, if anything, by that concept? Or, to say it
better, what is given to thought in play? In order to find a clue toward the answers to those
question, we take a look at the ways in which play comes to the fore in Heidegger and Ni-
etzsche. Some of the characteristics of play will also be determined by such an analysis,
making it possible to ascertain the concreteness of the paradox of play.
Toward the end of the lecture course on The Principle of Reason, Heidegger distin-
guishes the notion of being as ground, as ultimate foundation (Grund), which he sees as
characteristic of Western metaphysics and the notion of being as Abgrund, as abyss, that he
wants to oppose to such a tradition. 16 And he asks:
does the nature of the play let itself be suitably determined in terms of being
qua ground/reason, or must we think being and ground/reason, being
qua abyss in terms of the nature of play?” 17
Before setting to answer such a question, it is important to grasp its paradoxical status. In
fact, what Heidegger suggests, albeit in form of a question, seems a pure contradiction. The
second part of his interrogation asks whether it is possible to think being and ground in
terms of the nature of play. The alternative presented in the first part of the question,
though, asks whether the essence of play is thinkable in terms of being as ground. This
would be an effort striving to isolate the “nature” of play, its essence. But the nature of play
is precisely what is required in order to opt for the second part of the question, what Heideg-
ger thinks is needed in order not to think being as ground. And yet, the question was pre-
sented as an antinomy: either the first half is chosen, or the second, but not the two together.
Instead it seems as if, in order to go beyond being as ground, in order to go beyond the
16. In order to appreciate the subtext of this Heideggerian statement is important to remember that the
Abyss (Abgrund) is the Schellingian term that Hegel picks up as a nickname for Schelling’s characterization
of the absolute. The characterization that he derides in the Phenomenology as “the night in
which all cows are black”. The positive use of the term by Heidegger is an explicitly anti-Hegelian
gesture.
17. Martin Heidegger, The Principle of Reason (Bloomington: Indiana UP, 1984) 112.
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scope of Western metaphysics, we would require the most metaphysical of the procedures:
a determination of the “essence” of play. The task is impossible, it seems, since a determi-
nation of the essence of play presupposes that being be thought in terms of Grund, and it
forbids, therefore, to think being as Abgrund. The apparent contradiction disturbs the sym-
metry of a question that strives to present two opposing ways of interpreting the relation-
ship between being and play. In fact, there is a third term in play: thought. The condition of
intelligibility of the question requires that thought, as soon as it deals with play, renounce
any determination of its ground without renouncing to determine its nature. Therefore, the
task of thinking “being as abyss starting from the nature of play,” as Heidegger says, be-
comes a challenge for thought itself that here seems to have reached its limit. To think play
(in the sense of Spiel, of course), and even more to think the abyss on the basis of play, can
only mean to think differently because it requires that thinking must abandon its traditional
efforts to think the nature of being as based on their ground. In other words, Heidegger’s
question requires, in order to be properly understood, a reexamination of the relationship
between play and thinking. A relationship that must be reconsidered in both its senses:
when play is the object of thinking and when thinking is the object of play. It might be pos-
sible to condense what I have been saying so far in a single question that is presupposed by
the Heideggerian interrogation: “How to think play?” This question has to be heard in its
intrinsic duplicity as a question about both play and thinking, as a combination of “how to
think play,” and “how to think play.” To put it differently, the Heideggerian text seems to
bring to light the issue of a “play’s thought” that he delivers as a task to philosophy. What
is important, to understand the radicality of the Heideggerian questioning, is to heed both
senses of the genitive in a complex unity. The issue at stake is to understand how play can
arrive to thought because thought belongs to play. And conversely.
Heidegger presents this issues as preliminary to a philosophy of being as Abgrund, as
abyss. In other words, he ties any possible overcoming of Western metaphysics to an inter-
rogation of the nature and consequences of the reciprocal interpenetration of thought and
play, of Denken and Spiel. How does the text proceeds in this task?

S PIELEN, THE ABYSS, AND THE CHILD
Soon after the passage quoted above, Heidegger goes on to say that joining together
play and being as abyss can be considered a violent juxtaposition and perhaps even an ar-
bitrary, non serious, maybe even playful act. He goes on to answer this charge as follows:
It may seem so as long as we keep on neglecting to think in terms of the
Geschick of being, and that means neglecting to entrust ourselves to the liberating
engagement in the legacy of thinking and to do so in a way that recollectively
thinks upon it. (112/186)
Let us focus on the first part of Heidegger’s answer. Play’s thinking and its relationship with
being as Abyss, Heidegger claims, are arbitrary only if one neglects to think them in the
context of the Geschick of being. In the next few paragraphs, which conclude the whole lec-
ture course, Heidegger first goes back to Heraclitus’s notion of logos and then recalls the
well known Heraclitean fragment 52 on play. 18 This may suggest that the connection be-
tween Geschick and play—which, Heidegger affirms, is crucial to a non-arbitrary introduc-
tion of the latter into philosophy—has to be understood in the context of history of
philosophy: as a return to the Greek origins of Western philosophy and more specifically
to the reflection on play that is already present in the Greeks. Such an interpretation, al-
though not completely incorrect, misses the deeper point of Heidegger’s remark, because
it would reduce the Geschick of being to the history of philosophy, whereas, as the previous
lectures have explained at length, the Geschick des Seins is rather what makes history pos-
sible. If play’s thought is required from the thought of the Geschick of being then it is in the
Geschick itself that the reason of such a violent reapprochment has to be found and not in
the first sources of Western philosophy. But what has Heidegger to say on Geschick? Let
us read from the eighth lecture:
When we use the word Geschick in connection with being, then we mean
that being hails us and clears and lights itself, and in clearing it furnishes the
temporal playspace (Zeit-Spielraum) wherein beings can appear. (62/109). 19
The destiny of being, its Geschick, is strictly related to the play because Geschick itself is
18. See Heraclitus fragment 52 (Diels): “The age of the world, a child who plays moving the pieces of the
game: a child’s kingdom.”
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just the furnishing of an appropriate playspace and the taking place of play on it. Being, in
its clearing, opens up a space wherein beings can appear. Such a space must be understood
as a playspace, that is, as a space in which play may take place. It would be wrong, however,
to think that the space opened up by being becomes a terrain onto which play may take
place. This becomes clearer if we consider for a moment the meanings of “play” and
“game.” Both, and particularly the latter, can refer to the set of rules and conventions that
make possible the occurrence of the single ludic event (e.g. the game of tennis, generally
considered) or to the specific, concrete event (e.g. the 1996 final of the Wimbledon tourna-
ment). The Heideggerian text cannot adopt the second meaning of the term Spiel, because
that would entail that the appearing of beings is ruled by the institution of a game in an
“empty” space opened up by the destiny of Being. In other words, we would have to pre-
suppose a two-stage process: first the deployment of a space and then the institution of a
play/game that makes possible the disclosing of beings as objects of the game itself.
The text, instead, suggests just the opposite: the Geschick of being furnishes the space
wherein the concrete playing can take place. This means that the Geschick of being is noth-
ing else but the institution of a game, the mise en place of a game that sees beings as its
objects. To put it slightly differently: the mise en place of a game that allows, when played,
the disclosing of being within its boundaries. The principle of sufficient reason, if we fol-
low this interpretation, becomes therefore the rule of the game of the West, since it consti-
tutes the space within which beings can be properly “comprehended.” 20 The second
mentioned meaning of game/play and the Geschick of being come to coincide: the destiny
of being is a Spiel. In the very last page of Der Satz vom Grund, Heidegger goes back to
the Heraclitean fragment 52 and translates it as follows:
19. Spielraum is usually translated into English as “leeway”, or more simply as “play” in the mechanical
sense. Here, Heidegger is leveraging upon the original meaning of Spielraum as the space where play,
e.g. movement, can take place, in order to add the temporal element as well. A literal translation would
then bring something like the “spatiotemporal leeway.” However, such a translation would obliterate
the crucial reference to play and emphasize the mechanical meaning of play. Since both solutions are
unsatisfactory, in the following I will alternate between “leeway” and “playspace” when referring to
the Heideggerean uses of Spielraum and Zeit-Spielraum.
20. In the proper, literal sense of the word: beings can both be understood and confined and they are understood
because they are confined.

S PIELEN, THE ABYSS, AND THE CHILD
The Geschick of Being, a child that plays, shifting the pawns: ´the royalty
of a child—that means, the αρχε, that which governs by instituting grounds,
the being of beings. The Geschick of being: a child that plays. (113/187)
This brief remark is far from being an exhaustive reflection on the nature of play and espe-
cially on the nature of the play of thinking, but at least points in the proper direction. The
issue lying ahead, fact, could be summed up by saying that in order to determine the nature
of play one has to determine “what the play plays, who plays it and how the playing is to
be thought here” [111 (186)]. What I have been saying so far about the interconnection be-
tween play and Geschick answers, at least partially, the first two questions—the what and
the who parts of the problem: the game is played by being in its Geschick. But what is being
played in this game? Nothing less that the possibility of beings’ disclosure and appearing.
Beings as such are at stake in the play of Geschick: their being depends on the institution
of a playspace provided by the Geschick of being because beings can appear only within
such a space and according to the modality provided and prescribed by the game being
played. It is for this reason, I believe, that Heidegger, when referring to one being in par-
ticular, e.g. the mortals, affirms that “one here deals with a game where they are in play and
at stake.” (ib.).
This very preliminary answer to the “who” part of the interrogation about play indi-
cates where we can find out “how” the play takes place: we must inquire about the Geschick
of being as the operation of instituting a game, as the creation of the Zeit-Spielraum, the
spacetime of the game and the space/time play). A further step is possible if we keep in
mind an additional component of the meaning of Spiel: play as the leeway, as the infinites-
imal space that makes movement possible. Play, in short, in the sense of the possibility of
articulation of joints. It follows that the subject of the interrogation becomes the Geschick
of being insofar as it constitutes the successive articulations of the spacetime within where-
in beings can appear. What can we discover along this path? Let us go back to the text quot-
ed above.
It should be noticed that Heidegger/Heraclitus do not say “Aion/Geschick: a Spiel,” be-
cause otherwise the meaning of play as concrete event would be privileged and, as a con-
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sequence, the Geschick of being could be interpreted as the specific realization of a game
instituted by someone else. On the contrary, they say “Aion/Geschick: a child that plays.”
There are no psychological or mythological undertones in this accent on the ludic world of
the child. The reference to such a world highlights a precise, and, supposedly, extremely
relevant, feature of play by pointing to the relevance of child’s play. What is important
about the way children play? Simply put, child’s play is creative. Creativity, here, means
just that the child at play is capable, contrary to most adults, to invent the game while it
plays. Child’s play is creative because it comports—in the same event—the institution as
well as the execution of the act of playing. The child invents the rules of the game and, by
so doing, creates a leeway which is not of course, spatial at all, but represents the spatiotem-
poral field within which actions are possible. It is precisely this aspect, I believe, that
Heidegger wants to emphasize by recalling the Heraclitean fragment and by underlining his
reference to the world of the child. But there is more in that reference. In particular, there
is another aspect of child’s play that Heidegger brings to the front in the lines immediately
following the previous quotation. He says:
Why does it play, the great child of the world-play Heraclitus brought into
view in the Aion? It plays because it plays. The because withers away in the
play. The play is without a “why”. It plays since (weil) it plays. [ib.]
Play, as I have stressed in the previous pages, has no external finality, it is perfectly self-
contained. Or rather: play resists the application of the very concept of finality, it resists the
application of the concept of a final cause that finds it raison d’être outside play itself. Does
this mean that play is totally arbitrary? Does this mean that the distinctive mark of any ludic
phenomenon is its improvised, poetic, extemporaneous character, as Nietzsche once em-
phasized? 21 The situation is actually more complex. Play, and especially child’s play, is nei-
ther arbitrary nor rigorous, but both at the same time.
“Play is without a why,” Heidegger affirms, and “it plays since it plays (es spielt weil
es spielt).” This does not mean that play is completely arbitrary, but rather that the mode of
being of play refers only to itself and only from and in itself is its rigor to be found. The
21. Friedrich Nietzsche, Thus Spoke Zarathustra (Harmondsworth, Engl.: Penguin Books, 1978) 25.

S PIELEN, THE ABYSS, AND THE CHILD
mode of being of the child at play, his acting, is governed absolutely by the rules of the
game that delimits the playspace: no transgression is possible, lest the game itself is dis-
solved. But the “foundation” of the rules, their “ground” in the proper metaphysical sense
of Grund is totally absent because the rules have been created by the player itself who is
free to change them at will and anytime. Therefore, we must affirm that Spiel is constituted
by rules whose value is absolute within the real of play (within the spatiotemporal leeway,
the Zeit-Spielraum), but whose Grund is arbitrary. However, such a characterization is still
insufficient insofar as it suggest a clear-cut division between the institution and the execu-
tion of the rules. What is worse, such a characterization suggests a bipartite and essential
static process in which an initial “legislative” phase is followed by successive and properly
ludic executive stage. What is most essential in the ludic process—and I believe, in the on-
tological context within which Heidegger talks— is precisely the absence of such a division
which can be retraced only a posteriori. We might say that such a clear-cut division is valid
only in abstracto and more precisely if we abstract from the time of play. Time exists, with-
in the game, as the changing of the rule, as a creation of new rules that replace the old ones.
The intrinsic compenetration of arbitrariness and rigor that is typical of play comports
necessarily that the being of the player is always, and at the same time, inside and outside
play, because it has to be inside the game being played as long as it is following the rules
and outside of the played game and inside the playing game, as it were, insofar as it finds
itself creating the rules that define a new playspace. The being of the player is the being at
the limit, or, better, the being living on the limit, the being living on the ever renewing limit
that divides the time of play when the player is totally absorbed within the Spielraum from
the time when the Spielraum itself is defined. “It plays since it plays,” says Heidegger, and
in the clause we should hear the intrinsic and essential duplicity of play that finds in itself
its rigorous, and therefore arbitrary, law.
It is this double movement, I believe, that thinking must appropriate in order to become
a thinking of play. Or rather, it is the double movement that play must give to thinking so
that the latter may become play’s thinking. Play’s thinking can only be the thinking of the
limit, the thinking that positions itself on the limit of the articulation constituted by the des-
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tiny of being. Such a thinking must be equally ready to play according to the rules of the
Zeit-Spielraum that the Geschick of Being has opened up to men as well as it must be ready
to question such rules by seeing through their absolute arbitrariness.
If purposelessness is the aspect of play that Heidegger emphasizes the most, a different
characterization is given by Nietzsche. In his case as well, however, the overcoming of
metaphysics is tied to the advent of play. Play is no doubt one of the recurrent themes of
Nietzsche’s thought, and it usually point to Nietzsche’s call for an affirmation of life against
the nihilistic negation incarnated in the ascetic ideals. In his language, play—and more par-
ticularly the Heraclitean child at play—points to the age when nihilism will have been over-
come, the age in which life, instead of being continuously negated or at best tolerated and
justified for a task that does not belong to it, will eventually be affirmed in its randomness
and in its self-renewing becoming. But is it play an adequate figure to use for such an am-
biguous task? Don’t we witness an intimate contradiction, a basic incompatibility between
the affirmation of life, chance, and mortality that Nietzsche assigns to play and the mode
of being of play itself?
In fact, play seems to indicate the exact opposite of what Nietzsche wishes, at least be-
cause the actualization of play absorbs the player inside play itself and negates whatever
part of the being of the player is not playing. In other words, the mode of being of play rep-
resents, or so it seems, the ultimate and most definitive negation of the will of the player
because the player can play only by submitting his own self to the play. Play is, at least in
part, the mark of the most absolute negation because it can exist only be negating indepen-
dence of the players’ being. It is this negation that causes the now ecstatic now frantic rap-
ture that the player experiences when its participation to the game being played reached the
peak. It is this negation that causes the frantic euphoria that players—and gamblers in par-
ticular— experience so often, and that represents play’s ultimate reward. It is the experi-
ence of the negation of the will, of the identification with the dice being thrown, the
experience of the absolute communion with the roulette’s wheel, almost as if the latter were
endowed of an autonomous life. If this is the case, however, how can play be the sign of the
Nietzschean affirmation of the individual’s life against the stricture of an ascetic ideal that

S PIELEN, THE ABYSS, AND THE CHILD
puts the meaning of life in an another world? How , and why, can Nietzsche think that the
love of chance and the identification with the rolling dice is essentially different from the
love of God?
Let us begin from the opening pages of the Zarathustra. In his first discourse, he nar-
rates three metamorphoses: he tells the story of the spirit that became a camel, then a lion,
then a child. The camel is the spirit in the age of nihilism, the animal that interprets life as
a succession of weights to be carried, and that accepts life only because it despises it. When
the camel becomes a lion, the spirit experiences the will as affirmation of independence, as
a vindication of its independence and of its freedom. However, the definitive overcoming
of nihilism, according to Zarathustra, can happen only in the age of the child, of the playing
child. He says:
The child is innocence and forgetting, a new beginning, a game, a selfspinning
wheel, a first movement, a sacred “Yes-saying.”
For the game of creation, my brothers, a sacred “Yes-saying” is needed:
now the spirit wills his own will, and he who had been lost to the world conquers
(gewinnt) his own world22 The first Zarathustrean illustration of play is all contained in these two concluding sentenc-
es of his first discourse. The paradoxical status of play, however, is already well-delineated,
in spite of the concise description. Play is compared to forgetting, to movement, and, most
importantly, to a self-spinning wheel. Zarathustra’s image is much more than a metaphor
since play, in all the Indo-European languages has an essential connection with movement
or, to be more precise, with the freedom of movement. The engineeristic meaning of Spiel,
play, gioco, juego, etc. all point to the space between the mechanical components that war-
rants the possibility of their movement. In this sense, play is the closed space within which
its constitutive movement can take place forever. This means, as it has often been noticed,
that to play means always, although not exclusively, to be played, and in all the meanings
22. Friedrich Nietzsche, Thus spoke Zarathustra (New York: Viking Press; 1966) tr. Walter Kaufmann, 27.
Cf. the German: “Unschuld ist das Kind und Vergessen, ein Neubeginnen, ein Spiel, ein aus sich
rollendes Rad, eine erste Bewegung, ein heiliges Ja-sagen. Ja, zum Spiele des Schaffens, meine Brüder,
bedarf es eines heiligen Ja-sagen: seinen Willen will nun der Geist, seine Welt gewinnt sich der
Weltverlorene.” Friedrich Nietzsche, Also sprach Zarathustra (Berlin: de Gruyter:1968) 27.
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of the term “played”: moved around, entertained, tricked, operated upon, etc. etc.
The emphasis here is on play being prior to the players, on the played game taking pri-
ority over the players: to play means to submit oneself to the rules of the game and the best
player is the one who, by being closest to the rules of the game, is at the same time the far-
thest from himself. The maximum participation to the game being played requires the max-
imum self-forgetfulness, this is what Zarathustra stresses: the player is never as
participating on the game as when he negates himself in order to be ecstatically carried out-
side himself and within the playspace.
The mode of being of play—which, as self-spinning wheel expresses the eternal be-
coming that does not need any justification since it eternally re-presents itself—contains an
essential moment of negation because the player must annihilate itself into the game being
played. The epochal event wished by Zarathustra—the instauration of the world of play—
comports the end of the player(s) or, at least, the end of the separation between the players
and the play. The advent of play, it seems, is the death of the player. This is what Nietzsche
seems to say in the second part of the previous quotation when he states that “play is a sa-
cred yes-saying”, that is, play is the purest of the affirmations. The subject of this affirming
is the spirit (Geist) transformed into a playing/playful child and therefore into a player who
affirms the play of the world and who wills his own will.
If interpreted in this sense, however, the figure of play recedes from form the age of
the Overman and of the overcoming of nihilism and gets closer and closer to this present
age, to the age of nihilism. Play becomes closer and closer to the final stage of the asceti-
cism, the stage when the ascetic ideal will reach its “triumph in the ultimate agony.” 23 Such
a triumph represent the victory of the end that will have been finally reached, the triumph
of death that is, at the same time, the extreme ecstasy. The spirit willing the advent of play
wills, then, its own death or, to say it better, it wills its own self-annihilation. We witness
here the extreme paradox of play, that brings together the affirmation and negation in a sin-
gle act comporting the affirmation of the negation of the players. Is this consequence con-
23. Friedrich Nietzsche, On The Genealogy of Morals (Oxford: Oxford University Press, 1996), III, 11.

S PIELEN, THE ABYSS, AND THE CHILD
sistent with Nietzsche’s wishes and his effort toward the overcoming of metaphysics of
negation?
It might be said that the peculiarity of play that I have been illustrating rests on a mis-
taken identification between man and player, between man and the subject of the cosmic
play of chance and becoming. Man, one might say, is rather to be considered an object of
play, “one of the most unexpected and exciting lucky strikes in the game played by the
‘great Heraclitean child’—be it Zeus or chance.” (II, 16)
This may be true, but it remains true as well that the negation of man, the annihilation
representing the apotheosis of nihilism is not any less essential because the affirmation re-
quires a different subject than man in order to be affirmed. The connection between affir-
mation and negation outlined above is perfectly legitimate because it points to the essential
and necessary triumph of nihilism, e.g. the non-existence of man, that is a required step to-
ward proceed to the age of affirmation. What is crucially important, however, in order to
capture correctly this transition is to understand its negative moment, e.g. man’s annihila-
tion. The value and consequence of such an ultimate negation changes radically, as Gilles
Deleuze has extensively proved, according to whether is referred to the “last man” or, in-
stead, to the “man who wants to perish.” The negation that play requires from the player is
possible only if play affirms its reality against the player’s: it is possible only if the submis-
sion to the game being played and to the space that it delimits is totally unconditional. Only
such an unconditional submission, although and precisely because it can only be given by
a mortal being, can be transformed into an affirmation, into an act of “active destruction”,
as Nietzsche says elsewhere. The man who wants to perish, e.g. the true player, wills his
own destruction operated by the play, wants to submit his being to the affirmation of the
play, wants the play against his will. It is precisely at that stage that he will reach the point
where the “negation changes sign, it becomes affirmative power and preliminary condition
for the further deployment of the affirmation.” 24 Altogether different is the behavior of the
“last man” who cannot, in his intrinsic passivity affirm his own negation. The last man is a
bad player because he never participates entirely to the game, he does not understand its
24. Gilles Deleuze, Nietzsche and Philosophy (New York: Columbia UP, 1983) 243.
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mortal seriousness and the dedication that it would require. He conceives it only as an
“playful entertainment that must not be too challenging.” 25 On the contrary, the spirit of the
last metamorphosis, the spirit who wants the advent of play, is the man who wants to perish
and who affirms the willingness to his own destruction by means of his unconditioned, se-
rious, and intrinsically mortal adhesion to the world of play. In that act, he throws the bridge
the reaches beyond man, beyond nihilism and beyond the abyss.
Spiel, then, is not just a paradoxical figure. It is essentially ambiguous, if we follow
Nietzsche, because it is ambiguous— in the literal sense of the of a “road with two direc-
tions”—the status of that extreme phase of nihilism that Spiel stands for.
5. The great beyond
A first result of this short journey through Heidegger’s and Nietzsche’s texts is a pos-
itive, although extremely tentative answer to the first question about the problematic rela-
tionship between play and the end of philosophy. Indeed, there seems to be something quite
similar that comes to light in each case, beyond the different emphasis specific to the single
texts, whenever the concept of play is used. Two different but strictly interrelated aspects
seem to stand out as particularly prominent: motion and closure. On the one hand, the free-
dom of movement that is peculiar to play—and is reflected in its mechanical cognates—is
constantly emerging. The Nietzschean “self-spinning wheel” is in a certain sense the mark
of it, but we see it also in the Hegelian circle, and in the Heideggerian emphasis on play’s
because, on its self-moving character. On the other hand, the rigid self-enclosedness of
game and play comes out as crucial. Play, in itself, assumes the characteristic of a space that
is totally self-contained and cannot admit of anything else outside itself. The “rules of the
game,” from this point of view, mark the impossibility of any opening between the
gamespace (Spielraum) and what lies outside of it. This, however, in spite of the total arbi-
trariness of the rules themselves. Seriousness and playfulness come to play from the same
25. Friedrich Nietzsche, Zarathustra, Preface, 5.

T HE GREAT BEYOND
source, from the severity of arbitrary rules. The connection between the two aspect is not
difficult to see: the free movement is made possible by the closure whose goal, in turn, is
nothing but the free movement itself.
Is this cluster of similarities enough to establish the positive existence of a common
concept at the end of the different paths we have examined? It is certainly not enough to
ascertain an identity, since, as we have seen, differences in accents are far from being ab-
sent—and they may all point to substantially different concepts. There seems to be a certain
latitude in the concept of play, so much so that we might consider it, at least provisionally,
more like a space than a concept, we may take it as an opening in which something happens.
But what happens, precisely? Why do free movement and closure re-emerge in connection
with the end of philosophy and why, furthermore, do they get caught under the name of
“Play”? Moreover, which come first between the properties of play (closure, freedom of
movement, etc.) and play itself? In other words, is the emergence of play that gives prom-
inence to them or is it the opposite?
These questions are undoubtedly premature. The preliminary evidence represented by
previous, brief excursions into the Nietzschean and Heideggerian texts can just lend some
credibility to what is, at this stage, but a suggestive hypothesis, namely the existence of an
unexpectedly wide and deep connection between the search for truth and the realm of Spiel.
Before going a bit deeper into it, and thus reaching a stage where the previous questions
could be addressed, it may be useful to reflect on why such an hypothesis may be sugges-
tive and how it could be more firmly grounded.
First, the truth of the hypothesis would be significant in that it would open up a vast
terrain to be charted, whose exploration may bring answers to a number of very important
questions. The inquiry about the conditions of possibility of philosophy, to say it in a very
Kantian form, would be displaced: the answer to the end of philosophy and, therefore, the
answer to the possibility of the truth of being, variously reinterpreted, would have to be
found through an analysis of the relationshup between Spiel and philosophy. The answer
has to be found elsewhere, and perhaps with different means from philosophy’s own. The
first result would then be a displacement of the question about philosophy, a displacement
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of the locus of the truth about philosophy itself. But since the difference, in philosophy at
least, between method and substance is close to nil, this would entail that such a displace-
ment would bring us very close to finding the solution of philosophy itself. Or, to say it
differently, it would bring us closer the solution, or, perhaps, the dis-solution, of the task
that philosophy set for itself, quite a long time ago. Then the hypothesis is suggestive be-
cause it suggests that an answer (either positive or negative) to philosophy may perhaps be
found, although in a different place than where we have been looking so far.
Moreover, since what would come together in a form still to be satisfactorily articulat-
ed is not just philosophy, but “non-philosophy,” and “non-metaphysics” as well, the breadth
of the terrain the hypothesis implies makes it suggestive as well. For it would allow us to
bring together a number of disparate efforts and to understand not so much their unity
(since there might be none) as their reciprocal interrelations.
To find an inroad toward the paradox of the ends of philosophy joining in play, I will
start from a distinction between two senses of the positive reading of end of philosophy, of
the end of philosophy as achievement, that Heidegger puts forth in the essay The End of
Philosophy and the Task of Thinking. According to Heidegger, one might distinguish be-
tween the two senses of completion (Vollendung) and perfection (Vollkommenheit) in the
Hegelian, positive reading of the end of philosophy. The ground for the distinction lies in
the fact that the completion of metaphysics is the completion of a possibility that was
opened at the dawn of philosophy, e.g. the opening of truth, ratio, etc. as presence, as what
shines and it is given its full presence. However, Heidegger remarks, we may ask about the
opening itself in which that shining, that lighting, takes place. That unquestioned opening
that makes philosophy as metaphysics possible without being questioned, because unques-
tionable, by philosophy itself, by the metaphysics, is what is given as a task for thinking.
The end of philosophy as stepping beyond metaphysics is therefore a questioning of the
place or of the limit in which philosophy takes place.
Thinking, then, receives its task insofar as it assumes its direction from the un/thought
that lies unthought in the completion of philosophy. It might even be that it has to wait for
the completion of philosophy in order to think what has been left unthought in that very

T HE GREAT BEYOND
completion. This is why the two readings of end as completion and as of “failure” may
come together in a common place. The “end“ takes place in that place achieved by the com-
pletion of philosophy by Hegel (according to Heidegger). In other words: it is only when
and if the end as completion takes place, when the circle has achieved itself and reached its
beginning that a different place starts to appear, a space for thinking that is not philosophy
as metaphysics.
The crucial question, then, is to ask what happens at and in that place, in that space
where the end happens. What happens at the end is also, and necessarily, an end and a new
beginning. To put it differently: if the distinction between completion and perfection put
forth by Heidegger has any validity, then the space for thinking as non-metaphysics can
take place only in that difference between the two, in that fissure between completion and
perfection that do not come together in Hegel’s circle. A difference that can become mani-
fest only by reflecting on the structure and shape and inner necessity of that place, of that
end that philosophy reaches.
Thus, to join our previous discussion, it follows that if that end as completion at the
summit of the Hegelian circle assumes the shape of game or play structure, the Heidegge-
rian question can be rephrased in the following forms: What is left unthought in that game
and play? What is the structure of that play? Who plays it? etc. As a consequence, it would
not be surprising to find so much engagement with the concept of play if that concept is
what comes to light at the end and in the end. It would not be surprising because it seems
to follow from what I have been saying so far that play, Spielen, is both ends. Play is a
bridge of sort, or rather an open space, in the sense that by being at the end it would allow
us to understand both the completion of philosophy and to open a space for a non-philos-
ophy. Play becomes crucial because, being the completion (or its structure) brings us back
to the original possibility (to express it in Heidegger’s words). It would take us back to a
beginning that opens the space for a leap beyond.
What I would like to stress here, is that closure and freedom of movement within an
enclosed space bring about the notion of play, but such a notion is meaningful only after
the closure itself—or the end, which is the same—have been reached. Spiel becomes then
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the limit of philosophy in the sense that represents what borders it and what philosophy can
attain if it manages to complete its course.
How do we proceed, then, in the task lying ahead? Three methodologically separate
issues confront us, and although it will be in practice impossible to pursue them separately,
it might useful to discuss them as distinct. Moreover, the discussion will provide the ratio-
nale for the next step this work will undertake.
First, we need to decide what is needed to confirm the hypothesis, e.g. what is needed
in order to establish a multifaceted connection to Spiel. Second, once it were confirmed, we
need to decide what is needed in order to carry out a thourough exploration of the discov-
ered terrain. Third and last, we need to decide where to go in order to pursue the two pre-
vious point and how to handle the concept of Spiel.
Let us begin from the latter point.Two main “fields” need a close investigation: the
non-philosophical tradition that stands in opposition to philosophy and the non-metaphys-
ical tradition that construes itself as in opposition as Western metaphysics. It is more diffi-
cult to tackle non-philosophy than non-metaphysics because while the latter is guided by a
self-conscious opposition, be it grounded or not, to a certain well-established tradition in
philosophy, the former, on the contrary does not, usually, self-comprehend itself as non phi-
losophy. Therefore, even before we can start investigating about the possibility of an es-
sential connection between non-philosophy and Spiel, we must establish, with sufficient
precision, that non-philosophy exists. Therefore, my first task will be to establish the exist-
ence of significant cases of non-philosophy as determinate negation of philosophy in the
“proper” sense. This is what I will do in chapter IV, which will therefore provide the ground
for the establishment of an essential connection with Spiel.
Indeed, although Nietzsche and Heidegger come from the same Continental tradition,
the use of play in connection with the overcoming of philosophy is certainly not limited to
that tradition. Indeed, one of the most extensive uses of “play” concepts come from ‘posi-
tive’ disciplines that are located outside of the philosophical domain but entertain a very
strong relationship with philosophy. Two clear examples are provided by the research on
higher cognitive processes pursued by Artificial Intelligence and by the anthropological ap-

T HE GREAT BEYOND
proach practiced by Claude Lévi-Strauss. It can be shown that, in both cases, what is at
stake is the identification, description (and possibly replication) of the most basic structures
and processes proper to the human being. Moreover, the structure in terms of which they
come to understand and explain their chosen field is derived from the domain of game:
whether problem-solving or worshipping, man is basically seen as participating in a closed,
discrete, combinatorial system of oppositions, of moves and countermoves. The human
subject, whether a master able of getting around in the world by a careful planning of moves
and countermoves or a pawn thrown, malgré lui, in a sempiternal conflict of Kings and
Queens, is always understood from the point of view of play.
The fact that one school chooses the "social" field of activity whether the other one
opts for the more individualistic area of cognition is by itself an interesting topic to be dis-
cussed. But the function of the chosen field within the research projects (e.g. the reason ori-
enting in favor of the actual choice) is actually the same: in both cases what is chosen is
somehow at the core of humanity (of "being human", that is): cognitive processes and prob-
lem solving abilities on the one hand, collective institutions and religious beliefs on the oth-
er. The core issue is readily acknowledged to be philosophical: the mind, the subject,
consciousness, constitute the ultimate topic of interest, not the efficiency of search algo-
rithms or the myths of the Bororo Indians. It is because philosophy has failed to provide an
understanding of the mind, of the human subject, of consciousness and so on, that new sci-
entific disciplines have to be founded to take up the challenge. Philosophy’s dominion is
over, they seem to say, and the time has come for a new approach to the basic issue it had
been struggling with and eventually succumbed to.
What is at stake is very similar to what we have hinted above with reference to Ni-
etzsche and Heidegger: nothing less than the end of philosophy. In fact, the underlying ar-
gument that both AI and Structuralism share might be paraphrased as follows: "If our
method proved so fruitful on mythology, and if the production of myths is the quintessential
human activity setting men apart from other beings, then the method must be applicable to
other, more peripheral, fields of human activity.” This paraphrase can be translated into Ar-
tificial Intelligence’s terms by substituting “thinking” for “mythology” and “production of
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myths”. Herbert Simon’s work is a good example: he recently extended cognitive science’s
concepts and methods to literary criticism in the effort to provide a “solid foundation” to
the latter discipline. Unsurprisingly, one of the results of his analysis is that literary criti-
cism has to be considered a branch of cognitive science.
Accordingly with the plan just sketched, in the next chapter I willprovide an analysis
of non-philosophy and see how the two target disciplines mentioned above fit in that cate-
gory.

CHAPTER III
PHILOSOPHY,
NON-PHILOSOPHY,
AND SCIENCE
in which a new category, non-philosophy, comes to join the familiar
distinction between science and philosophy, and why Artificial Intelligence
and Structuralism belong to it.

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1. Non-Philosophy
There is always something ludicrous in philosophical discourse
when it tries, from the outside, to dictate to others, to tells
them where their truth is and how to find it, or when it boasts of its
alleged capacity to instruct their process with naive positivity; but it
is entitled to explore what might be changed, in its own thought,
through the practice of a knowledge that is foreign to it.
Michel Foucault
In the preceding chapters, I have insisted that philosophy’s goal is Truth, namely the
truth about the world we live in. This, at least, if “philosophy” is interpreted in the sense in
which Hegel, and the tradition up to him, interpreted the word. This, of course, is a rather
rough generalization, but it has its validity nonetheless, as long as the nature of the truth
about the world and the means to provide it are left open. It then applies equally well to the
all-encompassing philosophical effort characteristic of German idealism, where philoso-
phy provides a truth that is essentially intuitive, as well as to the Kantian project, where phi-
losophy establishes the limits of the validity of a truth provided by the sciences, as to the
most skeptical traditions, where philosophy provides a way to clear the grounds from false
claims. In all cases, and regardless of whether philosophy is content-full and synthetic, or
content-less and analytic, it nonetheless represents the only supreme instance that can en-
compass the whole spectrum of knowledge and pronounce on its limit, purposes, utility, va-
lidity etc. for man. As Socrates says in the Euthydemos, for example, seeking knowledge
(e.g. “philosophizing”) is necessary for a happy life and the most supreme knowledge is
provided by the science that grasps the validity and the correct uses of the specific sciences:
“geometers, astronomers, mathematicians (these too are hunters for, in fact, each of them

N ON-PHILOSOPHY
does not build the figures, but retrieve those that exist already) all these do not know how
to use their own crafts, but only know how to hunt and deliver their discoveries to the dia-
lecticians so that the latter can use them...” 1 One of the most important consequences of
such an interpretation concerns the scope of philosophical inquiry. Once it has been decided
that philosophy aims at the truth of the world as such, it follows that it is almost impossible
to delimit a clearly defined domain bounding the scope of the research. Hegel stresses, as
we have seen, that both empirical and formal sciences, on the contrary, have defined do-
mains within which they pursue their research. This is not meant to suggest that the char-
acterization is originally Hegelian. Just the opposite: its spirit (and most of its letter) is
clearly Aristotelian. Let us remember the opening sentences of Metaphysics, Γ: “There is a
science that investigates being as being and the attributes which belong to it in virtue of its
own nature. [...] None of the other sciences considers being as being in general but, after
having delimited a portion of it, investigates the attributes of this part.” 2 Not only such a
distinction goes back to the beginnings of philosophy, but it has also become entrenched in
everyday language. The common use of the word “philosophy” (like in “Apple’s philoso-
phy about the personal computer”) denotes precisely a very general view, an abstract view
that guides practices. However, although the general conception is widely shared across the
history of philosophy, it remains that the particular formulations can be significantly differ-
ent and I prefer to refer my discussion, for the sake of concreteness and precision, to the
specific formulation that it receives in the Hegelian text. Of course, the boundaries of the
domains in questions may be more or less clearly defined—often, it is only when a science
has reached a certain theoretical maturity that its object can be fully specified, since the def-
inition of the domain itself is a relevant part of the scientific effort.
In the Lectures on the History of Philosophy, Hegel exploits this distinction between
“empirical sciences” and philosophy to point out that the former can afford (which doesn’t
mean that they always do, nor that they have to) the luxury to proceed by a progressive ac-
1. See Plato, Euthydemos (282d,290c-d) in Edith Hamilton and Huntington Cairns, eds., The collected
dialogues of Plato (New York: Pantheon Books, 1961), 396, 404. At this level of generality, philosophy
has not changed much from Plato to Hegel.
2. Aristotle’s Metaphysics, Γ 1003, 21-25
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cumulation of results, whereas philosophy cannot. From what he says, it seems as if the
proposed distinction exhausts the space of theoretical possibilities: a science (e.g. Wissen-
schaft) can either have an unlimited domain—and we call this effort “philosophy” in the
fullest meaning of the word—or it can have a well-bounded field of inquiry—in which case
we are confronted with one of the many empirical sciences. 3 The Hegelian distinction be-
tween the different kinds of “objects” pursued by the different sciences has an immediate
impact on their own methods: it is precisely because the domain of the empirical disciplines
is limited that their “empirical methods” have a chance. The scientific method can be used
because it has already been determined, beforehand, where the ultimate source of authority
lies. Namely, in the information collected from the well-delimited field of inquiry (with
whichever method, be it naive or extremely sophisticated. That is irrelevant in this context).
On the contrary, the philosophical sciences are unable to take advantage of such a method,
because there is no single, well-defined field to make appeal to. As a consequence, philos-
ophy is obliged to proceed a priori, with all the problems that follow and that Hegel dis-
cusses in the pages I have tried to explore above.
Hegel’s characterization may prompt two different kinds of responses. One might ac-
cept the distinction and reject, at the same time, the value attached to it. So much the worse
for philosophy, one might say: the irremediable vagueness of its object dooms it to a per-
petually non-scientific status. In the best possible scenario, philosophy can try to open up
3. As explained above, I do not mean to imply that this formulation is originally Hegelian, although I will
refer explicitly only to Hegel in order to keep the argument presented in this chapter within the boundaries
of the general investigations outlined in the first two chapters of this work. Within the horizon of
German Idealism, Fichte’s articulation of the hierarchy between philosophy and the sciecnes is almost
identical to Hegel’s. In Concerning The Concept of Wissenschaftslehre, for example, he says that each
“empirical” (broadly construed) science is constituted by a systematic articulation of propositions descending
from a first principle, i. e. an axiom, in modern terminology. But “how can the certainty of
the first principle itself be established? […]it would take a science to answer these questions: the science
of science as such. “ and he concludes: “The nation which discovered this science would deserve
to call it in its own language, in which case it could be called simply “science” [Wissenschaft] or “Theory
of Scientific Knowledge” [Wissenschaftslehre]. And accordingly, what has previously been called
“philosophy” would be the “science of science as such.” See Johann G. Fichte, “Concerning the Concept
of the Wissenschaftslehre,” Early Philosophical Writings, (Ithaca: Cornell University Press, 1988)
107-108. Similar ideas are expressed by Schelling in the almost contemporary Ideas for a Philosophy
of Nature, not to speak of the Kantian discussion of the topic in the Doctrine of Method of the first
Critique.

N ON-PHILOSOPHY
new fields of inquiry, but it will have to turn over the newly discovered terrains to the spe-
cialized, empirical sciences if there has to be any hope of gaining real knowledge. Philos-
ophy’s task is to play an avant-garde, exploratory role until the heavy troops of science
arrive to consolidate the conquest. This interpretation has become a common sense of sort
in the discussion of the relationship between philosophy and the empirical sciences. Parti-
sans of this interpretation like to point out the progressive detachment of empirical disci-
plines from the main body of philosophical inquiry as a proof of their views. In the English-
speaking world, this interpretation is perhaps best known through the words of William
James, who called philosophy “the residuum of questions still unanswered. “The opposi-
tion between philosophy and the sciences — he wrote at the end of his career in Some prob-
lems of Philosophy— is unjustly founded, for the sciences are themselves branches of the
tree of philosophy. As fast as questions got accurately answered, the answered were called
‘scientific,’ and what men call ‘philosophy’ is but the residuum of questions still unan-
swered.” 4 Thus, the coming of age of physics from a branch of “natural philosophy” to a
fully-fledged, mathematized scientific discipline represents the paradigmatic example of a
development that sees in the progressive (and still incomplete) maturation of psychology
its last instance. Critics of the Western philosophical tradition on both sides of the Atlantic
share this view 5 .
In a somewhat similar vein, someone might accept the Hegelian distinction as the in-
dication that philosophy, if viable at all, needs a radical reform that will give it a badly need-
ed object of inquiry. Thus, for example, one might propose that philosophy can (or has to)
become “applied” in order to survive. In a sense, the “linguistic turn” in analytic philoso-
phy, as well as Wittgenstein’s ruminations about philosophical problems dissolving them-
selves, can be traced back to such an issue.
4. See William James, Some Problems of Philosophy (Cambridge: Harvard University Press, 1979) (Orig
ed. 1911) 12. James, however, is careful not to dismiss, indeed, to defend, metaphysics, e.g. the narrower
meaning of philosophy stripped down of its scientific branches. His “Radical Empiricism” aspire
to be a fully fledged metaphysical system where such issues as the question of being find, if not a
final answer, at least a proper treatment.
5. This view may be pushed as far as claiming that philosophy has actually reached its self-effacing goal
since “all” possible fields have been turned over to the sciences. Jürgen Habermas has suggested this
view over and over again, most notably in The Discourse of Modernity .
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Another variation on the same theme is provided by Heidegger’s meditation on the re-
lationship between science and metaphysics. While not denying the Hegelian distinction,
Heidegger casts it in a new light insofar as he strives to retrieve the essential link between
the two project that unites them beyond their differences. Thus, he claims that the connec-
tion between science and metaphysics is not denied, but rather confirmed, by the abandon-
ment of a-priori procedures in favor of mathematical, scientific methods. In both “The Age
of the World Picture” and “The Essence of Technology” he stresses that the peculiar under-
standing of the real in terms of object and objectivity makes possible mathematical (math-
ematized) sciences. In other words, the relinquishing of traditional metaphysical (e.g. a-
priori) procedures is necessitated by metaphysics itself which sees its transfiguration and
accomplishment in the empirical-mathematical science and its crowning achievement in
cybernetics.
This brief hint suggest that Heidegger’s basic approach to the relationship between em-
pirical science and the tradition of Western philosophy is not very different from the basic
framework I have outlined above. Heidegger assumes the basic Aristotelian criterion and
adds to it a very interesting explanation of the reasons why, temporally speaking, Meta-
physics had to convert into the sciences. In other words, he adds a logical and causal rela-
tionship between the two parts of the basic opposition (namely, science and metaphysics)
and sees a relevant part of the development of Western philosophy as the process of trans-
formation of the former into the latter. A process he judges completed with the emergence
of the “science of control,” e.g. cybernetics. 6 It should be remarked, however that the basic
framework, however enriched, is left unaltered. The difference between the sciences and
metaphysics is still conceptualized in the same way Aristotle (and Hegel) understood it. In-
stead, I would like to argue for a more complex articulation of the basic framework which
6. Martin Heidegger, “The Age of the World Picture,” The Question Concerning Technology and other
essays (New York: Harper and Row, 1977) 118-120 (on the interpretation of the mathematical character
of science on the basis of ta mathemata, e.g. what is already known). See also “The End of Philosophy
and the Task of Thinking,” Basic Writings…, 375-377, on the necessary completion of
philosophy into the sciences and its crowning discipline, cybernetics. Finally, the same theme is picked
up again in “Science and Reflection,” where science it is more precisely thematized as the theory of
the real, and an analysis of the definition is provided, in The Question Concerning Technology and other
essays…, 155-160.

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would do more justice to the richness of certain contemporary theoretical endeavors and
help explain the great excitement they brought about when they burst onto the intellectual
scene.
The basic distinction between science and metaphysics proposed by Aristotle and ex-
ploited by Hegel is binary and exhaustive: there is no third possible position between them.
Instead, I would like to suggest that a third (at least) possibility exists between the two out-
lined. The Hegelian distinction, in fact, is constructed upon a double (and strictly interre-
lated) opposition that concern both the object and the method of the discipline. Thus,
philosophy is “general”, as it were, and “a-priori,” whereas, empirical disciplines, e.g. the
sciences, are “specific” and (consequently), “a-posteriori.” The issue is whether there are
any other possible combination in the 2x2 matrix individuated by this double criterion. The
double opposition can perhaps be summarized in the following table, where the problem-
atic categories are represented by a question-mark:
General
Scope
Specific
Method A priori Philosophy ?
A posteriori ? Empirical Sciences
Is there anything corresponding, re-
spectively, to “a-priori” + “specific”
and “a posteriori” + “general”? The
category identified by “a-priori” +
“specific” is perhaps more familiar. It individuates the specific a-priori principles of a par-
ticular field, or, in a slightly broader construal, the necessary assumptions built-in in any
given scientific discipline. The best known, and philosophically stronger use of this cate-
gory is perhaps represented by the Kantian “Metaphysics of Nature”. According to Kant’s
definition such a Metaphysics—the only one that can possibly reach the dignity of a scien-
tific discipline, according to Kant—contains the basic and highest premises of natural sci-
ences. A similar use of the term “metaphysics”, and one quite directly influenced by the
Kantian framework, can be found in the fairly influential concept of “descriptive metaphys-
ics” proposed by Peter Strawson. “Descriptive metaphysics “is the discipline aiming at a
description of the way we necessarily think about the world, instead of being the effort to
provide the most general description of the world as it is. 7
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By suggesting that the “narrower” (relatively speaking) meaning of the term “meta-
physics” may be more familiar than its dual relative, I by no means intend to suggest that
its use is uninteresting nor that its relationship with the broader and more classical sense of
metaphysics is trivial. Rather, I want to isolate and differentiate this particular effort, as pre-
sented by the philosophical literature, from the other abstractly possible endeavors that the
proposed classification seems to allow. Furthermore, the double classification seems to
gain a certain, initial plausibility and explanatory value by the fact that the categories it in-
dividuates, far from being empty, have instead a rich history behind them. Or so it seems
so far, since the last remaining slot is more difficult to fill: it would designate a theoretical
effort striving to provide an explanation of the “world as such”, without using the typical
“a-priori” procedure characteristic of philosophy. The program of such an “empirical meta-
physics” would seem particularly daunting in light of the strong connection between scope
and method outlined above. The crucial issue is about the method, which is necessarily de-
termined by the scope. Can there be a non a-priori absolute knowledge? A discipline can
be “empirical”, that is, can receive its ultimate directive from the empirical field because it
is limited to and by it, to express the point in a somehow Hegelian language. To put it slight-
ly differently: sciences can be “empirically grounded” because they (have to) disregard the
issue of the constitution of the objects they study. They start from within a horizon of rea-
sonableness that has been set in advance by “common sense”. They stick to the “facts.” And
they can do it because they do not have to worry about what makes a fact. They know where
to go to find an answer to a question, where to find the facts that will disprove or not a the-
ory they propose.
An “empirical philosophy,” on the other hand, would be in the uncomfortable position
of having to find empirical answers without having any pregiven domain to rely upon.
What would be the shape of such a discipline? Would it be just a sum-total of the various
disciplines in a grand unified scheme of things? Or would it come up with an original meth-
7. What Strawson calls, instead, “revisionary metaphysics.” See Peter Strawson, Individuals (London:
Methuen, 1959). A related use of metaphysics in this narrower sense is at work in such analysis of the
most general presuppositions at work in contemporary physics as provided, for example, by Lawrence
Sklar and Adolph Grünbaum.

N ON-PHILOSOPHY
odology which is not “empirical” in the traditional sense, while, at the same time, not being
a-priori? Or, finally, would not it be just philosophy in disguise, that is, good old fashioned
a priori metaphysics?
Instead of assuming that the resulting “non-philosophy” would have to be empirical, I
would like to focus, for lack of the better characterization that will be eventually given be-
low, on the broader, negative characterization: I would assume the category I am looking
for filled if the methodology of the discipline at issue is not a-priori in a precisely deter-
minable way. It remains to be seen whether such a broad and generic characterization can
be turned into a more precise definition. However, instead of trying to provide an answer
to the issue in abstract, let me postpone any discussion about the crucial methodological
issue that such a “non-philosophical” discipline would face and confront a preliminary,
concrete question: do we know of any research programme that aspire to be as comprehen-
sive as philosophy but, at the same time, rejects the characteristic “a priori” procedure prop-
er to the latter? In the next sections I will argue that two major research efforts of these
century fit quite nicely into such a category: Artificial Intelligence and Structuralism. Such
efforts would deserve to be called “non-philosophical” insofar as they would reject one (es-
sential) aspect of philosophy while, at the same time, accepting another essential feature.
This double connection results into a relation between the disciplines in question and tra-
ditional philosophy that it is much stronger than the usual relation between the sciences and
metaphysics. 8 This seems a sufficient basis to go on arguing, as I will do, that both disci-
plines should not be considered “sciences” in the strict sense of the term. But before I turn
to the arguments supporting the claims, I need to explain better what the claim means. In
particular, I need to explain what it does not mean.
8. In the term “non-philosophy,” the negative particle should be interpreted as a Hegelian determinate negation:
it negates some aspect(s) of the concept it is applied to, and it keeps some other, thus establishing,
as a matter of fact, a concrete relationship between the two.
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2. On the various meanings of “X is
not a science”
Before I proceed to a more thorough analysis of Artificial Intelligence’s scope and
methods, I need to clear the ground from a methodological objection that may be immedi-
ately raised. My answer, I hope, will also clarify the scope of my own interest in AI.
By putting Artificial Intelligence at the center of my interests here, I may be accused
of committing a double simplification: first, Artificial Intelligence is usually taken to be
only one components of a broader, and more diversified research program generally known
as Cognitive Science(s) that includes disciplines as diverse as neurophysiology, linguistics,
psychology and philosophy. Thus, I might be accused of taking the part for the whole. My
answer to this objection is that research in Artificial Intelligence is at the core, in a very
strong sense, of the mosaic of disciplines included under the umbrella of Cognitive Sci-
ence: the model of the mind as an information-processing machine essentially analogous to
a (digital) computer is the basic model of Artificial Intelligence and it is such a model that
has been exported to other disciplines. To put it differently: it is not linguistics per se (that
is, in virtue of its topic + methodology + history), nor philosophy per se that grant those
disciplines access to the ”mind’s new science.” Rather, it is, and quite explicitly, linguistics’
(and philosophy’s) willingness to accept AI’s basic model and apply to its field that makes
it a viable candidate for the new discipline. (need: refs to basic texts in AI/Cognitive Sci-
ence research, plus the masters of the field, and in particular Pylyshyn et similar). Thus, I
am quite justified in putting Artificial Intelligence squarely at the center of my analysis. A
second objection may be raised, however: it might be said that I am again, simplifying to
the extreme insofar as I take the central model of AI (information-based processing, etc.)
as the paradigm of Cognitive Science. It is true, one might say, that the aggregation of dis-
ciplines forming Cognitive Science has been built upon AI’s basic model, but not necessar-
ily. There is more to cognitive science that cognitivism (as what I called the basic model is
often called), it is sometimes proclaimed. Francisco Varela has been the most vocal propo-
nent of this view, and his appeals for a broader and richer definition of Cognitive Science

O N THE VARIOUS MEANINGS OF “X IS NOT A SCIENCE”
have emphasized this point. 9 I do not dispute that a different Cognitive Science might be
built upon different hypothesis and assumptions. It remains, as a matter of fact, that actual
Cognitive Science is built upon cognitivism and that cognitivism is best embodied by clas-
sic Artificial Intelligence research (a fact that Varela would readily acknowledge). There-
fore, if the focus of the investigation is put on what Cognitive Science is—and not on what
it should and perhaps will be—there should be no doubts about the legitimacy of my
claims.
Let us now turn to a discussion of the “scientificity” of research conducted in Artificial
Intelligence. The topic is not easy to handle because, in a day and age when the sciences,
and especially the so-called “hard sciences” like physics, are considered the touchstones of
truth and objectivity, to claim that a certain discipline X is not a science can easily be con-
strued as a frontal attack against X’s legitimate status within the intellectual community.
The highly regarded status of science almost automatically assures that any effort to prove
that X is not a science will be interpreted as an effort to ban X from the scientific commu-
nity, to undercut its grants proposals and to take away its graduate students. In other words,
such an effort will be interpreted as a power claim targeting the institutional status of a cer-
tain discipline by means of an attack against its intellectual legitimacy. Moreover, when the
effort at issue here comes from philosophy—a discipline that is “non scientific” by defini-
tion,— one is assured that all his efforts will be dismissed as mere “ideology” in the tech-
nical sense of the word. 10 Workers in the field X will consider the analysis as the result of
a preconceived and preassumed devaluation of their field (“X is not a science” being
enough of derogatory term to assure anyone of what is really at stake); they will conclude
9. See, for example, Francisco Varela, Evan Thompson, and Eleanor Rosch, The embodied mind (Cambridge:
MIT Press, 1991) chap. 3, 37-57.
10. For the sake of precision: most of the times. the term “ideology” is used in the negative sense of “unscientific.”
Technically speaking, however, “ideology” is the strategy that takes a particular set of beliefs,
only partially true or true only with respect to a particular domain, as generally valid because of
the underlying interests of the person or of the group that holds it. It might perhaps be called a case of
(collective) self-deception, if such a term were not so controversial. This use was canonized by Marx
(for example in The Sacred Family) when he criticized contemporary German theories as a largely unconscious
expression of the economic forces at work at the times. It is in this sense that I will be using
the term, and it is in this sense that the philosophical critiques of AI and, respectively, AI’s critique of
cybernetics can be considered “ideological” by the criticized party.
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that the analysis cannot lead anywhere, that it cannot certainly bring about any truth, and
that it is not worth bothering with. John McCarthy, for example, dismisses the three most
famous critiques of Artificial Intelligence provided by Hubert Dreyfus, Joseph Weizen-
baum, and John Searle as “ideological” oppositions, by noting:
AI has some ideological opponents. Some think it impossible in principle,
although none of them has attempted an actual mathematical argument. 11
Similar arguments are employed by Marvin Minsky, although in a different setting. He
goes through several “common sense” objections to the impossibility of truly intelligent
machine (“Humans are creative—computers can only repeat instructions,” or “Computers
can apply pre-given problem solving strategies—humans find new ones,” etc.) and every
time explains that the supposed “critique” is just an expression of ignorance that has been
reified into a presumptive superiority of human beings. For example, on the issue of cre-
ativity, he says:
I do not blame anyone for not being able to explain [creativity]. I do object
to the idea that, just because we can’t explain it now, then no one ever
could imagine how creativity works.
Perhaps our superstitions about creativity serve some other needs, such as
supplying us with heroes with such special qualities that, somehow, our deficiencies
seem more excusable. 12
AI’s complaint about being treated “unfairly” because of ideological presupposition is not
totally ungrounded. A few comments are necessary, though, in order to understand better
what is at stake.
First of all, it should remembered that Artificial Intelligence itself has employed, and
all too successfully, the same strategy in the past. In the early 1960s a major funding war
erupted between two competing paradigms striving to assert themselves as the correct ap-
proach to the computational study of higher cognitive faculties: the older discipline of cy-
11. John McCarthy, “AI Needs a Basic Research Document”, available at URL://sail.stanford.edu/pub/airesearch/basic.html.
See also John McCarthy, “AI Needs more Emphasis on Basic Research,” AI Magazine,
1983.
12. Marvin Minsky, “Why People Think Computers Can’t,” AI Magazine, 3, 4, Fall 1982.

O N THE VARIOUS MEANINGS OF “X IS NOT A SCIENCE”
bernetics and the up and coming Artificial Intelligence. The two fields were basically after
the same public and private funds and a major competitions ensued. In fact, I think that
when John McCarthy points to the lack of a “mathematical argument” against AI he is im-
plicitly referring to the victory reported by AI vs. cybernetics. The fatal blow was repre-
sented by the publication of a study by Marvin Minsky and Seymour Papert, Perceptrons,
in which the authors (two leading figures of the still young Artificial Intelligence) proved
mathematically some intrinsic theoretical limitations of the cybernetic approach. However,
it has been pointed out repeatedly in recent years—after interest in the cybernetic approach
rose again, as the emerging connectionist paradigm revived some of the old intuitions—
that Minsky and Papert strategy had been far more subtle that it was thought. The book
proves mathematically the limitations of a specific subclass of cybernetic devices (so called
one-layer nets) but it actually implies rhetorically, without ever stating so, that the results
may be generalized to the whole class of machines which can be possibly built by following
the cybernetic lead, e.g. to multi-layered machines. 13
The “extra-mathematical” motivations behind the study are well illustrated by Papert
himself in an article published some 20 years later in Daedalus, where he recounts the story
of the struggle between cybernetics and early AI and admits that
Yes, there was some hostility in the energy behind the research reported in
Perceptrons, and there is some degree of annoyance at the way the new
movement has developed; part of our drive came, as we quite plainly acknowledged
in the book, from the fact that funding and research energy
were being dissipated on what still appear to me (since the story of new,
powerful network mechanisms is seriously exaggerated) to be misleading
attempts to use connectionist methods in practical applications. 14
13. See Marvin Minsky and Seymour Papert, Perceptrons (Cambridge, MA: MIT Press, 1967), especially
introduction and last chapter. A critique has been provided by Rumelhart and McClelland «ref. big
work», and Hubert Dreyfus and Stuart Dreyfus, “Making a Mind Versus Modeling the Brain: Artificial
Intelligence at a Branching Point,” in Margaret Boden, (ed.) The Philosophy of Artificial Intelligence
(Oxford: Oxford University Press, 1990). Heinz von Foerster, then a leader of the cybernetic movement,
recalls in a recent interview how the funds effectively dried up after the publication of Perceptrons
and the founding of the AI laboratory, led by Minsky and Papert, at MIT in the early 1960s. See
Stefano Franchi, Güven Güzeldere, and Eric Minch, “Interview with Heinz von Foerster,” Stefano
Franchi and Güven Güzeldere, eds., Constructions of the Mind, Special issue of the Stanford Humanities
Review, 4, 2, 1995, 288-306.
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The strategy at work shows quite clearly, I think, that the use of mathematics is actually
not essential to the implementation or even to the success of the critique. The goal is the
same, regardless of whether formal methods are used: the “scientific” status of a research
program is attacked with the clear intention to move the discipline at stake from the “fund-
able” sciences to the unworthy, un-scientific curiosities that only historian care about.
There is no doubt that certain attacks against Artificial Intelligence from philosophical
quarters have exploited the same strategy. The very first version of Hubert Dreyfus’s well-
known book—titled “Alchemy and Artificial Intelligence”— exhibits on its cover the op-
position hinted above. Dreyfus tries to prove that Artificial Intelligence is as scientific as
alchemy—that is, not very much— whereas it aspires to be (and sells itself as) a science as
“hard” as chemistry. 15 In such cases, both the attacker and the attacked share the value judg-
ment about “science” and struggle, by all means necessary, over whether such a coveted
label should, or should not, be awarded to the discipline. The background giving meaning
to these disputes, therefore, is constituted by the extremely charged opposition between
“science” and “not science.” The opposition is usually reinterpreted, implicitly at least, as
a very generic and ill-defined opposition between “scientific” vs. “unscientific” efforts,
with the usual understanding that whatever is “scientific” is worth pursuing and whatever
is “unscientific” is intellectual garbage in the worst cases and wishful self-deceptive think-
ing at best. “Alchemy” plays its role within this opposition: it represents the serious, but
radically misguided, efforts of generations after generations of self-deceived (and, conse-
quently, powerfully deceiving) researchers that could lead and actually led nowhere but to
an enormous waste of intellectual power and public money. “Chemistry,” on the other hand,
14. Seymour Papert, “One AI or Many?” Daedalus, 117, 1 (1988) 5, emphasis in the text. It should be emphasized
that Papert, in his reconstruction of the era, suggests the picture of two more or less equally
well established research programs (AI and Cybernetics) struggling around scarce resources, when, in
fact, the opposite is true: first, cybernetics was by far the more “solid” research program, since AI was
just at the beginning; and second, research funds were about to deluge the field under the form of military
research grants given by DARPA. It is important to keep these coordinates in mind to gain a better
appreciation of the markedly “rhetorical” character of Perceptrons.
15. Hubert Dreyfus, Alchemy and Artificial Intelligence (Santa Monica, Calif.: Rand Corp, 1965). An expanded
version of this report became What Computers Can’t Do (New York: Harper and Row, 1972).

O N THE VARIOUS MEANINGS OF “X IS NOT A SCIENCE”
represents the paradigm of a well-built and methodologically sound enterprise that will
reap its efforts with well-grounded truths.
Moreover, another powerful opposition plays in the background of this querelle: the
distinction between the “blind” but fruitful proceedings of the sciences—always intent in
accumulating data but never too sure of what they are really doing—and the empty but
nonetheless ever so self-reflective demeanor of philosophy. A consequence of this opposi-
tion (deeply entrenched in our philosophical tradition) is that philosophy, endowed with an
all-encompassing gaze, is capable of licensing patents of respectability to any discipline
since its conceptual analysis can discern whether any given field can live up to its scientific
ambitions. It is no mystery that, nowadays at least, the sciences do not take too well on phi-
losophy’s self-appointed role, especially because of the practical relevance of any judgment
concerning “science” vs. “non-science” in the institutional setting. Debates like those initi-
ated by Dreyfus and Searle can be extremely useful, since they often force the contenders
to make explicit their arguments and to lay bare the deeply seated assumptions of their re-
spective fields. They come with a price, though: often, in their search for powerful argu-
ments against the perceived weaknesses of the opponent they leave less room than it would
be desired for the analytical examination of the adversary. For example, both Dreyfus’s crit-
icism of AI and AI’s criticism of Cybernetics take the form “What X can’t do, and why.”
Dreyfus’s book bears its strategy on its cover, and it would only have been fairer and more
descriptive of the book’s content (although, perhaps, less in the scientific style) if Minsky
and Papert had been similarly titled “What cybernetics can’t do.” By assuming such strat-
egies, however, both works assume as given what is not obvious at all: namely, (a) that the
discipline in question belongs to engineering since it has to do or produce something, and
(b) that its success will be measured by the functionality of its artifacts. One of the goals I
will take up in the next sections is precisely the discussion of such assumptions. In other
words, the question left unaddressed is “To which standards must AI be held up to?”. The
answer depends, in large part, upon the precise location of AI in the theoretical-practical
field. Only if Artificial Intelligence is an engineering discipline must it be judged by the
quality of its productions. Conversely, only if AI is a science must it be judged by the qual-
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ity of its theories, and so forth. Whatever the answer, it is clear that, in an highly ambiguous
case like AI’s, the positioning of the discipline must be decided (logically) prior to the as-
sessment of the output.
It should also be stressed that the way the question has been formulated in the above
paragraph does not preclude that the answer may not be unique. In fact the answer can, in
turn, depend upon the level of the analysis. More generally, the answer to the positioning
question depends necessarily upon the analysis that prompted such a question to be asked.
Thus, the answer I will give must be always be considered together with the general frame-
work which inscribes it: the relationship between science and philosophy presented in the
first section of this chapter.
To be more precise, in the following pages I will try to clarify the position of Artificial
Intelligence (first) and Structuralism (second) within a very specific—and hopefully more
clearly defined—opposition: the above mentioned distinction between science and philos-
ophy that Hegel (following Aristotle) sets up on the basis of their relative scope. No value-
laden distinction between science and non-science is assumed, nor is it implied that science
is more (or less) “scientific” (in the sense of “rigorous”) than its more metaphysical coun-
terpart. The analysis will try to situate two specific disciplines within a sufficiently precise
philosophical framework—namely, the framework provided by classical Western philoso-
phy. Furthermore, the goal is not to grant or deny patents of scientific legitimacy to Artifi-
cial Intelligence or to Structuralism. Rather, the goal is to clarify the relationship with
philosophy, a relationship that both disciplines, in a number of different ways, see as ex-
tremely important to their self-understanding. The ultimate goal, moreover, is to gain clar-
ity about philosophy itself by a confrontation, e.g. non-philosophy, and not to issue licenses
of scientific respectability.
I will provide just a few, preliminary examples to illustrate how the opposition and
confrontation with philosophy has been a constant preoccupation in the founding texts of
the new disciplines. Pioneers of both Artificial Intelligence and various branches of Struc-
turalism are constantly engaged in contrasting their work with what philosophers have done
in the previous two thousands years. At the dawn of the computer revolution, in 1948,

O N THE VARIOUS MEANINGS OF “X IS NOT A SCIENCE”
Warren McCulloch states in clear and unequivocal terms the ambition behind the novel use
that he has in mind for the nascent computer technology. He says:
Even Clark Maxwell, who wanted nothing more than to know the relation
between thoughts and the molecular motions of the brain, cut short his query
with the memorable phrase, “But does not the way to it lie through the very
den of the metaphysician, strewn with the bones of former explorers and abhorred
by every man of science?” Let us peacefully answer the first half of
his question “Yes,” the second half “No,” and proceed serenely. Our adventure
is actually a great heresy. We are about to conceive of the knower as a
computing machine. 16
Similar assertions, although less colorful, can be found a few years later in the early texts
that open the history of Artificial Intelligence proper. Herbert Simon is among the more ac-
tively involved in the confrontation with philosophy, and the pages of The Sciences of the
Artificial where he assign to the new science the study of the “whole man fully equipped
with glands and viscera” are well-known. 17 Joëlle Proust has shown that Newell and Si-
mon’s work can easily be read as an updated form of the transcendental inquiry inaugurated
by Kant. As she writes upon explaining the concept of symbolic system they developed,
Ce n’est donc pas la manière dont un sujet parvient à construire ses
propres représentations qui intéresse l’I.A. [an approach that would make AI
homologous to psychology] mais ce sont le contraintes formelles [and
therefore non-empirical, strictu sensu] qui doivent être satisfaites par un
système symbolique physique pour qu’il puisse accomplir des tâches
exigeant de l’intelligence. De même donc que Kant déplaçait l’axe de la
réflexion de la nature humaine vers le conditions de possibilité d’une
16. Warren McCulloch, “Through the Den of the Metaphysician,” Embodiments of Mind (Cambridge:
MIT Press, 1989) 143. The article contains the (revised) text of a lecture given at the University of
Virginia in October 1948. Such convictions were typical of the cybernetic movement, in all its phases,
although the degree of emphasis tended to vary from researcher to researcher. One of the most vocal,
Heinz von Foerster, came to reproach Artificial Intelligence (and some cyberneticians) for having repudiated
the original vision that animated the first theoretical uses of computers in favor of a narrowly
defined technical research. See Interview…, 298. One of the few (if not the only) analysis of the philosophical
implications of the early cybernetics is provided by Jean-Pierre Dupuy, Aux origines des sciences
cognitives (Paris: La Découverte, 1994).
17. Herbert Simon, The Sciences of the Artificial (Cambridge: MIT Press, 1969) 65.
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science de la nature, d’une mathématique, d’une métaphysique, etc., Newell
et Simon proposent de ne pas tant rester fixé sur l’objectif de modéliser tel
ou tel comportement humain intelligent que de s’attacher à découvrir le
conditions générales, intersystématiques, de l’activité intelligente. 18
Marvin Minsky has even coined a term, “pre-computation philosophy,” to distinguish
the Artificial Intelligence approach from classical philosophy, a term with obvious negative
connotations which forms an integral part of AI’s machine de guerre. “Pre-computation”
philosophy is the investigation of the mind that took place before the advent of AI, which,
it goes by itself, is the only true philosophy worth the name. For example, in an on-line de-
bate that took place on a newsgroup devoted to the discussion of the philosophy of Artificial
Intelligence, Minsky affirmed:
In my view, pre-computation philosophy—both professional and commonsensical—is
so ridden with obsolete “dumbbell” assumptions that none
of us can see very far. To me, the obscurity of subjective experience is a consequence
of each part of the brain's limited access to the other parts. But I
see no reason why it would be impossible for a much larger, more knowledgeable
machine to have much more to say about your (or mine) internal
brain patterns, and to predict and explain all its images, feelings, changes in
dispositions -- yea, unto all its most minute subcognitive ingredients.
Now, you might object that, still, that great human-mind-understanding machine
would be missing something, namely the “actual experience” of being
you, yourself. But to convince me of this, you'll have to say something very
precise and interesting about what it would be missing. I would not consider
it interesting to hear that it's missing “important subjective attributes.” 19
As for the Structuralism championed by Claude Lévi-Strauss, it will be sufficient to
remember the passage in one of the opening chapters of Tristes Tropiques where a confron-
tation between philosophy and structural anthropology is explicitly set up. Lévi-Strauss,
18. Joëlle Proust,
“L’intelligence artificielle comme philosophie,” Le Débat, 47, (1983) 93, my emphasis.
Proust’s article is one of the very few discussions of the relationship between AI and philosophy that
positions the former within the larger philosophical framework of Western philosophy.
19. Marvin Minsky, “Re: Critique of computationalist AI (was Re: Mechanism),” on-line posting, newsgroup
comp.ai.philosophy, Usenet, 8 May 1993. A similar position is defended in The Society of Mind
(New York: Simon and Schuster, 1986).

O N THE VARIOUS MEANINGS OF “X IS NOT A SCIENCE”
who was a philosopher by training, concludes his survey of the various philosophies with
some sharp comments on existentialism, and writes:
The raising of personal preoccupations to the dignity of philosophical
problems is far too likely to lead to a sort of shop-girl metaphysics, which
may be pardonable as a didactic method, but is extremely dangerous if it allows
people to play fast-and-loose with the mission incumbent upon philosophy
until science becomes strong enough to replace it: that is, to
understand being in relationship to itself and not in relationship to myself. 20
In spite of their relative vagueness, these few quotations provide some essential coor-
dinates for the discussion to follow. First, they force a few terminological remarks. In these
texts, the key terms “philosophy” and “science” have a stronger meaning than it is usually
attributed to them in recent discussions of the topic. As the quoted authors make clear,
tends to be a synonym for and my analysis will adopt this
interpretation of the term. In so doing, I will leave aside two other interpretations that are
much more common in contemporary discussions focusing on the “Philosophy of Artificial
Intelligence.” Often, such analysis will use the locution “philosophy of X” to indicate either
an examination of the conceptual foundations of discipline X or an assessment of the inter-
nal (logical, etc.) structure of X. Philosophy, in this context, becomes a quite contentless
tool to be applied to the discipline that does not bring along any new information but just a
more or less sophisticated analytic methodology. 21 In other words, “philosophy” is used in
the sense of special metaphysics discussed above as the “narrower a-priori inquiry.”
The use of the term in the texts at stake here, instead, is quite substan-
tive. So much so, in fact, that it may be generally taken, at least provisionally, as equivalent
to the Aristotelian “science of being as being” mentioned above. This interpretation broad-
ens the scope quite considerably, far beyond certain interpretations of the term as, for ex-
ample, “theory of rationality,” which has been used in other discussions of the relationship
20. Claude Lévi-Strauss, Tristes tropiques (Paris: Plon, 1955); Engl. tr. Tristes Tropiques (New York: Penguin
Books, 1992) 58.
21. This is the sense of “philosophy” at work in most of the essays contained in the popular anthologies
edited by John Haugeland, Mind Design (Cambridge,: MIT Press, 1985) and Margaret Boden, The
Philosophy of Artificial Intelligence…
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between philosophy and AI. Robert Cummins and John Pollock, for example, in the intro-
duction to a volume of essays on philosophy and AI, write: “The articulation of a theory of
rationality is a complicated matter and has been the topic of philosophical investigations in
epistemology, decision theory and practical reasoning literally for centuries.” 22 They
ground the possibility of a fruitful collaboration between the two disciplines in the mutual
interest for such a theory. This interpretation is less formal than the previous one but, still
too narrow to do justice to the specific problems the texts present.
This terminological remark prompts me to emphasize a different, and more substantial
element of my analysis. In identifying AI (and Structuralism) with the term of “non-philos-
ophy” I explicitly want to underline both the similarity and the difference between them and
philosophy, in this extremely broad sense. The negative particle stresses a difference that
can (or does) takes place only within a strong continuity. It is, in other words, a determinate
negation that can take place only because something essentially (historically, at least) be-
longing to philosophy is maintained whereas, at the same time something else (historically
essential to it as well) is denied.
Thus, what is at stake is not the determination of whether Artificial Intelligence has any
“rightful” claim to being a science, whether it is or not conceptually confused or internally
inconsistent. 23 Nor is it a discussion of the fruitful contributions that philosophy can bring
to AI and Structuralism or vice versa. The different question I will try to ask concerns, in-
stead, what is involved in Artificial Intelligence’s conflictual relationship with philosophy.
I will argue that the subject matter of both Artificial Intelligence and Structuralism (more
or less self-consciously) is equivalent to the subject matter of philosophy and that this hap-
pens precisely because of the peculiar relationship of negation that these disciplines enter-
tain with the history of Western metaphysics (or some samples thereof). I cannot, of course,
consider “Western philosophy” in its entirety, nor do I think it is feasible. Such an approach
would probably make impossible any precise delimitation of the thesis to be discussed.
22. Robert Cummins and John Pollock, Philosophy and AI; essays at the interface (Cambridge: MIT
Press, 1991), 4.
23. See John Searle, for an example of a philosopher defending all these three thesis.

O N THE VARIOUS MEANINGS OF “X IS NOT A SCIENCE”
Rather, I will examine the philosophical texts belonging to the Western canon that are
called up, most of the times, from within the Artificial Intelligence field.
I will argue that the relationship between AI and Western philosophy has enabled the
former to carve out a very original space for itself between science and philosophy that
makes it, at the same time, non-philosophy and non-science. This conclusion has a number
of consequences, most of which concern philosophy rather than Artificial Intelligence, that
I will explore in the next chapter. Moreover, I will point out that this original relationship
between science and philosophy necessarily involve a third term: engineering. Indeed, in
order to be non-philosophy (and since it is not a science) Artificial Intelligence’s method-
ology cannot be a-posteriori (empirical) nor a-priori (i.e., in AI’s terms, it cannot take the
form of a “metaphysical,” “arm-chair” philosophizing). Methodological issues become
crucial, in fact, because it is only by avoiding the pitfalls of “empiricism” (which is impos-
sible in principle) and “theoreticism” (which would turn the disciplines into old fashioned
Metaphysics) that Artificial Intelligence and Structuralism can hope to carve out an original
space for themselves. In the case of Artificial Intelligence, the way out of the conundrum
is to resort to the computer as the tool allowing to “synthetize,” that is, to recreate the mind
under investigation. To put it differently, the methodology can escape the a-priori/a-poste-
riori dichotomy by becoming synthetic. This is why the “Artificial” component plays such
a strong and prominent role within the discipline: it is the tool that does the job. It is how-
ever, just a tool used to reach a goal that lies beyond the confines of engineering, insofar as
the final product is not a technological artifact, but rather the replication of the mind.
An analysis of the complex relationship between science and philosophy as instantiat-
ed by AI must therefore examine not two, but three terms—science, philosophy, and engi-
neering—and try to determine how the creative interplay of these three components brings
about the characteristic identity of Artificial Intelligence as non-philosophy.
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3. Between engineering, science, and
philosophy.
The first and provisional definition of Artificial Intelligence provided in popular intro-
ductions to the field usually goes as follows: AI is the research effort directed toward the
construction of intelligent machines. These, in turn, are normally defined as those machines
whose behavior would be considered intelligent if exhibited by humans. Examples of intel-
ligent behaviors are problem-solving activities (like playing games, scheduling deliveries,
etc.), pattern-recognition tasks (and especially its most conspicuous example: vision), lan-
guage understanding, etc. Consequently, among the sub-fields of Artificial Intelligence we
find such areas like: “planning and problem solving”, “automatic deduction”, “vision,”
“learning,” etc. 24 The research is highly technical and requires sophisticated intellectual and
practical tools to be carried out. High-speed digital computers are the hardware of choice,
while sophisticated programming languages, not to speak of non-standard logical notation
systems, are the tools of the trade. Its practitioners have, usually although not always,
strong backgrounds in mathematics or computer science and carry out their research in lab-
oratories usually located within the school of engineering of major universities or in private
labs sponsored by the manufacturing industry. Furthermore, most AI research in the US is
and has been sponsored by a federal agency not precisely known for indulging in philo-
sophical speculations: the Department of Defense. 25 Thus, AI seems to be as far as possible
from any philosophical concern: rather, it looks like a precisely defined discipline within
the broader engineering field.
24. From the table of contents of one of the most widely used textbooks in the field: Avron Barr, Paul Cohen,
and Edward Feigenbaum, eds., Handbook of Artificial Intelligence (Los Altos, CA: Kaufmann,
1982), 3 voll.
25. There are no exhaustive data on the percentage of AI research sponsored by the military through DAR-
PA (Defense Agency etc.). A conservative estimate would probably put the figure at about 70%. See
Tom Athanasiou, “High Tech Politics: The Case Of Artificial Intelligence,” The Socialist Review, 17,
2 (1987) 6-37; Paul Edwards, The Closed aWorld (Cambridge: MIT Press, 1996); and Philip Mirowski,
“When Games Grow Deadly Serious: The Military Influence On The Development Of Game Theory,”
Economics and National Security, C.D.W. Goodwin, ed., (Durham: Duke UP, 1991)

B ETWEEN ENGINEERING, SCIENCE, AND PHILOSOPHY.
To see how the situation may be different we need to take a brief look at some concrete
production of Artificial Intelligence by performing a little thought experiment. We will
imagine a possible interaction with two AI artifacts: the first is CHESS, one of the first
computer programs capable of playing chess, and the second is SHRDLU, one of the most
successful programs able to converse in natural language. 26
CHESS (Simon, Newell)
Imagine having a meeting with CHESS and its designer(s).
You are sitting in a room, in front of computer console,
and the researchers explain to you that they have written a
program that can carry on a real, meaningful game of
chess.
That is, the program can exchange chess moves with you,
follow the rules of chess, and understand what it’s doing.
The interaction with the program is quite simple: you type
your move on the keyboard and the computer answer
with a move of its own.
They invite you to test the truthfulness of their assertions
by playing a game with the computer. You accept, pick
up the black pieces, and the following exchange ensues:
Your commands are shown in this type,
the computer’s replies in this type,
and the researchers’ in this one.
1. P-Q4 N-KB3
2. N-QB3
White prepares to occupy the center with P-K4, but
the text move has the disadvantage of blocking the
Queen’s Bishop pawn, which when advanced to
Queen Bishop Four, controls Queen Five with a
pawn.
2. ... P-Q4
3 Q-Q3
This move does prepare P-K4; However, (1) minor
pieces should generally be developed before the
Queen, (2) the Queen is now subject to early attack
by Black’s minor pieces, and (3) the text move decreases
the mobility of the King’s bishop.
3. ... P-QN3
4. P-K4 B-N2
5. P X P
Best I think. if, for example, (a) 5. P-K5, N-K5 gives
Black strong control of Queen Four and King Five
with a devastating P-QB4 to follow shortly; while
(b) 5. P-B3 leaves White no good squares on which
to develop his King side pieces
.......................
SHRDLU (Winograd)
Imagine having a meeting with SHRDLU and its designer(s).
You are sitting in a room, in front of computer console,
and the researcher(s) explain to you that they have written
a program that can carry on a conversation in English
about a restricted “block-world.”
That is, the program can talk with you, follow the rules of
English, and know what it’s talking about. The interaction
with the program is quite simple: you type your sentence
on the keyboard and the computer answer with a sentence
of its own.
They invite you to test the truthfulness of their assertions
by chatting with the computer. You accept, and the following
exchange ensues:
Your commands are shown in this type,
the computer’s replies in this type,
and the researchers’ in this one.
1. Pick up a big red block
OK
The systems answers “OK” when it carries out a
command. In order to pick up the red block, it had
to clear it off by finding a space for the green one
and moving the green none away.
2. Grasp the pyramid.
I don’t understand which pyramid you
mean
There are three pyramids in the scene, so the program
does nothing.
3. Find a block which is taller than the one you are
holding and put it into the box.
The system has to figure out what is meant by
“one” and “it,” as well as using deduction to decide
which block is holding.
By “it” I assume you mean the block
which is taller than the one I am
holding.
Printed out to keep us informed.
OK
26. The interactions (and the comments provided by the authors) are taken, respectively, from Allen Newell,
J.C, Shaw, and Herbert Simon, “Chess Playing Programs and the Problem of Complexity,” Edward
Feigenbaum and Julian Feldman, (eds.), Computers and Thought (New York: McGraw-Hill, 1963) 66-
67, and Terry Winograd, “A Procedural Model of Language Understanding,” Roger Schank and Kenneth
Colby, eds., Computer Models of Thought and Language (San Francisco: Freeman, 1973) 152-
186.
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The question I would like to ask is: “how do you who have experienced an interaction
with CHESS or SHRDLU relate to your experience?” Or, in other words, “Which kind of
experience do you think you have just had?”
Many answers are possible. For example, you might consider your experience similar
to the one you might have in a car dealership, when the car salesman shows you a new mod-
el of a car, praises its virtues and eventually invites you to take it out for a test drive. That
is, is you just had the experience of interacting with an artifact, tested its functions, related
them to your needs and, finally, assessed your (typically, financial) judgment. In short, you
would consider CHESS and SHRDLU from the point of view of engineering. If this is the
case, then you might fairly ask: are there artifact equivalent to automobiles in sight in the
AI field? Is there anything as reliable, universal, robust, already available, or at least in
sight? And, more importantly, which kind of artifact would that be?
Alternatively, you might consider your experience similar to the one you might have
when observing, from behind a one-way glass, some children playing in an experimental
preschool class. The expert (typically, a psychologist) observes the children working
around a puzzle, or building a tower out of wooden blocks, and explains to you what is be-
hind their actions, why they act the way they act, why they stumble the way they do, etc.
In short, you had a learning experience: you just learned something about the way children
think, build, etc.. If this is the case, you might ask: what do we learn from CHESS and
SHRDLU? In particular, are we learning something about us (e.g. us human being)? If so:
what are we learning, exactly? Are we learning what people actually do (or how people ac-
tually function) when they speak or play chess? (but then it is a machine that play chess and
speaks English. How do we its performance relate to humans?).
Alternatively, you might consider your experience similar to the one you might have
if, for example, you were witnessing Socrates interrogating Ion on the art of playing music.
The expert, a philosopher, interrogates a practitioner about his trade and points out its de-
fining characteristics for the benefit of the observers who learn what it means to play music,
e.g. what is the essence of the musical craft. Similarly, in this occasion you are learning

B ETWEEN ENGINEERING, SCIENCE, AND PHILOSOPHY.
what it means to speak and play chess. What in essence, speaking a language or playing
chess is all about (and, therefore, what it should be when properly performed); in other
words, are we learning what these activities consist in, regardless of whether human per-
formance is always, as a matter of fact, concretely up to the task.
Different answers to this questions have a profoundly different effect, as it should be
apparent, on the status of Artificial Intelligence. The first kind of answer puts AI in the field
of engineering, the second pulls it toward psychology, the third one drives it more and more
in the philosophical field. Moreover, the three questions are not mutually exclusive: after
all, you might have a learning experience in a car dealership as well, if you decide to speak
with the head mechanic instead of the sales manager. Arguably, all eight possible combina-
tions can be (and, presumably, have been) defended on AI’s behalf, although with different
intensity.
More generally, I think these three possible answers can be assumed to constitute the
three poles around which both the self-understanding of Artificial Intelligence and its con-
sideration from the standpoint of outside observers is organized. I will now go through the
three different perspective, one at a time, and will focus on the reasons that speak against
a positioning of AI in that field.
The first reason why the engineering side can be is because of the actual lack of results
when the output of AI research is judged according to industrial standards. In spite of all
the promises that have come out of the field, there is quite a dearth of reliable, industrial
strength AI products on the marketplace. In fact, I think it would be fairly safe to assert that
if we leave aside the tools that people use to write AI programs, the industrial relevance of
AI products is so negligible to be non existent. Moreover, this judgment is now shared by
many workers in the field.
However, this objection to the engineering viability of AI, although quite powerful
from the practical point of view, can be quite easily disposed of in the theoretical realm.
After all, it might be claimed that it is impossible to predict how long it will take to develop
the insights and intuitions that are required to reach the industrial goals.
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This line of defense seems quite reasonable. At least it shows that anyone wishing to
deny industrial respectability to AI bears the burden of a proof. However, the defensive
strategy points to a second, and deeper problem. It might be true that no one can predict
how long it is going to take to reach the crucial insight. But it is of course more than legit-
imate to ask which kind of insights are needed. In other words, it is legitimate to ask, what
is still missing and what should be found in order to be able to build intelligent artifacts.
Although the engineering aspect is clearly crucial to any definition of AI, it is not dif-
ficult to see why the latter cannot be “just” an engineering discipline like, for example, avi-
onics. It is not too difficult to understand what a an airplane is, presumably, and then start
working on how to design and build one. More importantly, even before airplanes actually
existed, it would not have been so difficult to figure out what would count as one, e.g. what
would be considered a successful example of a flying artifact. The issue is not so simple
with “human intelligence”. So much so, in fact, that the discussion of the test proposed by
Alan Turing to determine which behavior would be considered intelligent—discussions of
the test adequacy, shortcomings, etc.—occupies a relevant space in the literature about Ar-
tificial Intelligence. Thus, the study of the behavior—e.g. the clarification of the goal— that
AI allegedly will replicate on a machine takes up a significant fraction of the research ef-
forts. In other words, the engineering effort has to go hand in hand with a theoretical effort
since it calls for an understanding of intelligence that is logically, although not practically,
prior to the construction of the machine that will implement it. 27
The provisional definition given above tends to shift, in the declaration of AI practitio-
ners, to a more inclusive formulation that includes the more theoretical aspect. In a pro-
grammatic document about AI, John McCarthy offers a definition that balances very
elegantly both the practical and the theoretical issue facing AI as an engineering discipline:
27. It might be mentioned, as an aside, that philosophical reflections on and about Artificial Intelligence
carried out in Europe emphasize its engineering aspect much more that its American counterpart. This
is probably due to the institutional framework surrounding the research. In Europe, The study of computers’
hardware and software tends to be performed within the institutional boundaries of “Electronic
or “Electric Engineering” rather than in Computer Science departments, as in the US. As a (partial)
consequence, research in Artificial Intelligence tends also to assume a more practical orientation.

B ETWEEN ENGINEERING, SCIENCE, AND PHILOSOPHY.
The goal of AI is to understand intelligence well enough to make machines
that reach human level intelligence. Achieving this goal probably requires
new ideas and therefore cannot be scheduled. 28
McCarthy’s definition does not seem to take AI too far astray into theoretical space.
After all, it can be argued that every engineering discipline is faced with a similar difficulty
at the moment of its inception: the construction of an internal combustion engine, for ex-
ample, depended and called for quite a bit of basic research in thermodynamics. Still there
is an important difference concerning the reference of “intelligence.” The term is actually
used in a strictly metonymic form in the expression “Artificial Intelligence.” As Turing’s
paper makes clear, the real goal of the research is not “intelligence” per se, but the broader
category of thinking in general. It may be worth remembering that, in spite of its title,
“Computing Machinery and Intelligence” (the paper in which Turing proposed his test)
contains the word “intelligence” only once and in a peripheral section. Instead, its very first
sentence makes clear what is at stake, since Turing opens by saying: “I propose to ask the
question: ‘Can machines think?’” and then goes on to propose its test as a more precise ren-
dering of such a vaguely stated question. 29
This, of course, is nothing new. That Artificial Intelligence studies the “mental” in gen-
eral, the mind as such, is common currency in the field. Philosophers, in particulars, like to
stress this point, but AI practitioners as well are very much aware of the bearings of their
research. Thus, it is not only from the usual critics of AI, like John Searle and Hubert Drey-
fus, that we hear this thesis but also from the leading figures in the discipline like John Mc-
Carthy, Marvin Minsky, Herbert Simon and Allen Newell, etc. 30 What I am stressing here
is the strict connection between the theoretical drive that aims at the study of “thinking”
28. John McCarthy, “AI Needs a Basic Research Document,” available at http://www-formal.stanford.edu/jmc.
29. Alan Turing, “Computing Machinery and Intelligence,” The Philosophy of Artificial Intelligence, Margaret
Boden, ed., (Oxford: Oxford University Press, 1990) 40; the essay was originally published in
1950. The term intelligence occurs toward the end of the paper, in the section devoted to the possibility
and feasibility of a learning machine, when Turing remarks that “by the exercise of intelligence” the
AI researcher should be able to speed up the selection of better and better forms of thinking machines,
i.e. he should be able to accelarate the machine equivalent of the natural evolutionary processes that
has most likely brought about “natural” human intelligence (62). In short, the only use of the word “intelligence”
in the paper means something very different from its use in AI.
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and the engineering goal to implement the results of the research in a human-built artifact.
The relationship between the two goals is at the same time essential to Artificial Intelli-
gence and more problematic than it is usually taken to be. In other words the coexistence
of the two goals poses a problem, a genuinely technical problem that resurfaces constantly
every time the status of the discipline is at stake.
In fact, if AI is a science, at least insofar as it concerns its theoretical side, it is a science
of Thinking, or of thinking processes; even better, it is, or would be the science of cognitive
faculties, the science of cognition, for short. The fact is, there are two disciplines, at least,
claiming to fill the same role of a science of cognition: philosophy and psychology. AI can
be, and has been, seen as a part of psychology, perhaps even as the leading discipline within
psychology. This view is shared by many authors. Margaret Boden, for example proposes
a definition of the field that is markedly different from what we have seen so far:
By “Artificial Intelligence” I therefore mean the use of computer programs
and programming techniques to cast lights on the principles of intelligence
in general and human thought in particular. In other words, I use the
expression as a generic term to cover all machine research that is somehow
relevant to human knowledge and psychology, irrespective of the declared
motivation of the particular programmer involved. 31
It is interesting to see that the practical side of AI, on this view, tend to be relegated to the
status of a tool—perhaps an important tool, maybe even a crucial tool, but a tool nonethe-
less—serving the goal of another, classically established discipline. “To cast lights on the
principle of intelligence in general and human thought in particular” is one of the goals of
psychology, at least if the latter is broadly construed. What sets AI apart, therefore, is just
the “use of computer programs and programming techniques”. In other words, Psychology
30. See for example, the opening pages of John Searle’s “Minds, Brains, and Programs,” The Behavioral
and Brain Sciences, 3, (1980), 417-24. and Dreyfus. Quote again from the Founding fathers, see Simon,
Newell, etc. for example. Note that this is not so obvious in other both institutional and geographic
contexts. Often, the issue is downplayed, for example by Margaret Boden in the introduction to her
anthology Philosophy of Artificial Intelligence (Oxford: Oxford University Press, 1990), whre the
whole problem is dealt with in three sentences, at the expenses of a better understanding of the field,
and especially of its relevance to philosophy.
31. Margaret Boden, Artificial Intelligence and Natural Man (New York: Basic Books, 1977) 5.

B ETWEEN ENGINEERING, SCIENCE, AND PHILOSOPHY.
turns into Artificial Intelligence whenever it uses programs and resorts to “machine re-
search.” The engineering aspect—the fact that Artificial Intelligence practitioners actually
have to “build” something, generally a computer program—becomes almost incidental,
theoretically speaking, since its relevance is confined to methodological issues. Boden be-
ing a professional psychologist, her position may be considered not totally unbiased. Allen
Newell, however, expresses a similar point in a different and subtler form when he says:
AI provides the theoretical infrastructure for the study of human cognition.
[...] Being an infrastructure, AI fills an entire spectrum of specific
roles—from enforcing operational thinking about processes, to a theoretically
neutral language of processing, to metaphors about the kinds of processing
that might occur in the mind. 32
The relationship between the stated scientific goals of psychology and its engineering-
derived methodology brings about important tensions that are well-known to workers in the
field. Three, at least, merit to be mentioned, because their combined effect is to pull Artifi-
cial Intelligence away from both psychology and engineering towards the third, philosoph-
ical pole. One of the consequences of the assumption of AI as an infrastructure for
psychology, is that psychological theories tend to assume the form of a computer program.
That is, the computer program simulating the behavior under investigation—or, alterna-
tively, the program plus the commentary provided by its author—represents a theoretical
explanation of the phenomenon. Thus, a chess playing-program that successfully simulates
the performance of a chess player (or a fragment thereof) is taken to provide a theory of that
performance. In other words, we can understand why a player behaved the way he did and
possibly predict the way he would behave in a specific situation, by looking at the strategy,
structure, searches, etc. implemented by the computer program. The trouble with this posi-
tion is that programs incorporate theoretical and extra-theoretical considerations as well. In
any engineering discipline, the design of an artifact depends crucially (and often exploits)
the characteristics of its “raw material”, regardless of whether it is steel, plastic, or comput-
32. Allen Newell, Unified theories of cognition (Cambridge: Harvard University Press, 1990) 40, my emphasis.
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ing hardware. It is no different in software design: many decisions are forced by the “raw
material” the programmer has to deal with and many design decisions have to be taken in
order to keep the problem tractable, e.g. to make the simulation work. As a consequence, it
becomes difficult to determine what counts as an explanation, i.e. what and where is the
psychological theory. A simple example, to make the problem clear: to keep the complexity
of the problem within the possibilities of the hardware available at the time, some chess
playing programs were forced to play on a 6x6 board, with no bishops, no en passant cap-
tures and no castling allowed. 33 It might be imagined that a chess expert would have serious
objections to the plausibility of the resulting simulation, since the game played differs sub-
stantively, and perhaps radically, from the game of chess.
Newell is well aware of this difficulty and calls it the irrelevant specification problem.
His proposed solution, however, is almost paradoxical since he suggests a unified theory of
cognition where every specification is relevant because the “theory comes closer to speci-
fying all of the details of the simulation, which is to say, all that is needed to make the sim-
ulation run”. 34 This suggestion involves, it seems, that the problem will go away when the
engineering aspect will have taken over completely, that is, when the simulation will be in-
distinguishable from the original. How to determine, however, at which level the similarity
should stop? In particular, how would it be possible, on such a view, to claim that simula-
tions run on computers can exhibits psychological plausibility? Sooner or later, some deci-
sion or other will have to do with a “substratum” that is irrelevant to the subject matter of
psychology: the materiality of the computer will not go away.
This last remark brings me to the second point of tension between AI-engineering and
AI-psychology, a problem that can be seen as the reverse of the first problem. It may be
claimed that AI works in abstracto (e.g. it is not empirical enough) because it does not
study “actual people” in “actual situations” but rather relies on idealized models. As Daniel
Dennett has remarked 35 —and countless texts could be provided from AI’s “founding fa-
thers”—at least part of the work done in Artificial Intelligence must conducted ‘top-down,’
33. Allen Newell, J.C, Shaw, and Herbert Simon, “Chess Playing Programs....,” 47.
34. Allen Newell, Unified theories…, 23.

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since it takes its lead from necessarily simplified models of intelligence in order to proceed
to their implementation as computer programs. This procedure has prompted some scien-
tists to raise the charge of “idealism” against AI—not by chance a philosophical term—be-
cause of its disregard of the empirical data. This remark, and regardless of the truth of the
objection, is extremely telling of the difficulty faced by Artificial Intelligence in its efforts
of scientific self-justification: the constraints imposed by its engineering-like component—
the necessity of keeping models simple so that programs can actually be written—exert a
pressure on the discipline that tends to pull it away from empirical science (psychology)
and move it closer to philosophy, albeit the latter is interpreted, most often, in a derogatory
sense.
The third difficulty is related to the first two as well, and it represent just another side
of the tension between the engineering and the scientific souls of AI. Artificial Intelligence
has often been accused by psychologists of performing “wild generalizations” in order to
keep its “theories” tractable and formalizable. In other words, psychologists of different
specializations and theoretical orientations have objected that even before it reaches the de-
sign phase, an in fact in order to reach it, AI has to abstract, from the outset, from all the
interesting psychological facts. Thus, its models are based on “ideal competencies” that are
so far from the real cases to bear no relevance to them. One of the most trenchant critiques
of this kind has been offered by John Marshall in a review of Marvin Minsky’s The Society
of Mind. 36 Marshall’s strategy is simple: he examines several of the ideas proposed by Min-
sky about memory, perception, etc., and in each instance he quotes the relevant psycholog-
ical literature by pointing out that the issue tackled by Minsky has already been addressed.
With the important difference that the psychological treatment of, say, memory, did in fact
thematize specific problems, extracted specific data, and proposed specific, testable, re-
peatable explanations instead of what he takes to be just vague intuitions on ill-defined sub-
35. Daniel Dennett, “Artificial Intelligence as Philosophy and as Psychology,” Brainstorms (Cambridge:
MIT Press, 1978) 109-126. See also Daniel Dennett, “When Philosophers Encounter Artificial Intelligence,”
Daedalus, 117, 1 (1988) 283-295, for a defense of the engineeristic virtues of AI vs. its alleged
philosophical (in the negative sense) and scientific (in the strong sense) shortcomings.
36. John Marshall, “Close enough for AI?” Journal of Semantics, 5 , 169-173.
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jects. He concludes his review by saying: “Once Bob Dylan had troubles tuning his guitar.
After many tries he concluded: ‘This is close enough for folk music.’ Perhaps The Society
of Mind is close enough for AI.”
Daniel Dennett raises the same point in “Artificial Intelligence as Philosophy and as
Psychology,” and notices that professional psychologists often put together AI and philos-
ophy in their disdain, joining the two fields in the “armchair” category. That is, both AI
practitioners and philosophers alike enjoy indulging in armchair speculations with a “blithe
indifference to the hard-won data of the experimentalist.” 37 The “broad generalizations and
bold extrapolations” of Artificial Intelligence, in other words, betray its essential proximity
to the method of philosophy. The implicit consequence of all this is quite interesting: far
from being the crucial tool that brings an unprecedented degree of rigor to psychology, the
engineering aspect of AI requires an “unscientific” disregard for the gritty details that are
the essence of the experimental method. Engineering pulls AI, as it were, out of the scien-
tific field altogether, and brings it back to philosophy, the un-empirical discipline par ex-
cellence.
Yet, the relationship between AI and philosophy has never been easy. In fact, even the
presumption of similarity between the two fields sound pure blasphemy to most researchers
in the field. In a recent paper, Philip Agre provides a vivid illustration of how deep the anti-
philosophical feelings run (and especially ran) in the AI community. He remembers how,
in his days in graduate school in AI, his fellow students “would convene impromptu two
minutes hate sessions to compare notes on the futility and arrogance of philosophy. ‘They
have had two thousand years and look what they’ve accomplished.’ Now it’s our turn.’” 38
The totally unbridgeable distance was remarked over and over again, and, as Agre remarks,
was often expressed in a difference between “doing” and “Just talking.” Philosophy just
talks about things—as one incredulous student put it to him once he had learned of Agre’s
37. DanielDennett, “Artificial Intelligence as…,” 110.
38. Philip Agre, “The Soul Gained and Lost,” Stanford Humanities Review, 4, 2, 1995, 1. Agre underlines
how the strictly scientific borders of AI have been policed with great fervor. Only “the great old men”
were allowed to talk “about” the field and take trips into other disciplines, and often, if not always, in
different institutional settings.

B ETWEEN ENGINEERING, SCIENCE, AND PHILOSOPHY.
own broader interests—whereas AI “does” something: it proves theorems, writes pro-
grams, builds hardware.
Agre’s anecdote captures the essential of the antagonistic relationship between AI and
philosophy. In fact, its three crucial elements are all contained in the AI’s rebuttal against
philosophy: “They had a two thousand year head start and look what they did with it.” First,
the perceived similarity of intents: philosophy started to work on the same problems and is
presumably still working on them. Second, the necessity to gain a distance: the effort has
been so ineffectual that anyone wishing to advance in the same field has better find a dif-
ferent path toward the goal. Third and last, the recognition of the crucial difference: AI is
going to succeed (or, at any rate, to fare better) because it has the tools to do something in-
stead of wasting time talking over things. It should be emphasized that the emotional over-
tones of the original statement can be toned down without changing the content in any
substantial way. Thus, it may be granted that philosophy has had some good insights, in its
two thousands year of bickering, but was unable to put it to proper use for a lack of proper
methods. This slight rephrasing allows some collaborations between the two fields without
violating their respective autonomies. Artificial Intelligence is allowed to look to philoso-
phy for some raw and fuzzy ideas to turn into neatly polished mathematical form. The big
“head start” may even make some kind of philosophical awareness necessary, as several AI
scientists have claimed in recent years. Similarly, philosophy is encouraged to follow AI’s
lead and switch its methodology to a more precise style of inquiry that would allow for
some experimental testing of its intuitions.There are many examples of such appeals for a
more intensive collaboration between the disciplines and Agre’s own strategy, in fact, falls
within this category. Other appeals for a stricter collaboration between philosophy and AI
have come, for example, from Yoav Shoam, John McCarthy, and Pat Hayes (all from the
AI field) and from Daniel Dennett and Aaron Sloman, among others, from the philosophi-
cal camp. AI workers sometimes go as far as proposing to look at philosophy as “the reser-
voir of problems that AI should be working on,” in Shoam’s words, whereas philosophers,
in general, stress that the “precision” provided by AI is exactly what philosophy needs in
order to make real advances on classical philosophical areas like epistemology, the philos-
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ophy of mind, etc. 39 Instead, Aaron Sloman, whom we take here as representative of a large
class of instances, provides the classical form of this argument: “computer programs pro-
vide the only currently available language for formulating rigorous and testable theories
about such processes [as perceiving, thinking, remembering, etc.] So I conclude that in or-
der to make real advances […] philosophers, like psychologists and linguists, will need to
learn about the developments in the design of computing systems, programming languages
and artificial intelligence models.” 40
Shoam’s and Sloman’s claims make particularly clear, however, that the relationship
between AI and philosophy, is presently quite conflictual, because it is either AI that must
take over from philosophy a set of problems or intuitions and develop them differently, or
it is philosophy that has to radically change its methodology, and in fact turn into AI, in or-
der to achieve real progress. AI is allowed to turn its gaze toward philosophy, only if it
maintains its theoretical distance, unless that distance is vanished by the elimination (or su-
blation?) of philosophy itself in a time to come. In order to understand the sources of the
present conflict between AI and philosophy, therefore, it is important to turn the gaze from
the utopian future to the reality of the present. In other words, it is necessary to consider
these claims in a broader framework and try to determine what can be concluded about AI’s
identity from its conflictual relationship with philosophy.
We must preliminarily acknowledge two related issues, though, to guide the discus-
sion. The first one is methodological and concerns the epistemological status of these
claims: they represent AI’s self-perception and, as such, consist of wishes and self-judg-
ments. It follows that they cannot be taken as true nor dismissed as inescapably biased.
Rather, they represent important clues in any assessment of the relationship between AI and
39. See Yoav Shoam, “Agent-oriented programming,” Artificial Intelligence 60, 1 (1993) 51-92.; John
McCarthy, “What has AI in Common with Philosophy?”, Proceedings of IJCAI ‘95 (Los Altos, CA:
Morgan Kaufman,1995), now available at: http://www-formal.stanford.edu/jmc/,Güzeldere and I have
advocated a similar position in Güven Güzeldere and Stefano Franchi, “Mindless Mechanisms, Mindful
Constructions,” Stefano Franchi and Güven Güzeldere, eds., Constructions of the Mind, Special issue
of the Stanford Humanities Review, 4, 2, 1995, ix-xxxi.
40. Aaron Sloman, The Computer Revolution in Philosophy: Philosophy, Science and Models of Mind,
(Hassocks, Sussex: Harvester Press, 1978) 83; see also Daniel Dennett, Consciousness Explained
(Cambridge: MIT Press, 1993),

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philosophy that must be followed and assessed in their respective merit. The second point
is more substantial: these claims seem to stand in sharp conflict with the objections to AI
that have been raised from the scientific field, and in particular by psychologists and cog-
nitive scientists. The crux of Artificial Intelligence’s relationship with philosophy, in other
words, seems to consist in a clash between AI’s self image and its external perception from
within the scientific field. Psychologists object that work in AI is too unrigorous and vague
to be part of science, and it should be considered part of philosophy instead. AI retorts,
somewhat violently, that it has gained a sufficient theoretical distance from philosophy to
be considered a full-fledged scientific discipline. Thus, the confrontation between AI and
philosophy is mediated by the objections moved from the scientific quarters: if these were
found to be justified, then AI would be pulled, perhaps inexorably, toward philosophy, and
its efforts to carve an autonomous theoretical space doomed to failure. To decide the issue,
then, we need to look again at the content of these scientific objections.
First, we may recognize that the dispute is not over what Artificial Intelligence is
about, over its subject matter. In this respect, the self-perception and the outside gaze are
remarkably in agreement. Rather, the dispute concerns AI’s methods —too un-theoretical
and engineering-like—and approach—too broad and philosophical. Furthermore, it is im-
portant to notice that what is contended is not the substance of the methods and approach,
but rather their scientific value. The method and the approach, however, are precisely what
AI takes to be its characteristic points of pride. In other words, the disagreement is remark-
ably not about what AI is about, nor is it about how it goes about its business, but whether
its engineeristic theoretical gaze is a virtue or a liability. AI sees it as its crucial advantage,
while scientists retort it makes not a science of AI.
The first objection targeted AI’s crucial reliance on computer programs, and denied
that they may have any theoretical dignity. Of course no AI practitioner would deny that AI
depends on programs. More importantly, she would contend that it is precisely by using
programs that her discipline can start doing something and turn philosophy’s idle talking
into concrete, testable results. The second and third objections concerned the abstract and
generalizing approach typical of a discipline that focuses on intelligence in general and tar-
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gets the “mental” as such. AI would not deny this claim, and in fact these are precisely its
points of contact with philosophy that we have seen acknowledged above. The proximity,
and sometimes the direct lineage from philosophy, is explicitly claimed. The two images,
the internal and the external one, then agree and can be summarized perhaps, by saying that
Artificial Intelligence is closer to philosophy than science would like (or, to be more pre-
cise, psychology would like). The crucial issue, for us who are trying to bring to a close this
quest for an AI’s identity, is whether the distance is small enough to turn AI into “just” phi-
losophy. The answer can only be negative and for the same reasons, although reversed, that
made impossible the identification with a science strictu sensu.
The most important reason has to do, once again, with the crucial relationship between
Artificial Intelligence and Engineering, and most specifically with that specific form of en-
gineering called Computer Science. The implementation of insights about human intelli-
gence into computer programs forces the translation of those insights into a mathematical
or semi-mathematical susceptible of a conversion into a computer language. This engi-
neeristic requirement brings about a reliance upon mathematics (or rather upon the lan-
guage of mathematics) that is not only essential to all work done in Artificial Intelligence,
but has become part of the field-self-image as one of its necessary theoretical constituent.
As I stressed above, AI couches its difference from philosophy in terms of doing vs. talking,
and it is precisely the possibility of translating insights about intelligence into a formalized
or semi-formalized language that allows AI to do something, e.g. to write programs and run
them on computers. This relationship brings about a curious situation: AI needs mathemat-
ical formalism in order to formalize theories of intelligence (or of the “mental” in general),
but it is not, however, primarily interested in a mathematical theory of the mind. AI is not
in the business of building a mathematical (or mathematically founded) psychology be-
cause the process of formalization is only a means toward a different goal, namely the im-
plementation of computer programs. This has important consequences: first, mathematics
is seen as a substantially language, and not as a theory; second, the mathematics to be used
is limited to the algebraic-logical formalisms that computers can understand because they
have been designed upon it from the very start. There is very little impetus, from within

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even the most mathematically oriented AI research, to explore other branches of mathemat-
ics, like, for example, theories of the continuum like differential topology which have been
independently proposed, in the psychological arena, as more suitable tools for the job. Phil-
ip Agre puts the point well when he says that
the first priority for AI is to get something working on a computer [and]
AI people see formalization as a trajectory with an endpoint, in which the
vagueness and ambiguity of ordinary language are repaired through mathematical
definition, and they are not greatly concerned with the semantic violence
that might be done to that language in the process of formal
definition. 41 (ib.)
Agre’s point may perhaps be strengthened: it is not so much the reliance upon mathe-
matics that engenders the semantic violence, but the use of a specific mathematical formal-
ism as a tool toward an extra-mathematical goal. It is this characteristic approach that is the
real cause of the violence, because, insofar as the richness of mathematics itself is not, nor
can it be, explored, AI’s theories of the mental are forced into the straitjacket of the logico-
algebraic formalisms that can be used on a computer. Most importantly, once the necessar-
ily limited formalizations have been applied to the originally richer intuitions and the re-
sulting programs have been implemented, the original richness is put aside and all the
attention is focused on the performance, in a broad sense, of the programs themselves. As
Agre rightfully points out, “formalization becomes a highly organized form of social for-
getting—and not only to the semantics of words, but to their historicity as well. This is why
the historical provenance and intellectual developments of AI’s underlying ideas claim so
little interest among the field’s practitioners.” (ib., my emphasis)
Agre’s remark about the necessary impoverishment of humanistic insights brought
about by formalization is perhaps the most important consequence of AI’s original conju-
gation of science, philosophy, and science. Again, the impoverishment is not caused by the
use of mathematics per se, but rather by the peculiar role that a certain form of mathematics
plays within the specific brand of engineering that AI builds upon. 42 Nonetheless, it is the
41. Philip Agre, “The Soul Gained and Lost…,” 16, my emphasis.
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root of the conflict between AI and philosophy that is often couched in the terms of a false
opposition between the unreliable, “messy,” and vague descriptions provided by the latter
against the “precise,” “testable,” and “precise” theories of the former. In other words, the
gap between what philosophy feels as its most proper (be it the notion of consciousness as
Bewußtsein as historically transmitted by the Western “Continental” tradition or the qualia
at the center of the “semantic” discussions in the analytic philosophy of mind) and the ex-
planations provided by AI marks the distance between AI and philosophy, and the former
inadequacy to explain the latter’s phenomena.
In short, AI is a science that seems to be dragged constantly back to philosophy in the
opinion of a good numbers of its adepts and critics. On the other hand, since the “big head
start” enjoyed by philosophy did not help it much toward the resolution of problems con-
cerning the mind. it is clear that some radical difference between the two fields has to be
found. The need for “scientificity” pulls AI away from philosophy—the non-scientific dis-
cipline par excellence— but the efforts to provide a solid foundation of its content brings
it back toward it. As a result, AI finds itself exposed on both fronts: psychologists do not
recognize in its wild generalizations “tested” on biologically and psychologically implau-
sible artifacts anything similar to the hard data won on the field; philosophers, on the other
hand, tend to see in the models proposed by AI a naive reformulation of ideas that pretend
to ignore the centuries-long scrutiny philosophy has submitted them to.
Therefore, Artificial Intelligence cannot be just philosophy because of the use of an en-
gineering-like, empirical methodology that lacks necessity, and requires a necessary sim-
plification of the “subtle” insights provided by the philosophical method. But its content is
42. To put it differently: if it were a mathematical form of psychology, AI would have a very different relationship
with mathematics itself, because then the “gnawing doubts about whether the conceptions
of human life being formalized along the way are sufficiently subtle, accurate or socially responsible,”
in Agre’s words, would not only be allowed, and in fact encouraged and rewarded, at least as reflections
on the best mathematical ways to preserve some extra-mathematical intuition. Mathematization,
in other words, is not, or at least not always, synonymous with formalization, as Jean Petitot has underlined,
for example, in “Unità delle matematiche,” Enciclopedia Einaudi (Torino: Einaudi, 1982)
v15,1034-1085. For a further discussion of the necessary impoverishment caused by formalization and
the necessity to distinguish between formalization and precision, see Brian Cantwell Smith, The Rise
of Objects (Cambridge, MIT Press, 1996).

B ETWEEN ENGINEERING, SCIENCE, AND PHILOSOPHY.
close enough to have inherited philosophy’s assumptions and approach. Close enough, at
least, to make its definition as a science impossible.
The conclusion to be drawn, then, is that everyone is right, although the results may
not necessarily please those who work in AI. The field is too “empirical” (for lack of a bet-
ter term) to be philosophy, but it is too philosophical to be science. This conclusion parallels
what we had concluded in the previous discussions about AI and the other disciplines in
enters in contact with. To put it a bit dramatically, we might say that, in every instance, Ar-
tificial Intelligence is at the same time inside and outside the given field. Thus, it belongs,
essentially, to the field of engineering insofar as it deals with the production of working ar-
tifacts for human consumption. But it is not totally within it because what exactly the arti-
fact are supposed to be or to do is not completely specified. Similarly, it is essentially
similar to psychology insofar as it strives to provide a theoretical explanation of human
cognitive abilities and skills. Yet, it is not psychology because the level at which it ap-
proaches the phenomena is too coarse and the method it uses is not theoretical enough. Fi-
nally, it shares an essential similarity with philosophy insofar as it approaches the “mind”
at the same level of generality; but it falls outside of philosophy’s boundary in its reliance
of an engineering-like methodology.
This conclusion may seem disparaging: I set out to ask whether AI should be consid-
ered engineering, science, or philosophy and I have concluded that it does not belong to any
of those fields. But in fact, the analysis gives us a very positive indication, because it im-
poses a strong requirement on the possible answer to the question. Any satisfactory analysis
of the phenomenon Artificial Intelligence must do justice to its three components and, pos-
sibly, come up with an account explaining (1) why all three are present and (2) what is the
relationship among them that makes it impossible to resolve AI into any of them. It is with
our eyes on this goal that we turn to the next section.
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4. Artificial Intelligence as a nonphilosophical
project
Seen from the inside, i.e. from the standpoint of its practitioners, AI is the discipline
that can finally provide a rigorous, scientific explanation of the most elusive phenomenon
ever to confront scientific progress: mind itself. A popular account of the field, for example,
calls it “the mind’s new science.” 43 Under this common interpretation, AI is the theoretical
effort striving to conquer the last topic still unexplained by Western science and philosophy.
Marvin Minsky, for example, called the “AI problem one of the hardest science has ever
undertaken.” 44 (some “ultimate frontier” rhetoric is far from absent in all popular and not
so popular discussions on the topic).
Once the scientific credentials of AI have been so established, the connection with
Western philosophy is easily built. It takes two seemingly different forms, according to the
intellectual locations of their supporters. Researchers within the field claim that their dis-
cipline is the “negation” of philosophy: AI has transformed the idle, “armchair” specula-
tions of two thousands years of philosophy into a serious, empirically-grounded scientific
effort that will finally unveil the mysteries of the mind. The opposition thus built rests on
two claims: (a) that AI is a science in the traditional sense, and mst importantly, (b) that phi-
losophy’s inquiry into the working of the mind are (or were) a hopelessly misguided (be-
cause a-priori) scientific effort. In a nutshell, this interpretation identifies the object of
traditional philosophy (or most of what goes under this name) as a narrowly construed phe-
nomenal field, e.g. the “mind.” The field could perhaps have been empirically investigated,
given the appropriate intellectual and social conditions, in a proper scientific (e.g. “empir-
ical”) way. Unfortunately, either because of its basic theoretical leanings or because the
times were not yet mature for real science, philosophy decided to use the wrong method-
43. For example by Howard Gardner in his well-known book: The Mind’s New Science: a History of the
Cognitive Revolution (New York: Basic Books, 1985).
44. from an interview contained in Gina Kolata, “How Can Computers Get Common Sense?” Science, 217
(1982).

A RTIFICIAL INTELLIGENCE AS A NON- PHILOSOPHICAL PROJECT
ological approach and resorted to “armchair speculations” that doomed its efforts and kept
the “mind” wrapped in a web of mysteries for two thousands years.
Conversely, philosophers have built a bridge between the contents of the two investi-
gations in terms of one fundamental intuition which would allegedly cross over from West-
ern philosophy into Artificial Intelligence. According to John Haugeland, for example,
contemporary computational inquiries into the realm of mental phenomena are guided by
one basic insight: the basic mental operation is the manipulation of symbols regardless of
their meanings. It so happens that what digital computers do best is precisely to manipulate
symbols in any specifiable manner whatever. As a consequence, artificial intelligence is in-
volved with computers, and technology at large, almost in spite of itself. As he puts it, “con-
temporary computer technology is relevant only for economic reasons: electronic circuits
just happen to be (at the moment) the cheapest way to build flexible symbol manipulating
systems.” 45 Artificial Intelligence is then deemed to be a science, in the narrow, strict mean-
ing of the term, (e.g. not in the sense of Wissenschaft I used in the previous chapter): a sci-
ence of the mind, or of the “mental.”
This interpretation is extremely interesting because, in spite of the big gap it strives to
open between “idle philosophizing” and “serious scientific investigations,” it actually
brings past philosophy and modern science so close that they almost coincide in scope. In
fact, it is easy to see that the core of the dispute is about the methods used, whereas the sub-
ject matter drifts essentially untouched from the Greek dawn of Western thought to present-
day cognitive psychology. The thesis on the relationship between AI and philosophy can
thus be rephrased, in a slightly more technical form, as follows: the content of the two in-
vestigations is considered essentially similar (if not identical), whereas the form is deemed
radically different (empirical vs. a-priori). In short, the “classical interpretation” of AI,
which I have explored in the previous section, can be summed up by saying that Engineer-
45. John Haugeland, Artificial Intelligence. The Very Idea (Cambridge: MIT Press, 1985) 5. The claim
that computers are, essentially, symbol manipulators has not gone unchallenged. The most sustained
attack against this thesis (which is crucial to the understanding of AI as a science just outlined) has
been mounted by Brian Cantwell Smith, The Age of Significance (Cambridge: MIT Press, forthcoming
1998). I will not discuss this here, since my thesis about AI as non-philosophy is largely independent
of it.
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ing (e.g. computer science) is what allows AI to wrench away a topic from philosophy (the
study of the mind) and turn it into the subject matter of a new science. However, since the
use of engineering techniques will only affect the “formal,” i.e. methodological component
of the enterprise, the subject matter for this new science will entirely be provided by phi-
losophy. The relationship between AI and philosophy is thus very simple: same content,
different form. AI can be the negation of philosophy because it keeps the former while re-
jecting the latter. This is the interpretation that we have seen at work in the preceding sec-
tions, when we discussed all the problems that make it, ultimately, unacceptable. Even
leaving aside all those difficulties, it must be underlined that the meaning of this claim var-
ies with the content of philosophy. Only if the latter can be “scientificed,” i.e. if it can be
brought in accord with (possible) scientific practices, can AI claim to be a science.
This is possible by postulating what may perhaps be called the F-Y continuum, a po-
sition best expressed by Daniel Dennet when he says:
One can ask how any finite system how any neuronal network with such
and such physical features could possibly accomplish human color discriminations[…]or
one can ask, with Kant, how anything at all could possibly
experience or know anything at all. Pure epistemology thus viewed, for instance,
is simply the limiting case of the psychologists’ quest. 46
Thus, the spectrum of investigations carried out by philosophers and psychologists can
be viewed as a true continuum, with the two disciplines occupying the opposite ends. If we
follow Dennett’s argument, it may seem as if the spectrum should actually be interpreted
as a field modulating not only the methods of the discipline in questions, but also their con-
tent, i.e the content of the questions they ask. Indeed, at the one end we find the “pure ana-
lyisis of concepts” performed by the philosophers, while at the other end we are confronted
with the empirical investigations carried out by psychologists. However, at a more general
level, according to Dennett, these differences disappear into the homogeneity of an inquiry
into the mode of functioning of the mind. Philosophy and psychology share the same topic
46. Daniel Dennett, “Artificial Intelligence as…,” 111, Dennett’s emphasis.

A RTIFICIAL INTELLIGENCE AS A NON- PHILOSOPHICAL PROJECT
but change in approach from the more general to the more specific: totally top-down for
philosophy, totally bottom-up for psychology, with AI resting somewhere in the middle:
AI can be as abstract and as “unempirical” as philosophy in the questions
uit attempts to answer, but at the same time, it should be as expplicit and as
particularistic in its models as phychology as its best. (113)
In other words, the substratum of the continuum is built on the identity of topic (and
more precisely, identity of a basic intuition), while the differentiation is provided by the dif-
ferent form (i.e the different methods/approaches). Thus, the “abstract” character of re-
search in AI is justified by postulating a higher level of similarity between philosophy and
science itself (under the guises of psychology). It is this similarity that allows AI to share
its content with philosophy without, however, being tainted with the latter’s fruitless “arm-
chair philosophizing.” To put it slightly differently: AI can have the same content of phi-
losophy with a different form because it is science itself that shares with it the same content
with a different form.
But this description is stuill inadequate to render the meaning and scope of Φ−Ψ con-
tinuum situation postulated by Dennett. Indeed, since the difference between philosophy
and psychology is provided by a gradient of “attention to empirical details,” and since such
a concern is, in itself, a (and perhaps the most typical) scientific preoccupation, it follows
that the continuum represents only a differentiation among different ways of doing science,
and not, as Dennett would have it, a bridge betwee science and philosophy. To put it differ-
ently:Dennett can build his bridge between science and philosophy because philosophy has
never been in the picture in the first place, having effectively being reduced to an “abstract”
form of scientific investigation in the traditional sense. We are not confronted, then, with a
difference between science and philosophy along the axis of same content/different form,
but rather with an identity between (abstract) science and (concrete) science where all the
content come from science and there is no philosophy left, either as content or as form.
This fact has some remarkable consequences for the status of Artificial Intelligence.
As I remarked at the end of the previous section, a solution to the question about AI identity
must preserve the distinctive characters of the three fields that we have seen it trodding up-
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on: engineering, philosophy, and science. Any efforts to reduce it to one of these three poles
would fall short of the desired solution, and , in particular, the effort to identify AI with a
straightforward scientific discipline, like psychology, would open the flanks to the usual
charges of “wild speculations,” “armchair philosophizing,” etc. But the postulation of a Φ−
Ψ continuum does precisely that: its reduction of philosophy to science blocks off any pos-
sibility of a reconciliation of the three poles that have to maintained in any efort toward a
correct solution to the problem of AI’s identity. Artificial Intelligence is not (partly) philos-
ophy any longer, since philosophy has disappeared from the picture. It is just a more “ab-
stract” form of science, and therefore open to all the criticisms that scientists, i.e.
psychologists, have moved against it unless it decides to relinquish its psychological and
philosophical claims and rest content with being a sub-field of engineering devoted to the
design of certain classes of software applications. And we have seen how difficult it is to
reconcile Artificial Intelligence, or at least the guidelines provided by its founding fathers,
with either branches of the alternative.
Moreover, the Φ−Ψ continuum hypothesis is extrememly implausible for philosophy it-
self. It is indeed questionable that Kant’s search, no matter how inspiring it may have
proved to psychologists, can be interpreted as an “elevated” form of psychology as Dennett
depicts it, or that, similarly, Descartes’s epistemology can be considered equivalent to a se-
ries of empirical hypothesis, as Haugeland seems to suggests. 47 Indeed, the gesture that re-
duces questions that were, for the mentioned philosophers, first and foremost metaphysical
inquiries into the “truth of being” to semi-abortive scientific investigations, is itself an in-
tegral part of a specific kind of metaphysics. The reduction of the truth of being to the truth
47. I cannot enter into a detailed discussion of Kant’s view of psychology and of the role of epistemology
within Descarte’s metaphysics. However, at least one text from the first Critique should be mentioned,
because it provides the framework of the argument that might be provided in favor of the rejection of
a reductionist interpretetation of Kant’s philosophy along Dennett’s lines. In the Architectonic of Pure
Reason, Kant asks: How are we to regard empirical psychology, which has always claimed its place in
metaphysics? […] I answer that it belongs where the proper (empirical) doctrine of nature belongs,
namely, by the side of applied philosophy, the a priori principles of which are contained in pure philosophy;
it is therefore so far connected with applied philosophy, though not to be confounded with it.
Empirical psychology is thus completely banished from the domain of metaphysics; it is indeed already
excluded by the very idea of the latter science.” See Immanuel Kant, Critique of Pure Reason…,
664 (A848/B876). All emphasis except the last one are Kant’s.

A RTIFICIAL INTELLIGENCE AS A NON- PHILOSOPHICAL PROJECT
of science, in other words, is no less metaphysical than its identification with the word of
God. Thus, the obliteration of the specificity of philosophy that the hypothesis of the Φ−Ψ
continuum performs at its constative level, as it were, is contradicted by its performative
aspects, to borrow Austin’s terminology, since it is overdetermined by a reductionist meta-
physics that contradicts its stated thesis.
What happens, instead, if, following the classical Aristotelian distinction, we keep
open the difference between science and philosophy that I have been insisting upon since
the beginning of this chapter (and of this work)? Artifical Intelligence, we said, can be seen
as a discipline that shares the content with philosophy but adds a different form. The mean-
ing of this claim varies with the scope of “content.” In the classical interpretation, the basic
assumption is that content of philosophy, say of Descartes’s, can be brought over to science
by a suitable change of methods because it is epistemologically equivalent to an scientific
hypothesis on a par with those used in empirical sciences. However, if the subject matter
of philosophy, its content, is more properly understood, as truth in the broadest sense, then
the meaning of the claim that philosophy has the same content as AI changes radically be-
cause, by forbidding any Dennett-like “continuum” between philosophy and psychology,
it forces us to reverse the sense of the relationship betweeen AI and philosophy.
Far from being a scientific reduction of raw ideas provided by philosophy, AI is an
attempt, and cannot be anything but the attempt to provide a metaphysics with non-philo-
sophical means. This, in short, is what it means to have the same content but a different
form. Artificial Intelligence is then a non-philosophy in the technical sense of determinate
negation suggested above: it stands in a determinated opposition to philosophy because it
receives from the former the full scope of its inquiry, but it rejects the philosophical “tac-
tics”, in Dennett’s words, i.e. the a-priori investigations that have always characterized the
philosophical demarche. Engineering techniques, i.e. the implementation of computer pro-
grams, fill up the gap that is thus left open: they are the right tools for the job, so to speak,
since they allow AI to answer its questions synthetically, instead of proceedeing a-priori.
Thus, the crucial relevance of engineering techniques within a generally non-engineering
context that I emphasized above, is explained. The production of artifacts is only second-
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arily relevant to Artificial Intelligence, while the methodological reliance on synthetic
methods in service of “philosophical” goals is all that matters. 48
5. Structuralism and philosophy
“Structuralism” is rather loose term encompassing a wide range of disciplines and an
equally wide range of methodologies spanning different periods and different countries.
Broadly speaking, it may be used to refer to the American school of linguistics that flour-
ished under the influence of Leonard Bloomfield in the years around WWII, but also to the
work in the foundations of mathematics carried out in France by the team of mathemati-
cians collectively known as Bourbaki, 49 not to mention the work in biology and later in psy-
chology of the Swiss Jean Piaget. 50 Its most common denotation, however, it is easier to pin
down: it usually refers to the movement that swept France during the late 1950s and 1960s
in the so-called “sciences humaines.” 51 The “movement”—which, in spite of a few at-
tempts, was never actually a concerted effort—attempted to build a unified methodology
for a broad range of disciplines ranging from psychoanalysis to history exploiting the in-
48. This conclusion about the philosophical status of Artificial Intelligence agrees, although it has proceeded
along very different lines, with the famous diagnosis about Cybernetics pronounced by Heidegger
in the “The End of Philosophy and the Task of Thinking” and elsewhere. In the Der Spiegel
interview, for example, Heidegger claims that, in the modern era, metaphysics will achieve its long
standing goal by dissolving into the sciences, for example into psychology, logic, political science. The
role of philosophy, i.e. the role of an overarching investigation that, similarly to old-fashioned philosophy,
harmonizes the results of the sciences into a global vision, will be taken up, according to Heidegger,
by Cybernetics, the “technological” (i. e. engineeristic) science of control, or the science that
“corresponds to the deternination of man as an acting social being.” The difference here is that Heidegger
stresses the continuity between philosophy and cybernetics by interpreting the latter as as the final
stage of the history of metaphysics, while my interpretation emphasizes, instead, the dis-continuity between
the two. Thus, although I agree with Heidegger on the philosophical assessment of Cybernetics
(or of Artificial Intelligence, since the difference does not really matter in this context) I would need a
Hegelian Aufhebung to bridge the dis-continuity between philosophy and non-philosophy and bring
my interpretation in tune with Heidegger. And I am not sure that such a move would be granted by the
context of this analysis. See Martin Heidegger, “Only A God Can Save Us,” transl. Maria Alter and
John Caputo, The Heidegger Controversy, Richard Wolin, ed., (New York: Columbia University Press,
1991) 107ff. and “The End of Philosophy…,” 376.
49. «ref Bourbaki work»
50. Jean Piaget, Le Structuralisme (Paris: PUF, 1968); Engl. tr. Structuralism (New York: Basic Books,
1970)

S TRUCTURALISM AND PHILOSOPHY
sights provided by the “pilot discipline,” e. g. linguistics. More specifically, it tried to build
on the “structural analysis” of language first provided by the Swiss linguist de Saussure at
the beginning of the century and later developed by the Prague’s school of linguistic under
the leading influence of Prince Nikolai Troubetzkoy and, somewhat later, Roman Jakob-
son. Once thus narrowed, the term “Structuralism” becomes a little more manageable and
can be used to refer to the works of four French theorists who reached their peaks between,
roughly, 1955 and 1975 and worked in four different disciplines: the anthropologist Claude
Lévi-Strauss, the psychoanalyst Jacques Lacan, the literary critique Roland Barthes and the
philosopher Michel Foucault. As any definition, this is controversial, since it may be con-
sidered both too narrow and too broad. On the one hand, only Lévi-Strauss, and to a lesser
degree Lacan, associated himself explicitly with “structuralism,” while Foucault, for exam-
ple, has always refused to be so labeled, although his first books, and especially Les mots
et les choses (1966) was widely, and perhaps justly, considered one of Structuralism’s man-
ifestos and best applications. On the other hand, other figures were also closely linked with
structuralism, for example the semioticians Algirdas J. Greimas and Umberto Eco, as well
as the philosophers Louis Althusser and Gilles Deleuze. 52
In what follows, I will focus on the works of one the four mentioned leading figures:
the anthropologist Claude Lévi-Strauss. Although the relationship between his works and
the general “structuralist” movement are far from absent—and so my analysis could apply
to a broader context—I will remain within the narrower domain of his works since the ex-
ploration of the broader picture would require a totally different enterprise. Therefore, if
from time to time the terms “structuralism” or “structuralist” are used without a further
qualification to narrow their scope, they should be interpreted to apply first and foremost
to the Lévi-Straussian brand of anthropological structuralism.
51. “Sciences humaines has a different, and broader, scope from “Humanities.” It encompasses (or encompassed,
in the years under consideration) the social sciences as well as literary criticism, semiotics,
rhetorics, psychoanalysis, etc. It is also strongly connoted, since it assumes that a “scientific” methodology
will be used in those fields.
52. See Algirdas Greimas, Du sens: Essais semiotiques (Paris: Seuil, 1970) and Du Sens II (Paris: Seuil,
1983), Umberto Eco, Trattato di semiotica generale (Milano: Bompiani, 1975), Louis Althusser and
Etienne Balibar, Lire “le Capital” (Paris: Maspero, 1970-73) Gilles Deleuze and Felix Guattari, L’
Anti-Oedipe (Paris: Seuil, 1972).
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There are several reasons pointing toward the non-philosophical status, in the sense ex-
plained above, of Structuralism. In this section, I will briefly indicate the circumstantial ev-
idence surrounding Lévi-Strauss’s work that seems to suggest that his relationship with
philosophy is very similar to AI’s. I will provide a more detailed discussion, conducted on
the basis of the internal features of the theory proposed by Lévi-Strauss, after the analysis
of the central concept of “structure” will have been carried out in chapter 5. Then, in chapter
6 below, I will follow the thread of Lévi-Strauss debate with the philosopher Paul Ricoeur
to provide a more conclusive assessment of Structuralism’s non-philosophical status. In
this section, I will just indicate the main coordinates of Lévi-Strauss’s confrontation with
philosophy in order to provide the guidelines of the assessment to follow later on.
The preliminary evidence can be found, mainly, in the introductory chapter of Lévi-
Strauss’s autobiographical work, Tristes Tropiques, in the Introduction for a collection of
works by the anthropologist Marcel Mauss that he edited a few years earlier in 1950, and,
finally, in an exchange with the editors of the philosophical journal Cahiers pour l’Anal-
yse—Jacques Derrida and Jean Mosconi—that took place in 1967.
The principal features of this confrontation are very similar to the characteristic traits
of the debate between AI and philosophy: it is a conflict born from an excessive proximity,
from a similarity of intents that makes it difficult to keep the two projects apart in spite of
their alleged incommensurable differences. This feeling of closeness is shared by both
Lévi-Strauss and his fellow opponents. In “The Making of an Anthropologist,” for exam-
ple, Lévi-Strauss recounts how his intellectual apprentissage began with a degree in phi-
losophy at the Sorbonne where he studied with the future leaders of the phenomenological-
existentialist movements: Jean-Paul Sartre, Simone de Beauvoir, Maurice Merleau-Ponty.
However, he is quick to add that he grew quickly bored of the intelletual gymnatics that
philosophy had been reduced to, and that seemed the only sufficient condition for a quick
success in the field. He enjoyed good academic success and was well respected in the philo-
sophical circles—he was, in other words, a “well trained philosopher.” But the secret of his
success, he explains, was based on his mastery of the philosophical art
du calembour qui prend la place de la réflexion; les assonances entre les

S TRUCTURALISM AND PHILOSOPHY
termes, les homophonies et les ambiguït´s fournissant progressivement la
matière de ces coups de théâtre speculatifs à l’ingeniosité desquels se
reconnaissent les bons travaux philosophiques.” 53
We see the first sign of the excessive proximity: his success derived from his being a better
philosopher than the philosophers themselves were. So good, in fact, that he was able—as
a true philosopher would do, we may add—to unmask the pretensions of philosophy and of
the philosophers and to see through their intellectual parlour games. On other hand, how-
ever, the opposition he sets up in the text quoted above, an opposition he will repeat inces-
santly every time he attacks philosophy, is as philosophical as it can be: Lévi-Strauss, in
fact, opposes the true reflection that his discipline will provide to the apparently true, i.e.
doxastic, reflection of the philosophers. In a passage that follows by a few pages the previ-
ous one and that I have already quoted at the beginning of this chapter, the opposition re-
ceives its clearest expression: “the mission incumbent upon philosophy until science
becomes strong enough to replace it [is] to understand being in relationship to itself and not
in relationship to myself.” (57. In short, structural anthropology is different from philoso-
phy not just because it is different, but rather because it is better—because it will succeed
where philosophy failed. This, you will have noticed, is exactly the same position that we
saw Artificial Intelligence holding “against” philosophy. But structuralism, like AI, can be
better than philosophy because it is not so different: it pursues the same goal—i.e. to un-
derstand being as being, or, as Lévi-Strauss puts it, “being in relationship to itself”—with
different means, and of course with the means of science. Commenting upon the Essay on
the Gift by Marcel Mauss, Lévi-Strauss observes that “what happened in that essay , for the
first time in the history of ethnological thinking, was that an effort was made to transcend
empirical observations and to reach deeper realities.” 54 The exaplanation of these deeper
realities, we might add, is what would contitute an explication of “being in relationship to
itself,” i.e. it would contitute a science of being as being, to put in Aristotelian terms.
53. Claude Lévi-Strauss, Tristes tropiques…, 55.
54. Claude Lévi-Strauss, Introduction to the Work of Marcel Mauss (London: Routledge, 1987) 38, my
emphasis. This essay was originally published in 1950 as the introduction to Sociologie et Anthropologie
(Paris: PUF, 1950) a collection of works by Marcel Mauss that included the Essai sur le don.
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Once again, however, the science in name of which structuralism proceeds toward his
non-philosophical ambition is a science to come: it is a future science of anthropology that
aspires to gain its legitimate status alongside the regular natural sciecne but that, nonethe-
less, will have to wait decades, if not more, befire the goal is accomplished. As in the case
of AI and psychology, structuralism takes itself to be scientific, to be, in its case, a social
science. Similarly, however, the social scientists, although they all greatly esteem the ac-
complishments of the upcoming discipline, are quick to point out that structuralism is too
enamored of “grand theories” and “rationalistic generalizations” to really belong with the
empirical sciences. For example, the British anthropologist Edmund Leach, himself an ad-
mirer and sometimes a follower of Lévi-Strauss, had the following comment on Lévi-
Strauss’ first book, The Elementary Structures of Kinship:
This work is of interest to all anthropologists even though its details are
open to the same kind of objections ass before—namely, that Lévi-Strauss
is liable to become so fascinated by the logical perfection of the “systems”
nhe is describing that he disregards the e,mmpirical facts. 55
Similar sentiments are echoed on the opposite side of the Atlantic by Clifford Geertz, when
he says that
in Lévi-Strauss’s work the two faces of anthropology—as a way of going
at the world and as a method of uncovering lawful relations among empirical
facts—are turned in toward one another so as to force a direct confrontation
between them rather than (as it is more common among ethnologists)
out away from one another as to avoid such a confrontation and the inward
stresses that go with it. This accounts both for the power of its work and for
its general appeal. […] But it also accounts for the more intraprofessional
suspicion that what is presented as High Science may really be an ingenious
and somewhat roundabout attempt to defend a metaphysical position, advance
an ideological argument, and serve a moral cause. 56
55. Edmund Leach, Claude Lévi-Strauss (Chicago: University of Chicago Press, 1970) 109. This opposition
between ingenious and potentially fertile ideas that are pushed too far for their own’s sake unless
they are tamed by a robust dose of empiricism, is the constant leitmotiv of Leach’s book, perhaps the
most popular introduction to Lévi-Strauss’s thought in English-speaking countries

S TRUCTURALISM AND PHILOSOPHY
Geertz does not hide that he is of the latter persuasion, since he thinks that more work
“in the field,” i.e. a more robust dose of empiricism, and less “intellectualism,”i.e. less
philosophical pretensions, would suffice “to make any doctrine of man which sees him as
the bearer of changeless truths of reason—an “original logic” proceeding from the “struc-
ture of the mind”—seem merely quaint, an academic curiosity.” (359, my emphasis).
The feeling that Structuralism may be close (and perhaps too close) to a “metaphysical
position”is shared, and mostly accompanied with sympathy, by the philosophers whom
Lévi-Strauss will later deride in Tristes tropiques—the phenomenologists and the existen-
tialists who fought against the “old” metaphysics and for a general renewal of philosophy
in France from the late 1940s. Most of them plauded of Lévi-Strauss’s early works, they
reviewed them favourably on their journals, and then quickly proceeded to an attempt of
annexation of structuralism’s methods and result that was nonetheless careful to point out
the essential limitations of the latter’s method and the ineliminable necessity of a philo-
sophical supervision of the anthropologist’s work. The situation is reversed: if structuralism
was too philosophical for the scientists, it is now too scientific for the philosophers. Again,
this is exactly the opposition that we saw at work when we discussed Artificial Intelligence,
and the argument follow very similar lines. Lévi-Strauss’s work is very close to the philos-
ophers’ own, and his thesis can be readily accepted. Simone de Beauvoir, for example,
while reviewing The Elementary Structures of Kinship, underlines “the agreement between
the descriptions contained in the book with the theses held by the existentialists,” and Mau-
rice Merleau-Ponty, a few years later, will hold that the “results of psychology, sociology,
and anthropology have revealed that traditional philosophy hagd too nartrow a conception
of humanitiy and of rationality. It is therefore necessary to inaugurate a collaboration be-
tween the philosopher and the sociologist so that the former may “broaden reason in order
to make it capable of understanding what in us and in the others preceeds and exceeds rea-
son.” 57 However, Merleau-Ponty, as Sartre before him and Ricoeur, later, is also quick to
underlines that even if the results of structural anthropology (“les descriptions” mentioned
56. Clifford Geertz, “The Cerebral Savage: On the Work of Claude Lévi-Strauss,” The Interpretation of
Cultures (New York: Basic Books, 1973) 346. This essay was originally published in 1967, at the peak
of the Structuralist movement in France.
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by de Beauvoir) are very close to the theses of the philosopher, they should not come too
close, since they would threatens the very possibility of philosophy as such. “only the
philosophical consciousness of intersubjectivity, he adds in the same essay from which we
quoted above, allows us, in the last instance, to understand scientific knowledge. Without
it, the meaning of scientific knowledge will escape indefinitely”(127).
Thus, structuralism receives from philosophers a treatment that is similar, although re-
versed, to the one it gets from social scientists: interesting results but it has better defer to
the philosophers a real understanding of the meaning of its discoveries. The situation, how-
ever, is not symmetric, because what make scientists wary of Lévi-Strauss’s generalizations
toward an understanding of “deeper realities” is his suspicious affinity with philosophy.
However, philosophers are not worried—as one might expect from a symmmetric reversal
of the scientists’ criticism—from an excessive dose of science. Rather, they are worried
that the scientist may be taking himself to be a philosopher, in which case he will necessar-
ily miss the meaning of his results, as Merleau-Ponty stresses. In short, the sour point of
both confrontations is constituted by what may perhaps be called the “philosophical con-
tamination” of Lévi-Strauss’ work. Either structuralism is too philosophical to be scientific,
or it takes itself to be philosophical, when the metaphysical business of understanding
deeper realities should rather be left to the professionals. This excessive proximity with
philosophy, to put it differently, cannot be accepted by the philosophers because structural-
ism refuses to be assimilates and it proves unwilling to defer to philosophy the explanation
of any meaning that may lie hidden in its results. It refuses to do so because, as Lévi-Strauss
proclaims again and again, structuralism business is rather to end philosophy, i.e. to termi-
nate it (since it is the science, presumably, that has become “strong enough to replace it”).
The parallel with the AI case we explored above is apparent. Although Lévi-Strauss never
coined, as Minsky did, a term like “pre-structuralist philosophy,” his position does not seem
that different.
57. See Simone de Beauvoir, Les Temps modernes, (1949); Maurice Merleau-Ponty, Signes (Paris: Gallimard,
1960) 154.

AI, STRUCTURALISM, AND SPIEL
Of course, such an excessive proximity was destined to breed comtempt, under the
guises of a full scale conflict between the philosophers and the anthropologist. The first
scuffles were to happen with Jean-Paul Sartre, who criticized structural anthropology in the
Critique de la raison dialectique, and was harshly rebutted by Lévi-Strauss in the last chap-
ter of La pensée savage. 58 Then, in the early 1960s, came the debate with the hermeneutic
philosopher Paul Ricoeur that was to continue, although mstly indirectly for the rest of the
decade. I will discuss at length this full-scale confrontation with philosophy in chapter 7
below, sicen a full analysis of the key concepts of structuralism is preliminary to any at-
tempt to gain more clarity on the “non-”philosophical status of Lévi-Strauss’ project.
6. AI, Structuralism, and Spiel
In the previous chapter, I argued that a clearer understanding of the relationship be-
tween Spiel and the end of philosophy could possibly be reached if it were possible to find
examples of non-philosophical discipliens whose theoretical articulation depended essen-
tially on the concept of Spiel or some particuular articulation thereof (given the intrinsic
complexity of the latter concept).
After the long trip through Artificial Intelligence and the previous brief excursus on
Structuralism, it should now be clear why, an in which sense, these two theoretical efforts
can be considered as relevant examples of “non-philosophy” (in a sense, however, still to
further specified for what concerns Structuralism). The next two chapter will provide an
analysis of their relationships with the issue of Spiel, and, in particular with the concept of
game that they articulate as a particular instantiation of the much larger Spiel. Chapter IV
will be devoted to show how Artificial Intelligence entertains an essential relationship with
58. The main texts of this debate are Jean-Paul Sartre, Critique de la raison dialectique (Paris: Gallimard,
1959) and “L’anthropologie,” now in Situations IX, (Paris: Gallimard ; Lévi-Strauss response is contained
in La pensée savage (Paris: Plon, 1962) ; Engl. tr. The Savage Mind (Chicago: Chicago UP,
1966) 245-269, plus a few largely implicit references scattered in Tristes Tropiques and in the introduction
and conclusion of Mythologiques.
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game through its key concept of Search-space. Chapter V, instead, will perform a similar
task with respect to structuralism and the concept of structure.

CHAPTER IV
CHESS, GAMES,
AND FLIES
in which it is shown that Artificial Intelligence depends on chess
more than it thinks, and what does that mean.

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C HESS, GAMES, AND FLIES
1. The Drosophila of AI.
I am writing these lines in June 1997, exactly 40 years after Herbert Simon’s prediction
that 10 years of work would be sufficient to build a computer program that “would routine-
ly beat the world’s best players.” Although it has taken 4 times longer than predicted, it is
fresh news that Deep Blue, a machine developed by IBM, has finally beaten the chess world
champion, Garry Kasparov, in a much publicized event. Simon’s prediction has come true.
Does this mean that AI has finally achieved its goal? Not quite, in fact, not the least because
Deep Blue is not an example of Artificial Intelligence: it uses rather conventional (from
AI’s perspective) programming techniques and gains its strength from the speed of its hard-
ware. In fact, Stephen Coles, when predicting the eventual success of Deep Blue, comment-
ed: “[Simon] will not be happy with the method by which his dream was accomplished—
machinomorphic brute force rather than a stepping stone to a universal set of principles
about human thought processes that would help us scale up to a broader class of intellectu-
ally interesting grand challenges.” 1 Paradoxically enough, we might even say that the suc-
cess of Deep Blue and its non-AI techniques marks the failure rather than the success of
Artificial Intelligence. But how did it happen that the sorts of AI came to be tied to the ex-
ploits of a chess-playing machine? Is it a rather accidental event, as AI researcher have al-
ways claimed, or does it point to a deeper connection? In this chapter, I will address these
questions by providing a conceptual reconstruction of the history of Artificial Intelligence’s
1. L. Stephen Coles, “Computer Chess: The Drosophila of AI,” AI Expert, 9, 4 (April 1994) 30.

T HE DROSOPHILA OF AI.
involvement with games. In other words, I will provide an analysis of the complex web of
interaction between AI and other disciplines—and especially game-theory—that led to the
development of the few crucial concepts that were to become the cornerstones of the re-
search in the field: search-space, move, strategy, heuristics.
In the first decade of Artificial Intelligence—roughly from the late 1950s to the
1960s—substantial work went into the development of programs devoted to play games
and solve puzzles. Chess was a favorite topic, although it was not the only game to receive
the researchers’ attention. One of the brightest successes of early AI was a checkers playing
program devised by A. L. Samuel at the IBM Laboratories, while efforts went also into the
development of programs capable of solving cryptarithmetic puzzles, the Hanoi tower puz-
zle, and other “mathematical recreations.” 2 The reasons behind such an interest in games
may seem, at first, to be purely accidental. Games, or at least a certain kind of games, pro-
vided clearly defined test cases on which the strength of the theories and techniques under-
2. On checkers see A. L. Samuel, “Some Studies on Machine Learning using the Game of Checkers, The
IBM Journal of Research and Development, 3, July 1959, 211-229, later in E. Feigenbaum and Feldman
Computers and thought (San Francisco: McGraw Hill, 1963) 71-105. Interest in checkers has recently
been revived by the exploits of a team based at the University of Alberta, Canada, whose
program, Chinook, is the first world Human-Machine champion (i.e. it won the title in a tournament
open to both “human and non-human forms of intelligence”)
The literature on computer chess is immense. For a brief synopsis on the history of checkers playing
programs, see L. Stephen Coles, “Computer Chess: The Drosophila of AI….” The first studies on
chess-playing machine were done by Turing and Shannon, who provided the basic framework, later
substantially enriched by Herbert Simon, who wrote the first actually running program in 1955 (with
Allen Newell, and Cliff Shaw), first at the Rand Corporation and later at Carnegie Mellon; see Allen
Newell, J.C Shaw, and Herbert Simon, “Chess-Playing Programs and the Problem of Complexity,” The
IBM Journal of Research and Development, 2, October 1958, 320-335, also in E. Feigenbaum and
Feldman Computers and Thought..., 39-70. Computer chess has now become almost a sub-discipline
of computer science, with its specialized journal, conferences, etc., although it does not enjoy any
longer the “exemplary status” that was its own. For a brief history of the development see Allen Newell
and Herbert Simon, Human Problem Solving (Englewood Cliffs, NJ: Prentice Hall, 1970) «add chap.
ref», and David E. Welsh, Computer chess (Dubuque, Iowa: W.C. Brown Publishers, 1984); for a recent
assessment of the possible evolution of the field see Mikhail Donskoy and Jonathan Schaeffer,
“Perspectives on falling from grace,” T. Anthony Marsland and Jonathan Schaeffer, eds., Chess, Computers,
and Cognition, (Berlin: Springer-Verlag, 1990), and Herbert Simon and Jonathan Schaeffer,
“The Game of Chess,” Handbook of Game-Theory with Economic Applications, Robert J. Aumann and
Sergiu Hart, eds., (Amsterdam: Elsevier Science Publishers, 1992) vol. 1, 1-17. The Hanoi tower gathered
attention only later: in 1958 Simon learned of its use in experimental psychology and started to
work on it, with Allen Newell, to test heuristic search capabilities of their early programs. See Herbert
Simon, Models of my life (New York: Basic Books, 1991).
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C HESS, GAMES, AND FLIES
lying the computer programs could be easily tested and in some cases even measured by
the strength of the playing program. But the character of the relationship was one-sided: no
specific features of the games could be part of the theories and techniques themselves.
Chess, however, enjoyed a particular status, and it gathered more attention than all the other
games put together. The game attracted the researchers’ attention well before the Artificial
Intelligence paradigm, in the 1940s, when it was routinely used by John von Neumann in
his lectures on Game Theory. 3 In fact, it is after hearing a lecture from von Neumann on
chess at the RAND Corporation in 1952, that Herbert Simon started working on what was to
become the very first program in Artificial Intelligence. The interest in chess increased con-
sistently in the following years and work on chess quickly became so overwhelmingly pop-
ular in the first phase of Artificial Intelligence’s history that its role as a theoretically neutral
test case for theories of thinking in general started to be questioned rather often.
In particular, the highly structured, logical environment provided by chess was not al-
ways accepted as a standard task to measure the presumably general theories provided by
Artificial Intelligence. 4 The rhetorical weapon used against many of these critiques was to
identify chess as AI’s Drosophila, with reference to the fruit-fly whose fast reproductive
cycle made it into a favorite test bed for genetic theories for almost a century. Herbert Si-
mon, one of those most responsible for chess’s popularity, used the analogy widely since
the early 1960s, when AI’s interest in chess was still at its peak. He reports that he used it
routinely in the question and answer sessions after his talks, to defend the study of chess
and other games as a worthwhile research-project. 5
I intend to explore this relationship a bit more deeply, although most likely along dif-
ferent lines from the classic objections Simon and Newell were responding to with their
3. Robert J. Leonard in “Creating a Context for Game Theory,” Toward a History of Game Theory, Annual
Supplement to Volume 24 of History of Political Economy, Roy Weintraub, ed., (Durham: Duke
UP, 1992) 51 reproduces, from the von Neumann’s manuscripts archives in Princeton, the outline of a
series of three lectures that von Neumann gave in Seattle 1940 (before the publication of the book). It
recites: “1. The general problem. The case of Chess. 2. The notion of the “best Strategy.” 3 Problems
in games of three or more players.”.
4. See for example, the rather elaborate defense of chess as a research tool contained in Allen Newell and
Herbert Simon, Human Problem Solving …, in the chapter devoted to the topic.

T HE DROSOPHILA OF AI.
analogy. 6 The goal is to find out whether chess, and other games, just happened to present
favorable features allowing to test AI programs or whether there has been any kind of back-
ward influence from the characteristics of chess to AI’s theories. In the latter case, of
course, the relevance of game for AI research would take a wholly different meaning, as-
cending from the role of a classically interpreted instrument to a more substantially theo-
retical component. In other words, I will try to find out whether there is something more
essential, besides and beyond the accidental, in the encounter between AI and chess. More-
over, if this turns out to be the case, it must be determined which kind of influence it might
have been, and how it influenced not only the research in Artificial Intelligence, but also
the understanding of games that is at the center of my interests.
The effort does not entail that my analysis will rely upon a clear cut theoretical distinc-
tion between tools and theories that has been extensively, and convincingly, challenged in
the last 15 years. It entails, however, that the distinction was (and still is, for the most part)
clear-cut in the self-perception of the involved scientists. It is precisely in this sense that AI
researchers like Simon wanted to exploit the Drosophila analogy: as a rhetorical weapon
that, by demoting chess to the role of a theoretically neutral tool chosen for its standard and
objective features, saves the seriousness of the theory used to explain chess-competence.
Therefore, we are fully allowed to assume a distinction that was internal to the field under
investigation as a starting point toward a more comprehensive analysis of the concepts, the-
ories, and tools at work. In other words, the distinction may prove to be as untenable as the
5. For example in Herbert Simon, Models of My Life…, 327, and in several other places. In a private communication,
Simon reported that he is not sure whether he or Allen Newell actually coined the analogy.
According to John McCarthy (personal communication), the analogy itself might have been first proposed
by Alexander Kronrod, then the head of the group that wrote the Soviet chess program at the
Institute of Theoretical and Experimental Physics in Moscow in 1965-68. Kronrod, however, might
have gotten it from Herbert Simon, as McCarthy acknowledges.
6. Objections tended to distribute in different classes depending on the period. Arguments from classic,
optimizing-oriented game-theory directed operation research against heuristic methods, especially at
the beginning «see HPS for ref, and current work in game-theory»; charges of reductionism—chess
are too structured, logical, (“hard”) to provide a good example of standard thinking skills—came later
from cybernetics and the anti-symbolic school in general, most recently from Rodney’s Brooks group
at MIT «ref»; More technical, AI-internal critique of problem-solving activities vs. other tasks as the
legitimate focus of AI, prevailed in the late 60s in the debate that opposed the so-called “scruffy” vs.
“clean” AI.
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works of Latour and Woolgar, Fujimura, and others have shown. The exploration of the
consequences of this fact in the specific case of AI is precisely what is as stake in what fol-
lows. 7
I will start by taking a closer look at the complex relationship theory/tool involved in
the Drosophila case, the bearer of the Artificial Intelligence’s analogy. Since AI’s case, as
I will argue, is even more epistemologically complicated, it will be useful to start from a
simpler occurrence of the same relationship. In a recent, comprehensive study, Robert
Kohler argues that the relationship between genetic theory and the experimental equipment
used to advance it (e.g. the fruit fly) has to be understood as a mutually reinforcing loop
that acted in both directions. 8 The interaction between genetics and Drosophila can best be
understood as a process represented by a diagram (something Kohler does not use) of the
following sort:
Genetics
Breeder
reactor
Drosophila
Three main components make up the picture: genetics, as a discipline with its theories,
practitioners, tools, etc.; Drosophila, as a living being with its biological, genetic, and so-
cial features; and, most importantly, what Kohler calls the “breeder reactor,” namely the ca-
pability of Drosophila plus genetics’ manipulations to turn out an ever increasing number
of mutants. It is this last element that, although made possible by other two, operates as the
7. See for example Bruno Latour and Steve Woolgar, Laboratory Life: the Construction of Scientific
Facts (Princeton: Princeton UP, 1986);Joan Fujimura, Crafting Science (Cambridge: Harvard UP,
1996); Joan Fujimura and Adele Clarke, eds., The Right Tools for the Job: At Work in Twentieth Century
Life Sciences (Princeton: Princeton UP, 1992).
8. Robert Kohler, Lords of the fly (Chicago: Chicago UP, 1994).

T HE DROSOPHILA OF AI.
engine of the whole process by propelling it back and forth between the two other compo-
nents. In fact, the most characteristic feature of the Drosophila/Genetics interaction is that
there is more than one passage in each direction: rather, it is a continuously operating, pos-
itive-feedback circle that alters substantially its members each time it goes through a half-
revolution. In other words, the relationship is a complex process that produces not only a
theory (the genetic theory of the chromosome) as its outcome, but also a new experimental
object (the “standard” fly) as well as a new way of doing genetics (the large scale, mass-
production, quantitative experiments devised in the “fly room” at Columbia). But let us
proceed one step at the time.
The interaction started somewhat causally. At the beginning, as Kohler shows, the in-
troduction of Drosophila in Thomas Hunt Morgans’s laboratory at Columbia was quite ca-
sual, and most likely not determined by theoretical reasons. Rather, it was the nice fit
between Drosophila’s life-cycle and robustness, on the one hand, and the growing need to
provide hands-on laboratory experience to unskilled undergraduate students living on a 9
months schedule, on the other, that was largely responsible for the insect’s promotion in the
lab.
Drosophila started to assume a more central role when Morgan himself began some
work on experimental evolution by trying to induce variations through intensive inbreeding
and selection among large populations of flies. For a while, the experiments were inconclu-
sive, until some mutants, among which was the famous white eye-color mutant, came up,
rather unexpectedly, in the summer of 1910. Two interesting events followed. First, when
it became clear that the causes of the mutations were to be found in scaled-up production
and not in spontaneous, environment-induced evolution, Morgan’s experimental work on
Drosophila shifted substantially from experimental evolution to hereditary genetics. What
we see, in short, is how the unexpected results forced a redirection of the theoretical interest
in the scientist’s practice. The second event is even more interesting. The appearance and
complex mechanics of mutant combinations (white, vermilion, peach eye-colors, etc.) was
at first accounted for in terms of classic neo-Mendelian formulas: that is, by postulating the
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existence of dominant and recessive traits in particular genes, and by explaining the appear-
ance of visible mutants by their combinations.
However, very soon the Drosophila colonies started to work all too well for the neo-
Mendelian paradigm. Unlike Gregor Mendel’s famous green/yellow peas or Cuénot’s
brown/white/yellow coated mice, Morgan’s fruit flies did not stabilize into a few diverse
variations of the same morphological element. New mutants continued to come up and each
new eye-color (for example) implied that the Mendelian formulas had to be rewritten. Since
the formulas explained the visible characters as an exhaustive combination of basic genes
(later traits), each unexpected mutation sent the geneticists back to the drawing board. 9 This
fact (plus other facts, I am simplifying here) directed Morgan’s group away from neo-Men-
delian explanations toward a different, and more stable, theory of hereditary variation, e.g.
the theory of the gene, and toward the postulation of crossing-over and linkage mechanisms
during chromosome splitting. In turn, the shift from one theory to the other forced another
change in experimental work: neo-Mendelian searches for possible variations were aban-
doned in favor of the technique of genetic mapping that permitted a more stable, quantita-
tive account of mutations capable of almost indefinite expansion (60).
This shift, however, forced a change in the relationship between the insect, the theo-
rists’ and the theory, that now affected directly the fruit fly. In order to obtain the precise
quantitative mapping that the new theory required, the Drosophila stocks had to be liberat-
ed from all the “genetic noise” generated by other kinds of genes naturally occurring in wild
fruit flies. As Kohler puts it, in order to be turned into “a standard experimental instrument
[...] every new type of genetic noise—lethals, suppressors, modifiers—had to be identified
and eliminated, one by one. Drosophila, so to speak, had to be debugged.” 10 The history of
the interaction between genetic theory and Drosophila does not stop here. Kohler shows,
for example, how the standard form of the “constructed” insect that was essential to the suc-
cess of the precise, quantitative genetic mapping turned into a major liability when scien-
9. Kohler, for example, reports Morgan’s desperation when, after having reworked the Mendelian formula
for the third time in two years of intensive labor, yet another eye-color mutant popped up unexpectedly.
See Morgan and Bridges’ s report quoted in Robert Kohler, Lords of the Fly…, 60-61.
10. Robert Kohler, Lords of the Fly…, 66.

T HE DROSOPHILA OF AI.
tists belonging to the fly group tried to expand their research in hereditary genetics toward
the genetics of development and evolution, where the relationship between environment
and naturally occurring variations became the focus of the analysis. However, I think the
point of the Drosophila example is by now sufficiently clear.
Four points should be retained from the biological analogy. First, there is more than
one passage in each directions, since the interaction itself is a complex process that is con-
stantly retroacting upon itself. Second, and perhaps more importantly, each passage sub-
stantially alters at least some relevant aspects of one of the members of the relationship. For
example, the “standard fly,” an animal painstakingly constructed in the lab throughout a
minute debugging of its genetic material, is a different animal from the original fruit fly that
entered it. Third, the engine propelling the relationship to move back and forth is constitut-
ed by Drosophila’s unexpected capability to generate an ever increasing number of mutants
when undergoing the intense, large-scale inbreeding and selection procedures devised by
the scientists, what Kohler calls the Drosophila’s breeder-reactor autocatalytic features.
Last, but not least, the output of the whole process should not be forgotten: the theory of
the gene. In fact, the theory can best be understood as the object emerging, at the epistemo-
logical level, out of the positive-feedback interaction between geneticists and Drosophila
that the insect’s fantastic (and induced) mutational capacities animated.
The similarities with the introduction of the study of chess into Artificial Intelligence,
as we will see, are remarkable. What makes AI/chess’s case more complex, however, is
that, at the beginning of the process, the two terms of the relationship are far less stable than
their corresponding biological counterparts. Genetics was working along some well stabi-
lized lines at the dawn of this century: the Darwinian framework plus the great amount of
work in heredity that came out of the rediscovery of the Mendelian paradigm. The revolu-
tion the fly group started, in other word, took place within a well-established tradition. On
the contrary, the difficulties intrinsically inherent in the definition of its topic, which I have
explored earlier, made Artificial Intelligence far less stable than genetics. Moreover, and as
importantly, Artificial Intelligent was born at the same time as, and virtually because of, the
interaction with chess. Suffice here to remember that Herbert Simon and Allen Newell be-
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gan working on chess around 1952 at the RAND Corporation and traveled to the founding
event of Artificial Intelligence, the 1956 Dartmouth summer seminar, well armed with
ideas, and first results. Claude Shannon, himself one of the four organizers of the seminar,
is responsible for the first introduction of chess into computer science, although from a dif-
ferent perspective than Simon’s and Newell’s.
Even more uncertain is the position of chess. In spite of all the changes it would un-
dergo, Drosophila, after all, entered the scientific arena with a well-understood ontological
status and at a well-defined epistemological level. No theoretical reasons set Drosophila
apart from other living beings. It was a living being, but not a “special” living being, like a
virus, for example, whose “borderline” zoological status may bias the experiments in a spe-
cific direction. Second, Drosophila is inconspicuously simpler, or more convenient to
study, than other beings. Whatever the Drosophila does not have in terms of internal func-
tional organization, or does have (reproductive speed, for example) must be theoretically
irrelevant, lest biological research wastes its time on a simplistic case instead of focusing
its energy on a methodologically simpler object. This second point, in turn, entails that the
“object” Drosophila must be sufficiently well understood, at least in principle, in order to
tear apart its “general biological characteristics” from its “particular drosophiliac” features,
so to speak.
Chess does not enjoy the advantages of its flying companion. First, even if we restrict
the topic of AI to intelligent “behavior,” it is not so obvious that playing games is an exem-
plary case of it. Second, it is not granted that chess is a relevant example of ludic activities
in general (I have dwelt on this point at length in chap. II above). Even worse, a case might
be mounted that playing chess is a particularly extreme version of playing in general, mak-
ing therefore chess more like a “virus” than like a “Drosophila.” Third, it is not even grant-
ed what chess is (because we do not know, broadly speaking, what game/play is)—whereas
there are little doubts as to what a fruit fly, genetically speaking, consists of. Thus, the task
of pulling apart the “generally cognitive” characteristics of chess from its “particularly lu-
dic” ones becomes especially thorny. Fourth, and last, once the proper understanding of
chess is provided, it must be explained what makes it simpler, and why the simplicity is not

G AME THEORETIC GAMES
reductive. The effort focusing on chess as a relevant example of intelligent behavior must
start by defining a certain view on the game that selects some relevant features and declares
them as relevant, or by assuming which features of chess are relevant and which are not.
Yet, the outcomes of the AI/chess process are at least as clean and polished as the the-
ories and tools produced by the biologist. This entails not only that the process is more elab-
orated, since the distance traveled is greater. More importantly, it entails that the dynamic
interaction between Artificial Intelligence and chess produces theories that redefine, and
substantially, their very objects. In other words, the product of the process is as much a the-
ory of thinking as it is a powerful conceptualization of Artificial Intelligence and of chess.
And, by extension, of games.
It is precisely for this reason that I am interested in the relationship between Artificial
Intelligence and chess. First, because, as we seen above, Artificial Intelligence can be in-
terpreted as a special kind of scientific metaphysics, or “non-philosophy,” as I have called
it. And second, because the “non-philosophical” effort comes to its realization through an
essential link with the concept of game. More importantly, the research in Artificial Intel-
ligence, not only uses the concept of game, but, in virtue of the loop it establishes with it,
comes to a conceptualization of it. In other words, it does not just pick up a pre-given intu-
ition of play/game (that is, Spiel, in my terminology), but tries to capture it in a precise con-
cept on the basis on one of its components, namely the game element. An analysis of the
concept provided by AI will therefore help us quite a bit in our efforts to elucidate the rea-
sons underlying the connections between the end of philosophy and play.
2. Game theoretic games
Let us examine how the interaction got started. Games were brought onto the scientific
limelight by John von Neumann, who provided the basic framework for a mathematical
concept of game and proved some important mathematical results about solvability. 11 Von
Neumann, however, was interested in a different use of games: he wanted to use them as
the basis for a model providing a basic mathematical understanding of the kind of behavior
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occurring in social interactions like economic transactions and strategic confrontations be-
tween social groups. Although he used insights from actual gaming practices—especially
from games with less than perfect information, like poker—his work had little to do with
psychology and individual cognitive capabilities. 12 It was instead a rather classical example
of the applied mathematics he had been pursuing all his life: he used mathematical tech-
niques to turn a potentially useful but imprecise concept into a powerful analytical tool.
Chess, it turns out, presents a rather uninteresting case for classical game theory, since
it rather easily proved that it admits of a solution. Rather, they play an important heuristic
function, being one the favorite examples von Neumann and Morgenstern use to illustrate
their definitions of games in general. Since these definitions will provide the framework
for any conceptual understanding of chess in Artificial Intelligence and beyond, it is impor-
tant to review them, although briefly.
The basic concepts of game theory—game, play, move, strategy and solution— are de-
fined by von Neumann and Morgenstern in a single page of their work. The concept of
game is rather counterintuitive: they distinguish
between the abstract concept of a game and the individual plays of that
game. The game is simply the totality of the rules which describe it. Every
particular instance at which the game is played—in a particular way—from
beginning to end, is a play. (49, their italics.)
11. The history of game theory is actually richer, and it includes, at least, the contributions by the French
mathematicians Emile Borel in the 1920s and 1930s. Borel provided the first clear definition of pure
and mixed strategies and proved the minimax theorem for some limiting cases. However, it is John
(then Johann) von Neumann who proved the general form of the theorem in 1928, while still at Göttingen.Unfortunately,
the historical literature on game theory is not that abundant. A detailed reconstruction
of a immediate context preceding and following the publication of von Neumann and
Morgestern’s major work in 1944 is provided by Robert J Leonard in “Creating a Context…,” 29-76.
See also Émile Borel, “La théorie du jeu et les équations intégrales à noyau symétrique gauche,”
Comptes Rendus de l’Académie des Sciences, 173 (1921) 1304-1308; “Sur les jeux où interviennent
l’hasard et l’habilité des jouers,” Elements de la théorie des probabilités, (Paris: Librairie Scientifique,
1924).
12. In fact, it has been argued that von Neumann and Morgenstern emphasis on strategy vs. Moves in Theory
of Games, and their shift away from minimax interpretation was precisely an attempt to move away
from the psychological dimension generating the “circularity of the ‘I think he thinks that I think’ logic
of strategically interdependent situations”; Andrew Schotter, “Oskar Morgenstern’s Contribution to
the Development of the Theory of Games,” Roy Weintraub (ed.), Toward a History…, 106.

G AME THEORETIC GAMES
There are two important elements to underline. First, in everyday language, “game” tends
to oscillates between a narrow meaning in which it denotes just the particular instance at
which the game is played—we might say, for example, “a game of chess”, “it was a life
and death game,” etc.—and, on the other hand, a broad meaning in which it denotes the
whole complex range of phenomena—the context, so to speak—within which the specific
event takes place. Most often, it is not easy to decide exactly how broad is the context
picked out by “game” in the latter sense.
For example, is or is not the history of chess part of the game of chess? Certainly not
to many casual chess players. But any player who goes as far into the game as to read an
introductory book of chess technique is immediately confronted with “internal” history
even in the most technical contexts. Openings, for example, are discussed according to their
current viability, or their popularity in the past. Even the basic concepts of the game are
very often presented in a historical context. For example, the sometimes subtle difference
between attack and defense is often presented by comparing the flamboyant style so popu-
lar a century ago with the elaborate, calculated defenses that are now prevailing. Given that
many chess players have reached this very elementary level of sophistication, it is probably
fair to say that the concept of “game” can be taken to be at least this broad. Or consider the
following comment, made by a journalist reporting on one of the final matches of the 1996
world championship between Karpov and Kamsky while trying to explain how they came
to a bizarre endgame:
A typical excessively hypermodern situation arose after 15… Nd8: there
was no contact between the warring armies and there was just one open file.
It had the look of an extravaganza by Richard Reti from the 1920’s. 13
Thus, at one of the spectrum we have the narrow concept most economically represented
by the score of a game published in a newspaper, or a book. Such a description is a game
of chess in the sense that it seems perfectly legitimate to call it that way. At the other end,
we may have a description as complex as that provided by the Japanese writer Kawabata
13. Robert Byrne, “Karpov Adjourns Play in a Drawish Endgame,” The New York Times, Tuesday, July 9,
1996, B2.
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for a very similar intellectual pastime, the game of go. 14 Kawabata—at the time a journal-
ist—provides what anthropologists would call a “thick” description of the Japanese go
championship that encompasses the whole gamut of experiences evoked by and enshrined
into the event, from a technical analysis of the game itself (with go scores, diagrams, and
all), to the generational clash between the defendant and the young challenger, to the dif-
ferent styles of play throughout the centuries, to the role of go in Japan’s social and eco-
nomic life. It is fair to say that one of the goals of the book is to describe, through the
magnifying lenses of a single event, the game of go.
The point here is not to decide which of the two meanings of “game” is more adequate,
since both, of course, are. The point is that von Neumann and Morgenstern’s definition does
not fall anywhere in the continuum spanned by the common uses of “game.”
Instead, they chose the narrow construal and went up one logical level. To say that
“game” is the “totality of the rules which describe it” means that a game is a set of abstract
possibilities describing the possible ways, in fact all the possible ways, in which the game
can be played, if the attention is focused on the rules only. To put it differently, game, as
they define it, is an abstraction from a concretely given event, that cannot correspond to any
possible concrete event because it belongs to a different logical level. 15 This is a very im-
portant step that has to be kept in mind, especially because it will have some important re-
percussion on the following evolution of game-related concepts with their roots in game
theory, like AI’s and Structuralism’s.
stern,
A second related point concerns the concept of rule. For von Neumann and Morgen-
the rules of game […] are absolute commands. If they are ever infringed
then the whole transaction by definition ceases to be the game described by
those rules. (ib., my emphasis.)
As a first approximation, this is obviously true: any willful violation of the rules puts the
14. Yasunari Kawabata, The Master of Go (New York: Knopf, 1972).
15. Of course, it is not the concept itself that belongs to a higher level but the very object that the concept
denotes.

G AME THEORETIC GAMES
player outside the game and, in most occasions, effectively brings it to an end. If I were to
start moving my rook as a bishop, I would quite effectively be putting an end to the game
of chess I might have been playing, unless my opponent were to follow me and do the same.
However, von Neumann and Morgenstern do not directly allow this possibility. Since the
game is just the rules that describe it, and since the rules are absolute commands, it follows
that any change in the rules will correspond to a different game.
But this is seldom the case. Should we say that the game of chess before the universal
adoption of the rule governing the en passant capture by pawn is a totally different game,
as the theory would require, from the game of chess after the adoption of the rule? Even in
the most formal, “intellectual” games, many rules are the results of negotiations between
the players, either at the individual or at the social level. 16 Often, moreover, the negotiation
involves the most basic rules of the game, as anyone who has ever observed children play-
ing simulation games will witness. 17 In game theory, instead, rules are essentially static and
possess no latitude. Even more static, however, are the definitions of move and strategy.
A move, quite intuitively, is
the occasion of a choice between various alternatives, to be made either
by one of the players or by some device subject to chance, under conditions
precisely prescribed by the rules of the games. (ib.)
Less intuitive is the crucial concept of strategy that is built on top of move. Von Neumann
16. Alan Aycock, “Derrida/Fort-da: deconstructing play”, in Postmodern Culture, v.3, n.2, January 1993,
contains one of the few anthropological analysis of chess that examines the concrete event of chess
playing and offers a very different perspective on rules perfect closure, etc. See also «ref to Aycock’s
Play and Culture’papers» for additional data on the multiplicity of chess scenarios (tournament play,
Blitzkrieg games, etc.) and the different conventions enforced by the players in the different occasions.
More general critiques of the conception of rule outlined above can be found in the present debate on
Artificial Intelligence, its ambitions and shortcomings. See for example H.M. Collins, Artificial Experts,
Social Knowledge and Intelligent Machines (Cambridge: MIT Press, 1990).
17. Note that this extremely static interpretation of the rules by von Neumann and Morgenstern is often
attributed to an excessive reliance of their theory on real games, whereas they should have paid more
attention, it is argued, to the economic behavior that the theory allegedly models. See, for example,
Philip Mirowsky “What Were von Neumann And Morgenstern Trying To Accomplish?” Toward A History
Of Game…, 141. In other words, “mere games” like chess have fixed rules, whereas “real games”
like war are subject to continuous negotiations. Instead, I think it will be progressively clearer that, if
a criticism can be raised, is that they did not pay enough attention to “mere games.”
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and Morgenstern imagine that players may form a plan about their behavior in a game by
deciding, beforehand, which alternative they will choose for each set of alternatives pre-
sented by each move. They call such a plan a strategy. As they observe,
if we require each player to start the game with a complete plan of this
kind, i.e. with a strategy, we by no means restrict his freedom of action. […]
This is because the strategy is supposed to specify every particular decision
only as a function of just that particular amount of actual information which
would be available for this purpose in an actual play (79, my emphasis).
What is peculiar about the definition of strategy, is that the concept of move, with its intrin-
sically related temporal aspect, disappears, at least for any practical purpose. In fact, since
a strategy has to be formed before the player begins to play, and since a strategy is the con-
junction of all the choices that the player will make, it follows, trivially, that the whole
course of action has to be planned beforehand. This conception of strategy differs some-
what from the usual meaning of the term: it is not a general rule of behavior that the player
chooses at the beginning as a general maxim to guide him through the actual mechanisms
of the actual game, when it will be tailored to the specific circumstances. Thus, “take con-
trol of the center” is considered to be a good strategic rule in chess, but its concrete realiza-
tion is not given in advance. Instead, the formulation of a game-theoretic strategy requires
that all possible games must have been plotted in advance in order to select the advanta-
geous from the disadvantageous behaviors. There is no game-theoretic strategy that pre-
scribes to “take control of the center;” rather, there is a set of strategies that describe the
sequence of moves that actually occupy the center. In other words, the concept of strategy
is intrinsically linked to the idea of game as a set including all possible games. It follows
that, in order to choose a strategy, all possible games must have been devised even if the
player is to play a single game. To put it differently, the games as described by von Neu-
mann’s and Morgenstern’s theory are purely static, since the dynamic element of the inter-
action provided by the actual exchange of moves has to be planned before the interaction
starts.

G AME THEORETIC GAMES
The typical graphical representation of a game present in Game Theory and Economic
Behavior will make this point clear. Consider the children’s game of “Matching Pennies.”
In this game, the two players agree that one will be “even” and the other will be “odd.” Each
one then shows a penny. The pennies are shown simultaneously, and each player may show
either a head or a tail. If both show the same side, then “even” wins the penny from “odd;”
if they show different sides, “odd” wins the penny from “even. It would be natural to try to
analyze this game by proceeding as follows: “let’s imagine that ‘even’ plays Tails, then if
‘odd’ plays ‘tails’, ‘even’ wins, otherwise ‘odd’ wins.’ And similarly or the other case.
Let’s denote with +1 a win by ‘even’ and -1 a win by ‘odd’“. 18 This may bring to the fol-
lowing tree-like representation, in which each level stands for a move, in order to capture
the dynamic aspect:
Instead, the standard game-theoretic description is a matrix where each row represents
one player’s strategy (not move) and each column stands for the other’s, with each single
cell representing the final result:
Show Heads Show Tails + 1 Show Heads Show Tails
+ 1
Show Heads Show Tails
- 1
Even Strategy 1
Odd
“show heads”
Strategy 1
“show heads”
Strategy 2
“show tails”
+ 1 - 1
- 1 + 1
Strategy 2
“show tails”
18. This is actually von Neumann and Morgenstern first example of a matrix representation of a game in
normalized form, see John von Neumann and Oskar Morgenstern, The Theory of Games and Economic
Behavior (Princeton: Princeton UP, 1944) 94,111. Hereafter referred to as TGEB.
- 1
+ 1
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The matrix representation is usually called the “normal” or “normalized” form of a
game, as opposed to the “extensive” form (e.g. the tree-like representation). The latter was
actually first devised by Tucker some ten years after the publication of Theory of Games.
Notice that I am not accusing von Neumann and Morgenstern of having used a some-
how “wrong” representation. That would not only be silly, but also plainly wrong, from the
point of view of game theory. In fact, many of the sophisticated distinctions and concepts
provided by the theory (dominant strategy, zero-sum, equilibrium, etc.), are immediately
evident when the game is represented in normal form and rather obscure in the extensive
form. The point here is to show the relationship between game-theory and chess (as an in-
stance of a large class of games) and how the former basic concepts make the latter quite
irrelevant. In this context, moreover, the issue is not that the matrix does not permit to ex-
press the complete game of chess; the tree-like one does not either, since in both case we
would have to do with immensely large objects. The point is that the normalized form does
not allow to think about the complexity, since there are no moves in it, only outcomes. In
the case of games whose complexity lies along the temporal axis (e.g. the moves), the
games itself escapes completely the formalism.
We have now come to the last basic concept of the theory. A solution for a game is,
intuitively, a strategy that can maximize, for a player, his minimum guaranteed payoff: the
payoff that a player may won no matter what the opponent(s) strategy may be. The problem
of game theory, then, is to find if, for a given game, a solution exists. On the basis of the
previous definitions, von Neumann and Morgenstern are able to provide a taxonomy of
games along different, independent, dimensions: number of players, perfect or imperfect
information (like most card-games), cooperative vs. non-cooperative, zero-sum (one play-
er’s loss is the other player’s win) and non-zero-sum. For each class, they set to solve the
problem of game theory. The simplest case turns out to be the class of 2-person, zero-sum,
perfect information game, whose best example is, yet again, chess. For this class of games,
the theory provide a theorem, sometimes called the Fundamental theorem or the maximin
theorem, that assures of the existence of a solution in any case. 19

G AME THEORETIC GAMES
After this excursus on the basic concepts of game theory as presented by von Neumann
and Morgenstern in their 1944 work, let us go back to chess and examine how it moved out
of game theory’s concerns to become a central topic in Artificial Intelligence’s research.
First, it should be noted that from the strictly game-theoretical point of view chess is a
quite uninteresting if not altogether trivial example. In fact, chess is, essentially, even sim-
pler than the game of “matching pennies” described above. The only difference is that the
greater complexity of the game translates into a bigger matrix: more strategies are available
to the players because there are more moves and because every move offers more alterna-
tive choices. However, since any game-theoretic treatment of a game requires the prelimi-
nary computation of the strategies, the complexity of chess escapes the theory. To win (or
at least not to lose) at chess is enough to calculate the outcome of every possible strategy
available to White and Black and then compute which one to use by means of the “mini-
max” technique they describe. 20 Practically, such a technique is not applicable to chess,
since it would require the computation of the outcome of any possible chess game, but
mathematically is a fait accompli. As a consequence, chess becomes only slightly more in-
teresting than “Heads and Tails,” and in the context of game-theory serves, at most, the
same original purpose of Drosophila at Columbia: it is a convenient didactic tool that may
come handy since most students are already familiar with it, but is quite unfit for serious
theoretical work. Game theory focuses on other, and qualitatively different, kinds of com-
plexities. Once established the existence of a solution for the simplest class of two-person
zero-sum games (to which chess belongs), von Neumann and Morgenstern tried to extend
19. The more general form of the minimax theorem for two-person zero-sum games is essentially what
von Neumann proved in his 1928 paper. The result had already been shown to hold for chess, (which
is an instance of a class of games providing an additional constraint, i.e. perfect information) by another
mathematician belonging to the Hilbert school in Göttingen, Ernst Zermelo, in 1913. See his
“Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels,” Proceedings of the Fifth
International Congress of Mathematicians, 1913, vol. 2, 510-504.
20. Or, to say it in game-theoretical jargon, “assign a value to each one of the terminal nodes and then minimax
your way back to the beginning.” See Johann von Neumann, “Zur Theorie des Gesellschaftsspielen,”
Mathematische Annalen, 100, (1928), 295-320; TGEB 143-165. This assumption has
been challenged, recently, by alternative approaches to the theory of games, see for example Steven
Brams, Theory of Moves (Cambridge: Cambridge University Press, 1994). Although Brams does not
deal with chess, his approach renders it far less trivial, mathematically speaking. Perhaps it is the beginning
of another of those turnaround which Drosophila experienced so dramatically in genetics.
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C HESS, GAMES, AND FLIES
their analysis, first to multi-person games and then to non-zero-sum games. 21 This program
brings game-theory farther and farther away from real games people play and into more
and more complicated examples of “games” that have little, if anything, in common with
games as we know them. In fact, the only link between “games” and the “theory of games”
is provided by the general definition illustrated above. An immediate consequence of the
program is that any interest in “empirical” games is lacking in game theory. In fact, “Theory
of Games” should be considered a misnomer for the original work that came out in 1944:
a less glamorous but more accurate description would probably be “a game-inspired math-
ematical theory of rational behavior.” A game like chess, therefore, lacks any interest for
game-theorists and, as a consequence, the game-theoretic community who set to work to
expand von Neumann and Morgenstern’s basic theory, in the 1950s, did not initiated any
backward loop toward a direct investigation of the game itself with the tools they had pro-
vided. 22
The gap between the complexity of a concrete game of chess and the sophisticated ma-
chinery provided by von Neumann and Morgenstern was so paradoxically big that it started
to be used as an objection against game-theory. Martin Shubik, for example, remembers
that when he went to Princeton to study economics and game theory with Morgenstern, im-
mediately after the war, encountered considerable skepticism in the economics department.
The standard objection raised by the economists was that if “game theory could not even
solve the game of chess, how could it be of use in the study of economic life, which is con-
siderably more complex than chess?” 23 The game theorists responded with what has now
21. The two steps are in fact closely linked in TGEB, since the programmatic strategy is to treat a n-person
non-zero sum game as a n+1-person zero-sum game. This strategy has been questioned in the following
development of game theory.
22. The most well-known debate in the years immediately following the publication of TGEB is the discovery,
by Arnold Tucker, of the famous Prisoners’ dilemma, an example of a two-person, incomplete
information game with no equilibrium point that was bound to become one of the paradigmatic
“thought experiments” in game-theory. In spite of being formally called a “game,” however, it is
doubtful whether the Prisoners’ dilemma should be called a “game” in the common sense of the word.
See H. Kuhn and A. W. Tucker, Contributions to the Theory of Games, vol. 2, (Princeton: Princeton
University Press, 1953) and the popular work by Richard Powers, Prisoner’s Dilemma (New York:
Beach Tree Books, 1988). A brief historical recollection on the invention of the dilemma can be found
in Howard Raiffa,” Game Theory at the University of Michigan, 1948-1952,” Toward a History…,
Roy Weintraub, ed., 171-173.

G AME THEORETIC GAMES
become the standard reply to be found in any textbook on the subject; for example, Roger
McCain writes:
Game theory may be about poker and baseball, but it is not about chess,
and it is about such serious interactions as market competition, arms races
and environmental pollution. But game theory addresses the serious interactions
using the metaphor of a game: in these serious interactions, as in
games, the individual’s choice is essentially a choice of a strategy, and the
outcome of the interaction depends on the strategies chosen by each of the
participants. 24
It should be noted that both the economists’ and the game-theorists’ critiques converge
on decreeing the theoretical irrelevance of chess. For the former, the inability of game the-
ory to solve the game is a sure sign that the theory is totally off the mark: it has better focus
on serious, concrete economic facts instead of getting lost in analysis that cannot even come
to terms with recreational activities. Games should be abandoned altogether, chess first and
foremost. For the latter, chess offers the wrong kind of complexity, a complexity peculiar
to the non-serious sphere, but the basic metaphor can be exported to the serious realm of
strategic interaction, where it will prove its worthiness. On both counts, however, chess is
not to be taken seriously, and anyone working on them should be prepared to defend his
work against forthcoming criticism. Chess is off the loop of serious theoretical work, to put
it differently, and can serve, at most, as a didactic introduction to the basic “metaphor” of
the field to be offered in the first chapter of game-theory textbooks. 25 Chess’s case is cer-
tainly not unique in the field, and many other “real” games have endured the same (math-
23. Martin Shubik “Game Theory at Princeton, 1949-1955: A Personal Reminiscence,” Roy Weintraub,
ed., Toward a History of Game Theory…., 152.
24. Roger A. McCain, “Lecture notes of a class in Economics and Game Theory,” URL: http://williamking.www.drexel.edu/top/class/game-toc.html.
My emphasis.
25. Note that, in game-theory, this tends to be case still now. Robert Aumann and Sergiu Hart, for example,
are editing a monumental three-volume work, Handbook of Game Theory with Economic Applications
(New York: North Holland 1991-forthcoming) which opens with a chapter on chess co-authored by
Herbert Simon and Jonathan Schaeffer. The contribution is presented as follows: “Historically, the first
contribution to Game Theory was Zermelo’s 1913 paper on chess, so it is fitting that the “overture” to
the Handbook deals with this granddaddy of all games. The chapter covers chess-playing computers.
Though this is not mainstream game theory, the ability of modern computers to beat some of the best
human chess players in the world constitutes a remarkable intellectual and technological achievement,
which deserves to be recorded in this handbook.” (iv, my emphasis).
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C HESS, GAMES, AND FLIES
ematical) treatment: they are picked up as a source of intuition and then relegated to an
introductory, paradigmatic function. Poker, for example, has become the “standard” non-
perfect information game; “heads and tails” the standard example of the simplest example
to require the use of mixed strategies; more recently, the game of “Nim” has become the
paradigmatic introduction to combinatorial game theory. However, what is characteristic
of, and perhaps unique to, chess, is that it experienced a second scientific life. That life be-
gan immediately after the publication of Game Theory and Economic Behavior and began,
once again, with John von Neumann
3. Combinatorial explosions
The first event that brought chess back into the scientific limelight has to do with the
intellectual evolution of von Neumann and his personal involvement with the RAND corpo-
ration in Santa Monica. RAND (literally, Research and National Development) was a research
institute heavily funded by the military (specifically, the Air Force) that had been created
in 1946 in order to preserve in postwar years the intense collaboration among scientists fu-
eled by War World II that had proved so fruitful to the national military interests. 26 Santa
Monica became one of the centers, with Princeton and, on a lesser scale, Michigan, where
mathematicians worked in developing game-theory and von Neumann was immediately
hired as a consultant. In the immediate postwar years, however, his own interests started to
shift toward the design and construction of electronic computers and, consequently, toward
the automatic resolutions of problems posed by, among other things, game-theory. The pos-
sibility was far from being purely theoretical, since the combination of von Neumann the-
ory and military interests had brought about the construction of one of the first computers
at RAND, appropriately called (apparently against his protestations), the JOHNNIAC.
It is in this context that he started lecturing on chess again, every time emphasizing the
immense complexity of the task ahead. Von Neumann, it should be remarked, lectured on
26. See Philip Mirowski, “When Games Grow Deadly Serious…,” for a detailed analysis.

C OMBINATORIAL EXPLOSIONS
the difficulty of practically finding the “solution” of chess whose existence was guaranteed
by the fundamental minimax theorem. Such a solution would be what we may call an “op-
timal” solution: it would provided a “strategy” that assures the chess player either of a win
or a tie, not of a method to play passably good chess. Therefore, he was not interested in a
chess-playing computer since he was trying to find chess-solving algorithms that a machine
could use. 27
As a consequence of von Neumann’s shifting interests, chess (and games) were
brought into the orbit of computer science, or rather into the orbit of computers, while being
understood within the conceptual framework of game theory. The “optimizing” perspective
of the theory, however, still dominates the theoretical agenda: the researchers were after a
solution in terms of a minimaxing algorithm and the task seemed impossibly prohibitive,
even on a fast computer. Even more importantly, there need not be any direct link between
the algorithm being used and how the game is actually played. In fact, this last aspect is
totally irrelevant as it is irrelevant to the automatic solution of differential equations that
human beings normally do not use numerical algorithms when they play the game of alge-
bra. The two conceptual steps that bridge this gap are taken in rapid succession by Turing
and Shannon and then by Simon and Newell in the early 1950s. It is their work that closes
the circle and allows chess to become as productive for Artificial Intelligence as Drosophila
had been for genetics.
In a few years span, Alan Turing and Claude Shannon publish two papers describing
the basic design principles that would allow a computer to play chess, although they never
come to write the actual programs. However, their use of the game is still outside Artificial
Intelligence, broadly construed: they want to prove, by demonstrating the practical possi-
bility of a chess-playing machine, that computers are able to manipulate symbols and not
just number-crunchers perennially devoted to solving differential equations as most people,
at the time, took them to be. The quality of the game played by a machine, its intelligence,
so to speak, was thus less important than the demonstration that such a machine could ex-
27. To put it differently, he was exploiting the connection between game-theory and linear programming
that was beginning to consolidate around 1950s.
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C HESS, GAMES, AND FLIES
ist. 28 To be more precise, a chess-playing machine would perhaps demonstrate some intel-
ligence, but the degree of intelligence would not be tied to the quality of the game played.
Chess, in other words, are still used in the “exemplary” mode as an instance of a more
general paradigm, namely symbolic thinking, which can be tested on the simpler domain
provided by games. To put it differently, chess may enter the computer scene because the
problem of “solving” the game, crucial to game theory, has been put aside. “Playing” the
game becomes the central concern, because being able to play an intellectual game like
chess is taken to be a significant test of cognitive abilities. Paradoxically, the quality of the
game being played is less important that the fact that a machine can “play” the way humans
are supposed to. Turing, for example, tested his design for a chess playing computer against
a person who had never played the game before and was taught the rules only a few hours
earlier. The experiment is significative and could not be farther away from game theory’s
concerns. The program’s ability to follow the rules of chess, and perhaps pursue a goal, e.
g. its ability to think, is what is tested, not its absolute performance. Game theory wanted
to find solutions for the games of war and stock bargaining, and could not care less if an
untrained human secretary (Turing’s test case) is or is not capable of understanding their
rules. In the passage from von Neumann to Shannon and Turing, instead, the emphasis
shifts from solving a game expressed in a static form to understanding the process of a dy-
namically conceived game. Does this mean that the concept of a “solution” has to be aban-
doned altogether or is there room for an idea that would bring together the two pieces of
the puzzle? Is it possible to come up with a new conceptualization of “game” that would
allow the theorist to find a solution for the game of chess (as von Neumann wanted), while
allowing a computer to play the game (as Shannon and Turing wanted)? And which kind of
28. This may explain why neither Shannon nor Turing thought so important to actually write the programs;
also, it may explain why the crucial concept of heuristics rules, the technique that would allow a dramatic
improvement in the programs’ performances, was missing, in fact was the only missing element,
from Shannon’s design principle. Claude Shannon, “A Chess-Playing Machine,” Scientific American,
February, 182 (1950) 48 ff., later in James Newman ed.,The World of Mathematics (New York: Simon
and Schuster, 1956) vol. 4; Claude Shannon, “Game-Playing Machines,” Journal of the Franklin Institute,
260, 6 (1955) 447-453; Alan Turing’s program and his hand simulation are presented in Bertrand
Bowden, Faster than Thought, a Symposium on Digital Computing Machines (London: Pitman,
1953) 288-295.

C OMBINATORIAL EXPLOSIONS
“solution” would it be? Of course, “solution” has to be used in scare quotes since it is no
longer the game theoretic concept provided by von Neumann. In fact, the definition of a
different concept of solution is precisely one of the first backward effects from chess to Ar-
tificial Intelligence, as we will see. That idea was born from a three-some composed of Her-
bert Simon, Allen Newell and Cliff Shaw, all of whom were working at RAND, either full-
time or as consultants, in 1950s. Let us begin by examining the first conceptual step by fol-
lowing the work of Claude Shannon.
In two short articles written in 1950, Claude Shannon entertains the possibility of a
thinking machine, and focuses his attention explicitly on a computer playing chess. If such
a machine existed, he suggested, its behavior would probably be considered “by some psy-
chologists” as a thinking process. It would first have to try out in the abstract various pos-
sible solutions to a given problem (e.g. a move in the chess game), in order to evaluate the
results of these trials and then to carry out the chosen solution. 29 The background of the ar-
ticle is in place: the construction of a chess-playing machine is being examined in order to
illuminate the possibility of a thinking machine in general, i.e. a machine able to exhibit
internal processes and structures essentially similar to human cognitive processes. I stress
this point because in order to appreciate what Shannon is about to say on the internal struc-
ture of the machine we should not forget that the implicit referent are the human cognitive
processes, and the structures and algorithm he presents are supposed to help either in a bet-
ter understanding of the human mind or in an actual reduplication of (parts of) it.
The basic problem can be split in three parts: (a) a translation system from chess posi-
tions to sequence of numbers must be chosen, (b) “a strategy must be found for choosing
the moves to be made” (2126), and (c) this strategy must be translated into “a sequence of
elementary computer orders, or a program” (ib.). The first and third problem are irrelevant
for what interests us here, concerned as they are with the problem of translating from hu-
man level to machine level. However, the problems (a) and (c) will prove very important
in later development of AI. (a) stands for the whole issue of knowledge representation, e.g.
the problem of how to translate the relevant information into an efficient set of data struc-
29. Claude Shannon, “A Chess-Playing Machine...,” 2132.
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C HESS, GAMES, AND FLIES
tures that a computer can manipulate; (c), in turns, can be seen as pointing toward finding
an adequate computer language to express the program itself, an issue that has kept AI busy
for many years to come, from the development of IPL, the ancestor of list-processing lan-
guages invented by Simon, Newell, and Shaw, to the development of LISP by John McCar-
thy. 30 Thus, Shannon’s choice of the search problem (i. e. (b)) as the most important one
might seem to reduce Artificial Intelligence to the problem solving activities that became
the specific characteristics of the “Carnegie” school of AI, i.e. the school led by Simon and
Newell. But in fact, its choice makes clear the different epistemological relevance of the
problems at hand. Problem (b), searching in a state-space, is conceptually prior to both (a),
representation of the states, and (c), efficient processing, as Shannon immediately sees. It
is precisely because searching turns out to be the problem, and a much harder problem that
early AI had thought, that expressive representation of knowledge and efficient processing
become important. Marvin Minsky, who, although close to Shannon in the years under con-
sideration, became known for his work on “frames,” e. g. a knowledge representation tech-
nique conceptually belonging to problem (a), was very much aware of this fact. In an
influential article published in 1960, Steps toward Artificial Intelligence, Marvin Minsky
argues that search is the basic approach, sound but inefficient. The other fields of research
are basically attempts to reduce the massive inefficiency of thorough searches through ei-
ther an appropriate reduction of the search space (planning, learning) or an adequate im-
provement of the navigation through the search space (pattern-recognition). 31
Shannon describes the basic problem of chess playing, e.g. problem (b), as follows:
A straightforward process must be found for calculating a reasonably
30. For a history of the development of LISP see Herbert Stoyan, “Early LISP History,” available at
URL:http://www8.informatik,uni-erlangen.de/html/lisp/histlit1.html, and Herbert Stoyan, LISP-Anwendungsgebiete,
Grundbegriffe, Geschichte, (Berlin: Akademie Verlag:,1980).
31. Marvin Minsky, “Steps toward Artificial Intelligence,” Edward Feigenbaum and Julian Feldman
(eds.), Computers and Thought (New York: MacGraw-Hill, 1963) 406-450. This essay had been circulating
in draft form, as a technical report, since late 1956, e.g. immediately after the Dartmouth seminar
and was instrumental in providing a first organization of the field. Minsky has repeated, and in
fact broadened, his claim in Society of Mind where he calls the possibility of space-searching the “puzzle-principle
that is philosophically basic to AI since it establishes the possibility of a creative machine
insofar as it guarantees the existence of a solution that the machine might find but the programmer does
not know about. See Society of Minds…, 73-74.

C OMBINATORIAL EXPLOSIONS
good move for any given chess position. (2127, my emphasis).
Although Shannon is thinking “the game of chess” in game-theoretic terms, he abandons
in a single gesture two tenets of the theory. First, he shoves aside the concept of a “solution”
for the game of chess and proposes instead to find “reasonably good moves.” Second, he
abandons the game-theoretic and deeply static concept of strategy by focusing the atten-
tion, instead, on moves. In other words, Shannon is proposing to shift the attention from the
static matrix of a game to the dynamic process that makes the game. This move allows him
to see chess’s taunted complexity in a totally new light. Or rather, it allows him to provide
a framework to think such a complexity. This last point becomes clear when we look at how
he frames the solution for his point (b) above:
The program designer can employ here the principles of correct play that
have been evolved by expert chess players. These empirical principles are a
means of bringing some order to the maze of possible variations of a chess
game. Even the high speeds available in electronic computers are helplessly
inadequate to play perfect chess by calculating all possible variations of a
chess game. In a typical chess position there will be about 32 possible
moves with 32 possible replies— already this creates 1024 possibilities.
Most chess games last 40 moves or more for each side. So the total number
of possible variations in an average game is about 10120. A machine calculating
one variation each millionth of a second would require over 1095 years to
decide on its first move! Other methods of attempting to play perfect chess
seem equally impracticable; we resign ourselves, therefore, to having the
machine play a reasonably skillful game, admitting occasional moves that
may not be the best. This, of course, is precisely what human players do: no
one plays a perfect game” (2127. my emphasis) 32
32. Shannon was actually pessimistic about the size of chess’s search space. Its size is now generally taken
to be of the order of O(10 44 ). See Jonathan Schaeffer, Experiments in Search and Knowledge, Ph. Dissertation,
University of Waterloo, CA, 1986, Jonathan Schaeffer, One Jump Ahead (New York: Springer
Verlag, 1997), and Jonathan Schaeffer, Joseph Culberson, Noeman Treolar, Brent Knight, Paul Lu
and Duane Szafron, “Reviving the game of checkers” D.N.L. Levy and D.F. Beal, eds., Heuristic Programming
in Artificial Intelligence; The Second Computer Olympiad (London: Horwood, 1991) 119-
136. Checkers’ search space is approximately 5X10 20 , with approximately. 10 18 legal positions, e.g.
states).
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C HESS, GAMES, AND FLIES
Let me try to convey a deeper appreciation of Shannon’s program with the help of a
(traditional) tree diagram. Consider the following figure. The ovals, or nodes, represent
possible configurations of the chessboard, and the lines connecting them stand for the ac-
tion performed when a chess piece is moved.
.
Possible move 1
P move 21 P move 22 P move 41
We can consider the initial position of the chessboard as the root of the tree, the first row
as the possible first moves by the white player, the second row as the possible counter-
moves by the black player, the third possible counter-counter-moves by the white player,
etc. It is this tree that has, as Shannon reports, approximately 10120 nodes. Set issues of size
aside for a moment, however, and focus on the structure.
The tree can be created one step (one node, that is) at the time by the recursive appli-
cation of the rules of the game. The complete tree is of course impossible to create, but the
search procedure does not have to rely on a complete tree if it settles for less than optimal
results (Whereas a less-than-complete game theoretic matrix is useless, since maximin
techniques require the whole matrix to operate).
Start
P move 2 P move 3 P move 20
P move 42
The second thing to notice is that the tree does not represent the “perfect” game, or in-
deed any game, but the collection of all possible chess games, from the most trivial to the
grandmaster’s masterpiece. In fact, every complete vertical path of the tree begins with the
initial position and terminates, after a variable number of moves, either with a victory for
white or black or with a draw, and as such stands for a complete game. The tree as a whole
represents the space of “chess” as such. Individual games can be recomprehended as proper
parts of the complete structure (i.e. as complete vertical paths.) The perfect game would be-
come possible after the complete tree is in place, since to play it is necessary to know the
.
White
Black
White

C OMBINATORIAL EXPLOSIONS
possible outcome of all the possible moves, i.e. it is necessary to read the tree from the bot-
tom up. This is why Shannon points out that the first move would take the machine 1095
years.
The dimensions of the graph need also a short comment. The vertical axis represents
the flow of the game, from the beginning to the end. It might be called the syntagmatic or
compositional axis, borrowing some terms from Jakobson, since every step in that direction
adds something to the game being played. The horizontal axis, on the other hand, is Jakob-
son’s paradigmatic or substitutional dimension, since every step along it represents an al-
ternative choice in the game being played. Shannon stresses the vertical dimension partly
because the main business of his hypothetical machine is to play chess, i.e. to traverse the
tree vertically, and partly because he obtains the horizontal dimension for free, so to speak,
from the close and perfectly explicit character of chess rules. It is not so obvious that in oth-
er domains the task of explicating the space of possibilities would be so simple, as we will
see later with Lévi-Strauss.
Since game-theory reasons in terms of “strategies,” it is forced to build the complete
tree before it can apply its theoretical tools since a strategy, by definition, has to take care
of all possible occurrences. The complexity of chess, therefore, lies outside the theory itself
and has to be tamed before the latter can display its prowess. For Shannon, instead, the
complexity is expressed in terms of states—that is, chess positions—not strategy, and this
makes all the difference. States can be generated on the fly by the application of the rules
of chess, which form a small manageable set. The complexity of chess is now an integral
part of the theory itself: it is the “combinatorial explosion” in the number of states that a
small number of rules can generate. The problem, therefore, becomes how to tame such a
complexity by finding ways to keep the size of the tree under control.
By accepting most of the basic game-theoretic apparatus and, at the same time, relin-
quishing the crucial concept of strategy, Shannon has provided a framework that makes
chess’s complexity thinkable. Moreover, his suggestions about how to tame such complex-
ity will make the study of chess relevant and will be crucial in establishing a strict connec-
tion between Artificial Intelligence and chess. “This [e.g. finding moves that may not be
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C HESS, GAMES, AND FLIES
best] is precisely what human players do: no one plays a perfect game,” he says. Therefore,
the “solution” of the game of chess might be found in the human way of playing chess and,
on the reverse, the performance of a chess-playing computer may be measured against hu-
man performance.
This last point, however, is still a hint in Shannon’s paper and will not receive its full
development until the works of Simon and Newell. What, on the other hand, seems un-
doubtedly his, is the “discovery” of the combinatorial explosion of states as the result of the
dynamic application of the rules. Although this may seem quite a discouraging result, in
fact it plays a role analogous to the breeder reactor’s properties we had seen at work in the
Drosophila/genetics interaction. The “complexity” of the insect lay in its ability to produce
an ever increasing number of mutations when interacting with the experimental methods of
the geneticists. These mutations, by challenging the scientists’ tools, were forcing them to
refine their theories to keep up with the insect’s capacities. Similarly, chess’s “ability” to
turn out ever new forms of combinatorial explosions under the scientists’ pressure to keep
it under control forces them to devise more and more refined methods (read, “theories”) to
keep up with the game’s “complexity.” In both cases, the productive relationship can be es-
tablished because there is a conceptual framework that makes the object’s complexity
thinkable and that allows the search for a solution to start. In genetics’ case, this was the
theory of the gene, in Artificial Intelligence is the conception of a game as a search-space,
e.g. as a space of single, static positions generated recursively by the application of the rules
of the game.
The framework provided by Shannon shifts all the emphasis in the study of chess from
“solving the game,” to “searching the space for an acceptable solution.” The problem of Ar-
tificial Intelligence becomes how to search that space for a solution as good as a human be-
ing could find, providing thus, in a single stroke, a theory of thinking and a theory of chess.
It is the solution of this problem that attracts the attention of Herbert Simon and Allen New-
ell.
Around 1950, Herbert Simon was a young economist working in the “backwaters”
area of industrial organizations and had already published a substantial work, Administra-

C OMBINATORIAL EXPLOSIONS
tive Behavior. In the book, a study of the way employees work in very large and generally
public structures, he had argued that real problem-solving decision cannot and do not hap-
pen by finding the optimal solution to a given problem. In real-life situations, problem solv-
ers (like managers) have to give up the hope to find the best solution because they can count
only upon limited information and do not have the best possible strategies available to
them. They can only rely on rules-of-thumbs, on heuristic rules derived from past experi-
ences to take decisions. The solutions they are looking for will be “satisfactory” solutions
that are “good enough” for the given, specific situation in which the problem has to be
solved and not optimal solutions valid in general. Simon called “satisficing”, as opposed to
“optimizing” this typical organizational behavior. 33 This approach is very consonant with
most of game theory’s approach to economic behavior, in its insistence on seeing rationality
as always bounded by very effective constraints. Simon was in fact an early reader of von
Neumann and Morgenstern’s work, and published a very positive review of the book, the
very first one to come out, in fact, in 1945. 34 However, he was very critical of the concept
of “solution” of a game, a concept that he associated with the impossible search for an “ob-
jective” optimal rational behavior as it could be judged from a third-person perspective. In-
stead, he insisted on satisficing as the best expression of first-person, subjective rationality
that would prove much more useful in the comprehension of intelligent, decision-making
behavior. 35
Allen Newell’s work provided a different angle on the same issue: how to find an ef-
fective way to tame the intrinsic complexity of the search space that has now become ex-
pressible. Newell, 10 years Simon’s junior, had been a student of the mathematician George
Polya while a physics undergraduate at Stanford in the late 1940s, and had become well-
33. Herbert Simon, Administrative behavior (New York: MacMillan, 1947).
34. Herbert Simon, “review of Theory of Games and Economic Behavior,“The American Journal of Sociology,
1945.
35. See for example Simon’s contribution to the Santa Monica conference in 1952, now in Robert Thrall,
ed., Decision Processes (New York: Wiley, 1954). See also his comment on those years in an interview
to Vernon Smith: “I was profoundly dissatisfied with the concept of “solution” in von Neumann and
Morgenstern—it seemed to me to confirm the complexity of the problem rather than solve it.” in Vernon
L. Smith, “Game Theory and Experimental Economics,” Roy Weintraub, ed., Towards a History…,
253.
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C HESS, GAMES, AND FLIES
acquainted with his work on heuristics. Polya had diverted his attention from the then com-
mon study of the formal structures of proofs as they are presented to the mathematical com-
munity (and as formal logic studies them), and focused instead on the “solving methods”
that bring the mathematician to the discovery of those proofs. He had provided an articulate
summaries of heuristic methods that, although not guaranteeing a solution, can provide the
crucial insights that will bring to it. 36 It is easy (it always is, post factum) to see the conver-
gence between Simon’s concerns and the basic premises of Polya’s studies that the young
Newell had absorbed.
After a year of graduate school at Princeton—where he met most of the leading game-
theorists, but that left him very dissatisfied with the purely mathematical approach to game
theory that was dominant in those years—Newell joined RAND to work on “applied” math-
ematics. There he met Herbert Simon, who, although teaching in Pittsburgh, had been hired
as a consultant and started to spend a few summers there. 37
In his autobiography, Simon notes that he got involved with RAND through the Cowles
commission and started to attend summer seminars in Santa Monica in 1952. The first prod-
uct of his interaction with the game-theorists was the article “A Behavioral Model Of Ra-
tional Choice,” originally a RAND technical report. The paper contained an appendix on
chess that was stimulated by a talk on the topic given by von Neumann that summer. Simon
writes that he thought von Neumann was “overestimating the difficulties substantially, and
moreover I believed I had some solutions for them which I proposed in the appendix [later
excised from the public version].” He later recalls that immediately after he met Newell,
whom he recognized as being far more advanced on the topic, he put his plans for a running
chess-playing program on hold until they started collaborating intensely on the project to-
ward the end of 1955. Soon joined by Cliff Shaw, a system programmer at RAND, they began
working toward the implementation of a program incorporating the profoundly different in-
terpretation of game-theory we have just outlined. The report of their effort was published
36. George Polya, How To Solve It (Princeton: Princeton UP, 1944). Polya writes in the preface to his celebrated
book: “This study [of solving methods], that some authors call heuristics, now is out of fashion.
However, it has a glorious past and, perhaps, a future.” (iii).
37. Herbert Simon, Models Of My Life…,166 and 202.

C OMBINATORIAL EXPLOSIONS
in 1958 as “Chess-Playing Programs and the Problem of Complexity,” and marks a land-
mark in the AI literature on chess. In fact, it marks a landmark in AI in general since, by
bringing to a conclusion the early phase of the interaction with games, it provides the guide-
lines of a general theory about problems solving and its measurement through the applica-
tion of computer programs to chess that will remain stable for a long time to come.
At the beginning of their ground-breaking article, Simon, Newell and Shaw state clear-
ly what is at stake in the research: the program’s ability to play chess provides a measure
of “recent progress in understanding and mechanizing man’s intellectual attainments.” 38
The argument supporting the claim is quite simple: “Chess is the intellectual game par ex-
cellence,” they say, and
Without a chance device to obscure the contest, it pits two intellects
against each other in a situation so complex that neither can hope to understand
it completely, but sufficiently amenable to analysis that each can hope
to outthink his opponent. [...] If one could devise a successful chess machine,
one would seem to have penetrated the core of human intellectual endeavor.
(39, my emphasis) 39
First of all, the scope of the project has substantially changed, veering off from applied
mathematics to, should we say, philosophy: the researchers’ aim is no longer, or not only,
to discover useful techniques to analyze complex situations, but rather to penetrate the “hu-
man intellectual core.” This is possible because the emphasis has shifted from the general
inquiry into rationality that was specific to the original game-theoretic project to a more
specific, and yet more ambitious, search for the subjective roots of that rationality. In other
words, Simon and Newell will strive to obtain a description of the rational agent as it works,
that is, a description of the process that brings rationality about.
In this opening act, therefore, we see that the “core” of thinking, or the core of intel-
lectual behavior, is constituted by problem solving, and problem solving is well exempli-
38. Allen Newell, J.C Shaw and Herbert Simon, “Chess-Playing Programs…,” 39.
39. Note, also, that this approach marks quite a distance from the current standard interpretation of intelligence
as whatever behavior can fool a human being into thinking that s/he/it is human, e.g. the socalled
Turing test. In its early phase, AI was explicitly much more ambitious, since it was not just the
outcome of the intelligent process counted, but also, and especially, the process itself.
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C HESS, GAMES, AND FLIES
fied by taming the complexity of a chess game. A theory of thinking must therefore provide
not only a explanation of how the goal, the solution, can be reached, but also a replication
of the performance. Since the solving process is what is at stake, the process itself will have
to be replicated, not just the underlying principle. The computer assumes then a central role,
because it is only by simulating on a computer the “blind” search of a solution abstractly
possible in the game-tree that we can expect a true confirmation of a theory 40
The second point to emphasize concerns the basic problem that such a theory must
solve: combinatorial explosion, or complexity, whose measure is given by the sheer, direct-
ly unmanageable size of the game-tree. Newell, Simon, and Shaw’s answer to the problem
proceeds along two lines: first of all, we have better consider only a subset of all possible
chess positions, and more precisely only those which have a meaning for a normal chess
game. This is where “heuristics” and “satisficing” come into play. No exact, optimal rule
for identifying this subset exists, of course, but one can rely on the knowledge gathered by
past chess grandmasters and accumulated in a small number of rules of thumb, or general
strategic guidelines. In particular, the authors compile a number of overall “goals” that a
chess player must achieve, loosely speaking, in order to win, like, for example, “keep the
king safe,” “develop the pieces,” “do not block your own pawns,” etc. Only moves that con-
tribute toward the satisfaction of the specified goals are considered, thus greatly reducing
the size of the search. In terms of the diagram, these rules amount to a pruning of the tree
along the horizontal axis. The second pruning strategy proceeds along the other axis: in-
stead of considering the whole game—which is, on the average, 80 levels deep—we con-
sider only the first four or five levels below the level at which the move is being played.
The effectiveness of these strategies, and especially their adequacy as a model of chess
competence in particular and thinking processes in general, can of course be seriously ques-
tioned. Indeed, it has been questioned more than once. 41 But my point is different. Heuris-
40. See, for example, Newell and Simon reservations, along these lines, against Turing hand-simulation of
his chess-playing programming in Human Problem Solving…, 671 ff.
41. See Hubert Dreyfus’s books and especially Mind over machines (New York: The Free Press, 1986)
where an alternative model of human expertise is presented (and later attributed to the co-author of the
book, Stuart Dreyfus).

C OMBINATORIAL EXPLOSIONS
tics poses the final touch to the interaction between AI and chess that allows the closure of
the feedback circle and triggers even more theoretical attention on the game. Heuristics is
about chess (king’s safety, etc.), and it is about reducing chess’s intrinsic complexity.
Chess, as a consequence, is studied more and more as a space to search on the basis of more
and more sophisticated heuristic functions. This is what chess is for AI, and will ever be.
But not only: a whole, concrete view of games emerges, games as the closed space that iso-
lates it from anything outside and makes potentially meaningful whatever lies inside. On
the rebound, AI is precisely what comes out of this article, as I have already suggested
above: heuristic search in a search-space game-theoretically defined. “Thinking” must be
explained in terms of satisficing a set of rigid constraints by searching heuristically the
space that those constraints (e.g. rules) define. And the best way to provide and test a de-
tailed theory of thinking is by writing a computer program that will effectively search such
a space.
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C HESS, GAMES, AND FLIES

CHAPTER V
STRUCTURES
(AND SPACES)
in which Lévi-Strauss’s structural explanations of kinship and myths
are explained, and then compared to chess and search-spaces.

212
S TRUCTURES (AND SPACES)
1. Games and Structures
A whole mythology is deposited in our language
Ludwig Wittgenstein
The relationship between Lévi-Strauss’s Structuralism and games is almost symmetric
to Artificial Intelligence’s. AI was interested in games since its very start, but it claimed that
such an interest was merely instrumental, and it deployed the Drosophila analogy to fend
off any charge to the contrary. Lévi-Strauss, on the contrary (and especially in the period
under consideration here) claimed repeatedly that his structures were directly modeled on
games. However, he never cared to deepen the claim by either analyzing games or by show-
ing the concrete relationships that may hold between his structures and games.
For example, in an early study on kinship, after having provided some detailed struc-
tural analysis of various kinship systems and explained how they regulate everyday life, he
comments: “The whole field of kinship becomes a chessboard on which a very complicated
game is played.” 1 A few years later, in “La structure et la forme,” Lévi-Strauss comments
on the different parts of a story, as analyzed by Propp, in the following terms:
Propp designates such a whole by a term which the English translator renders
as “move” and which we prefer to call “partie” in French, which means
both the principal division of a tale and a card or chess game. We are indeed
dealing with both things at once, since, as we have seen, the tales containing
several parties are characterized by the non-immediate recurrence of the
1. Claude Lévi-Strauss, Le regard eloigné (Paris: Plon, 1983) 85; Engl. tr. The View from Afar (New York:
Basic Books, 1985) 56. The specific essay dates back to 1955.

G AMES AND STRUCTURES
same functions, as in successive card games one periodically shuffles, cuts
deals, plays, and takes the tricks. In other words, one repeats the same rules
in spite of different deals. 2
Lévi-Strauss goes as far as to quote von Neumann and Morgenstern’s work, and he of-
ten presents the theory of games as the ideal language for a possible future science of com-
munication that will unify sociology, economics and linguistics, e.g. the three disciplines
that deal with the issue of the exchange (respectively, of women, goods, and messages)
among human beings. He seldom ventures, though, into a discussion of the basic concepts
of game-theories, limiting himself to present it as a tool that will prove indispensable. One
of the few specific remarks concerns the different goals of parlor games and kinship sys-
tems:
The former are constructed in such a way as to permit each player to extract
from statistical regularities maximal differential values, while marriage
rules, acting in the opposite direction, aim at establishing statistical
regularities in spite of the differential values existing between individuals
and generations. In this sense they constitute a special kind of “upturned
game.” 3
As he immediately adds, however, such a difference does not mean that “societal” games
cannot be treated with the same (game-theoretical) methods. Yet, we are not given further
details on this point, and we have seen above that a precise characterization of the basic
concept of game, strategy, move, etc., is crucial for a proper understanding of game theory.
Edouard Delruelle is the author of one of the few studies on Lévi-Strauss’s work to pay at-
2. Claude Lévi-Strauss, Anthropologie Structurale Deux (Paris: Plon, 1973) 149. Engl. tr. Structural Anthropology,
volume 2 (Chicago: University of Chicago Press, 1976) 124, Lévi-Strauss’s emphasis. The
essay was first published in 1960.
3. Claude Lévi-Strauss, Anthropologie Structurale (Paris: Plon, 1958) 329; Engl. Tr. Structural Anthropology,
(New York: Basic Books, 1963) 298. Lévi-Strauss actual formulation is a bit different, and in
fact more strongly put, than the English translation: ”On pourrait dire que les secondes constituent des
«jeux à l’envers,» ce que ne les empèche pas d’être justiciables des mêmes méthodes.” The same point
about the specificity of “anthropological games” is repeated, in the context of the distinction between
“games” and rites,” in the first chapter of La Pensée Sauvage. See also the “ouverture” of Histoire de
Lynx, which opens the book on a chessboard theme, and the discussion of such a narrative move provided
in the preface: Claude Lévi-Strauss, La pensée savage …Engl. tr. 30-33; Histoire de Lynx (Paris:
Plon, 1991), 20-22 and 9-13; Engl tr. The Story of Lynx (Chicago: Chicago University Press, 1995).
213

214
S TRUCTURES (AND SPACES)
tention to the philosophical concept of game (rather, jeu). However, Delruelle does not tar-
get the concept of jeu itself as used by Lévi-Strauss and he deals even less with the formal
constructs of game-theory, besides some passing remarks. Instead, he starts from a very
rough characterization of the concept, and sets forth to defend it against the French critiques
of Lévi-Strauss coming from philosophical quarters (Claude Lefort, Paul Ricoeur, Gilles
Deleuze, and Jacques Derrida). The formal rapprochement between the mathematical con-
cept of game and Lévi-Straussian structures that I will suggest in this chapter and in the
next, however, is far from being uncontroversial. On the contrary, many a commentator ex-
ploit Lévi-Strauss’s lack of precise analysis of the concept of game to claim a very loose
and only “metaphorical” (in an almost derogatory sense) connection between any rigorous
mathematical idea and the basic concepts of structuralism. Any solution to the issue, there-
fore, will have to proceed through a patient work of analysis of the sources. 4
We can start by remarking that Lévi-Strauss seems to add a particular slant to the con-
cept of rule, because whenever he mentions it in a more or less rigorous game-theoretic
context he tends to oppose the rules of the game to the subject that will follow them. For
example, in the same essay from which we quoted above, he notes that game theory would
help make clear that anthropology consists
exclusively of the study of rules and [has] little concern with the nature
of the partners (either individual or groups) whose play is being patterned
after these rules. [...] What is important is to find out when a given a player
can make a choice and when he cannot. (ib.)
In other words, Lévi-Strauss seems to stress the interpretation of a rule as a constraint rad-
4. Edouard Delruelle, Claude Lévi-Strauss et la philosophie (Bruxelles: de Boeck, 1989). For a very general,
and sometimes generic, introduction to Lévi-Strauss’s use of mathematics see the recent article
by Mauro W. Barbosa de Almeida,” Symmetry and Entropy. Mathematical Metaphors in the Work of
Lévi-Strauss,” Current Anthropology, 31, 4 (1990) 367-377 and the trenchant reply by Terence Turner,
“On Structure and Entropy: Theoretical Pastiche and the Contradictions of «Structuralism»,” Current
Anthropology, 31, 5, (1990) 563-568. Turner charges Lévi-Strauss with an incoherent application of
mathematical concepts necessitated by a reductive interpretation of structure that divorces it “from the
individual social and cultural forms that are its putative bearers” (566). He proposes alternative renditions
in “Narrative Structures and Mythopoesis: A critique and reformulation of structuralist approaches
to myth and poetics,” Arethusa, 10 (1977), 103-163, and “Le denicheur d’oiseaux en contexte,”
Anthropologie et Sociétés, 4, (1980), 85-115; the latter essay is a direct critique of Lévi-Strauss’s analysis
of the Bororo myth that opens The Raw and the Cooked.

G AMES AND STRUCTURES
ically limiting the freedom of choice of the individual(s) rather than its constitutive aspect
that makes possible the operation of a rational agent. It almost seems as if the rules of the
games belonged to a diverse, superior order of rationality than the strategy that the players
will follow. However, this claim must be understood in the historical context: in 1952, when
the essay was written, French philosophy was completely dominated by the Sartrean, exis-
tentialist brand of humanism, with its accent on the unlimited freedom of the individual fac-
ing death as the only possibility to live an authentic life. Not only it is not difficult to read
Lévi-Strauss’s emphasis on the rule vs. the individual (the “subject”) as a well-aimed dig at
existentialist philosophy, but it is exactly how it was being read. Lévi-Strauss’s interpreta-
tion tries instead to undermine the very opposition between the rules of a game and the free-
dom of the player (an opposition that, as we have seen, make little sense within a game-
theoretic framework) by doing away with the notion of freedom altogether. He will then be
able to recover the active character of a rule by transposing it to a different logical (and on-
tological) level, a level where there are no subjects left to embody a presumptive freedom.
But I am anticipating part of a discussion that can only be conducted in precise terms after
a deeper analysis of the concept of game that is supposed to bear it. We have already seen
some concept of game at work, and this particular interpretation may or may not prove con-
sistent with them, and in particular with the idea of game as thematized by game-theory. To
get an answer, we will have to see how Lévi-Strauss’s explanations of social facts fare with
respect to the concepts we have seen above.
The theoretical work necessary to confirm Lévi-Strauss’s claim, therefore, will follow
a direction that is exactly the opposite to that followed with Artificial Intelligence. In AI’s
case, I wanted to show the “essentiality” of its relationship with games and could take for
granted as relevant, to a certain extent, its analysis of the concept. In Lévi-Strauss’s case,
instead, the goal is to show that his very general claims on the relevance of games to struc-
turalism are in fact true, despite the lack of specific work on games. My strategy, then, will
be to explore the essential features of the crucial concept of structure and to compare it to
Artificial Intelligence’s “search-spaces” to show their similarities and differences. I will
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216
S TRUCTURES (AND SPACES)
consider Lévi-Strauss’s claim verified if Artificial Intelligence’s analysis of games in terms
of search-spaces will be proved equivalent to Lévi-Strauss’s structures.
2. From language to myth
Every structuralist, as well as any secondary source on the subject, presents his own
genealogy of the structural method, usually starting from de Saussure, and quickly diverg-
ing thereafter. Lévi-Strauss presents his own reconstruction starting from the so-called Pra-
gue School of structural linguistics, whose main representatives were Roman Jakobson—
whom he met in New York in the 1940s and introduced him to the discipline—and Nikolai
Troubetzkoy. In phonology, Troubetzkoy rejected the naturalistic approach of the XIX cen-
tury which took sounds as the privileged object of study, and concentrates his attention on
the highly theoretical notion of phoneme. Phonemes are complex, abstract (i.e. “unobserv-
able”) entities whose number is much smaller than the number of possible sounds and
which constitute a relational system, since what counts is not the sound(s) to which a pho-
neme corresponds in the actual utterance but rather the other phoneme(s) to which it is op-
posed. 5 Here is a summarized definition, formerly offered by Troubetzkoy, and reported,
with whole-hearted support, by Lévi-Strauss in 1947. 6
The method can be summed up by four principles, which I paraphrase as follows:
1.The method does not treat terms as independent entities—it considers instead relations
between terms
2.It introduces the concept of system [closed system, actually] and
3.It aims at discovering general laws [connecting relations together]
4.Finally, it shifts from the study of the conscious linguistic phenomena to their unconscious
infrastructure
In short, a structure is a closed system of relations connected by necessary laws underlying
5. In fact, it is a known fact from phonetics that although utterable sounds constitute a continuum, what
is often called the “vowel trapeze,” the linguistic sounds, e.g. the different vowels perceived as different
by a speaker/hearer of determinate language, are in fact very few. Certain sounds can therefore be
empirically possible and linguistically non-existent depending on whether they are distinctive or nondistinctive.
Troubetzkoy provided several examples, which Lévi-Strauss quotes, in his classic work,
Principes de Phonologie (Paris: Klinsieck, 1949) 34-44.
6. Claude Lévi-Strauss, Anthropologie Structurale…,; Engl. tr. 63. (The essay was written in 1947).

conscious phenomena.
F ROM LANGUAGE TO MYTH
This definition gives us just a preliminary characterization, but one nonetheless useful
in order to see structures at work. Let us proceed to a further, but still preliminary refine-
ment of the method with a canonical example drawn from linguistics before approaching
the analysis of anthropological endeavors like the study of kinship systems or the study of
mythology.
Lévi-Strauss, declaring in a bold move that anthropology deals with a different kind of
reality, but is a science of the same type of linguistics, applies the same definition and meth-
od to his discipline. In his first important work, The Elementary Structures Of Kinship, he
describes the general problem facing anthropology as essentially similar to the problem
facing the linguist when confronted with the strange phenomenon of different sounds hav-
ing different roles in different languages and yet seemingly following some hidden rule.
Since the problem was solved in phonology through the introduction of an abstract entity,
the phoneme, an analogous solution must be found in anthropology. In the study of kinship,
says Lévi-Strauss, we observe that the number of psychological “attitudes” (like “affection-
ate,” “warm,” “hostile,” etc.) that individuals may have toward each other is almost unlim-
ited, yet we find that societies actually use only a very small number of them within their
kinship systems. Moreover, not only the attitudes are often very different, sometimes soci-
eties adopting kinship systems with very similar terms (e.g. “wife, “husband,” uncle,” etc.)
have diametrically opposed attitudes regulating the behavior between the elements of the
system. Any explanation of this difference based on the biological features of the terms,
therefore, is bound to fail, since they require that
each detail of terminology and each special marriage rule is associated
with a specific custom as either its consequence or its survival. We thus meet
with a chaos of discontinuity. No one asks how kinship systems, regarded
as synchronic wholes, could be arbitrary products of a convergence of several
heterogeneous institutions (most of which are hypothetical), yet nevertheless
function with some sort of regularity and effectiveness. 7
7. Claude Lévi-Strauss, Anthropologie Structurale…, 42; Engl. tr. 35.
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218
S TRUCTURES (AND SPACES)
The problem can only be solved by abandoning a search based on a direct relationship be-
tween the empirical, historical data and the various kinship terms and postulating, instead,
an underlying system of relations governing the use (e.g. the meaningfulness) of such
terms.
His analysis of the kinship systems finds a formal, abstract structure constituted by
four terms: brother, sister, father and son. The different relations existing between pairs of
terms of the system (Lévi-Strauss calls them “attitudes,” like “warm and familiar” or “rigid
and antagonist”) are mutually constraining so that he can formulate a general law of the fol-
lowing form: “The relation between maternal uncle and nephew is to the relation between
brother and sister as the relation between father and son is to that between husband and
wife. Thus if we know one pair of relations it is always possible to infer the other.” 8 In other
words, the dazzling multitude of kinship systems can be explained as the result of the com-
bination of a relatively small number of basic attitudes between pairs of terms of the sys-
tem. It is the relations among the terms, and not the terms themselves (consistently with the
dictates of Troubetzkoy’s structural linguistics mentioned above) that provide an explana-
tion of the surface, empirically given phenomena.
On the basis of this analysis, Lévi-Strauss can extrapolate a general explanation for the
kinship systems: “The primitive and irreducible character of the basic unit of kinship is ac-
tually a direct result of the incest taboo. This is really saying that in human society a man
must obtain a woman from another man who gives him a daughter or a sister.” 9 It is impor-
tant to underline the dynamic character of this explanation: since the exchange of women
from one group to the other will be reciprocated in the next generation, it follows that kin-
ship systems, in Lévi-Strauss’ view, operates as an active set of rules that dictate the tem-
poral development of the society at issue. In other words: a kinship system is not
constituted by a set of constraints that limit an originary freedom to choose one’s partner,
a freedom owned by a subject who ultimately will exercise it anyway, although within the
socially imposed laws. Rather, the opposite is true: the marriage rules, if seen as rules reg-
8. Claude Lévi-Strauss, Anthropologie Structurale…, 52; Engl. tr. 42.
9. Claude Lévi-Strauss, Anthropologie Structurale…, 56; Engl. tr. 46.

F ROM LANGUAGE TO MYTH
ulating an exchange and not as constraints limiting an initial freedom, play a most active
role in the social process, because they allow the formation of a social bond by moving
around, at each generation, the individual actors from one sub-group to another one. The
marriage rules are both creative—they create the social ties between groups—and dynam-
ic—they allow the social group to perpetuate in time from one generation to the next. In
Lévi-Strauss’ own words
kinship is not a static phenomenon; it exists only in self-perpetuation.
Here we are not thinking of the desire to perpetuate the race, but rather of
the fact that in most kinship systems the initial disequilibrium produced in
one generation between the group that gives the woman and the group that
receives her can be stabilized only by counterprestations in following gen-
erations. 10
This dynamic aspect is extremely important, and especially for our purposes, because it
makes clear that for Lévi-Strauss the “game of marriage” is really a game—and not only in
the loose metaphorical sense of being a structure endowed with “formal” rules. Rather, it
is a game in the more technical sense explored above: it is a dynamic process that possesses
the resources to propel itself forward, to “self-perpetuate” itself from one generation to the
next. The steps taken by one generation when deciding which wife to choose, therefore, are
analogous to the chess-player move, although, instead of Black and White playing their
game, we may have more players involved, each one of them corresponding to one of the
sub-group of the given society. Lévi-Strauss’s identification of the game of marriage with
a chess game is justified, in the first instance, at least, by his truly game-theoretic interpre-
tation of the concept of rule (of marriage) as the active and creative component that turns a
collection of actors into a structured dynamic interaction of players exploiting the strategies
that the rules make possible. 11
10. Claude Lévi-Strauss, Anthropologie Structurale…, 57; Engl. tr. 47.
11. Further evidence in favor of a game-theoretic interpretation of rules in Lévi-Strauss is provided by another
contemporary essay, “Race et Histoire,” published in 1952, where the analysis is broadened to
consider the interactions among different cultures as a complex game in which the players may employ
contrasting strategies in order to maximize their (and, ultimately, humanity’s, this being a non-zero
sum game) advantage. See Anthropologie Structurale Deux…, 412-422; Engl tr. 354-362.
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S TRUCTURES (AND SPACES)
Two more points need to be stressed in this first, preliminary account of structures, the
first concerning the formal and symbolic character of the described systems, and the second
pertaining to their ontological status. The structures Lévi-Strauss tries to uncover are for-
mally describable, at least in principle. That is, they can be expressed, in the usual fashion,
as axiomatized formal theories, using some kind of mathematical logic. Second, the anal-
ysis of kinship or of mythological thought deals with systems that are supposed to be ab-
stract structures mediating our relationship with the world. In other words, they are
unconscious, in the strict technical sense of enjoying a logical and epistemological prece-
dence on conscious, observable behavior. The basic act of differentiation, of taxonomic
classification, is what Lévi-Strauss sees at work in the “Savage mind,” and it is precisely
what constitutes culture as such: a system of abstract (i.e. non-perceptually founded) clas-
sifications that mediates every exchange between man and nature and/or man and man and
actually constitutes a system of conceptual understanding. Man’s relation to the world is
never naive and immediate, but always mediated by the taxonomic system. In the words of
Lévi-Strauss: “Savage thought does not distinguish the moment of observation and that of
interpretation any more than, on observing them, one first registers an interlocutor’s signs
and then tries to understand them: when he speaks, the signs expressed carry with them
their meanings.” 12
The structural method, therefore, needs to find a closed structure regulated by a formal
law ruling the unconscious relations in order to explain the observable (“conscious”) phe-
nomena. Let us see how this requirement translates into a theory when applied to the study
of myths.
For starters, it must remarked that the decision to apply the structural method to my-
thology is dictated by strong epistemological reasons: what we, twentieth century observ-
12. Claude Lévi-Strauss, La pensée sauvage …;Engl. tr. 223. Although to be commended for the effort, the
English title cannot but conveys the impression that the work is a revived XVII century overambitious
travel-book on the “alien” minds of the primitive. Notice, instead, that pensée, in French, is actually
both “thinking” and “thought” and, furthermore, that pensée sauvage can be read both in the subjective
and objective genitive, being both the pensée of the savages and the savage in/of the pensée The book
wants to show, in fact, that the two are essentially the same and that they are not so savage. “Thinking
in the wild,” may be a closer, although perhaps less elegant rendition.

F ROM LANGUAGE TO MYTH
ers, see as fascinating stories that people without writing tell each other, are actually what
those same people consider, most often, as dearest to their existence since they constitute
the core of their religious systems. The attempt to find a formally determinable structure
underlying mythological production, therefore, aims at discovering the basic structure of
those human societies. And, by induction and/or extrapolation, some basic elements of hu-
man culture in general.
In 1955, Claude Lévi-Strauss published the first in a long series of studies dedicated to
the study of religious beliefs—”The Structural Study Of Myth”—that exemplifies the basic
elements of his structural approach. This essay was published almost ten year before the
appearance of the first volume of Mythologiques, Lévi-Strauss massive four-volume work
devoted to the interpretation of myths. However, as it has been recognized by many an in-
terpreter, it can be taken to represent the theoretical and methodological foundation upon
which Lévi-Strauss was to build his understanding of mythology in the following twenty
years of his career. Lévi-Strauss himself may be said to recognize, implicitly, the corner-
stone position of “The Structural Study of Myth,” since he will refer continuously to it in
all the conceptual discussions contained in his later books. Indeed, even if Lévi-Strauss has
never been shy of self-quotation, a frequency analysis would probably show that no other
text of his is quoted more often. I will closely follow his exposition in order to underline
the basic features of the structure that, he claims, underlies every myth. 13
Lévi-Strauss starts from an antinomy commonly felt in the field at the time of his writ-
ing: the content of myths is both too arbitrary to support any unified explanation—myths
do not possess a common structure constraining their narration—and too repetitive, since
the mythographer encounters the same themes and characters all over again, although in
ever new forms and stories. This basic antinomy is the principal cause of the constant os-
13. Marcel Hénaff is one of the few commentators who disagree with this thesis; he contrasts a linguistic
(and game-based) phase of Structuralism that he sees developed around the thesis contained in the
mentioned essay to a music-based phase that will prevail after 1964, e.g. with Mythologiques. However,
I think he mistakes for a theoretical shift what is in fact to be considered an intrinsic development
allowing Lévi-Strauss to address some crucial philosophical issues left unattended to in the earlier essay,
as I will argue in the next chapter, sections 6 and 7. See Marcel Hénaff, Claude Lévi-Strauss (Paris:
Belfond, 1991) 172-192
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222
S TRUCTURES (AND SPACES)
cillation in the interpreters: either the myth is reduced to the expression of some universal
conflict of humanity (without any convincing proof, however, since the different myths
present wildly different versions) or it is reduced to the illustration of some specific belief
hold by the society at issue (without even attempting to explain the astonishing cross-cul-
tural similarities). The basic problem of the study of myth, as Lévi-Strauss interprets it, is
yet again very similar to the problem facing phonology:
On the one hand, it would seem that in the course of the myth anything is
likely to happen. There is no logic, no continuity. […] With myth, everything
becomes possible. But on the other hand, this apparent arbitrariness is
belied by the astounding similarity between myths collected in widely different
regions. Therefore the problem: if the content of a myth is contingent
[on the conditions of the local society who invented it], how are we going to
explain the fact that myths throughout the world are so similar? 14
Lévi-Strauss’s solution is simple: both aspects of the myth, the seemingly arbitrary specific
character and the abstract and repetitive general features, must be retained in the unified
explanation. He adds an important qualification, however, inspired by the analogous treat-
ment of language in structural linguistics: although the specific elements of the myths must
be preserved, what counts as universal are not the elements themselves but rather their re-
ciprocal relations. As he says, “if there is a meaning to be found in mythology, it cannot
reside in the isolated elements which enter into the composition of a myth, but only in the
way those elements are combined.”(210) These elementary pieces, called gross constitu-
ents elements, are nothing else that the single sentences composing the myth under scrutiny,
whose sequential composition gives rise to the story.
Lévi-Strauss recalls at this point the Saussurian distinction between langue and parole,
the first being the structural side of language that belongs to a reversible time and the sec-
ond the temporal, irreversible side. The important difference between language and myth,
when considered as systems, is that in a myth both aspects—the atemporal, structural side
and the temporal, situated narration—are simultaneously present. A given myth is always
and simultaneously a story which retells specific events and a universal pattern that re-pre-
14. Claude Lévi-Strauss, “The Structural Study Of Myth,” Anthropologie Structurale…,229;Engl. tr. 208.

F ROM LANGUAGE TO MYTH
sents itself. Lévi-Strauss’s irreverent example is the treatment of the Revolution in the dis-
course of the contemporary French Politician: it is both “a sequence belonging to the past
[...] and a timeless pattern which can be detected in contemporary French society and which
provides a clue for its interpretation, a lead from which to infer future developments” (209).
Myth’s strange temporality provides the ground for Lévi-Strauss’s basic hypothesis
about the mythological structure: “The true constituent units of a myths are not the isolated
relations, but bundles of such relations, and it is only as bundles that such relations can be
put to use and combined so as to produce a meaning” (211). A first analogy is provided by
an orchestra score, a piece of writing which can actually be read along two different axis:
the score can be read and is actually executed diachronically from left to right in order to
obtain the melody. But the score can also be “read” from top to bottom, synchronically, to
get at the underlying harmony of the piece. In other words, “all the notes written vertically
make up one gross constituent unit, that is one bundle of relations” (212). The musical no-
tation facilitates immensely the double order of reading: part of what Lévi-Strauss wants to
get at is a system of notation capable of rendering the “double” structure of a myth, e.g. a
narration normally considered only temporal and unilinear. We have reached a crucial point
in the illustration of the structural method:
the myth will be treated as an orchestra score would if it were unwittingly
considered as a unilinear series; our task is to reestablish the correct arrangement.
Say, for instance, we are confronted with a sequence of the type:
1,2,4,7,8,2,3,4,6,8,1,4,5,7,8,1,2, 5,7,3,4,5, 6,8. the assignment being to put
all the 1’s together, all the 2’s, the 3’s, etc.; the result is a chart:
1 2 4 7 8
2 3 4 6 8
1 4 5 7 8
1 2 5 7
3 4 5 6 8
We shall attempt to perform the same kind of operation on the Oedipus
myth. (213)
We should not be misled by the trivial simplicity of the numerical example, which presents
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S TRUCTURES (AND SPACES)
as given what actually has to be found in the myth: the correct indexing of the various ele-
ments. The task of the anthropologists, in fact, is far from trivial: they have to retrieve, be-
low the surface of the mythical narration, the deeper correspondences that bind together the
character and actions of the narrated story and represent its ultimate meaning. The applica-
tion to the Oedipus myth produces the following structure (which must be read from left to
right, to reproduce the narrative order, and from top to bottom to appreciate the four basic
“chords”, i.e. the basic relations generating the myth):

Cadmos seeks his
sister Europa, ravished
by Zeus
Oedipus marries his
mother, Jocasta
Antigones buries
her brother,
Polynices, despite
prohibition
F ROM LANGUAGE TO MYTH
How are we to read such a bi-dimensional chart? If we follow the natural order, we find a
skeletal version of the well-known myth, or, to be more precise, a rendition of a very old
(Homeric) version. This is of course the order in which the myth is told, or sung, in the com-
munity. The division by column, instead, stresses the “chords” to which the narration comes
continuously back, row after row. This redundancy is not to be imputed to some defective
feature of mythology. On the contrary, it represents, according to Lévi-Strauss, one if its
most basic characters: the oral narration repeats a basic structure in order to make it more
evident and easier to grasp for listeners who do not enjoy the privilege of a written text to
ponder over.
Thus, the linear diachronic order is governed by an intrinsic necessity analogous to
what we saw above in the case of games: as every board position in chess is generated by
a “move”—by the alteration of the previous position according to a rule—so each succes-
sive step in the myth’s plot is obtained by a development of the previous one according to
a specific rule. More precisely, by a development which belongs to the unit expected to
come next.
The Spartoi kill one
another
Oedipus kills his father,
Laios
Eteocles (Oedipus’
son), kills his brother,
Polynices
Cadmos kills the dragon
Oedipus kills the Sphinx
Labdacos (Laios’ father) = lame
(?)
Laios (Oedipus’ father) = leftsided
(?)
Oedipus = swollen foot (?)
Lévi-Strauss goes even further than merely suggesting the existence of a rule govern-
ing the temporal (diachronic) development of myths according to an atemporal (synchron-
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226
S TRUCTURES (AND SPACES)
ic) pattern. In the 1955 essay he proposes, in fact, a concrete formulation of the rule in
question, e.g. of the law instantiated by every single myth. As he says:
it seems that every myth (considered as the aggregate of all its variants)
corresponds to a formula of the following type:
F x(a) : F y(b) . F x(b) : F a-1(y)
Lévi-Strauss’s explanation of the law of the myth, which he usually calls “la formule cano-
nique,” or the “canonic formula,” is however quite cryptic in its original formulation, since
all he adds is that:
with two terms, a and b, being given as well as two functions, x and y, of
these terms, it is assumed that a relation of equivalence exists between two
situations defined respectively by an inversion of terms and relations, under
two conditions: (1) that one term be replaced by its opposite (in the above
formula, a and a-1; (2) that an inversion be made between the function value
and the term value of two elements (above, y and a). 15
Instead of trying to provide an explanation of the canonical formula on the basis of this
short and dense text, I will start from a less formal discussion of the internal articulation of
the structure of the myth and will come back to it at the end if this section. It is important
to keep it in the background, however, because Lévi-Strauss’s formal definition of the “law
of the myth” implies that when he speaks about “rules” we are not to take the term in the
general sense usually adopted in the social sciences, namely as the expression of an empir-
ically observed regularity that may nonetheless be violated in particular occasions. The for-
mulation of a formal law of the myth, or the possibility thereof, implies that the “rule” at
issue here is more akin to a rule of arithmetic, whose violation, far from being a manifes-
tation of creativity would only bring to incorrect results. We have already seen that a similar
interpretation of the concept of rule is at work in game-theory and in Artificial Intelligence
and we will show that the same interpretation is at work in Structuralism.
Let us begin, then, with a brief illustration of the four basic relations represented in the
vertical columns. The general structure is organized, according to Lévi-Strauss, along a pair
15. Claude Lévi-Strauss, Anthropologie Structurale…, 252-253; Engl tr. 228. Emphasis in the original.

F ROM LANGUAGE TO MYTH
of oppositions. The first column denotes a general overrating of blood relations: the char-
acters of the myth are relatives who keep or want to keep “too close” to each other against
social prescriptions to the contrary (Oedipus and Jocasta, Antigones and Polynices) and
therefore get into “social” troubles. The second column, conversely, represents an under-
rating of blood relations: the mythological characters are close relatives who acts as if they
were strangers (Oedipus and Laius) or even enemies (the Spartoi, Eteocles and Polynices)
and get into “natural” troubles, as it were, because they forget or are unaware of their con-
sanguinity and follow social laws alone. This opposition can be interpreted as a represen-
tation of the conflict between two commonly perceived origins of mankind in the society
in question: on the one hand, we have the hypothesis of an autochthonous origin (along the
model of plants) which would bring to a devaluation of family bonds. On the other, we find
the idea of the sexuate, biological origin of man which is emphasized in the first column.
The conflict is reproduced, at a different level, in the second half of the structure. The third
relation designates the killing of a monster, which is generally of chtonian origin, whereas
the last one points to general difficulties with walking or with standing upright, a feature
that myths commonly bestow on beings born from the earth.
Thus, one could say that the myth tries to instantiate a conflict between the two per-
ceived origins of mankind and on this regard, although the problem obviously cannot be
solved, the Oedipus myth provides a kind of logical tool which renders the contradiction
acceptable. It does so by showing that it is a common feature of human life; as Lévi-Strauss
expresses it: “by a correlation of this type, the overrating of the blood relation is to the un-
derrating of the blood relations as the attempt to escape autochthony is to the impossibility
to succeed in it. Although experience contradicts theory, social life validates cosmology by
its similarity of structure. Hence cosmology is true.” (216)
This interpretation of Oedipus has been widely criticized by scholars of Greek thought
and culture and Lévi-Strauss’ response has usually been to remind the readers that his use
of Oedipus was just meant to illustrate the basic procedure of the structural method on a
well-known myth rather than to suggest a real interpretation on a topic far off his area of
expertise. By and large, he has not answered these critiques, preferring instead to defend
227

228
S TRUCTURES (AND SPACES)
his applications of structural analysis to the American mythology. It should be noted, how-
ever, that the critiques have either accepted the basic tenets of Structuralism and tried to
correct Lévi-Strauss’s analysis by suggesting a different interpretation of the mythic mate-
rial, or they have rejected the structural method in toto on the basis of general theoretical
considerations (charges of reductivism and/or of rationalism, etc.) that do not affect the
concrete articulation of the structure Lévi-Strauss proposes but aim instead at showing its
untenable philosophical consequences. Since our goal, on the contrary, is not to discuss the
validity of Lévi-Strauss’s interpretation of this particular myth, but precisely to reflect on
the formal characteristics of the structure which makes it possible, we can largely dispense
with a discussion of the controversy that this essay has stirred and turn instead our attention
to a closer analysis of the structural apparatus. 16
Consider the four columns identified by the analysis. Each of them may be considered
as a variation, in a different narrative context, of the same element, as the same “move”
played again and again: a new family member slain, a new monster killed, a new crippling
arising, etc. Each column, in other words, “transforms” the same basic element, and the
whole structure can be defined as “the group of transformations of a small number of ele-
ments.” 17
Let me add a bit of notation here, just to understand what Lévi-Strauss has in mind with
this and other mathematical remarks. Suppose we denote with x the “killing of the father
(by the son)”, then 1/x might denote the (reciprocal) transformation of x, e.g. the killing of
the son (by the father)”, 1-x the killing of the brother (by the brother)”, etc. All these trans-
formations of the same element make up the bundle of relations defined as “underrating of
16. Examples of the first “integrative” category of critics are Michael P. Carroll, “Lévi-Strauss on the Oedipus
Myth: A Reconsideration,” American Anthropologist, 80 (1978), 805-814, and Jean-Pierre Vernant,
“The Lame Tyrant: From Oedipus to Periander;” “Ambiguity and Reversal: On the Enigmatic
Structure of Oedipus Rex,” both republished in Tragedy and Myth in Ancient Greece, Jean-Pierre Vernant
and Pierre Vidal-Nacquet, eds., (New York: Zone, 1988); an example of the second, “total” kind
of critiques is furnished by Robert C. Marshall, “Moses, Oedipus, Structuralism, and History,” History
of Religions, 28, 3 (1989), 245-266
17. Claude Lévi-Strauss, Anthropologie Structurale Deux…, 164; Engl tr. 137. The notion of group is taken
by Lévi-Strauss in its technical algebraic meaning: the closed structure formed by a set of elements
and an operation completely defined on them and provided of a neuter element

F ROM LANGUAGE TO MYTH
blood relations” and previously assigned to the second column. Once the procedure has
been repeated for all the basic relations, the whole structure of the myth analyzed can be
represented by a matrix of the following form:
.....
Lévi-Strauss comments the matrix by saying:
If our conception is adopted, the order of chronological succession is reabsorbed
into an atemporal matrix structure, the form of which is indeed
constant. The shifting of functions is then no more than one of their modes
of permutations (by vertical columns or fractions of columns. 18
The matrix above represents only a partial view of the structure, though, as we might have
guessed from the analogy with the chess-game: the matrix corresponds to a specific, par-
ticular version of the myth, i.e. to a specific chess-game. In fact, the transition from one col-
umn to the next represents a specific, single application of the basic rules (e.g. the laws of
the myth), more or less like the transition from the initial chessboard position to the position
produced by the application of the pawn-moving rule to the king pawn. The matrix as a
whole, then, should not be mistaken for the analogous device used in game-theory to rep-
resent the game, e.g. the space of all possible strategic interactions made possible by a set
of rules. Rather, Lévi-Strauss’s matrix represents a partie, or a play, in strict game-theoretic
terminology. In other words, it bears more resemblance to a single vertical path within the
search-space than to the space itself.
w -x 1/y 1-z
-w 1/x 1-y z
1/w 1-x y -z
1-w x -y 1/z
........ ......... ......... .........
......
Thus, we might ask: what would properly describe the entire space of all possible Oe-
dipus/chess myths/games? A stack of matrices, of course: as Lévi-Strauss says, “we shall
......
......
18. Claude Lévi-Strauss, Anthropologie Structurale Deux…, 165; Engl tr. 138.
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230
S TRUCTURES (AND SPACES)
then have several two-dimensional charts, each dealing with a variant, to be organized in a
three-dimensional order, as shown in fig.16, so that three different readings becomes pos-
sible: left to right, top to bottom, front to back (and viceversa)”(217). The diagram referred
to as fig.16 by Lévi-Strauss is a representation of a stack of cards of the following form:
Note that this representation works if and only if the relations binding the homologous
cells belonging to the different matrixes of the stack are of the same order as those binding
the cells within a single matrix. The stack is not just a juxtaposition of matrices, but really
a higher order matrix with three dimensions. It comes natural to ask if one needs more di-
mensions to do justice to the complexity of myth and to its many aspects. Lévi-Strauss rec-
ognizes immediately that the simple stack cannot correspond to the complete structure he
envisioned, since the analysis could and should be enlarged to encompass multiple frames
of references. But “as soon as we try to enlarge the comparison, the number of dimensions
required increases until it appears quite impossible to handle them intuitively.” The struc-
ture becomes so complex that, according to Lévi-Strauss, “progress depends largely on the
cooperation of mathematicians who would undertake to express in symbols multidimen-
sional relations which cannot be handled otherwise” (219). The final result is that there is
no single “true” version of the myth which all the others copy or distorts. Every version,
from ancient Greece to Freud, belongs to the myth.
1
2
3
4
...
It might seem a strange assertion to put Freud’s version of Oedipus on a par with
Sophocles’s, but according to Lévi-Strauss it is just a consequence of the hierarchical rela-
tion between hidden structure and surface appearance that we have already seen at work in
AI. A different version always belongs to the same myth, if the four basic relations are re-

F ROM LANGUAGE TO MYTH
spected, and it must be so, for the structure to be such. Indeed, if a newly discovered version
proved irreducible to the analysis, it would not show the insufficiency of the method but
the necessity of a more sophisticated description of the underlying structure. Again, there
is no true, original version of the myth, as well as there is no “authentic” and original game
of chess. Rather, the opposite is true: anyone of the almost infinite series of narrations is a
“true” version insofar as it represents a further example of the combinatorics generated by
the application of the basic rules. 19
The basic rule governing the transformation from one version of a myth to another is
the “canonical formula” we mentioned, with no further discussion, at the beginning of this
section. A particularly clear explanation and explicit application of the law to the mythic
material of the Americas is given by Lévi-Strauss in, “The Jealous Potter,” a study of a se-
ries of South and North American myths written almost 30 years after the publication of the
essays on “The Structural Study of the Myth.” The cycle analyzed in the book begins with
a myth belonging to the Jivaro, a South American population living on the eastern slopes
of the Andes between Ecuador and Peru. It tells the story of a woman named Aôho (a word
meaning Goatsucker, a nocturnal bird) who had two husbands, Sun and Moon; Sun was
warm and powerful, while Moon was cold and weak, and Aôho preferred the former to the
latter. Moon took offence and climbed up to the sky on a vine, blew on Sun and eclipsed it.
Aôho tried to follow Moon into the sky bringing with her a basketful of clay, but Moon saw
her coming and cut the vine. Aôho fell to the ground and was transformed into the bird that
bears her name, the Goatsucker, while the clay scattered on the earth, where it can now be
found. 20
19. An even more “playful” interpretation of Oedipus is presented by Lévi-Strauss in the last chapter of
La potière jalouse (Paris: Plon, 1985): Engl tr. The Jealous Potter (Chicago: University of Chicago
Press, 1988) where the structure of Sophocles’s Oedipus Rex is shown homologous to Eugène Labiche’s
farcical play’s The Italian Straw Hat. Lévi-Strauss concludes the analysis by saying: “The
scheme, however, remains the same: it consists of a set of rules aimed at bringing coherence to elements
that are at first presented incompatible or even contradictory.” (264/202). Lévi-Strauss commented
the Oedipus myth in at least one other occasion: his inaugural address at the Collège de France
(1960), now in Anthropologie structurale deux…, 32-35; Engl tr. 21-24.
20. This is of course a summary of the summarized version of the first variant of the first myth retold as
by Lévi-Strauss, but it will suffice to illustrate the application of the canonical formula. See Claude
Lévi-Strauss, La potière jalouse…, 23-24; Engl. tr. 14-15.
231

232
S TRUCTURES (AND SPACES)
The myth poses many questions to the interpreter: what is the relation between the art
of pottery and jealousy? Why does a nocturnal, plaintive bird like the Goatsucker plays a
central role in it? Or, more generally, what is the relation that binds together the clay of pot-
tery, the Goatsucker and jealousy?
Lévi-Strauss does not provide a direct answer to these questions but proceed, instead,
to a reconstruction of the internal dynamic process presiding to the development of the
myth and its relations with other myth from neighboring area in order to bring out its con-
stitutive structure. He remarks that the myth confronts us with two characters and two
“functions:”
- the Woman (w) and the Goatsucker (g) are the two characters, e.g. the bearers of particular
attitudes and “functions;”
- Jealousy (j) and Pottery (p) are the two functions, e.g. two attitudes that can be applied
to the characters to modify them.
After having shown that, in South American mythology, the Goatsucker itself “functions”
as a jealous bird or as a cause for jealousy, Lévi-Strauss establishes a relationship between
the first two character of the following form:
F j(g) : F p(w)
e.g. the jealous goatsucker (i.e. the function “jealous” applied to the goatsucker) stands in
relation to the woman potter (i.e. the function “potter” applied to the “woman”). It remains
now to find out how to apply the remaining part of the formula, e.g. the second correlation.
If we remind that the original formulation was
F x(a) : F y(b) . F x(b) : F a-1(y)
and transpose j for x, g for a, and p for y, we obtain a relation of the following form:
F j(g) : F p(w) . F j(w) : F g-1(p)
which we can comment, with Lévi-Strauss, as
the “jealous” function of the Goatsucker is to the “potter” function of the
woman as the “jealous” function of the woman is to the “reversed Goatsucker”
function of the potter. What does this mean? (79/57)

F ROM LANGUAGE TO MYTH
It means that, in order to complete the double relationship prescribed by the canonical
formula, one needs to find a double congruence that relates, on the one hand, the woman
and the bird with respect with jealousy and, on the other, a bird with pottery. Lévi-Strauss
is indeed able to find a bird, the Ovenbird common in North America and in North Amer-
ican myths, that fulfills this congruence. The Ovenbird is a “reversed” Goatsucker since it
is a diurnal animal (vs. the nocturnal features of its opposite), it carefully builds a nest
whereas the Goatsucker its the eggs on the ground, and it sings joyfully instead of emitting
a sad, repetitive cry. The mythographer’s task, therefore, becomes to investigate the fea-
tures of this bird as it appears in mythology, and to find out whether the Ovenbird myths
can be interpreted as reversed Goatsucker myths. Or, in other words, whether the myths in
which the Ovenbird appears can be considered as “variants” of the Jivaro myth from which
the analysis started.
The answer, as expected, is indeed positive and the analysis of North American my-
thology brings forth a rich material confirming what Lévi-Strauss calls his “transcendental
deduction,” i.e. the deduction of a missing link in the logical organization of the mythic ma-
terial conducted solely according to theoretical considerations. Lévi-Strauss follows the
transformations from one myth to another across the two continents, and is eventually able
to reconstruct, after several applications of the canonical formula, a double series of oppo-
sitions organized along the axis container/contained that is actualized in the myth as fol-
lows:
Potter’s clay undergoes extraction from the earth, then modeling, and then
firing to become a container designed to receive a content: food. Food itself
undergoes the same treatment, but in reverse: it is first placed in a clay container,
then cooked, then processed in the body through the operation of digestion,
and finally is ejected in the shape of excrement:
clay → extraction → modeling → firing → container
excrement ← ejection ← digestion ← cooking ← food 21
21. Claude Lévi-Strauss, La potière jalouse…, 232; Engl tr. 175.
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234
S TRUCTURES (AND SPACES)
Thus, at the end of the journey across the myths concerning pottery, Lévi-Strauss does
not disclose the “meaning” of the original myth. Rather, he shows that there can be no an-
swer, no “meaning,” at the content level because the myth (as the ensemble of its variants)
rather organizes a series of contents. This organization articulates, in turn, the passage be-
tween nature and culture: “the lesson taught by these myths, say Lévi-Strauss, is that earth
must no longer be what men eat but must instead be cooked, like food, in order to enable
men to cook what they eat.” (234/176). The myths, in other words, articulate the distinction
between humanity and nature and since this articulation is governed by a series of transfor-
mations governed by the canonic formula, it follows that he canonic formula itself—inter-
preted as the general law presiding the very possibility of a distinction between nature and
culture and instantiated in mythical cycles—is what, ultimately, turns men into humans.
The formula, it is important to stress it for our current purposes, allows the transition
among myths through the transformation of the same theme across different codes and
across different cultural areas. This concept of transformation, in turn, is embodied in its
most salient form in the formula’s last element (F a-1(y)), where we witness what has been
called a “double twist,” or a torsion surnumeraire, which switches a function to a term (y)
and, at the same time, a term into its opposite (a-1). It is this double reversal that, by con-
necting different codes and different myths, allows the cycle to proceed from one step to
the next until, ideally, the closure of the set has been fully exploited with a return to the
point of origin. 22 This closure, however, is not static: it is not given once and for all at the
outset, It is, rather, dynamically reached by the myths that propel themselves forward, one
step at a time and from one move to the next, through the peculiar structure of the formula
that governs their development. In this sense, the canonical formula and its “double twist”
can be seen to play a role quite analogous to the “atom of kinship” that, as we saw above,
ties together different components of the social groups by regulating an exchange that re-
22. The numerous reformulations of Lévi-Strauss’s formula, like Mark Mosko’s, in “The Canonical Formula
of Myth and Non-Myth,” American Ethnologist, 18, 1 (1991) 126-51, that try to replace the problematic
last element with a simpler F x(a) : F y(b) . F x(b) : F y(b), and reducing it to a form of analogy miss,
therefore, its most important aspect.An important discussion of the intrinsic complexity of the formula
is contained in a special issue of L’Homme recently published: Emmanuel Désveaux and Jean Pouillon,
eds., La formule canonique des mythes, L’Homme, 35, 135 (1995).

S EARCH- SPACES AND STRUCTURES
peats itself at each successive generation. If the “great game of marriage” could proceed
because of the intrinsic dynamics of the structure devised by Lévi-Strauss to explain the
phenomenon of kinship as an exchange of women, the same is true, at a different level, for
mythology: myths, when considered as the ensembles of their variants, are really like a
game, because they appear as a self-propelling series of discontinuous moves tying togeth-
er different themes, and taking place within a combinatorial universe defined by a basic
rule, e.g. by the canonical formula.
3. Search-spaces and structures
Let us now attempt a closer comparison of Artificial Intelligence’s and Structuralism’s
theoretical objects. To begin with, one might notice that there are at least two levels to be
considered in a comparative analysis of AI’s search-spaces and Lévi-Straussian structures.
First, I will deal with “internal” features of the objects of our interest, starting from the
properties they seem to share like closure, discreteness, compositionality, and ending with
what might be considered a point of divergence: the seeming overabundance of structural-
ity in Lévi-Strauss's model. Then, in the next chapter, I will address what might be consid-
ered “external” issues, questions concerning the “origin” of structures and their role in the
larger philosophical discussion.
Let us tackle closure first. There is no doubt that the multi-dimensional structure un-
derlying a myth makes up a closed system. To be more precise, the possibly infinite struc-
ture generated by the various transformations within a single bundle of relations and the
permutations among them make up the closed system of the myth. Any permutation of the
four basic relations we saw at work in Oedipus will produce a new version of the same
myth, as well as any transformation of a specific element of the same relation into another.
Although Lévi-Strauss does not dwell on closure, we may rest assured on this point at least
from his explicit reminder of the analogous notion of system used in structural linguistics,
where the property of closure is an integral part of the axioms of the discipline. The system
generated by the structural law of the myth, as well as by the rules of chess, is closed and
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S TRUCTURES (AND SPACES)
it is so by assumption. Or rather, as Lévi-Strauss would put it, “structural anthropology not
only proclaims that mythemes are always parts of a system: it shows concrete mythological
systems and elucidates their structure.” 23
Notice that the closure of the set under the prescribed operation does not imply that the
group must be finite but only that the application of the basic operator will necessarily pro-
duce another element of the set. Thus, the natural numbers form a group under addition,
since every application of the + operator on two natural numbers produces another natural
number and there are of course an infinite number of them available. However, since the
group that Lévi-Strauss deals with is a group of permutations, it is reasonable to think that
the set is finite. It could be infinite only if there were an infinite number of relations among
the basic constituent elements of the set, something that does not seem plausible, at least
from the explanatory point of view, since the purpose of the theory is precisely to make
sense of a possibly infinite number of observable elements in terms of a manageable (and
therefore, not just finite, but small) number of units.
In the case of chess-like search-spaces the point is obvious: by definition, there is no
chess-game which cannot be played by following the rules of chess, since the game is sim-
ply the totality of the rules which describe it. 24 Games are perfect illustrations of closed sys-
tems: they set up a system of conventions which defines what properly belongs to the
universe of the game and what does not. Moreover, is the “conventionality” that matters,
and not the content of the rules. Indeed, the content can be void because all-encompassing
and the game would still be a game: the mere existence of a conventional rule as a rule de-
fines it as such. Consider for example, the yes/no game that delights so many children when
they reach a sufficient command of language: the child decides that she wants to play by
assuming that all the other’s answer will have their meaning switched. What is peculiar of
this game is that there is no way to exit it: each linguistic interaction, be it used playfully
23. This is Jakobson’s formulation, actually, which Lévi-Strauss quotes as the dictum that anthropology
must follow in Anthropologie Structurale…, 40; Engl. tr. 33.
24. This is of course von Neumann's original definition, but it is reported almost verbatim in Anthropologie
Structurale…, 329; Engl tr. 314-5. See also Edouard Delruelle, Claude Lévi-Strauss et la philosophie…,
50-52.

S EARCH- SPACES AND STRUCTURES
or not (e.g. be it used with the intent to play or not), is still within the game, since the latter
is, formally, a meta-linguistic game played with the rules of language. 25
In short, games, especially if widely construed as in the previous example, provide
such a nice illustration of closed systems that one is tempted to propose an identity between
the two concepts.
Second, discreteness. It might seem obvious, but the structures we have seen at work
above are essentially discrete. Games, myths and the like, on the contrary, are generally not.
At least on the surface, since it is difficult to see how any sport, child's game, complex nar-
ration and so on could be adequately described as composed by a small set of elements and
some operations completely defined on them (otherwise the system could not be closed).
In fact, if the underlying structure is composed of discrete elements and laws of com-
position defined on them, then it is possible to generate the surface phenomena via an al-
gebraic, combinatorial procedure: each phenomenon embodying one of the possible
combinations of the basic elements. If it is impossible to retrieve discrete elements a formal
treatment is still possible, but at a price neither of our authors is much willing to pay: the
introduction of measurable quantities which makes possible the use of classical analytic
equations. Lévi-Strauss is explicit in his rejection of a quantitative mathematics which, he
thinks, has generally fared quite poorly in the human sciences (economics, mathematical
psychology, demography) because of the oversimplification necessary for the introduction
of measurable quantities. On the contrary, he sees as crucial to the social sciences the intro-
duction of the new, qualitative mathematics:
there are many branches of mathematics — set theory, groups theory, topology,
etc. — which are concerned with establishing exact relationships
between classes of individuals distinguished from one another by discontinuous
values and this very discontinuity is the essential characteristics of
25. In Philosophical remarks, Wittgenstein notes: “I can play with the chessmen according to certain rules.
But I can also invent a game in which I play with the rule themselves. The pieces of the game are now
the rules of chess, and the rules of the game are, say, the rules of logic. In that case I have yet another
game and not a metagame.” See Ludwig Wittgenstein, Philosophical Remarks (New York: Harper and
Row, 1975) 319. Children seem to agree with Wittgenstein wholeheartedly, and display even more sophistication
since they play, in language, with the rules of language.
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qualitative sets in relation to one another and was the feature in which their
alleged ‘incommensurability,' ‘inexpressibility,’ etc., consisted of. 26
The point to underline here is that, if our analysis is correct, the almost obsessive insistence
on combinatorics is just the surface effect of the properties of discreteness and closure pre-
viously outlined.
And in fact research on AI is extremely committed to the combinatorial approach.
Haugeland, for example, affirms that “the versatility of thought is attributed to a combina-
torial structure essentially like the compositionality of symbolic systems. Artificial Intelli-
gence embraces this fundamental approach—to the point indeed, of arguing that thoughts
are symbolic systems.” 27
But what combinatorics makes undoubtedly more vivid is the problematic relation of
the algebraic structure with respect to the object of analysis. Often, the existence of a dis-
crete structure is explicitly posited at an unconscious level as the explicative grounding of
a range of surface phenomena which are essentially continuous. The basic insight of struc-
tural phonology taken up by Lévi-Strauss is precisely of this kind: below the sensible ex-
perience of a continuous spectrum of infinite sounds lies the level of a small number of
discrete phonemes. Analogously in anthropology, according to Lévi-Strauss an almost in-
finite ensemble of myths or of kinship terms can be explained from a small number of aptly
posited elementary particles. The relations between the two levels is first and foremost
epistemological: the deep structure can explain the surface level because the former ele-
ments and laws can reproduce the latter's phenomena.
The solution to this problem differs substantially in Artificial Intelligence and Struc-
turalism and a proper discussion requires a more general consideration of the relationship
26. Claude Lévi-Strauss, “The mathematics of man”, International Social Sciences Bulletin, Unesco, Paris,
vol. VII, 4, 1954, 586, emphasis added. In “Social structure,” a contemporary essay later republished
in Structural anthropology, we can read a very similar passage, but with the exempla of the
quoted theories: von Neumann and Morgenstern's Theory of Games, Norbert Wiener's Cybernetics and
Shannon and Weaver's Theory of communications. See Claude Lévi-Strauss, Anthropologie Structurale…,
310; Engl tr. 283.
27. John Haugeland, Artificial Intelligence…, 93.

S EARCH- SPACES AND STRUCTURES
between the structures’ closure and their relationship to a substrate. The next chapter will
address this issue in detail.
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CHAPTER VI
ANACLASTIC
SUPPLEMENTS
in which the reader is shown why games need a supplement to fix
them in place, and why AI’s own does not quite work as desired.

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1. Game, Spiel, and the End
At the end of chapter 2, I proposed to interrogate the strong connection between the
“end of philosophy” (in all its aspects) and Spiel I had retrieved on Hegel by examining the
same connection in other, non-philosophical domains. I then proposed a search articulated
by four basic questions that can be summarized as follows:
(a) find out whether the concept of Spiel could be found playing a similarly crucial role
in other, non-philosophical efforts that are likewise striving to put philosophy to an end.
(b) find out how the concept of Spiel is internally articulated. i.e. find out which, if any,
concrete concept of game/play the disciplines in question would build from the very rich
and possibly contradictory range of phenomena we may associate with the words “game”
and “play,” a range that seemed to be polarized by the opposition serious games vs. chil-
dren’s play.
(c) find out how the conception of Spiel discovered in step (b) above would relate to
the more general (non-)philosophical discourse and its end. In particular, how it would deal
with the issues of the sense of the relationship between Spiel and end, and of the subject of
Spiel.
(d) finally, assess whether the particular conception(s) of Spiel described at (a)and (b)
would be up to the task required by (c). In other words, assess whether the goals of the non-
philosophical projects, their ends, could be reached by the use of the particular concepts of
Spiel deployed.

T HE SUPPLEMENT
We now have an answer for the first two questions: we have seen that Artificial Intel-
ligence and Structuralism can indeed be understood as non-philosophy and that their
projects depend on a particular interpretation of Spiel as game. We have also seen that this
concept of game receives a fine theoretical articulation in two very similar, but not identi-
cal, theoretical objects—search-spaces in the former case and structures in the latter—that
are crucially related to their overall goals.
It is now time to move to the second part of the proposed program and try to answer
the last two questions: first, how—that is, in which sense and for whom—do search-spaces
and structures bring non-philosophy to an end? Second: do they succeed in the task?
Both conceptions fail, I will argue, and for very interesting reasons. The described
structures run into troubles at two levels: as a theory of Spiel and as a non-philosophy of
mind (or esprit). Since the root of the trouble is the same, the choice of which side to ana-
lyze is actually indifferent, since either will bring us to the other one.
I will then start from the inability of the structure as described to provide a theory of
the (individual or collective) mind. The failures have to do not so much with the particular
disciplines in question but with the inability of the proposed conceptions of game to suc-
cessfully force the multifariousness of Spiel into one of its poles. Thus, the time spent will
not be spent in vain, insofar as we will learn something, and hopefully something impor-
tant, about game, Spiel, and the end.
2. The supplement
In the previous chapter, I have emphasized that search-spaces and structures are totally
closed, in the sense that every operation performed on their elements can only produce an-
other element of the set (another chess-position, another mytheme, etc.). Search-spaces and
structures, to put it a little differently, must be totally self-contained in order to perform
their theoretical, and especially their philosophical tasks. It is very important to discuss in
some detail this concept of closure, because the assessment of AI’s—and, respectively,
Structuralism’s— (non-)philosophical success depends on it. In particular, we need to un-
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derstand what is closed off by the theoretical objects, i.e. what lies outside of it. And, con-
versely, what is “closed in,” i.e. what is captured within the field delimited by the formal
operations that define it.
Let us think, once again, of what would happen to AI’s conception of chess if the
search-space corresponding to it were not self-contained. Troubles may arise at two levels:
first, there may be more to the game of chess that just a structured set made up of chess
positions and rules. Second, the structured set itself may not be closed, either because it
would be possible to produce a position on the chessboard by not following the rules, or
because an application of the rules would bring about an illegal position on the chessboard.
In both cases, the search-space would not constitute a correct characterization of the game
of chess, since something would escape it.
A little Venn-like diagram may help clarify the issue. (For the sake of brevity, the dis-
cussion is conducted in terms of the Artificial Intelligence representation of chess. A sub-
stitution of the equivalent structuralist terms would yield the same results, as it is made
explicit later in the text.)
Let us suppose that A represents the set of all the legal configurations of chess-pieces
on a chessboard, e.g. all the possible configuration that can be encountered in real chess
games as the game has been played since it came into existence. Let us then take B to rep-
resent the set of all the possible configurations of pieces generated by the rules of the game
as embodied into an Artificial Intelligence chess-playing program, e.g the set of all the
nodes in the search space representing the complete game of chess: 1
A
Legal chess positions
“ Castle King Queen-side”
“ Move pawn forward”
Positions produced by AI rules
1. More correctly, the comparison should be conducted in terms of chess-games in real-life chess and,
respectively, complete vertical paths in AI-generated search spaces, rather than in terms of configurations
of chess pieces on a board and the corresponding nodes of the search spaces. I am simplifying
for the sake of clarity.
B

T HE SUPPLEMENT
Furthermore, let suppose that C represents the game of chess in its more general sense.
C
The game of chess as it is really played, e.g.
"in itself"
The claim of self-containment can be interpreted as a double requirement on the rela-
tionships among A, B, and C. First, it is clear that no situation like the following can arise:
A
B
A and ~B B and ~A
B and A
Irreproducible Iegal
chess positions
Illegal rule-produced
chess positions
There cannot be configurations that the rules cannot generate nor there can be rule-
generated configurations that do not count as legal positions. 2 If we consider only the rules
governing the movement of the pieces, the coincidence between A and B seems, nowadays
at least, fairly trivial to accomplish, because it just means that the machine must be able to
play a “legal” game of chess. 3 However, we have seen that it is crucial to Artificial Intelli-
gence that “heuristic” rules be included as well in its repertoire, e.g. rules that govern the
2. Completeness and consistency, roughly speaking, must endow the relationship between A and B.
3. The task was far from trivial, instead, when computing machines were primarily considered number
crunchers and the basic tools needed to represent chess-positions and transitions between them did not
exist yet. In fact, the early literature on chess-playing machine quotes this as a major accomplishment.In
the early stages of development of computer science, the expressive needs of Artificial Intelligence
programs represented a major stimulus toward the development of higher-level programming
languages, like IPL, the predecessor of LISP (later developed by John mcCarthy) that Simon, Shaw and
Newell, had to invent in order to pursue symbolic programming and, of course, LISP itself. See Allen
Newell, J.C. Shaw, and Herbert Simon, “Chess-Playing Programs and the Problem…,” 63 ff, and
above, sect. IV.3 for a detailed discussion of this issue.
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choice of “plausible” positions. This means that we must read “legal” as “acceptable to a
competent chess player,” e.g. a grandmaster. As a consequence, the required coincidence
between A and B becomes far less trivial than it may appear. The incompetence of an au-
tomated chess player, in fact, could be measured by the size of the two side areas of the di-
agram, since A and ~B includes all the positions that a competent human player would use
but the machine cannot fathom and, conversely, B and ~A comprehends all the “blunders”
that a grandmaster would never make.
The two outside portions of the ovals must be empty, or, what amounts to the same, it
must be the case that A=B. This set, let us call it AB for brevity, represents the competence,
in the Chomskian sense, of an ideal chess player, be it human or not.
Furthermore, and this is the most interesting philosophical claim, no similar situation
can arise between AB and C.
C
AB
C and ~ AB
C and AB
~C and AB
Aspects of chess
irreducible
to chessboard
configurations
Irrelevant chess configurations
The set C represents the game of chess played “in real life,” the activity we see per-
formed in a chess club, in a living room, or at a park. Therefore, the portion of the diagram
labelled C and ~AB would denote whatever part of the game of chess (and not just the game
of chess in the narrow sense of game that we have seen developed by AI, but chess as an
instance of Spiel) is not captured by rule-produced configurations. For example, shouting
at the opponent, making snide remarks about the opponent’s ability to play the game, etc.,
all relevant parts of the game of chess in the blitzkrieg games usually played around the
formal tournaments, would certainly qualify as instances of the first set, e.g. C and ~AB.
Conversely, ~C and AB would stand for legal configurations of pieces on the chessboard
that have nothing to do with the game itself: for example, opening moves that the theory of
the game has discarded, at least for the time being, as unproductive, would qualify as mem-

T HE SUPPLEMENT
bers of ~C and AB. 4 Both these aspects must be shown to be irrelevant to the game of chess
as it really is, or to the myths as they really are, if total closure is to be achieved. In short,
the game of chess as embodied in a search-space is totally self-contained only if the three
sets are equivalent: A=B=C.
The crucial issue, it will have been reckoned already, is represented by the relationship
between C, the “real game,” and AB, the game interpreted as the product of the rules. No
one can deny that, prima facie, the elements contained in the two sets are quite different:
wiping out the pieces on the chessboard in a fit of anger can happen in real life but not on
a computer screen: humans have “fun” playing the game of chess, and sometimes get mad
at it, while computers do not seem to. The issue is whether the superficial differences hide
a substantial identity to be retrieved at a deeper level, so that the fits of anger of a frustrated
player or the expressions of delight generated by an “elegant combination” can be shown
to be either irrelevant to the game of chess or considered an epiphenomenon indirectly gen-
erated by the rules themselves. To put it differently, the issue is to determine whether the
portion we have labelled C and ~ AB can be shown to be, at a deeper level than phenomenal
reality, to be empty or producible as a result of the rules contained in AB. The fate of AI and
Structuralism as successful (non-)philosophies hangs on this point, as I will show.
Notice, however, that the violation of one of these constraints, in itself, does not nec-
essarily condemn search-spaces (or structures) as a viable explanatory device to understand
some significant portion of games (or, respectively, of myths). A good deal, and perhaps
most, of what is relevant to playing the game of chess can be understood in terms of navi-
gating a search-space with the appropriate heuristics rules. Proof of this fact is that we can
actually build automatic chess-players that can perform at an excellent level. At the episte-
mological level, then, the lack of self-containment would not be all that bad, since it would
result in a partial but nonetheless still useful—that is, explanatory—theory. Things stand
differently at the philosophical level. We have seen that Artificial Intelligence is not just af-
ter a “good explanation” of certain aspects of cognitive activity when considered from a
4. For a discussion of the first class of examples see Alan Aycock, “Finite Reason: A Construction of
Desperate play,” Play and Culture, 5, 2, (1992) 182-208.
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well-defined theoretical angle. AI is after the real thing: it wants to provide a theory of what
thinking is by exhibiting the actual process. Similarly, Lévi-Straussian structuralism is not
after yet another “explanation” of kinship and religion: it is after what kinship and religion
actually are. This means that nothing—that is, nothing relevant to thinking, kinship and re-
ligion, respectively—is theoretically allowed to escape search-spaces and structures. If kin-
ship is a complex structure regulating the exchange of women that forms the social bond—
as Lévi-Strauss claims—then there cannot be a form of kinship that cannot be generated by
the basic structure. Otherwise, we would not get what kinship is, what it is in itself, to use
the Hegelian jargon. Any kind of incompleteness that search-spaces and structures may
show—for example, the lack of an account of emotions, for AI—can only be accepted as
temporary, as a partial shortcoming of a basically sound approach that will, in due time, be
able to accommodate them. Thus, although they may actually be incomplete given their
present state of development, both AI’s and Lévi-Strauss’s theoretical objects must be ca-
pable to attain, in principle, total self-containment.
This point is seldom acknowledged in the literature on AI. On the contrary, the core of
almost all the debates in the so-called “philosophy of AI” disregards the issue of the rela-
tionship between C and AB to focus its attention exclusively on the relationship between A
and B.
Thus, for example, disagreements over the possibility of a complete mapping between
the elements of A and B represents the core of almost all the debates in the so-called “phi-
losophy of AI” literature. Critics point out some incompleteness of the basic AI model in
order to show that self-containment cannot be attained and therefore the overall philosoph-
ical project of Artificial Intelligence is doomed unless it recomprehends itself as a mere tool
to be used in empirical psychology (e.g. unless it recomprehends itself as “weak AI,” in
John Searle’s terminology). AI’s supporters retort that the criticism misses the point be-
cause the incompleteness pointed at is just a temporary limitation that has been pragmati-
cally enforced in order to focus on a simpler model, but will be removed when the theory
is more developed. 5 It should be emphasized, however, that this issue is, in principle, the
least contentious, and the less philosophically interesting of the two relationships among

T HE SUPPLEMENT
the three sets A, B, and C. The mandated equivalence A=B, thus, provides the completeness
and consistency required from the formal objects devised by AI and Structuralism and guar-
antees, therefore, their explanatory adequacy. The issue, here, is purely extensional: it is a
requirement on a formalism that may be not too powerful nor too poor. But the terms in A
and B belong to same domain: chess positions algebraically rewritten, for example, or
myths broken down to sentence-like mythemes. The problem is to determine whether the
empirically given configurations can be reproduced (e.g. generated) by the rules governing
structures or search-spaces. This does not mean that the issue is trivial, nor that its accom-
plishment does not require a good deal of theoretical effort, especially when, as in Lévi-
Strauss’s case, the available material, e.g mythical narratives, are given in a form very dif-
ferent from what the theory needs (e.g. mythemes) in order to construct its structures. The
reduction of chess games to ordered series of chessboard configurations is a relatively eas-
ier task, once it has been decided to focus the attention on that aspect of the game. On the
contrary, the reduction of the wealth of semi-continuous narratives into single, discrete el-
ements is far from trivial and, in itself, no small accomplishment. The same may be said for
AI’s search-spaces that deal with “fuzzy” domain where the definition of a “state” and a set
of rules governing the transition between states is not empirically given, like, for example,
vision or natural language processing. Yet, for all their importance as technical achieve-
ments, and in spite of all the ink that has been spilled on the matter, the relevance of AI and
Structuralism as successful non-philosophies does not hang on the resolution of this point. 6
Or rather, to be more precise: this is not the most difficult issue to solve, it is just a prelim-
inary to the real challenge that concerns the nature of the relationship between C and AB,
between the “world” and the object of the spaces or structures. The really thorny and philo-
sophically interesting issue is how to think the relationship between objects belonging to
5. See, for example, the debate following the publication of Hubert Dreyfus’s book, What Computers
can’t do, and the controversy around John Searle’s critique of AI’s “strong research program” program
presented in the issue of The Behavioral and Brain Sciences that contained his original paper (“Brains,
Minds and Programs”) and the peers’ commentaries.
6. In fact, one is tempted to grant AI researchers their wish and let empirical research decide the issue
instead of curtailing any prospect of a possible solution via principled philosophical arguments on the
impossibility of the relationship as such. Such an answer would at least clear the ground and redirect
the debate toward the more challenging philosophical issue.
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two different orders of reality; how, in other words, to connect the formalism to the real
world of lived chess games and embodied myths.
And yet, this formulation is already misleading because, by resorting to the term “for-
malism” it suggests or presupposes that we are interpreting the elements of AB as “formal”
objects connected, via some mapping function, to an external pre-given domain. The notion
of “formality,” however, represents precisely a solution to the problem at issue, a problem
which is solved as much by the framing of the terms as by the invention of some sort of
correspondence between the two domains. In other words, we should not be tricked into
thinking that the problem can be reduced to finding a way to bind together the elements of
AB and C. Part, and perhaps the most important part, of the problem, is precisely to deter-
mine how to interpret the terms themselves. The crucial step is taken when we assign a sta-
tus, both logical and ontological, to the terms of the relationship.
Search-spaces and structures belong to a different ontological level than chess games
and religious behavior since chess games are not, prima facie, collections of rules, nor are
rituals groups of permutations of basic relations. Yet, there can be no principled separations
between the two levels, lest the philosophical claims put forward by the two schools are
given up. The necessary self-containment of the theoretical objects makes the co-existence
of these two levels all the more difficult to solve: it must be possible to understand [or
think] how the basic elements of search-spaces and structures can be exhaustively mapped
onto the wide range of surface phenomena. Search-spaces and structures are ontologically
“detached” from the phenomenical level and must be so in order to obey the requirement
of closure. We need a relationship between the elements of the envisioned search-spaces
and structures and the concrete phenomena that they are supposedly underlying. 7
7. Instead of “detachment,” I could have used the more common term “abstraction” which, etymologically,
means the same thing, “ab-trahere” meaning “leading away” in the sense of “separating, “taking
apart,.” However, “abstraction” is such a loaded word in this context, that “detachment” has seemed
preferable. To characterize search-spaces and structures as “abstract” (or even worse, “formal”) might
lead us to think that we know what we are referring to because we are familiar with the term, whereas
the effort I am engaged in is precisely to try to understand what detachment involves and how it can
be dealt with.

T HE SUPPLEMENT
Notice, again, that the detachment entailed by self-containment is problematic only at
the philosophical level: it is because a group of permutations of basic relations represents
what a myth actually is, that its detachment from the surface level, e.g. the narrative se-
quence, of the myth represents a problem. If it were just a possible explanation of how my-
thology might work, the ontological gap between the structure and the myth would be
relatively harmless. A search-space or a structure may then be interpreted as a “model” of
the surface phenomena that gains its relevance from its explanatory power. We may be able
to understand, or rather to model, a myth in several different ways, Structuralism’s being
one of them, according to different, extra-theoretical needs. However, if Lévi-Strauss’s
claim that the myth is just a group of permutations of basic relations is to hold, then we need
an account of what connects the basic relations to the surface elements of the myth and not,
for example, to any other surface phenomenon, be it mythological or not, because the group
of transformations is, in a sense, ever more real than the concrete, historically handed-down
myth, since it commands the generation, replications, and transformations of the elements
that make up the surface, observable phenomena.
In the previous chapter, we have seen that Lévi-Strauss advances a general formula,
which he calls the “canonical law,” as the underlying structure of any group of myths, for-
mula that takes the form of F x(a) : F y(b) :: F x(b) : F a -1 (y). In our present terminology, the
canonical law stands out as a succinct expression of the set AB, whereas the Oedipus myth
stands for the set C. The problem we have to address is the relationship between that for-
mula and the myth given that we cannot interpret the former as a model of the latter but, on
the contrary we need to read the latter myth as a product, or as a n expression generated by
the formula itself (and analogously for AI). We need to find out what warrants this asym-
metrical and hierarchical relationship and to which ontological level do structures and
search-spaces belong.
So far, our discussion of search-spaces and structures has been limited to an analysis
of the internal organization of these theoretical objects developed by AI and Structuralism.
The described features (closure, discreteness, etc.) are silent on the problem at issue, pre-
cisely because they concerns only their inside. We now need to examine what it would be
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tempting to call their “external” features, so to speak. However, it is misleading to use the
term “external,” since by definition none of those features can violate the requirement of
total self-containment and therefore they cannot be “external” in the proper sense of the
word. I prefer to call the addition that is needed in order to fix the games in place, their
“supplementary” features, with reference to a concept whose articulation has been explored
by Jacques Derrida, and which will become important in the discussion of Structuralism.
The next two sections will be devoted to a comparison of search-spaces and structures that
will highlight their different ways to cope with the “supplementary features” of their ob-
jects. Such a comparison will allow me to criticize, on the basis on the Lévi-Straussian cri-
tique of formalism, Artificial Intelligence’s “supplement.” The last section of the chapter
will examine in details Lévi-Strauss’s solution to the problem.
3. Form and content
There is no doubt that search-spaces and transformation groups are both deeply de-
tached from the material substrate they account for. 8 However, there are several different
ways of being in a detached relation with a substrate, and, in fact, Artificial Intelligence and
Structuralism opt for two very different solutions. To get a grip on the difference, let us be-
gin by remarking that, generally speaking, structural relationships do not necessarily entail
a total separation from the substratum that bears them in order to work as such. On the con-
trary, in several cases, the materiality of the concrete substratum is in fact an integral part
of the structure itself. This is clearly the case in the perhaps prototypical meaning of the
8. My discussion of formality in this section follows, for the particular case of its use by Artificial Intelligence,
John Haugeland’s treatment in Artificial Intelligence. The very Idea. My understanding of formality
“at large”, e.g. as a particular and heavily theory-laden answer to a philosophical problem, is
deeply influenced by the work of Brian Cantwell Smith, who provides the best analysis of a seemingly
simple but really daunting philosophical notion. See Brian Cantwell Smith, The Rise of Objects …,
and especially The Age of Significance, vol. II Formal Symbol Manipulation….
Smith’s influence on my thoughts on formality translates into a much weaker, but I think more accurate,
definition than the one proposed by Haugeland for AI-systems. He splits formality into token-manipulation,
finite playability and digitality. Part of the first two notions is expressed above by
discreteness and closure but I think we diverge significantly on the third term, digitality. See John
Haugeland, Artificial Intelligence…,48 ff.

F ORM AND CONTENT
very word “structure”, derived from the vocabularies of architecture and engineering.
“Structure,” from the Latin structura, is the nominal form of the verb struere, to build, and
literally means the result of the process—namely, con-structing—that produces an orga-
nized, and possibly lawful, arrangement of material. Thus, a structure of concrete, for ex-
ample, is what it is in virtue of both the reciprocal organization of the various beams and
pieces and the materials they are made of. A concrete beam can enter in a relationship with
another one precisely because it is made of (a particular kind of) concrete, not just because
of its size, length, and depth. Were we to change the material substrate—and use playdough
instead of concrete, for example—while keeping the same “structural” organization, we
would obtain a very different structure indeed. It matters so much whether the beams are
made of steel, wood, or playdough, that in fact a different structural organization may be
called for to achieve the same function with different materials.
All this is quite clear, and not particularly surprising, but it is also clear that this sense
of concrete structure is not what might be used by AI and Structuralism. In fact, whether
the chessmen are made of wood or of iron, should not matter too much to the search space
that controls their movements, and similarly the substratum of the myth should not matter
too much to the functioning of the religious structure. When we say that a search space is
a “formal structure” we cannot, therefore, rely on the ordinary meaning of “structure” and
just add the qualifier “formal,” because that qualifier, by suppressing the relevance of the
substratum, takes away one of the elements that defines what a structure is. To put it blunt-
ly: prima facie, the term “formal structure” (or “abstract”, or “detached” structure) is an
oxymoron whose content is empty. To make sense of it, we need to backtrack and try to
understand what we are detaching the structures from, first of all, and whether they can still
work as structures once the detachment has taken place.
As a first approximation, a detached structure can be defined as follows: the material
“substance” of the involved elements can be dispensed with. This definition is very close
to a classical slogan of the Structuralist years: only positions count. In other words, the val-
ue of a term within the system is given by its position with respects to other terms. What
matters are the relations between the terms and not the terms themselves. Thus, a chess-
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board configuration is distinguished from other configurations by the effect of the move(s)
that ties (and at the same time differentiates) them, not by the material substrate that bears
the configurations themselves. And this is why the structure is “formal”: because it can ab-
stract from the particular, material content of the terms (kinship terms, mythological, clas-
sification, chessmen material) and concentrate on the form. Whose form, though? Two
radically different approaches are possible: one can concentrate either on the forms of the
single terms taken in isolation—i.e. their exterior shapes, their internal composition and so
on— or on the form of the system the terms are inserted in, i.e. on the latter’s organization.
In the former case, one would oppose the form of a term to its content, in the latter, instead,
the form of the system to its substance. The first route is taken by AI, the second by Lévi-
Strauss. Let us begin by examining the latter, and perhaps less familiar, opportunity. Here,
the relevant opposition is between substance and position, and their respective import in
the determination of the value of the term.
The tradition followed by Lévi-Strauss goes at least as back as de Saussure’s Cours de
linguistique générale, where the value of a term (of a linguistic element, in his case) is not
given by its content, but by the system of oppositions in which the term is found: within a
language, he remarks, all the words expressing similar ideas limit one another. In French,
for example, synonyms like redouter, craindre, avoir peur, possess their own value only
because of their reciprocal oppositions: “If redouter didn’t exist, all its content would go its
rivals [like craindre and avoir peur]. Thus, the value of a term whatsoever is determined
by what surrounds it.” 9 Notice that, for de Saussure, the “content” of a linguistic term (here,
the concept associated to redouter) is not “abstracted from” in the determination of its val-
ue. Rather, it is the difference in content between redouter/craindre/avoir peur that makes
up their linguistic values. To make another (Saussurian) example: mouton and sheep have
very different values in French and English because, among other things, “when speaking
of a piece of meat served at the table the English speaker says mutton and not sheep. The
difference in value between sheep and mouton depends upon the second term [e.g. mutton]
9. Ferdinand de Saussure Cours de linguistique générale (Paris: Payot, 1982) 160; Engl. tr. Course of
General Linguistics (Chicago: Open Court, 1983) 114.

F ORM AND CONTENT
that the former possesses and the latter does not.”(ib.) The form that gets thematized, there-
fore, is produced by all the oppositions that bind together and at the same time separates
the various terms within a system. In other words: there is not a formal side of the term
sheep that can be neatly separated from its content. Rather, for de Saussure, there is a series
of oppositions that differentiates sheep from mutton, for example, and it is this series of op-
position that can be called formal. The system is formal because it detaches (e.g. it “ab-
stracts” from) the single terms whose value is determined “not positively, in terms of their
content, but negatively, by contrast with other items in the same system. What characterizes
each most exactly is being what others are not” (Leur plus exacte caractéristique est d’être
ce que les autres ne sont pas). 10
In structural linguistics, and in structural anthropology as well, the abstraction entails
a shift of the attention from the terms to their mutual relationships that leaves aside the con-
tent of the terms considered in themselves and focuses instead on their mutual oppositions.
Consider one last example, this one proposed by Louis Hjelmslev, perhaps the most rigor-
ous structural linguist to follow in de Saussure’s path:
Confront the following correspondences between Danish, German and
French:
træ
skov
Baum
Holz
Wald
arbre
bois
forêt
we may conclude from this fact that in one of the two entities that are
functives of the sign function, namely the content, the sign function institutes
a form, the content-form, which from the point of view of the purport
is arbitrary, and which can be explained only by the sign function and is obviously
solidary with it. In this sense, Saussure is clearly correct in distinguishing
between form and substance. 11
10. Ferdinand de Saussure, Cours…, 162; Engl. tr. 115. Emphasis added
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The structural perspective comports, in other words, a jump to a higher logical level,
that of the system in its entirety. The classic definition of language is but a consequence:
“Language is a form and not a substance [because] in language there is nothing but differ-
ences.” 12 Interestingly enough, de Saussure illustrates his position with the help of chess,
an analogy regularly called into play when the fundamental relation among form, substance
and value is at stake. 13
In spite of the common reliance on the same analogy, however, a very different defini-
tion of form is at work in Artificial Intelligence. Instead of being contrasted with substance,
in AI form is opposed to a content which can be assigned to it by an interpretation. The
claim that a (linguistic, logic, etc.) system is formal can be reduced to several distinct as-
sumptions, sometimes called the principle of arbitrariness of the linguistic sign and the
principle of compositionality:
1. single terms can always be properly isolated from the system and successively split
into neatly separated form and content.
2.the system can be properly described at the level of the form (by means of the laws of
composition described in the axioms, i.e. by the rules of the system) and the content
can always be recovered later through an interpretation.
The first consequence of these two principle is that the same formal system can receive
11. Louis Hjelmslev, Prolegomena to a Theory of Language (Madison: University of Wisconsin Press,
1961) 54. Louis Hjelmslev’s “algebraic” interpretation of de Saussure has sometimes been contrasted
with Jakobson’s approach, which is easier to integrate with an historic view of language evolution: for
Hjelmslev, so goes the claim, the historical evolution of a (linguistic) system is always subordinated
to the formal possibilities that the a-historic structure embodies, whereas for Jakobson the structure is
the product of the its evolution. Lévi-Strauss’s interpretation of structuralism seems to occupy an intermediate
position, in spite of his close personal relationship with Roman Jakobson, insofar as he insists,
on the one hand, on the logical priority of the structure over its historical evolution while he
stressing, at the same time, the impossibility to abstract from the ”substance of expression.” I will
come back to this latter point below in sec. 4. "Structure and Substance". For a comparison of Louis
Hjelmslev’s and Roman Jakobson’s approaches see Jorgen Dines Johansen, “Il ne faut pas oublier le
pain: Signification and Value in the Structuralist and Glossematic Conceptions of the Sign,” Journal
of Pragmatics, 9, 5 (1985) 567-590; Krystof Pomian, “Struttura,” Enciclopedia Einaudi (Torino: Einaudi,
1981) v. 13, 723-764.
12. Ferdinand de Saussure, Cours …, 169; Engl tr. 120.
13. Ferdinand de Saussure, Cours..., 43, 153-54 and especially the whole section 4 of chp.III, part.1, 125
ff; Engl. tr. 87 ff. For a discussion of the relevance of the chess image in Saussure, see Tullio de Mauro,
Introduzione alla Semantica (Bari: Laterza, 1965) 165-202; John Hewson, “Saussure's Game of
Chess,” Papers from the Fourth Annual Meeting of the Atlantic Provinces Linguistic Association, A.M.
Kinloch, and A.B. House, eds., (Fredericton, Can.: New Brunswick University Press, 1980) 108-116.

F ORM AND CONTENT
completely different interpretations or, even more interestingly, that two different formal
systems can be attached to the same content through different interpretations. Chess, for ex-
ample, can be formally analyzed as composed by a square, 8x8 chessboard and 2 sets of 16
pieces belonging to 6 different kinds (King, Queen, Bishop, Knight, Rock and Pawn) plus
a few rules for movement, check and capture. But an indefinite number of alternative rep-
resentations is possible. We can define chess played on sticks, spheres and cubes, with
wooden chessman, iron chessman and so on and so forth. Here, for example, is one (not so
original) variation: “monodimensional” chess, a game obtained by replacing the square
board by a long stick divided in 64 units, conveniently numbered from 0 to 63. Pieces are
as usual but movement rules become very complicated. 14
Although it is doubtful that anyone would find much fun in playing monodimensional
chess, from the standpoint of Artificial Intelligence the two games are the same: two iso-
morphic realizations of a same structure. (The fact that people, in fact, do have fun, when
playing the game of chess, whereas monodimensional chess, while being “equivalent” to
it, is hardly playable by humans should alert us to the existence of a possible problem.) The
important thing here is that AI’s definition of formality is such that the hypothetical content
assigned to a position in the ideal structure is exactly maintained if the rules have been care-
fully defined.
In other words, the attribution of meaning to symbols occurring within the structure
can always be performed at the last minute because the (syntactic) rule governing the
movements of the pieces do not touch it at all. According to the formalist, symbols have
14. Consider pawns, the simplest piece, and let us limit to White's pieces: at the beginning they occupy
cases 8-15 and the possible moves for each of them can be found by adding 8 (or 16, for their first
move) to the original position. The rule for capture is a bit more complex: a pawn can capture a piece
which is 7 or 9 units far from him. Rules for all the other pieces can be given -- although the exercise
starts to be boring very quickly -- so that an exact 1-to-1 translation from one representation to other
can be given which respects all the relations among the pieces. For example, if we number the cases
from 0 to 63, the first two moves of the Sicilian opening (1. e2-e4 e7-e5 2. Kg8-f6 Kb8-c6) become:
1. 12-28 52-36 2. K6-21 K57-42). The example is in fact quite simple, since it preserves the distinction
between a fixed chessboard and pieces moving on them. But the relationship could be reversed: we
might imagine a game chess played on a moving (and topologically quite interesting) chessboard with
fixed pieces. John Haugeland exploits a trick of this kind in his example of a different version of solitaire
given in Artificial Intelligence…, 60 ff.
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actually two independent lives, as Haugeland has put it: a syntactic life in which they are
shuffled around according to formal rules, and a semantic life in which they have a content
because an external interpretation has come into play. 15 It might be worth noting that de
Saussure was far from believing this. In fact, he likened, in a well-known image, form and
content to the two sides of the same sheet of paper (i.e. the same substance): it is impossible
to cut the one without cutting also the other. According to another structuralist, Algirdas
Greimas (who follows closely Hjelmslev here), the formal systems described by logic, al-
gebra and chess can perform such a neat separation between form and content only because
they are essentially missing the level of content (“le plain du contenu”). Hence, they are not
languages at all since “the semantic interpretation that might be given will reproduce the
same articulations (of the expressive level) and it will be interpreted according to the same
rules as the interpreted form.” 16
If it is indeed doubtful, I think, that mathematics and chess lack content, as Greimas
asserts here, he seems to be right in claiming that, under the formalistic interpretation, there
is no content left worth the name. The content lies outside the formal structure and it is
linked to it, in a arbitrary way, by a chosen function.
But what is distinctive of game and play is not the absence of a content; rather, their
peculiarity is that their content is given on the inside, so to speak, by means of the rules and
appears throughout the confrontation that the rules rule. A game is not content-less and
therefore purely “formal,” it is rather self-enclosed in the sense that it does not need any-
thing external to it in order to find its meaning. This is true for football as for chess, and
this is why football played on a video arcade is not the same game as football played on a
field, as well as chess played on a mono-dimensional chessboard is not the same game as
chess. They are different games, in principle no better and no worse, but the fact that AI’s
rendition of games is not able to discriminate between them indicates that the structures ex-
15. See John Haugeland, Artificial Intelligence...., 100. The two principles above are a close rephrasing of
his principles of symbolic systems as found at p.90
16. See Algirdas J.Greimas and Julien Courtès, Sémiotique. Dictionnaire raisonné de la théorie du langage
(Paris: Hachette, 1979) 193.

F ORM AND CONTENT
pressing games, e.g. search spaces, are too weak and need a different and stronger charac-
terization in order to capture the difference.
To put it differently: the prescription of formality, although it does not seem to violate
the requirement of closure, in fact enforces it in the wrong way, by closing off what instead
should be comprehended within the scope of the “formal” structure. AI games, as a conse-
quences, are not a proper rendition of the concept of Spiel that we are after, since they miss
one of its basic feature. Moreover, the attempt to take in what the structure inevitably ex-
cludes proves impossible, because it would entail a substantial recourse to something that
lies beyond the structure itself, therefore violating closure. The situation, in fact, is even
more tangled, since the whole relationship between “internal” and “external” that Ai’s in-
terpretation of detachment as formality engenders is truly paradoxical, and of the specific
kind of paradoxes generated by the logic of the supplement. Let us define the latter by
means of a passage by Jonathan Culler:
The supplement is an inessential extra, added to something complete in
itself [e.g. self-enclosed] but the supplement is added in order to complete,
to compensate for a lack in what was supposed to be complete in itself. 17
The supplement, in other words, is both an accessory, inessential addition that forms the
core of the inside and a crucial component added from the outside. The logic of the supple-
ment is at work whenever an allegedly external element is called in “to supplement” pre-
cisely because there has always been a lack in what is supplemented. Derrida, in De la
grammatologie, discusses the logic of the supplement in a variety of contexts taken from
Rousseau’s texts. One of the most pregnant, and the one at the origin of the term, concerns
Rousseau’s definition of masturbation as a “dangerous supplement.” Masturbation, accord-
ing to Rousseau’s Confessions, is just a supplement, an addition, and a perverse one, to
“normal” sexual activity. However, Rousseau makes clear that it is a particularly adequate
addition, since it can replace or substitute quite efficiently for “normal” sexuality. As Der-
rida points out, however, in order to function as an indistinguishable replacement, mastur-
17. Jonathan Culler, On Deconstruction. Theory and Criticism after Structuralism (Ithaca: Cornell UP)
202. and Jacques Derrida, Of Grammatology…, 95-157 for a discussion of the logic of the supplement.
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bation must essentially resemble what it replaces, “and indeed the fundamental structure of
masturbation—desire as auto-affection focusing on an imagined object that one can never
fully possess is repeated in other forms of [“normal”] relationships, which can thus be seen
as moments of a generalized masturbation.” 18
The relationship between the pure formal structure and the accessory interpretation
function obeys this supplementary logic, because, on the one hand, search spaces, as purely
formal structures, are too weakly defined to be able to capture relevant elements of chess
games. They, in other words, “shake” insofar as it is impossible to pin them down to a spe-
cific content. It is impossible to connect them to their intended content, since there is no
substance neither in the terms nor in the space as a whole. The space is close, we may say,
but what it encompasses is empty. Or rather, in what amounts to the same thing, the content
of the search space is ever changing, since any content can be attached by a suitable inter-
pretation function. On the other hand, then, the interpretation function is crucial since it is
only because of its work that a content can be recovered. In Derridean terms, the interpre-
tation function fills a lack that is “originary,” e.g. a lack that has always been present at the
very core of the theoretical object and the supplement, e.g. the interpretation function, is as
“internal,” as “essential,” and as intrinsic to the structure as that very core. The function,
however, is declared as not being a part of the search space: it is rather an addendum, a the-
oretically irrelevant addition that connects from the outside the terms to their contents. And
yet, it is precisely this supplement that transforms a search space from a collections of signs
into the space of chess. The interpretation function is needed, crucially needed—but it is
marginally irrelevant. It is what makes search spaces into the spaces of chess—but it is out-
side that space proper. The supplementary role played by the interpretation function—
which is generated, let me stress it one last time, by Artificial Intelligence’s interpretation
of detachment as formality— marks the inability of search spaces to live up to the ambi-
tions set for them by AI non-philosophical project. The requirement of closure cannot be
achieved.
18. See Jacques Derrida, Of Grammatology…, 149ff. The last quotation is taken from Jonathan Culler, On
Deconstruction…, 104

S TRUCTURE AND SUBSTANCE
This does not mean that our trip through Artificial Intelligence has been useless, nor
that we should not pay any more attention to AI’s games as search spaces. First, we must
remember that the problem we have considered arose in the context of our discussion of
formality as one, and AI’s specifically, possible interpretation of the detached relationship
between the formal object and its substratum. The other characteristic of search-space that
we have discussed, here and in the previous chapter (compositionality, discreteness, etc.)
are left untouched by this discussion and can, therefore, be kept. They represent, in a sense,
the lesson to be learned from AI. But we have to backtrack, e.g. to keep those features and
examine different ways to solve the issue of detachment and self-containment. If game is
to be successful as a rendition of Spiel, there must be a way to have the game’s “content”
on the inside, e.g. within the scope of closure. Second, we need to keep in mind that AI’s
interpretation of the detachment between an abstract structure and its substratum represents
a very common solution to the problem. So much so, in fact, that we will see it resurface
again and again in the debates concerning Structuralism. It is extremely important, there-
fore, to keep it in the background in order to contrast it with the very different solution pro-
vided by Lévi-Strauss. Third and last, we will need to go back to this interpretation one last
time when we will discuss what happens to the game-based reduction of the concept of
Spiel that AI performs and to game-based non-philosophies in general if the “supplement”
that formality inevitably entails is accepted. For now, however, we will keep these points
in the background while we move to the alternative rendition of detachment provided by
Structuralism.
4. Structure and Substance
Lévi-Strauss would never agree with this interpretation of formal structures, and it is
important to consider carefully why and how he disagrees. The issue is not so simple, since
he sees formalism both as a fallacy and as a step in the right direction. He condemns “for-
malism” and especially the principle of complete arbitrariness (i.e. of complete separabili-
ty) first of all as a methodological fallacy which would make impossible any properly
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construed formal analysis. He opposes the concept of structure to the concept of form, and
shows in empirical analysis how the two approaches sensibly differ. A review of it will al-
low us to see the essential shortcoming of AI’s interpretation of the concept of game and
the inadequacy of the supplement provided by the concepts of interpretation and formality.
The non-formalistic structural analysis Lévi-Strauss is striving for depends crucially
on three interrelated points. First, on the assumption of an algebraic model which is richer
in structure; second, on a different view of the relationship between content, substance and
form, and finally on a completely different philosophical position about the ontological sta-
tus of the described structures and the related status of the human subject. Let us go through
the three one at the time, in order to assess the differences with the American counter-part.
In La structure et la forme, Lévi-Strauss’s critique may be summed up by saying that “the
form is defined by opposition to a substance which is alien from itself; but structure has no
separate content: it is the content itself apprehended in a logical organization conceived as
a property of the real.” 19 We can read this statement as a concise rephrasing of the de Sau-
ssurian principle illustrated above: a structural approach calls for a consideration of a given
content from a logically higher standpoint. More concretely, here is Lévi-Strauss’s exam-
ple:
In the myths and tales of the Indians of South and North America, the
same action is attributed — depending on the tales — to different animals.
To simplify, let us consider birds: eagle, owl, raven. Will we distinguish, as
Propp does, between the constant function and the variable characters? No,
because each character is not given in the form of an opaque element, confronted
with which structural analysis should come to a stop, telling itself to
go no further. When, after the fashion of Propp, the narrative is treated as a
closed system, one could no doubt believe the opposite. 20
The structural analysis must not disregard the specific substance the element is made of,
delivering the final deciphering of its meaning to an additional, supplementary interpreta-
tion. The complete separability between form and meaning claimed by both Propp’s and
19. Claude Lévi-Strauss, Anthropologie Structurale deux…, 139. Engl. tr. 115.
20. Claude Lévi-Strauss, Anthropologie Structurale deux…, 161. Engl. tr. 135. Emphasis added.

S TRUCTURE AND SUBSTANCE
classical AI’s approaches would claim that the value of the specific character is completely
determined by the rules that govern its appearance in the myth, or in the chess-game,
whereas Lévi-Strauss denies the possibility of such an operation.
The crux of the matter, in fact, is represented by the first of the two formalist principles.
Let us recall it, in the formulation given above:
single terms can always be properly isolated from the system and successively
split into neatly separated form and content.
As I have stressed above, this principle rests on the assumption that arbitrariness intervenes
at the level of the terms, e.g. as the dominant feature of the relationship that ties together
its two constitutive components: the form and the content. It is only because the relation-
ship between them is totally arbitrary that they can be neatly isolated and be dealt with sep-
arately by syntax and semantics. The arbitrariness, in turn, is codified by the existence of
an interpretation function that allows to retrieve the meaning of any isolated term from its
form.
Lévi-Strauss, however, stresses that permutability does not mean arbitrariness. To un-
derstand the meaning of a simple element is not to attach an interpretation to it, but “to per-
mute it in all its contexts” and to figure out the reciprocal relation among them, e.g. among
the contexts in which the terms appear and function. The structural analysis takes advan-
tage of the closure of the system in a sense unattempted, it seems, in the classical AI tradi-
tion. In a much stronger sense, since the system is closed because it excludes everything
outside it and because it binds together what falls within. The closure of the system means
that all its elements are bound together by significant relations, not only on the diachronic
axis representing the temporal succession of moves but on the synchronic axis as well. In
the case of chess, this would mean that every horizontal layer (corresponding to one move)
is characterized by a set of relations, and not by a mere juxtaposition.
The difference between the two approaches is conceptually extremely significant al-
though, perhaps, technically not too difficult to bridge. I will begin, then, with a “technical”
discussion of the relationship between trees and matrixes, i.e. with a discussion of the pos-
sible convertibility of AI’s and Structuralism’s conception of their theoretical spaces. The
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point at stake, in this first phase of the analysis, is to ascertain whether it is possible to in-
dividuate an iso- or homeomorphic relationship leading from one approach to the other.
Once we have shed some light on the technical side we will move on to the more intricate
conceptual discussion.
Let me go back to the two schemes we have seen in the previous chapter. We have seen
that the space of possible configurations of, respectively, chess games and myths are rep-
resented by the tree-like graph of chess suggested by Shannon and by the stack of matrixes
envisioned by Lévi-Strauss. We might think the two structures are isomorphic since every
card in Lévi-Strauss’s stack correspond to a branch of the tree in Shannon’s chess. In other
words, it is possible to establish a correspondence between the elements of the two formal
objects merely by “folding” Shannon’s branches onto themselves to fit into Lévi-Strauss’s
stacked cards:
But this mapping, while it does justice to discreteness and closure, fails to preserve all
the synchronic relations discovered by the analysis of the myth, as we have seen in the Oe-
dipus case. In fact, here is how Lévi-Strauss describes the further level of relations in the
essay just quoted:
To understand the meaning of a term is always to permute it in all its context.
In the case of oral literature, these contexts are first provided by the set
of the variants, that is, by the system of compatibilities and incompatibilities
that characterizes the permutable set. That the eagle appears by day and that
the owl appears by night in the same function already permits the definition
of the former as a diurnal owl and of the latter as a nocturnal eagle, and this
signifies that the pertinent opposition is that of day and night. [From other

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contexts] is then to be noticed that the eagle and the owl together are put in
opposition to the raven, as predators to scavenger, while they are opposed
to each other at the level of day and night; and that the duck is opposed to
all three at the new level of pairs ski-land and ski-water. Thus a “universe of
the tale” will be progressively defined, analyzable in pairs of oppositions,
diversely combined within each character who — far from constituting a
single entity — is a “bundle of differential relations,” in the manner of the
phoneme as conceived by Jakobson. 21
We understand then that the “universe of the tale” becomes sensibly different from the
game of chess as depicted by AI. An interesting question arises, though: is it formally pos-
sible to analyze the objects at the center of AI’s attention along Lévi-Straussian lines?
The Structural analysis uses two complementary methods when confronted with a
myth. The first one consists in breaking up the tale into analogous elements and showing
that each one represents a variation of the same theme. This is the method used by Lévi-
Strauss in the analysis of the Oedipus myth discussed in the previous chapter. The second
method, use most extensively in Mythologiques, consists in “superimposing a syntagmatic
sequence in its totality—in other words a complete myth—on other myths or segments of
myths” 22 and to look for the same kind of repetitions or transformations as they might occur
from one myth to the other. The first approach, in short, is intra-mythical, while the second
is inter-mythical. To make available to AI the Structuralist methodology we only have to
take a single game of chess—e.g. a complete vertical path in AI’s tree-like diagram—to be
a syntagmatic structure, and therefore the equivalent of a myth. Both the intra- and inter-
mythical approach now become available as intra-game and inter-game analysis of the
game of chess.
We will try to sketch what would be required to carry out the latter method, in order to
understand even better the differences between the two approaches. First, the stack of ma-
trixes representing a Lévi-Straussian structure is richer in internal relationships than its Ar-
21. Claude Lévi-Strauss, Anthropologie Structurale deux…, 161-2. Engl. tr. 135.
22. Claude Lévi-Strauss, Le Cru et le Cuit…, Engl. tr. 307. See also John Peradotto, “Oedipus end Erichtonius:
Some Observations of Paradigmatic and Syntagmatic Order,” Arethusa, 10 (1977), 85-101, for
a discussion of Lévi-Strauss’s double methodology.
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tificial Intelligence counterpart. Second, the structure of a myth, for example, is constructed
“bottom-up”, e.g. it is built from a complete description of all the narrative variants that are
actually found in the literature. Each variant constitutes its own context, and the basic rela-
tions used to build the group that generates the structure are found by permutating the ele-
ments in all their contexts.
Thus, a first attempt at a formalization of chess, for example, into a structure (as op-
posed to a search-space) would start not from an abstract description of the “moves” of the
game, e.g. the higher level constraints that make the game possible, but rather from a col-
lection of chess games equivalent of the single variants of a myth: the single games of
chess. It would then proceed to isolate the basic elements of the game, the chess equivalent
of the gross constituent units of the myth. It is not totally clear what these would be. If we
remember that, in the myth, such units are basically found at the sentence level (by analogy
from linguistics) we may try to found a sentence equivalent in the internal dynamic of the
game of chess. A single move of a determinate piece may too small of a unit, whereas a
sequence of moves representing, for example, the development of a piece, e.g. the expres-
sion of a certain action that a piece perform, may probably be better suited to the task. The
concept of heuristic rules can perhaps be reintroduced, with modifications, at this level of
the analysis as the sequence of moves a chess piece (or more) uses to carry out a task like
“occupying the center,” “protecting the king,” etc. From an Artificial Intelligence perspec-
tive, heuristic rules act as a higher level constraint on the search-space that introduce mean-
ingful relations: they act as a constraint higher than the moves themselves that made up the
space in the first place. Thus, they seem a natural candidate for the similar, higher level role
that the gross constituent units play within Lévi-Strauss’s theoretical approach.
The analysis would then proceed, on the basis of the catalog of existing games, to re-
trieve the relations tying together the single constituents and, from then, would try to con-
struct a group binding all the relations in a tidy structure. It should be noted that this
approach to the game of chess, if carried out, would come up with the formalization of a
different object than “the” game of chess that game-theory inspired to Artificial Intelli-
gence. In fact, it would be misleading to call it the game of chess: by analogy with Lévi-

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Strauss’s characterization of Propp’s enterprise we should call it the universe of chess. The
universe is both broader and narrower than the game. Broader, because it encompasses and
aims at explaining more than just the games that are virtually possible: it focuses on the
game that have actually being played, in all the contexts in which they occurred. Thus, for
example, the past history of the game, which, as we have seen, is unrecoverable from Ar-
tificial Intelligence’s standpoint, becomes instead accessible since it may represent just one
of the dimensions along which the (hyper)stack of matrices develops. We have seen how
Lévi-Strauss stresses, in the context of his programmatic analysis of the Oedipus myth, that
the diachronical evolution of the myth from Greece to Freud can be accounted as another
set of variants along the chronological axis. In the same spirit, the evolution of chess—or
of same parts of it like, say, the Sicilian opening—from its XVII century beginnings to Kar-
pov’s finesses, become just another set of relations to be accounted for. The same argument
can be repeated, of course, for other, non-chronological dimensions: for spatial/geograph-
ical distributions, social role, etc.
On the other hand, the universe is narrower than the total space of chess, insofar as it
does not pretend to account for all the possible games that may be played in abstracto, e.g.
starting from the rules only. To put it differently, the immense tree containing 10 120 nodes
imagined by Shannon and Simon is not within Lévi-Strauss’s perspective since the struc-
ture-enforced constraints are much stronger than just the simple rules of the game. As a
consequence, not all the abstractly possible games are in fact possible, but only those that
find a place in one of the matrixes embodying the different relations. Thus, although the
two approaches can, to a certain extent, be translated into one another, there is neither a sim-
ple isomorphism between them, nor a homeomorphism from Structuralism to Artificial In-
telligence, as it might have appeared at first sight in virtue of greater richness (in terms of
accounted relations) of the former approach. Although, as I have tried to show, there is an
inner core that is shared by both approaches, their different takes on the crucial issue of the
relationship between the theoretical objects and the substance of those objects pull them
apart quite considerably. It is sometimes easy to confound the two approaches—AI’s and
Structuralism’s—because at times they seem to follow the same path when they contrast an
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“abstract matrix of possibilities” to a more limited set of concrete occurrences, the former
constructed by a combinatorics of simple elements and the latter retrieved in the real instan-
tiations of some elements of the that matrix. In this sense, the tree representing the state
space of chess is the “abstract “space of possibilities,” while the games played are a subsets
of vertical paths. Analogously, the abstract matrix that include the oppositions between
“dead” vs. “living” beings, “Chtonian” vs.”aerial” characters, etc., is opposed to the actual
myths that exploit only a few of those possibilities. But there is a crucial difference between
the matrix of abstract possibilities that can be constructed from the oppositions found in
practice, e.g. in the actual myths, or actual games, and, on the other hand, the matrix or the
tree that can be generated from the composition of atomic elements according to rules. The
difference, once again, lies (a) in the different levels at which the theoretical gaze is directed
and (b) in the different roles played by the “praxis” that embody abstract structures. In AI’s
case, we see, (a) single elements that are (b)defined “independently” from their meaning,
e.g. chess pieces whose mutual relationships are assumed as given. On the contrary, Lévi-
Strauss and Structuralism in general focus their attention to (a) the system of opposition as
(b) they are found in the actual practices, e.g., in the example presented above, oppositions
of differential characters (diurnal vs. nocturnal, chtonian vs. aerial, etc.) as found in the ac-
tual myths.
In other words, it might be possible to construct a state space for AI along Structuralist
lines, and then conjugate it with the more traditional AI tools and techniques. However,
such a “technical” operation is far from being philosophically neutral, since it comports a
totally different interpretation of the meanings of the terms embodied in the various struc-
tures or spaces. Lévi-Strauss’s move away from the classical opposition form/content im-
plies the abandonment of a classical theory of reference whereby the terms are attached to
the things they stand for through the theoretical couple form/content. This switch may be
all for the best since we have already hinted at the fact that AI’s own philosophy might get
it into some troubles. Or, it may instead be taken as a symptom of the even deeper troubles
that AI faces, since it seems to be forced to abandon as basic a tenet as the aforementioned
theory of reference. Whatever, the case, it is clear that a further discussion is needed in or-

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der to get a better understanding of the philosophical difference between the two anti-philo-
sophical projects, both in terms of their assumptions and in terms of the choices opened up,
or closed off by them.
5. Structuralism, Philosophy, and AI
The consequences of the structural explanation of terms are not only wide and deep,
but affect particularly the viability of the game-based approaches as “non-philosophies” in
the sense described above. In fact, most if not all the philosophical debates surrounding
both Artificial Intelligence and Structuralism can be shown to stem from this point. My dis-
cussion will follow the guidelines provided by a debate between Lévi-Strauss and the phi-
losopher Paul Ricoeur that started in the early 1960s and continued, in increasingly harsher
and more radical tones, for over a decade. The first encounter took place on the pages on
the journal Esprit soon after the publication of La pensée savage, the book in which Lévi-
Strauss generalizes his researches on myths by applying the structural method to the wider
interrogation of “primitive” mentality in general. It then continued in a series of articles
published by Ricoeur in the following years and in numerous, although almost always in-
direct, discussions of Ricoeur’s critiques contained in Lévi-Strauss articles and books pub-
lished after 1963.
Although the first part of my discussion will thus be focused on Lévi-Strauss’s work,
it should be read in the wider context of both AI and Structuralism, and not just because of
the substantive analogies between the two approaches that I have described so far. In fact,
when Ricoeur criticizes Structuralism’s philosophical pretensions, he appeals to a view of
language—and a theory of reference, in particular—that he sees embodied in the work John
Searle, e.g. the work of Artificial Intelligence’s staunchest and most indefatigable critic.
This view, according to Ricoeur, is
the theory of proper names and definite descriptions, from which Strawson
and Searle derive their theory of the identifications of particulars, [and
it] turns on that fundamental characteristic of language, that the truth of a
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proposition has to do not with its ‘sense’ (ideal), but with its ‘reference,’ that
is, in the last resort its capacity to correspond to what is[…] 23
We can consider this text as a simple indication of the larger, and more intricate, framework
surrounding the whole debate: a “Continental” philosopher advocating a hermeneutic un-
derstanding of language like Ricoeur criticizes Structuralism by appealing to a theory of
reference that underlies John Searle’s critique of Artificial Intelligence. I will start to dis-
entangle the various issues involved beginning from the first term of the relationship:
Ricoeur’s critique of Lévi-Strauss.
Ricoeur, a philosopher coming from the phenomenological tradition, is willing to ac-
knowledge the merits of the structural approach but he is ready to underline its shortcom-
ings. The most important limitations, he points out, concern the meaning of the structure
governing a given myth or group of myths. The structural organization of thought may be
interesting, in itself, as a study of the different possibilities of mediation of the meaning in-
tentions. But he claims that the true problem that a structural approach will leave unsolved
is the following: how can “structural comprehension instruct a comprehension directed to-
ward the recovery of the signifying intention?” 24 This is a problem only philosophy can
solve, according to Ricoeur, because
while the structuralist explanation seems to encompass almost everything
when synchrony takes place over diachrony, it provides us only a kind of
skeleton, whose abstract character is apparent, when we are faced with an
overdetermined content, a content which does not cease to set us thinking
and which is made explicit only through the series of recoveries by which it
is both interpreted and renewed. (51, my emphasis)
23. Paul Ricoeur, Main Trends in Philosophy (New York: Holmes and Meers, 1979) 265. First edition published
in 1970.
24. Paul Ricoeur, “Structure et herméneutique,” Esprit, 31, 322, nov. 63, 606, previously published as Paul
Ricoeur, “Symbolique et temporalité,” Ermeneutica e tradizione (Atti del Congresso Internazionale,
Roma, gennaio 1963) Archivio di Filosofia, 3, 1963, 12-31 and now in Paul Ricoeur, Le conflit des
interprétations (Paris: Seuil, 1969) 53; Engl. tr.The Conflict of Interpretations (Evanston, Ill.: Northwestern
UP, 1974) 39. The quoted issue of Esprit was dedicated to a discussion of Lévi-Strauss’s La
pensée savage and contained also articles by the anthropologist Jean Cuisinier, the linguist Nicolas Ruwet,
and the historian Marc Gaboriau followed by a round table between Lévi-Strauss and the editors
of Esprit (among whom is Ricoeur).

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The structural approach will forever be a scientific enterprise unable to go to the core
of the problem; the philosopher, instead, is concerned with the meaning of the words, for
which linguistic laws serve as instrumental mediation, forever unconscious (52).
Ricoeur provides a concrete example of the hermeneutic comprehension of religious
text on the basis of the body of myths contained in the Old Testament. He claims that the
sens of the sacred text is organized by at least three “noyaux de sens,” three agglomerations
of meaning: each being organized by a network of events: the first is represented by the an-
nouncement of Jahve’s coming and the deliverance form the Egyptian captivity, the second
is centered around David’s mission and the third focuses on the events after the Jews’ di-
aspora. For the correct comprehension of these agglomeration of meaning, Ricoeur stress-
es, a taxonomy of oppositions constructed along Structuralist lines is useless, because the
correct method of understanding must recover the “intellectual labor” (le travail intellectu-
el) that, starting from the mythical structure, was able to construct the identity of the nation
of Israël as a historical entity. The speculative theology embedded in the texts has a minimal
role in this process; the most important part, instead, is played by the constant interpretation
and re-interpretation of those biblical texts within a historical framework:
Le travail théologique sur ces événements est en effet lui-même une
histoire ordonnée, une tradition interprétante. La réinterprétation, par
chaque génération, du fond de traditions confère à cette compréhension de
l’histoire une caractère historique, et suscite un dévéloppement qui a une
unité signifiante impossible à projeter dans un sistème. […] il est
remarquable que c’est par ce travail de réinterprétation de ces propres
traditions que le peuple d’Israêl s’est donné une identité qui est elle-même
historique. 25
This is why the “taxonomic” structure of oppositions that, undoubtedly, can be discov-
ered within the biblical text, must be seen as a mere instrument, as the tool that enables the
mediation between the people of Israël and its own history: the meaning of the text is not
to be found in its structure, but in the active acts of interpretations that the structure makes
25. Paul Ricoeur, “Structure and Herméneutique…,” 49.
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possible, to be sure, but that will inevitably transcend it. In Ricoeur’s perspective, the ex-
ample is important because it shows the primacy of history, and especially of a historically
situated act of interpretation, over the synchronic coexistence of terms in opposition within
a myth that the Structuralists stress over and over. The historical primacy of history—the
fact that Israël’s own interpretation of its texts is constituted by a a series of events and not
by a speculative theology—entails that the current understanding of the text must be his-
torical as well. A structural analysis of the biblical text, according to Ricoeur, would skim
the surface of what constitutes the true meaning of the text for the people who has been con-
stantly involved with it. Rather, a correct comprehension will take the form of a “re-telling”
insofar as it will try to repeat, in a different context, the original “deployment” of sense that
“a présidé à l’elaboration des traditions du fond biblique.”
Structuralism, instead, misses this level of temporality that is inherent in the myths and
cannot account for the recovery of meaning that may happen through a structure but by
means of an act that will transcends it to reach beyond. Therefore, the “science structurale”
is valuable as a preliminary analysis of the conditions that may constraint those interpreta-
tive acts, but it is not sufficient to a truly philosophical, or hermeneutic understanding. It is
a science of the instrumental mediation that cannot—and should not dare to, as Ricoeur will
say later—overstep its boundaries into the philosophical domain.
The essential coordinates of the philosophical debate around Structuralist are thus laid
out: on one side stands the Hegelian project of a philosophy of the subject who understands
himself, reflexively, also as being: “une philosophie de soi et de l’être,” in Ricoeur’s words.
Hermeneutics, on this interpretation, comprehends itself as a scaled down, relativized ver-
sion of the Hegelian Logic that recognizes the intrinsic impossibility of providing a com-
plete, and truly Hegelian, description of all the categories and accepts the lesser goal of
supplying, at given time, an historically bound fragment of such an interpretation. On the
opposite side stands the Kantian project of providing an a-historical grid of formal, or pure-
ly syntactical, categories that the subject will be forced, unreflectively, to use in its daily
operations. The focal point that enables the dialogue between these two traditions, as
Ricoeur makes clear, is the subject, since both Kant’s and Hegel’s efforts must be read as

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two different ways of providing an understanding of the human subject and the (pre-)con-
ditions of its dealing with the world through language.
Structuralism, so goes the basic line of Ricoeur’s argument, is an incomplete form of
Kantism that must be brought back to Hegel through a necessary integration with herme-
neutics in order to be able to provide a full account of human subjectivity. In fact, according
to Ricoeur, the structural thought is necessarily incomplete because it lacks the moment of
self-reflexivity. In other words, because it does not reflect on the moment of the decipher-
ments, e.g. on the necessary step whereby the abstract mediating structures are “put to use,”
so to speak, by the human subject who lives immersed in and conditioned by them. Struc-
turalism, according to Ricoeur, misses necessarily this moment because of its exclusive em-
phasis on the syntactic manipulation of symbols and its disregard for semantics. As a
consequence, it ends up necessarily incomplete, and, therefore it will be up to a
philosophie réflexive de se comprendre elle-même comme
herméneutique, afin de créer la structure d’accueil pour un’anthropologie
structurale; a cet égard, c’est la fonction de l’herméneutique de fair
coïncider la compréhension de l’autre—et de ses signes dans les multiples
cultures—avec la compréhension de soi et de l’être. 26
Ricoeur suggests that, at the limit, such a comprehensive approach integrating both the
“syntactic” aspect provided by Structuralism (e.g the moment of the “form”) and the “se-
mantic” aspect provided by a self-reflexive philosophie like hermeneutics (the moment of
the “content”) will in fact resemble the Hegelian project of constructing a Science of Logic
as a comprehensive system of Being as Subject, albeit it will be a Logic which is aware of
its ineliminable partiality. As he puts it:
A la limite, cette appropriation et cette reconnaissance [e.g. the integrated
approach] consisteraient en un récapitulation totale de tous les contenus
signifiants dans un savoir de soi et de l’être, comme Hegel l’a tenté, dans un
logique qui serait celle des contenus, non celle des syntaxes. Il va de soi que
nous ne pouvons produire que de fragments, qui se savent partiels, de cette
26. Paul Ricoeur, “Structure et Herméneutique,” …54; Engl. tr. 51. All emphasis in the quotations from
Ricoeur’s article are mine unless otherwise noted.
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On the contrary, an understanding, like Structuralism’s, that misses the “plan du contenu”
by favoring the syntactic aspect is bound to oscillate among different “rough outlines of
philosophies” (ébauches de philosophies) all more or less incomplete. At times, the Struc-
turalist project resembles
un kantisme sans sujet transcendental, voire un formalisme absolu, qui
fonderait la corrélation même de la nature et de la culture.
However, as Ricoeur is quick to point out, such a project, (and besides, we may add, being
almost an oxymoron in Kantian terms) is unable to give an account of the philosophical
problem of the relationship of men with the world and with the other, because it addresses
the wrong logical level:
ce ne sont pas de lois linguistiques que nous cherchons à totaliser pour
nous comprendre nous-même, mais le sens des paroles, par rapport à auquel
les lois linguistiques sont la médiation intrumental à jamais inconsciente. Je
cherche à me comprendre, en reprenant le sens des paroles de tous les
hommes; c’est à ce plan que le temps caché devient historicité de la tradition
et de l’interprétation. (55/52)
According to Ricoeur’s interpretation, Structuralism is bound to miss the level of the con-
crete interpretative acts that retrieve the content, or rather the meaning, whose expression
has been made possible by the unconscious linguistic grid. Therefore, the only option open
to the Structuralist who wants to recover the praxis, the concrete praxis in which human
beings are involved whenever they speak, worship or play chess, consists in shifting the fo-
cus of attention by 180 degrees and turn the structure into the objective order of reality:
“there is in fact, in The Savage Mind, the sketch of a very different philosophy, where the
order is the order of things, and thing itself.” 27 Ricoeur reads Lévi-Strauss’s emphasis on
the concept of species, in La pensée savage, as evidence of this point, since the species,
27. Paul Ricoeur, “Structure et Herméneutique, …, 56/53. It will be noticed that “the order of things” is
precisely the English title of the book that was to become, perhaps, the best known (albeit reluctantly)
Structuralist manifesto: Le mots et le choses by Michel Foucault, published just three years later.

S TRUCTURALISM, PHILOSOPHY, AND AI
whose status Lévi-Strauss has shown to be deeply interlinked within a elaborate set of
structures, belongs, by definition, to a level of “presumptive objectivity.” The taxonomic
classifications embedded and made possible by the structures are thus to be considered as
part of a different “philosophical sketch” where the ontological status of the structures has
radically changed.
The crucial point that Ricoeur wants to bring home, is that the “structuralist science”
does not allow to choose between the two rival interpretations because these conflicting and
mutually incompatible “philosophical sketches” are all necessary to make it coherent as a
form of philosophy. Structuralism, then, is bound to oscillate between these incomplete
forms of philosophies because it misses the essential link with the facticity of a subject
who—always located within a historical frame and therefore constrained by a horizon con-
stituted by the history of previous interpretations—strives to recover the sense of the words
that come to him always mediated by the unconscious linguistic structure. Thus, Structur-
alism is forced to privilege, alternatively, one of the two terms of the relationship: some-
times it emphasizes the formal aspect and sometimes it stresses the praxis, but it can never
bring the two together. In either case it is doomed to fail, if left to itself, because in the
former case it postulates an unconscious linguistic grid without being able to account for
the subject (be it empirical or transcendental) who will be able to use it in its daily practices.
In the latter, and symmetrical, case, it reifies the structure by turning it into the structure of
things and a thing itself, e.g. it transforms the unconscious linguistic grid that has to medi-
ate between the subject and reality into an objectively real structure of reality that consti-
tutes praxis itself, that is, into a superstructure of praxis. The structuralist’s pendulum, in
Ricoeur’s words, swings from one of these extremes to the other according to the necessi-
ties of the moment, but is unable to go beyond these “rough outlines of philosophies” and
provide a satisfactory solution to the philosophical problem of integrating men within their
historical world. Such a solution can only come from a marriage with hermeneutics, since
philosophy is the necessary supplement that Structuralism lacks. Ricoeur, in facts, con-
cludes his critique by saying that there cannot be any:
structural analysis without a hermeneutic comprehension of the transfer
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of sense [intelligence herméneutique du transfer de sens], without that indirect
giving of meaning which founds the semantic field, which in turns provides
the ground upon which structural homologies can be discerned.
And conversely, there is no
hermeneutic comprehension without the support of an economy, of an order
in which the symbol signifies. Taken by themselves, symbols are threatened
by their oscillation between sinking into the imaginary and
evaporating in allegorism; their richness, their exuberance, their polysemy
expose naive symbolists to intemperance and complacency. (63/60)
Thus, according to Ricoeur’s analysis of what may perhaps be called the “formalist-syntac-
tic” inadequacy, Structuralism must rest content with a limited, although necessary role.
Syntactic analyses are an indispensable supplement to philosophical understanding but
cannot become autonomous because they miss a fundamental level of human practices. If
Ricoeur’s analysis is correct, the subalternity of the formal/syntactic disciplines will only
turn into full-blown supplementarity— in the sense explained above—as soon as the disci-
plines in question overstep their assigned boundaries and pretend to be taken as complete
“philosophies.” It cannot be otherwise, since they will be forced to presuppose nothing less
than that “indirect giving of meaning which founds the semantic field, which in turns pro-
vides the ground” upon which the syntactic transformation can be performed, be it a rule-
based AI-like move or a permutation of a group of relations. To put it a bit differently,
Ricoeur’s analysis leaves only two possibilities open to and all game-based approaches that
rely on the concept of closure of the semantic field: they can either abandon the non-philo-
sophical ambitions and accept a technical status, or they can raise their theoretical aim by
finding a way to recover the contents of the practices (the “semantics) while preserving clo-
sure.
Structuralism (or AI) are thus demoted, in a traditional metaphysical gesture, to the
role of helping disciplines that can provide useful “technical” insights on the “abstract” me-
chanical structure of the semantic question—but disciplines that cannot help leaving the
real philosophical issues for the philosophers to solve. Lévi-Strauss, however, is quite un-
comfortable with such a reductive interpretation of his work, and points out that the philo-

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sophical work carried out by the structures provides an explanation of how meaning came
about in the first place: as a the kind of permutation of groups of relations operated on
meaningless elements that he finds at work underneath the surface of myths. In Lévi-
Strauss’s more radical view, there is no room left for philosophy in the traditional sense, as
Ricoeur is quick to recognize and as Lévi-Strauss himself will elaborate in greater detail
his challenge to philosophy in the following years: in the introduction (Ouverture) to My-
thologiques, which I will discuss in the next section, he answers Ricoeur by responding to
the latter claim of partiality of an interpretation within an historically bound context with
the elaboration of the concept of Anaclastic unity (structural analysis of myths is a myth of
myths).
Generally speaking, though, we can notice that the two options outlined by Ricoeur
correspond quite closely, in my opinion, to successive developments followed by Artificial
Intelligence and Structuralism, although the path that these two disciplines have taken are
somewhat intricate. In the former case represented by AI, we see that the reliance upon the
formalistic distinction between form and content accompanied by the privileging of the
former term over the latter has exposed it to the kind of fallacies that Ricoeur outlined in
his critique. Although AI as such has definitely not published any grand manifesto pro-
claiming a theoretical shift from a general philosophy to a technical, “supplementary” (or
subordinate) discipline, it is not difficult to see that this is exactly what has historically hap-
pened in the scientific practice of the field. With a few exceptions (mostly coming from phi-
losophers embracing AI rather that from researchers active in AI research) 28 research in
Artificial Intelligence has quietly turned into a technical discipline that is more interested
in the development of logical tools or new algorithms than in providing an exhaustive rep-
lication of the inner workings of the human mind in general.
Lévi-Strauss, on the contrary has chosen the opposite path: by upping the ante and re-
fusing any formalistic interpretation, he aims instead toward an integrated picture that tak-
en into full account that level of human practices that, according to Ricoeur, a formalist
account will necessarily miss. To use the philosophical framework that Ricoeur sketched in
his article, such an integration should move him toward the Hegel-like pole of the philo-
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sophical axis and away from the Kant-like formalism of the unconscious that he was re-
proached for. However, it is not at all easy to provide an account of and eventually assess
his theoretical move because in his responses to Ricoeur contained in the quoted issue of
Esprit and in later works as well, he has repeatedly proclaimed his full acceptance of
Ricoeur’s label for his project: kantisme sans sujet transcendantale, he affirmed, represents
an excellent description of his very project. In other words, Lévi-Strauss seems to be mov-
ing in the opposite direction than we expect, or perhaps seems to be saying one thing and
doing something very different.
Let us now examine these two paths in turn by going back to their common root: the
possibility of a reduction of meaning to the product of the structure’s operation. This is the
crucial step that Structuralism takes and AI does not. What does it mean?
Lévi-Strauss’s answer is clear: it is misleading to think of a possible complementarity
and opposition between syntax and semantics, between structural analysis and philosophi-
cal interpretation, because one of the most important result of the notion of structure as de-
veloped by the “phonologic revolution” is that “meaning derives always from the
combination of elements which are not meaningful in themselves.” Therefore, what the phi-
losopher is after would constitute
a meaning of meaning, a meaning which lies behind the meaning; where-
28. It will have been noticed that the distinction between the “philosophical” vs. the “technical” option corresponds
quite closely to John Searle’s famous distinction between “strong” and weak” AI as put forward
in “Minds, Brains, and Programs,” an article he published in 1980. At the time AI was still quite
attached to its grand philosophical project, as the many reactions to Searle’s article from inside the
field bear witness, while in the following years the research has become “weaker” and “weaker,” so to
speak, i.e. more and more technical and less and less philosophical. In fact, the “grand vision” of Artificial
Intelligence seems to be accepted, nowadays, only by philosophers like John Pollock or Daniel
Dennett, whose debates with AI’s self-appointed terminator, John Searle, fill the pages of many magazines.
A good indication of the theoretical shift that has occurred in AI practice is provided by the
essay by John McCarthy quoted above in Chapter IV, in which McCarthy recounts his flabbergasted
reaction when a doctoral student in AI could not relate her dissertation project to the goal of explaining
the mind, nor, which is worse, could appreciate the importance of the issue. Of course the issue that
should be addressed is whether there is anything left to AI once the non-philosophical ambition has
been stripped off. I tried to provide an answer to this question, although implicitly, in chapter IV above.
See John Searle, “Minds, Brains, and Programs…”; John Pollock, How to Build a Person (Cambridge,
Ma: MIT Press, 1989) and its sequel Cognitive Carpentry: a Blueprint for How to Build a Person
(Cambridge, Ma: MIT Press, 1995);Daniel Dennett, Consciousness Explained …; and John McCarthy,
“AI needs more emphasis on basic research…”

S TRUCTURALISM, PHILOSOPHY, AND AI
as in my view meaning is never a first phenomenon: meaning is always reducible.
In other words, behind every meaning there is always something
meaningless and the reverse is not true. For me, signification is always phenomenical.
29
It cannot be stressed enough that we have reached here the crucial point of our com-
parison between Structuralism and Artificial Intelligence, that is also a comparison between
two dominant attitudes on the opposite sides of the Atlantic. The real watershed is to be
found in Lévi-Strauss’s willingness to accept, and indeed to claim, that signification is in-
deed a “result” of the structural transformations (e.g. permutations) of groups of relation-
ships (e.g. oppositions) operated upon elements that are themselves void of meaning. The
structural approach, in other words, considers the meaningfulness of the symbols that it ar-
ranges in tables and groups as a result of the manipulation, and not as a pre-given phenom-
enon that can just be assumed (as AI would have it) or that can be left to philosophy to
account for (as Ricoeur would like).
The AI tradition, as I have insisted above, considers the meaningfulness of the symbols
an extra-theoretical starting point, an assumption that it can put aside while concentrating
all its attention on syntactic, e.g. “formal,” combinations that will “preserve” the semantic
content of the atomic elements it started from. “Take care of syntax, and semantics will take
care of itself,” is the AI dictum epitomizing a separation of concerns between the semantic
and syntactical spheres that in fact relies upon the logical and epistemological priority of
the former in order to turn the latter into an object of study. 30 That is, AI relies on the as-
29. Claude Lévi-Strauss, “Réponses à quelques questions,” in Esprit, 31, 322, nov. 63, 637, emphasis added.
30. On the deep reliance on semantics of AI and the “formalistic tradition” in general, see Brian Cantwell
Smith, The Rise of Objects …15 ff. and especially the full discussion of “formalism” as anti-semantics
in the second volume of The Age of Significance. In the Derridean terms sketched above, Smith’s operation
is a full-fledged deconstruction of the formalist tradition, with syntax and semantics playing
the role, respectively, of speech and writing in the by now classical Derridean analysis carried out, for
example, in De la Grammatologie. “Semantics,” e.g the pregiven meaningfulness of symbols, is, like
writing, what the formalists cannot accept within their theories, but is nonetheless what grounds them
from the outside. Except, of course, that the theories themselves foreclose the existence of any outside
of this kind. Semantics, in other words, plays, according to my interpretation of Smith’s work, the paradigmatic
role of a Derridean supplement within the formalist project which is exemplified here by the
Artificial Intelligence tradition.
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sumption that the meaningfulness of symbols is not what the theory is all about: it is a pre-
supposition that the theory will not explain but that it must assume as the ground on which
it will operate. This position is perfectly congruent with Ricoeur’s interpretation of Struc-
turalism and it does indeed leave quite a considerable room for the work of the philosopher
who will have to provide an explanation of how semantics came about in the first place.
Thus, the debate between Ricoeur and Lévi-Strauss helps us understand the critical
step that the two game-based non-philosophies we are examining have to take in order to
escape philosophy’s objections. If they are content to presuppose semantics and limit their
theoretical scope, “formalistically,” to a theory of syntactic manipulation, then it will be up
to philosophy to complete and complement their “merely” technical approach. Artificial In-
telligence does not take this critical step, nor could it take it even if it were willing to, given
its reliance on the concepts of form and content tied together by an interpretation function.
Therefore, formalist approaches like AI’s end up caught in a double bind: on the one hand
they are, theoretically speaking, forced to leave room for philosophy, as Ricoeur’s point
makes clear; on the other hand, they are programmatically incapable of doing so unless they
renounce the “non-philosophical” ambitions and accept to be reduced to a pure “technical”
(e.g. “engineeristic”) discipline that the philosopher may found useful but that can never
solve, nor indeed even approach, any true philosophical problem.The interpretation of Ar-
tificial Intelligence’s impasse I have just offered may perhaps show that the classical cri-
tiques advanced, from diverging sides, by John Searle, Hubert Dreyfus and the
Connectionists movement are in some sense necessitated by the inadequate rendering of
detachment within the AI filed. All critiques, in fact, try to ground meaning outside AI’s
formalistic structres, e.g. they relinquish the requirement of closure. Searle’s celebrated
‘Chinese room’ argument wanted to show, inter alia, that no formal structure can ever have
a signifying intention, that no original intentionality can be originated by a computer pro-
gram. Intentionality, for Searle, is a bio-physical process analogous to digestion and lacta-
tion—e.g. it belongs to that ‘level of content’ that lies programmatically (but
‘supplementarily’) outside of AI’s search-spaces. Connectionism can be similarly interpret-
ed as the effort to abandon the non-philosophical ambitions of AI in favor of a classical

T HE CHALLENGE OF CLOSURE
methodology that aims at modeling on computer hardware an essentially biological pro-
cess. Dreyfus’s critique, on the other hand, is very close to Ricoeur’s, insofar as it stresses
the existence of an unformalizable level of meaning-creating practices that lies behind (and
reaches beyond) the formalized structures.
The debate between Ricoeur and Lévi-Strauss’ around formalism makes clear (hope-
fully) that the interpretation of game that adopts total arbitrariness and complete separabil-
ity (the two tenets of the AI/formalistic procedure to fix the game into place) puts itself into
an unstable position that calls for an external, but impossible, grounding that can be either:
(a) “philosophical,” like Ricoeur’s search for a meaning of meaning through herme-
neutics, and its equivalent in the AI’s field: Dreyfus’s Heideggerian critique;
(b) or “biological,” like Searle’s “solution” that ties everything back to the concrete or-
ganization of the “physical.”
In either case, AI’s project fails, since it cannot, in principle, admit anything external
to its game-like search-spaces and both (a) and (b) —the first pushing upward toward philo-
sophical skies, the second pulling it downward toward a “biological physicalism”—deny
the required closure.
My analysis, however, suggests that these critiques do not really go to the root of the
issue. The problem lies with the intrinsic inability of the formalistic solution to detachment
to preserve closure. Therefore, the application to AI of an alternative solution to the prob-
lem of detachment, like Structuralism’s, would be able to salvage AI’s “grand” program un-
scathed. This does not mean that Structuralism does not face problems of its own, as we
will see in the next section.
6. The challenge of closure
In the previous section, we have seen that Ricoeur’s critique points out a set of signif-
icant problems for the formalistic understanding of abstract game-like structures that we
have seen exemplified by Artificial Intelligence. We turn now to a discussion of the positive
alternative that Lévi-Strauss proposes against hermeneutics’ interpretation of Structural-
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ism, and it seems best to start again from an analysis of the definition that, in Ricoeur’s
eyes, summarizes the theoretical impasse faced by Structuralism: “Kantism without a tran-
scendental subject.” This definition has enjoyed a good deal of fortune, not the least be-
cause of Lévi-Strauss apparent endorsement, most famously in the “Ouverture” that opens
Mythologiques, where he says:
In allowing myself to be guided by the search for the constraining structure
of the mind (esprit), I am proceeding in the manner of Kantian philosophy,
although along different lines leading to different conclusions. […] I
am perfectly aware that it is this aspect of my work that Ricoeur is referring
to when he rightly describes it as “Kantism without transcendental subject.”
But far from considering this restriction as indicating some deficiency, I see
it as the inevitable consequence, on the philosophical level, of the ethnographic
approach I have chosen. 31
In spite of Lévi-Strauss’s polemic endorsement, however, it is important to emphasiz-
es, for a correct understanding of his position, that Ricoeur’s definition amounts to a defin-
itive condemnation, both in Kantian terms and in Ricoeur’s own, non-Kantian perspective.
In fact, a Kantism without transcendental subject is a contradiction in terms, since Kant’s
main purpose was precisely to define the limits of human reason in order to establish the
field of human freedom: the human subject lives freely in a world that is different from the
merely natural world of an objective nature subjected to necessary rules. A Kantism of the
unconscious, then, would be worse than a ridiculous parody of the Kantian project, e.g. the
effort to deprive the human subject of his freedom and to reduce it to the ranks of mere ne-
cessity. It would indeed be a totally inconsistent project, since the categorial grid analyzed
and justified in the Critiques contains the categories of a subject who perceives, thinks and
acts through them, and it is the transcendental, as opposed to the pure empirical, status of
the subject that validates the grid itself. If we take away the subject and its transcendental
status, the Kantian project is reduced to an empty formalism that cannot be pinned down
31. Claude Lévi-Strauss, Mythologiques I, Le cru et le cuit (Paris: Plon, 1964) 18-19; Engl tr. The Raw and
the Cooked (Chicago: Chicago UP, 1983) 10-11, emphasis added. The passage repeats almost verbatim
Lévi-Strauss’s response to Paul Ricoeur in the Esprit debate.

T HE CHALLENGE OF CLOSURE
on any concrete substratum and cannot be filled by any content. Which is precisely why
Ricoeur’s coined his famous definition: because he wanted to stress that the formal grid is
senseless—and not just meaningless, but deprived of any philosophical sense, motivation,
and justification—unless it is supplemented by an analysis of the subject that uses it. In
Ricoeur’s perspective, moreover, this subject cannot be the a-historical transcendental sub-
ject bequeathed by Kant, but must be conceived as a historically situated being which op-
erates within a horizon of meaningfulness continuously renewed by the interplay between
the individual hermeneutic efforts and the set of discourses and symbols handed down by
tradition.
Ricoeur’s definition, in other words, summarizes in a single phrase the theoretical di-
lemma of structuralism: either it is a formalism that cannot be used to explain how a human
being operates in the world unless it is supplemented by a (possibly hermeneutic) under-
standing of the subject,or it converts into an empty idealism of forms that will not explain
anything because it will be always cut off from a reality that it cannot possibly account for
having excluded it from the analysis in the first place.
We may tempted to leave aside any Kantian connotation, Lévi-Strauss’s approval not-
withstanding, and remark that Ricoeur seems to have forgotten that structuralism differen-
tiates itself from formalism precisely because while form is defined in opposition to
content, “structure has no distinct content; it is the content itself apprehended in a logical
organization conceived as a property of the real.” 32 There is no need, therefore, to postulate
the existence of a separate investigation that would deal with the content, since structural-
ism itself is such an investigation. These remarks seem to push structuralism’s conception
of structure towards the other axis of the philosophical opposition presented by Ricoeur,
namely toward the Hegelian system. This thesis has been proposed, in the context of the
same debate, by Kostas Axelos, who suggested that Hegel is the father of Structuralism in-
sofar as he is the author of “a speculative genealogy, a phenomenology of spirit, this gene-
32. Claude Lévi-Strauss, Anthropologie Structurale deux, …139; Engl. tr. 115. Emphasis added. The passage
quoted concludes the first programmatic paragraph of the essay (originally published in 1960)
quoted at length above where Lévi-Strauss develops his distinction between formalism and structuralism.
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alogical development being nothing else than the development of an initial and total
structure that is the structure of the Greater Logic.” 33
Indeed, structuralism seems to be much closer to Hegel’s than to Kant’s philosophy, at
least insofar as the “subject” whose necessary laws the structural analysis strives to discov-
er is the collective spirit, e.g. Geist. In other words, the identification of the “subject”—in
the almost grammatical sense—of the a-priori laws with the trans-individual, social, and
unconscious spirit whose evolution the individual cannot but follow—in other words: the
substance— seems to push structuralism, almost inevitably, toward the Hegelian re-elabo-
ration of critical philosophy. As Lévi-Strauss makes clear, his enterprise is not an analysis
of the spaces of freedom opened up to the human subject, but rather the opposite. His goal,
as he says during the debate and will repeat in the introduction to Mythologiques, provides
“a sort of inventory of mental constraints, [it is] an effort to reduce the arbitrary to an order,
to discover a necessity immanent to the delusion of freedom.” If such an order can be dis-
covered in mythology, “where [the spirit] seems to be the most free to follow his creative
spontaneity [...], if, in this field, the spirit is enchained and determined in all its operations,
a fortiori, it must be so everywhere.” 34
The Hegelian rapprochement, however, falls short of a real identity of methods and
conceptions, as it is apparent as soon as we consider the relationship between the object of
Structuralist analysis and the subject of the structure. It is crucial to the Hegelian project
that there is a mediation whereby the object is internalized as subject and, conversely, the
subject can externalize itself as an object: the dialectical progression—and therefore the
logic of the contents—can start only if the relationship between the objective and the sub-
jective side can be mediated one with the other. 35 But nothing of this sort happens, accord-
33. Kostas Axelos, in Esprit, …, 646.
34. Claude Lévi-Strauss, “Réponses à quelques questions…” 630, emphasis added. “Spirit”, of course, is
the French esprit, which is semantically uncommitted between the individual (and mostly conscious)
mind and the abstractly philosophical spirit which can support a collective and unconscious reading.
35. I am relying upon the particularly lucid Hegelian critique presented by Lawrence Krader, “Beyond
Structuralism: The Dialectics of Diachronic and Synchronic Methods in the Human Sciences, The Unconscious
in Culture. The Structuralism of Claude Lévi-Strauss in Perspective, Ino Rossi, ed., (New
York: E.P. Dutton &Co, Inc., 1974) 336-361. A different, but equally critical, Hegelian approach to
Structuralism is presented by Stanley Diamond, “The Myth of Structuralism,” in the same collection.

T HE CHALLENGE OF CLOSURE
ing to Lévi-Strauss, since the objective practices do not return into the subject as an
internalization of the latter: in fact the practices are as external to the structure as the indi-
vidual’s thoughts. Conversely, there is no proper externalization of the subject, in the He-
gelian sense, into the object since, once again, the interaction between the two passes
through the mediation of a structure which is external to both.
This lack of mediation raises a problem that Hegel himself had in fact already dis-
cussed in the Preface to the Phenomenology, namely in the section “Against the Schema-
tizing Formalisms”:
Instead of the inner life and self-movement of its existence [Dasein], this
kind of simple determinateness of intuition—which means here self-knowledge—is
predicated in accordance with a superficial analogy, and this external,
empty application of the formula is called a ‘construction.’ […] What
results from this method of labelling all that is in heaven and earth with the
few determinations of a general schema, and pigeonholing everything this
way, is nothing less than a ‘report clear as noonday’ on the universe as an
organism, viz. a synoptic table like a skeleton with scraps all over it[…]and
just as all the flesh and blood has been stripped from this skeleton, and the
no longer living thing (Sache) has been packed away in the boxes, so in the
report the living essence of the thing (Wesen der Sache) has been stripped
away or boxed up dead. 36
The point of Hegel’s critique is that insofar as the schemas (or the schematizing for-
malism) is not produced by the concept itself in its interaction between the subject and the
object, it is bound to remain an empty and totally arbitrary construction that can be applied
to everything because it does not explain anything. In other words, since the schema is not
borne out of the dialectical interaction between the subject ant the object that takes place
within the concept, the schema exists only in the mind of the investigator, and not in the
things themselves. Thus, the Hegelian critique raises an immediate problem concerning the
ontological status of the schema, or structure. Moreover, and because of the ontological un-
36. Georg W. F. Hegel, Phenomenology of Spirit …, 31(§51 in Miller’s translation.) See also Lectures on
the History of Philosophy…, v.3 268-270. The passage in the Phenomenology is a critique of Schelling’s
philosophy of nature, taken up again, and applied most extensively to Schelling’s followers, in
the Lectures.
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certainties, it raises an even more pressing epistemological problem that concerns the very
conditions of possibility of any structural investigation: what is the epistemological status
of the structural theory that the anthropologist describes but cannot find instantiated either
in the subject nor in the object but that acts only as their unconscious mediator? What, in
other words, guarantees that the structural level is reachable and scientifically describable,
once it has been admitted that it cannot be retrieved in the things as they are given, and what
distinguishes it from a pure figment born out of a vivid imagination of the scientist?
The impossibility to provide a Hegelian interpretation of the logic of contents claimed
by Lévi-Strauss against Ricoeur shows that such a response falls short of providing a full
answer to the issues raised by the latter, and in particular to the charge of formalism. Indeed,
once the “content-ful” property of the structure has been claimed, it remains to be explained
how the structure can interact with the substance it mediates and, furthermore, how the an-
thropologist can grasp it in a scientific way. This does not mean, as it has sometimes been
reproached to Lévi-Strauss, that Structuralism needs to be integrated by dialectics, be it He-
gelian or not. Rather, it means that the problem that dialectics is called up to solve needs to
be addressed: the problem of the mediation between subject and object through the self-
development of the “structure” that progressively externalizes itself in this very mediation.
It is an important first step to remark that the structure is not purely formal since it instan-
tiates a logic of the contents, but unless the “external” articulation of the mediating struc-
ture with what it mediates is explicitly addressed at both the ontological and
epistemological levels, Ricoeur’s charge of formalism will be effective again, at a higher
logical level, in the manner prefigured by the Hegelian critique.
Thus, neither accepting Ricoeur’s “Kantian” identification, nor reversing to an oppo-
site “Hegelian” paradigm helps to solve the philosophical problems, although it helps iden-
tifying which problems are at stake. However, it may have helped Lévi-Strauss score
rhetorical points against the thinkers who were dominating the contemporary philosophical
debate in France by preempting the relevance of a subject-centered critique of his work. 37 In
37. It is worth remembering that behind Ricoeur, who was in fact quite open to the scientific contributions
of Structuralism, looms large the shadow of the more powerful—and much less sympathetic—master
of the French scene: Jean-Paul Sartre.

T HE CHALLENGE OF CLOSURE
other words, by accepting an intrinsically inconsistent philosophical classification, Lévi-
Strauss would less be committing himself to a philosophical position than rejecting the rel-
evance of philosophy altogether—with its tools, concepts and history—to the anthropolog-
ical project. An interpretation bound to find support in the well-known tirades against
philosophy contained in “Making of an anthropologist” (in Tristes tropiques) as well as in
the final pages of L’homme nu, where Lévi-Strauss proclaims that he has never had any phi-
losophy of his own, “apart from a few rough convictions that I have come back to, less
through the development of my own thought than through the progressive erosion of what
I was taught and that I once taught myself.” 38 What do we gather, then, from this excursus
into Lévi-Strauss’s quibbles with the philosophers? It would almost seem as if the exchang-
es we outlined are to be considered just merely academic disputes better read as symptoms
of underlying power struggles than debates with some real bearing on the conceptual issues
at stake.
Let us start by acknowledging that Ricoeur is absolutely right in his dismissal of Lévi-
Strauss’s —and, more generally, game-based approaches’ —philosophical claims. First,
because he points out, quite rightly, that leaving the issue of content aside reduces game-
based approaches like Structuralism, in his interpretation, and AI, in mine, to technically
useful formalisms that cannot be philosophically self-sustaining. Thus, when he questions
what he sees as game-based (non)philosophy inability to recover the level of content, he is
asking them a question that they must answer in order to be up to the challenge. In other
words, the theoretical possibility to supplant philosophy passes necessarily through the an-
swer to that question about content. Moreover, as Ricoeur and the other quoted critics make
clear, there is no ready-made philosophical answer to be found in the history of philosophy:
Not in Kant, not in Hegel, not in Husserl, etc. As a matter of fact, the effort to adapt the
former philosophies to Structuralism makes them ipso facto prone to impassable contradic-
tion: Kantism lacks its transcendental subject, Hegelianism loses its no subject-object me-
diation, and so forth.
38. Claude Lévi-Strauss, L’homme nu, …, 570; Engl. tr. 638, emphasis added.
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Moreover, and most importantly, Ricoeur is “philosophically “right insofar as he is up-
holding the rights of philosophy to handle the philosophically relevant questions: he recog-
nizes, in other words, the “challenge” of structuralism all the way through and defends
philosophy against and over it. In fact, a few years after the quoted debate took place, he
explicitly stated this point in an article that deals with the défi de la sémiologie, the chal-
lenge that Structuralism—and, by extension, semiology in general—brings against philos-
ophy. In his own words:
Avant de proposer un détour, la linguistique structurale impose un défi à
la philosophie du sujet: le défi consiste en ceci que la notion de signification
est placée dans un autre champ que celui des visées intentionelles d’un sujet.
Autrement dit, le système de signes n’a plus de dehors, il a seulement un
dedans; ce dernier postulat, qui l’on peut nommer le postulat de la clôture
des signes, résume et commande tous les autres. C’est bien lui qui constitue
le défi majeure pour la phénoménologie. Pour celle-ci, le langage n’est pas
un objet, mais un médiation, c’est-à-dire ce par quoi et à travers quoi nous
nous dirigeons vers la réalité; il consiste à dire quelque chose sur quelque
chose; par là, il s’échappe vers ce qu’il dit, il se épasse et s’établit dans un
mouvement intentionelle de référence. Pour la linguistique structurale, la
langue se suffit à elle-même: toutes ses différences lui sont immanentes; et
c’est un système qui précède le sujet parlant. 39
It would misleading to read in these words, and in Lévi-Strauss’s, just the symptom of
the ongoing battle between the “scientists” and the “philosophers,” as it has sometimes
been said. 40 But it is not just the scientist, it’s rather a very different conception of philoso-
phy, a non-philosophy, that is, that comes forward. What comes out with extreme clarity is
that the philosopher senses in the structuralist attack a direct threat to philosophy’s chance
39. Paul Ricoeur, “La question du sujét et le défi de la sémiologie,” Le conflit des interpretations…, 246-
7; Engl. tr. 250-1.
40. Marcel Hénaff, for example, Claude Lévi-Strauss…, 196-198, stresses the “incompatibility” between
the philosopher’s and the anthropologist’s approaches, but reduces the conflict to an instance of a more
general querelle between science and philosophy, while Edouard Delruelle, Claude Lévi-Strauss et la
philosophie…, 81-82, sees the issue at stake but fails to follow through its implications for philosophy
and Structuralism in general. This point has been clearly seen by Jean-François Lyotard, “Mais les indiens
ne cueillent pas des fleurs,” Annales, 1, (Jan-Feb 1965).

T HE ANACLASTIC ILLUSION OF A TRANSCENDENTAL UNITY
of survival: the concept of meaning as generated by a “closed field of signs” goes directly
against philosophy’s whole conceptualization of the subject by shifting the responsibility
for a philosophical answer outside of philosophy itself. If successful, Structuralism would
really constitute the endpoint of a trajectory philosophy undertook very long ago. Ricoeur
contends that the challenge is doomed to fail because the “postulate” of the closure of the
semantic field will never be able to account for the content that language, when seen as a
mediator, allows to convey, nor for the practices that recover that content in the historically
mediated linguistic exchange. We do not know, yet, whether Structuralism can answer raise
up to this challenge. What we do know, however, are the its precise terms: the relationship
between closure and content is the crucial issue at stake, and the “termination” of philoso-
phy or the “termination” of Structuralism is the prize to be awarded.
7. The anaclastic illusion of a
transcendental unity
This discussion of the rather difficult relationships between Lévi-Strauss’s project and
the philosophical paradigms provided by Hegel and Kant makes clear that if the reduction
of meaning to meaningless elements vindicated by the structural analysis avoid the formal-
ist pitfalls it does, on the other hand, open up a whole new series of problems. Moreover,
these problems do not consist in idle speculations on the possible philosophical implica-
tions of the analysis of myths, but rather impinge on the very conditions of possibility of
structural analysis and, by consequence, on the scientific status of its findings. No self-
standing structural analysis of myths is possible unless the ontological status of the struc-
ture that the analysis retrieves is specified and the epistemological relationship that enables
the anthropologist to discover it is fully clarified. It is certainly true, as Hénaff, for example,
has remarked, that what the philosophers refuse to acknowledge is that there is “no refusal
of an interpretation of contents in the structuralist approach, but rather an impossibility of
carrying it out because structuralism cannot propose an interpretation which would consti-
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tute an ultimate sense, nor can it propose a [privileged] level of reference that would con-
stitute a level of truth.” On the contrary, the only kind of “interpretation” that a mythologist
can provide is to evidentiate the pertinent traits within a group of myths, their transforma-
tions, etc., and “thereby to understand how a group of myths constitutes the representation
of given world and strives to provide answers to some questions, not as statements, but in
the very play of those representations.” 41 The “privileged level” sought by the philosopher
survives, we might add, but it is not is not a level at all, and certainly not a level of reference
to be found outside the structure: rather it is the play itself of the elements within the struc-
ture. The “truth,” if there is any room left for this term, is the truth of the structure as seen
from the inside, in the rearrangements of the various places that the terms can occupy.
Therefore, two strictly related questions are left unanswered, at this stage of the anal-
ysis, by Lévi-Strauss: (a) what is the reality of the structure whose play commands a group
of (transformations of) myths and (b) what is the status of the truth about that very structure
that is being discovered, about its play, when it is discovered by the anthropologist who is
necessarily positioned outside it?
However, the existence of these problems, and even their formulation in rather classi-
cal terms we have just given, does not entail that the solution to the problem must be found
within the confines of philosophy strictu sensu. The philosophical solutions we have
sketched above with reference to Kant and Hegel, and most especially the use of the con-
cepts of subject and object, might not be adequate for Lévi-Strauss’s structural analysis. In-
deed, we should rather expect the opposite to be true, if the structuralist project is to be
consistent with its professed goal of bringing philosophy to an end. In other words, it might
be the case that the effort to unfold the implication of the structural method, still to a large
extent absent in the work of the early 1960s (e.g. before Le cru et le cuit) will bring about
a rethinking, a non-philosophical rethinking of those capital philosophical categories as
subject and object. At any rate, the questions raised by the philosophers, and the impossi-
bility to fit Lévi-Strauss’ model within either a Kantian or Hegelian model, brings up a
problem whose solution is crucial to Structuralism, a problem that may be summed up in a
41. Marcel Hénaff, Claude Lévi-Strauss…, 197.My emphasis.

T HE ANACLASTIC ILLUSION OF A TRANSCENDENTAL UNITY
single question and that I will be tackling next: is the reality of the structure to be found
only in the eyes of the beholder?
Lévi-Strauss provides a full answer to these interrogatives in his major work, the four
volumes Mythologiques, which he published between 1964 and 1973. Particularly relevant
to our concerns here are the “Ouverture,” e.g. the introductory chapter to the first volume
of the series, Le cru et le cuit, and the conclusion to the last one, L’Homme nu, titled “Fi-
nale.” In “Ouverture” Lévi-Strauss—after the answer to Ricoeur quoted above—deepens
his reflection by defining the ontological and epistemological implications of his project
through an optical analogy. We quote the passage in its entirety:
The science of myth may therefore be termed “anaclastic,” if we take this
old term in the broader etymological sense which includes the study of both
reflected rays and broken rays. But unlike philosophical reflection, which
claims to go back to its own source, the reflections we are dealing with here
concern rays whose only source is hypothetical. Divergence of sequences
and themes is a fundamental characteristic of mythological thought, which
manifests itself as an irradiation; by measuring the directions and angles of
the rays, we are led to postulate their common origin, as an ideal point on
which those deflected by the structure of the myth would have converged
had they not started, precisely, from some other point and remained parallel
throughout their own course. As I shall show in my conclusion, this multiplicity
is an essential characteristic, since it is connected with the dual nature
of mythological thought, which coincides with its object by forming a
homologous image of it but never succeeds in blending with it, since
thought and object operate on different levels. […] Myths, like rites, are “interminable.”
And this essay, which is also both too brief and too long, has
had to conform to the requirements of that thought and to respect its rhythm.
It follows that this book on myth is itself a kind of myth. If it has any unity,
that unity will appear only behind or beyond the text and, in the best hypothesis,
will become a reality only in the mind of the reader.[…]
And a few pages later:
This is why it would not be wrong to consider this book itself as a myth:
it is, as it were, the myth of mythology. However, this code, like the others,
has neither been invented nor brought it from without (quémandé au de-
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hors). It is inherent in mythology itself, where we simply discover its pres-
ence. 42
The study of myths can be termed an “anaclastics” because, like the latter, it devotes
itself to the study of the medium through which myths’ content, e.g. themes and sequences,
are refracted and reflected to assume their final outward appearance. It is therefore irrele-
vant whether the point of origin of the rays is real or hypothetical, as Lévi-Strauss affirms,
since the object of interest is constituted by the pattern of refractions and not by the content
that is being refracted. It is the hubris of the philosopher that pretends to ascertain a final
original point: the mythological reflection is content to remain at the level of the phenom-
ena—e.g. the transmitted myths—and to study the visible transformations within an empir-
ically and historically given group. This provides a first element toward the explanation of
the epistemological issue: according to Lévi-Strauss, the objectivity of the structure can be
discovered from the outside, e.g. by an anthropologist situated outside the community up-
holding the myths, because the objectivity of the structure resides in its form, and not in its
contents. More precisely, the objectivity of the structure is to be found in the transforma-
tions that it operates on the elements that pass through it and gets diffused and refracted.
The results of the transformations themselves may be illusionary, insofar as they depend on
the postulation of an hypothetical source whose existence may be challenged and, in fact,
moved by a different analysis. Thus, for example, the analysis of the group of South-Amer-
ican myths as produced by a series of transformations organized along the triplet Raw/
42. Claude Lévi-Strauss, Le cru et le cuit, …, 13, 20; Engl. tr. 5, 12. Emphasis added. The definition of the
analysis of myths as “un-terminable” refers of course to the psychoanalytic distinction first discussed
by Freud in “Terminable and Interminable Analysis.” The psychoanalytic therapy, like mythology, can
be ‘unendlich’ because the concept of a “normal ego (Ich) of this sort is, like normality in general, an
ideal fiction,” according to Freud, who adds that “every normal person, in fact, is only normal on the
average. His ego approximates to that of the psychotic in some part or other and to a greater or lesser
extent; and the degree of its remoteness from one end of the series and of its proximity to the other will
furnish us with a provisional measure of what we have so indefinitely termed ‘alteration of the ego’.”
Sigmund Freud, The Standard Edition of the Psychological Works of Sigmund Freud (London: Hogarth
Press, 1964) v. XXIV, 235. See also the essential disturbance of the Ego contained in the essays
on the disease of civilization and the use made by Lacan, especially in La direction de la cure. Note
also that Freud introduces the concept of “alteration of the Self, in the mentioned essay, to explain this
phenomenon, a concept with obvious similarities to the refractive and anaclastic features of Lévi-
Strauss’s medium of mythology.

T HE ANACLASTIC ILLUSION OF A TRANSCENDENTAL UNITY
Cooked/Rotten that Lévi-Strauss attempts in the volume bearing the same name may not
correspond to an ultimate “scientific” reality and may exist only in the eyes of the anthro-
pologist. More prosaically, it may be revised by further ethnographic and historical data
that may suggest a different source. However, it is only, or perhaps most importantly, the
mode of operation of the structure itself that escapes such a possibility of revision, insofar,
at least, as it can be found at work in the given data (où nous retrouvons sa présence).
We need to be careful, therefore, in interpreting Lévi-Strauss’s declaration that his
“book on mythology is itself a kind of myth […] whose unity will become a reality only in
the mind of the reader.” The unity at stake here, e.g. the “content” of the book, is exactly
homologous the content of the myths the book studies: as such its relevance is only mar-
ginal, since it depends on a common source that is only hypothetical. To the reader who
“believes” in the content of Mythologiques, the book will have acquired a meaning analo-
gous to the meaning of the eagle-hunters myth for the “primitive” Bororo Indian who be-
lieves in it: the book, as well as the myth, will have explained situations, interpreted real-
life conundrums, etc. As a matter of fact, the “meaning” of the book as such can change at
any moment, accordingly with the evolution of the society, our Western society, within
which it is being read. This, however, does not mean at all that the character of the structure
the book describes is illusionary and “mythological” as well. On the contrary, the modes of
transformation of the contents of a book that is itself mythological in character will neces-
sarily be homologous to the structure of the myths it studies and will, therefore, confirm the
objective results of the analysis. In short, the mythological character of Mythologiques,
then, far from consisting in a diminished scientific status, is, as it were, the mark of its “ob-
jectivity.”
We can see here the magnitude of the theoretical shift entailed by this move and, at the
same time, the truly “end-like” features of Structuralism when applied to philosophy: phi-
losophy itself, e.g. the search for truth, is recomprehended as a particular myth, or as a par-
ticular group of myths which is generated by a certain pattern of permutations/
transformations of sequences and themes within our own culture. Structuralism, therefore,
can really represent the “terminator” of philosophy insofar as it sees the latter—that is, phi-
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losophy and its cardinal concepts, like truth, subject, object, etc.—as the particular posi-
tions occupied by meaningless elements within a broader game of chess—or of
permutations
This last point becomes clearer if we consider that the anaclastic analogy must be read
in its full force: the “reflections” generated by the medium belong to a closed field since
they are the elements of a closed set with a finite number of elements and a finite, in fact a
very small number, of rules of transformations. To put it differently, the medium whose re-
fractive properties the anaclastic science studies is closed upon itself: it is not a semi-trans-
parent layer that separates an inner mythological construction from an outside where the
references of the sequences and themes belong. Rather, it is a warped surface, a crystal ball
of sorts where the rays, once entered, can never escape but keep bouncing, reflecting, and
refracting ad libitum, although not ad infinitum, and thus generate “in-terminable” contin-
uations according to the same medium-related pattern.
The truth of philosophy, e.g. the meaning of meaning that Ricoeur, according to Lévi-
Strauss, pretends to discover, is thus the illusion that the glass-cage can be opened, or
shoved aside, to find out what lies beyond it, it is the effort to hypostasize the reality of a
source that can only be hypothetical by asserting its ultimate reality. It is a delusory pre-
tense, though, because it is the glass-cage itself that produces the reality of the source, or
the illusion of the source thereof, throughout its reflections and refractions, e.g. its anaclas-
tic properties. There are no refractions without a refractive medium, no broken rays without
a breaking surface: properly speaking, there is nothing, that is, nothing meaningful, beyond
the glass, since meaning is precisely the effect of the glass itself on non meaningful ele-
ments. If meaning is an effect, the meaning of meaning in the traditional philosophical
sense, e.g. truth, is an effect as well, an effet de vérité which can serve a role for the believer
who is a full participant to the myths of a given culture but has no bearing outside of it. We
see, then—and quite unsurprisingly, given Lévi-Strauss reliance on the concept of game—
that the crucial feature that distinguishes the Structuralist project from philosophy passes
through the concept of closure, of the closure of the structured field whose operations pro-
duce meaning, a concept opposed to the end (even in its relativized, hermeneutic form that

T HE ANACLASTIC ILLUSION OF A TRANSCENDENTAL UNITY
it takes up in Ricoeur) that the philosophical quest would reach by reaching out beyond the
given semantic field to its hypothetical (and now, for philosophy, real) origin. We see also
that the investigation of the anthropologist, contrary to the claims of his philosophical crit-
ics, does not, in fact, violate the requirement of closure, since it does not assume the possi-
bility of an external stance in order to investigate the refractive properties of a medium, e.g.
in order to build an anaclastic science. It goes by itself that this science cannot attain the
prized, absolute truth that the philosopher would like, because it can never escape the pris-
on-house of that second order language constituted by myths: “Par opposition au discourse
épistémique, le discourse structurel sur les mythes, le discours mytho-logique doit être lui-
même mytho-morphe” as Derrida noted. 43
However, we find that Lévi-Strauss holds a somewhat ambiguous position on this
point, as it is made evident by the long passage quoted above. On the one hand, the dis-
course on myths cannot help but being a sort of mythology, on the other it is granted the
same epistemological status as scientific truths, because its mythological character is war-
ranted by an “essential characteristic” of mythological thought. In other words, the study
of myths is essentially mythological, since its mythological character respects the true na-
ture of mythical thought: it is, paradoxically enough, a true mythology. This may well be,
but it necessary to understand what is meant here by “truth”, if, as Lévi-Strauss analysis
itself makes clear, the concepts of philosophy do not necessarily escape the closure of a cer-
tain structural field. If, in other words, truth itself is part of a certain structural configura-
tion, of a certain mythology, then it is less and less clear how mythology could be “true.”
It may even seem that Structuralism wants to have it both ways: at one level, it denies the
prise of philosophy over its project, by considering it as a particular field of investigation,
a specific mythology, but in a second moment it claims to apply to itself those concepts
whose validity it had disqualified in the first step. As true anaclastics, as mythology of
myths, structural anthropology lies outside philosophy’s scope, but as a true anaclastics, it
comes, once again, totally inside it.
43. Jacques Derrida, “La structure, le signe et le jeu dans le discourse des sciences humaines,” L’´écriture
et la différence (Paris:Seuil, 1967) 419.
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The problem is that there are in fact two logical levels that need be considered when
discussing the concept of closure of the structural field. On the one hand, the field is com-
pletely closed at the level of the substance of the myths, as we have seen, since the mean-
ings of the terms is given wholly on the inside, through the workings of operators
transforming and opposing meaningless elements. The structural analysis is a true anaclas-
tic science that does not require the hypostatization of an external absolute reality, nor does
it invalidate the stance of the investigator. The issue that remains to be discussed, however,
concerns the status of the rules of transformations, which, at this point, are the only ele-
ments that are still stable in this whole complex system we have been exploring. The rules
constitute the true center of the structure, in the sense that they make the structurality of the
structure possible: it is only because of their existence and operational closure that the ele-
ments can be shuffled around and refractively gain their meanings. It is not clear, however,
whether the center itself, e.g the structure’s operationality, is inside or outside the structure.
Whether, in other words, the rules themselves can be subjected to the play that allows the
pieces of the game to derive their meanings from the positions they find themselves in, or
whether, instead, the rules escape the operational closure of the structure by pointing, be-
yond themselves, to an external anchorage that would keep them in place, unmovable and
fixed. As Derrida as pointed out in a well-known essay, there are in fact, two interpretations
of the structure which are distinguished by the role of the center, and two relationships that
can tie it to the structurality of the structure. On the one hand, one can see the center as be-
ing outside the structure, as the only locus in the structure where the substitutions that the
center (the rules) make possible, are not allowed. This view, which, according to Derrida is
typically found in philosophy, depicts the concept of a centered structure which
is in fact the concept of well-founded game, a game constituted since a
founding immobility and a reassuring certitude, an immobility which is itself
out of the game. (410)
The rules of the games, its invariants, to use the structuralist terminology, would then
receives their status from the outside, and their structurality is based on a double role: they
can assure—in fact, produce—the circulation of the terms because an instance brought in

T HE ANACLASTIC ILLUSION OF A TRANSCENDENTAL UNITY
from without has declared their unmovable status, their “eternal truth.” Thus, Lévi-Strauss
is right when he claims, at the end of the same passage quoted above, that the anthropolo-
gist does not bring in from without the code of mythology, that he simply describes it from
the inside—as he is allowed to do— by noticing its operational effects on the mythological
sequences and themes. He is right inasmuch as he refers to the operationality of the rules
discovered, to their mode of functioning, and to that alone. He is not allowed to make same
claim, however, if he refers to the theoretical move that allows that operationality to be
fixed in place (and time) once and for all. That, he would have brought in from without,
because there is nothing inside the anaclastic structure that can grant such an unmovable
role to any element playing inside it. In fact, in this second view of the structure, one sees
that the center “does not have a natural location, that it is not a fixed place, but rather a func-
tion, a kind of non-place where substitutions of signs are played ad infinitum.” Once the
center of the structure—which, once again, is nothing less that its structurality, i.e. the prin-
ciple or rule allowing the refractions and reflections of its constitutive elements—once the
center has been so defined, it is easy to see that “a constant or invariant is defined less by
its permanence and duration than by its function as a center, if only relative.” 44 This point
has two important consequences: first, it entails that the structuralist approach does not
need a fixed, immutable structure in order to work as such. The center may temporary with-
out ceasing to be a center, if it continues to perform its function, e.g. if it continues to rule
the transformations among the different elements. Second, and consequently, it means that
there may be room for the development of a whole “dynamics” of structures, insofar as the
shifts that allow the center to change place—or, in other terms, the decisions that allow the
rules of the game to change —may not be totally free and unconstrained. To put it differ-
ently: the recognition that the center is a pure function which can move in time and space,
44. Gilles Deleuze and Félix Guattari, Mille plateaux (Paris: Minuit, 1980); Engl. tr. A Thousand Plateaus
(Minneapolis, Minnesota UP) 411, 95. A proper discussion of Deleuze and Guattari’s argument for this
statement would unfortunately require a space we cannot afford here. But its relevance and importance
to a proper understanding of Lévi-Strauss cannot be underestimated, especially because it goes
through a discussion of music‘s evolution (the center of the structure being the diatonic center of harmonic
attraction in the classic period) and it is precisely on the basis of a discussion of music that Lévi-
Strauss tries to establish, especially in “Finale,” the “stability” and “truth” of the structural laws regulating
myths‘ refractions.
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allows on the one hand to disregard the epistemological issue of the absolute validity of the
structural law, but opens up, at the same time, the possibility, and indeed the necessity, of
developing a thought that does justice to such movable centers, to such dynamic structures,
to such ever-changing games.
Lévi-Strauss, however, does not seem to recognize the importance of this point, and
the texts are, to say the least, quite ambiguous on the issue. Every time he defends his non-
philosophical position, he mostly dwells on the difference between formalism and structur-
alism, and on this basis responds to the philosophical critiques coming from the hermeneu-
tic or the existentialist fields. In other words, he defends the notion of closure in the first
logical sense, as the closure of the phenomenal field with respect to a set of rule which al-
low the interpretation of the generation of meaning from meaningless elements. When it
comes to a discussion of the status of that closure, the discussion gets shorter and shorter
and it is generally conducted by equating the structural law that can be found in mythology
to the general laws that the natural sciences find in nature. The structural law of the myth,
therefore, would be a law regulating the behavior of the human spirit in the same sense in
which the law of gravitation regulates the behavior of bodies in space. However, the situa-
tion gets soon more and more complicated, and not just because the sciences of nature, be-
ing a product of the human spirit, would be subjected to anaclastics while being its external
model, but also, and conversely, because the natural sciences work on symbols that refer to
things whereas the sciences humaines work on symbols that refer to symbols that refer to
things and can therefore have only a derivative character, as Lévi-Strauss sometimes states.
Lévi-Strauss, to put it differently, seems to think that Structuralism can be successful only
if the structurality of the structure, the status of its rules, can be fixed outside the structural
realm in the immutable laws of the spirit and then pinned down to the bio-chemical com-
position of the human brain. On the other hand, however, he is conscious of the problematic
status of such an empirical underpinning and develops subtler and subtler models of the re-
lationship between natural and human sciences. 45
Such an external justification, however, is not only unnecessary, it is in fact impossible
to provide within the conceptual orbit of structuralism and, moreover, opens the flanks to

T HE ANACLASTIC ILLUSION OF A TRANSCENDENTAL UNITY
a whole series of problems that have been pointed out especially well, although from very
different perspectives, by Jean Petitot and Jacques Derrida. I will examine their critiques in
turn, and provide an outline of the problems the structuralist model runs into by avoiding
the discussion of this point and a sketch of the venues which are opened up.
I will consider first the internal reform proposed by Jean Petitot in a series of books
and articles published from the early 1980s on. He begins by pointing out that in almost
every case, biochemical biology and mathematics aside, the ontological status of the struc-
ture is deeply ambiguous. The problem may be stated as follows “As the ideal form of the
organization of a substance, structure is not a perceptible phenomenon [...] This is why ev-
ery structure is a theoretical object which is at the same time ideal and real.” 46 Because of
their ideal status, which is nonphenomenal in the classical (perceptible) sense of the term,
structures are therefore ontologically ambiguous. As eidos, the structure cannot be de-
tached from the substance in which it is actualized, from the ousia where it becomes sub-
stance. It is as the same time an intelligible framework and a structured object. But must it
be considered given or posited? In the first case an ontological (realist) conception of struc-
ture will be developed, in the second case, an epistemological (nominalist) one.” 47 Petitot
claims that the prevalent epistemological attitude is the source of all (literally) the problems
encountered by structuralism. Consequently, he wants to develop a realist conception with-
out, however, falling into naive holistic-idealist doctrines. In his own words:
[outside mathematics] the problem is no longer to abstract levels of structure
but to theorize the natural phenomena of self-organization. Then the
concept of structure no longer corresponds to properties of objects but to a
45. See Claude Lévi-Strauss, L’Homme nu …, 574; Engl. tr. 642, for example, where Lévi-Strauss affirms:
“there is a fundamental difference between the two, arising from the twofold fact, firstly, that the physical
and natural sciences operate on symbols of phenomena while the social sciences operate on symbols
of phenomena which are themselves symbols in the first place, and secondly, that, in the former
instance, the adequate approximation of the symbol to the referent is demonstrated by the ‘grip’ (prise)
exercised by scientific knowledge on the world around us, whereas the practical ineffectiveness of the
social sciences does not allow us, at least for the time being, to assume any adequate correspondence
between the representative symbols and the represented symbols.”
46. Jean Petitot, Morphogenèse du sense (Paris: PUF, 1985) 30.
47. Jean Petitot, “Structure,” Thomas A. Sebeok, ed., Encyclopedic Dictionary of Semiotics (Berlin: Mouton
de Gruyter) 993.
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conceptual category whose content must be founded, whose objective value
(ontological thrust) must be (transcendentally) deduced, and whose explanatory
force must be legitimated. In all domains (biology, psychology, anthropology,
semiolinguistics) where structure has a real empirical value and
is necessary for understanding (if not for explaining) specific phenomena,
its theoretical function is to get beyond the conflict between, on the one
hand, objectivist-reductionist explanations, which consider organized
wholes as systems of interacting components, and, on the other hand, holistic-idealist
comprehensions which consider organized wholes as amorphous
material substrata imparted with essences foreign to them. 48
Petitot wants to avoid two interpretations of “structure” (which, nonetheless, he sees
prevailing): (a) any naturalistic reductionism which interpret structure as a mere combina-
tion of elementary “particles” whose ontological basis is granted (where “particles” are
broadly taken as the elementary objects of the given discipline: genes, synaptic connec-
tions, or whatever); (b) any idealistic-vitalistic position seeing as “structure” the theory im-
posed by the mind on an amorphous matter per se completely undifferentiated. It should be
clear enough from what I have said so far, as well as from the presentation of the antinomy
he wants to avoid, that he has in mind some kind of Kantism. In fact, his project is explicitly
labelled an “updated version of Criticism” and the genealogy of structuralism he presents
goes back to the Critique of Judgement.
Insofar as the nominalist position is concerned, Petitot's argument goes as follows: 1)
to attain objectivity and scientific status, the classical structuralist theoretician (here, the
polemical objective is mainly Greimas) considers the structure(s) he uses as a conceptual
system which he immediately tries to formalize into an axiomatic theory through an appro-
priate logic. That is, he tries to posit some basic concepts and a system of rules that will
enable him to generate all the possible configuration of the structure (remember Lévi-
Strauss on kinship system: 4 basic terms plus a system of emotional attitude literally gen-
erate, by simple permutation, all possible kinship systems. Another relevant example is the
classical treatment of chess in (GOF)AI.) However, the approach, labelled by Petitot as the
“formalization of the descriptive meta-language” (i.e. the system of rules), cannot elucidate
48. Jean Petitot, “Structure…” 999.

T HE ANACLASTIC ILLUSION OF A TRANSCENDENTAL UNITY
the objective content of the structure involved but, at best, only the logical architecture of
the theory.
The problem is, simply stated, that the explanatory power of the scientific theory is
completely lost or, better, overwhelmed by the hyper-generativity of the rule-system. I shall
try to make clear Petitot's diagnosis with the example of chess: a “theory” of chess which
would reduce the game to a system of rules (properly formalized and axiomatized) would
be completely useless in the effort of interpreting a determinate, actual game (say, Karpov-
Kasparov IV). The theory being so powerful that it can generate all possible games, it can
only determine whether a certain object is a chess game or not. A remarkably poor result
for a theory of chess, since what is interesting in the game is that 90% (and maybe more)
of the possible games are never played. In other words, a “real” theory of chess (and, actu-
ally, what a chess player mean by the term) must deal with strategies, openings, forced sac-
rifices, etc. The concept might seem trivial, and perhaps it is in the case of chess. Petitot's
thesis, however, is not, since he claims that many contemporary disciplines are exactly in
the situation of the hypothetical chess theorist. Consider biology, for example:
The genome controls form and development. Its mastery and its control
therefore enable the control of its effects. But this does not imply the nonexistence
of autonomous, specific, and ideal morphological constraints. By
equating genetic control with determining cause, it is postulated without
further inquiry that there is nothing more to explain in what is being controlled.
As Jacques Monod claimed, form is causally reducible to the primary
structure of proteins: the remainder being dependent only upon
thermodynamics processes. [...] Indeed, the neo-Darwinian paradigm is a
conceptual system whose apparent ‘evidence’ precisely renders unintelligible
morphological phenomena. It attributes these merely to chance and negates
any necessity in the order of form, any laws of the form. 49
Briefly, the first immediate consequence of the nominalistic approach is that it is im-
possible to give an account of the self-determination and of the dynamic stability of the
structures as Gestalten, and therefore of their closure. This is the theoretical source, accord-
49. Jean Petitot, “Structure…” 1001.
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ing to Petitot, of any doctrine, like Chomsky's innatism, for example, that is forced to find
its ultimate grounds outside the discipline itself.
The final diagnosis is that static structuralism is a first step, but is too narrowly con-
ceived to be adequate. If what must be understood is “the self-limitation of the generative
capacity of syntax (Thom)” one must introduce “dynamics underlying the formal kinemat-
ics described by formal languages.” The real problem, he claims, “is not to formalize de-
scriptive meta-languages, but rather to find or to build specific mathematical objects which
would allow to model adequately the specific natural phenomena constituted by the struc-
tures, and thus to objectify them.”
Where is to be found such a mathematical object? Since the categories used by Struc-
turalism are always “rooted in a topological intuition (position, junction, paradigmatic cat-
egorization, connection, etc.) [...] the schematization of the structural categories depends
entirely on the possibility of mathematically determining ‘the positional intuition’ playing
the role of ‘a pure form of intuition’ for structural phenomena. It depends hic et nunc on the
elaboration of a geometry of position.” 50 Finally, Petitot finds in the work of René Thom
the first efforts towards “a general mathematical theory of morphogenesis.” His solution,
in short, consists in grounding the functional role of the center of the structure in a mathe-
matization that would account for the center’s dynamics. i. e. its temporal and spatial evo-
lution. This would allow Structuralism to maintain a traditional concept of truth—in fact,
it would it would make Lévi-Strauss’s anaclastic science very similar to mathematized nat-
ural sciences like physics.
It is not clear, however, whether the problem concerning the ontological level of the
structure would not come up again at a higher logical level, namely the level of the mathe-
matical object formalizing the dynamics of the structure. Once again, it seems that a “dy-
namic structuralism” would be left with only two options: it could choose to “reify” (in a
strong sense) the structures by assuming their coincidence with a specific natural, e.g. phys-
ical, reality by turning the structure into a “thing,” with all the unpleasant consequences that
Ricoeur has already uncovered for us. Alternatively, it would have to abandon the claim to-
50. Jean Petitot, “Structure…,” 1019. Petitot’s emphasis.

T HE ANACLASTIC ILLUSION OF A TRANSCENDENTAL UNITY
ward an “absolute” truth in the traditional sense and turn toward a truly non-philosophical
reinterpretation of philosophy and epistemology tout court. Jean Petitot seems to opt for the
first alternative, if we are to judge from a recent essay, where he says:
Le “tournant morphologique” su structuralisme opéré par la théorie des
catastrophes ouvre un vaste territoire qui reste encore à explorer
entièrement. Il permet de constituer le structuralisme théorique en «système
physique». […] Loir de devenir obsolète comme le voudrait un certain
irrationalism contemporain, le structuralisme garde présentement toute sa
pertinence et toute sa force. Son programme de recherche est loin d’être
épuisé, bien au contraire, puisqu’à travers la théorie de l’(auto)organisation
et la physique mathématique des phénomènes critiques il est en train
d’établir sa jonction avec le sciences naturelles. 51
The “present-day irrationalist” Jean Petitot alludes to in the text is of course Jacques
Derrida, who instead chooses the second option and decides to challenge the Structuralist
ambition to objectivity. He presents an argument that aims to unveil the illusory character
of an “absolute” structuralist enterprise, e.g. of a structuralism where the center enjoys an
absolute, non-structural status.
I will discuss Derrida’s critique mostly on the basis of his criticism of the notion of text
and its principles of structural organization. It should be emphasized, in order to appreciate
the relevance of Derrida’s effort to our present theme, that the “textual” character of Lévi-
Straussian structures is stressed—and quite naturally so, given the linguistic foundations of
Structuralism—by Lévi-Strauss himself, for example in Finale, where he says: “In other
words, the operations of the senses have, from the start, an intellectual aspect, and the ex-
ternal data belonging to the categories of botany, geology, zoology, etc. [e.g. the non-phe-
nomenal elements that are rearranged and transformed by the mind at work in the mythical
51. Jean Petitot, “Approche morphodynamique de la formule canonique du mythe,” L’Homme, 106-107,
(1988), 46. Petitot reiterated his position in 1993, in occasion of a round table on the “canonical formula
of the myth” organized by Emmanuel Désveaux and Jean Pouillon where he pointed out that “if
the categorization process [that generates the transformations/oppositions, etc.] is implemented as a
neural network, then the generative potentials become truer potentials in the physical sense, i.e. they
become “energy” functions whose minima determine the terms of the categorization.” See Jean Petitot,
“Note complémentaire sur l’approche morphodynamique de la formule canonique du mythe,” L’Homme,
135, july-sept. 1995, 18.
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sequences] are never apprehended intuitively in themselves, but always in the form of a
text, produced through the joint action of the senses and the understanding.” 52
In Signature Event Context, Derrida directs his analysis precisely at what constitutes a
text, at what, in other words, allows to structure signs as belonging to a text and to the status
of the principles involved. The first example is taken from Husserl’s analysis of grammat-
icality in the Logical Investigations, where the issue at stake is precisely to carve out the
most general principles defining what counts as a meaningful expression from a possibly
inordinate series of signs. There, Husserl had drawn a distinction between senseless (sinn-
los), and meaningful (sinnvoll) expressions. The paradigmatic example of the first class is
“Green is or,” which, strictly speaking, is not even an expression, but at best something that
claims or seems to be an expression, whereas “Square circle” and “Red spot,” although re-
spectively “objectless” and “objectful,” are both unambiguously meaningful. The sense of
the distinction is clear: the existence of a system of rules (syntactic, in this case) defines the
borders of grammaticality and so the whole set of grammatical expressions. In structuralist
jargon: the syntactic rules defines the very structure of language, in all its potentialities.
But Derrida rejects the very possibility of such an objective definition, and denies that
the “objective” borders of language may be identified, even in the simpler case of syntax,
and even as an ideal principle. Even the most sinnlos expressions, he says, e.g. the ungram-
matical, unsyntactical “Green is or” [or “Vert is ou”] may be made sinnvoll, may be forced
to signify. And this happens not only in the contingent case in which, by means of the trans-
lation of German into French ‘le vert est ou’ might be endowed with grammaticality ou be-
coming where when heard où: ‘Where has the green (of the grass) gone?’ But “even ‘green
is or’ still signifies an example of agrammaticality.” 53 If this does not usually happen, i.e.
if the possible 2 nd order meaning is excluded from the space of possibility it is only be-
cause, according to Derrida, “It is only in a context determined by a will to know, by an
epistemic intention, by a conscious relation to the object as an object of knowledge within
52. Claude Lévi-Strauss, L’Homme nu…, 607; Engl. tr. 678. Lévi-Strauss’s emphasis.
53. Jacques Derrida, “Signature Event Context,” Margins (Chicago: Chicago UP, 1982) 320. Emphasis in
the text.

T HE ANACLASTIC ILLUSION OF A TRANSCENDENTAL UNITY
an horizon of truth — it is in this oriented contextual field that “green is or” is unaccept-
able.”(ib.)
Thus, the particular context allows us to overlook the general principle, i.e. that it is
always possible to endow anything with meaning, to insert it into a network of differences
(even signatures “mean” Derrida will say in a moment). “This is the possibility on which I
wish to insist: the possibility of extraction and of citational grafting which belongs to the
structure of every mark, spoken or written, and which constitutes every mark as writing
even before and outside every horizon of semiolinguistics communication; as writing, that
is as a possibility of functioning cut off, at a certain point, from its ‘original’ meaning and
from belonging to a saturable and constraining context.” (320)
Every sign, linguistic or non-linguistic, spoken or written (in the usual sense of this op-
position), as a small or large unity, can be cited, put between quotation marks; thereby it
can break with every given context, and engenders infinitely new contexts in an absolutely
nonsaturable fashion.
This does not suppose that the mark is valid outside its context, but on the
contrary that there are only contexts without any center of absolute anchoring.
This citationality, duplication, or duplicity, this iterability of the mark is
not an accident or an anomaly, but it is that (normal/abnormal) without
which a mark could no longer even have a so-called ‘normal’ functioning.
(325)
The principle above is then applied to Austin’s definition of the ‘normal’ performative
acts (i.e. marriages, ship-launching, etc.) as opposed to ‘deviant’ utterances of the same acts
on stage, or reported, etc. Derrida’s point, of course, is that is precisely the possibility of a
‘deviant’ use on stage by an actor that makes possible the ‘normal’ use of the same words
by the civil officer or priest. Ultimately, says Derrida, Austin is able to fix the context, to
define the normality of normal language, only by means of an appeal to the intention of the
speaker, to consciousness and its intended meaning. He then goes on to a general conclu-
sion about contexts. “For a context to be exhaustively determined, in the sense demanded
by Austin, it at least would be necessary to for the conscious intention to be totally present
and actually transparent for itself and others, since it is a determining focal point of the con-
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text. The concept of or quest for the “context” therefore seems to suffer here from the same
theoretical and motivated uncertainty as the concept of ‘ordinary’, from the same meta-
physical origins: an ethical and teleological discourse of consciousness.” (ib:327)
The possibility of an infinite number of contexts, and then of always different mean-
ings, involves what Derrida calls the dissémination as opposed to the more trivial polyse-
mia. This possibility entails—to bring back Derrida’s argument to our discussion of Lévi-
Strauss—that the center of the structure cannot be fixed once and for all. On the contrary,
the rules that make permutations and transformations possible are themselves always ex-
posed to an intrinsic “trembling,” since no absolute anchoring is possible. The possibility
of meaning, and especially the possibility of reference is thus not denied by Derrida, con-
trary to what most of his critics claim. Just the opposite is true: there is always an excess of
meaning and an excess of reference, since it is constitutively impossible—at least within
the Structuralist paradigm that interests us here—to fix both of them from the outset.
Derrida concludes that
We are not witnessing an end of writing which, to follow McLuhan’s
ideological representation, would restore a transparency or immediacy of
social relations; but indeed a more and more powerful historical unfolding
of a general writing of which the system of speech, consciousness, meaning,
presence, truth, etc., would only be an effect, to be analyzed as such. It is
this questioned effect that I have called elsewhere logocentrism. (329)
It is thus clear that the whole point of Derrida’s deconstruction is precisely to give an
“explanation” (where explanation is to be read more as a tool for analysis that anything
else) of the “rise” of (of the relevance) determinate domains. And the general point seems
to be that “truth” about a particular domain (and, therefore, its constitution), is not given as
a social consensus, but, rather, is produced and produced by means of exclusions, of the
instaurations of differences, of hierarchies and so forth. So there is a whole economy of
forces which, by means of exclusions and segregations, produces fields and domains, and
the role of deconstruction is to investigate, to retrace this differences in the texts and, even-

T HE ANACLASTIC ILLUSION OF A TRANSCENDENTAL UNITY
tually, to point out how the text contains in itself the possibility of the inversion of the dif-
ferences on which it is based.
This brief excursus into Petitot’s and Derrida’s criticisms and positive programmes in-
dicates the range of issues that are opened up once the fixity of the structure’s center is re-
nounced in favor of a functional interpretation of the center as the pure locus of the
structural organization that is itself subjected to an ever-shifting dynamic process. More-
over, Petitot’s and, even more pointedly, Derrida’s criticism make clear that Structuralism
cannot avoid confronting this issue, lest is remains caught in a ambiguous and contradictory
situation in which it wishes to overcome the traditional philosophical grounding of mean-
ing in an a-historical, essentially “natural” truth that has always found its ultimate ground-
ing in the essential features of “man” while, at the same time, it proclaims to have finally
banished the mythological and self-delusional adoration of man from the realm of human
intellectual endeavors.
This ambiguity in well-caught by Derrida, when he points out that the structural enter-
prise, in the texts of Lévi-Strauss, has in fact two faces which are necessitated by this the-
oretical ambiguity:
Il y a donc deux intérpretations de l’intérpretation, de la structure du signe
et du jeu: l’une cherche à déchiffrer, rêve de déchiffrer une vérité ou une
origine échappant au jeu et à l’ordre du signe, et vit comme un exil la
nécessité de l’intérpretation. L’autre, qui ne’est plus tourné vers l’origine,
affirme le jeu et tente de passer au-delà de l’homme et de l’humanisme, le
nom de l’homme étant le nom de cet être qui, à travers l’histoire de la
métaphysique […] a rêvé la présence pleine, le fondement rassurant,
l’origine et la fine du jeu. 54
It is difficult to deny Derrida’s assessment when Lévi-Strauss affirms explicitly this
duplicity by asserting, for example, that the conflict between philosophy and structuralism
54. Jacques Derrida, La structure, le signe, … 427. Emphasis in the text. Among the nostalgic texts Derrida
is implicitly referring to here, are the well-known pages on the corrupting influence of writing on a
primitive society contained in Une leçon d’écriture, and commented at length by Derrida himself. See
Claude Lévi-Strauss, Tristes tropiques…, 288 ff, and Jacques Derrida, De la grammatologie…, Engl.
tr. 118 ff.
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consists in a choice between “a rationality without a subject or a a subject without a ratio-
nality”, or when he states that structuralism’s goal is to reintegrate man in nature while, at
the same time, it makes “possible to disregard the subject—that unbearably spoilt child
who has occupied the philosophical scene for too long now, [and] “foresees the twilight of
man.” 55
However, the success of Structuralism as non-philosophy depends rather on the over-
coming of a form of rationality that is consubstantial with metaphysics in it constant refer-
ral to an absolute, “natural” origin, an overcoming that is made possible by accepting a
purely functional interpretation of the structurality of the structure as what is produced, at
a determined moment in space and time, as a result of an economy of forces. The structur-
ality of the structure, its center, is always a temporary point of equilibrium, which, by being
intrinsically temporary is always, to a certain extent, “different” from itself, insofar as it
cannot be stably anchored to any illusionary outside. The semi-transparent medium whose
refractive/reflective properties an anaclastic science will study—to use Lévi-Strauss own
image—is itself always in flux, in a perennially magmatic but nonetheless semi-crystalline
state which allows it to produce its transformations without ever coming to a definite re-
pose.
However, it is evident that the acceptance of an enlarged reading of anaclastic science
pulls Structuralism further and further away from the game-based model with which I start-
ed my discussion. In fact, the most salient characteristic of games, as we have seen, is to be
found in the existence of a fixed set of rules that allow the manipulation of the elements
they are defined upon. A game, in the definition of von Neumann and Morgenstern that
Lévi-Strauss has embedded in his own work, is “nothing but the totality of it rules.” This
definition is bound to fall apart once the status of the rules is recognized as subject to a con-
stant evolution and renegotiation, as the temporary point of equilibrium of an ever changing
flux. This does not mean, however, that game collapses into the void of a contradictory or,
worse, vacuous definition. It simply means that the game-based model needs to be enlarged
55. “le sujet—unsupportable enfant gaté”: Claude Lévi-Strauss, L’Homme nu…, 614; Engl. tr. 687.

T HE ANACLASTIC ILLUSION OF A TRANSCENDENTAL UNITY
to encompass those characteristics that we have seen best associated, in current English lan-
guage, with the semantic area of play.
Indeed, the very usage of the word jeu by Derrida, in the texts cited as well as else-
where, exhibits precisely this slippage from the game-like to the play-like semantic com-
ponents of jeu, and represent a good indication of the trajectory that the structuralist
paradigm seems bound to follow within the space of Spiel. In Derrida’s words,
cette thématique structuraliste de l’immédiateté rompue est donc la face
triste, négative, nostalgique, coupable, rousseauiste, de la pensée du jeu
dont l’affirmation nietzschéenne, l’affirmation joyeuse du jeu du monde et
de l’innocence du devenir, l’affirmation d’un monde de signes sans faute,
sans vérité, sans origine, offert à une interprétation active serait l’autre face.
Cette affirmation determine alors le non-centre autrement que comme perte
du centre. Car il ya un jeu sûr: celui qui se limite à la substitution des pièces
données et existantes, présentes. Dans le hasard absolu, l’affirmation se
livre aussi à l’indétermination génétique.” 56… The present endpoint of his trajectory, whose path is often marked in Derrida’s work
by the opposition between jeux and jeu, or between the jeu sûr and the jeu that is submitted
to a game of absolute chance, marks also the end of our investigation into Artificial Intel-
ligence and Structuralism. We set out to determine whether these two programs could suc-
cessfully articulate an “end of philosophy” based upon the reduction of the complexity of
Spiel onto the game-like component and we have seen that both, in a very particular sense
of the word, miss the target. Artificial Intelligence because, in spite of providing a very rich
articulation of the concept of game—in fact, in spite of having indeed created such a con-
cept as a theoretical entity—it is unable to provide a satisfactory treatment of the relation-
ship tying together the rules and their content. AI remains caught into the formalist, and
fallacious, opposition between form and content. Structuralism, on the other hand, solves
satisfactory the latter problem through a much richer articulation of substance and structure
that ends up in a the project of an “anaclastics science” representing a direct challenge to
the most basic philosophical concepts. Structuralism itself, however, proves unable to bring
56. Jacques Derrida, “La structure, Le signe et le jeu…” 428.
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this challenge to a conclusion within the boundaries of a game-like model: “play,” a concept
that had been reduced, under the undoubtable influence of game-theory, to a particular in-
stance of the broader concept of game, makes a remarkable come-back and proves to be
essential to the project of broader, non-philosophical anaclastics on whose brink Lévi-
Strauss’s work, after all his revolutionary breakthroughs, seems to stop only to retreat into
an all too complicated dialectics of nature, rationality and subject.

CHAPTER VIII
A MOVABLE
CONCLUSION
where it is said that this work has only explored part of the complexity
of Spiel, and what is left to bring it to an end.

308
A MOVABLE CONCLUSION
1. After game-based Spielen
At the beginning of this long investigation, I set out to explore the complex space of
Spiel that, if we are to follow the lead provided by Hegel and by Heidegger in his wake,
seems to lie at the end of philosophy. I also underlined that part of the difficulty of the task
ahead lied in the extreme ambiguity of Spiel itself, a space that is torn between the two in-
extricable, but apparently incompatible poles of game and play. I also claimed that we
could perhaps gain some clarity on the issue by finding suitable examples of “non-philos-
ophy” with a demonstrable theoretical reliance on some aspect of the concept of Spiel.
We have now completed the first part of the journey. Artificial Intelligence and Struc-
turalism, as we have seen, proved to be truly “non-philosophical” attempts built around an
extremely sophisticated game-based reduction of Spiel in the context of the end of philos-
ophy. We have also seen that they both fall short, although for different reasons, of the re-
quired completeness and closure that the end of philosophy require if it is really to be
brought about. However, as partial characterizations of Spiel as game (but not of Spiel it-
self) they are valid. We have also seen that he characterization of game in terms of structure
provided by Lévi-Strauss finds its limit, eventually, in the impossibility to bring itself to
accommodate the components that are normally associated with the opposite pole of
Spielen, with the free, self renewing activity characteristic of play and not of games. In par-
ticular, the conception of Spiel as the totality of the rules that describe it, a concept that
Structuralism inherits from game theory through the mediation of cybernetics and Artificial
Intelligence, proves unable to rise to the non-philosophical challenge set by Structuralism.

A FTER GAME- BASED SPIELEN
Play, then, far from being a “particular instance at which the game is played—in a par-
ticular way—from beginning to end,” as von Neumann would have, is back in the game
with full swing.fall well short of the required closure.
The last section of the prelude to this work provided a response, couched in the poetic
language of Kafka and illuminated by the prophetic comments provided by Giorgio Agam-
ben. A fuller articulation of the answer, and a real conclusive chapter, however, will have
to wait. We can only hope that our masters, and especially the ultimate master, will grant
us the time and the strength to bring that conclusion to an end.
309

310
A MOVABLE CONCLUSION

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