2. Philosophy - Stefano Franchi

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S TRUCTURES (AND SPACES)
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.