Preproceedings 2006 - Austrian Ludwig Wittgenstein Society

In modern chess we find many examples of players
who have applied theories that illustrate the concept of
logical multiplicity of rules as,for instance Bent Larsen and
David Bronstein. Let’s illustrate this with a diagram:
The rule that is broken here is that there shall not be
many moves made with pawns during the opening, but in
this case it is perfectly justified by a strategy of restriction
that is fully appropriate for the position. It reminds us of the
notion of rule-independence as described by the
theoretician John Watson (1998). Let’s take a closer look
at this definition:
“Many changes have taken place in modern chess, for
instance, with respect to new ideas about the
weaknesses, the relative strength of the minor pieces,
the value of exchange and considerations on time and
mobility. But the predecessor, and to some extent the
precursor of those changes has been a certain
philosophical concept so deeply embodied in us today
that we almost do not even notice it. I call it the ‘ruleindependence
concept’… It is simply the dispossessing,
made by chess players, of the manifold generalities,
rules and abstract principles that directed classic chess
and still do prevail on our text books. Furthermore, the
rejection of the very concept of ‘rule’ has been taking
place in favor of a pragmatic research of particular game
situations. The intense study of a large amount of game
positions combined with a dramatic growth of playing
frequency by the majority of professional players has led
to a new way of looking at chess knowledge. This way of
looking at it could be described in terms of ‘unconscious
principles’ or also subtle clues that cannot be verbally
expressed, that are continuously modified and measured
to refine the judgment of the diverse positions. A ‘sense’
has been developed for positional chess… [that]
abandons (completely or to a great extent) the dogma.
This is rule-independence.”
The above diagrams are taken from an actual chess game.
They show rule-independence in the sense of classic
chess: the rule that the knights should be moved towards
the center of the chessboard. The diagrams show that
both white knights move towards the sides of the board.
Technical analysis proves that it is the right strategy
independent of what the so-called “classic rules” tell us.
We can confidently say that in contemporary chess there
are thousands of examples that confirm the ruleindependence
concept.
Wittgenstein, Language and Chess - Eduardo Bermúdez Barrera
But what is it that allows us to relate Watson’s
concept of rule-independence to Wittgenstein’s concept of
logical multiplicity of the rules? We shall turn to the
propositions of what is known as Hypermodern School and
thus, to Reti- The goal of the school was “not to consider
each position in accordance to a general law, but rather
according to the principle inherent to the positions.”
Let us revise three quotes (Wittgenstein 1992 and
Waismann 1973) to illustrate this idea:
“Wir reden von dem räumlichen und zeitlichen
Phänomen der Sprache; nicht von einem unräumlichen
und unzeitlichen Unding. Aber wir reden von ihr so, wie
von den Figuren des Schachspiels, indem wir
Spielregeln für sie angeben, nicht ihre physikalischen
eigenschaften beschreiben. Die Frage »was ist ein
Wort« ist analog der »was ist eine Schachfigur (etwa der
Schachkönig).«“
“[…] The game of chess does not consist of moving
wooden pieces… The essence of chess is not the
wooden figures. What is characteristic of chess is the
logical multiplicity of the rules…”
“[…] It does not matter what the aspect of a pawn is,
because the set of rules of the game is what gives its
logical place to the pawn. The pawn is a variable, as the
x is in logic.”
My suggestion is to integrate Watson’s concept of
rule-independence in Wittgenstein’s concept of logical
multiplicity. I included long quotes from current chess
theory to suggest that the notion of logical multiplicity (as
understood and applied by Wittgenstein as an analogy for
arithmetic and grammatical rules) is well oriented. This
analysis has proven Moore to be wrong, for no skilled
chess player takes rules to be only the legal movements of
the pieces, but rather also includes in his understanding of
the concept the rules of strategy. Chess constituted an
unbeatable analogy for his intuition of what grammar rules
really are. Basic knowledge of chess strategy is advisable
for those interested in developing a deeper understanding
of Wittgenstein’s theory of language.
“Now language is the work of thought: and hence all that
is expressed in language must be general. What I only
mean or suppose is mine: it belongs to me -- this
particular individual. But language expresses nothing but
generalities; and so I cannot say what I merely mean.”
With respect to these words taken from Hegel 1991,
I shall say that current chess theory confirms the richness
of Wittgenstein’s use of the analogy of chess. Many of
Wittgenstein’s notions of language do say much more than
he actually wanted to say when he used the analogy. His
intention was rather to show concepts that couldn’t be
adequately expressed by means of articulated language.
And that is why he used analogies for grammatical rules
and games rules. Finally, the analogy of chess has
perhaps its limitations, but an analysis of them is a task for
a different stage of the research on this topic.
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