2. Philosophy - Stefano Franchi

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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.