2. Philosophy - Stefano Franchi

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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.