2. Philosophy - Stefano Franchi

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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