2. Philosophy - Stefano Franchi

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A NACLASTIC SUPPLEMENTS
ing to Petitot, of any doctrine, like Chomsky's innatism, for example, that is forced to find
its ultimate grounds outside the discipline itself.
The final diagnosis is that static structuralism is a first step, but is too narrowly con-
ceived to be adequate. If what must be understood is “the self-limitation of the generative
capacity of syntax (Thom)” one must introduce “dynamics underlying the formal kinemat-
ics described by formal languages.” The real problem, he claims, “is not to formalize de-
scriptive meta-languages, but rather to find or to build specific mathematical objects which
would allow to model adequately the specific natural phenomena constituted by the struc-
tures, and thus to objectify them.”
Where is to be found such a mathematical object? Since the categories used by Struc-
turalism are always “rooted in a topological intuition (position, junction, paradigmatic cat-
egorization, connection, etc.) [...] the schematization of the structural categories depends
entirely on the possibility of mathematically determining ‘the positional intuition’ playing
the role of ‘a pure form of intuition’ for structural phenomena. It depends hic et nunc on the
elaboration of a geometry of position.” 50 Finally, Petitot finds in the work of René Thom
the first efforts towards “a general mathematical theory of morphogenesis.” His solution,
in short, consists in grounding the functional role of the center of the structure in a mathe-
matization that would account for the center’s dynamics. i. e. its temporal and spatial evo-
lution. This would allow Structuralism to maintain a traditional concept of truth—in fact,
it would it would make Lévi-Strauss’s anaclastic science very similar to mathematized nat-
ural sciences like physics.
It is not clear, however, whether the problem concerning the ontological level of the
structure would not come up again at a higher logical level, namely the level of the mathe-
matical object formalizing the dynamics of the structure. Once again, it seems that a “dy-
namic structuralism” would be left with only two options: it could choose to “reify” (in a
strong sense) the structures by assuming their coincidence with a specific natural, e.g. phys-
ical, reality by turning the structure into a “thing,” with all the unpleasant consequences that
Ricoeur has already uncovered for us. Alternatively, it would have to abandon the claim to-
50. Jean Petitot, “Structure…,” 1019. Petitot’s emphasis.