Alain Badiou: Philosophy and Its Conditions by Gabriel Riera

By Gabriel Riera

An advent to Badiou's philosophical concept and its implications for different humanistic disciplines and the social sciences.

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22. " This page intentionally left blank. TWO The Ontological Dispute Badiou, Heidegger, and Deleuze Miguel de Beistegui (Translated by Ray Brassier) Alain Badiou's philosophical project can be succinctly summarized. It consists in a genuinely metaphysical attempt to free thought from the double horizon of unic· ity (whereby it posits itself as ontology) and transcendence (whereby it is theology). It is to the extent that for such thought "the norm for what is thinkable consists in the unification of the singular entity beneath the power of the one" (CTOT 25) that the latter continues to be superimposed onto the entity and immanent being superimposed onto that transcendence.

Given that such a reduction involves both a combinatorial component, regarding the inscriptional properties of the formal language, and a semantic component, regarding the interpretation and truth of the expressions of that language, Bell considers category theory to be unable to achieve its foundational ends. This would be owing to the fact that it cannot make any claims to providing a specifically categorical definition of a set or class. As mentioned before, even its key notion, functor or relation, requires a class do· main: a category within which a transformation may occur.

7. C. McLarty, "U ses and Abuses ofthe History of Topos Theory," British Journal for the Philosophy of Science 41 (1 990): 351 -75. 8. ·P. Marquis, "Category Theory," Stanford Encyclopedia of Philosophy (1 996-97), online edition. 9. Dansein is, of course, a play on Dasein, with the accent placed on the French dans, a spatial preposition equivalent to the English in. The result produces a neologism of the type, insein, though the English term clearly loses the pun. 1 0. R. Lavendhomme, Lieux du sujet: Psychanalyse et mathematique (Paris: Editions du Seuil, 2001).

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