By Gabriel Riera
An advent to Badiou's philosophical suggestion and its implications for different humanistic disciplines and the social sciences.
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Additional info for Alain Badiou: Philosophy and Its Conditions
In line with the philosophical inquiry here developed, there is a significant distinction between Being and possible universes. Regarding possibility, one requires a local, indeed localizable, class of propositions. Enter topos theory, "allowing one to understand in depth how logical variability is marked, which is also the contingent variability ON ALAIN BADIOU'S TREATMENT OF CATEGORY THEORY 41 of appearing with respect to the strict and necessary univocity of being·multiple" (CTOT 1 99). We have now come full circle-Badiou's ordering depends on a rad· ical choice in favor of an intrinsic ontology.
Even more, Kant literally banished the interest oflogic in the Critique of Pure Reason, and mathematics in its ON ALAIN BADIOU'S TREATMENT OF CATEGORY THEORY 33 wake, for failing to show great potential in formalizing pure and practical reason and judgment. In what should no longer surprise us, Kant had in fact based his own method on a categorical approach. The Aristotelian thesis that " Being is said in multiple ways" undergoes an interpretative correction in Badiou's work. " Ontology becomes transitory insofar as its deals with beings or existents (seiendes).
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.