By Gabriel Riera
An creation to Badiou's philosophical proposal and its implications for different humanistic disciplines and the social sciences.
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Additional info for Alain Badiou: Philosophy and Its Conditions
But category theory takes shape from the notion of difference. To shelter his thesis from objections, it is therefore of capital importance for Badiou to localize the notion of difference in all of its varieties as derived from logic, and not as a fluctuating manifold. Because as a fluctuating and irreducible manifold, if differ· ence were to condition ontology, the ontological decision would entail two legiti· mate versions (two absolute and competitive universes). Where there are at least two ontologies, the manifold would then lend itself to an anarchic violence whose consequence would perhaps prove Heidegger right regarding his declaration that only a God can save us.
When physics is concerned, it is to the physical, indeed material, dimension of corre sponding multiples posited as real. By contrast, Badiou's realist theory of the manifold seeks to capture the inconsistent extensions: the basic preconditions in tegrated to a certain minimal sense of order that end up granting the idea of the manifold a semiautonomous existence from any individual observer. The being of an inconsistent multiple is not so dispersed as to refuse being pegged by a name which is precisely what Badiou emphasizes as the intricate crux of mathematics and ontology.
However, he has also had to confront category theory, which has vied for foundational status within the field of mathematics. Albeit in schematic form, in what follows we will attempt a philosophical reconstruction of this ontology to confront it with the notion of cat· egory. Badiou's work in the 1 990s, which has still not been published in definitive form in English, dealt with how to situate category theory within his thesis on on· tology. If with Jacques Ranciere one may characterize Badiou's work as a massive critique of the notion of the One, then how to arrange two suitors to the sole uni· fied position of fundament becomes a delicate, although capital, task to establish.