By Alain Badiou
Explores the hyperlink among arithmetic and ontology.
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Extra resources for Briefings on Existence: A Short Treatise on Transitory Ontology
Plato, (Paris: Editions du Seuil, 1986). Parmemdes. 9. Lucretius. On the Nature 10. Plato. The Republic, of Things. I: 4 2 5 . VI. 511c. I 1. Lucretius, On the Nature of Things, 1: 9 1 0 . 2. Mathematics is a Thought 1. Aristotle. Metaphysics. M. 2. 10. 1076bl(). 2. , M. 3, 30; 1078a21. 3. Ibid.. M. 3, 30; 107861. 4. , M. 3 , 30: I078a34. 5. , M. 3, 30; 1 0 7 8 a 3 4 - 3 5 . 6. , M. 2, 1077b 1-2. 7. Nicolas Bourbaki was the name of the distinguished mathematics group centered in France which undertook to lay mathematics out clearly in terms of m o d e m analysis based on Set Theory.
In the categorical presentation, one proceeds to geometric descriptions of universes and notices that to such and such a disposition of universes such and such a logical disposition is immanently correlated. Therefore, logic becomes an intrinsic dimension of possible universes. Or, more fundamentally, the descriptive characterization of a thinkable ontological state entails logical properties that are themselves presented in the space of Being, or the universe, that thought describes. In this reversal, two things disappear: • First, the formal and linguistic antecedence of the logical, or more generally the grammatical, over the position of a universe or over an ontological decision; • Then, the way mathematics is enfolded by logic.
But it does not decide on a particular universe. Unlike Leibniz's God, we d o not have any reason to consider some such mathematical universe as the best of possible universes. F r o m this point of view, and in virtue of its being a rational inspection of possibilities, topos theory is appropriate to logical thought. It is the apparatus wherein the logic of the constraining correlations between ontology and logic is thought out. " N o w ontology is not reducible to the logic of the onto-logical.
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