Briefings on Existence: A Short Treatise on Transitory by Alain Badiou

By Alain Badiou

Explores the hyperlink among arithmetic and ontology.

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If description accepts the multiplicity of the void, or its absence, then it pluralizes its foundation. In the Heraclitean tradition, it is instituted as alteration or becoming. It is easy to make sense in a topos of the notion of empty object or empty letter. The following astonishing theorem may then be proved, as well as shown to be an "onto-logical-onto" theorem. Let a constraining correlation between the coupling of an ontological and logical feature on the one hand, and another ontological feature, on the other.

Real mathematics is not a mathematized inspection of possible mathematical universes. Real mathematics decides upon one universe. The upshot is that the relation between logic and mathematics is like the one existing between a general investigation of an ontology's logical resources and an ontological decision that entails its logical consequences. This also means that logic is definitional, whereas real mathematics is axiomatic. This is how, if you axiomatically decide 119 120 Briefings on Existence thai the thought of Being is crafted in the framework of Set Theory, you will have to accept that your logic is classical.

9. First Remarks on the Concept of Topos There are no notes in this chapter. Notes 179 10. First Provisional Theses on Logic 1. Leibniz, The Monculology, ed. and trans. Robert Latta, sec. htm. 2. Stephane Mallarme, "Igitur," in Selected Poetry and Prose, and trans. Mary Ann Caws ( N e w York: N e w Directions, 1982). ed. 3. S. html. ) 11. The Being of Number 1. Surreal numbers are "the most natural collection of numbers which includes both the real numbers and the infinite ordinal numbers of Georg Cantor.

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