Mathematics of the Transcendental

Alain Badiou teaches at the École Normale Supérieure and at the Collège International de Philosophie in Paris, France. In addition to several novels, plays and political essays, he has published a number of major philosophical works.A. J. Bartlett is an Adjunct Research Fellow at the Research Unit in European Philosophy at Monash University, Australia. He is the author of Badiou and Plato: An Education by Truths, and with Justin Clemens and Jon Roffe author of Lacan, Deleuze, Badiou, forthcoming.Alex Ling is Research Lecturer in Communication and Media Studies at the University of Western Sydney, Australia. He is the author of Badiou and Cinema, and Badiou Reframed, forthcoming.

• Translator's Introduction \ Preface \ Part I: Topos, or Logics of Onto-logy: An Introduction for Philosophers \ 1. General aim \ 2. First definitions \ 3. The size of a category \ 4. Limit and universality \ 5. Some fundamental concepts \ 6. Duality \ 7. Isomorphism \ 8. Exponentiation \ 9. Universe 1: closed Cartesian categories \ 10. Structures of immanence 1: philosophical grounds \ 11. Immanence 2: sub-object \ 12. Immanence 3: elements of an object \ 13. 'Elementary' clarification of exponentiation \ 14. Logic 1: central object (or sub-object classifier) \ 15. True, false, negation and more \ 16. Central object as linguistic power \ 17. Universe 2: the concept of Topos \ 18. Ontology of the void and of difference \ 19. Mono., Epi., Iso., Equa., and other arrows \ 20. Topoi as logical places \ 21. Internal algebra of 1 \ 22. Ontology of the void and excluded middle \ 23. A classical miniature \ 24. A non-classical miniature \ Part II: Being-There \ Introduction \ A. Transcendental structures \ B. Transcendental connections \ B2. Of transcendental connections and logic in its usual sense (propositional logic and first order logic of predicates)\ B3. Transcendental connections and the general theory of localisations: topology \ C. Theory of appearing and of objectivity \ D. Transcendental projections: theory of localisation \ E. Theory of relations. The status of worlds \ Index

[Badiou's] mathematics is precise and correct ... I am impressed by the lucidity of [his] remarks on the philosophical significance of category theory, especially in relation to set theory, and I invite philosophically minded mathematicians to be so too.