Mathematics of the Transcendental


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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

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Alain Badiou, one of the world's most celebrated contemporary philosophers, provides readers with a complete elaboration of his understanding and use of Category Theory.

About the Author

Alain Badiou teaches at the Ecole Normale Superieure and at the College 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.


[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. * Notices of the AMS *
Battered photocopies of Badiou's hand-drawn primer on category theory were prized possessions among the small group of people in Paris who gathered to attend his Saturday morning seminars in the mid-1990s, and coupled with the companion volume on Being-There also translated here, Topos remains a vital source of information for one of the most important and most challenging sequences of Badiou's philosophical trajectory. In addition to the distinctive light they shed on the transition from volume one to two of Badiou's Being and Event, both these texts are also of great interest and pedagogical value in their own right: non-specialists won't find a clearer, more accessible and more stimulating philosophical introduction to these crucial fields of contemporary mathematics. * Peter Hallward, Author of Badiou: A Subject to Truth and Professor of Philosophy, Kingston University, London, UK. *

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