In Mathematics of the Transcendental, Alain Badiou painstakingly works through the pertinent aspects of category theory, demonstrating their internal logic and veracity, their derivation and distinction from set theory, and the 'thinking of being'. In doing so he sets out the basic onto-logical requirements of his greater and transcendental logics as articulated in his magnum opus, Logics of Worlds.

Previously unpublished in either French or English, Mathematics of the Transcendental provides Badiou's readers with a much-needed complete elaboration of his understanding and use of category theory. The book is vital to understanding the mathematical and logical basis of his theory of appearing as elaborated in Logics of Worlds and other works and is essential reading for his many followers.

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.

“[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.

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