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Previously unpublished in either French or English, Mathematics of the Transcendental provides Badiou's readers with a much-needed complete elaboration of his understanding and use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.
Previously unpublished in either French or English, Mathematics of the Transcendental provides Badiou's readers with a much-needed complete elaboration of his understanding and use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.
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 localization
E. Theory of relations. The status of worlds
Index
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 localization
E. Theory of relations. The status of worlds
Index