Mathematics of the Transcendental: Onto-logy and being-there

 

Alain Badiou, A.J. Bartlett e Alex Ling

Bloomsbury Academic | 2014 | 291 páginas | rar - pdf | 2,74 Mb

link (password : matav)

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. This important book combines both his elaboration of the disjunctive synthesis between ontology and onto-logy (the discourses of being as such and being-appearing) from the perspective of Category Theory and the categorial basis of his philosophical conception of 'being there'.
Hitherto unpublished in either French or English, Mathematics of the Transcendental provides Badiou's readers with a much-needed complete elaboration of his understanding and use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 an essential aid 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.

TABLE OF CONTENTS
Translators’ Introduction: The Categorial Imperative 1
PART ONE TOPOS, OR LOGICS OF ONTO-LOGY: AN INTRODUCTION FOR PHILOSOPHERS 11
1 General Aim 13
2 Preliminary Definitions 17
3 The Size of a Category 21
4 Limit and Universality 27
5 Some Fundamental Concepts 29
6 Duality 37
7 Isomorphism 41
8 Exponentiation 45
9 Universe, 1: Closed Cartesian Categories 51
10 Structures of Immanence, 1: Philosophical Considerations 55
11 Structures of Immanence, 2: Sub-Object 59
12 Structures of Immanence, 3: Elements of an Object 63
13 ‘Elementary’ Clarification of Exponentiation 67
14 Central Object (or Sub-Object Classifier) 71
15 The True, the False, Negation and More 77
16 The Central Object as Linguistic Power 85
17 Universe, 2: The Concept of Topos 89
18 Ontology of the Void and Difference 95
19 Mono., Epi., Equ., and Other Arrows 99
20 Topoi as Logical Places 113
21 Internal Algebra of 1 123
22 Ontology of the Void and Excluded Middle 141
23 A Minimal Classical Model 147
24 A Minimal Non-Classical Model 151
PART TWO BEING THERE: MATHEMATICS OF THE TRANSCENDENTAL 163
Introduction 165
A. Transcendental Structures 171
B. Transcendental Connections 183
B.1. Connections between the transcendental and set-theoretic ontology: Boolean algebras 183
B.2. Connections between the transcendental and logic in its ordinary sense (propositional logic and first order predicate logic) 195
B.3. Connection between the transcendental and the general theory of localizations: Topology 202
C. Theory of Appearing and Objectivity 217
D. Transcendental Projections: Theory of Localization 235
E. Theory of Relations: Situation as Universe 249
Appendix: On Three Different Concepts of Identity Between Two
Multiples or Two Beings 265
Translator’s Endnotes 269
Index 277