โ Scribed by Alain Badiou
No coin nor oath required. For personal study only.
The political regime of global capitalism reduces the world to an endless network of numbers within numbers, but how many of us really understand what numbers are? Without such an understanding, how can we challenge the regime of number?In Number and Numbers Alain Badiou offers an philosophically penetrating account with a powerful political subtext of the attempts that have been made over the last century to define the special status of number. Badiou argues that number cannot be defined by the multiform calculative uses to which numbers are put, nor is it exhausted by the various species described by number theory. Drawing on the mathematical theory of surreal numbers, he develops a unified theory of Number as a particular form of being, an infinite expanse to which our access remains limited. This understanding of Number as being harbours important philosophical truths about the structure of the world in which we live.In Badiou's view, only by rigorously thinking through Number can philosophy offer us some hope of breaking through the dense and apparently impenetrable capitalist fabric of numerical relations. For this will finally allow us to point to that which cannot be numbered: the possibility of an event that would deliver us from our unthinking subordination of number.
Contents......Page 4
Translator's Preface by Robin Mackay......Page 6
0.
Number Must Be Thought......Page 10
PART 1. Genealogies: Frege, Dedekind, Peano, Cantor......Page 14
1.
Greek Number and
Modern Number......Page 16
2.
Frege......Page 25
3. Additional Note on a
Contemporary Usage of Frege......Page 33
4.
Dedekind......Page 40
5.
Peano......Page 55
6.
Cantor: 'Well-Orderedness'
and the Ordinals......Page 61
PART 2:
Concepts: Natural Multiplicities......Page 68
7.
Transitive Multiplicities......Page 70
8. Von Neumann Ordinals......Page 76
9.
Succession and Limit.
The Infinite......Page 82
10.
Recurrence, or Induction......Page 92
11.
Natural Whole Numbers......Page 102
PART 3:
Ontology of Number:
Definition, Order, Cuts, Types......Page 108
12.
The Concept of Number:
An Evental Nomination......Page 110
Additional Notes on Sets of Ordinals......Page 121
13.
Difference and Order
of Numbers......Page 124
14.
The Concept of Sub-Number......Page 140
15.
Cuts: The Fundamental
Theorem......Page 148
16.
The Numberless Enchantment
of the Place of Number......Page 165
PART 4:
Operational Dimensions......Page 190
17.
Natural Interlude......Page 192
18.
Algebra of Numbers......Page 207
Conclusion......Page 218
19.
In Conclusion:
From Number to Trans-Being......Page 220
Notes......Page 224
Index......Page 240
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The political regime of global capitalism reduces the world to an endless network of numbers within numbers, but how many of us really understand what numbers are? Without such an understanding, how can we challenge the regime of number? In Number and Numbers Alain Badiou offers an philosop
The political regime of global capitalism reduces the world to an endless network of numbers within numbers, but how many of us really understand what numbers are? Without such an understanding, how can we challenge the regime of number? In Number and Numbers Alain Badiou offers an philosophi
The political regime of global capitalism reduces the world to an endless network of numbers within numbers, but how many of us really understand what numbers are? Without such an understanding, how can we challenge the regime of number?In Number and Numbers Alain Badiou offers an philosophically pe
The political regime of global capitalism reduces the world to an endless network of numbers within numbers, but how many of us really understand what numbers are? Without such an understanding, how can we challenge the regime of number?In Number and Numbers Alain Badiou offers an philosophically pe
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