DescriptionThe 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.
I Genealogies: Frege, Dedekind, Peano, Cantor.
1 Greek Number and Modern Number.
3 Additional Note on a Contemporary Usage of Frege.
6 Cantor: 'Well-Orderedness' and the Ordinals.
II Concepts: Natural Multiplicities.
7 Transitive Multiplicities.
8 Von Neumann Ordinals.
9 Succession and Limit. The Infinite.
10 Recurrence, or Induction.
11 Natural Whole Numbers.
III Ontology of Number: Definition, Order, Cuts, Types.
12 The Concept of Number: An Evental Nomination Additional Notes On Sets Of Ordinals.
13 Difference and Order of Numbers.
14 The Concept of Sub-Number.
15 Cuts: The Fundamental Theorem.
16 The Numberless Enchantment of the Place of Number.
IV Operational Dimensions.
17 Natural Interlude.
18 Algebra of Numbers.
19 In Conclusion: From Number to Trans-Being.
“A bracing alternative both to the sterile and dry discussions that constitute much of the literature on mathematics and to the daily incursion of pie-charts, mortgage payments and bills that make up most of our dealings with numbers. Badiou’s own ‘history of eternity’ is a manifesto for the future of mathematics, and of philosophy’s role in appreciating that future.”
The Philosophers' Magazine
“Badiou’s major foray into the philosophy of mathematics displays his trademark blend of intricacy and daring. His purpose is to renew our sense of the dignity, even majesty of numbers – and so bolster our resistance to a world of brute calculation.”
Peter Dews, University of Essex