Number Must Be Thought.
I Genealogies: Frege, Dedekind, Peano, Cantor.
1 Greek Number and Modern Number.
2 Frege.
3 Additional Note on a Contemporary Usage of Frege.
4 Dedekind.
5 Peano.
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.
Index.
Alain Badiou is Professor of Philosophy at the École Normale Supérieure.
“Breathtaking ... Badiou announces a new epoch in philosophy.”
Slavoj Žižek “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
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