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Ideas of Alain Badiou, by Text
[French, b.1937, Born in Morocco. Chair of Philosophy at the École Normale Supérieure.]
1998

Briefings on Existence


p.27

12318

The female body, when taken in its entirety, is the Phallus itself

1

p.40

12320

Ontology is (and always has been) Cantorian mathematics

10

p.119

12331

Logic is definitional, but real mathematics is axiomatic

1011b24

p.107

12338

We must either assert or deny any single predicate of any single subject

11

p.125

12332

The modern view of Being comes when we reject numbers as merely successions of One

11

p.125

12333

Each type of number has its own characteristic procedure of introduction

11

p.126

12334

There is no single unified definition of number

11

p.126

12335

Numbers are for measuring and for calculating (and the two must be consistent)

11

p.128

12336

A von Neumann ordinal is a transitive set with transitive elements

11

p.128

12337

There is 'transivity' iff membership ∈ also means inclusion ⊆

14

p.158

12339

Aristotle removes ontology from mathematics, and replaces the true with the beautiful

14

p.160

12340

There is no Being as a whole, because there is no set of all sets

14

p.165

12341

Logic is a mathematical account of a universe of relations

14

p.167

12342

Topos theory explains the plurality of possible logics

2

p.52

12321

The axiom of choice must accept an indeterminate, indefinable, unconstructible set

2

p.53

12322

Must we accept numbers as existing when they no longer consist of units?

2

p.55

12323

Existence is Being itself, but only as our thought decides it

2

p.56

12324

Consensus is the enemy of thought

3

p.59

12325

Philosophy has been relieved of physics, cosmology, politics, and now must give up ontology

6

p.98

12326

The primitive name of Being is the empty set; in a sense, only the empty set 'is'

6

p.99

12327

The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory

7

p.103

12329

If mathematics is a logic of the possible, then questions of existence are not intrinsic to it

7

p.103

12328

Platonists like axioms and decisions, Aristotelians like definitions, possibilities and logic

8

p.110

12330

In ontology, logic dominated language, until logic was mathematized

Prol

p.22

12316

For Enlightenment philosophers, God was no longer involved in politics

Prol

p.26

12317

The God of religion results from an encounter, not from a proof

2004

Mathematics and Philosophy: grand and little

p.11

p.11

9808

Philosophy aims to reveal the grandeur of mathematics

p.12

p.12

9809

Mathematics inscribes being as such

p.16

p.16

9811

It is of the essence of being to appear

p.17

p.17

9812

In mathematics, if a problem can be formulated, it will eventually be solved

p.19

p.19

9813

Mathematics shows that thinking is not confined to the finite

p.20

p.20

9814

All great poetry is engaged in rivalry with mathematics
