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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 12335 Numbers are for measuring and for calculating (and the two must be consistent)
11 p.126 12334 There is no single unified definition of number
11 p.128 12337 There is 'transivity' iff membership ∈ also means inclusion ⊆
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