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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 The female body, when taken in its entirety, is the Phallus itself
1 p.40 Ontology is (and always has been) Cantorian mathematics
10 p.119 Logic is definitional, but real mathematics is axiomatic
1011b24 p.107 We must either assert or deny any single predicate of any single subject
11 p.125 The modern view of Being comes when we reject numbers as merely successions of One
11 p.125 Each type of number has its own characteristic procedure of introduction
11 p.126 There is no single unified definition of number
11 p.126 Numbers are for measuring and for calculating (and the two must be consistent)
11 p.128 A von Neumann ordinal is a transitive set with transitive elements
11 p.128 There is 'transivity' iff membership ∈ also means inclusion ⊆
14 p.158 Aristotle removes ontology from mathematics, and replaces the true with the beautiful
14 p.160 There is no Being as a whole, because there is no set of all sets
14 p.165 Logic is a mathematical account of a universe of relations
14 p.167 Topos theory explains the plurality of possible logics
2 p.52 The axiom of choice must accept an indeterminate, indefinable, unconstructible set
2 p.53 Must we accept numbers as existing when they no longer consist of units?
2 p.55 Existence is Being itself, but only as our thought decides it
2 p.56 Consensus is the enemy of thought
3 p.59 Philosophy has been relieved of physics, cosmology, politics, and now must give up ontology
6 p.98 The primitive name of Being is the empty set; in a sense, only the empty set 'is'
6 p.99 The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory
7 p.103 If mathematics is a logic of the possible, then questions of existence are not intrinsic to it
7 p.103 Platonists like axioms and decisions, Aristotelians like definitions, possibilities and logic
8 p.110 In ontology, logic dominated language, until logic was mathematized
Prol p.22 For Enlightenment philosophers, God was no longer involved in politics
Prol p.26 The God of religion results from an encounter, not from a proof
2004 Mathematics and Philosophy: grand and little
p.11 p.11 Philosophy aims to reveal the grandeur of mathematics
p.12 p.12 Mathematics inscribes being as such
p.16 p.16 It is of the essence of being to appear
p.17 p.17 In mathematics, if a problem can be formulated, it will eventually be solved
p.19 p.19 Mathematics shows that thinking is not confined to the finite
p.20 p.20 All great poetry is engaged in rivalry with mathematics