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Single Idea 12327
[filed under theme 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
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Full Idea
As we have known since Paul Cohen's theorem, the Continuum Hypothesis is intrinsically undecidable. Many believe Cohen's discovery has driven the set-theoretic project into ruin, or 'pluralized' what was once presented as a unified construct.
Gist of Idea
The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory
Source
Alain Badiou (Briefings on Existence [1998], 6)
Book Ref
Badiou,Alain: 'Briefings on Existence', ed/tr. Madarsz,Norman [SUNY 2006], p.99
A Reaction
Badiou thinks the theorem completes set theory, by (roughly) finalising its map.
The
24 ideas
from 'Briefings on Existence'
12318
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The female body, when taken in its entirety, is the Phallus itself
[Badiou]
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12320
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Ontology is (and always has been) Cantorian mathematics
[Badiou]
|
12331
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Logic is definitional, but real mathematics is axiomatic
[Badiou]
|
12338
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We must either assert or deny any single predicate of any single subject
[Badiou]
|
12332
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The modern view of Being comes when we reject numbers as merely successions of One
[Badiou]
|
12337
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There is 'transivity' iff membership ∈ also means inclusion ⊆
[Badiou]
|
12334
|
There is no single unified definition of number
[Badiou]
|
12335
|
Numbers are for measuring and for calculating (and the two must be consistent)
[Badiou]
|
12333
|
Each type of number has its own characteristic procedure of introduction
[Badiou]
|
12342
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Topos theory explains the plurality of possible logics
[Badiou]
|
12341
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Logic is a mathematical account of a universe of relations
[Badiou]
|
12340
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There is no Being as a whole, because there is no set of all sets
[Badiou]
|
12323
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Existence is Being itself, but only as our thought decides it
[Badiou]
|
12322
|
Must we accept numbers as existing when they no longer consist of units?
[Badiou]
|
12321
|
The axiom of choice must accept an indeterminate, indefinable, unconstructible set
[Badiou]
|
12324
|
Consensus is the enemy of thought
[Badiou]
|
12325
|
Philosophy has been relieved of physics, cosmology, politics, and now must give up ontology
[Badiou]
|
12327
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The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory
[Badiou]
|
12326
|
The primitive name of Being is the empty set; in a sense, only the empty set 'is'
[Badiou]
|
12329
|
If mathematics is a logic of the possible, then questions of existence are not intrinsic to it
[Badiou]
|
12328
|
Platonists like axioms and decisions, Aristotelians like definitions, possibilities and logic
[Badiou]
|
12330
|
In ontology, logic dominated language, until logic was mathematized
[Badiou]
|
12316
|
For Enlightenment philosophers, God was no longer involved in politics
[Badiou]
|
12317
|
The God of religion results from an encounter, not from a proof
[Badiou]
|