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Single Idea 12329
[filed under theme 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
]
Full Idea
If mathematics is a logic of the possible, then questions of existence are not intrinsic to it (as they are for the Platonist).
Gist of Idea
If mathematics is a logic of the possible, then questions of existence are not intrinsic to it
Source
Alain Badiou (Briefings on Existence [1998], 7)
Book Ref
Badiou,Alain: 'Briefings on Existence', ed/tr. Madarsz,Norman [SUNY 2006], p.103
A Reaction
See also Idea 12328. I file this to connect it with Hellman's modal (and nominalist) version of structuralism. Could it be that mathematics and modal logic are identical?
Related Idea
Idea 12328
Platonists like axioms and decisions, Aristotelians like definitions, possibilities and logic [Badiou]
The
24 ideas
from 'Briefings on Existence'
12318
|
The female body, when taken in its entirety, is the Phallus itself
[Badiou]
|
12320
|
Ontology is (and always has been) Cantorian mathematics
[Badiou]
|
12331
|
Logic is definitional, but real mathematics is axiomatic
[Badiou]
|
12338
|
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
|
There is 'transivity' iff membership ∈ also means inclusion ⊆
[Badiou]
|
12335
|
Numbers are for measuring and for calculating (and the two must be consistent)
[Badiou]
|
12334
|
There is no single unified definition of number
[Badiou]
|
12333
|
Each type of number has its own characteristic procedure of introduction
[Badiou]
|
12342
|
Topos theory explains the plurality of possible logics
[Badiou]
|
12340
|
There is no Being as a whole, because there is no set of all sets
[Badiou]
|
12341
|
Logic is a mathematical account of a universe of relations
[Badiou]
|
12323
|
Existence is Being itself, but only as our thought decides it
[Badiou]
|
12321
|
The axiom of choice must accept an indeterminate, indefinable, unconstructible set
[Badiou]
|
12324
|
Consensus is the enemy of thought
[Badiou]
|
12322
|
Must we accept numbers as existing when they no longer consist of units?
[Badiou]
|
12325
|
Philosophy has been relieved of physics, cosmology, politics, and now must give up ontology
[Badiou]
|
12327
|
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]
|