more on this theme
|
more from this text
Single Idea 9813
[filed under theme 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
]
Full Idea
Mathematics teaches us that there is no reason whatsoever to confne thinking within the ambit of finitude.
Gist of Idea
Mathematics shows that thinking is not confined to the finite
Source
Alain Badiou (Mathematics and Philosophy: grand and little [2004], p.19)
Book Ref
Badiou,Alain: 'Theoretical Writings' [Continuum 2006], p.19
A Reaction
This would perhaps make Cantor the greatest thinker who ever lived. It is an exhilarating idea, but we should ward the reader against romping of into unrestrained philosophical thought about infinities. You may be jumping without your Cantorian parachute.
The
30 ideas
from Alain Badiou
|
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
|
The modern view of Being comes when we reject numbers as merely successions of One
[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]
|
|
12337
|
There is 'transivity' iff membership ∈ also means inclusion ⊆
[Badiou]
|
|
12342
|
Topos theory explains the plurality of possible logics
[Badiou]
|
|
12341
|
Logic is a mathematical account of a universe of relations
[Badiou]
|
|
12340
|
There is no Being as a whole, because there is no set of all sets
[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]
|
|
12323
|
Existence is Being itself, but only as our thought decides it
[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]
|
|
9808
|
Philosophy aims to reveal the grandeur of mathematics
[Badiou]
|
|
9809
|
Mathematics inscribes being as such
[Badiou]
|
|
9811
|
It is of the essence of being to appear
[Badiou]
|
|
9812
|
In mathematics, if a problem can be formulated, it will eventually be solved
[Badiou]
|
|
9813
|
Mathematics shows that thinking is not confined to the finite
[Badiou]
|
|
9814
|
All great poetry is engaged in rivalry with mathematics
[Badiou]
|