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Single Idea 9916
[filed under theme 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
]
Full Idea
Poincaré once exclaimed, 'Convention, yes! Arbitrary, no!'.
Gist of Idea
Convention, yes! Arbitrary, no!
Source
report of Henri Poincaré (talk [1901]) by Hilary Putnam - Models and Reality
Book Ref
'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.430
A Reaction
An interesting view. It mustn't be assumed that conventions are not rooted in something. Maybe a sort of pragmatism is implied.
The
16 ideas
with the same theme
[maths is entirely created by the human mind]:
9916
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Convention, yes! Arbitrary, no!
[Poincaré, by Putnam]
|
8684
|
Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality
[Russell/Whitehead, by Friend]
|
14248
|
We could accept the integers as primitive, then use sets to construct the rest
[Cohen]
|
15939
|
For intuitionists it is constructed proofs (which take time) which make statements true
[Dummett]
|
18068
|
Arithmetic is made true by the world, but is also made true by our constructions
[Kitcher]
|
18070
|
We develop a language for correlations, and use it to perform higher level operations
[Kitcher]
|
18069
|
Arithmetic is an idealizing theory
[Kitcher]
|
18072
|
Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori)
[Kitcher]
|
9222
|
The objects and truths of mathematics are imperative procedures for their construction
[Fine,K]
|
9223
|
My Proceduralism has one simple rule, and four complex rules
[Fine,K]
|
10255
|
Presumably nothing can block a possible dynamic operation?
[Shapiro]
|
10254
|
Can the ideal constructor also destroy objects?
[Shapiro]
|
10264
|
Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ'
[Chihara, by Shapiro]
|
9608
|
There are no constructions for many highly desirable results in mathematics
[Brown,JR]
|
9645
|
Constructivists say p has no value, if the value depends on Goldbach's Conjecture
[Brown,JR]
|
8706
|
Constructivism rejects too much mathematics
[Friend]
|