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Single Idea 8684
[filed under theme 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
]
Full Idea
Russell and Whitehead are particularly careful to avoid paradox, and consider the paradoxes to indicate that we create mathematical reality.
Gist of Idea
Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality
Source
report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Michèle Friend - Introducing the Philosophy of Mathematics 3.1
Book Ref
Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.51
A Reaction
This strikes me as quite a good argument. It is certainly counterintuitive that reality, and abstractions from reality, would contain contradictions. The realist view would be that we have paradoxes because we have misdescribed the facts.
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]
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8684
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Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality
[Russell/Whitehead, by Friend]
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14248
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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]
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18068
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Arithmetic is made true by the world, but is also made true by our constructions
[Kitcher]
|
18070
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We develop a language for correlations, and use it to perform higher level operations
[Kitcher]
|
18069
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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]
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9223
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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
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Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ'
[Chihara, by Shapiro]
|
9608
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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]
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