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Single Idea 10255
[filed under theme 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
]
Full Idea
Presumably within a dynamic system, once the constructor has an operation available, then no activity can preclude the performance of the operation?
Gist of Idea
Presumably nothing can block a possible dynamic operation?
Source
Stewart Shapiro (Philosophy of Mathematics [1997], 6.5)
Book Ref
Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.194
A Reaction
There seems to be an interesting assumption in static accounts of mathematics, that all the possible outputs of (say) a function actually exist with a theory. In an actual dynamic account, the constructor may be smitten with lethargy.
The
16 ideas
with the same theme
[maths is entirely created by the human mind]:
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9916
|
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]
|
|
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]
|
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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]
|
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18069
|
Arithmetic is an idealizing theory
[Kitcher]
|
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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
|
My Proceduralism has one simple rule, and four complex rules
[Fine,K]
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10255
|
Presumably nothing can block a possible dynamic operation?
[Shapiro]
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10254
|
Can the ideal constructor also destroy objects?
[Shapiro]
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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]
|
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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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