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Single Idea 9222
[filed under theme 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
]
Full Idea
I call my new approach to mathematics 'proceduralism'. It agrees with Hilbert and Poincaré that the objects and truths are postulations, but takes them to be imperatival rather than indicative in form; not propositions, but procedures for construction.
Gist of Idea
The objects and truths of mathematics are imperative procedures for their construction
Source
Kit Fine (Our Knowledge of Mathematical Objects [2005], Intro)
Book Ref
'Oxford Studies in Epistemology Vol. 1', ed/tr. Gendler,R/Hawthorne,J [OUP 2004], p.89
A Reaction
I'm not sure how an object or a truth can be a procedure, any more than a house can be a procedure. If a procedure doesn't have a product then it is an idle way to pass the time. The view seems to be related to fictionalism.
The
16 ideas
with the same theme
[maths is entirely created by the human mind]:
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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]
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15939
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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]
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18069
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Arithmetic is an idealizing theory
[Kitcher]
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18070
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We develop a language for correlations, and use it to perform higher level operations
[Kitcher]
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18072
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Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori)
[Kitcher]
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9222
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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]
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10255
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Presumably nothing can block a possible dynamic operation?
[Shapiro]
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10254
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Can the ideal constructor also destroy objects?
[Shapiro]
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10264
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Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ'
[Chihara, by Shapiro]
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9608
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There are no constructions for many highly desirable results in mathematics
[Brown,JR]
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9645
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Constructivists say p has no value, if the value depends on Goldbach's Conjecture
[Brown,JR]
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8706
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Constructivism rejects too much mathematics
[Friend]
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