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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism

[maths is entirely created by the human mind]

16 ideas
Convention, yes! Arbitrary, no! [Poincaré, by Putnam]
Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend]
We could accept the integers as primitive, then use sets to construct the rest [Cohen]
For intuitionists it is constructed proofs (which take time) which make statements true [Dummett]
Arithmetic is made true by the world, but is also made true by our constructions [Kitcher]
We develop a language for correlations, and use it to perform higher level operations [Kitcher]
Arithmetic is an idealizing theory [Kitcher]
Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher]
The objects and truths of mathematics are imperative procedures for their construction [Fine,K]
My Proceduralism has one simple rule, and four complex rules [Fine,K]
Presumably nothing can block a possible dynamic operation? [Shapiro]
Can the ideal constructor also destroy objects? [Shapiro]
Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro]
There are no constructions for many highly desirable results in mathematics [Brown,JR]
Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR]
Constructivism rejects too much mathematics [Friend]