more from this thinker     |     more from this text

Single Idea 9645

[filed under theme 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism ]

Full Idea

If we define p as '3 if Goldbach's Conjecture is true' and '5 if Goldbach's Conjecture is false', it seems that p must be a prime number, but, amazingly, constructivists would not accept this without a proof of Goldbach's Conjecture.

Clarification

'Goldbach's Conjecture' is probably true, but has not been proved

Gist of Idea

Constructivists say p has no value, if the value depends on Goldbach's Conjecture

Source

James Robert Brown (Philosophy of Mathematics [1999], Ch. 8)

Book Ref

Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.113

A Reaction

A very similar argument structure to Schrödinger's Cat. This seems (as Brown implies) to be a devastating knock-down argument, but I'll keep an open mind for now.

The 16 ideas with the same theme [maths is entirely created by the human mind]:

9916 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]