more from James Robert Brown

### Single Idea 9645

#### [catalogued under 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 Reference

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.