[FOM] Some informative questions about intuitionistic logic and mathematics

[Mark van Atten]

On 03 Nov 2005 22:10:18 -0500, Richard Heck wrote:

 > It is
 > perfectly consistent (by her standards) for her also to claim that there
 > is no sentence that is neither true nor false.

Moreover, she can prove this; for assume that she knows that neither p 
nor not-p can ever be proved, then in particular she knows that p can 
never be proved, but on the proof interpretation that amounts to having 
a proof of not-p, and we have a contradiction.

A piece of paper in the Brouwer archive shows that Brouwer had this 
argument around the time of his thesis (probably _after_ rather than 
before); for some reason he never published it.

Best wishes,
Mark.

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