[FOM] Some informative questions about intuitionistic logic and mathematics
Mark van Atten
Mark.vanAtten at univ-paris1.fr
Mon Nov 7 05:11:09 EST 2005
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.
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