FOM: Intuitionism

[Neil Tennant]

> my question is this:  would an intuitionist accept the statment
> "either p is provable, not-p is provable, or neither is provable"? I 
> think  the answer is probably "no," but I'm not entirely sure.  To me,
> not being an intuitionist, it seems pretty plain that at least one of
> these must be true, but I don't think there is any guarantee of there
> being a proof--the standard for intuitionists.
> 
> -Lucas Wiman

You are correct in thinking that the answer is negative, when by
"provable" one means "provable in some system that we could eventually
acknowledge as sound", rather than "provable in such-and-such formal
system".

On the open-ended interpretation, your third disjunct would be impossible.
Thus the whole disjunction would reduce to the excluded middle claim
"either p is provable or not-p is provable", which of course the
intuitionist does not accept.

Neil Tennant