FOM: intuitionism

[wwtx@uchicago.edu]

As I understand intuitionism, the proposition that p is provable is equivalent
to (or even the same as) the proposition P itself: for both are warranted by
producing a proof of p. Therefore, the proposition "either p is provable, not-p
is provable, or neither is provable" is equivalent to ``p or not-p or (not-p and
not-not-p) which is equivalent to ``p or not-p'', which of course is not
intuitionistically valid.

Bill Tait

Quoting wiman lucas raymond <lrwiman at ilstu.edu>:

> Anyway, 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.