FOM: Reply to Professor Segal
wtait at ix.netcom.com
Thu Sep 3 09:38:07 EDT 1998
I want to comment on a small point in Adian's reply to Professor
Siegal. He writes
> After those statements I think that the finger points at Dieudonne.
> In his last book, The Music of Mathematics he makes the same mistake
> that he made in his position papers of fifty years previously: he went to
> his grave believing that truth and provability are identical.
> That is an intuitionist position:
That may be the intuitionistic position according to some philosophers,
such as Michael Dummett; but it was never stated by either Brouwer of
Heyting (or so I think). Anyway, it is not a reasonable position. For
a mathematical proposition A (as opposed to a formal sentence
interpreted in a structure), the proposition that A is true is the same
as the proposition A. The view that the only warrant for asserting A is
a proof of A does not distinguish intuitionistic mathematics from
classical. Certainly a difference between the two concerns what is to
count as a proof.
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