FOM: intuitionistic and classical truth
neilt at mercutio.cohums.ohio-state.edu
Thu Sep 3 21:03:43 EDT 1998
Bill Tait says that for a mathematical proposition A, A is equivalent
to the proposition that A is true. Moreover, the only warrant for
asserting A would be a proof of A.
The classicist and intuitionist would both agree with these points.
Where they part company is in saying *what truth consists in*. For the
intuitionist, "A is true" is (analytically, conceptually) equivalent
to "There exists a proof of A".
>From that conceptual identification the intuitionist then argues
further that the proofs whose existence constitute truth should not
contain any strictly classical moves. Thus the intuitionist ends up
saying, in effect, that "A is true" is (analytically, conceptually)
equivalent to "There exists a (suitably intuitionistic) proof of A".
The further argument just referred to is pretty involved; and it is at
this locus that Dummett's contribution is most important.
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