FOM: reply to Detlefsen, McLarty, Tait
wtait at ix.netcom.com
Thu Sep 10 09:34:31 EDT 1998
Neil Tennant wrote
> In closing, I'd like to say that I'm glad that Bill Tait agrees that
> the three claims
> A is true
> A is provable
> are, for the intuitionist, (conceptually or analytically)
> equivalent. This fact fits in with the above account too.
I did not really agree with this. I said in effect that I know of no
place where either Brouwer or Heyting (and I can probably safely add:
any of the mathematical intuitionists---as opposed to philosophical
interpreters) pronounced on this matter. I also said that neither of the
second and third proposition really occur in mathematics. But, if they
were to be given a meaning and if one agrees that the meaning of a
mathematical proposition is given when it has been specified what is to
count as a proof of it, then all three propositions mean the same, since
the only reasonable account of either of the last two is that its proofs
are precisely the proofs of A.
On the other hand, in view of my ill-tempered remarks to Neil in my last
posting, for which I apologize, I undoubtedly deserve to have my tail
twisted in this way.
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