Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!ames!ucsd!sdcsvax!beowulf!demers
From: demers@beowulf.ucsd.edu (David E Demers)
Newsgroups: comp.ai
Subject: Re: Natural Paradox
Keywords: Counterexample, Evidence, Belief, Proof, Provability
Message-ID: <5898@sdcsvax.UUCP>
Date: 11 Feb 89 00:12:08 GMT
References: <1706@tank.uchicago.edu> <9526@ihlpb.ATT.COM> <44585@linus.UUCP>
Sender: nobody@sdcsvax.UUCP
Reply-To: demers@beowulf.UCSD.EDU (David E Demers)
Organization: EE/CS Dept. U.C. San Diego
Lines: 29

In article <44585@linus.UUCP> bwk@mbunix.mitre.org (Barry Kort) writes:
->In article <9526@ihlpb.ATT.COM> arm@ihlpb.UUCP (55528-Macalalad,A.R.) writes:
->
-> > It would be very interesting, though, to see a statement which
-> > was 'provable' yet not 'provable' that it's 'provable.'
->
->Consider the statement:
->
->	Fermat's Last Theorem is provable.
->
->Many mathematicians believe the above statement to be true.
->(Otherwise, they wouldn't continue searching for a proof of
->Fermat's Last Theorem.)  But as of this writing, there is no
->proof that Fermat's Last Theorem is provable.
->
->Perhaps Fermat's Last Theorem is true but unprovable.

We already know that {under appropriate circumstances} there
are TRUE but UNPROVABLE statements; however, are there PROVABLE
statements about which one cannot PROVE they are provable?  

I agree with the poster who argued no.  If the statement is provable,
then one simply needs to exhibit the proof in order to prove
its provability.

Dave DeMers				demers@cs.ucsd.edu
Computer Science & Engineering - C-014
UCSD
La Jolla, CA 92093