Path: utzoo!utgpu!watmath!clyde!att!ihlpb!arm
From: arm@ihlpb.ATT.COM (Macalalad)
Newsgroups: comp.ai
Subject: Re: Natural Paradox
Message-ID: <9526@ihlpb.ATT.COM>
Date: 3 Feb 89 15:57:49 GMT
References: <1706@tank.uchicago.edu>
Reply-To: arm@ihlpb.UUCP (55528-Macalalad,A.R.)
Organization: AT&T Bell Laboratories - Naperville, Illinois
Lines: 17

In article <1706@tank.uchicago.edu> staff_bob@gsbacd.uchicago.edu (bob kohout) writes:
<to David Chalmers>
>
>Even your statement that 'if a sentence is provable, then it's 
>PROVABLE that it's provable' does not hold. For many years,
>one could not show the four color problem was provable, and yet it
>was. Only upon discovery of a proof is your claim valid, but the
>'provability' of a logicaL statement is invariant.
>
Sorry to jump into this argument, but isn't the 'provability' of
the 'provability' of a logical statement also invariant?  This
doesn't take away too much from the rest of your argument, which
basically distinguished between 'true' and 'provable' statements.
It would be very interesting, though, to see a statement which
was 'provable' yet not 'provable' that it's 'provable.'

-Alex