Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!nrl-cmf!ukma!tut.cis.ohio-state.edu!bloom-beacon!bu-cs!buengc!bph
From: bph@buengc.BU.EDU (Blair P. Houghton)
Newsgroups: comp.ai
Subject: Re: Natural Paradox
Message-ID: <2073@buengc.BU.EDU>
Date: 8 Feb 89 22:43:20 GMT
References: <1706@tank.uchicago.edu> <9526@ihlpb.ATT.COM> <kXuo9-y00V4=88uEVm@andrew.cmu.edu> <2053@buengc.BU.EDU> <0XvA3xy00Xoj82iV53@andrew.cmu.edu>
Reply-To: bph@buengc.bu.edu (Blair P. Houghton)
Followup-To: comp.ai
Organization: Boston Univ. Col. of Eng.
Lines: 35

In article <0XvA3xy00Xoj82iV53@andrew.cmu.edu> ap1i+@andrew.cmu.edu (Andrew C. Plotkin) writes:
>/>/ It would be very interesting, though, to see a statement which
>/>/ was 'provable' yet not 'provable' that it's 'provable.'
>/>
>/>How would you know it if you saw it? If you could point at it and say "That
>/>statement is provable, but you can't prove it!" how would you know that the
>/>first part of the claim is true, without invalidating the second part?
>/
>/Remember Rolle's theorem?
>
>No. Clarify?

I don't know about how you learned Calculus, but when I went through it
the first time the book mentions Rolle's theorem (having to do with the
idea that a continuous function that is positive at one point and
negative at another must be zero at some point in-between) and says it's
gotta be true, but that they wouldn't dare prove it.  Every other theorem
in a first-year calc book gets proven.  Rolle's doesn't.  I've never
seen a basic Calc book that proves it.  That also means I've never seen
it proven.

I seem to remember someone along the lines of Einstein as having said
that he couldn't prove it; but it's gotta be provable; it's the
cornerstone of the proofs of almost every theorem that follows it in
the book I first used.

Okay, so they're provable, but can we prove that they're provable?

It means we have to prove Rolle's Theorem.

				--Blair
				  "Mathematically.  Saying it's
				   obviously true doesn't work in
				   math.  That's why it's math,
				   and not theology."