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From: torkel@sics.se (Torkel Franzen)
Newsgroups: comp.ai.philosophy
Subject: Re: Intuition and doubt (was Re: Minds, machines, and Godel)
Message-ID: <1991Jan23.180914.8116@sics.se>
Date: 23 Jan 91 18:09:14 GMT
References: <7129.9101231301@s4.sys.uea.ac.uk>
Sender: news@sics.se
Organization: Swedish Institute of Computer Science, Kista
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In-Reply-To: jrk@information-systems.east-anglia.ac.uk's message of 23 Jan 91 13:01:37 GMT

In article <7129.9101231301@s4.sys.uea.ac.uk> jrk@information-systems.east-
anglia.ac.uk (Richard Kennaway CMP RA) writes:

  >But I am raising a comparable hullabaloo - that is to say, hardly any at
  >all.  I just use mathematics, I don't concern myself with whether it's true.
  >"Truth" in mathematics is not a metaphysical or deplorable concept, just an
  >unnecessary one.

  This doesn't even begin to touch on the question I raised. You were
saying, of a particular theorem of elementary analysis of the form
"every natural number has property P", with P a primitive recursive
predicate, that we have no reason whatever to believe that every
natural number has property P, except that no counterexample has been
found. So my question is, would you extend this to every theorem of
analysis? If it were proved in elementary analysis that the equation
x^n+y^n=z^n has no non-trivial solution for n>2, would you proclaim to
the net that we still have no reason whatever to believe that this is
so, except that no counterexample has been found? I rather suspect
not. And as long as you prefer to ignore this issue, you have said
nothing of consequence regarding consistency.