Path: utzoo!utgpu!news-server.csri.toronto.edu!bonnie.concordia.ca!uunet!samsung!usc!apple!agate!ucbvax!information-systems.east-anglia.ac.uk!jrk
From: jrk@information-systems.east-anglia.ac.uk (Richard Kennaway CMP RA)
Newsgroups: comp.ai.philosophy
Subject: Re: Intuition and doubt (was Re: Minds, machines, and Godel)
Message-ID: <7129.9101231301@s4.sys.uea.ac.uk>
Date: 23 Jan 91 13:01:37 GMT
Sender: daemon@ucbvax.BERKELEY.EDU
Lines: 28

In article <1991Jan23.045926.17528@sics.se> torkel@sics.se (Torkel Franzen)
writes:

> What is this talk about 'intuiting truth'?

Talk like this:

> the axioms are true

Why do you believe the axioms are true?  Formalising the proof in elementary
analysis, besides the objections you mention of certain schools of
philosophy, won't tell you that arithmetic is consistent unless you believe
that the axioms of elementary analysis are true.

To get truth out of a mathematical argument, you - obviously - have to
supply truth yourself at some point.

> What is mere ritual is to reject this particular proof while not raising
> any comparable hullabaloo about mathematical proofs in general.

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.

--
Richard Kennaway          SYS, University of East Anglia, Norwich, U.K.
Internet:  jrk@sys.uea.ac.uk		uucp:  ...mcsun!ukc!uea-sys!jrk