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From: jrk@information-systems.east-anglia.ac.uk (Richard Kennaway CMP RA)
Newsgroups: comp.ai.philosophy
Subject: Re: Minds, machines, and Godel
Message-ID: <703.9101211032@s4.sys.uea.ac.uk>
Date: 21 Jan 91 10:32:27 GMT
Sender: daemon@ucbvax.BERKELEY.EDU
Lines: 32

In <1991Jan20.230731.579@sics.se> torkel@sics.se (Torkel Franzen) writes:
<  Hmm..on the basis of the fact that no contradiction has yet surfaced
<you regard the consistency of first order arithmetic as "uncontroversial"...
<By the same token, then, since no counterexample to Fermat's last theorem
<has been found, you regard it as "uncontroversially" true...And for any
<conjecture that has not yet been settled in ZFC, you regard it as
<"uncontroversial" that it is undecidable in ZFC...

First-order arithmetic and ZFC have received a great deal more usage than
any particular conjectures such as FLT.  No, I dont regard FLT as
uncontroversially true.  And for that matter, by "uncontroversially true"
- I should have said just "uncontroversial" - I dont mean any more than
that I'm willing to take arithmetic and ZFC for granted, and not worry
about the possibility that the house of cards may fall down one day.  I
wouldn't do that with FLT.

<However, your apparent doctrine
<that any statement of the form "for all k, P(k)" that has not been 
<refuted is "uncontroversially" true is merely silly from the point of view
<of ordinary mathematics.

Such a doctrine would indeed be uncontroversially silly.  It isnt mine though.

<  In other words: if you claim that there is evidence that first order
<arithmetic is consistent, you had better come up with something more
<convincing.

I am not claiming any such thing.

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