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From: G.Joly@cs.ucl.ac.uk (Gordon Joly)
Newsgroups: comp.ai.philosophy
Subject: Godel's Proof (was Re: Help!).
Message-ID: <1306@ucl-cs.uucp>
Date: 27 Nov 90 11:49:20 GMT
Sender: news@cs.ucl.ac.uk
Lines: 29


In article <4168@media-lab.MEDIA.MIT.EDU>, minsky@media-lab.media.mit.edu (Marvin Minsky) writes
< In other words, none of this makes sense to me.  I see Godel's theorem
< as asserting that consistency is incompatible with heuristics, in the
< sense that there is no way to ensure only true assertions in suitably rich
< systems.  Very sad, but has nothing to do with our rich, heuristic,
< fallible brains.

Godel only produced one major work; his brain was fallible and he
suffered from depression for the latter part of his life.

I have asked mathematicians of note who tell me that Godel's theorem
doesn't bother them. There is still have plenty of work to do. (But
not for the following reasons).

In a suitably rich *axiomatic* system, Godel's proof tells us to
expect to find statements we cannot prove in that axiomatic system.
One escape, in a system with N axioms, is to label that unprovable
statement axiom N+1.

Godel's proof goes on to say that N will tend to infinity; so we end
up asserting all that we cannot prove. But that is getting us into
talk.politics territory ;-)

Anyway, are heuristics axiomatic systems?

Gordon Joly                                       +44 71 387 7050 ext 3716
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Computer Science, University College London, Gower Street, LONDON WC1E 6BT