Newsgroups: comp.ai.philosophy
Path: cantaloupe.srv.cs.cmu.edu!rochester!udel!gatech!howland.reston.ans.net!cs.utexas.edu!uunet!psinntp!scylla!daryl
From: daryl@oracorp.com (Daryl McCullough)
Subject: Re: Penrose's new book
Message-ID: <1994Nov8.142555.9215@oracorp.com>
Organization: Odyssey Research Associates, Inc.
Date: Tue, 8 Nov 1994 14:25:55 GMT
Lines: 39

-----------------------Quoted Stuff---------------------------

Daryl:

As a matter of fact, regardless of whether or not our reasoning is
computational, if we are *certain* that our reasoning is consistent,
then it isn't consistent. Penrose mistakenly thinks that Godel's
incompleteness theorem only applies to computational systems. It
applies to *any* set of statements in a language capable
of sufficient self-reference...including the set of statements believed
by Roger Penrose. If Penrose is convinced that his own reasoning process
is obviously free of contradictions, then he is just wrong.

Jeff:

Since when does Godel's theorem say "if we are *certain*..."?

Daryl:

It doesn't.

Jeff:

So why _were_ you saying "if we are *certain*" above?

--------------------------------------------------------------

I was making an analogy between (1) Theory T proves statement S, and
(2) Person P is certain of statement S. I used "is certain of" rather
than "believes", because there can be all sorts of degrees of
belief. The point I was making was that just as no consistent theory T
can prove the statement "T is consistent", no consistent human being P
can be certain of the statement "P is consistent" (meaning "No
contradiction can arise from the set of statements that P is certain
of").

Daryl McCullough
ORA Corp.
Ithaca, NY
