Newsgroups: sci.logic,comp.ai.philosophy
Path: cantaloupe.srv.cs.cmu.edu!bb3.andrew.cmu.edu!news.sei.cmu.edu!cis.ohio-state.edu!math.ohio-state.edu!uwm.edu!news.alpha.net!news.mathworks.com!yeshua.marcam.com!charnel.ecst.csuchico.edu!olivea!news.hal.COM!decwrl!netcomsv!netcom.com!oresmus
From: oresmus@netcom.com (Bruce Smith)
Subject: Re: Expressibility (was "Penrose's new book)
Message-ID: <oresmusCyD7HD.C9E@netcom.com>
Organization: NETCOM On-line Communication Services (408 261-4700 guest)
References: <1994Oct26.172830.3987@oracorp.com> <1994Oct27.020638.28742@news.media.mit.edu>
Date: Fri, 28 Oct 1994 04:08:01 GMT
Lines: 40
Xref: glinda.oz.cs.cmu.edu sci.logic:8741 comp.ai.philosophy:21451

minsky@media.mit.edu (Marvin Minsky) writes:

>.... In particular, when you try to
>express commonsense ideas that happen to be self-referent you expose
>yourself to diagnalization.  If it were more often understood how
>pervasive this is, then computer science students would be more
>suspicious of first order logic.  When do you need self-reference?
>Certainly when you make up things like
>
>(1)   the liar's paradox.
>
>Of course everyone know that this leads to trouble.  But you also need
>it in order to emply advice like
>
>(2)	"To solve a problem, use heuristics appropriate to that kind
>of problem -- but don't use ones that have led in the past to poor
>results."
>
>And so on.  Imagine (as Russell once did) making a system (like
>stratification) in which (1) is not expressible.  Then you can
>probably avoid Russell's paradox, which is the same as the liar's
>paradox.  But I see Godel's theorem as saying that you can't make (1)
>inexpressible without making useful things like (2) inexpressible,
>too.

I think that if "in the past" in (2) is taken literally, there is
no problem with expressing this in a consistent system, since it
has no self-reference -- it defines the set of heuristics to use
at time T based on some function of the ones that were used at
*previous* times.

If, instead, we considered

(3)	"To solve a problem, use heuristics appropriate to that kind
of problem -- but don't use ones which lead to poor results."

then I agree that there would be a problem with self-reference.

- Bruce Smith
oresmus@netcom.com
