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From: zeleny@oak.math.ucla.edu (Michael Zeleny)
Subject: Re: Expressibility (was "Penrose's new book)
Message-ID: <1994Oct27.200840.13718@math.ucla.edu>
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Organization: The Phallogocentric Cabal
References: <1994Oct27.020638.28742@news.media.mit.edu> <RV.94Oct26231109@tahoe.cs.brown.edu> <1994Oct27.184439.12619@news.media.mit.edu>
Date: Thu, 27 Oct 94 20:08:40 GMT
Expires: December 31, 1994
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Xref: glinda.oz.cs.cmu.edu sci.logic:8735 comp.ai.philosophy:21438

In article <1994Oct27.184439.12619@news.media.mit.edu> 
minsky@media.mit.edu (Marvin Minsky) writes:

>In article <RV.94Oct26231109@tahoe.cs.brown.edu> 
>rv@tahoe.cs.brown.edu (rodrigo vanegas) writes:

>>In article <1994Oct27.020638.28742@news.media.mit.edu> 
>>minsky@media.mit.edu (Marvin Minsky) writes:

>>>
>>>   (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."

>>I don't understand.  How does (2) make use of self-reference?  

>I should have been more precise.  (2) is advice referring to advice.
>In general commonsense reasoning depends on a lot of statements about
>when to apply other statements, and these often include self-referent
>loops.  

Advice referring to advice is meta-advice, and may be correctly and
adequately treated as such either by Tarski or by Russell, without
self-reference or other violations of predicativity.

>There's some discussion of this in "The Society of Mind," for example,
>in Chapter 17.   

For correctives of common errors about predicative reasoning, see
Alonzo Church's classic "Comparison of Russell's resolution of the
Semantical antinomies with that of Tarski" in the 1976 JSL, reprinted
with corrections in Robert L. Martin's _Recent Essays on Truth and the
Liar Paradox_, Oxford, 1984, and available on request as a PostScript
pre-print of the forthcoming collected edition of Church's papers, in
exchange for notification of any possible misprints.  Also see Allen
Hazen's chapter on predicative logics in the first volume of the
_Handbook of Philosophical Logic_, which justly characterizes the
Church article as "perhaps the best introduction available to any
topic in the whole of logic".

cordially,                                                    don't
mikhail zeleny@math.ucla.edu                                  tread
writing from the disneyland of formal philosophy                 on
"Le cul des femmes est monotone comme l'esprit des hommes."      me
