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Article 5534 of comp.ai.philosophy:
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>From: minsky@media.mit.edu (Marvin Minsky)
Subject: Re: New Foundations (was Re: penrose)
Message-ID: <1992May10.151743.23216@news.media.mit.edu>
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Cc: minsky
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References: <1992May6.220605.26774@unixg.ubc.ca> <1992May8.015202.10792@news.media.mit.edu> <1992May9.184456.7359@guinness.idbsu.edu>
Date: Sun, 10 May 1992 15:17:43 GMT
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In article <1992May9.184456.7359@guinness.idbsu.edu> holmes@opal.idbsu.edu (Randall Holmes) writes:
>In article <1992May8.015202.10792@news.media.mit.edu> minsky@media.mit.edu (Marvin Minsky) writes:
>...lots of deletions...
>>  Wow, gee.  Now "being careful" becomes part of the thesis!  Well,
>>van Quine was awfully careful when he formulated "new foundations".
>>And Barkley Rosser found the mistake.  The system was in fact
>>inconsistent.
>>
>
>This is deceptive.  "New Foundations" is not known to be inconsistent;
>Quine made a mistake in stating the stratification restrictions for
>relations, as opposed to sets, which enabled Rosser to deduce the
>Burali-Forti paradox.  (Quine has made a number of mistakes in stating
>conqeuquences of NF and its variants, like everyone else who has
>worked with this system). The set comprehension axiom of New
>Foundations is consistent...

 Torkel Franzen has corrected me about that: "the inconsistency was
not in NF but the first version of Quine's system ML (in which he had
an impredicative class comprehension axiom)."  In any case my
complaint is that Penrose seems to be confusing "an algorithm for
producing arithmetical truths" with "a procedure that can be carried
out by a computer program" -- and this is the cornerstone of his
assertion that the brain is not an algorithm.  In other words, he
seems to insist on regarding a human's activity as the production of
some sort of formal proof in some consistent logic.  I find this an
astonishing and absurd assumption and cannot see why so many
philosophers, e.g., Lucas, go along with it.  (Quine does not, by the
way.)

.


