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Article 2390 of comp.ai.philosophy:
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>From: ian@cambridge.oracorp.com (Ian Sutherland)
Newsgroups: sci.philosophy.tech,sci.logic,sci.math,comp.ai.philosophy
Subject: Re: Penrose on Man vs. Machine
Keywords: analytic arguments, reflection principle, standard model
Message-ID: <1991Dec23.213632.18047@cambridge.oracorp.com>
Date: 23 Dec 91 21:36:32 GMT
References: <1991Dec22.131401.6869@husc3.harvard.edu> <1991Dec23.042312.10049@cambridge.oracorp.com> <1991Dec23.112144.6884@husc3.harvard.edu>
Organization: ORA Corp, 675 Mass Ave, Cambridge, MA 02139
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In article <1991Dec23.112144.6884@husc3.harvard.edu> zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:
>MZ:
>>>As you undoubtedly are aware, all analytic arguments contain their
>>>conclusion in their premisses.  Penrose argues that we are capable of
>>>outdoing any algorithm; in order to do so he has to assume an equally
>>>powerful, but intuitively more plausible premiss.  It appears to me that he
>>>has succeeded in doing so, since the premiss that we can *potentially*
>>>determine the partial correctness of an arbitrary program by semantic
>>>reflection appears to me as intuitively unexceptionable as A.A.Markov's
>>>abstraction of potential realizability, which stipulates e.g. that the
>>>successor operation can be applied to an arbitrarily large integer.
>
>IS:
>>The premise is not that we can "potentially" determine the partial
>>correctness of an arbitrary program, it is that we CAN determine said
>>correctness.  If there's even one program we CAN'T determine the
>>partial correctness of, it may be the very one which describes our
>>reflection process.
>
>Don't be taken in by terminology.  Markov, who is, in effect defining his
>point of disagreement with Yessenin-Volpin (even though as a Politically
>Correct toady, he daren't speak the name of his dissident colleague), does
>not, qua constructivist, say that integers like 10^10^10 exist only
>potentially;

I wasn't saying anything about Markov.  YOU use the word "potentially"
in the text quoted above.  It is YOUR use of the word "potentially"
that I'm disagreeing with.

>MZ:
>>>In other words, by rejecting the assumption made by Penrose, you are
>>>implicitly committing yourself to ultra-intuitionism and its concept of
>>>feasible numbers.
>
>IS:
>>Perhaps I misinterpret your remarks (couched as they are in what
>>SEEMS TO BE quite heavy sarcasm) but I think not, not quite anyway.
>
>My apologies for not having used the Internet idiot crutch, the ubiquitous,
>reprehensible "smiley" punctuation.

I can't IMAGINE you using a "smiley" Mr. Zeleny.  I'd suspect some
evil force of having replaced you with a doppelganger if I ever saw
such a thing in a posting of yours.
-- 
Ian Sutherland                          ian@cambridge.oracorp.com

Sans peur


