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Article 2392 of comp.ai.philosophy:
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>From: zeleny@brauer.harvard.edu (Mikhail Zeleny)
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: <1991Dec23.190337.6899@husc3.harvard.edu>
Date: 24 Dec 91 00:03:36 GMT
References: <1991Dec23.042312.10049@cambridge.oracorp.com> 
 <1991Dec23.112144.6884@husc3.harvard.edu> <1991Dec23.213632.18047@cambridge.oracorp.com>
Organization: Dept. of Math, Harvard Univ.
Lines: 76
Nntp-Posting-Host: brauer.harvard.edu

In article <1991Dec23.213632.18047@cambridge.oracorp.com> 
ian@cambridge.oracorp.com (Ian Sutherland) writes:

>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.

MZ:
>>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;

IS:
>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.

I was hoping to have made it clear that I was using that word in the same
sense as Markov.  Compare the discussion of "mathematical possibility" in
the book by Charles Parsons, "Mathematics in Philosophy".

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.

MZ:
>>My apologies for not having used the Internet idiot crutch, the ubiquitous,
>>reprehensible "smiley" punctuation.

IS:
>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.

Thank you, Mr Sutherland, but I am my own evil doppelganger ;-)

>-- 
>Ian Sutherland                          ian@cambridge.oracorp.com
>
>Sans peur

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