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Article 2522 of comp.ai.philosophy:
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>From: zeleny@zariski.harvard.edu (Mikhail Zeleny)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech,sci.logic
Subject: Re: Penrose on Man vs. Machine
Message-ID: <1992Jan7.105117.7193@husc3.harvard.edu>
Date: 7 Jan 92 15:51:02 GMT
References: <1992Jan7.031553.24886@oracorp.com>
Organization: Dept. of Math, Harvard Univ.
Lines: 43
Nntp-Posting-Host: zariski.harvard.edu

In article <1992Jan7.031553.24886@oracorp.com> 
daryl@oracorp.com writes:

>Mikhail Zeleny writes:

MZ:
>> The point is not whether human beings can solve all instances of the
>> halting problem, or tell whether an arbitrary collection of axioms is
>> consistent, but that each time they do so in any particular case,
>> their reasoning is essentially non-algorithmic, as claims Penrose.

DMC:
>But, as I have pointed out, the argument that human reasoning is
>non-algorithmic depends on the assumption that humans can solve all
>instances of the halting problem.

And, as I have pointed out, your reasoning can only convince those who
share your formalist understanding of mathematics.  Since the notions of a
program halting on a given input, or a theory being consistent are
fundamentally second-order, i.e. non-recursive, our ability to understand
them is sufficient evidence of our ability to perform non-algorithmic
tasks.  Indeed, it is arguably true that all understanding is fundamentally
non-algorithmic; however, in view of our past disagreements, I shan't
repeat an argument to that effect, limiting myself to the claim that it is
intuitively obvious to me that I am capable of understanding.

>Daryl McCullough
>ORA Corp.
>301A Harris B. Dates Dr.
>Ithaca, NY 14850-1313


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