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Article 2540 of comp.ai.philosophy:
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>From: jcollier@ariel.ucs.unimelb.edu.au (John Donald Collier)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech,sci.logic
Subject: Re: Penrose on Man vs. Machine
Message-ID: <1585@ariel.ucs.unimelb.edu.au>
Date: 8 Jan 92 07:06:55 GMT
References: <1992Jan7.031553.24886@oracorp.com> <1992Jan7.105117.7193@husc3.harvard.edu>
Followup-To: comp.ai.philosophy
Organization: University of Melbourne
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In <1992Jan7.105117.7193@husc3.harvard.edu> zeleny@zariski.harvard.edu (Mikhail Zeleny) writes in reply to Daryl McCullough:

>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.

What has seemed intuitively obvious in the past has often turned out
on closer examination to be completely false. 

It is quite unclear that we understand the second-order concepts
involved in any way that avoids the arguments that you are trying to
reply to. How can you tell that your understanding is not
representable in first order language? Certainly anything you can do
with it is so representable. So what's the point in arguing for
something more?  It seems pretty empty to me.

-- 
John Collier 			Email: jcollier@ariel.ucs.unimelb.edu.au
HPS -- U. of Melbourne		  	Fax:   61+3 344 7959
Parkville, Victoria, AUSTRALIA 3052


