From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!rpi!think.com!wupost!micro-heart-of-gold.mit.edu!news.media.mit.edu!minsky Thu Jan  9 10:34:22 EST 1992
Article 2583 of comp.ai.philosophy:
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>From: minsky@media.mit.edu (Marvin Minsky)
Subject: Re: Penrose on Man vs. Machine
Message-ID: <1992Jan9.002732.29965@news.media.mit.edu>
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Cc: minsky
Organization: MIT Media Laboratory
References: <1992Jan8.160615.23680@oracorp.com>
Date: Thu, 9 Jan 1992 00:27:32 GMT
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In article <1992Jan8.160615.23680@oracorp.com> daryl@oracorp.com writes:
>Mikhail Zeleny writes:
>
>> 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.
>
>I almost let this claim slip by without comment, but it is completely
>incorrect. The question of whether a Turing machine program halts on a
>given input is definitely *not* second-order! It is perfectly definable
>in first-order Peano arithmetic. Perhaps you meant that it is not a
>*recursive* notion?

Woops.  The question of whether a Turing machine halts on a
*particular* input is in fact recursive.  It either does or it
doesn't, and in the Kleene forumlation of the theory it is a copnstant
function which is either always 1 or always 0.

I wonder how much of this thread has made the mistake of thinking that


