From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!wupost!uunet!psinntp!scylla!daryl Thu Jan  9 10:34:04 EST 1992
Article 2553 of comp.ai.philosophy:
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>From: daryl@oracorp.com
Subject: Re: Penrose on Man vs. Machine
Message-ID: <1992Jan8.160615.23680@oracorp.com>
Organization: ORA Corporation
Date: Wed, 8 Jan 1992 16:06:15 GMT

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?

In another post, Mikhail Zeleny writes:

> I trust that you understand the concept of a finite order group.  On
> the other hand, no Turing machine could duplicate that feat, given
> that the second-order concept of finitude is inherently beyond the ken
> of a recursive mind.  Case closed.

I agree that finiteness is a second-order concept, but there is no
evidence that one must have a second-order mind to understand the
concept of finiteness, any more than one must have an infinite mind to
understand the concept of infinity, or an uncountably infinite mind to
understand the concept of uncountable infinities.

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



