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>From: ian@cambridge.oracorp.com (Ian Sutherland)
Newsgroups: sci.philosophy.tech,sci.logic,sci.math,comp.ai.philosophy
Subject: Re: Penrose on Man vs. Machine
Keywords: the limits of human understanding: no such thing
Message-ID: <1991Dec27.051804.6985@cambridge.oracorp.com>
Date: 27 Dec 91 05:18:04 GMT
References: <1991Dec23.165606.5935@oracorp.com> <1991Dec23.135321.6894@husc3.harvard.edu>
Organization: ORA Corp, 675 Mass Ave, Cambridge, MA 02139
Lines: 68

DMC:

>Therefore, in these cases, Penrose' arguments amount to the following:
>
>    (1) Assuming that we can tell which Turing machines H are partially
>        correct for solving the halting problem, then our reasoning
>        is nonalgorithmic.
>
>    (2) Assuming that we can tell which theories are sound, then our
>        reasoning is nonalgorithmic.
>
>In other words, assuming that we can do things that no machine can do,
>then we can do things that no machine can do.

MZ:
>Quite so.  As I stated earlier, all analytic arguments can be
>construed as a form of begging the question by an opponent who doesn't
>accept the intuitive validity of their premises.

DMC:

>Agreed, the point of such an argument is to reduce the truth of some
>questionable statement to the truth of some statements that we find
>more intuitively valid. However, I think that Penrose' premises, that
>we can solve all instances of the halting problem, and that we can
>tell whether an arbitrary collection of axioms is consistent, is much
>*less* plausible than his conclusion, that our minds are not
>algorithmic.

MZ:

>Our intuitions differ.  This, in effect, is what your criticism of Penrose
>amounts to.  Fine; this is how all philosophy, from Plato to Kripke, has
>been done.  Just try not to delude yoursenf into thinking that you have
>refuted his argument.

It may be that this is all the response that can reasonably be made,
Mr. Zeleny, but could you give some reasons why you feel that human
beings can solve all instances of the halting problem, or tell
whether an arbitrary collection of axioms is consistent?  I think
that there are purely physical arguments that can be made that
suggest that the human brain is the processing agent then a single
human can't possibly do more than a single finite automaton (albeit
with a very sophisticated program and a LARGE number of states).  What
would you say to such arguments?  Do you believe that some of this
processing goes on OUTSIDE the physical brain?  Do you believe that
neurons in a person's brain can manifest infinitely many different
states that can cause infinitely many different distinguishable
behaviors?  Do you believe that there's some kind of physical
mechanism in human brains that effectively acts as a nonrecursive
oracle?

At the risk of being labeled ignorant, I'd appreciate it if any
responses to the above would eschew references to various "isms" or
existing philosophical schools of thought on these matters, and
simply explain.  I am not a professional philosopher (merely an
amateur lover of knowledge :-) and, judging from references in some of
your recent postings, any such references will go right past me.

>There is, however, ample *empirical* evidence of consistency of ZFC; surely
>this result must be considered as part of mathematics.

Surely it is NOT, since "empirical evidence" of the sort you mention
has no weight in mathematics.
-- 
Ian Sutherland                          ian@cambridge.oracorp.com

Sans peur


