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Article 2787 of comp.ai.philosophy:
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>From: rdouglas@cs.wpi.edu (***** Rob Douglas ****)
Newsgroups: sci.philosophy.tech,sci.logic,sci.math,comp.ai.philosophy
Subject: Re: Penrose on Man vs. Machine
Message-ID: <1992Jan16.182450.9851@wpi.WPI.EDU>
Date: 16 Jan 92 18:24:50 GMT
References: <1991Dec23.165606.5935@oracorp.com> <1991Dec23.135321.6894@husc3.harvard.edu> <1991Dec27.051804.6985@cambridge.oracorp.com> <1991Dec27.184248.6939@husc3.harvard.edu> <17455.296842ba@amherst.edu>
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In article <17455.296842ba@amherst.edu>, djvelleman@amherst.edu writes:
|> 
|>   A while back, the following claim was made:
|> 
|> In article <1991Dec27.184248.6939@husc3.harvard.edu>,
zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:
|> > 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.
|> 
|>   The discussion has drifted away from this issue, but recently it has
|> returned.  Perhaps it is appropriate therefore to respond to this claim.
|>   This whole discussion started out, I think, with a discussion of Penrose's
|> "Godelian argument".  For analyzing that argument, the point is precisely
|> whether human beings can solve all instances of the halting problem, or tell
   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|> whether an arbitrary collection of axioms is consistent.  The argument depends
|> on this as an unstated premise; without it, the argument fails.  It may
|> very well be true that our reasoning is "essentially non-algorithmic", as
|> Mr. Zeleny claims (although I doubt it), but the question was not whether or
|> not this is true, but rather whether or not Penrose's argument establishes
|> it.  I don't think it does.
|> 

In article <1992Jan15.190843.1636@wpi.WPI.EDU>, rdouglas@cs.wpi.edu (***** Rob Douglas ****) writes:
|> 
|> On a slightly different note: I seem to remember having seen an argument that
|> claimed to prove that the human mind was more powerful than a Turing machine.
|>  It essentially stated that a human being can solve the halting problem, and
|> we all know that a Turing machine cannot, so a human is more powerful. 
|> This is not true. In order to solve the halting problem, the solver has to be
|> guaranteed to give an answer to every yes/no question.  I know of at least one
|> question which no person is yet guaranteed to answer
|> correctly yes or no.  Is the problem <IS P = NP?> solvable? No person can
|> tell you the answer.  Therefore, humans cannot solve the halting problem.
|> 

I just saw this post about whether or not humans can solve every instance of
the halting problem.  I only know of only one instance of the halting problem.
In order to be able to be said to solve the halting problem, by definition of the
problem, one has to be able to tell correctly which machines will halt for which
inputs, and which will not.  This means it includes every machine.  As I have
pointed out, human's cannot solve the halting problem.

-- 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~  Rob Douglas                         |  email:                       ~ 
~  AI Research Group                   |       rdouglas@cs.wpi.edu     ~
~  Worcester Polytechnic Institute     |  Fuller Labs Room 239         ~
~  Computer Science Department         |  (508) 831-5005               ~
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-- 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~  Rob Douglas                         |  email:                       ~ 
~  AI Research Group                   |       rdouglas@cs.wpi.edu     ~
~  Worcester Polytechnic Institute     |  Fuller Labs Room 239         ~
~  Computer Science Department         |  (508) 831-5005               ~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


