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From: bill@synapse.nsma.arizona.EDU (Bill Skaggs)
Newsgroups: comp.ai.philosophy
Subject: Re: Minds, machines, and Godel
Message-ID: <898@organpipe.UUCP>
Date: 21 Jan 91 23:55:54 GMT
References: <28154@cs.yale.edu> <1991Jan19.055638.27731@bronze.ucs.indiana.edu> <28203@cs.yale.edu> <1991Jan21.022919.13895@bronze.ucs.indiana.edu> <4963@media-lab.MEDIA.MIT.EDU>
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In article <4963@media-lab.MEDIA.MIT.EDU> 
minsky@media-lab.media.mit.edu (Marvin Minsky) writes:
>
>  [ . . . quotation . . . ]  
>
>But how 'bout accepting:
>
>
>  The set of arithmetical statements encompassed by human
>  competence includes statements that are outside the capacities of
>  any Turing Machines that are restricted to deducing the theorems of 
>  certain consistent deductive systems -- and whose output strings are
>  interpreted only in that sense.
>
>And this would be of little interest to AI-ers.  At least, to those
>trying either to make smart machines or constructive theories of
>psychology or brain function.

	I'm not quite sure I know how to parse your sentence.  If I
understand it, it means:

	For any consistent deductive system S of a certain class, 
	there exists an	arithmetical statement A such that:  1) A is 
	encompassed by human competence; and 2) A is outside the 
	capacity of any Turing Machine TM which is restricted to
	deducing consequences of S.

	I think Roger Penrose would agree with this assertion (though
I wouldn't).  Penrose seems to believe in a Platonic notion of absolute
mathematical truth to which humans have priveleged access.  He seems to
think that the collapse of quantum wave-functions, which (he says) 
cannot be modeled by differential equations, is crucial to this access.

	If I accepted Penrose's argument (I don't), and I were interested
in building a machine with human intelligence, I would be trying to 
figure out how to incorporate quantum effects into it.  So these sorts
of considerations *could* be of interest to AI people, if only they
were correct.