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From: smaill@dcs.ed.ac.uk (Alan Smaill)
Subject: Re: Penrose's new book
In-Reply-To: rickert@cs.niu.edu's message of 21 Oct 1994 23:59:33 -0500
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References: <389im1$86u@mp.cs.niu.edu> <1994Oct22.005737.2249@math.ucla.edu>
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Date: Sun, 23 Oct 1994 11:26:15 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:21252 sci.philosophy.tech:16156

Neil Rickert writes:
In article <38a67l$g8i@mp.cs.niu.edu> rickert@cs.niu.edu (Neil Rickert) writes:


rickert> In <1994Oct22.005737.2249@math.ucla.edu>
rickert> zeleny@oak.math.ucla.edu (Michael Zeleny) writes:

>> The property in question involves the ability to judge the
>> consistency of an arbitrarily complex formal system.

rickert> Such a formal system might be so complex that no human could
rickert> even read the complete set of axioms within his or her
rickert> lifetime.  For a system of such complexity, there could be no
rickert> ability to judge.

Penrose's argument applies to something like the collective mathematical
community.  From that point of view, there is no need to restrict attention
to a single lifetime.

>> It is highly implausible that any finite increase in complexity
>> will a priori rule out the possibility of making a correct judgment
>> in this matter.

rickert> This asserted implausibility rests on an undemonstrated
rickert> assumption that you have solved the problem of eternal life.

Again, the individual lifespan is not important here.

-- 
Alan Smaill                       JANET: smaill@uk.ac.ed.lfcs
LFCS, Dept. of Computer Science   UUCP: ..!mcvax!ukc!lfcs!smaill
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