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From: zeleny@sawtelle.math.ucla.edu (Michael Zeleny)
Subject: Re: Penrose's new book
Message-ID: <1994Oct22.195802.12955@math.ucla.edu>
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Organization: The Phallogocentric Cabal
References: <389im1$86u@mp.cs.niu.edu> <1994Oct22.005737.2249@math.ucla.edu> <38a67l$g8i@mp.cs.niu.edu>
Date: Sat, 22 Oct 94 19:58:02 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:21237 sci.philosophy.tech:16152

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

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

>>In article <389im1$86u@mp.cs.niu.edu> 
>>rickert@cs.niu.edu (Neil Rickert) writes:

>>>If Penrose's argument were a purely mathematical argument, you might
>>>have a point.  But Penrose's argument is intuitive, rather than
>>>mathematical.  It is an appeal to one's sense of plausibility.

>>Consider the issue in a different light.  Penrose imputes a certain
>>closure property to the theory of human cognitive performance.

>Yes, indeed, he does so impute.  It is rather foolish of him.

You must have attended the Marvin Minsky school of scientific debate.

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

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

This is certainly a novel angle.  Are you really suggesting that
senescence is a *cognitive* necessity?

>>                 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.

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

The key term here is "a priori".  Recall that we are talking about
abstract matters -- unless you manage to demonstrate that mortality
is essentially linked with cognition, I can just stipulate that the
mathematician is to ingest a periodic dosage of the elixir of youth,
just as you might stipulate that your Turing machine is to scrounge
around for extra tape.  Recall that the brain cells do not age.

>>                                     Any evidence that human cognitive
>>performance cannot be adequately modelled by finitistic theories --
>>exempli gratia, a plausible application of classical analysis thereto
>>-- will have the same effect.

>There is no persuasive evidence that human performance escapes finite
>limitations.

The beauty of the reflective argument is that it need not posit such
transcendence.  All Penrose requires is the cognitive implausibility
of an a priori fixed finite bound.  Incidentally, you seem to be
making the mistake of taking finitude to imply temporal boundedness.

>>                               In a nutshell, mathematical Platonism
>>furnishes adequate grounds for repudiating finitism, and the premisses
>>of AI along with it. 

>I don't hold to the Platonist school.  But even if one is a
>Platonist, there is nothing in that philosophy which would repudiate
>finite limitations on human cognitive abilities.

Platonism says that the forms lie within the human cognitive range.
The countervailing doctrine, which places a fixed bound on cognition,
is finitism.  Unfortunately, since the concept of finitude provably
resists all attempts at finite characterization, I never found the
doctrine intelligible.

cordially,                                                    don't
mikhail zeleny@math.ucla.edu                                  tread
writing from the disneyland of formal philosophy                 on
"Le cul des femmes est monotone comme l'esprit des hommes."      me
