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From: zeleny@oak.math.ucla.edu (Michael Zeleny)
Subject: Re: Penrose's new book
Message-ID: <1994Oct24.031910.4610@math.ucla.edu>
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Organization: The Phallogocentric Cabal
References: <38a67l$g8i@mp.cs.niu.edu> <1994Oct22.195802.12955@math.ucla.edu> <38egde$p9l@mp.cs.niu.edu>
Date: Mon, 24 Oct 94 03:19:10 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:21268 sci.philosophy.tech:16166

In article <38egde$p9l@mp.cs.niu.edu> 
rickert@cs.niu.edu (Neil Rickert) writes:

>In <1994Oct22.195802.12955@math.ucla.edu> 
>zeleny@sawtelle.math.ucla.edu (Michael Zeleny) writes:

>>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:

>>>>              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 was not my intention to so suggest.  However I do believe it to
>be the case for the type of cognitive apparatus we have.

Even if true, this belief would not suffice.  You would need a tight
nomological connection between cognitive function and disposition to
aging and decrepitude.  I am unaware of any evidence for that.

>>>>                 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.

>Finite life expectancy is not required to demonstrate cognitive
>limits.  The finite totality of atoms on earth, or even within the
>cosmos according to some cosmological theories, suffices to set
>finite limits.

You might have mentioned the finitude of brain cells, which arguably
entails a finite bound on the number of discernible brain states.  But
none of this suffices to buttress your case.  Recall that pervasive
physical atomism of the sort you presuppose, is by no means a foregone
conclusion -- there is some debate as to whether or not it is implied
by quantum theory.  Moreover, physical atomism entails atomic psycho-
semantics only on the assumption of psycho-physicalism, which requires
independent support.  Indeed, though Penrose does not interpret it so,
the Lucas argument can be taken as militating against certain forms of
physicalism.

>Was Penrose talking about abstract matters, or about human
>intelligence?  If all Penrose claims is that a finite computer could
>not emulate a abstract imagined eternal and infinite intelligence not
>restricted by the physical limitations of life on earth, then I will
>grant him that.

The question of Platonism is, to what extent man embodies an abstract
and unbounded intelligence.  Incidentally, this point gives rise to an
empirically verifiable prediction -- given the immminent convergence
of our computational resources with the bounds ascribed to the brain,
we might be able to witness a mathematical contest between software
and its human custodians, comparing it to the historical record of
mathematical growth.

>>                        Recall that the brain cells do not age.

>If brain cells do not age, but cognitive abilities do deteriorate
>with age, you would seem to have good empirical support for the idea
>that mortality is essentially linked with cognition.

Perhaps so, but your entailment is going in the wrong direction --
recall that the challenge is to establish that mortality is implied by
cognition, rather than to belabor the obvious -- but according to
Descartes, hardly conceptually necessary -- dependence of cognitive
function on the integrity of its physical substratum.

>>>>                                     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.

>This gives the idea of argument from ignorance a whole new meaning.
>With sufficient ignorance, much seems implausible, and apparently the
>implausibility resulting from that ignorance is to be considered a
>legitimate arguing point.

I see the matter in a different light.  After all, it is your side who
tell me that I am doomed to the failure of recognizing the felicity of
a faithful model of my cognitive performance.

>>>>                               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.

>To "lie within the human cognitive range" is such a vague condition,
>that it could easily be consistent with finitism.

Not if the condition is taken in its conventional sense -- see for
instance Bernays' classic article reprinted by Benacerraf and Putnam.

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
