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From: curry@hpl.hp.com (Bo Curry)
Subject: Re: Zeleny on predictability
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Date: Thu, 3 Aug 1995 16:21:58 GMT
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: curry@hpl.hp.com (Bo Curry) writes:
: >It appears that your claim about confuting predictions
: >ultimately rests on the (in my view prior) claim that the
: >interpretation of such predictions is *impossible* through
: >"syntactic manipulation". If that's so, then you can't use
: >your purported ability to confute predictions as evidence for
: >the latter claim.

Michael Zeleny (zeleny@oak.math.ucla.edu) wrote:
: I did no such thing.  Arithmetic affords an example of a domain in
: principle amenable to such interpretation.  Those who claim otherwise,
: uniformly fail to specify the putative intrinsic factor necessarily
: responsible for human interpretive failure, contingent spatiotemporal
: limitations notwithstanding.  I find the expectation of such cognitive
: barrier infinitely more mysterious than the competing hypothesis that
: humans can always make a fortuitous guess concerning the consistency
: status of any true extension of PA.  Note that the latter is borne out
: by historical experience, whereas the former is justifiable by naught
: but an a priori imputation of unspecifiable intellectual limitations.

I do not doubt that "humans can always make a fortuitous guess".
I just don't see that such a guess qualifies as knowledge. Nor
does my reading of history lead me to believe that humans have
acquired, or will ever acquire, knowledge "concerning the
consistency status of any [arbitrary] true extension of PA".

Even if it were true that humans have this ability, it remains
to be shown that machines do not. You cannot simply *assume*
that they do not.

This whole argument seems often to be going around in circles.
Your claim (and Penrose's) depends on demonstrating (a) that
machines are subject to fundamental limitations on their
possible knowledge, (b) that humans are not subject to
similar limitations, and (c) that the limitations so
distinguishing humans from machines are in fact important ones.
Indeed, all three points have been addressed. However, it
seems to me that the rules and definitions change between
the answers y'all give to (a) and to (b).

I guess we won't come to agreement now. But I find Penrose's
argument, and its defense here, very unsatisfying. I've
enjoyed listening in on [the more civil parts of] the
discussion, though.

Bo

