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>From: zeleny@zariski.harvard.edu (Mikhail Zeleny)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech
Subject: Re: Infinite Minds?
Message-ID: <1992Mar19.100550.10019@husc3.harvard.edu>
Date: 19 Mar 92 15:05:48 GMT
References: <1992Mar17.181431.20297@gpu.utcs.utoronto.ca> <1992Mar18.183651.26822@cs.ucf.edu>
Organization: Dept. of Math, Harvard Univ.
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In article <1992Mar18.183651.26822@cs.ucf.edu> 
clarke@acme.ucf.edu (Thomas Clarke) writes:

>> [...]

>Wild conclusions?  I merely try to make the point that it is plausible
>that the brain may not function digitally.  Until the Church-Turing thesis
>is rigorously proved or disproved, the question remains open.   

Pardon my intrusion, but what the fuck does Church's thesis (Turing, a
student of his, was rather a latecomer) have to do with the claim of
digital brain functioning?  As a matter of fact, McCulloch and Pitts, with
their semantical finiteness (<=> digital functioning) assumption already
implicit in the quaint title of their original AI manifesto, ``A Logical
Calculus of the Ideas Immanent in Nervous Activity'', made an explicit,
specious, unjustified identification of ``computability by an organism''
with Turing computability (of course, this didn't stop them from making
counterfactual claims contradicting the preceding: ``every net, if
furnished with a tape [...] can compute only such numbers as can a Turing
machine, [...and] each of the latter numbers can be computed by such a
net''; --- pray tell, where does the tape come from?), concluding with a
monumental misreading of Church's Thesis by conflating computability and
effective computability: ``This is of interest as affording a psychological
justification of the Turing definition of computability and its
equivalents, Church's $\lambda$-definability and Kleene's primitive
recursiveness: if any number can be computed by an organism, it is
computable by those definitions, and conversely.'' (See Boden's Philosophy
of AI anthology, page 37.)  Of course, this should have read: ``if any
number can be *effectively* computed by an organism, it is computable by
those definitions, and conversely''; however in this case it would have
been a non sequitur.

For the record, Church's thesis made its first appearance in 1935, in
Church's article ``An Unsolvable Problem of Elementary Number Theory''.
Church identified the class of *effectively* computable functions with that
of $\lambda$-definable functions, provably equivalent to that of recursive
functions; Turing, who at the time was Church's graduate student at
Princeton, merely extended the thesis in 1936 to what came to be known as
Turing machines, by proving that the class of functions computable thereby
is equivalent to the above.

Please try to avoid attributing this sort of nonsense to innocent parties.

`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'
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: Mikhail Zeleny                                                     :
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