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Article 2610 of comp.ai.philosophy:
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>From: chandra@cannelloni.cis.ohio-state.edu (B Chandrasekaran)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech,sci.logic
Subject: Re: Penrose on Man vs. Machine
Message-ID: <1992Jan9.221032.12622@cis.ohio-state.edu>
Date: 9 Jan 92 22:10:32 GMT
References: <1992Jan9.110732.7279@husc3.harvard.edu> <1992Jan9.190644.331@nynexst.com> <gtall.694991248@ogre>
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In <1992Jan9.190644.331@nynexst.com> gene@nynexst.com (Gene Miller) writes:

>
>    1) When I think of 5 pennies, I may "see" a picture of them in my mind,
>    perhaps as the vertices of a "W".
>
>    2) When I think of aleph_0 pennies, I may "see" them lined up ahead
>    of me, like the ties of a railroad track, going off to the horizon,
>    with no visible end. The projective geometry that allows me to
>    "see" the infinitude of the set is unconscious, requiring no
>    symbolic reasoning.
>
>    3) When I think of open sets of the real line, I may "feel" the line as
>    a "necklace", with the points as little hard beads on a string. When the
>    string is broken, the bead at which it is broken terminates one of
>    necklace segments, and the other segment is left unterminated (open).
>
>Do not these visual and kinesthetic images serve as aids in reasoning
>about these objects?
>
>Similarly, could not all mathematical reasoning (including the
>consistency of arithmetic) be based on built-in or learned
>perceptual and motor capabilities intended to manipulate things
>in the physical world (occasionally aided by symbol manipulation).
>
>>And could not this alleged "analogue computer" be simulated on a
>>digital computer?
>
>Note: More rigorous phrasing of these ideas are welcomed.

The idea that "understanding" is anchored on perceptual and kinesthetic
representations is very much in the air.  At least part of the puzzle
of the CR can be resolved by positing mediation by images in various
perceptual modalities.  A year or so ago I wrote a note elaborating on
this. Anyone interested, let me know and I will see if I can dig that
up.


