Re: representing patterns and structures (Pat Hayes)
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Date: Tue, 22 Nov 1994 14:05:28 -0600
To: (Fritz Lehmann),,
From: (Pat Hayes)
Subject: Re: representing patterns and structures
Precedence: bulk
At  6:05 PM 11/21/94 -0600, Fritz Lehmann wrote:
>     Pat Hayes said:
>------------begin quote-------
>Years ago, complicated
>interactive CAD systems allowed notions of 'grouping', so you could specify
>eg. a pattern of holes all of a certain diameter* .....
>........<Fine, until> you wanted to
>fill in just one of these holes. This was impossible if the thing was
>specified this way, since in a real sense that particular hole-token didnt
>actually exist in the internal representation.
>-----------end quote------------
>     This issue is a very deep one, ..........

Nah, its not this full of philosphical gold-dust. Remember that in these
CAD systems this drawing exists on a screen right in front of you: the
answer to 'which hole' is 'this one right here, where the lightpen is
pointing'. And to say that the holes are intensional just introduces
unnecessary jargon. Things arent intensional, descriptions are; but if this
description is intensional then any description more complicated than a
simple indexical ("that one") is intensional (which indeed they all are, in
a sense, but not a very useful sense.)

I dont think this kind of discussion is necessary. I dont think we need get
involved with Criteria Of Identity in order to make useful progress on
figuring out how to describe exceptional cases to general patterns, and
treat the result as a pattern.

>     The only ways I see to approach this are to A. Be very careful about
>intensional descriptions --- you can (carefully) _describe_ the hole to
>be filled-in by inspecting all holes to see if any qualify under the
>description (you don't know the cardinality of the set of qualifying
>holes is one). 

These are just descriptions, thats all. Consider for example a pattern like

* * * * *
* * * * *
  * * *
* * * * *
* * * * *

which could be defined as something like 'a 5x5 square array with the
middles of the sides missing'. My point was only to suggest it might be
productive to think about the vocabulary necessary to say things like this
'the middles of the sides' (that the CAD system couldnt say). Calling these
'intensional' just raises dust. They are geometric/topological/...
descriptions, just as extensional as any other descriptions.

 B. Identify individuals only in the real physical world
>(as opposed to the abstract geometrical world), 

I agree. In fact, Idont believe in the 'abstract geometrical world'. It
seems to exist because mathematicians routinely treat isomorphism as
identity because they are only interested in structure which is preserved
under isomorphism. Theres no need to get one metaphysical knickers in a
twist over this harmless habit. 

However, Fritz, I would expect you NOT to hold this opinion, given your
enthusiasm for higher-order logics. The relations over which HO quantifiers
range are paradigm examples of individuals which arent in the real physical
world. The natural way to describe the meaning of an apparently 'abstract'
word is as a predicate or relation on physical individuals, as in 

"isa(x bottle) => round(x)"

Pat Hayes

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