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Article 1946 of comp.ai.philosophy:
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>From: bill@NSMA.AriZonA.EdU (Bill Skaggs)
Newsgroups: sci.philosophy.tech,comp.ai.philosophy
Subject: Re: Existence
Message-ID: <1991Dec7.205153.2222@arizona.edu>
Date: 8 Dec 91 03:51:52 GMT
References: <1991Dec6.204854.2218@arizona.edu> <1991Dec7.070815.6257@husc3.harvard.edu> 
 <1991Dec7.123551.2220@arizona.edu> <1991Dec7.173732.6277@husc3.harvard.edu>
Reply-To: bill@NSMA.AriZonA.EdU (Bill Skaggs)
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Mikhail Zeleny:
>Mathematical realism is a necessary assumption if you want to explain the
>meaningfulness of mathematical discourse, and especially if you want to
>account for the truth of its theorems, whose terms must be regarded as
>denoting before they can be ascribed any truth-value.

All right, good.  You have begun to tell us how you want to use
the word "exist".  You want it to carry the consequence that if
a thing does not exist, statements about that thing have no
meaning.  Or, contrapositively, if a statement about something
is meaningful, then that thing exists.

There are certainly advantages to this usage, but let me point out
that it also leads to a certain amount of awkwardness.  In your
usage, if  "Sherlock Holmes did not exist" is true, then the 
statement "Sherlock Holmes lived at 221 Baker Street" is
meaningless.  Since the statement is *not* meaningless, you
have to believe that Sherlock Holmes existed, in some sense,
don't you?

I prefer not to force "exist" to carry this baggage.  I would
like to ascribe meaning to statements about fictional things --
then I am free to treat mathematical entities as useful fictions
without getting into trouble, am I not?

MZ:
> . . . given that it is not clear what sort of distinction between 
>the two will respect the practice of modern mathematics, . . .

I don't accept this appeal to the "practice of modern mathematics".
When I was doing mathematics, I was interested in these sorts of
questions, but I couldn't talk to anybody about them because 
nobody cared.  Modern mathematicians are too busy studying the
properties of Hilbert space (for example) to worry about whether
Hilbert space "exist"s.  The few who are willing to express
opinions are mostly formalists or operationalists.

	-- Bill


(I've stopped cross-posting to rec.arts.books -- this discussion
doesn't belong there.)


