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Article 1953 of comp.ai.philosophy:
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>From: zeleny@zariski.harvard.edu (Mikhail Zeleny)
Newsgroups: rec.arts.books,sci.philosophy.tech,comp.ai.philosophy
Subject: Re: Existence
Message-ID: <1991Dec8.103340.6300@husc3.harvard.edu>
Date: 8 Dec 91 15:33:38 GMT
References: <1991Dec7.123551.2220@arizona.edu> <1991Dec7.173732.6277@husc3.harvard.edu> <1991Dec7.205153.2222@arizona.edu>
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In article <1991Dec7.205153.2222@arizona.edu> 
bill@NSMA.AriZonA.EdU (Bill Skaggs) writes:

>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.

BS:
>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.

No.  First of all, you are running afoul of the Parmenides Principle: all
that can be said, has to deal with things that exist.  Furthermore, you
have to substitute `truth-value' for `meaning' in the above.  To paraphrase
in a way that makes sense: if a term does not denote, statements containing
that term are neither true nor false; on the other hand, their
meaningfulness depends on the meaningfulness of the said term.

BS:
>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?

This is getting complicated, but I'll try to explain.  Your statement
`Sherlock Holmes did not exist' can only be regarded as true if analyzed as
elliptic.  My preferred analysis is as follows: `The concept expressed by
the name `Sherlock Holmes' had no extension.'  (Russell would do it
differently: `There was no unique object satisfying all of the properties
abbreviated by the name `Sherlock Holmes'.')  But this is only true in an
ordinary context; in indirect speech (oratio obliqua), according to Frege,
the name `Sherlock Holmes' denotes the concept it expresses in ordinary
context.  So while the statement `Sherlock Holmes lived at 221 Baker
Street' is neither true nor false (yet meaningful, unlike `Grzpuntzl lived
at 221 Baker Street'), it can be treated as ellipsis of a true statement
that has the term occurring in oratio obliqua: `Arthur Conan Doyle tells us
that Sherlock Holmes lived at 221 Baker Street.'  Hence the importance of
recognizing the author for semantic analysis of fictional utterances.

BS:
>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?

The problem with treating mathematical entities as useful fictions is that
we want them to be true in an ordinary context of the proof-theoretic
turnstile (\vdash for the TeX-literate) : `|-- 7 + 5 = 12'; we don't want
to say that only `Mathematicians claim that 7 + 5 = 12' is literally true.
Of course, for a deconstructionist, the latter alternative would be
preferable, simply because she wants to deny the truth of scientific
discourse. 

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

BS:
>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.

Sorry, Bill, this consideration carries no weight.  You can indeed do
mathematics unreflectively, concentrating on the syntactical aspects;
however once you begin to think about its meaning, semantic issues like the
above rear their ugly heads.  I submit that this is the reason that so many
mathematicians, when pondering philosophical matters, come to embrace
Platonism. 

>	-- Bill

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

On the contrary, anything having to do with semantics of fictional
discourse certainly belongs in rec.arts.books.


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