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Article 1964 of comp.ai.philosophy:
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>From: bill@NSMA.AriZonA.EdU (Bill Skaggs)
Newsgroups: rec.arts.books,sci.philosophy.tech,comp.ai.philosophy
Subject: Re: Existence
Message-ID: <1991Dec8.175957.2225@arizona.edu>
Date: 9 Dec 91 00:59:56 GMT
Article-I.D.: arizona.1991Dec8.175957.2225
References: <1991Dec7.123551.2220@arizona.edu> <1991Dec7.173732.6277@husc3.harvard.edu> 
 <1991Dec7.205153.2222@arizona.edu> <1991Dec8.103340.6300@husc3.harvard.edu>
Reply-To: bill@NSMA.AriZonA.EdU (Bill Skaggs)
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In article <1991Dec8.103340.6300@husc3.harvard.edu> zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:
>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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>: Mikhail Zeleny                                                     :
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