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Article 1930 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: <1991Dec7.070815.6257@husc3.harvard.edu>
Date: 7 Dec 91 12:08:13 GMT
References: <1991Dec5.202144.3220@vax.oxford.ac.uk> <1991Dec6.165648.6234@husc3.harvard.edu> <1991Dec6.204854.2218@arizona.edu>
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In article <1991Dec6.204854.2218@arizona.edu> 
bill@NSMA.AriZonA.EdU (Bill Skaggs) writes:

William Chesters, Wadham College, Oxford:
>>Platonism isn't the only philosophy of mathematics you know!  There are 
>>people who (horror) don't think real numbers exist.

Mikhail Zeleny, Harvard, Mass:
>>Their opinions are absolutely irrelevant to mathematics as it stands.

Bill Skaggs, Center for Neural Systems, Memory, and Aging, Arizona
>This is a fantastic exchange, because it wonderfully illustrates the
>most common trap philosophers fall into, which I call the "In the
>beginning was the word" fallacy:  the assumption that words have
>well-defined meanings, independent of how they are learned and used,
>and that by careful analysis we can uncover those meanings.

You are being presumptious here.  In philosophical discourse, we allow the
meaning of words to be determined in part by the arguments of philosophers
who used them before us, who applied their analytic powers to the study of
concepts, rather than word meanings as such.  Philosophical discourse,
unlike the discourse of modern linguistics, is highly prescriptive,
conforming to the precedent set by this tradition; however, since it often
resembles natural language, an outsider can easily fall into the common
trap of assuming that philosophical terms have the same meaning as their
vulgar homonyms.

BS:
>The word at issue here is "exist".

And the relevant tradition is exemplified by the writings of Plato,
Aristotle, Anselm, Berkeley, Kant, Russell, Quine, and Church.

BS:
>What does it mean to say "Real numbers exist"?  Both Chesters and
>Zeleny believe that this sentence is either true or false.  In fact
>it is merely meaningless.

Only to those unduly preoccupied with vulgar discourse.

BS:
>The meanings of words are learned by watching how other people use
>them.  Many words are only used when certain conditions are present,
>and in the absence of those conditions are meaningless.  "Existence"
>is one of those words.  When it is applied to a name or to a concrete
>description, we all have some notion of what it means:  when I say
>"Benjamin Disraeli existed but Sherlock Holmes did not", we all know
>that one of the consequences of this is that an archaeological
>study of 221B Baker Street is unlikely to turn up traces of the
>presence of Sherlock Holmes, whereas a study of Disraeli's residence
>(wherever it was) is likely to yield something.  When I say "The
>present king of France does not exist", we all know that one of the 
>consequences is that it makes no sense to ask "What is his name?"

The way the meaning of a word is learned in natural conditions has no
bearing on its specialized use, determined by a different sort of
consensus. 

BS:
>When the attempt is made, though, to apply "existence" to abstract
>descriptions, we find no consensus.  People ordinarily don't use
>the word under those conditions, and when somebody tries to, we
>don't understand what is meant.  We don't know what the consequences
>are.  ***"Real numbers exist."***  So what?  What are the consequences?
>What difference does it make whether the number pi "exists"?

None whatsoever to the hoi polloi.  What the fuck are you doing posting to
a philosiophy newsgroup?

BS:
>It is of course possible to extend a word into a domain in which it
>is not ordinarily used, by explicitly agreeing to use it under
>specific conditions.  Mathematicians are doing this when they make
>axioms such as "Through any two points there exists exactly one
>straight line."  This axiom is an agreement on how to use the words
>"point", "line", and "exist".   To think of it as asserting a fact
>about points and lines is to be very confused. 

To you, the vast majority of mathematicians would appear very confused.
Given your self-professed appreciation of consensus, I find your lack of
reflection unpardonable.

BS:
>If we remember that words are only defined as precisely as they
>are used -- including words such as "existence" and "truth", we
>will avoid a lot of useless squabbling.

See Plato and Tarski on truth, and avoid a lot of useless squabbling.

>	-- Bill


`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'
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: Mikhail Zeleny                                                     :
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