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From: ellis@spar.UUCP (Michael Ellis)
Newsgroups: net.philosophy
Subject: Re: Metaphysics
Message-ID: <481@spar.UUCP>
Date: Fri, 23-Aug-85 07:57:28 EDT
Article-I.D.: spar.481
Posted: Fri Aug 23 07:57:28 1985
Date-Received: Sun, 25-Aug-85 00:52:19 EDT
References: <969@sphinx.UChicago.UUCP> <608@mmintl.UUCP>
Reply-To: ellis@spar.UUCP (Michael Ellis)
Organization: Schlumberger Palo Alto Research, CA
Lines: 42

>>Numbers are constructs/patterns designed by the mind to
>>represent reality.  After all, there's no such physical thing as a 3.4.
>>Nevertheless, numbers are real, and, in fact, your science depends on
>>them quite heavily. [Beth Christy]
>
>Are numbers real?  This is not obvious.  There is a great deal of
>disagreement on this subject -- not least among mathematicians.
>...
>The third group, which is probably the largest, thinks numbers are real,
>but doesn't really know what they are.  A good answer to that question
>would be most appreciated. [Frank Adams]

    Bertrand Russell's analysis of the nature of numbers is the most
    appealing I've heard. He starts with the classical paradox..

	I have red apples     => Each apple was red
	I have ten fingers    => Each finger was ten???

    From Russell's History of Western Philosophy (Simon and Schuster):

    "The complete answer, as regards propositions in which `ten' occurs is
    "that, when these propositions are fully analyzed, they are found to
    "contain no constituent corresponding to the word `ten'. To explain
    "this in the case of such a large number as ten would be complicated; let
    "us therefore, substitute
     		   `I have two hands'
    "This means:

	"There is a such that there is b such that a and b are not identical
	"and whatever x may be, `x is a hand of mine' is true when, and only
	"when, x is a or x is b

    "Here the word `two' does not occur. It is true that two letters a and b
    "occur, but we do not need to know that they are two.. Thus numbers are,
    "in a precise sense, formal.

    It is left as an exercise for the diligent reader to remove any
    numerical reference from:

       	       	  `I have ten fingers' 

-michael