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From: franka@mmintl.UUCP (Frank Adams)
Newsgroups: net.philosophy
Subject: Re: Metaphysics
Message-ID: <608@mmintl.UUCP>
Date: Mon, 19-Aug-85 18:12:55 EDT
Article-I.D.: mmintl.608
Posted: Mon Aug 19 18:12:55 1985
Date-Received: Fri, 23-Aug-85 04:47:40 EDT
References: <969@sphinx.UChicago.UUCP>
Reply-To: franka@mmintl.UUCP (Frank Adams)
Organization: Multimate International, E. Hartford, CT
Lines: 25
Summary: Are numbers real?


In article <969@sphinx.UChicago.UUCP> beth@sphinx.UChicago.UUCP
 (Beth Christy) writes:
>  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.

Are numbers real?  This is not obvious.  There is a great deal of
disagreement on this subject -- not least among mathematicians.  Have
you ever heard of intuitionism?

Mathematical philosophers basically fall into three groups.  One is the
formalists, who insist they are just manipulating rules, and that any
applicability to anything else is strictly incidental.

The intuitionists believe that mathematical objects (numbers, for short),
are solely constructs of the mind.  They conclude that the only valid
proofs are those which show how to accomplish the thing being proved.
In particular, they deny the "law of the excluded middle": that for any
proposition P, either P is true or P is false.  Thus one cannot prove
P by showing that not-P is contradictory.

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.