Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site spar.UUCP Path: utzoo!watmath!clyde!burl!ulysses!ucbvax!decvax!decwrl!spar!ellis 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