Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site mmintl.UUCP Path: utzoo!linus!philabs!pwa-b!mmintl!franka 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.