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Article #5045Re: Continuos vs. discrete models Was: The size of electrons, ...
From: Robert Firth
Date: Mon, 16 Nov 1992 13:12
Date: Mon, 16 Nov 1992 13:12
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In article <350@mtnmath.UUCP> paul@mtnmath.UUCP (Paul Budnik) writes: >This well known result is called the Lowneheim and Skolem theorem. The >idea of the proof is that a formal system is a computer program for enumerating >theorems. The names of all real numbers created by such a program are >obviously countable. Well, yes, the names of any set of things created by an "enumeration" program muct be countable, by definition. But that's not what you originally claimed. You said: >For example the real numbers definable in any consistent formal system >are countable. By what sleight of hand did "definable" change into "enumerable"? Isn't that the old constructivist premise (or fallacy, as most of us think).
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Path: arc1-ca.pugleaf.net!sparky!uunet!ogicse!das-news.harvard.edu!cantaloupe.srv.cs.cmu.edu!crabapple.srv.cs.cmu.edu!fs7.ece.cmu.edu!news.sei.cmu.edu!firth From: firth@sei.cmu.edu (Robert Firth) Newsgroups: sci.physics Subject: Re: Continuos vs. discrete models Was: The size of electrons, ... Message-ID: <1992Nov16.131202.17710@sei.cmu.edu> Date: 16 Nov 92 13:12:02 GMT Article-I.D.: sei.1992Nov16.131202.17710 References: <1992Nov7.214329.24552@galois.mit.edu> <1992Nov13.194334.20447@sun0.urz.uni-heidelberg.de> <350@mtnmath.UUCP> Organization: Software Engineering Institute Lines: 16