Re: Do completed infinite totalities exist? Was: Lowneheim-Skolem theorem

Article View: sci.logic

Article #569

#569

From: Torkel Franzen
Date: Sat, 21 Nov 1992 18:54

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   >Everything in mathematics is "relative" to some formal system. To talk
   >about what is absolutely true independent of a formal system is philosophy
   >not mathematics.

  The distinction is quite simple. "Provability in T" is an example of a
concept that has a formal system as a parameter, "uncountable" is an
example of a concept that has no formal system as a parameter, whether
explicit or implicit.

  "Absolute truth" has nothing to do with this. It's just a matter of what
we say and mean in mathematics. The notion that "everything in mathematics is
relative to some formal system", on the other hand, is the expression of
some philosophical doctrine.

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Newsgroups: sci.logic
Path: arc1-ca.pugleaf.net!sparky!uunet!paladin.american.edu!news.univie.ac.at!hp4at!mcsun!sunic!sics.se!torkel
From: torkel@sics.se (Torkel Franzen)
Subject: Re: Do completed infinite totalities exist? Was: Lowneheim-Skolem theorem
In-Reply-To: paul@mtnmath.UUCP's message of 21 Nov 92 16:49:29 GMT
Message-ID: <TORKEL.92Nov21195445@bast.sics.se>
Sender: news@sics.se
Organization: Swedish Institute of Computer Science, Kista
References: <1992Nov17.124233.24312@oracorp.com> <TORKEL.92Nov20160605@lludd.sics.se>
 <369@mtnmath.UUCP>
Date: Sat, 21 Nov 1992 18:54:45 GMT
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