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Article #708Re: A note on Modal Logic that has nothing to do with Ikky Sex
From: Randall Holmes
Date: Tue, 22 Dec 1992 20:07
Date: Tue, 22 Dec 1992 20:07
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An additional comment: One expects trouble with Tarski's paradox when expressing the model theory of ZFC inside ZFC itself, of course. One can build a language inside ZFC which contains constants for all the objects of ZFC, but one cannot define satisfaction, and so truth, for sentences of this language. One can, of course, add truth for sentences of this language as a primitive notion (or reference for terms of this language) and state the necessary axioms for it, but this notion of truth will not be adequate in turn for sentences of the language augmented with the truth predicate. But there is no problem with defining truth in any given _model_ of ZFC (such models are sets), so this is not really a limitation on the model theory of ZFC in ZFC; it reflects the fact that the intended interpretation of ZFC is not the theory of a model of ZFC. -- The opinions expressed | --Sincerely, above are not the "official" | M. Randall Holmes opinions of any person | Math. Dept., Boise State Univ. or institution. | holmes@opal.idbsu.edu
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Newsgroups: sci.philosophy.tech Path: arc1-ca.pugleaf.net!sparky!uunet!pmafire!mica.inel.gov!guinness!opal.idbsu.edu!holmes From: holmes@opal.idbsu.edu (Randall Holmes) Subject: Re: A note on Modal Logic that has nothing to do with Ikky Sex Message-ID: <1992Dec22.200746.2507@guinness.idbsu.edu> Sender: usenet@guinness.idbsu.edu (Usenet News mail) Nntp-Posting-Host: opal Organization: Boise State University References: <1992Dec21.180311.14665@guinness.idbsu.edu> <1992Dec22.013357.18774@husc3.harvard.edu> <1992Dec22.195444.2427@guinness.idbsu.edu> Date: Tue, 22 Dec 1992 20:07:46 GMT Lines: 22