Meaning, Presuppositions, Truth-relevance, G�del's Theorem and the Liar Paradox
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From: Daryl McCullough on 13 Aug 2010 06:49 In article <bf5be029-eddb-4306-8c37-63a4941e487f(a)g6g2000pro.googlegroups.com>, Newberry says... > >On Aug 12, 8:48=A0am, stevendaryl3...(a)yahoo.com (Daryl McCullough) >wrote: >> Newberry says... >> >> >Goedel's sentence is not true because it is vacuous, and we do not >> >regard vacuous sentences as true. >> >> On the contrary! We certainly do. >> >> Look, *EVERY* theorem of pure first order logic is, in a sense, >> vacuously true. For any other first-order theory, a sentence S >> is a theorem if there is a finite conjunction A1 & A2 & ... & An >> of axioms such that >> >> A1 & A2 & ... & An -> S >> >> is vacuously true. In a sense, then, logical deduction amounts to >> showing that certain sentences are vacuously true, given certain >> assumptions. >> >> Your goal of banishing the vacuously true sentences amounts to >> banishing the use of logic. > >I do not think this is correct. For example > >P v ~P > >is a theorem of truth-relevant logic. > >P v ~P v Q > >is not. I suggest reading sectio 2.2. > >> >> -- >> Daryl McCullough >> Ithaca, NY >
From: Daryl McCullough on 13 Aug 2010 07:35
Newberry says... >I do not think this is correct. For example > >P v ~P > >is a theorem of truth-relevant logic. If P is necessarily true, then P v ~P is vacuous, right? So P v ~P is not always true. -- Daryl McCullough Ithaca, NY |