```Date: Jan 29, 2013 4:41 AM
Author: fom
Subject: Re: Formally Unknowability, or absolute Undecidability, of   certainarithmeticformulas.

On 1/28/2013 11:28 PM, Nam Nguyen wrote:> On 28/01/2013 6:20 AM, Frederick Williams wrote:>> Nam Nguyen wrote:>>>>> I meant, what would "tomorrow", "today" have anything to to with>>> _mathematical logic_ ?>>>> Oh, a lot.  Look up 'temporal logic'.  In my day it was something of a>> curiosity of interest only to philosophers (hiss, boo, etc) but now it>> is of much interest to computer scientists among others.>> It seems you aren't aware, but the assumed logic of this thread here> is the familiar FOL=.>How can that be if you are requesting alternativeinterpretations of quantification?However, the answer to your question concerning "tomorrow" and"today" is found in the relationship of model theory todescription theory.Originally, Frege spoke of incomplete symbols suchasx+2=5because they require a "name" to have a "truth value".Modern model theory is a bit senseless because theyuse a parameterized theory (set theory) to justifyspeaking of "truth" for an object language.  If youactually read Tarski's paper, it explicitly excludesconsideration of how the "objects" of an interpretationtransform incomplete symbols to complete symbols (thosewith a truth value).  This reflects the Russellianposition that "naming" is an extra-logical function.One gets to an explicit discussion of names and indentitywithin a model in Abraham Robinson's "On ConstrainedDenotation".  Whether or not one agrees with Robinson, itreturns the question of truth valuation to the role ofdescriptions and reference.Having gone this far, the next issue is the relation betweendemonstratives and descriptions.  This involves indexicals.Kaplan produced a decent intensional logic of demonstrativesthat makes plain the relation between demonstratives anddescriptions.  Since it utilizes indexicals, temporalmodal operators play a role.To say thatx+2=5is true becausethere exists an "object" y such thaty+2=5is different from saying that3+2=5is true.That is the difference between using a "set"and a "name".The history of description theory explains why thisis not taught in mathematical logic.  But that historicalbasis has been collapsing for over 50 years.  This changehas simply been ignored by the mathematical community.
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