```Date: Jan 29, 2013 4:17 AM
Author: fom
Subject: Re: Formally Unknowability, or absolute Undecidability, of certain<br> arithmetic formulas.

On 1/28/2013 11:38 PM, Nam Nguyen wrote:> On 28/01/2013 12:06 AM, fom wrote:>> On 1/27/2013 11:22 AM, Nam Nguyen wrote:>>>>> In this thread, we propose a solution to this differentiation>>> difficulty: semantic _re-interpretation_ of _logical symbols_ .>>>> It sounds more like "coordinated interpretation.">>>> That is what mathematical realism is already doing.>> The existence quantifier is co-interpreted with some>> notion of truth.  This is the historical debate>> from description theory addressing presupposition failure.>>>> One of the foundational insights of Frege's researches>> was to interpret contradiction existentially.  In>> contrast, Kant interpreted contradiction modally.>> This would suggest non-existence and impossibility>> are already coordinated in such a way that the>> two forms of logic branch at the outset.>>>> There are, of course, intensional logics that>> mix the senses of these logics.  This is where>> the terms "de re" and "de facto" find their>> nuanced meanings in relation to quantifier-operator>> order.>>>> No one, of course, has tried to use anything>> like an arithmetical numbering to provide>> correlated, but distinct, model theories to>> interpret a single situation (quantificational>> logic) so as to eliminate irrelevant modal>> possibilities.>> Would you have any link on "coordinated interpretation"?I was simply paraphrasing what your proposal sounds like.>> I'm not sure if all of those logic's would be related to my proposal> here, which is simply re-interpreting the logical symbols _ in any_> _which way_ one would feel pleased, provided that:>> a) The re-interpretations be cohesively meaningful (and logical).>> b) Certain corresponding provision for formula's truth and falsehood>     be available.Look for work on "free logics."  There are axiomatizationsthat define "existential import."  Consequently, the usualexistential quantifier is primitive, but the model theorysupports quantification over a class partitioned intosubstantive and non-substantive objects.
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