Date: Jan 28, 2013 2:06 AM
Author: fom
Subject: Re: Formally Unknowability, or absolute Undecidability, of certain<br> arithmetic formulas.
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.