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.