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'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.
-- ---------------------------------------------------- There is no remainder in the mathematics of infinity.