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Topic:
Formally Unknowability, or absolute Undecidability, of certain arithmetic formulas.
Replies:
22
Last Post:
Jan 29, 2013 8:21 PM



fom
Posts:
1,968
Registered:
12/4/12


Re: Formally Unknowability, or absolute Undecidability, of certain arithmetic formulas.
Posted:
Jan 29, 2013 4:17 AM


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 _reinterpretation_ of _logical symbols_ . >> >> It sounds more like "coordinated interpretation." >> >> That is what mathematical realism is already doing. >> The existence quantifier is cointerpreted 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 nonexistence 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 quantifieroperator >> 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 reinterpreting the logical symbols _ in any_ > _which way_ one would feel pleased, provided that: > > a) The reinterpretations 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 axiomatizations that define "existential import." Consequently, the usual existential quantifier is primitive, but the model theory supports quantification over a class partitioned into substantive and nonsubstantive objects.



