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Re: Formally Unknowability, or absolute Undecidability, of certain
arithmetic formulas.
Posted:
Jan 29, 2013 12:38 AM
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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.
--
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There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI
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