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Topic: Formally Unknowability, or absolute Undecidability, of certain arithmetic
formulas.

Replies: 22   Last Post: Jan 29, 2013 8:21 PM

 Messages: [ Previous | Next ]
 namducnguyen Posts: 2,777 Registered: 12/13/04
Re: Formally Unknowability, or absolute Undecidability, of certain
arithmetic formulas.

Posted: Jan 29, 2013 12:38 AM

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.

NYOGEN SENZAKI
----------------------------------------------------

Date Subject Author
1/27/13 namducnguyen
1/27/13 Frederick Williams
1/27/13 namducnguyen
1/27/13 Frederick Williams
1/27/13 namducnguyen
1/27/13 Jesse F. Hughes
1/27/13 namducnguyen
1/28/13 Jesse F. Hughes
1/28/13 namducnguyen
1/28/13 namducnguyen
1/28/13 Frederick Williams
1/29/13 namducnguyen
1/29/13 fom
1/28/13 Frederick Williams
1/29/13 namducnguyen
1/28/13 ross.finlayson@gmail.com
1/29/13 Michael Stemper
1/29/13 namducnguyen
1/28/13
1/28/13 fom
1/29/13 namducnguyen
1/29/13 fom
1/29/13 Graham Cooper