Date: Jan 29, 2013 2:42 AM Author: Graham Cooper Subject: Re: Formally Unknowability, or absolute Undecidability, of certain<br> arithmetic formulas. On Jan 28, 3:22 am, Nam Nguyen <namducngu...@shaw.ca> wrote:

> In some past threads we've talked about the formula cGC

> which would stand for:

>

> "There are infinitely many counter examples of the Goldbach Conjecture".

>

> Whether or not one can really prove it, the formula has been at least

> intuitively associated with a mathematical unknowability: it's

> impossible to know its truth value (and that of its negation ~cGC) in

> the natural numbers.

>

> The difficulty to prove such unknowability, impossibility, is that

> there are statements that are similar in formulation but yet are

> known to be true or false. An example of such is:

>

> "There are infinitely many (even) numbers that are NOT counter

> examples of the Goldbach Conjecture".

>

> The difficulty lies in the fact that there have been no formal

> logical way to differentiate the 2 kinds of statements, viz-a-viz,

> the unknowability, impossibility.

>

> In this thread, we propose a solution to this differentiation

> difficulty: semantic _re-interpretation_ of _logical symbols_ .

>

> For example, we could re-interpret the symbol 'Ax' as the

> Specifier (as opposed to Quantifier) "This x", and 'Ex' as

> the Specifier "That x". And if, for a formula F written in L(PA)

> (or the language of arithmetic), there can be 2 different

> "structures" under the re-interpretations in one of which F is true

> and the other F is false, then we could say we can prove

> the impossibility of the truth value of F as an arithmetic

> formula in the canonical interpretation of the logical

> symbols 'Ax' and 'Ex'.

>

> (Obviously under this re-interpretation what we'd mean as a language

> "structure" would be different than a canonical "structure").

>

> Again, this is just a proposed solution, and "This x" or "That x"

> would be not the only choice of semantic re-interpretation.

> As long as the semantic re-interpretation makes sense, logically

> at least, it could be used in the solution.

>

> But any constructive dialog on the matter would be welcomed and

> appreciated, it goes without saying.

>

> --

> ----------------------------------------------------

> There is no remainder in the mathematics of infinity.

>

> NYOGEN SENZAKI

> ----------------------------------------------------

the only UN-PROVABLE sentences are idiotic nonsense like

X = 'not (exist( proof( X )))'

Really UN-PROVABLE, UN-COUNTABLE, UN-COMPUTABLE

are ALL Superfluous Self Inflicted Diatribe!

-------

The only WITNESS to missing computable reals is CHAITANS OMEGA!

based on :

S: if Halts(S) Gosub S

UN COMPUTABLE!

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Just use the HALT values to make a POWERSET(N) instead!

x e P(N)_1 IFF TM_1(x) Halts

Now it proves a powerset N *IS* countable!

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Really, abstract mathematics is the biggest century long con to ever

exist under the guise of 'WEVE FORMALLY PROVED IT ALL!'

You haven't formally proven ANY OF ALL THE UN-DOABLE RUBBISH!

You redid the same errors with Calculus and BIJECTION / ONTO self

defeating function definitions instead!

|N| = |GODEL NUMBERS| = |FUNCTIONS|

= |CHOICE FUNCTIONS| = |SETS|

by your own AOC.

You don't have a SINGLE INFINITE LENGTH FORMULA to even have un-

countable many functions - the whole notion of un-representable

functions is an oxy moron.

Herc