```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 likeX = 'not (exist( proof( X )))'Really UN-PROVABLE, UN-COUNTABLE, UN-COMPUTABLEare ALL Superfluous Self Inflicted Diatribe!-------The only WITNESS to missing computable reals is CHAITANS OMEGA!based on :S:  if Halts(S) Gosub SUN COMPUTABLE!-------Just use the HALT values to make a POWERSET(N) instead!x e P(N)_1  IFF  TM_1(x) HaltsNow it proves a powerset N *IS* countable!-------Really, abstract mathematics is the biggest century long con to everexist 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 selfdefeating 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-representablefunctions is an oxy moron.Herc
```