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
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!
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.