Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Math Forum
»
Discussions
»
sci.math.*
»
sci.math
Notice: We are no longer accepting new posts, but the forums will continue to be readable.
Topic:
Formally Unknowability, or absolute Undecidability, of certain arithmetic formulas.
Replies:
22
Last Post:
Jan 29, 2013 8:21 PM




Re: Formally Unknowability, or absolute Undecidability, of certain arithmetic formulas.
Posted:
Jan 29, 2013 2:42 AM


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, vizaviz, > the unknowability, impossibility. > > In this thread, we propose a solution to this differentiation > difficulty: semantic _reinterpretation_ of _logical symbols_ . > > For example, we could reinterpret 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 reinterpretations 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 reinterpretation 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 reinterpretation. > As long as the semantic reinterpretation 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 UNPROVABLE sentences are idiotic nonsense like
X = 'not (exist( proof( X )))'
Really UNPROVABLE, UNCOUNTABLE, UNCOMPUTABLE
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!

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 UNDOABLE 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 unrepresentable functions is an oxy moron.
Herc



