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



Re: Formally Unknowability, or absolute Undecidability, of certainarithmeticformulas.
Posted:
Jan 27, 2013 3:02 PM


Nam Nguyen wrote: > > On 27/01/2013 12:07 PM, Frederick Williams wrote: > > Nam Nguyen 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. > > > > No one thinks that but you. > > If I were you I wouldn't say that. Rupert for instance might not > dismiss the idea out right, iirc. > > > Its truth value might be discovered tomorrow. > > You misunderstand the issue there: unknowability and impossibility > to know does _NOT_ at all mean "might be discovered tomorrow". > > It's impossible to know of a solution of n*n = 2 in the naturals > means it's impossible to know of a solution of n*n = 2 in the naturals. > Period. > > It doesn't mean a solution of n*n = 2 in the naturals "might be > discovered tomorrow", as you seem to have believed for a long time, > in your way of understanding what unknowability or impossibility > to know would _technically mean_ .
I am not talking about the words 'unknowability' and 'impossibility to know' the meanings of which I know. Nor am I talking about 'It's impossible to know of a solution of n*n = 2 in the naturals.' I'm talking about 'There are infinitely many counter examples of the Goldbach Conjecture'.
 When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him. Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting



