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