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Re: Formally Unknowability, or absolute Undecidability, of certain
arithmeticformulas.
Posted:
Jan 27, 2013 2:26 PM
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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_ .
--
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There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI
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