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Topic: Formally Unknowability, or absolute Undecidability, of certain arithmetic
formulas.

Replies: 22   Last Post: Jan 29, 2013 8:21 PM

 Messages: [ Previous | Next ]
 namducnguyen Posts: 2,777 Registered: 12/13/04
Re: Formally Unknowability, or absolute Undecidability, of certain
arithmeticformulas.

Posted: Jan 27, 2013 2:26 PM

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_ .

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

Date Subject Author
1/27/13 namducnguyen
1/27/13 Frederick Williams
1/27/13 namducnguyen
1/27/13 Frederick Williams
1/27/13 namducnguyen
1/27/13 Jesse F. Hughes
1/27/13 namducnguyen
1/28/13 Jesse F. Hughes
1/28/13 namducnguyen
1/28/13 namducnguyen
1/28/13 Frederick Williams
1/29/13 namducnguyen
1/29/13 fom
1/28/13 Frederick Williams
1/29/13 namducnguyen
1/28/13 ross.finlayson@gmail.com
1/29/13 Michael Stemper
1/29/13 namducnguyen
1/28/13
1/28/13 fom
1/29/13 namducnguyen
1/29/13 fom
1/29/13 Graham Cooper