Date: Apr 6, 2013 1:06 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224
On 6 Apr., 18:25, Nam Nguyen <namducngu...@shaw.ca> wrote:

>

> >> Goldbach conjecture is false. <==> Counter example exists. <==>

> >> Counter example can be found. <==> Goldbach conjecture is decidable.

>

> >> The second equivalence requires to neglect reality. But in mathematics

> >> this is standard.

>

> > But, to start with, how would one _structure theoretically prove_ the

> > 1st equivalence:

>

> > "Goldbach conjecture is false. <==> Counter example exists."

>

> > ?

>

> > Logically:

>

> > (A _specific_ counter example exists) => (Goldbach conjecture is false).

I disagree. There is an equivalence, not merely an implication. "GC is

false" is the same statement as "There exist at least one counter

example to GC".

>

> > How would one _prove_ ( i.e. _structure theoretically verify_ ) the

> > other-way-around?

I do not claim that GC, i.e. the absence of a counter example could be

proved like FLT has been proved or like the sum of the first 10^20

natural numbers can be calculated on a pocket calculator although most

of them cannot be written on that calculator. But it might be possible

that some bright head finds a way to prove GC, i.e., to decide GC

other than by its failure.

Therefore I have to correct my above chain of equivalences: The last

one is only an implication. Counter example can be found. ==> Goldbach

conjecture is decidable.

Regards, WM