On 2/14/2011 2:11 AM, Stephen Paul King wrote:
Hi Bruno,
Umm, I did not mean to upset you personally. I find your ideas to be very interesting and even elegant, but there is an 800 Pound Gorilla in the Room that needs to be addressed and it is the nature of the assumptions that we bring into our modelizations. Whether the Goldbach conjecture is true or false is a question that needs to have its premise examined. Can we examine all of the even integers to determine if they are the sum of two primes? No, obviously, but is the choice between falsity or truth necessarily sound? Does not there exist a difference between finite and infinite sets such that we can define measure and ratios on the finites but not on the infinites. The Goldbach conjecture is a conjecture about an infinite set and thus we may be prevented from proving the decidability of its truth by the fact that it is infinite and has the property of an isomorphism between a proper subset of the infinity and its whole.

We can't prove it's undecidable because that would constitute a proof that it's true. And there must be infinitely many such conjectures.


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