On 2/14/2011 2:11 AM, Stephen Paul King wrote:
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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