Philosophy Now Forum

∀N ∈ (even whole numbers greater than 2)
∃x ∈ Prime_Numbers
∃y ∈ Prime_Numbers
| (x + y = N)

Unless there exists a sequence of steps that confirm that each N is a sum of two primes (AKA a proof) then the Goldbach conjecture is false.

Copyright 2022 Pete Olcott

PeteOlcott wrote: ↑Mon Mar 07, 2022 3:00 am Unless there exists a sequence of steps that confirm that each N is a sum of two primes (AKA a proof) then the Goldbach conjecture is false.

Why the fuck would you even equate provability with truth?

Specifically from the prism of model theory: why the fuck would you reduce/constrain the concept of "truth" to a mere grammar?

Do you not understand the implication of Rice's theorem?

Skepdick wrote: ↑Mon Mar 07, 2022 8:17 am

PeteOlcott wrote: ↑Mon Mar 07, 2022 3:00 am Unless there exists a sequence of steps that confirm that each N is a sum of two primes (AKA a proof) then the Goldbach conjecture is false.

Why the fuck would you even equate provability with truth?

The alternative would be: I guess that X is true therefore X is true.

PeteOlcott wrote: ↑Sun Mar 20, 2022 7:43 pm The alternative would be: I guess that X is true therefore X is true.

The alternative would be true in a model.

PeteOlcott wrote: ↑Mon Mar 07, 2022 3:00 am ∀N ∈ (even whole numbers greater than 2)
∃x ∈ Prime_Numbers
∃y ∈ Prime_Numbers
| (x + y = N)

Unless there exists a sequence of steps that confirm that each N is a sum of two primes (AKA a proof) then the Goldbach conjecture is false.

Copyright 2022 Pete Olcott

Copyright 2022 Age

PeteOlcott wrote: ↑Mon Mar 07, 2022 3:00 am ∀N ∈ (even whole numbers greater than 2)
∃x ∈ Prime_Numbers
∃y ∈ Prime_Numbers
| (x + y = N)

Unless there exists a sequence of steps that confirm that each N is a sum of two primes (AKA a proof) then the Goldbach conjecture is false.

Copyright 2022 Pete Olcott

The conjecture, like many in math/logic like this, is to seek a counter or disproof. They would reverse your concern by saying that we cannot KNOW whether it is false and so need a proof to assert it untrue. However, the caveate of excluding the numbers one or two proves that at least IF these are included, the conjecture is provable.

Can you see why they guessed this reasonable though? If one and two were included, it would be reduced to,

"For all even numbers, they can be defined by the sum of two odd numbers."

Given this is true, it seems intuitive that any even number is definable by say, "1 + x" , x being odd. The idea came up regarding the use of primes. And since any number is made UP of multiple additions of one, it is clearly intuitive that this must be true. But the expected degree of proof for logic/math problems requires some means to exclude certain ideas that cannot have any logical holes in it. Thus, the conjecture is a puzzle sought to be resolved one way or the other. Certainty is the concern, regarldless of its apparent trivialty. It makes is a challenge. For those who want to use the conjecture as a fact for some other problem, this separately demands that it be a discrete assumption that needs to be included in an argument.

Age wrote: ↑Mon Mar 21, 2022 3:57 am

PeteOlcott wrote: ↑Mon Mar 07, 2022 3:00 am ∀N ∈ (even whole numbers greater than 2)
∃x ∈ Prime_Numbers
∃y ∈ Prime_Numbers
| (x + y = N)

Unless there exists a sequence of steps that confirm that each N is a sum of two primes (AKA a proof) then the Goldbach conjecture is false.

Copyright 2022 Pete Olcott

Copyright 2022 Age

Copyright © 2022 Scott Mayers

Note that since I used the '©', mine is most true! Also, I will ask you for written permission and $1 before publishing anything that begins, "Copyright ©" followed by any name. Thanks kindly.

Scott Mayers wrote: ↑Mon Mar 21, 2022 4:52 am

Age wrote: ↑Mon Mar 21, 2022 3:57 am

PeteOlcott wrote: ↑Mon Mar 07, 2022 3:00 am ∀N ∈ (even whole numbers greater than 2)
∃x ∈ Prime_Numbers
∃y ∈ Prime_Numbers
| (x + y = N)

Unless there exists a sequence of steps that confirm that each N is a sum of two primes (AKA a proof) then the Goldbach conjecture is false.

Copyright 2022 Pete Olcott

Copyright 2022 Age

Copyright © 2022 Scott Mayers

Note that since I used the '©', mine is most true!

Also, I will ask you for written permission and $1 before publishing anything that begins, "Copyright ©" followed by any name. Thanks kindly.

What we have here is FURTHER PROOF of how just about EVERY 'thing' the adult human being did, in the days when this was being written, was for MONEY.

These adult human beings really were so GREEDY that they even wanted MONEY just for the absolutely FREE thoughts that arose. The amount of GREED that REALLY did exist, back in those days, was nearly INCOMPREHENSIBLE, that is; if it was NOT True.