Re: Truth Bearer or Truth Maker

Sometimes conjectures become theorems
when we move into a different model,
like when we leave arithmetic, and
go into set theory or analysis. A typical
example is the Goodstein sequence, which
becomes provable terminating in ZFC:
Goodstein's theorem is a statement about the
natural numbers, proved by Reuben Goodstein in 1944
https://en.wikipedia.org/wiki/Goodstein's_theorem
Because ZFC has stronger induction principles.
So maybe Goldbach's conjecture will
have the same fate, and sometime become
provable? Don't know. Isn't Terrence Tao
expert on everything prime numbers. He
had some success with the weak conjecture:
In 2012, Terence Tao proved this without
the Riemann Hypothesis; this improves both results.
https://en.wikipedia.org/wiki/Goldbach's_weak_conjecture

But its even not necessary to follow such
a strict program to regain the "finite"
character of logic. Even if we stick to
 classical logic, Gödels incompleteness
theorem shows that this classical logic
stil has some "finite" limitations,
 in that a axiomatization of arithmetic,
will still not fully capture the intended
model of arithmetic, in that the axiomatization
 will necessarily have at least one sentences
which is not truth bearing in Olcotts words:
 https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems
 Putting another Olcott label on the bottle
doesn't change the content of the bottle.