Re: Truth Bearer or Truth Maker

Obviously the current Artificial Intelligence
wave, with its incarnations such as ChatGPT
isn't that good, otherwise we might have heard
of some break through. Were some conjectures
meanwhile proved with the help of Artificial
Intelliegence, or is the current AI only
good at halucinating undirected nonsense from
existing knowledge, not able to complete an
unsolved conjecture?
Mild Shock schrieb:

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.