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> in math we can even prove that some things can never be proven No we can't. We can only prove that certain formal systems cannot resolve certain statements.
by bumbledraven 4y ago
> in math we can even prove that some things can never be proven
No we can't. We can only prove that certain formal systems cannot resolve certain statements. We might still invent other formal systems that are acceptable to us and that can resolve those statements.
- coldtea 4y ago>We might still invent other formal systems that are acceptable to us and that can resolve those statements. That's irrelevant, though, because a mathematical proof or a statement X is considered in the context of a specific formal system (and any isomorphic system). Proving that S can't be proven under formal system F will always be true regardless if you are able to prove the same statement in the formal system Z. For example, you can't say "I just disproved that triangle angles add to 180 degrees" just because you've proved they add to more than 180 degrees under a non-flat surface or non-Euclidean geometry. People saying "triangle angles add to 180 degrees" implicitly already mean "under Euclidean geometry and in a flat plane". It's just left implied, because it's goes without saying that they mean it within the system they expressed the problem and did the proof in.
- lanstin 4y agoAnd for those other systems, iF they embed arithmetic, we can effectively produce a statement that is visibly true and which that other system cannot prove.