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Surprisingly, a theorem being unprovable does not mean that the theorem is untrue, even if you can prove its unprovability! This was shown by Goedel (https://en
by ookdatnog 7y ago
Surprisingly, a theorem being unprovable does not mean that the theorem is untrue, even if you can prove its unprovability! This was shown by Goedel (https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...). He showed that there exists no system powerful enough to express theorems about the natural numbers which can prove all facts about natural numbers and be sound (ie not prove things that are untrue).
- marcosdumay 7y agoThat's not exactly what I'm saying. What I am saying is that it's impossible for it to be true and unprovable. If it is true, it means a proof exists. Also, I am talking about this specific problem.
- lonelappde 7y agoCan you prove that? "impossibility to prove" is different from "proven impossible" because hiding behind the loose English are different models of logics. That's what Godel theorems at e about.
- tromp 7y agoIt is possible to be true and unprovable. Truth does not imply provability (the reverse does hold). Gödel's statement, which essentially says "I am unprovable" is an example of a true, unprovable statement.