By proposition, I mean something like a statement or an argument. Such as "Sun always rises from the east." This, however, does not mean that I am moving away from the domain of mathematics, on this forum. If you can bring in arguments from epistemology, I will welcome you to do so, whole heartedly.
2026-04-06 16:15:00.1775492100
If a proposition can never be proven wrong, is it always true?
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From the Gödel incompleteness theorem, we know that there is a sentence which is true but there exists no deduction for it, so there is no prove for this theorem.
So in your case, if there exists no prove that you proposition is wrong, it could still be wrong. Even if you prove that there is no deduction to make you proposition wrong, it could still be wrong.