Probability is relative to an axiom systems. A more powerful system can prove statements that are true but not provable in a weaker system. For example "This

Probability is relative to an axiom systems. A more powerful system can prove statements that are true but not provable in a weaker system. For example "This sentence is not provable." (Godel's statement, written informally) is true, but not provable, in first order arithmetic logic. https://en.m.wikipedia.org/wiki/Diagonal_lemma https://en.m.wikipedia.org/wiki/Diagonal_lemma In constructivist mathematics, proving that a statement is not false is not a proof that it is true. Non-constructivist mathematics, on the other hand, has the axiom, for all P: P or not-P, also stated as not-not-P implies P.