哥德巴赫猜想
From the other direction, Jones might say, (3) "It is "possible" that Goldbach's conjecture is true; but also "possible" that it is false", and "also" (4) "if it "is" true, then it is necessarily true, and not possibly false". Here Jones means that it is "epistemically possible" that it is true or false, for all he knows (Goldbach's conjecture has not been proven either true or false), but if there "is" a proof (heretofore undiscovered), then it would show that it is not "logically" possible for Goldbach's conjecture to be false—there could be no set of numbers that violated it. Logical possibility is a form of "alethic" possibility; (4) makes a claim about whether it is possible (i.e., logically speaking) that a mathematical truth to have been false, but (3) only makes a claim about whether it is possible, for all Jones knows, (i.e., speaking of certitude) that the mathematical claim is specifically either true or false, and so again Jones does not contradict himself. It is worthwhile to observe that Jones is not necessarily correct: It is possible (epistemically) that Goldbach's conjecture is both true and unprovable.