Conjecture
Not every conjecture can be proven true or false. The continuum hypothesis, which describes the size of certain infinite sets, is an example. It was shown to be independent of the generally accepted axioms of set theory, which means that it cannot be proven true or false using those axioms. It is therefore possible to take this statement, or its negation, as a new axiom in a consistent manner (much as we can take Euclid's parallel postulate as either true or false).