structural:expansion
Relation to the necessary truths and contingent truths

The metaphysical distinction between necessary and contingent truths has also been related to a priori and a posteriori knowledge.

A proposition that is necessarily true is one in which its negation is self-contradictory; it is true in every possible world. For example, considering the proposition "all bachelors are unmarried:" its negation (i.e. the proposition that some bachelors are married) is incoherent due to the concept of being unmarried (or the meaning of the word "unmarried") being tied to part of the concept of being a bachelor (or part of the definition of the word "bachelor"). To the extent that contradictions are impossible, self-contradictory propositions are necessarily false as it is impossible for them to be true. The negation of a self-contradictory proposition is, therefore, supposed to be necessarily true.

By contrast, a proposition that is contingently true is one in which its negation is not self-contradictory. Thus, it is said not to be true in every possible world. As Jason Baehr suggests, it seems plausible that all necessary propositions are known a priori, because "ense experience can tell us only about the actual world and hence about what is the case; it can say nothing about what must or must not be the case."

Following Kant, some philosophers have considered the relationship between aprioricity, analyticity and necessity to be extremely close. According to Jerry Fodor, " positivism, in particular, took it for granted that a priori truths must be necessary." Since Kant, the distinction between analytic and synthetic propositions has slightly changed. Analytic propositions were largely taken to be "true by virtue of meanings and independently of fact", while synthetic propositions were not—one must conduct some sort of empirical investigation, looking to the world, to determine the truth-value of synthetic propositions.