Necessary and contingent propositions

A proposition is said to be necessary if it holds (is true) in all logically possible circumstances or conditions. “All husbands are married” is such a proposition. There are no possible or conceivable conditions in which this proposition is not true (on the assumption, of course, that the words husband and married are taken to mean what they ordinarily mean). In contrast, “All Model T Fords are black” holds in some circumstances (those actually obtaining, which is why the proposition is true), but it is easy to imagine circumstances in which it would not be true. To say, therefore, that a proposition is contingent is to say that it is true in some but not in all possible circumstances. Many necessary propositions, such as “All husbands are married,” are a priori—though it has been argued that some are not (see below Necessary a posteriori propositions)—and most contingent propositions are a posteriori.

Analytic and synthetic propositions

A proposition is said to be analytic if the meaning of the predicate term is contained in the meaning of the subject term. Thus, “All husbands are married” is analytic, because part of the meaning of the term husband is “being married.” A proposition is said to be synthetic if this is not so. “All Model T Fords are black” is synthetic, since “black” is not included in the meaning of Model T Ford. Some analytic propositions are a priori, and most synthetic propositions are a posteriori. Those distinctions were used by Kant to ask one of the most important questions in the history of epistemology—namely, whether a priori synthetic judgments are possible (see below Modern philosophy: Immanuel Kant).

Tautological and significant propositions

A proposition is said to be tautological if its constituent terms repeat themselves or if they can be reduced to terms that do, so that the proposition is of the form “a = a” (“a is identical to a”). Such propositions convey no information about the world, and, accordingly, they are said to be trivial, or empty of cognitive import. A proposition is said to be significant if its constituent terms are such that the proposition does provide new information about the world.

The distinction between tautological and significant propositions figures importantly in the history of the philosophy of religion. In the so-called ontological argument for the existence of God, St. Anselm of Canterbury (1033/34–1109) attempted to derive the significant conclusion that God exists from the tautological premise that God is the only perfect being together with the premise that no being can be perfect unless it exists. As Hume and Kant pointed out, however, it is fallacious to derive a proposition with existential import from a tautology, and it is now generally agreed that from a tautology alone, it is impossible to derive any significant proposition. Tautological propositions are generally a priori, necessary, and analytic, and significant propositions are generally a posteriori, contingent, and synthetic.

Logical and factual propositions

A logical proposition is any proposition that can be reduced by replacement of its constituent terms to a proposition expressing a logical truth—e.g., to a proposition such as “If p and q, then p.” The proposition “All husbands are married,” for example, is logically equivalent to the proposition “If something is married and it is male, then it is married.” In contrast, the semantic and syntactic features of factual propositions make it impossible to reduce them to logical truths. Logical propositions are often a priori, always necessary, and typically analytic. Factual propositions are generally a posteriori, contingent, and synthetic.

Necessary a posteriori propositions

The distinctions reviewed above have been explored extensively in contemporary philosophy. In one such study, Naming and Necessity (1972), the American philosopher Saul Kripke argued that, contrary to traditional assumptions, not all necessary propositions are known a priori; some are knowable only a posteriori. According to Kripke, the view that all necessary propositions are a priori relies on a conflation of the concepts of necessity and analyticity. Because all analytic propositions are both a priori and necessary, most philosophers have assumed without much reflection that all necessary propositions are a priori. But that is a mistake, argued Kripke. His point is usually illustrated by means of a type of proposition known as an “identity” statement—i.e., a statement of the form “a = a.” Thus, consider the true identity statements “Venus is Venus” and “The morning star is the evening star.” Whereas “Venus is Venus” is knowable a priori, “The morning star [i.e., Venus] is the evening star [i.e., Venus]” is not. It cannot be known merely through reflection, prior to any experience. In fact, the statement was not known until the ancient Babylonians discovered, through astronomical observation, that the heavenly body observed in the morning is the same as the heavenly body observed in the evening. Hence, “The morning star is the evening star” is a posteriori. But it is also necessary, because, like “Venus is Venus,” it says only that a particular object, Venus, is identical to itself, and it is impossible to imagine circumstances in which Venus is not the same as Venus. Other types of propositions that are both necessary and a posteriori, according to Kripke, are statements of material origin, such as “This table is made of (a particular piece of) wood,” and statements of natural-kind essence, such as “Water is H₂O.” It is important to note that Kripke’s arguments, though influential, have not been universally accepted, and the existence of necessary a posteriori propositions continues to be a much-disputed issue.