In logic and metaphysics, a modal property of a true proposition whereby it is not possible for the proposition to be false and of a false proposition whereby it is not possible for the proposition to be true. A proposition is logically necessary if it instantiates a law of logic or can be made to instantiate a law of logic through substitution of definitionally equivalent terms. Examples are “It is raining now or it is not raining now” and “All men are human beings” (assuming “men” can be replaced with “male human beings”).
Necessary propositions are sometimes said to be true or false (as the case may be) in all possible worlds. A contingently true or false proposition is thus one that is true in some possible worlds and false in others (e.g., “France is a democracy”). All true logically necessary propositions are analytic (&see; analytic-synthetic distinction) and knowable a priori. Some philosophers recognize a second category of “metaphysically” necessary propositions that are not analytic and generally not a priori; examples include identity statements such as “Water is H2O.”
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