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In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements.For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of Q is guaranteed by the truth of P.
Biological tests of necessity and sufficiency refer to experimental methods and techniques that seek to test or provide evidence for specific kinds of causal relationships in biological systems. A necessary cause is one without which it would be impossible for an effect to occur, while a sufficient cause is one whose presence guarantees the ...
Leibniz henceforth distinguishes two types of necessity: necessary necessity and contingent necessity, or universal necessity vs singular necessity. Universal necessity concerns universal truths, while singular necessity concerns something necessary that could not be (it is thus a "contingent necessity").
The commonly employed system S5 simply makes all modal truths necessary. For example, if p is possible, then it is "necessary" that p is possible. Also, if p is necessary, then it is necessary that p is necessary. Other systems of modal logic have been formulated, in part because S5 does not describe every kind of modality of interest.
Contingency is one of three basic modes alongside necessity and possibility. In modal logic, a contingent statement stands in the modal realm between what is necessary and what is impossible, never crossing into the territory of either status. Contingent and necessary statements form the complete set of possible statements.
Metaphysical necessity is contrasted with other types of necessity. For example, the philosophers of religion John Hick [2] and William L. Rowe [3] distinguished the following three: factual necessity (existential necessity): a factually necessary being is not causally dependent on any other being, while any other being is causally dependent on it.
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Necessary and sufficient condition, in logic, something that is a required condition for something else to be the case; Necessary proposition, in logic, a statement about facts that is either unassailably true (tautology) or obviously false (contradiction) Metaphysical necessity, in philosophy, a truth which is true in all possible worlds