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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.
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.
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.
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 ...
Modal logic is a kind of logic used to represent statements about necessity and possibility.It plays a major role in philosophy and related fields as a tool for understanding concepts such as knowledge, obligation, and causation.
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").
Treating logical truths, analytic truths, and necessary truths as equivalent, logical truths can be contrasted with facts (which can also be called contingent claims or synthetic claims). Contingent truths are true in this world, but could have turned out otherwise (in other words, they are false in at least one possible world).
That is, necessary truths depend upon the principle of contradiction." [11] The sufficient reason for a necessary truth is that its negation is a contradiction. [4] Leibniz admitted contingent truths, that is, facts in the world that are not necessarily true, but that are nonetheless true.