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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.
Intuitionistic modal logic treats possibility and necessity as not perfectly symmetric. For example, suppose that while walking to the convenience store we pass Friedrich's house, and observe that the lights are off. On the way back, we observe that they have been turned on. "Somebody or something turned the lights on" is necessary.
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
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 ...
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).
A posteriori necessity existing would make the distinction between a prioricity, analyticity, and necessity harder to discern because they were previously thought to be largely separated from the a posteriori, the synthetic, and the contingent. [3] (a) P is a priori iff P is necessary. (b) P is a posteriori iff P is contingent.