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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.
One of the earliest recorded instances of the proverb is in one of Aesop’s Fables, “The Crow and the Pitcher” from the mid 6th century BCE. Plato's Republic says "our need will be the real creator", [5] which Jowett's 1894 translation rendered loosely as "The true creator is necessity, who is the mother of our invention."
In writing, phrases commonly used as alternatives to P "if and only if" Q include: Q is necessary and sufficient for P, for P it is necessary and sufficient that Q, P is equivalent (or materially equivalent) to Q (compare with material implication), P precisely if Q, P precisely (or exactly) when Q, P exactly in case Q, and P just in case Q. [3]
For this reason, or perhaps for their familiarity and simplicity, necessity and possibility are often casually treated as the subject matter of modal logic. Moreover, it is easier to make sense of relativizing necessity, e.g. to legal, physical, nomological, epistemic, and so on, than it is to make sense of relativizing other notions.
Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. [1] A sentence is said to be a logical consequence of a set of sentences, for a given language , if and only if , using only logic (i.e., without regard to any personal interpretations of the sentences) the sentence must ...
Meaning and Necessity: A Study in Semantics and Modal Logic (1947; enlarged edition 1956) is a book about semantics and modal logic by the philosopher Rudolf Carnap.The book, in which Carnap discusses the nature of linguistic expressions, was a continuation of his previous work in semantics in Introduction to Semantics (1942) and Formalization of Logic (1943).
In English law, the defence of necessity recognises that there may be situations of such overwhelming urgency that a person must be allowed to respond by breaking the law. There have been very few cases in which the defence of necessity has succeeded, and in general terms there are very few situations where such a defence could even be applicable.
A modal verb is a type of verb that contextually indicates a modality such as a likelihood, ability, permission, request, capacity, suggestion, order, obligation, necessity, possibility or advice. Modal verbs generally accompany the base (infinitive) form of another verb having semantic content. [1]