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A synonym is a word, morpheme, or phrase that means precisely or nearly the same as another word, morpheme, or phrase in a given language. [2] For example, in the English language , the words begin , start , commence , and initiate are all synonyms of one another: they are synonymous .
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.
Modal logic differs from other kinds of logic in that it uses modal operators such as and .The former is conventionally read aloud as "necessarily", and can be used to represent notions such as moral or legal obligation, knowledge, historical inevitability, among others.
A principle in modal logic that asserts the interchangeability of quantification and possibility: necessarily, if there exists something, then there necessarily exists something. Basic Law V A principle proposed by Gottlob Frege in his attempt to reduce arithmetic to logic, stating that the extension of a concept is determined by the objects ...
Intentionality fallacy – the insistence that the ultimate meaning of an expression must be consistent with the intention of the person from whom the communication originated (e.g. a work of fiction that is widely received as a blatant allegory must necessarily not be regarded as such if the author intended it not to be so). [40]
Logical truths are generally considered to be necessarily true. This is to say that they are such that no situation could arise in which they could fail to be true. The view that logical statements are necessarily true is sometimes treated as equivalent to saying that logical truths are true in all possible worlds.
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This distinction begins to reveal the ordinary English meaning of the word "contingency," in which the truth of one thing depends on the truth of another. On the one hand, the mathematical idea that a sum of two and two is four is always possible and always true, which makes it necessary and therefore not contingent. This mathematical truth ...