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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.
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]
The Necessary and Proper Clause, also known as the Elastic Clause, [1] is a clause in Article I, Section 8 of the United States Constitution: The Congress shall have Power... To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government ...
A proposition is said to be necessary if it could not have failed to be the case. Nomological necessity is necessity according to the laws of physics and logical necessity is necessity according to the laws of logic, while metaphysical necessities are necessary in the sense that the world could not possibly have been otherwise. What facts are ...
"absolutely necessary" – otiose adverb: something is either necessary or it isn't. "However, this may be a ruse" – the word "however" appears 34 times in this article, mostly (as here) quite needlessly. "Howevers", as I well know, creep into one's prose unbidden, but they usually weaken the prose, and should be weeded severely.
A sine qua non (/ ˌ s aɪ n i k w eɪ ˈ n ɒ n, ˌ s ɪ n i k w ɑː ˈ n oʊ n /, [1] Latin: [ˈsɪnɛ kʷaː ˈnoːn]) or conditio sine qua non (plural: conditiones sine quibus non) is an indispensable and essential action, condition, or ingredient.
If the desire is to take a definite direction, it is absolutely necessary that the idea of the object, from which the pleasure is expected, should also be present and should control my activity." [7] For Charles Fourier, following desires (like passions or in Fourier's own words 'attractions') is a means to attain harmony.