Search results
Results from the WOW.Com Content Network
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.
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.
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 statement "If all objects are physical, and A. N. Prior exists, then A. N. Prior is physical" may be logically true by form, but not necessarily true.. Some philosophical distinctions are used to examine the line between contingent and necessary statements.
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).
The commonly employed system S5 simply makes all modal truths necessary. For example, if p is possible, then it is "necessary" that p is possible. Also, if p is necessary, then it is necessary that p is necessary. Other systems of modal logic have been formulated, in part because S5 does not describe every kind of modality of interest.
The concept of "necessary evil" is an idea that must be thoroughly rejected. Evil is not necessary, and to accept it as such is to perpetuate it. Evil must be opposed, rejected, and avoided at all costs. It should never be viewed as something that we must unavoidably and inevitably participate in. We trivialize evil when we refer to it as ...
Voy a subir arriba – I am going to go up upstairs, "arriba" not being necessary. Entra adentro – enter inside, "adentro" not being necessary. Turkish has many pleonastic constructs because certain verbs necessitate objects: yemek yemek – to eat food. yazı yazmak – to write writing. dışarı çıkmak – to exit outside.