Terms to describe a conditional relationship between two statements
This article is about the formal terminology in logic. For causal meanings of the terms, see Causality. For the concepts in statistics, see Sufficient statistic.
"Necessary But Not Sufficient" redirects here. For the novel by Eliyahu Goldratt, see Necessary But Not Sufficient (novel).
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. (Equivalently, it is impossible to have P without Q, or the falsity of Q ensures the falsity of P.)[1] Similarly, P is sufficient for Q, because P being true always implies that Q is true, but P not being true does not always imply that Q is not true.[2]
In general, a necessary condition is one (possibly one of multiple conditions) that must be present in order for another condition to occur, while a sufficient condition is one that produces the said condition.[3] The assertion that a statement is a "necessary and sufficient" condition of another means that the former statement is true if and only if the latter is true. That is, the two statements must be either simultaneously true, or simultaneously false.[4][5][6]
In ordinary English (also natural language) "necessary" and "sufficient" indicate relations between conditions or states of affairs, not statements. For example, being a male is a necessary condition for being a brother, but it is not sufficient—while being a male sibling is a necessary and sufficient condition for being a brother.
Any conditional statement consists of at least one sufficient condition and at least one necessary condition.
In data analytics, necessity and sufficiency can refer to different causal logics,[7] where necessary condition analysis and qualitative comparative analysis can be used as analytical techniques for examining necessity and sufficiency of conditions for a particular outcome of interest.
^"[M06] Necessity and sufficiency". philosophy.hku.hk. Retrieved 2019-12-02.
^Bloch, Ethan D. (2011). Proofs and Fundamentals: A First Course in Abstract Mathematics. Springer. pp. 8–9. ISBN 978-1-4419-7126-5.
^Confusion-of-Necessary (2019-05-15). "Confusion of Necessary with a Sufficient Condition". www.txstate.edu. Retrieved 2019-12-02.
^Betz, Frederick (2011). Managing Science: Methodology and Organization of Research. New York: Springer. p. 247. ISBN 978-1-4419-7487-7.
^Manktelow, K. I. (1999). Reasoning and Thinking. East Sussex, UK: Psychology Press. ISBN 0-86377-708-2.
^Asnina, Erika; Osis, Janis & Jansone, Asnate (2013). "Formal Specification of Topological Relations". Databases and Information Systems VII. 249 (Databases and Information Systems VII): 175. doi:10.3233/978-1-61499-161-8-175.
^Richter, Nicole Franziska; Hauff, Sven (2022-08-01). "Necessary conditions in international business research–Advancing the field with a new perspective on causality and data analysis" (PDF). Journal of World Business. 57 (5): 101310. doi:10.1016/j.jwb.2022.101310. ISSN 1090-9516.
and 25 Related for: Necessity and sufficiency information
In logic and mathematics, necessityandsufficiency are terms used to describe a conditional or implicational relationship between two statements. For...
Biological tests of necessityandsufficiency refer to experimental methods and techniques that seek to test or provide evidence for specific kinds of...
In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They...
called converse error, fallacy of the converse, or confusion of necessityandsufficiency, is a formal fallacy of taking a true conditional statement (e...
Logical symbols representing iff In logic and related fields such as mathematics and philosophy, "if and only if" (often shortened as "iff") is paraphrased...
greatly concerned with the logical statuses of propositions, e.g. necessity, contingency, and impossibility. In the twentieth century, possible worlds have...
categorical syllogism is not distributed. Modal fallacy – confusing necessity with sufficiency. A condition X is necessary for Y if X is required for even the...
scenes, and description. Currently, there is no consensus within the writing community regarding the number and composition of fiction-writing modes and their...
[citation needed] References feature in many spheres of human activity and knowledge, and the term adopts shades of meaning particular to the contexts in which...
field of logic and that of computer science. The topic can essentially be divided into three main areas: Theoretical foundations and analysis Use of...
A closed concept is a concept where all the necessary and sufficient conditions required to include something within the concept can be listed. For example...
location, the name for use in HTML documents, and the LaTeX symbol. The following symbols are either advanced and context-sensitive or very rarely used: As...
collects only scenarios that have been called a paradox by at least one source and have their own article in this encyclopedia. Although considered paradoxes...
called a proper name (although that term has a philosophical meaning as well) and is, when consisting of only one word, a proper noun. Other nouns are sometimes...
of Kripke and others (see Hilary Putnam), philosophers tend to distinguish the notion of aprioricity more clearly from that of necessityand analyticity...
the subject of continued debate. Treating logical truths, analytic truths, and necessary truths as equivalent, logical truths can be contrasted with facts...
the free dictionary. Antecedent (logic) Conjecture Necessityandsufficiency Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith...
language.] Affirming the consequent Modus ponens Modus tollens Necessityandsufficiency Plausible reasoning Matthew C. Harris. "Denying the antecedent"...
errors in definitions that were assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox...
this approach, especially in relation to modality, in his book Naming andNecessity. There is a presumption in the classic example of a definition that...
the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and "Socrates is a man" to the...
do it again and I don't want to do it again both presuppose that the subject has done it already one or more times; My wife is pregnant and My wife is...
practice of fitting the final selected model followed by reporting estimates and confidence intervals without adjusting them to take the model building process...