# material implication

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material implication
The truth-function of two propositions p, q, defined as false if p is true and q false, but true in the other three cases. It is normally written pq . The first logician to distinguish the four ways in which truth-values can be associated with two propositions (TT, TF, FT, FF) and to suggest identifying ‘if p then q ’ as the proposition true in every case except the second, was probably Philo of Megara, in the 4th century BC. See also material implication, paradoxes of.

Philosophy dictionary. . 2011.

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• material implication — noun An implication as defined in classical propositional logic, leading to the truth of paradoxes of implication such as Q (P P), to be read as any proposition whatsoever is a sufficient condition for a true proposition . Syn: material… …   Wiktionary

• material implication — noun : implication 2b(1) * * * Logic. equivalence (def. 4a). [1900 05] …   Useful english dictionary

• material implication — Logic. equivalence (def. 4a). [1900 05] * * * …   Universalium

• material implication, paradoxes of — The truth function of material implication gives a proposition p → q which is true except in the case in which p is true and q is false. It also corresponds fairly well to the conditional form ‘If p then q ’. But whenever p is false, p → q is… …   Philosophy dictionary

• Paradoxes of material implication — Implication, in logic, describes conditional if then statements, e.g., if it is raining, then I will bring an umbrella. There are many ways to formalise implication, of which material implication is one of the simplest. It equates the statement… …   Wikipedia

• material conditional — material implication …   Philosophy dictionary

• Material conditional — The material conditional, also known as material implication, is a binary truth function, such that the compound sentence p→q (typically read if p then q or p implies q ) is logically equivalent to the negative compound: not (p and not q). A… …   Wikipedia

• implication — implicational, adj. /im pli kay sheuhn/, n. 1. something implied or suggested as naturally to be inferred or understood: to resent an implication of dishonesty. 2. the act of implying: His implication of immediate changes surprised us. 3. the… …   Universalium

• Material nonimplication — Venn diagram of …   Wikipedia

• Implication — can refer to:* Logic: ** Logical implication as regarded in mathematical logic. ** Material conditional as regarded in philosophical logic.:* Entailment (pragmatics):Also, in linguistics, there are different specialized related notions::*… …   Wikipedia