- 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*p*→*q*. 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.
Academic.
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