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.