A History Of Connexivity

Abstract

Connexive implication is a type of implication first defined in the 4th Century B.C., a time of active debate when it was said that the very crows on the rooftops were croaking about what conditionals were true. In Sextus Empiricus’ Outlines of Pyrrhonism , which discusses four varieties of implication, including [1] material (Philonian) and [2] strict (Diodorean) implication, we read:” “[3] And those who introduce the notion of connection say that a conditional is sound when the contradictory of its consequent is incompatible with its antecedent.” [ Kneale, 1962 , 129] It follows from this definition that no conditional of the form “If p then not- p ” can be true, since the contradictory of not- p , i.e. p , is never incompatible with p . Accepting this in turn requires that “compatibility” be essentially a relational concept, and that whether or not A is compatible with B cannot be determined by examining A and B separately. Thus even “ p & ˜ p ” is not incompatible with itself, and “If p & ˜ p , then not-( p & ˜ p )” is connexively false.