 The truth-functional theory of the conditional was integral to Frege’s new logic (1879). It was taken up enthusiastically by Russell (who called it “material implication”), Wittgenstein in the Tractatus, and the logical positivists, and it is now found in every logic text. It is the first theory of conditionals which students encounter. Typically, it does not strike students as obviously correct. It is logic’s first surprise. Yet, as the textbooks testify, it does a creditable job in many circumstances. And it has many defenders. It is a strikingly simple theory: “If \(A, B\)” is false when \(A\) is true and \(B\) is false. In all other cases, “If \(A, B\)” is true. It is thus equivalent to “\({\sim}(A \amp{\sim}B)\)” and to “\({\sim}A\) or \(B\)”. “\(A \supset B\)” has, by stipulation, these truth conditions.