 If “if” is truth-functional, this is the right truth function to assign to it: of the sixteen possible truth-functions of \(A\) and \(B\), it is the only serious candidate. First, it is uncontroversial that when \(A\) is true and \(B\) is false, “If \(A, B\)” is false. A basic rule of inference is modus ponens: from “If \(A, B\)” and \(A\), we can infer \(B\). If it were possible to have \(A\) true, \(B\) false and “If \(A, B\)” true, this inference would be invalid. Second, it is uncontroversial that “If \(A, B\)” is sometimes true when \(A\) and \(B\) are respectively (true, true), or (false, true), or (false, false). “If it’s a square, it has four sides”, said of an unseen geometric figure, is true, whether the figure is a square, a rectangle or a triangle. Assuming truth-functionality — that the truth value of the conditional is determined by the truth values of its parts — it follows that a conditional is always true when its components have these combinations of truth values.