 The generally most fruitful, and time-honoured, approach to specifying the meaning of a complex sentence in terms of the meanings of its parts, is to specify the truth conditions of the complex sentence, in terms of the truth conditions of its parts. A semantics of this kind yields an account of the validity of arguments involving the complex sentence, given the conception of validity as necessary preservation of truth. Throughout this section we assume that this approach to conditionals is correct. Let \(A\) and \(B\) be two sentences such as “Ann is in Paris” and “Bob is in Paris”. Our question will be: are the truth conditions of “If \(A, B\)” of the simple, extensional, truth-functional kind, like those of “\(A\) and \(B\)”, “\(A \text{ or } B\)” and “It is not the case that \(A\)”? That is, do the truth values of \(A\) and of \(B\) determine the truth value of “If \(A, B\)”? Or are they non-truth-functional, like those of “\(A\) because \(B\)”, “\(A\) before \(B\)”, “It is possible that \(A\)”? That is, are they such that the truth values of \(A\) and \(B\) may, in some cases, leave open the truth value of “If \(A, B\)”? 