Abstract

This chapter looks at conditional disputations, discussing truth-conditions for conditionals, and adopting the Lukasiewicz conditional. Such a conditional is false when the antecedent is true and the consequent false, and true if the truth-value status of the consequent is at least as high as that of the antecedent. The Lukasiewicz conditional satisfies _modus ponens_, _modus tollens_, hypothetical syllogism, and contraposition, but only a restricted form of conditional proof. The examination also looks at another argument of Williamson, which defends bivalent versions of the Tarski biconditionals. It holds that his rationale for the biconditionals are subject to interpretation, and that interpretations that do not make them beg the question rationalise only non-bivalent versions.