Hypotheticals: Conditionals and Theticals

Abstract

1. For millennia philosophers have been grappling with the problem of the logic of conditionals-the problem of determining which principles of inference hold for conditional statements. Surprisingly enough (considering the nature of philosophers) there has been almost universal agreement on at least a small number of these principles, including, for example, modus ponens, modus tollens, hypothetical syllogism and contraposition. Most of the dispute about the logic of conditionals has concerned whether or not certain additional principles, such as those which generate the so-called paradoxes of material implication, hold for conditionals. Recently, however, several philosophers have presented putative counterexamples to hypothetical syllogism and to contraposition, and have argued that these patterns of inference are not valid for conditionals. I will try to show that these philosophers are mistaken because their examples involve certain hypothetical statements which are not genuine conditionals at all. Since this strategy presupposes that hypotheticals (i.e., 'if '-statements) can be legitimately divided into at least two categories (which I shall call conditionals on the one hand and theticals on the other), I must at least address the problem of providing a comprehensive account of hypotheticals.1 I shall first try to show that 'if '-sentences are used in ordinary discourse to make several distinguishable kinds of statements, one of these, the genuine conditional, involving an assertion that the state of affairs described by the apodosis is conditional upon, or a consequence of, the state of affairs described by the protasis. This kind of statement, in the making of which the speaker posits a consequential connection between the protasis-state and the apodosisstate, does seem to obey the principles of hypothetical syllogism and contraposition. Secondly, I shall try to show that the putative counterexamples to these principles involve theticals-hypotheticals which are not assertions that the apodosis-state is a consequence of the protasis-state. Finally, I shall attempt to show that the relevant theticals not only fail to obey the rules of hypothetical syllogism and contraposition, but fail to obey other basic principles, such as modus ponens and modus tollens. If my arguments are sound, it will follow that a theorist who tries to devise a logic of hypotheticals-