Abstract

The author has constructed a concept of conditionals by synthetizing and developing unconnected insights scattered through the literature. The result is incorporated in a formal deductive system, based on a series of "paradox-free" systems initiated by Alonzo Church and interpreted according to principles suggested chiefly by Everett Nelson and by Anderson and Belnap. The basic concept is the sufficiency relation holding between clauses of a conditional, or rather between the relevant states of affairs asserted by the clauses. The logic of sufficiency is developed by using a phenomenological method, much like that of the ordinary-language linguists, to place restrictions on truth-functional logic. For example, conjunction is replaced by adjunction [ = df. ~ ] and this concept is used to modify modus ponens and simplification. Relevance requirements avoid the paradoxes of material implication. These principles, together with a number of physical modalities and some modifications of the concept of induction, are used to attack Goodman's paradox and the paradoxes of confirmation, and to form a concept of cause. The formal system incorporates the principles judged desirable by the analysis of how conditionals are used in discourse. Mr. Barker is modest in his claims, emphasizing that his material is not original and saying only that some of the famous paradoxes "show signs of yielding." Interested students will be grateful for this monograph. It is a valuable compendium of widely scattered work of a difficult and complicated subject, and should be both helpful and stimulating. Moreover, it is particularly clear and readable.--L. G.