The Logic of Conditionals : An Application of Probability to Deductive Logic

Of the four chapters in this book, the first two discuss (albeit in consider- ably modified form) matters previously discussed in my papers On the Logic of Conditionals [1] and Probability and the Logic of Conditionals [2], while the last two present essentially new material. Chapter I is relatively informal and roughly parallels the first of the above papers in discussing the basic ideas of a probabilistic approach to the logic of the indicative conditional, according to which these constructions do not have truth values, but they do have probabilities (equal to conditional probabilities), and the appropriate criterion of soundness for inferences involving them is that it should not be possible for all premises of the inference to be probable while the conclusion is improbable. Applying this criterion is shown to have radically different consequences from the orthodox material conditional theory, not only in application to the standard fallacies of the material conditional, but to many forms (e. g., Contraposition) which have hitherto been regarded as above suspi- cion. Many more applications are considered in Chapter I, as well as certain related theoretical matters. The chief of these, which is the most important new topic treated in Chapter I (i. e.