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

Description

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. Front Matter....Pages I-XIII The Indicative Conditional....Pages 1-42 Mathematical Theory of Probabilistic Consistency and Universal Probabilistic Soundness....Pages 43-68 Motives for Wanting to Assure the Soundness of Reasoning; Truth and Probability as Desirable Attributes of Conclusions Reached in Reasoning....Pages 69-102 A Hypothesis Concerning Counterfactuals; Probability Change Aspects of Inference....Pages 103-147 Back Matter....Pages 148-161