Author: Richard L Epstein

Publisher: Advanced Reasoning Forum

Published: 2018-11-05

Total Pages: 204

ISBN-13: 0983452113

This series of books presents the fundamentals of reasoning well, in a style accessible to both students and scholars. The text of each essay presents a story, the main line of development of the ideas, while the footnotes and appendices place the research within a larger scholarly context. The essays overlap, forming a unified analysis of reasoning, yet each essay is designed so that it may be read independently of the others. The topic of this volume is the evaluation of reasoning about cause and effect, reasoning using conditionals, and reasoning that involves explanations. The essay "Reasoning about Cause and Effect" sets out a way to analyze whether there is cause and effect in terms of whether an inference from a claim describing the purported cause to a claim describing the purported effect satisfies specific conditions. Different notions of cause and effect correspond to placing different conditions on what counts as a good causal inference. An application of that method in "The Directedness of Emotions" leads to a clearer understanding of the issue whether every emotion need be directed at something. In the essay "Conditionals" various ways of analyzing reasoning with claims of the form "if . . . then . . ." are surveyed. Some of those uses are meant to be judged as inferences that are not necessarily valid, and conditions are given for when we can consider such inferences to be good. In "Explanations" verbal answers to a question why a claim is true are evaluated in terms of conditions placed on inferences from the explaining claims to the claim being explained. Recognizing that the direction of inference of such an explanation is the reverse of that for an argument with the very same claims is crucial in their evaluation. Explanations in terms of functions and goals are also investigated.

Author: Richard L Epstein

Publisher: Advanced Reasoning Forum

Published: 2018-11-05

Total Pages: 509

ISBN-13: 0983452172

This book presents the history, philosophy, and mathematics of the major systems of propositional logic. Classical logic, modal logics, many-valued logics, intuitionism, paraconsistent logics, and dependent implication are examined in separate chapters. Each begins with a motivation in the originators' own terms, followed by the standard formal semantics, syntax, and completeness theorem. The chapters on the various logics are largely self-contained so that the book can be used as a reference. An appendix summarizes the formal semantics and axiomatizations of the logics. The view that unifies the exposition is that propositional logics comprise a spectrum: as the aspect of propositions under consideration varies, the logic varies. Each logic is shown to fall naturally within a general framework for semantics. A theory of translations between logics is presented that allows for further comparisons, and necessary conditions are given for a translation to preserve meaning. For this third edition the material has been re-organized to make the text easier to study, and a new section on paraconsistent logics with simple semantics has been added which challenges standard views on the nature of consequence relations. The text includes worked examples and hundreds of exercises, from routine to open problems, making the book with its clear and careful exposition ideal for courses or individual study.