Logical forms. An introduction to philosophical logic. (Q2768758)

This book is an introduction to philosophical logic, or the philosophy of logic. It is essentially a textbook, designed with the novice in mind, and developing progressively to some quite sophisticated discussion. At the same time, it explores its central issues with enough depth and detail to make it well worth a professional philosopher's or logician's study. The book is about logical form, and the question of what are the logical forms of expressions in natural language, or how such expressions should best be formalized, and how they are related to the expressions of artificially designed formal languages. The goal is to give an account of validity of arguments in natural language as dependent on logical form. Three artificial languages are introduced, \({\mathbf P}\), essentially the language of the classical propositional calculus, \({\mathbf Q}\), essentially the language of classical first-order logic, and \({\mathbf Q}{\mathbf N}\), the result of adding modal operators to \({\mathbf Q}\). With all three there are serious questions about how well their sentences correspond in form or content to sentences of natural languages. For example, one may ask how well the material implication, \(\to\), of \({\mathbf P}\) formalizes `if-then' of English, or how well \(\forall x(Fx\to Gx)\) of \({\mathbf Q}\) formalizes sentences of the sort `All \(F\)'s are \(G\)'. In discussing such questions, the author introduces much of the current discussion from the philosophy of language and logic. Chapter 3, for example, is devoted to the conditional, distinguishing indicative from subjunctive conditionals, examining whether they are truth-functional, or even truth-conditional sentences, and considering the interconnections between conditionals and probabilities. Chapter 4 on quantification discusses many topics, such as theories of definite descriptions, names, including non-denoting names, adjectives and adverbs, predicate quantifiers, etc. Chapter 5 on modal logic takes one through many questions about possible worlds and Lewis's counterpart-theory. Chapter 6 draws it all together and examines the project of formalization itself. Though one might quibble over some of the author's arguments, he is non-dogmatic throughout, and acknowledges that there is much controversy on most of these topics. (One might also question whether the enterprise of philosophical logic is, or should be, so much concerned with the questions of formalizing natural language sentences, though the author is working within a well-entrenched tradition.) This is the second edition of this work. It differs from the first (1991) chiefly in the updated Chapter 3 on Conditionals and Probabilities, and sections on Predicate Quantifiers, on Free Logic, on Non-indicative and Counterfactual Conditionals, and on Counterpart Theory. The book has exercises throughout to illustrate its points, and each chapter ends with a list of Bibliographical Notes to set the discussion in context and to encourage the reader to pursue the primary sources for that discussion.