Machine generated contents note: 1. The Computability Concept;2. General Recursive Functions;3. Programs and Machines;4. Recursive Enumerability;5. Connections to Logic;6. Degrees of Unsolvability;7. Polynomial-Time Computability;Appendix: Mathspeak;Appendix: Countability;Appendix: Decadic Notation;.

“The church is not the Old Israel, even though the Old Israel looked beyond itself; the church is the Israel of God, the ‘remnant chosen by grace.’ ”.

A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional (...) coverage of introductory material such as sets. Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses. Reduced mathematical rigour to fit the needs of undergraduate students. (shrink)

Christopher Hookway has been influential in promoting engagement with pragmatist and naturalist perspectives from classical and contemporary American philosophy. This book reflects on Hookway’s work on the American philosophical tradition and its significance for contemporary discussions of the understanding of mind, meaning, knowledge, and value. -/- Hookway’s original and extensive studies of Charles S. Peirce have made him among the most admired and frequently referenced of Peirce’s interpreters. His work on classical American pragmatism has explored the philosophies of William James, (...) John Dewey, and Josiah Royce, and examined the influence of pragmatist ideas outside of the United States. Additionally, Hookway has participated in a number of celebrated exchanges with some of the most high-profile figures of twentieth- and twenty-first-century philosophy, including Karl-Otto Apel, Philip Pettit, Hilary Putnam, and W.V.O. Quine, through which his treatments of a large range of topics in epistemology and the philosophies of mind and language have been developed and promoted. The chapters in this book—which include contributions from several of Hookway’s former students and colleagues—include studies of Hookway’s engagement with the works of Peirce, James, and Dewey, his contributions to virtue epistemology, and his discussions of hope and pragmatist metaphysics. -/- Pragmatic Reason will be of interest to researchers and advanced students working on American philosophy, the history of analytic philosophy, and epistemology. (shrink)

The journal of symbolic logic began publishing in 1936. From the outset, the Journal included a Reviews Section, edited by Alonzo Church. The very first issue carried three pages of reviews, written by Bernays, Church, Rosser, and Quine.As the first issue stated, “It is intended that this section of the Journal shall serve as a complete bibliography of current literature in the field of symbolic logic, from January 1, 1936. To this end an effort will be made to include in (...) it, at least by title, all publications in this field, both books and articles in journals, and as far as possible these will be accompanied by signed reviews.” Thus the purpose of the Reviews Section was two-fold. For one, there was its bibliographical function: to provide a complete, suitably indexed, listing of all the publications—both books and journal articles—in symbolic logic, wherever and in whatever language published. And secondly, the reviews were to provide critical, analytical commentary on these publications, whenever possible.The Reviews Section should be viewed as a continuation and expansion of Church's A bibliography of symbolic logic. The Bibliography was a listing, with some annotations, of the publications in symbolic logic prior to 1936. It was published as volume 1, number 4 of the Journal. Church made the listing as complete as he could, of course. (shrink)

Kant suggests that moral metaphysics can be shown to be politically applicable by thinking of the analogically similar applicability of the principles of speculative reason to the external world of sense experience. Just as the categories of understanding, e.g., causality, substance, and so on must be schematized, i.e., given a temporal representation in order to be made applicable to the forms of sensuous intuitions, so also the principles of morality—most especially the idea of the autonomous will—must be schematized to be (...) made politically applicable. The paper shows how Kant employs his schematism in metaphysics to make the principles of morality applicable to political experience and concludes with observations on the moral and political implications of a politics that pays homage to Kantian morality. (shrink)

Kant suggests that moral metaphysics can be shown to be politically applicable by thinking of the analogically similar applicability of the principles of speculative reason to the external world of sense experience. Just as the categories of understanding, e.g., causality, substance, and so on must be schematized, i.e., given a temporal representation in order to be made applicable to the forms of sensuous intuitions, so also the principles of morality—most especially the idea of the autonomous will—must be schematized to be (...) made politically applicable. The paper shows how Kant employs his schematism in metaphysics to make the principles of morality applicable to political experience and concludes with observations on the moral and political implications of a politics that pays homage to Kantian morality. (shrink)

This book presents a collection of articles on applied general equilibrium analysis by major contributors to this field. This rapidly expanding method of analysis involves the use of computers to study entire economies and the interrelationships among firms, households and governments in these economies. There are also articles on the particular computational techniques involved in the numerical estimation of these equilibrium models and on several particular applications. Papers deal with the United States, Mexican and Australian economies. Other chapters provide an (...) analysis of long-run energy problems, fiscal federalism and economic planning. (shrink)