"This is a significant and ofren rather demanding collection of essays. It is an anthology purring together the uncollected works of an important twentieth-century philosopher. Many of the articles treat one or another of the more important issues considered by analytic philosophers during the last quarter-century. Of significant importance to philosophers interested in researching the many topics contained in Logic Matters is the inclusion in this anthology of a rather extensive eight-page name-topic index." --Thomist "The papers are arranged by topic: Historical Essays, Traditional Logic, Theory of Reference and Syntax, Intentionality, Quotation and Semantics, Set Theory, Identity Theory, Assertion, Imperatives and Practical Reasoning, Logic in Metaphysics and Theology. The broad range of issues that have engaged Geach's complex and systematic reasoning is impressive. In addition to classical logic, topics in ethics, ontology, and even the logic of religious dogmas are tackled .... the work in this collection is more brilliant and ingenious than it is difficult and demanding." --Philosophy of Science "Geach displays his mastery of applying logical techniques and concepts to philosophical questions. Compared with most works in philosophical logic this book is remarkable for its range of topics. Plato, Aristotle, Aquinas, Russell, Wittgenstein, and Quine all figure prominently. Geach's style is remarkably lively considering the rightly argued matter. Although some of the articles treat rather technical questions in mathematical logic, most are accessible to philosophers with modest backgrounds in logic." --Choice
A clear and accessible treatment of Gödel's famous, intriguing, but much misunderstood incompleteness theorems, extensively revised in a second edition.
Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.
The second volume of Jonathan Barnes' papers on ancient philosophy contains twenty-seven pieces under the broad heading of Logic. The essays were written over a period of some forty years. Some of them were published in obscure places (and two or three of them in a foreign language). The French essays have been done into English; and all the essays have been retouched, and a few of them substantially revised. The first three essays in the volume are of a general nature, being concerned with ancient views on the status of logic--and with the distinction between formal and material inferences. The next nine items deal with different aspects of Aristotelian logic--the copula, negation, the categories, homonymy, and the principle of contradiction. Then come three papers about the connection (or lack of connection) between Aristotelian logic and Stoic logic. Two of the pieces discuss Theophrastus' theory of 'hypothetical' syllogisms. After that, things run more or less chronologically--a short notice on the Dialecticians, three essays on aspects of Stoic logic, a pair of papers on ancient theories of meaning, items on adverbs and connectors, on Philoponus and Boethius, and on an anonymous tract written in the autumn of 1007 AD. All in all, there is matter to divert scholars and students of ancient philosophy.
For decades, the reigning scholarly wisdom about nuclear weapons policy has been that the United States only needs the ability to absorb an enemy nuclear attack and still be able to respond with a devastating counterattack. So long as the US, or any other nation, retains such an assured retaliation capability, no sane leader would intentionally launch a nuclear attack against it, and nuclear deterrence will hold. According to this theory, possessing more weapons than necessary for a second-strike capability is illogical. This argument is reasonable, but, when compared to the empirical record, it raises an important puzzle. Empirically, we see that the United States has always maintained a nuclear posture that is much more robust than a mere second-strike capability. In The Logic of American Nuclear Strategy, Matthew Kroenig challenges the conventional wisdom and explains why a robust nuclear posture, above and beyond a mere second-strike capability, contributes to a state's national security goals. In fact, when a state has a robust nuclear weapons force, such a capability reduces its expected costs in a war, provides it with bargaining leverage, and ultimately enhances nuclear deterrence. This book provides a novel theoretical explanation for why military nuclear advantages translate into geopolitical advantages. In so doing, it helps resolve one of the most-intractable puzzles in international security studies. Buoyed by an innovative thesis and a vast array of historical and quantitative evidence, The Logic of American Nuclear Strategy will force scholars to reconsider their basic assumptions about the logic of nuclear deterrence.
Provides an essential introduction to classical logic.
This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.
At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Godel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises."
The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them. Introduction to Mathematical Logic includes: propositional logic first-order logic first-order number theory and the incompleteness and undecidability theorems of Gödel, Rosser, Church, and Tarski axiomatic set theory theory of computability The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.
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
Logic for Philosophy is an introduction to logic for students of contemporary philosophy. It is suitable both for advanced undergraduates and for beginning graduate students in philosophy. It covers (i) basic approaches to logic, including proof theory and especially model theory, (ii)extensions of standard logic that are important in philosophy, and (iii) some elementary philosophy of logic. It emphasizes breadth rather than depth. For example, it discusses modal logic and counterfactuals, but does not prove the central metalogical results for predicate logic (completeness,undecidability, etc.) Its goal is to introduce students to the logic they need to know in order to read contemporary philosophical work. It is very user-friendly for students without an extensive background in mathematics. In short, this book gives you the understanding of logic that you need to dophilosophy.
The standard rules of probability can be interpreted as uniquely valid principles in logic. In this book, E. T. Jaynes dispels the imaginary distinction between 'probability theory' and 'statistical inference', leaving a logical unity and simplicity, which provides greater technical power and flexibility in applications. This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. New results are discussed, along with applications of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology. It contains many exercises and problems, and is suitable for use as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher. The book will be of interest to scientists working in any area where inference from incomplete information is necessary.
Many people find themselves dissatisfied with recent linguistic philosophy, and yet know that language has always mattered deeply to philosophy and must in some sense continue to do so. Ian Hacking considers here some dozen case studies in the history of philosophy to show the different ways in which language has been important, and the consequences for the development of the subject. There are chapters on, among others, Hobbes, Berkeley, Russell, Ayer, Wittgenstein, Chomsky, Feyerabend and Davidson. Dr Hacking ends by speculating about the directions in which philosophy and the study of language seem likely to go. The book will provide students with a stimulating, broad survey of problems in the theory of meaning and the development of philosophy, particularly in this century. The topics treated in the philosophy of language are among the central, current concerns of philosophers, and the historical framework makes it possible to introduce concretely and intelligibly all the main theoretical issues.
A respected Indian authority on sex presents his theory that pure sex is equivalent to the human life force and deconstructs societal layers of sexual repression and guilt to explain how people can restore sexual functioning to a state of healthy sensuality and self-discovery. Reprint. 10,000 first printing.
Why Marriage Matters offers a compelling and clear discussion of a question at the forefront of our national consciousness. It is the work of a brilliant civil rights litigator who has dedicated his life to the protection of individuals' rights and our Constitution's commitment to equal justice under the law. Above all, it is a thoughtful, straightforward book that brings into sharp focus the human significance of the right to marry in America -- not just for some couples, but for all. Whatever your personal beliefs, we all can agree that marriage equality provokes both passion and tension, and looms large in our nation's politics. Marriage means many things to many people -- emotionally, spiritually, intellectually -- but in these pages, Evan Wolfson demonstrates a truth that is undeniable: Marriage is the legal gateway to a vast array of tangible and intangible protections, responsibilities, and benefits, most of which cannot be replicated in any other way. Wolfson is a formidable legal thinker who has participated in landmark cases to end race discrimination in jury trials, to secure the rights of battered married women, and to challenge the abuse of power at the highest level in government. Now, with extraordinary clarity, fascinating stories, and legal and historical examples, he addresses the questions we as Americans are asking ourselves as we consider how marriage equality will affect our lives. Why is the word marriage so important? What are the stakes for America in this civil rights movement? How can people of different faiths reconcile their beliefs with the idea of marriage for same-sex couples? How will allowing gay couples to marry affect children? Here you will find thorough, honest answers -- some that may surprise you, some that will persuade you, many that will move you. Wolfson recalls the history of past battles over marriage and movements for equality, and articulates the everyday acts of discrimination that frame this current movement -- acts of discrimination that, if faced by non-gay Americans, would provoke a resounding cry of injustice. Marriage matters because it is a foundation upon which most Americans build dreams. It is the cornerstone of commitment one individual makes to another -- a commitment we are taught is the highest expression of love, dedication, and responsibility. In this, the most powerful, authoritative, and fairly articulated book on the subject, Wolfson demonstrates why the right to marry is important -- indeed necessary -- for all couples and for America's promise of equality.
In Vibrant Matter the political theorist Jane Bennett, renowned for her work on nature, ethics, and affect, shifts her focus from the human experience of things to things themselves. Bennett argues that political theory needs to do a better job of recognizing the active participation of nonhuman forces in events. Toward that end, she theorizes a “vital materiality” that runs through and across bodies, both human and nonhuman. Bennett explores how political analyses of public events might change were we to acknowledge that agency always emerges as the effect of ad hoc configurations of human and nonhuman forces. She suggests that recognizing that agency is distributed this way, and is not solely the province of humans, might spur the cultivation of a more responsible, ecologically sound politics: a politics less devoted to blaming and condemning individuals than to discerning the web of forces affecting situations and events. Bennett examines the political and theoretical implications of vital materialism through extended discussions of commonplace things and physical phenomena including stem cells, fish oils, electricity, metal, and trash. She reflects on the vital power of material formations such as landfills, which generate lively streams of chemicals, and omega-3 fatty acids, which can transform brain chemistry and mood. Along the way, she engages with the concepts and claims of Spinoza, Nietzsche, Thoreau, Darwin, Adorno, and Deleuze, disclosing a long history of thinking about vibrant matter in Western philosophy, including attempts by Kant, Bergson, and the embryologist Hans Driesch to name the “vital force” inherent in material forms. Bennett concludes by sketching the contours of a “green materialist” ecophilosophy.
This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.