The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of (basic) truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice (a lattice of truth values with two ordering relations) constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, a trilattice of truth values - a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi.

John Horty effectively develops deontic logic (the logic of ethical concepts like obligation and permission) against the background of a formal theory of agency. He incorporates certain elements of decision theory to set out a new deontic account of what agents ought to do under various conditions over extended periods of time. Offering a conceptual rather than technical emphasis, Horty's framework allows a number of recent issues from moral theory to be set out clearly and discussed from a uniform point of view.

cians concerned with using logical tools in philosophy have been keenly aware of the limitations that arise from the original con centration of symbolic logic on the idiom of mathematics, and many of them have worked to create extensions of the received logical theories that would make them more generally applicable in philosophy. Carnap's Testability and Meaning, published in 1936 and 1937, was a good early example of this sort of research, motivated by the inadequacy of first-order formalizations of dis 'This sugar cube is soluble in water'. positional sentences like And in fact there is a continuous history of work on this topic, extending from Carnap's paper to Shoham's contribution to the present volume . . Much of the work in philosophical logic, and much of what has appeared in The Journal of Philosophical Logic, was mo tivated by similar considerations: work in modal logic (includ ing tense, deontic, and epistemic logic), intensional logics, non declaratives, presuppositions, and many other topics. In this sort of research, sin.ce the main point is to devise new formalisms, the technical development tends to be rather shallow in comparison with mathematical logic, though it is sel dom absent: theorems need to be proved in order to justify the formalisms, and sometimes these are nontrivial. On the other hand, much effort has to go into motivating a logical innovation."

In the great libraries of Europe and the United States, hidden in fading manuscripts on forgotten shelves, lie the works of medieval Hebrew logic. From the end of the twelfth century through the Renaissance, Jews wrote and translated commentaries and original compositions in Aristotelian logic. One can say without exaggeration that wherever Jews studied philosophy - Spain, France, Northern Africa, Germany, Palestine - they began their studies with logic. Yet with few exceptions, the manuscripts that were catalogued in the last century have failed to arouse the interest of modem scholars. While the history of logic is now an established sub-discipline of the history of philosophy, the history of Hebrew logic is only in its infancy. The present work contains a translation and commentary of what is arguably the greatest work of Hebrew logic, the Sefer ha-Heqqesh ha-Yashar (The Book of the Correct Syllogism) of Levi ben Gershom (Gersonides; 1288-1344). Gersonides is well known today as a philosopher, astronomer, mathematician, and biblical exegete. But in the Middle Ages he was also famous for his prowess as a logician. The Correct Syllogism is his attempt to construct a theory of the syllogism that is free of what he considers to be the 'mistakes' of Aristotle, as interpreted by the Moslem commentator A verroes. It is an absorbing, challenging work, first written by Gersonides when he was merely thirty-one years old, then significantly revised by him. The translation presented here is of the revised version.

This book provides readers with a guide to both ordinal analysis, and to proof theory. It mainly focuses on ordinal analysis, a research topic in proof theory that is concerned with the ordinal theoretic content of formal theories. However, the book also addresses ordinal analysis and basic materials in proof theory of first-order or omega logic, presenting some new results and new proofs of known ones.Primarily intended for graduate students and researchers in mathematics, especially in mathematical logic, the book also includes numerous exercises and answers for selected exercises, designed to help readers grasp and apply the main results and techniques discussed.

As a philosopher, psychologist, and physician, the German thinker Hermann Lotze (1817-81) defies classification. Working in the mid-nineteenth-century era of programmatic realism, he critically reviewed and rearranged theories and concepts in books on pathology, physiology, medical psychology, anthropology, history, aesthetics, metaphysics, logic, and religion. Leading anatomists and physiologists reworked his hypotheses about the central and autonomic nervous systems. Dozens of fin-de-siecle philosophical contemporaries emulated him, yet often without acknowledgment, precisely because he had made conjecture and refutation into a method. In spite of Lotze's status as a pivotal figure in nineteenth-century intellectual thought, no complete treatment of his work exists, and certainly no effort to take account of the feminist secondary literature. Hermann Lotze: An Intellectual Biography is the first full-length historical study of Lotze's intellectual origins, scientific community, institutional context, and worldwide reception.

Recent work in argumentation theory has emphasized the nature of arguers and arguments along with various theoretical perspectives. Less attention has been given to the third feature of any argumentative situation - the audience. This book fills that gap by studying audience reception to argumentation and the problems that come to light as a result of this shift in focus. Christopher W. Tindale advances the tacit theories of several earlier thinkers by addressing the central problems connected with audience considerations in argumentation, problems that earlier philosophical theories overlook or inadequately accommodate. The main tools employed in exploring the central issues are drawn from contemporary philosophical research on meaning, testimony, emotion and agency. These are then combined with some of the major insights of recent rhetorical work in argumentation to advance our understanding of audiences and suggest avenues for further research.

Hegel on Being provides an authoritative treatment of Hegel's entire logic of being. Stephen Houlgate presents the Science of Logic as an important and neglected text within Hegel's oeuvre that should hold a more significant place in the history of philosophy. In the Science of Logic, Hegel set forth a distinctive conception of the most fundamental forms of being through ideas on quality, quantity and measure. Exploring the full trajectory of Hegel's logic of being from quality to measure, this two-volume work by a preeminent Hegel scholar situates Hegel's text in relation to the work of Plato, Aristotle, Descartes, Spinoza, Kant, and Frege. Volume I: Quality and the Birth of Quantity in Hegel's 'Science of Logic' covers all material on the purpose and method of Hegel's dialectical logic and charts the crucial transition from the concept of quality to that of quantity, as well as providing an original account of Hegel's critique of Kant's antinomies across two chapters. Volume II: Quantity and Measure in Hegel's 'Science of Logic' continues the discussion of Hegel's logic of being and considers all aspects of quantity and measure in his logic, including his basic categories of being, writings on calculus, philosophy of mathematics, as well as a comparative study of Hegel and Frege's approach to logic. Lucidly written, with characteristic philosophical depth and analysis, Houlgate's Hegel on Being explicates one of Hegel's most complex works, providing a vital reference for a generation of Hegel scholars and a major contribution to the literature on 19th century German philosophy.

This book offers an original philosophical perspective on exemplarity. Inspired by Wittgenstein's later work and Derrida's theory of deconstruction, it argues that examples are not static entities but rather oscillate between singular and universal moments. There is a broad consensus that exemplary cases mediate between singular instances and universal concepts or norms. In the first part of the book, Macha contends that there is a kind of differance between singular examples and general exemplars or paradigms. Every example is, in part, also an exemplar, and vice versa. Furthermore, he develops a paracomplete approach to the logic of exemplarity, which allows us to say of an exemplar of X neither that it is an X nor that it is not an X. This paradox is structurally isomorphic to Russell's paradox and can be addressed in similar ways. In the second part of the book, Macha presents four historical studies that exemplify the ideas developed in the first part. This part begins with Plato's Forms, understood as standards/paradigms, before considering Kant's theory of reflective judgment as a general epistemological account of exemplarity. This is then followed by analyses of Hegel's conceptual moment of particularity and Kuhn's concept of paradigm. The book concludes by discussing the speculative hypothesis that all our knowledge is based on paradigms, which, following the logic of exemplarity, are neither true nor false. The Philosophy of Exemplarity will be of interest to scholars and advanced students working in philosophy of language, logic, history of philosophy, and literary theory.

The Quantum of Explanation advances a bold new theory of how explanation ought to be understood in philosophical and cosmological inquiries. Using a complete interpretation of Alfred North Whitehead's philosophical and mathematical writings and an interpretive structure that is essentially new, Auxier and Herstein argue that Whitehead has never been properly understood, nor has the depth and breadth of his contribution to the human search for knowledge been assimilated by his successors. This important book effectively applies Whitehead's philosophy to problems in the interpretation of science, empirical knowledge, and nature. It develops a new account of philosophical naturalism that will contribute to the current naturalism debate in both Analytic and Continental philosophy. Auxier and Herstein also draw attention to some of the most important differences between the process theology tradition and Whitehead's thought, arguing in favor of a Whiteheadian naturalism that is more or less independent of theological concerns. This book offers a clear and comprehensive introduction to Whitehead's philosophy and is an essential resource for students and scholars interested in American philosophy, the philosophy of mathematics and physics, and issues associated with naturalism, explanation and radical empiricism.

There is, first of all, the distinction between that part of our belief which is rational and that part which is not. If a man believes something for a reason which is preposterous or for no reason at all, and what he believes turns out to be true for some reason not known to him, he cannot be said to believe it rationally, although he believes it and it is in fact true. On the other hand, a man may rationally believe a proposition to be probable, when it is in fact false. -from Chapter II: Probability in Relation to the Theory of Knowledge" His fame as an economist aside, John Maynard Keynes may be best remembered for saying, "In the long run, we are all dead." That phrase may well be the most succinct expression of the theory of probability every uttered. For a longer explanation of the premise that underlies much of modern mathematics and science, Keynes's A Treatise on Probability is essential reading. First published in 1920, this is the foundational work of probability theory, which helped establish the author's enormous influence on modern economic and even political theories. Exploring aspects of randomness and chance, inductive reasoning and logical statistics, this is a work that belongs in the library of any interested in numbers and their application in the real world. AUTHOR BIO: British economist JOHN MAYNARD KEYNES (1883-1946) also wrote The Economic Consequences of the Peace (1919), The End of Laissez-Faire (1926), The Means to Prosperity (1933), and General Theory of Employment, Interest and Money (1936).

The Routledge Companion to Pragmatism offers 44 cutting-edge chapters-written specifically for this volume by an international team of distinguished researchers-that assess the past, present, and future of pragmatism. Going beyond the exposition of canonical texts and figures, the collection presents pragmatism as a living philosophical idiom that continues to devise promising theses in contemporary debates. The chapters are organized into four major parts: Pragmatism's history and figures Pragmatism and plural traditions Pragmatism's reach Pragmatism's relevance Each chapter provides up-to-date research tools for philosophers, students, and others who wish to locate pragmatist options in their contemporary research fields. As a whole, the volume demonstrates that the vitality of pragmatism lies in its ability to build upon, and transcend, the ideas and arguments of its founders. When seen in its full diversity, pragmatism emerges as one of the most successful and influential philosophical movements in Western philosophy.

Intensional logic has emerged, since the 1960' s, as a powerful theoretical and practical tool in such diverse disciplines as computer science, artificial intelligence, linguistics, philosophy and even the foundations of mathematics. The present volume is a collection of carefully chosen papers, giving the reader a taste of the frontline state of research in intensional logics today. Most papers are representative of new ideas and/or new research themes. The collection would benefit the researcher as well as the student. This book is a most welcome addition to our series. The Editors CONTENTS PREFACE IX JOHAN VAN BENTHEM AND NATASHA ALECHINA Modal Quantification over Structured Domains PATRICK BLACKBURN AND WILFRIED MEYER-VIOL Modal Logic and Model-Theoretic Syntax 29 RUY J. G. B. DE QUEIROZ AND DOV M. GABBAY The Functional Interpretation of Modal Necessity 61 VLADIMIR V. RYBAKOV Logics of Schemes for First-Order Theories and Poly-Modal Propositional Logic 93 JERRY SELIGMAN The Logic of Correct Description 107 DIMITER VAKARELOV Modal Logics of Arrows 137 HEINRICH WANSING A Full-Circle Theorem for Simple Tense Logic 173 MICHAEL ZAKHARYASCHEV Canonical Formulas for Modal and Superintuitionistic Logics: A Short Outline 195 EDWARD N. ZALTA 249 The Modal Object Calculus and its Interpretation NAME INDEX 281 SUBJECT INDEX 285 PREFACE Intensional logic has many faces. In this preface we identify some prominent ones without aiming at completeness.

This accessible book provides a practical discussion of the main elements of argumentation as illustrated by 30 public arguments from a recent year on a wide variety of social, cultural, and scientific topics. Arguing is an important form of communication in any society and a principal way in which ideas are exposed, discussed, and modified. The real-life examples examined in this book reflect the different considerations that go into composing arguments and the range of strategies that can be chosen as vehicles for our positions. They demonstrate the roles that emotion can play along with other modes of conveying evidence, from the use of images to the use of gestures. They show the power of threats, comparisons, and consequences. What emerges is an instructive discussion that illustrates the way we argue and that shows argument, invention, and evaluation in action. This book is a stimulating read for anyone interested in argument and public discourse and can be used as a supplemental text for courses in argumentation, persuasive communication, critical thinking, composition, and informal logic.

Featuring fourteen new essays from an international team of renowned contributors, this volume explores the key issues, debates and questions in the metaphysics of logic. The book is structured in three parts, looking first at the main positions in the nature of logic, such as realism, pluralism, relativism, objectivity, nihilism, conceptualism, and conventionalism, then focusing on historical topics such as the medieval Aristotelian view of logic, the problem of universals, and Bolzano's logical realism. The final section tackles specific issues such as Glutty theories, contradiction, the metaphysical conception of logical truth, and the possible revision of logic. The volume will provide readers with a rich and wide-ranging survey, a valuable digest of the many views in this area, and a long overdue investigation of logic's relationship to us and the world. It will be of interest to a wide range of scholars and students of philosophy, logic, and mathematics.

This book explores the research of Professor Hilary Putnam, a Harvard professor as well as a leading philosopher, mathematician and computer scientist. It features the work of distinguished scholars in the field as well as a selection of young academics who have studied topics closely connected to Putnam's work. It includes 12 papers that analyze, develop, and constructively criticize this notable professor's research in mathematical logic, the philosophy of logic and the philosophy of mathematics. In addition, it features a short essay presenting reminiscences and anecdotes about Putnam from his friends and colleagues, and also includes an extensive bibliography of his work in mathematics and logic. The book offers readers a comprehensive review of outstanding contributions in logic and mathematics as well as an engaging dialogue between prominent scholars and researchers. It provides those interested in mathematical logic, the philosophy of logic, and the philosophy of mathematics unique insights into the work of Hilary Putnam.

This book presents the research achievements of Jin Yuelin, the first logician and a prominent philosopher in China, who founded a new philosophical system combining elements from Western and Chinese philosophical traditions, especially the concept of Tao. It consists of three sections: the first section interprets Jin's studies on Chinese philosophy, Russell's ideology and other general discussions in the field; section 2 includes Jin's studies on logic, which made him the founding father of modern logic in China; and section 3 presents Jin's ideas on politics, including his studies on Thomas Hill Green.

Propositions are routinely invoked by philosophers, linguists, logicians, and other theorists engaged in the study of meaning, communication, and the mind. To investigate the nature of propositions is to investigate the very nature of our connection to each other, and to the world around us. As one of the only volumes of its kind, The Routledge Handbook of Propositions provides a comprehensive overview of the philosophy of propositions, from both historical and contemporary perspectives. Comprising 33 original chapters by an international team of scholars, the volume addresses both traditional and emerging questions concerning the nature of propositions, and our capacity to engage with them in thought and in communication. The chapters are clearly organized into the following three sections: I. Foundational Issues in the Theory of Propositions II. Historical Theories of Propositions III. Contemporary Theories of Propositions Essential reading for philosophers of language and mind, and for those working in neighboring areas, The Routledge Handbook of Propositions is suitable for upper-level undergraduate study, as well as graduate and professional research.

George Berkeley's Principles of Human Knowledge is a crucial text in the history of empiricism and in the history of philosophy more generally. Its central and seemingly astonishing claim is that the physical world cannot exist independently of the perceiving mind. The meaning of this claim, the powerful arguments in its favour, and the system in which it is embedded, are explained in a highly lucid and readable fashion and placed in their historical context. Berkeley's philosophy is, in part, a response to the deep tensions and problems in the new philosophy of the early modern period and the reader is offered an account of this intellectual milieu. The book then follows the order and substance of the Principles whilst drawing on materials from Berkeley's other writings. This volume is the ideal introduction to Berkeley's Principles and will be of great interest to historians of philosophy in general.

Does game theory ? the mathematical theory of strategic interaction ? provide genuine explanations of human behaviour? Can game theory be used in economic consultancy or other normative contexts? Explaining Games: The Epistemic Programme in Game Theory ? the first monograph on the philosophy of game theory ? is a bold attempt to combine insights from epistemic logic and the philosophy of science to investigate the applicability of game theory in such fields as economics, philosophy and strategic consultancy. De Bruin proves new mathematical theorems about the beliefs, desires and rationality principles of individual human beings, and he explores in detail the logical form of game theory as it is used in explanatory and normative contexts. He argues that game theory reduces to rational choice theory if used as an explanatory device, and that game theory is nonsensical if used as a normative device. A provocative account of the history of game theory reveals that this is not bad news for all of game theory, though. Two central research programmes in game theory tried to find the ultimate characterisation of strategic interaction between rational agents. Yet, while the Nash Equilibrium Refinement Programme has done badly thanks to such research habits as overmathematisation, model-tinkering and introversion, the Epistemic Programme, De Bruin argues, has been rather successful in achieving this aim.

Russell's first book on philosophy and a fascinating insight into his early thinking A classic in the history and philosophy of mathematics and logic by one of the greatest philosophers of the 20th century This Routledge Classics edition includes a new foreword by Michael Potter, a renowned expert on analytic philosophy

Brilliant introduction to the philosophy of mathematics, from the question 'what is a number?' up to the concept of infinity, descriptions, classes and axioms Russell deploys all his skills and brilliant prose to write an introductory book - a real gem by one of the 20th century's most celebrated philosophers New foreword by Michael Potter to the Routledge Classics edition places the book in helpful context and explains why it's a classic

Superb insight into the development of Russell's thinking by the master himself Clearly and engaging written, charting his intellectual development from young idealist to celebrated sceptic This Routledge Classics edition includes a new foreword by Nicholas Griffin Ideal companion to Russell's own Autobiography, which is concerned with his incredibly colourful life rather than philosophy

Can OUGHT be derived from IS? This book presents an investigation of this time-honored problem by means of alethic-deontic predicate logic. New in this study is the leitmotif of relevance: is-ought inferences indeed exist, but they are all irrelevant in a precise logical sense. New proof techniques establish this result for very broad classes of logics. A profound philosophical analysis of is-ought bridge principles supplements the logical study. The final results imply incisive limitations for the justifiability of ethics as opposed to empirical science.