This work is a contribution to certain aspects of idealistic philosophy. It is a comparative study, yet it is not a comparison for the sake of comparison. This book examines the supra-rational Absolutism of the West developed under the Hegelian influence, and in the light of the criticisms shows the peculiar character of the Advaita Vedanta of Sankara. It is therefore not a mere exposition, but a criticism and construction. The discussions are not cosmological, but epistemological and metaphysical, approached from the side of logic. The work may also be viewed as a reorientation of Sankara's system. It places Sankara's philosophy in line with the idealistic philosophies of the West, so that we can understand the peculiarities of the former in terms of the latter. It thus discovers or brings into clearer light the guiding principle of Sankara's thought. It brings out the full significance of the principles of non-contradiction applied by Sankara as a test of truth and reality, and shows its difference from the same principle as understood by Hegel and the Hegelians. The aim of this work is to attempt at laying the metaphysical foundation of the logic of supra-rational Absolutism, the interpretation of Advaita is based mostly on polemical works.

First published in 1998, this volume has its origin in a meeting that was held in Santiago de Compostela University, Santiago de Compostela (Spain) in January 1996. The meeting was organized by the Department of Logic and Philosophy of Science in cooperation with the Association for Logic, Methodology and Philosophy of Science in Spain. Within analytical philosophy issues such as the definability of truth, its semantic relevance, its role in the distinction between formal and natural languages, the status of truth-bearers or in its case of truth-makers, have become a crossroads in the studies of logic, philosophy of science, philosophy of language, philosophy of mind, epistemology and ontology. Thus, in spite of what the title Truth in Perspective may suggest to the reader at first, the present volume is not only - though it is also a presentation of different theories or conceptions of truth. Most of the book presents a vision of different groups of philosophical questions in which the issue of truth appears embedded together with other related themes, from different points of view.

First published in the most ambitious international philosophy project for a generation; the Routledge Encyclopedia of Philosophy.
Logic from A to Z is a unique glossary of terms used in formal logic and the philosophy of mathematics.
Over 500 entries include key terms found in the study of:
* Logic: Argument, Turing Machine, Variable
* Set and model theory: Isomorphism, Function
* Computability theory: Algorithm, Turing Machine
* Plus a table of logical symbols.
Extensively cross-referenced to help comprehension and add detail, Logic from A to Z provides an indispensable reference source for students of all branches of logic.

Plato's formulation of the Principle of Non-contradiction (PNC) in Republic IV is the first full statement of the principle in western philosophy. His use of the principle might seem to suggest that he endorses the PNC. After all, how could one possibly deny so fundamental a principle-especially when it seems difficult to deny it without relying on it. However, the endorsement in the text is qualified. Socrates refers to the principle as one that he and his interlocutors will hypothesize and warns that if it should ever be shown to be false, all that follows from it will also be refuted. Scholars who have noticed this issue have tended to assume that the truth of the hypothesis in question can be guaranteed. Laurence Bloom argues against unthinkingly accepting this claim. He suggests that what emerges from the text is more sophisticated: Plato's concession that the PNC is hypothetical is a textual clue pointing us to a complex philosophical argument that grounds the PNC, as well as the sort of reasoning it grounds, in form. Indeed, in framing the problem in this way, we can read the Republic as providing an extended argument for form. The argument for forms that emerges is complex and difficult. It is not and cannot be a normal, discursive argument. Indeed, the argument cannot even be one that assumes the PNC; if it did so, it would fall prey to a vicious circularity. Rather, the argument rests on the very possibility of our hypothesizing the PNC in the first place. Our ability to hypothesize the PNC-and perhaps our inability not to hypothesize it-is the linchpin. When we ask questions such as "to what objects does the PNC apply?" or "how is it possible that we apply the PNC?," we are asking questions that lead us to the existence of form. The Principle of Non-contradiction in Plato's Republic also explores the soul of the knower-the very entity to which and by which the principle is applied in the text-and its underlying unity.

This text aims to present a comprehensive survey of methodological individualism in social, political and economic thought from the Enlightenment to the 20th century. Exploring the works of such figures as de Mandeville, Smith, Marx, Spencer, Durkheim, Simmel, Weber, Hayek, Popper and Parsons, the study underlines the contrasts between methodological collectivism and methodological individualism. The analysis offered here also reveals the theoretical presuppositions behind the collectivist and individualist traditions and the practical consequences of their applications. Infantino concludes in favour of individualism. This work touches upon issues in social and political theory, intellectual history, political philosophy, political economy and sociological theory.

This book brings together an influential sequence of papers that argue for a radical re-conceptualisation of the psychology of inference, and of cognitive science more generally. The papers demonstrate that the thesis that logic provides the basis of human inference is central to much cognitive science, although the commitment to this view is often implicit. They then note that almost all human inference is uncertain, whereas logic is the calculus of certain inference. This mismatch means that logic is not the appropriate model for human thought.
Oaksford and Chater's argument draws on research in computer science, artificial intelligence and philosophy of science, in addition to experimental psychology. The authors propose that probability theory, the calculus of uncertain inference, provides a more appropriate model for human thought. They show how a probabilistic account can provide detailed explanations of experimental data on Wason's selection task, which many have viewed as providing a paradigmatic demonstration of human irrationality.
Oaksford and Chater show that people's behavior appears irrational only from a logical point of view, whereas it is entirely rational from a probabilistic perspective. The shift to a probabilistic framework for human inference has significant implications for the psychology of reasoning, cognitive science more generally, and for our picture of ourselves as rational agents.

Logic has acquired a reputation for difficulty, perhaps because many of the approaches adopted have been more suitable for mathematicians than computer scientists. This book shows that the subject is not inherently difficult and that the connections between logic and declarative language are straightforward. Many exercises have been included in the hope that these will lead to a much greater confidence in manual proofs, therefore leading to a greater confidence in automated proofs.

Logic has acquired a reputation for difficulty, perhaps because many of the approaches adopted have been more suitable for mathematicians than computer scientists. This book shows that the subject is not inherently difficult and that the connections between logic and declarative language are straightforward. Many exercises have been included in the hope that these will lead to a much greater confidence in manual proofs, therefore leading to a greater confidence in automated proofs.

The ability to think clearly and the power to reason well set leaders apart from the crowd. All of us have these abilities, but some may not be able to use their capabilities to full advantage at home, at work, at school, or in group situations.
Think to Win is a clear and inviting guide through the amazing world of logical thinking and reasoning. Designed for all readers, this book explores crucial aspects of effective reasoning - that uniquely human characteristic that catapulted our species from the use of smoke signals to the computer, and from humble cave dwellings to space exploration.
Inspired by a student who once pleaded for a layperson's guide to "thinking well," S. Cannavo walks the reader through the various modes of thinking, understanding, and reasoning, making logical thought engaging through real-life examples. He offers essential tips on how anyone can be empowered through continual self-monitoring and self-improvement.
Want to feel better about yourself and your abilities? Do you want to explain yourself better, present a more convincing case, and ultimately be more successful? Think to Win will help you cultivate your rational intelligence.

If the phrase "the philosophy of difference" defines French anti-Hegelianism, then we have to say that there would be no philosophy of difference without Logic and Existence. Derrida's notion of differance, Deleuze's logic of sense, and Foucault's reconception of history all stem from this book. This first English translation of the virtually unknown Logic and Existence is essential for the understanding of the development of French thought in this century.

Logic and Existence, which originally appeared in 1952, completes the project Hyppolite began with Genesis and Structure of Hegel's Phenomenology of Spirit. Taking up successively the role of language, reflection, and categories in Hegel's Science of Logic, Hyppolite illuminates Hegelianism's most obscure dialectical synthesis: the relation between the phenomenology and the logic.

His interpretation of the relation between the phenomenology and the logic has the result of marking a rupture in French thought. Not only does Logic and Existence effectively end the humanistic reading of Hegel popularized by Kojeve in France before World War II, but also it initiates the great anti-Hegelianism of French philosophy in the sixties. Hyppolite's work displays the originality of Hegel's thought in a new way, and sets up the means by which to escape from it.

This introduction to modern formal logic also contains discussions on more philosophical issues, such as truth, conditionals and modal logic. It presents the formal material using informal explanations and arguments rather than rigorous development. Worked examples and exercises enable readers to check their progress. The aim is to equip students with: a complete and clear account of the truth-tree system for first order logic; the importance of logic and its relevance to many different disciplines; the skills needed to grasp sophisticated formal reasoning techniques necessary to explore complex metalogic; and the ability to contest claims that "ordinary" reasoning is well represented by formal first order logic. The issues covered include truth-functional and full first order logic, using the truth-tree or semantic tableau approach. Completeness and soundness proofs are given for both truth-functional and first order trees. Much use is made of induction, which is presented in a clear and consistent manner. There is also discussion of alternative deductive systems.

Contents:
Introduction. Part 1: Truth-Functional Logic Chapter 1. The Basics 1. Deductively Valid Inference 2. Syntax: Connectives and the Principle of Composition 3. Semantics: Truth-Functionality 4. Negation and Conjunction 5. Disjunction 6. Truth-Functional Equivalence 7. The Conditional 8. Some Other Connectives, and the Biconditional Chapter 2. Truth Trees 1. Truth-Functionally Valid Inference 2. Conjugate Tree Diagrams 3. Truth Trees 4. Tautologies and Contradictions Chapter 3. Propositional Languages 1. Propositional Languages 2. Object Language and Metalanguage 3. Ancestral Trees 4. An Induction Principle 5. Multiple Conjunctions and Disjunctions 6. The Disjunctive Normal Form Theorem 7. Adequate Sets of Connectives 8. The Duality Principle 9. Conjunctive Normal Forms Chapter 4. Soundness and Completeness 1. The Standard Propositional Language 2. Truth Trees Again 3. Truth-Functional Consistency, Truth-Functionally Valid Inferences, and Trees 4. Soundness and Completeness Part 2: First Order Logic Chapter 5. Introduction 1. Some Non-Truth-Functional Inferences 2. Quantifiers and Variables 3. Relations 4. Formalising English Sentences Chapter 6. First Languages: Syntax and Two More Trees Rules 1. First Order Languages 2. Two More Tree Rules 3. Tree Proofs Chapter 7. First Order Languages: Semantics 1. Interpretations 2. Formulas and Truth 3. The Tree Rules Revisited 4. Consistency and Validity 5. Logical Truth and Logical Equivalence Chapter 8. Soundness and Completeness 1. Applying the Tree Rules 2. Branch Models 3. Soundness and Completeness Theorems 4. Compactness Chapter 9. Identity 1. Identity 2. Tree Rules For Identity 3. Some Arithmetic 4. Functions and Function Symbols 5. Working with Equations 6. Is Identity Part of Logic? Chapter 10. Alternative Deductive Systems for First Order Logic 1. Introduction 2. H 3 ND 4. Comparisons 5. Intuitionism Chapter 11. First Order Theories 1. First Order Theories 2. Infinite Cardinals 3. Lowenheim-Skolem Theorems 4. Second Order Languages 5. Completeness 6. The Liar Paradox Chapter 12. Beyond the Fringe 1. Counterfactual Conditions 2. Modal Propositional Logic 3. Indicative Conditionals and 4. Conclusion. List of Notation. Answers to Selected Exercises.

"Coalescent Argumentation" is based on the concept that arguments can function from agreement, rather than disagreement. To prove this idea, Gilbert first discusses how several components--emotional, visceral (physical) and kisceral (intuitive) are utilized in an argumentative setting by people everyday. These components, also characterized as "modes," are vital to argumentative communication because they affect both the argument and the resulting outcome.
In addition to the components/modes, this book also stresses the goals in argumentation as a means for understanding one's own and one's opposer's positions. Gilbert argues that by viewing positions as complex human events involving a variety of communicative modes, we are better able to find commonalities across positions, and, therefore, move from conflict to resolution. By focusing on agreement and shared goals in all modes, arguers can coalesce diverse positions and more easily distinguish between minor or unrelated differences and core disagreements. This permits much greater latitude for locating shared beliefs, values, and attitudes that will lead to conflict resolution.

"Coalescent Argumentation" is based on the concept that arguments can function from agreement, rather than disagreement. To prove this idea, Gilbert first discusses how several components--emotional, visceral (physical) and kisceral (intuitive) are utilized in an argumentative setting by people everyday. These components, also characterized as "modes," are vital to argumentative communication because they affect both the argument and the resulting outcome.
In addition to the components/modes, this book also stresses the goals in argumentation as a means for understanding one's own and one's opposer's positions. Gilbert argues that by viewing positions as complex human events involving a variety of communicative modes, we are better able to find commonalities across positions, and, therefore, move from conflict to resolution. By focusing on agreement and shared goals in all modes, arguers can coalesce diverse positions and more easily distinguish between minor or unrelated differences and core disagreements. This permits much greater latitude for locating shared beliefs, values, and attitudes that will lead to conflict resolution.

This book, a rich collection authored by rhetorical scholars, unpacks how rhetoric contributes to argumentation studies. It begins with an introduction that identifies defining features of a rhetorical approach to argumentation which has several corollaries, including the special status of argumentation about action, the condition of uncertainty and the necessity of securing adherence from an audience. Chapters explore topics such as the properties of argumentation in the realm of rhetoric, the use of presentational devices, the role of rhetoric in the evolving formation of public morality, conditions for democratic argumentation, argument pedagogy, rhetorical insights into science communication, and other features within the realm of rhetorical argumentation. This book is relevant to students and researchers in linguistics, rhetoric, philosophy, argumentation studies, and communication studies. Previously published in Argumentation Volume 34, issue 3, September 2020

This long-awaited book replaces not one but both of Hughes and Cresswell's two previous classic studies of modal logic: "An Introduction to Modal Logic" and "A Companion to Modal Logic."
"A New Introduction to Modal Logic" has been completely rewritten by the authors to incorporate all the developments that have taken place since 1968 both in modal propositional logical and modal predicate logic, but without sacrificing the clarity of exposition and approachability that were essential features of the earlier works.
The book takes readers through the most basic systems of modal prepositional logic right up to systems of modal predicate with identity. It deals with both technical developments such as completeness and incompleteness, and finite and infinite models, and discusses philosophical applications, especially, in the area of modal predicate logic.

This book contains a selection of the papers presented at the Logic, Reasoning and Rationality 2010 conference (LRR10) in Ghent. The conference aimed at stimulating the use of formal frameworks to explicate concrete cases of human reasoning, and conversely, to challenge scholars in formal studies by presenting them with interesting new cases of actual reasoning. According to the members of the Wiener Kreis, there was a strong connection between logic, reasoning, and rationality and that human reasoning is rational in so far as it is based on (classical) logic. Later, this belief came under attack and logic was deemed inadequate to explicate actual cases of human reasoning. Today, there is a growing interest in reconnecting logic, reasoning and rationality. A central motor for this change was the development of non-classical logics and non-classical formal frameworks. The book contains contributions in various non-classical formal frameworks, case studies that enhance our apprehension of concrete reasoning patterns, and studies of the philosophical implications for our understanding of the notions of rationality.

Chapter 9 of Aristotle's "On Interpretation" deals with determinism, and here the two influential commentaries of Ammonius and Boethius have been published together. These are crucial works, for Ammonuis' commentary influenced the Islamic Middle Ages, while that of Boethius was of equal importance to medieval Latin-speaking philosophers. It was once argued that Boethius was influenced by Ammonius, and this work aims to show that this was clearly not the case. Ammonius draws on the fourth- and fifth-century Neoplatonists Iamblichus, Syrianus and Proclus. He arranges his argument around three major deterministic arguments and is our main source for one of them, the Reaper argument. Boethius, on the other hand, draws on controversies from 300 years earlier between Stoics and Aristotelians as recorded by Alexander of Aphrodisias and Porphyry.

The Collected Works of John Stuart Mill took thirty years to complete and is acknowledged as the definitive edition of J.S. Mill and as one of the finest works editions ever completed. Mill's contributions to philosophy, economics, and history, and in the roles of scholar, politician and journalist can hardly be overstated and this edition remains the only reliable version of the full range of Mill's writings. Each volume contains extensive notes, a new introduction and an index. Many of the volumes have been unavailable for some time, but the Works are now again available, both as a complete set and as individual volumes.

The Collected Works of John Stuart Mill took thirty years to complete and is acknowledged as the definitive edition of J.S. Mill and as one of the finest works editions ever completed. Mill's contributions to philosophy, economics, and history, and in the roles of scholar, politician and journalist can hardly be overstated and this edition remains the only reliable version of the full range of Mill's writings. Each volume contains extensive notes, a new introduction and an index. Many of the volumes have been unavailable for some time, but the Works are now again available, both as a complete set and as individual volumes.

If you keep removing single grains of sand from a heap, when is it no longer a heap? From discussions of the heap paradox in classical Greece, to modern formal approaches like fuzzy logic, Timothy Williamson traces the history of the problem of vagueness. He argues that standard logic and formal semantics apply even to vague languages and defends the controversial, realist view that vagueness is a form of ignorance - there really is a grain of sand whose removal turns a heap into a non-heap, but we can never know exactly which one it is.

Argumentation theory is a distinctly multidisciplinary field of inquiry. It draws its data, assumptions, and methods from disciplines as disparate as formal logic and discourse analysis, linguistics and forensic science, philosophy and psychology, political science and education, sociology and law, and rhetoric and artificial intelligence. This presents the growing group of interested scholars and students with a problem of access, since it is even for those active in the field not common to have acquired a familiarity with relevant aspects of each discipline that enters into this multidisciplinary matrix. This book offers its readers a unique comprehensive survey of the various theoretical contributions which have been made to the study of argumentation. It discusses the historical works that provide the background to the field and all major approaches and trends in contemporary research.
Argument has been the subject of systematic inquiry for twenty-five hundred years. It has been graced with theories, such as formal logic or the legal theory of evidence, that have acquired a more or less settled provenance with regard to specific issues. But there has been nothing to date that qualifies as a unified general theory of argumentation, in all its richness and complexity. This being so, the argumentation theorist must have access to materials and methods that lie beyond his or her "home" subject. It is precisely on this account that this volume is offered to all the constituent research communities and their students. Apart from the historical sections, each chapter provides an economical introduction to the problems and methods that characterize a given part of the contemporary research program. Because the chapters are self-contained, they can be consulted in the order of a reader's interests or research requirements. But there is value in reading the work in its entirety. Jointly authored by the very people whose research has done much to define the current state of argumentation theory and to point the way toward more general and unified future treatments, this book is an impressively authoritative contribution to the field.

Argumentation theory is a distinctly multidisciplinary field of inquiry. It draws its data, assumptions, and methods from disciplines as disparate as formal logic and discourse analysis, linguistics and forensic science, philosophy and psychology, political science and education, sociology and law, and rhetoric and artificial intelligence. This presents the growing group of interested scholars and students with a problem of access, since it is even for those active in the field not common to have acquired a familiarity with relevant aspects of each discipline that enters into this multidisciplinary matrix. This book offers its readers a unique comprehensive survey of the various theoretical contributions which have been made to the study of argumentation. It discusses the historical works that provide the background to the field and all major approaches and trends in contemporary research.
Argument has been the subject of systematic inquiry for twenty-five hundred years. It has been graced with theories, such as formal logic or the legal theory of evidence, that have acquired a more or less settled provenance with regard to specific issues. But there has been nothing to date that qualifies as a unified general theory of argumentation, in all its richness and complexity. This being so, the argumentation theorist must have access to materials and methods that lie beyond his or her "home" subject. It is precisely on this account that this volume is offered to all the constituent research communities and their students. Apart from the historical sections, each chapter provides an economical introduction to the problems and methods that characterize a given part of the contemporary research program. Because the chapters are self-contained, they can be consulted in the order of a reader's interests or research requirements. But there is value in reading the work in its entirety. Jointly authored by the very people whose research has done much to define the current state of argumentation theory and to point the way toward more general and unified future treatments, this book is an impressively authoritative contribution to the field.

Originally published in 1976. This comprehensive study discusses in detail the philosophical, mathematical, physical, logical and theological aspects of our understanding of time and space. The text examines first the many different definitions of time that have been offered, beginning with some of the puzzles arising from our awareness of the passage of time and shows how time can be understood as the concomitant of consciousness. In considering time as the dimension of change, the author obtains a transcendental derivation of the concept of space, and shows why there has to be only one dimension of time and three of space, and why Kant was not altogether misguided in believing the space of our ordinary experience to be Euclidean. The concept of space-time is then discussed, including Lorentz transformations, and in an examination of the applications of tense logic the author discusses the traditional difficulties encountered in arguments for fatalism. In the final sections he discusses eternity and the beginning and end of the universe. The book includes sections on the continuity of space and time, on the directedness of time, on the differences between classical mechanics and the Special and General theories of relativity, on the measurement of time, on the apparent slowing down of moving clocks, and on time and probability.