Philosophy in the medieval Latin West before 1200 is often thought to have been dominated by Platonism. The articles in this volume question this view, by cataloguing, describing and investigating the tradition of Aristotelian logic during this period, examining its influence on authors usually placed within the Aristotelian tradition (Eriugena, Anselm, Gilbert of Poitiers), and also looking at some of the characteristics of early medieval Platonism. Abelard, the most brilliant logician of the age, is the main subject of three articles, and the book concludes with two more general discussions about how and why medieval philosophy should be studied.

Originally published in 1991, this volume examines Hegel's political philosophy from the perspective of his argument for constitutional monarchy. It offers an interpretation of Hegelian theory that is relevant for the understanding of modern republican constitutions. Modern republican theories are assessed together with those of Plato, Kant and Marx in order to put Hegel's model to the most rigorous test. The arguments are based on fresh analysis of Hegel's system and on new translations of key passages in Hegel's text.

Originally published in 1982, this volume examines the sources of British Hegelian thinking, the lines of its development and intellectual relationships among members of the school. The sources in this book include twentieth century Marxians who pioneered the move 'back to Hegel' such as Gramsci and Lukacs. It includes brief biographical entries of the principal British Hegelians and of minor figures wo paved the way for Hegel's entry into British philosophy.

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

Are any of our beliefs justified? Are they rational? The skeptic thinks that our epistemic justifications are undeserved. Nicholas Nathan confronts the skeptic and questions the value of his argument.
Skeptical arguments are against justified and rational belief as well as for ignorance. Nathan argues that the truth value of trivial arguments are a matter of indifference. He tests this conjecture with a varied collection of counterexamples: arguments for ignorance, neo-Cartesian and infinite regress arguments, and also more critically with arguments against justified and rational belief.

This historical study investigates Ludwig Wittgenstein's early philosophy of logic and language, as it is presented in his Tractatus Logico-Philosophicus. Drawing on Wittgenstein's correspondence, and on his numerous pre-Tractatus manuscripts, the study makes a case for the Tractatus as an insightful critique of the philosophies of Bertrand Russell and Gottlob Frege - the Founding Fathers of analytic philosophy.
The book urges a re-assessment of the relative influence of these philosophers on the early Wittgenstein. It argues that the current vogue for "Fregean" readings of the Tractatus has tended to obscure the true depth and importance of Wittgenstein's involvement with Russell's philosophy. This case is built through a series of detailed studies of central logico-linguistic topics including: tautology, logical assertion, the picture theory of the proposition and the deductive inference.

An Invitation to Formal Reasoning introduces the discipline of formal logic by means of a powerful new system formulated by Fred Sommers. This system, term logic, is different in a number of ways from the standard system employed in modern logic; most striking is its greater simplicity and naturalness. Based on a radically different theory of logical syntax than the one Frege used when initiating modern mathematical logic in the 19th Century, term logic borrows insights from Aristotle's syllogistic, Scholastic logicians, Leibniz, and the 19th century British algebraists. Term logic takes its syntax directly from natural language, construing statements as combinations of pairs of terms, where complex terms are taken to have the same syntax as statements. Whereas standard logic requires extensive 'translation' from natural language to symbolic language, term logic requires only 'transcription' into the symbolic language. Its naturalness is the result of its ability to stay close to the forms of sentences usually found in every day discourse. Written by the founders of the term logic approach, An Invitation to Formal Reasoning is a unique introduction and exploration of this new system, offering numerous exercises and examples throughout the text. Summarising the standard system of mathematical logic to set term logic in context, and showing how the two systems compare, this book presents an alternative approach to standard modern logic for those studying formal logic, philosophy of language or computer theory. Fred Sommers is Professor Emeritus, Brandeis University, USA; George Englebretsen is Professor of Philosophy, Bishop's University, Canada.

Originally published in 1990. This study was first written in 1965 when interest in Leibniz was intensifying. The book looks in detail at the doctrine of necessity - that necessary truths are those derivable from the principle of identity by the substitution of definitions. It first considers views of philosophic predecessors, relating Leibniz' doctrine to Aristotle and Hobbes among others. The second section examines the conflict between his reductionistic and formalistic views and the opposing intuitionism and anti-reductionism of Descartes and Locke. The author critically examines the theory of necessity, including Leibniz's arguments against the views of Hobbes and Locke, concluding with distinctions between necessary and contingent truths.

This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. An Introduction to Substrucural Logics is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered:
* Proof Theory
* Propositional Structures
* Frames
* Decidability
* Coda
Both students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading.

The Oxford Handbook of Descartes and Cartesianism comprises fifty specially written chapters on Rene Descartes (1596-1650) and Cartesianism, the dominant paradigm for philosophy and science in the seventeenth century, written by an international group of leading scholars of early modern philosophy. The first part focuses on the various aspects of Descartes's biography (including his background, intellectual contexts, writings, and correspondence) and philosophy, with chapters on his epistemology, method, metaphysics, physics, mathematics, moral philosophy, political thought, medical thought, and aesthetics. The chapters of the second part are devoted to the defense, development and modification of Descartes's ideas by later generations of Cartesian philosophers in France, the Netherlands, Italy, and elsewhere. The third and final part considers the opposition to Cartesian philosophy by other philosophers, as well as by civil, ecclesiastic, and academic authorities. This handbook provides an extensive overview of Cartesianism - its doctrines, its legacies and its fortunes - in the period based on the latest research.

First published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

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 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.

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.

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.

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.

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.