Anyone who is accustomed to the view that contradictions cannot be true, and cannot be accepted, and who reads texts in the Buddhists traditions will be struck by the fact that they frequently contain contradictions. Just consider, for example.

The paper is a discussion of a result of Hilbert and Bernays in their Grundlagen der Mathemnatik. Their interpretation of the result is similar to the standard intepretation of Tarski's Theorem. This and other interpretations are discussed and shown to be inadequate. Instead, it is argued, the result refutes certain versions of Meinongianism. In addition, it poses new problems for classical logic that are solved by dialetheism.

The Hooded Man Paradox of Eubulides concerns the apparent failure of the substitutivity of identicals in epistemic (and other intentional) contexts. This paper formulates a number of different versions of the paradox and shows how these may be solved using semantics for quantified epistemic logic. In particular, two semantics are given which invalidate substitution, even when rigid designators are involved.

In both occidental and oriental traditions, philosophers have long treated the martial arts as pursuits worthy of philosophical reflection. This is the first substantial academic book to lay out the philosophical terrain within the study and understanding of the martial arts and to explore the significance of this fascinating subject for contemporary philosophy. The book is divided into three sections. The first section concerns what philosophical reflection can teach us about the martial arts, and especially the nature and value of (...) its practice. The second section deals with the other direction of the dialectical interplay between philosophy and the martial arts: how the martial arts can inform philosophical issues important in their own right. Finally, because many of the notable martial arts are of Asian origin, there are particularly close links between the arts and Asian philosophies - and Buddhism in particular - and therefore the last section is devoted to this topic. The essays in this collection deal with a wide range of philosophical issues: normative ethics, meta-ethics, aesthetics, phenomenology, the philosophy of mind, Ancient Greek and Buddhist thought. By demonstrating the very real nature of the engagement between the martial arts and philosophy, this book is essential reading for any serious student or scholar with an interest in the martial arts, Eastern philosophy, the philosophy of sport, or the study of physical culture. (shrink)

Logic is often perceived as having little to do with the rest of philosophy, and even less to do with real life. In this lively and accessible introduction, Graham Priest shows how wrong this conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory. Along the way, the basics of formal logic are (...) explained in simple, non-technical terms, showing that logic is a powerful and exciting part of modern philosophy. (shrink)

This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and (...) their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area. (shrink)

Mathematical pluralism is the view that there is an irreducible plurality of pure mathematical structures, each with their own internal logics; and that qua pure mathematical structures they are all equally legitimate. Mathematical pluralism is a relatively new position on the philosophical landscape. This Element provides an introduction to the position.

In Contradiction advocates and defends the view that there are true contradictions, a view that flies in the face of orthodoxy in Western philosophy since Aristotle. The book has been at the center of the controversies surrounding dialetheism ever since its first publication in 1987. This second edition of the book substantially expands upon the original in various ways, and also contains the author’s reflections on developments over the last two decades. Further aspects of dialetheism are discussed in the companion (...) volume, Doubt Truth to be a Liar, also published by Oxford University Press in 2006. (shrink)

Mathematical pluralism notes that there are many different kinds of pure mathematical structures—notably those based on different logics—and that, qua pieces of pure mathematics, they are all equally good. Logical pluralism is the view that there are different logics, which are, in an appropriate sense, equally good. Some, such as Shapiro, have argued that mathematical pluralism entails logical pluralism. In this brief note I argue that this does not follow. There is a crucial distinction to be drawn between the preservation (...) of truth and the preservation of truth-in-a-structure; and once this distinction is drawn, this suffices to block the argument. The paper starts by clarifying the relevant notions of mathematical and logical pluralism. It then explains why the argument from the first to the second does not follow. A final section considers a few objections. (shrink)

Towards Non-Being develops an account of the semantics of intentional predicates and operators. The account appeals to objects, both existent and non-existent, and worlds, both possible and impossible. This paper formulates replies to a number of the more interesting objections to the semantics that have been proposed since the book was published.

Graham Priest presents a ground-breaking account of the semantics of intentional language--verbs such as "believes," "fears," "seeks," or "imagines." Towards Non-Being proceeds in terms of objects that may be either existent or non-existent, at worlds that may be either possible or impossible. The book will be of central interest to anyone who is concerned with intentionality in the philosophy of mind or philosophy of language, the metaphysics of existence and identity, the philosophy of fiction, the philosophy of mathematics, (...) or cognitive representation in AI. (shrink)

Dialetheism is the view that some contradictions are true. This is a view which runs against orthodoxy in logic and metaphysics since Aristotle, and has implications for many of the core notions of philosophy. Doubt Truth to Be a Liar explores these implications for truth, rationality, negation, and the nature of logic, and develops further the defense of dialetheism first mounted in Priest's In Contradiction, a second edition of which is also available.

A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth-bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and false.

Fifteen leading philosophers explore metaphysical foundationalism, the idea that reality has an over-arching hierarchical structure ordered by relations of metaphysical dependence, where chains of entities ordered by those dependence relations terminate in something fundamental.

Graham Priest presents an original exploration of questions concerning the one and the many. He covers a wide range of issues in metaphysics--unity, identity, grounding, mereology, universals, being, intentionality and nothingness--and draws on Western and Asian philosophy as well as paraconsistent logic to offer a radically new treatment of unity.

This is a philosophical investigation of the nature of the limits of thought. Drawing on recent developments in the field of logic, Graham Priest shows that the description of such limits leads to contradiction, and argues that these contradictions are in fact veridical. Beginning with an analysis of the way in which these limits arise in pre-Kantian philosophy, Priest goes on to illustrate how the nature of these limits was theorised by Kant and Hegel. He offers new (...) interpretations of Berkeley's master argument for idealism and Kant on the antimonies. He explores the paradoxes of self reference, and provides a unified account of the structure of such paradoxes. The book concludes by tracing the theme of the limits of thought in modern philosophy of language, including discussions of the ideas of Wittgenstein and Derrida. (shrink)

This is the first introductory textbook on non-classical propositional logics.

Graham Priest presents an exploration of the development of Buddhist metaphysics, which is viewed through the lens of the catuskoti. In its earliest and simplest form this is a logical/metaphysical principle which says that every claim is true, false, both, or neither; but Priest shows how the principle itself evolves as the metaphysics develops.

Paraconsistent logic, logic in which inconsistent information does not deliver arbitrary conclusions, is one of the fastest growing areas of logic, with roots in profound philosophical issues, and applications in information processing and philosophy of science. This book contains selected papers presented at the First World Congress on Paraconsistency, held in Ghent in 1997. It contains papers on various aspects of the subject. As such, it should be of interest to all who want to learn what the subject is, and (...) where it is going. (shrink)

The article looks at the structure of impossible worlds, and their deployment in the analysis of some intentional notions. In particular, it is argued that one can, in fact, conceive anything, whether or not it is impossible. Thus a semantics of conceivability requires impossible worlds.

A counterpossible conditional is a counterfactual with an impossible antecedent. Common sense delivers the view that some such conditionals are true, and some are false. In recent publications, Timothy Williamson has defended the view that all are true. In this paper we defend the common sense view against Williamson’s objections.

Informal accounts of the sorites paradox usually emphasize that the problem is one of vagueness. The paper uses the idea of fuzzy truth values to provide a formal semantics which shows precisely how sorites-Type arguments are formally invalid.

The paper contains a short story which is inconsistent, essentially so, but perfectly intelligible. The existence of such a story is used to establish various views about truth in fiction and impossible worlds.

Graham Priest presents an expanded edition of his exploration of the nature and limits of thought. Embracing contradiction and challenging traditional logic, he engages with issues across philosophical borders, from the historical to the modern, Eastern to Western, continental to analytic.

The Law of Non-Contradiction - that no contradiction can be true - has been a seemingly unassailable dogma since the work of Aristotle, in Book G of the Metaphysics. It is an assumption challenged from a variety of angles in this collection of original papers. Twenty-three of the world's leading experts investigate the 'law', considering arguments for and against it and discussing methodological issues that arise whenever we question the legitimacy of logical principles. The result is a balanced inquiry into (...) a venerable principle of logic, one that raises questions at the very centre of logic itself. The aim of this volume is to present a comprehensive debate about the Law of Non-Contradiction, from discussions as to how the law is to be understood, to reasons for accepting or re-thinking the law, and to issues that raise challenges to the law, such as the Liar Paradox, and a 'dialetheic' resolution of that paradox. The editors contribute an introduction which surveys the issues and serves to frame the debate, and a useful bibliography offering a guide to further reading. This volume will be of interest to anyone working on philosophical logic, and to anyone who has ever wondered about the status of logical laws and about how one might proceed to mount arguments for or against them. (shrink)

The paper gives a semantics for naive (inconsistent) set theory in terms of substitutional quantification. Soundness is proved in an appendix. In the light of this construction, Several philosophical issues are discussed, Including mathematical necessity and the set theoretic paradoxes. Most importantly, It is argued, These semantics allow for a nominalist account of mathematical truth not committed to the existence of a domain of abstract entities.

The paper discusses where philosophy is going at the moment. Various current trends are singled out for comment. It then moves to the question of where it ought to be going. After a brief discussion of what this question means, it concludes that no guidance can be given except that each philosopher should pursue what they think to be important.