Graham Priest

"Paradox drives a good deal of philosophy in every tradition. In the Indian and Western traditions, there is a tendency among many philosophers to run from contradiction and paradox. If and when a contradiction appears in a theory, it is regarded as a sure sign that something has gone amiss. This aversion to paradox commits them, knowingly or not, to the view that reality must be consistent. In East Asia, however, philosophers have reacted to paradox differently. Many East Asian philosophers-both in the Daoist and the Buddhist traditions-have openly embraced paradox. They have taken compelling arguments for contradictory positions to suggest that the world is-at least in some respects, and often in very deep respects-inconsistent, and that our best theories of the world will therefore be inconsistent. This book is an initial survey of the writings of some influential East Asian thinkers who were committed to paradox, and for good reason. Their acceptance of contradiction allowed them to develop important insights that evaded those who consider paradox out of bounds"--

As far as disputes in the philosophy of pure mathematics goes, these are usually between classical mathematics, intuitionist mathematics, paraconsistent mathematics, and so on. My own view is that of a mathematical pluralist: all these different kinds of mathematics are equally legitimate. Applied mathematics is a different matter. In this, a piece of pure mathematics is applied in an empirical area, such as physics, biology, or economics. There can then certainly be a disputes about what the correct pure mathematics to apply is. Such disputes may be settled by the standard criteria of scientific theory selection (adequacy of empirical predications, simplicity, etc.) But what, exactly is it to apply a piece of pure mathematics? How is mathematics applied? By and large, philosophers of mathematics have cared more about pure mathematics than applied mathematics, and not a lot of thought has gone into this question. In this paper I will address the issue and some of its implications.

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.

Logic, in one of the many sense of that term, is a theory about what follows from what and why. Arguably, the correct theory has to be determined by abduction. Over recent years, so called logical anti-exceptionalists have investigated this matter. Current discussions have been restricted to deductive logic. However, there are also, of course, various forms of non-deductive reasoning. Indeed, abduction itself is one of these. What is to be said about the way of choosing the best theory of non-deductive inferences? It would seem clear that an anti-exceptionalist should hold that essentially the same method of choice should apply to non-deductive logic. A number of issues need to be faced in the process, not the least of which is the circularity involved in an abductive justification for a theory of abduction. This paper discusses matters.

In Metaphysics III, Chapter 4, Aristotle sets out and defends the Law of Non-Contradiction. The arguments are, however, rather less satisfactory than one might have expected, given the enormous historical influence the text has had. His major argument is a particularly tangled one, and the others are often little more than throw-away remarks. This essay is a commentary on the chapter, but its aim is less to interpret the text , than to see whether there is anything that Aristotle could have meant that would have served his purpose. Whilst other commentators have sometimes attempted this, they have always taken his conclusion to be correct, even if his arguments were not; I do not. The commentary is therefore a confrontation between Aristotle and modern dialetheism

We reply to various arguments by Otavio Bueno and Edward Zalta (‘Object Theory and Modal Meinongianism’) against Modal Meinongianism, including that it presupposes, but cannot maintain, a unique denotation for names of fictional characters, and that it is not generalizable to higher-order objects. We individuate the crucial difference between Modal Meinongianism and Object Theory in the former’s resorting to an apparatus of worlds, possible and impossible, for the representational purposes for which the latter resorts to a distinction between two kinds of predication, exemplification and encoding. We show that encoding has fewer forerunners in the history of philosophy than Bueno and Zalta want, and that there’s a reason why the notion has been found baffling by some.

There is at present a certain dispute about counterfactuals taking place. What is at issue is whether counterfactuals with necessarily false antecedents are all true. Some hold that such counterfactuals are vacuously true, appearances notwithstanding. Let us call such people vacuists. Others hold that some counterfactuals with necessarily false antecedents are true; some are false: it just depends on their contents. Let us call such people non-vacuists. As a notable representative of the vacuists, I will take Tim Williamson. On the other side, I will take the position defended by Berto, French, Priest, and Ripley. I will argue (unsurprisingly) that the better choice is Non-Vacuism. That, however, is a subsidiary aim of this paper. The main point is to illustrate the method of theory-choice.

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.

The paper establishes the general structure of the inconsistent models of arithmetic of [7]. It is shown that such models are constituted by a sequence of nuclei. The nuclei fall into three segments: the first contains improper nuclei: the second contains proper nuclei with linear chromosomes: the third contains proper nuclei with cyclical chromosomes. The nuclei have periods which are inherited up the ordering. It is also shown that the improper nuclei can have the order type of any ordinal. of the nationals. or of any other order type that can be embedded in the rationals in a certain way.

In this paper, I will describe a technique for generating a novel kind of semantics for a logic, and explore some of its consequences. It would be natural to call the semantics produced by the technique in question ‘many-valued'; but that name is, of course, already taken. I call them, instead, ‘plurivalent'. In standard logical semantics, formulas take exactly one of a bunch of semantic values. I call such semantics ‘univalent'. In a plurivalent semantics, by contrast, formulas may take one or more such values. The construction I shall describe can be applied to any univalent semantics to produce a corresponding plurivalent one. In the paper I will be concerned with the application of the technique to propositional many-valued logics. Sometimes going plurivalent does not change the consequence relation; sometimes it does. I investigate the possibilities in detail with respect to small family of many-valued logics.

In 1910, Jan Łukasiewicz published a groundbreaking book, On the Principle of Contradiction in Aristotle. The book contained a critique of the traditional attitude to the Principle of Non-Contradiction, and a reevaluation of its significance in the light of contemporary developments in logic. In the first half of the book, Łukasiewicz produced an analysis of Aristotle’s defence of the Principle in the Metaphysics, showing its deep inadequacy. In the second half of the book, Łukasiewicz, in his own terms, considers the pros and cons of the principle. The present paper provides an analysis and commentary on the second half of the book. Łukasiewicz is seen to be badly torn. Though he eventually endorses the principle, he does so, not in virtue of the evidence he considers, but in despite of it. In particular, he considers arguments against the Principle, drawn from Hegel, Meinong, and the paradoxes of self-reference, but rejects them for what appear to be patently inadequate reasons.