Graham Priest

This essay is a discussion of the Principle of Sufficient Reason in the context of fundamental principles of philosophy. The paper discusses what the Principle is, Leibniz's argument for it, a contemporary argument for it, given by Michael Della Rocca, and an argument drawn from Buddhist philosophy by Allison Aitken. It is argued that all such arguments fail. By the very statement of the Principle, if there is no justification for it, it is false. The paper therefore concludes that since there appears to be no other plausible argument for the Principle on the horizon, it is false. However, the paper suggests, it may be viewed as a regulative principle, in something like Kant's sense.

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.

Many writers have commented on connections between the work of Martin Heidegger (1889–1976) and Chan/Zen Buddhism—a school of Buddhism originating in China around the 6th Century. In this essay, we will explore one aspect of that connection, drawing on the work of the Japanese Zen philosopher Dōgen Kigen (1200–1253). Heidegger held that being is ineffable, and Dōgen held that ultimate reality is ineffable. Now, ineffability is an extreme form of indeterminacy: if something is ineffable it transcends any determinacy whatsoever. However, there is an obvious contradiction involved in talking about the ineffable, as do both Heidegger and Dōgen. Indeed, even to say that something transcends all determinacy is to give it a determination. Though Heidegger and Dōgen’s concerns are, prima facie, completely different, we will show that they both responded to the contradiction (or came to respond to it) in exactly the same way: they were dialetheists about the matter. Not only did they endorse the contradiction in question; they both, in much the same sense, endorsed the necessary entanglement of the speech of effability and the silence of ineffability. Finally, by looking at the work of Nishitani Keiji (1900–1990), we will show that the thoughts of Dōgen and Heidegger converge in the fact that the subject of the contradiction for both may, in fact, be seen as nothingness.

An überconsistent logic is one where the set of logical truths is inconsistent. Examples of such logics have been known for a long time. However, it has recently been recognized that this is an important new class of logics. Dialetheism is the view that some contradictions are true. Since logical truths are true, it might be thought that these logics provide an important new argument for dialetheism. However, matters are not that straightforward. This paper is an initial discussion of the matter. The first part of the paper provides the background on paraconsistency and dialetheism required for the discussion. The second half is a discussion of three überconsistent logics and their bearing on dialetheism. The first is the logic LP with a logical constant for the value both true and false; the second is Second-Order LP; the third is a certain kind of connexive logic.

Graham Priest presents a new, expanded edition of his highly original exploration of the nature and limits of thought. Drawing on recent developments in the field of logic, Priest shows that the description of such limits leads to contradiction, and argues that these contradictions are in fact true. 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 theorized by Kant and Hegel. He offers new interpretations of Berkeley's master argument for idealism and Kant on the antinomies. He explores the paradoxes of self-reference, and provides a unified account of the structure of such paradoxes. The book goes on to trace the theme of the limits of thought in modern philosophy of language, including discussions of the ideas of Wittgenstein and Derrida.The second edition includes new chapters on Heidegger and Nagarjuna, as well as reflections on reactions to the first edition. This clear, provocative, and systematic work offers a radically different approach to philosophy and logic.

Joel Hamkins has advanced a well known view to the effect that there is no unique universe of sets. There is simply a plurality of such universes. We have, then, a pluriverse. A natural objection to this view is that there is still a single universe: the totality, V, in which all the members of the pluriverse find themselves. In this paper I consider a reply to the objection, to the effect that there is no such thing as V in itself. Rather, each member of the pluriverse simply gives a different perspective on what V is like. This view is then generalised in the light of mathematical pluralism. What emerges is a vastly expanded and logic-neutral view of the pluriverse.

One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley–Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close by briefly discussing a general conception of conditionality that may unify the three given conceptions.

In the early 1950s Waismann wrote two essays entitled ‘Fiction’ and ‘A Note on Existence’. These were subsequently published in his Philosophical Papers (Reidel, 1977). In these papers he makes various claims concerning fictional objects. The topic of the paper was ground-breaking at the time. The point of the present paper is to discuss what he say about matters. It argues that the core claims of each paper are mistaken, though a number of Waismann’s arguments make points that were subsequently to be made more famous by others writing on the philosophy of language.

Colour is a puzzling phenomenon. Perhaps nothing could be more obvious than colour; but one thing that Modern Philosophy has taught us is that, concerning colour, things are not what they appear. We all naively think that things exist in the world with their objective colours. Grass in green; the sky is blue; coal is black. But in reality, colour is merely the way that things with certain objective properties—notably the ability to reflect, emit, or absorb electromagnetic radiation of particular frequencies—appear to sensory apparatuses of certain species-specific (and even individual-specific) kinds.

Graham Priest presents a new, expanded edition of his highly original exploration of the nature and limits of thought. Embracing contradiction and challenging traditional logic, Priest engages with issues across philosophical borders, from the historical to the modern, from Eastern to Western, and from the continental to the analytic. He has added new chapters on European and Indian philosophy, and reflections on responses to the book. This clear, provocative, and systematic work offers a radically different approach to philosophy and logic.