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.

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. (shrink)

We have seen that proofs of soundness of (Boolean) DS, EFQ and of ABS — and hence the legitimation of these inferences — can be achieved only be appealing to the very form of reasoning in question. But this by no means implies that we have to fall back on classical reasoning willy-nilly. Many logical theories can provide the relevant boot-strapping. Decision between them has, therefore, to be made on other grounds. The grounds include the many criteria familiar from the (...) philosophy of science: theoretical integrity (e.g., paucity of ad hoc hypotheses), adequacy to the data (explaining the data of inference —all inferences, not just those chosen from consistent domains!) and so on. This paper has not attempted to address these issues in general. All it demonstrates is that the charge that a dialetheist solution to the semantic paradoxes can be maintained only by making some intelligible notion ineffable cannot be made to stick. The dialetheist has a coherent position, endorsing the T-scheme, but rejecting DS, EFQ (even Boolean DS and EFQ) and ABS. And any argument to the effect that the relevant notions are both ineffable and intelligible begs the question. The case against consistent “solutions” to the semantic paradoxes therefore remains intact. (shrink)

In Contradiction advocates and defends the view that there are true contradictions (dialetheism), 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 in1987. 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 byOxford University Press in 2006. (shrink)

I argue that there is nothing about truth as such that prevents contradictions from being true. I argue this by considering the main standard accounts of truth, and showing that they are quite compatible with the existence of true contradictions. Indeed, in many cases, they are actually friendly to the idea.

The paper explains how a paraconsistent logician can appropriate all classical reasoning. This is to take consistency as a default assumption, and hence to work within those models of the theory at hand which are minimally inconsistent. The paper spells out the formal application of this strategy to one paraconsistent logic, first-order LP. (See, Ch. 5 of: G. Priest, In Contradiction, Nijhoff, 1987.) The result is a strong non-monotonic paraconsistent logic agreeing with classical logic in consistent situations. It is shown (...) that the logical closure of a theory under this logic is trivial only if its closure under LP is trivial. (shrink)

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)

Priest (2009) formulates a propositional logic which, by employing the worldsemantics for intuitionist logic, has the same positive part but dualises the negation, to produce a paraconsistent logic which it calls 'Da Costa Logic'. This paper extends matters to the first-order case. The paper establishes various connections between first order da Costa logic, da Costa's own Cω, and classical logic. Tableau and natural deductions systems are provided and proved sound and complete.

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.

When a wrongdoing occurs, victims, barring special circumstance, can aptly forgive their wrongdoers, receive apologies, and be paid reparations. It is also uncontroversial, in the usual circumstances, that wronged parties can aptly blame their wrongdoer. But controversy arises when we consider blame from third-parties after the victim has forgiven. At times it seems that wronged parties can make blame inapt through forgiveness. If third parties blame anyway, it often appears the victim is justified in protesting. “But I forgave him!” In (...) other cases, however, forgiveness seems irrelevant: B can forgive A, but it can still seem that third parties can aptly blame A for the wrong against B. This perplexity adds a dimension to ongoing discussion regarding criteria for apt blame and the related issues of standing and fittingness. This paper explores the status of third party blame after forgiveness. I argue that while post forgiveness blame is often inapt, in many other cases forgiveness is irrelevant. This difference is explained by appeal to the various relationships third parties might have to wronged parties, and how these differences affect the ways we blame and thereby blame’s aptness. (shrink)

The paper describes a new way of thinking about conditionals, in terms of information transfer between worlds. This way of looking at things provides an answer to some of the standard problems concerning conditionals, and undercuts the claim that indicative and subjunctive conditionals are distinct.

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.

The first half of this article is critical: it develops an interpretation of Kant as trying, and failing, to limit our judgments to phenomena and abstain from making claims about noumena, and an interpretation of Wittgenstein as trying, and failing, to develop a theory of meaning that abstains from attempting to say the unsayable. On the reading offered, both Kant and Wittgenstein find themselves saying things that by their own lights cannot be said: in Kant’s case, claims about noumena, and (...) in Wittgenstein’s case, structural claims. While Kant attempts a solution of the problem which also fails, Wittgenstein bites the bullet and leaves his Tractatus, for the most part, void and meaningless. The suggested response is a dialetheic approach—either as an alternative or, potentially, as an amendment to a Kantian or Wittgensteinian theory. According to this approach, certain problems in philosophy arise from true contradictions and thus require a theory that makes sense of contradiction. A subgroup of these problems (among them the noumenal and structural issues in Kant and Wittgenstein) are about things that both are and are not ineffable. The second half of the paper develops a dialetheic account of ineffability and a concise formal theory to ensure that contradiction at the limits of language does not spread to other areas. (shrink)

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)

This paper articulates Sylvan's theory of mathematical objects as non-existent, by improving (arguably) his treatment of the Characterisation Postulate. It then defends the theory against a number of natural objections, including one according to which the account is just platonism in disguise.

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)

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.

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 crucial question here is what, exactly, the conditional in the naive truth/set comprehension principles is. In 'Logic of Paradox', I outlined two options. One is to take it to be the material conditional of the extensional paraconsistent logic LP. Call this "Strategy 1". LP is a relatively weak logic, however. In particular, the material conditional does not detach. The other strategy is to take it to be some detachable conditional. Call this "Strategy 2". The aim of the present essay (...) is to investigate Stragey 1. It is not to advocate it. The work is simply an extended exploration of the strategy, its strengths, its weaknesses, and the various dierent ways in which it may be implemented. In the first part of the paper I will set up the appropriate background details. In the second, I will look at the strategy as it applies to the semantic paradoxes. In the third I will look at how it applies to the set-theoretic paradoxes. (shrink)

The view that everything is empty (śūnya) is a central metaphysical plank of Mahāyāna Buddhism. It has often been the focus of objections. Perhaps the most important of these is that it in effect entails a nihilism: nothing exists. This objection, in turn, is denied by Mahāyāna theorists, such as Nāgārjuna. One of the things that makes the debate difficult is that the precise import of the view that everything is empty is unclear. The object of this essay is to (...) put the debate in a new light. It does so by proposing a mathematical characterization of Emptiness—that is, the totality of empty things—showing that, whatever it is, it has a definite structure and is not, therefore, to be identified with nothingness. (shrink)

Boring Formless Nonsense intervenes in an aesthetics of failure that has largely been delimited by the visual arts and its avant-garde legacies. It focuses on contemporary experimental composition in which failure rubs elbows with the categories of chance, noise, and obscurity. In these works we hear failure anew. We hear boredom, formlessness, and nonsense in a way that gives new purchase to aesthetic, philosophical, and ethical questions that falter in their negative capability. Reshaping current debates on failure as an aesthetic (...) category, eldritch Priest shows failure to be a duplicitous concept that traffics in paradox and sustains the conditions for magical thinking and hyperstition. Framing recent experimental composition as a deviant kind of sound art, Priest explores how the affective and formal elements of post-Cagean music couples with contemporary culture's themes of depression, distraction, and disinformation to create an esoteric reality composed of counterfactuals and pseudonymous beings. Ambitious in content and experimental in its approach, Boring Formless Nonsense will challenge and fracture your views on failure, creativity, and experimental music. (shrink)

Jaina philosophy provides a very distinctive account of logic, based on the theory of ?sevenfold predication?. This paper provides a modern formalisation of the logic, using the techniques of many-valued and modal logic. The formalisation is applied, in turn, to some of the more problematic aspects of Jaina philosophy, especially its relativism.