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)
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.
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)
The argument from fine tuning is supposed to establish the existence of God from the fact that the evolution of carbon-based life requires the laws of physics and the boundary conditions of the universe to be more or less as they are. We demonstrate that this argument fails. In particular, we focus on problems associated with the role probabilities play in the argument. We show that, even granting the fine tuning of the universe, it does not follow that the universe (...) is improbable, thus no explanation of the fine tuning, theistic or otherwise, is required. (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)
The 'best-system' analysis of lawhood [Lewis 1994] faces the 'zero-fit problem': that many systems of laws say that the chance of history going actually as it goes--the degree to which the theory 'fits' the actual course of history--is zero. Neither an appeal to infinitesimal probabilities nor a patch using standard measure theory avoids the difficulty. But there is a way to avoid it: replace the notion of 'fit' with the notion of a world being typical with respect to a theory.
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.
IntroductionCurry’s paradox is well known.See, e.g., Priest , ch. 6. It comes in both set theoretic and semantic versions. Here we will concentrate on the semantic versions. Historically, these have deployed the notion of truth. Those who wish to endorse an unrestricted T-schema have mainly endorsed a logic which rejects the principle of Absorption, \\models A\rightarrow B\). High profile logics of this kind are certain relevant logics; these have semantics which show how and why this principle is not valid. Of (...) more recent times, paradoxes which are clearly in the same family have been appearing; but these concern the notion of validity itself. The standard semantics of relevant logics seem powerless to address these. But they can. This note shows how. The upshot can be seen as a return to the roots of relevant logic, in a sense to become clear.BackgroundThe Usual Curry ParadoxesLet us start with a couple of standard forms of the paradox. I .. (shrink)
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)
Curry’s paradox is well known. The original version employed a conditional connective, and is not forthcoming if the conditional does not satisfy contraction. A newer version uses a validity predicate, instead of a conditional, and is not forthcoming if validity does not satisfy structural contraction. But there is a variation of the paradox which uses “external validity”. And since external validity contracts, one might expect the appropriate version of the Curry paradox to be inescapable. In this paper we show that (...) this is not the case. We consider two ways of formalising the notion of external validity, and show that in both of these the paradox is not forthcoming without the appropriate forms of contraction. (shrink)
In his article in this issue, " 'How do Mādhyamikas Think?' Revisited," Tom Tillemans reflects on his earlier article "How do Mādhyamikas Think?" (2009), itself a response to earlier work of ours (Deguchi et al. 2008; Garfield and Priest 2003). There is much we agree with in these non-dogmatic and open-minded essays. Still, we have some disagreements. We begin with a response to Tillemans' first thoughts, and then turn to his second thoughts.Tillemans (2009) maintains that it is wrong to attribute (...) to Nāgārjuna or to his Mādhyamika followers a strong dialetheism, according to which some contradictions of the form p ∧ ¬p are to be accepted. He argues that, nonetheless, a weak dialetheism may be implicit in the .. (shrink)
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. (shrink)
The paper argues for realism in quantum mechanics. Specifically, the formalism of quantum mechanics should be understood as giving a complete description of quantum situations. When it is understood in this way, traditional primary properties of matter can be seen as similar to traditional secondary properties, though at a different level.
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.
In this paper we reply to arguments of Kroon (“Characterization and Existence in Modal Meinongianism”. Grazer Philosophische Studien 86, 23–34) to the effect that Modal Meinongianism cannot do justice to Meinongian claims such as that the golden mountain is golden, and that it does not exist.
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.
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. (shrink)
In his ‘On t and u and what they can do’, Greg Restall presents an apparent problem for a handful of well-known non-classical solutions to paradoxes like the liar. In this article, we argue that there is a problem only if classical logic – or classical-enough logic – is presupposed. 1. Background Many have thought that invoking non-classical logic – in particular, a paracomplete or paraconsistent logic – is the correct response to the liar and related paradoxes. At the most (...) basic level, the target non-classical idea is that some expressions, like ‘all and only the true propositions’, do not behave as we would expect from classical logic. Non-classical theorists argue that the class of all and only the truths is either incomplete or inconsistent: when you truly speak of all and only truths , you're either leaving some truths out, or you're letting some untruths in. Truth, in a slogan, is either gappy or glutty. Non-classicality is not a glib or easy-way-out response to the paradoxes. Innocuous-seeming notions can turn out to be philosophically substantial. Moreover, apparently correct forms of reasoning can turn out to be incorrect. To take a example, a glut theorist must hold that the following argument form is not in general valid. Either p is true or q is true. But p is untrue. So q is true. This argument form may strike our ears as acceptable. But if p is a truth value glut, then the inference fails to preserve truth. According to glut theorists, the inference breaks down in inconsistent contexts: if the subject matter involves gluts, then the inference is to be rejected. And the liar paradox, according to such theorists, shows that truth is exactly the kind of subject matter that yields inconsistency. In the …. (shrink)
One of Da Costa’s motives when he constructed the paraconsistent logic C! was to dualise the negation of intuitionistic logic. In this paper I explore a different way of going about this task. A logic is defined by taking the Kripke semantics for intuitionistic logic, and dualising the truth conditions for negation. Various properties of the logic are established, including its relation to C!. Tableau and natural deduction systems for the logic are produced, as are appropriate algebraic structures. The paper (...) then investigates dualising the intuitionistic conditional in the same way. This establishes various connections between the logic, and a logic called in the literature ‘Brouwerian logic’ or ‘closed-set logic’. (shrink)
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)
In this paper we introduce a paraconsistent reasoning strategy, Chunk and Permeate. In this, information is broken up into chunks, and a limited amount of information is allowed to flow between chunks. We start by giving an abstract characterisation of the strategy. It is then applied to model the reasoning employed in the original infinitesimal calculus. The paper next establishes some results concerning the legitimacy of reasoning of this kind - specifically concerning the preservation of the consistency of each chunk (...) and concludes with some other possible applications and technical questions. (shrink)
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. (shrink)
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. (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)
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 doctrine of the two truths - a conventional truth and an ultimate truth - is central to Buddhist metaphysics and epistemology. The two truths (or two realities), the distinction between them, and the relation between them is understood variously in different Buddhist schools; it is of special importance to the Madhyamaka school. One theory is articulated with particular force by Nagarjuna (2nd ct CE) who famously claims that the two truths are identical to one another and yet distinct. One (...) of the most influential interpretations of Nagarjuna's difficult doctrine derives from the commentary of Candrakirti (6th ct CE). In view of its special soteriological role, much attention has been devoted to explaining the nature of the ultimate truth; less, however, has been paid to understanding the nature of conventional truth, which is often described as "deceptive," "illusion," or "truth for fools." But because of the close relation between the two truths in Madhyamaka, conventional truth also demands analysis. Moonshadows, the product of years of collaboration by ten cowherds engaged in Philosophy and Buddhist Studies, provides this analysis. The book asks, "what is true about conventional truth?" and "what are the implications of an understanding of conventional truth for our lives?" Moonshadows begins with a philosophical exploration of classical Indian and Tibetan texts articulating Candrakati's view, and uses this textual exploration as a basis for a more systematic philosophical consideration of the issues raised by his account. (shrink)
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.
: Nagarjuna seems willing to embrace contradictions while at the same time making use of classic reductio arguments. He asserts that he rejects all philosophical views including his own-that he asserts nothing-and appears to mean it. It is argued here that he, like many philosophers in the West and, indeed, like many of his Buddhist colleagues, discovers and explores true contradictions arising at the limits of thought. For those who share a dialetheist's comfort with the possibility of true contradictions commanding (...) rational assent, for Nagarjuna to endorse such contradictions would not undermine but instead confirm the impression that he is indeed a highly rational thinker. It is argued that the contradictions he discovers are structurally analogous to many discovered by Western philosophers and mathematicians. (shrink)
‘What is philosophy?’ is a question that every professional philosopher must ask themself sometimes. In a sense, of course, they know: they spend much time doing it. But in another sense, the answer to the question is not at all obvious. In the same way, any person knows by acquaintance what breathing is; but this does not mean that they know the nature of breathing: its mechanism and function. The nature of breathing, in this sense, is now well understood; the (...) nature of philosophy, by contrast, is still very much an open question. One of the reasons this is so is that the nature of philosophy is itself a philosophical question, so uncontentious answers are not to be expected—if philosophers ever ceased disagreeing with one another our profession would be done for. Moreover, it is a hard philosophical question. Many great philosophers, including Plato, Hegel, and others, have suggested answers to it. But their answers would now be given little credence. In the thirty or so years that I have been doing philosophy there have been two views about the nature of philosophy which have had wide acceptance. These are the views of the later Wittgenstein and of Derrida. In the first two parts of this paper I will describe these views and explain why I find them unsatisfactory. I will then go on, in the final part of paper, to outline a view that inspires more confidence in me. (shrink)