The aim of the paper is to analyse Brandom’s account of Hegel’s conception of determinate negation and the role this structure plays in the dialectical process with respect to the problem of contradiction. After having shown both the merits and the limits of Brandom’s account, I will refer to Priest’s dialetheistic approach to contradiction as an alternative contemporary perspective from which it is possible to capture essential features of Hegel’s notion of contradiction, and I will test the equation of Hegel’s (...) dialectic with Priest dialetheism. (shrink)

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

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.

There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the truth – viz. that the same thing cannot at one and the same time be and not be": with these words of the Metaphysics, Aristotle introduced the Law of Non-Contradiction, which was to become the most authoritative principle in the history of Western thought. However, things have recently changed, and nowadays various philosophers, called dialetheists, claim that this Law does not (...) hold unrestrictedly – that in peculiar circumstances the same thing may at the same time be and not be, and contradictions may obtain in the world. This book opens with an examination of the famous logical paradoxes that appear to speak on behalf of contradictions (e.g., the Liar paradox, the set-theoretic paradoxes such as Cantor’s and Russell’s), and of the reasons for the failure of the standard attempts to solve them. It provides, then, an introduction to paraconsistent logics – non-classical logics in which the admission of contradictions does not lead to logical chaos –, and their astonishing applications, going from inconsistent data base management to contradictory arithmetics capable of circumventing Gödel’s celebrated Incompleteness Theorem. The final part of the book discusses the philosophical motivations and difficulties of dialetheism, and shows how to extract from Aristotle’s ancient words a possible reply to the dialetheic challenge. How to Sell a Contradiction will appeal to anyone interested in non-classical logics, analytic metaphysics, and philosophy of mathematics, and especially to those who consider challenging our most entrenched beliefs the main duty of philosophical inquiry. (shrink)

Things and Their Place in Theories Our talk of external things, our very notion of things, is just a conceptual apparatus that helps us to foresee and ...

A selective background -- Broadly classical approaches -- Paracompleteness -- More on paracomplete solutions -- Paraconsistent dialetheism.

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.

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)

This landmark book is now reissued in a new edition that has been vastly rewritten and updated to respond to recent Kantian literature.

This book is available either individually, or as part of the specially-priced Arguments of the Philosphers Collection.

Persistence through time is like extension through space. A road has spatial parts in the subregions of the region of space it occupies; likewise, an object that exists in time has temporal parts in the various subregions of the total region of time it occupies. This view — known variously as four dimensionalism, the doctrine of temporal parts, and the theory that objects “perdure” — is opposed to “three dimensionalism”, the doctrine that things “endure”, or are “wholly present”.1 I will (...) attempt to resolve this dispute in favor of four dimensionalism by means of a novel argument based on considerations of vagueness. But before argument in this area can be productive, I believe we must become much clearer than is customary about exactly what the dispute is, for the usual ways of formulating the dispute are flawed, especially where three dimensionalism is concerned. (shrink)

In his famous work on vagueness, Russell named “fallacy of verbalism” the fallacy that consists in mistaking the properties of words for the properties of things. In this paper, I examine two (clusters of) mainstream paraconsistent logical theories – the non-adjunctive and relevant approaches –, and show that, if they are given a strongly paraconsistent or dialetheic reading, the charge of committing the Russellian Fallacy can be raised against them in a sophisticated way, by appealing to the intuitive reading of (...) their underlying semantics. The meaning of “intuitive reading” is clarified by exploiting a well-established distinction between pure and applied semantics. If the proposed arguments go through, the dialetheist or strong paraconsistentist faces the following Dilemma: either she must withdraw her claim to have exhibited true contradictions in a metaphysically robust sense – therefore, inconsistent objects and/or states of affairs that make those contradictions true; or she has to give up realism on truth, and embrace some form of anti-realistic (idealistic, or broadly constructivist) metaphysics. Sticking to the second horn of the Dilemma, though, appears to be promising: it could lead to a collapse of the very distinction, commonly held in the literature, between a weak and a strong form of paraconsistency – and this could be a welcome result for a dialetheist. (shrink)

In the Resolution of the Second Antinomy of the first Critique and the Dynamics chapter of the Metaphysical Foundations of Natural Sciences, Kant presents his critical views on mereology, the study of parts and wholes. He endorses an unusual position: Matter is said to be infinitely divisible without being infinitely divided. It would be mistaken to think that matter consists of infinitely many parts—rather, parts “exist only in the representation of them, hence in the dividing”. This view, according to which (...) parts are created through division somehow, was criticized as obscure early on, and has not received much attention since. Against this trend, I show how a coherent position, which I call Mereological Conceptualism, can be extracted from the sparse textual basis. (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)

This is a 1988 philosophical introduction to Aristotle, and Professor Lear starts where Aristotle himself starts. The first sentence of the Metaphysics states that all human beings by their nature desire to know. But what is it for us to be animated by this desire in this world? What is it for a creature to have a nature; what is our human nature; what must the world be like to be intelligible; and what must we be like to understand it (...) systematically? Through a consideration of these questions Professor Lear introduces us to the essence of Aristotle's philosophy and guides us through the central Aristotelian texts - selected from the Physics, Metaphysics, Ethics, Politics and from the biological and logical works. The book is written in a direct, lucid style which engages the reader with the themes in an active, participatory manner. (shrink)

The Presocratics were the founding fathers of the Western philosophical tradition, and the first masters of rational thought. This volume provides a comprehensive and precise exposition of their arguments, and offers a rigorous assessment of their contribution to philosophical thought.

Lucy Allais presents an original interpretation of Kant's transcendental idealism. She argues that his distinction between things in themselves and things as they appear to us has both epistemological and metaphysical components. Kant is committed to a genuine idealism about things as they appear to us, but this is not a phenomenalist idealism. He is committed to the claim that there is an aspect of reality that grounds mind-dependent spatio-temporal objects, and which we cannot cognize, but he does not assert (...) the existence of distinct non-spatio-temporal objects. On Allais's account, we cannot understand Kant's idealism without a clear account of his notion of intuition and of the role of intuition in cognition: she understands Kantian intuitions as representations that give us acquaintance with the objects of thought. This enables us to make sense of Kant's central argument for his idealism in the Transcendental Aesthetic, and to see why he takes the complete idealist position to be established there. (shrink)

In this paper it is argued that the _Physical Monadology of 1756 has to be seen as an attempt to evade the same paradox as the one given in the second antinomy of the _Critique of Pure Reason. Since this attempt presupposes the claim that space rests upon relations between substances, it contradicts the thesis that it is a mere form of intuition, presented by Kant in his dissertation of 1770. Therefore, at least since 1770 the paradox of the divisibility (...) of matter rose up again so that Kant had to deal with it once again in his first _Critique. Remarkably, his key to solve the second antinomy is the same which ruled out his earlier solution of 1756 and gave rise to the paradox again, i.e., the ideality of space and time. But, contrary to the dissertation, in the _Critique it is substituted by the doctrine that our knowledge of objects depends on and is restricted to intuitively given objects and this is crucial to the solution of the second antinomy. Finally, it will be shown how Kant deals with the problem of the divisibility of matter in the _Metaphysical Foundations of Natural Science. (shrink)

In In Contradiction, Graham Priest shows, as clearly as anything like this can be shown, that it is coherent to maintain that some sentences can be both true and false at the same time. As a consequence, some contradictions are true, and an appreciation of this possibility advances our understanding of the nature of logic and language.

In Spandrels of Truth, Beall concisely presents and defends a modest, so-called dialetheic theory of transparent truth.

In his In Contradiction (1987), Priest levelled three powerful arguments against the received Russellian view of change and motion. He argued that his preferred paraconsistent theory of change, the Hegelian account, is immune from these objections. Here I argue that these three arguments are sound, but that the Hegelian account falls pray to them too. I conclude, however, that the Hegelian account is in a better position to tackle these challenges.

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.

INTRODUCTION MATHEMATICAL logic differs from the traditional formal logic so markedly in method, and so far surpasses it in power and subtlety, ...

Can God create a stone too heavy for him to lift? Can time have a beginning? Which came first, the chicken or the egg? Riddles, paradoxes, conundrums--for millennia the human mind has found such knotty logical problems both perplexing and irresistible. Now Roy Sorensen offers the first narrative history of paradoxes, a fascinating and eye-opening account that extends from the ancient Greeks, through the Middle Ages, the Enlightenment, and into the twentieth century. When Augustine asked what God was doing before (...) He made the world, he was told: "Preparing hell for people who ask questions like that." A Brief History of the Paradox takes a close look at "questions like that" and the philosophers who have asked them, beginning with the folk riddles that inspired Anaximander to erect the first metaphysical system and ending with such thinkers as Lewis Carroll, Ludwig Wittgenstein, and W.V. Quine. Organized chronologically, the book is divided into twenty-four chapters, each of which pairs a philosopher with a major paradox, allowing for extended consideration and putting a human face on the strategies that have been taken toward these puzzles. Readers get to follow the minds of Zeno, Socrates, Aquinas, Ockham, Pascal, Kant, Hegel, and many other major philosophers deep inside the tangles of paradox, looking for, and sometimes finding, a way out. Filled with illuminating anecdotes and vividly written, A Brief History of the Paradox will appeal to anyone who finds trying to answer unanswerable questions a paradoxically pleasant endeavor. (shrink)

one of kant's most famous claims is his dictum about existence. In the course of his criticism of the ontological argument, he writes:Being is obviously not a real predicate, i.e., a concept of something that could be added to the concept of a thing.One reason why this passage is so famous is that many people think that it anticipates a discovery about the logical form of existence claims that was later central for the development of analytic philosophy and its project (...) of overcoming metaphysical confusions by logical analysis. There are two prominent interpretations that read Kant's dictum along these lines. The first, and by far most popular, interprets Kant as holding a proto-Fregean view about existence.2... (shrink)

Heidegger also famously says that Being depends on Dasein, even though beings in general do not. This is perplexing. “Heidegger and the “There Is” of Being” offers an interpretation of what’s going on in the passages in which this sort of assertion is made.

In This Paper, I Identify a Problem, which the project that I will refer to as the ‘Being and Time Project’ (or ‘BTP’ for short) aimed to solve; this is the project within which Heidegger reinterpreted his early thought—and which he unsuccessfully attempted to bring to fruition—in, roughly speaking, the years 1925–28. The problem in question presents several faces: viewed from one angle, it concerns the unity of the concept of “Being in general,” from another, the integrity of the notion (...) of “Dasein,” and from another, the possibility of the perspective from which the philosopher does her work. The solution that the BTP would have offered turns on the claim that time is “the possible horizon for any understanding .. (shrink)

This book is a systematic history of one of the oldest problems in the philosophy of space and time: How is the change from one state to its opposite to be described? To my knowledge it is the first comprehensive book providing information about and analysis of texts on this topic throughout the ages. The target audience I envisaged are advanced students and scholars of analytic philosophy and the history of philosophy who are interested in the philosophy of space and (...) time. Authors treated in this book range from Plato, Aristotle, the logicians of the late Middle Ages, Kant, Brentano and Russell to contemporary authors such as Chisholm, Hamblin, Sorabji or Graham Priest, taking into account such theories as interval semantics or paraconsistent logic. For the first time, two main questions about the moment of change are explicitly kept apart: Which of the opposite states does the moment of change belong to? And does it contain an instantaneous event? The texts are discussed within a clear framework of the main systematic options for describing the moment of change, sometimes using predicate logic extended by newly introduced logical prefixes. The last part contains a new suggestion of how to solve the problem of the moment of change. It is centred around a theory of instantaneous states which provides a new solution to Zeno's Flying Arrow Paradox. (shrink)

The naive set theory problem is to begin with a full comprehension axiom, and to find a logic strong enough to prove theorems, but weak enough not to prove everything. This paper considers the sub-problem of expressing extensional identity and the subset relation in paraconsistent, relevant solutions, in light of a recent proposal from Beall, Brady, Hazen, Priest and Restall [4]. The main result is that the proposal, in the context of an independently motivated formalization of naive set theory, leads (...) to triviality. (shrink)

This volume consists of two lecture series given by Heidegger in the 1940s and 1950s. The lectures given in Bremen constitute the first public lectures Heidegger delivered after World War II, when he was officially banned from teaching. Here, Heidegger openly resumes thinking that deeply engaged him with Hölderlin's poetry and themes developed in his earlier works. In the Freiburg lectures Heidegger ponders thought itself and freely engages with the German idealists and Greek thinkers who had provoked him in the (...) past. Andrew J. Mitchell's translation allows English-speaking readers to explore important connections with Heidegger's earlier works on language, logic, and reality. (shrink)