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)

Is there a notion of contradiction—let us call it, for dramatic effect, “absolute”—making all contradictions, so understood, unacceptable also for dialetheists? It is argued in this paper that there is, and that spelling it out brings some theoretical benefits. First it gives us a foothold on undisputed ground in the methodologically difficult debate on dialetheism. Second, we can use it to express, without begging questions, the disagreement between dialetheists and their rivals on the nature of truth. Third, dialetheism has (...) an operator allowing it, against the opinion of many critics, to rule things out and manifest disagreement: for unlike other proposed exclusion-expressing-devices (for instance, the entailment of triviality), the operator used to formulate the notion of absolute contradiction appears to be immune both from crippling expressive limitations and from revenge paradoxes—pending a rigorous nontriviality proof for a formal dialetheic theory including it. (shrink)

The purpose of this essay is to shed some light on a certain type of sentence, which I call a borderline contradiction. A borderline contradiction is a sentence of the form F a ∧ ¬F a, for some vague predicate F and some borderline case a of F , or a sentence equivalent to such a sentence. For example, if Jackie is a borderline case of ‘rich’, then ‘Jackie is rich and Jackie isn’t rich’ is a borderline (...) class='Hi'>contradiction. Many theories of vague language have entailments about borderline contradictions; correctly describing the behavior of borderline contradictions is one of the many tasks facing anyone offering a theory of vague language. Here, I first briefly review claims made by various theorists about these borderline contradictions, attempting to draw out some predictions about the behavior of ordinary speakers. Second, I present an experiment intended to gather relevant data about the behavior of ordinary speakers. Finally, I discuss the experimental results in light of several different theories of vagueness, to see what explanations are available. My conclusions are necessarily tentative; I do not attempt to use the present experiment to demonstrate that any single theory is incontrovertibly true. Rather, I try to sketch the auxiliary hypotheses that would need to be conjoined to several extant theories of vague language to predict the present result, and offer some considerations regarding the plausibility of these various hypotheses. In the end, I conclude that two of the theories I consider are better-positioned to account for the observed data than are the others. But the field of logically-informed research on people’s actual responses to vague predicates is young; surely as more data come in we will learn a great deal more about which (if any) of these theories best accounts for the behavior of ordinary speakers. (shrink)

Kant’s most prominent formulation of the Categorical Imperative, known as the Formula of Universal Law (FUL), is generally thought to demand that one act only on maxims that one can will as universal laws without this generating a contradiction. Kant's view is standardly summarized as requiring the 'universalizability' of one's maxims and described in terms of the distinction between 'contradictions in conception' and 'contradictions in the will'. Focusing on the underappreciated significance of the simultaneity condition included in the FUL, (...) I argue, by contrast, that the principle is better read as requiring that one be able to will two things simultaneously without self-contradiction, namely, that a maxim be one's own and that it be a universal law. This amounts to a new interpretation of the FUL with significant interpretive and philosophical advantages. (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 Philosophical Logic, the Liar Paradox has been used to motivate the introduction of both truth value gaps and truth value gluts. Moreover, in the light of “revenge Liar” arguments, also higher-order combinations of generalized truth values have been suggested to account for so-called hyper-contradictions. In the present paper, Graham Priest's treatment of generalized truth values is scrutinized and compared with another strategy of generalizing the set of classical truth values and defining an entailment relation on the resulting sets of (...) higher-order values. This method is based on the concept of a multilattice. If the method is applied to the set of truth values of Belnap's “useful four-valued logic”, one obtains a trilattice, and, more generally, structures here called Belnap-trilattices. As in Priest's case, it is shown that the generalized truth values motivated by hyper-contradictions have no effect on the logic. Whereas Priest's construction in terms of designated truth values always results in his Logic of Paradox, the present construction in terms of truth and falsity orderings always results in First Degree Entailment. However, it is observed that applying the multilattice-approach to Priest's initial set of truth values leads to an interesting algebraic structure of a “bi-and-a-half” lattice which determines seven-valued logics different from Priest's Logic of Paradox. (shrink)

Naive speakers find some logical contradictions acceptable, specifically borderline contradictions involving vague predicates such as Joe is and isn’t tall. In a recent paper, Cobreros et al. (J Philos Logic, 2012) suggest a pragmatic account of the acceptability of borderline contradictions. We show, however, that the pragmatic account predicts the wrong truth conditions for some examples with disjunction. As a remedy, we propose a semantic analysis instead. The analysis is close to a variant of fuzzy logic, but conjunction and disjunction (...) are interpreted as intensional operators. (shrink)

Roy Sorenson offers a unique exploration of an ancient problem: vagueness. Did Buddha become a fat man in one second? Is there a tallest short giraffe? According to Sorenson's epistemicist approach, the answers are yes! Although vagueness abounds in the way the world is divided, Sorenson argues that the divisions are sharp; yet we often do not know where they are. Written in Sorenson'e usual inventive and amusing style, this book offers original insight on language and logic, the way world (...) is, and our understanding of it. (shrink)

This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical theory and (...) offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative achievements in contemporary logic, with deep roots in philosophical questions involving negation and consistency This book offers an invaluable introduction to a topic of central importance in logic and philosophy. It discusses the history of paraconsistent logic; language, negation, contradiction, consistency and inconsistency; logics of formal inconsistency and the main paraconsistent propositional systems; many-valued companions, possible-translations semantics and non-deterministic semantics; paraconsistent modal logics; first-order paraconsistent logics; applications to information processing, databases and quantum computation; and applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning. (shrink)

In this analysis of one of the most difficult and neglected topics in Hegelian studies, Songsuk Susan Hahn tackles the status of contradiction in Hegel's ...

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)

Contradiction is often confused with contrariety. We propose to disentangle contrariety from contradiction using the hexagon of opposition, providing a clear and distinct characterization of three notions: contrariety, contradiction, incompatibility. At the same time, this hexagonal structure describes and explains the relations between them.

One of the most important difficulties facing Kant’s Formula of Universal Law (FUL) is its apparent inability to show that it is always impermissible to kill others for the sake of convenience. This difficulty has led current Kantian ethicists to de-emphasize the FUL or at least complement it with other Kantian principles when dealing with murder. The difficulty stems from the fact that the maxim of convenience killing fails to generate a ‘contradiction in conception’, producing only a ‘contradiction (...) in the will’ when subjected to the two-fold test associated with the FUL. This result is thought to imply that the FUL allows us sometimes to kill for the sake of convenience. In this essay, I argue that the very diagnosis of the problem rests on a mistake, and that if the maxim of convenience killing generates a contradiction in the will, then acting on it is never permissible. (shrink)

We discuss the idea that superpositions in quantum mechanics may involve contradictions or contradictory properties. A state of superposition such as the one comprised in the famous Schrödinger’s cat, for instance, is sometimes said to attribute contradictory properties to the cat: being dead and alive at the same time. If that were the case, we would be facing a revolution in logic and science, since we would have one of our greatest scientific achievements showing that real contradictions exist.We analyze that (...) claim by employing the traditional square of opposition.We suggest that it is difficult to make sense of the idea of contradiction in the case of quantum superpositions. From a metaphysical point of view the suggestion also faces obstacles, and we present some of them. (shrink)

The goals of this paper are two-fold: I wish to clarify the Aristotelian conception of the law of non-contradiction as a metaphysical rather than a semantic or logical principle, and to defend the truth of the principle in this sense. First I will explain what it in fact means that the law of non-contradiction is a metaphysical principle. The core idea is that the law of non-contradiction is a general principle derived from how things are in the (...) world. For example, there are certain constraints as to what kind of properties an object can have, and especially: some of these properties are mutually exclusive. Given this characterisation, I will advance to examine what kind of challenges the law of non-contradiction faces; the main opponent here is Graham Priest. I will consider these challenges and conclude that they do not threaten the truth of the law of non-contradiction understood as a metaphysical principle. (shrink)

Transhumanism, the belief that technology can transcend the limitations of the human body and brain, is part of the family of Enlightenment philosophies. As such, transhumanism has also inherited the internal tensions and contradictions of the broad Enlightenment tradition. First, the project of Reason is self-erosive and requires irrational validation. Second, although most transhumanists are atheist, their belief in the transcendent power of intelligence generates new theologies. Third, although most transhumanists are liberal democrats, their belief in human perfectibility and governance (...) by reason can validate technocratic authoritarianism. Fourth, transhumanists are divided on the balance between democracy and the market. Fifth, teleological expectations of unstoppable progress are in tension with awareness of the indeterminacy of the future. Sixth, transhumanists are divided between advocates of ethical universalism and ethical relativism. Seventh, the rational materialist denial of discrete persistent selves calls into question the transhumanist project of individual longevity and enhancement. (shrink)

The papers in this volume present some of the most recent results of the work about contradictions in philosophical logic and metaphysics; examine the history of contradiction in crucial phases of philosophical thought; consider the relevance of contradictions for political and philosophical actuality. From this consideration a common question emerges: the question of the irreducibility, reality and productive force of (some) contradictions.

_The Contradictions of Modern Moral Philosophy_ is a highly original and radical critique of contemporary moral theory. Paul Johnston demonstrates that much recent moral philosophy is confused about the fundamental issue of whether there are correct moral judgements. He shows that the standard modern approaches to ethics cannot justify - or even make much sense of - traditional moral beliefs. Applied rigorously, these approaches suggest that we should reject ethics as a set of outdated and misguided claims. Rather than facing (...) up to this conclusion, most recent moral philosophy consists of attempts to find some ways of preserving moral beliefs. This places a contradiction at the heart of moral philosophy. As a resilt it is often impossible to tell whether a contemporary philosopher ultimately rejects or endorses the idea of objective right and wrong. On the basis of a Wittgenstein approach Paul Johnston puts forward an alternative account of ethics that avoids this contradiction and recognises that the central issues of ethics cannot be resolved by conceptual analysis. He then uses this account to highlight the contradictions of important contemporary moral theorists such as Bernard Williams, Alasdair MacIntyre, Thomas Nagel and Charles Taylor. (shrink)

Certain Buddhist texts contain statements that are prima facie contradictions. The scholarly consensus has been that such statements are meant to serve a rhetorical function that depends on the apparent contradictions being resolvable. But recently it has been claimed that such statements are meant to be taken literally: their authors assert as true statements that are of the form ‘p and not p’. This claim has ramifications for our understanding of the role played by the principle of non-contradiction in (...) Buddhist argumentation. I argue that these make the claim less plausible. (shrink)

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)

Putative examples of true contradictions in the social world have been given by dialetheists such as Graham Priest, Richard Routley, and Val Plumwood. However, we feel that it has not been decisively argued that these examples are in fact true contradictions rather than merely apparent. In this paper we adopt a new strategy to show that there are some true contradictions in the social world, and hence that dialetheism is correct. The strategy involves showing that a group of sincere dialetheists (...) can, given an appropriately formed institution, bootstrap contradictions into existence. We discuss objections and consider the implications of this finding for debates over logic. (shrink)

The Law of Non-Contradiction holds that both sides of a contradiction cannot be true. Dialetheism is the view that there are contradictions both sides of which are true. Crucial to the dispute, then, is the central notion of contradiction. My first step here is to work toward clarification of that simple and central notion: Just what is a contradiction?

Corporate social responsibility (CSR) has attracted increasing attention in business and research. Studies have documented how management concepts such as diversity management are translated and adapted to differential local sociocultural contexts outside their countries of origin. More research is needed concerning how CSR concepts are translated and practiced locally within particular organizations. This research is based on an organizational ethnography of the management of multiple social, ethical and business logics of CSR in a Danish frontrunner firm. The study contributes with (...) insights into the ongoing organizational management of potentially opposing logics in CSR. Findings show that managing contradictions of CSR is an ongoing challenge and accomplishment influencing whether ethical, social and business logics collide or reinforce each other. The study shows that when ethics are framed as means to economic ends, some social responsibilities have a tendency to be disregarded in practice. (shrink)

This paper explores the concept of digital modernity, the extension of narratives of modernity with the special affordances of digital networked technology. Digital modernity produces a new narrative which can be taken in many ways: to be descriptive of reality; a teleological account of an inexorable process; or a normative account of an ideal sociotechnical state. However, it is understood that narratives of digital modernity help shape reality via commercial and political decision-makers, and examples are given from the politics and (...) society of the United Kingdom. The paper argues that digital modernity has two dimensions, of progression through time and progression through space, and these two dimensions can be in contradiction. Contradictions can also be found between ideas of digital modernity and modernity itself, and also between digital modernity and some of the basic pre-modern concepts that underlie the whole technology industry. Therefore, digital modernity may not be a sustainable goal for technology development. (shrink)

I present an analysis according to which the current state of the definition of substitution leads to a contradiction in the system of Transparent Intensional Logic. I entail the contradiction using only the basic definitions of TIL and standard results. I then analyse the roots of the contradiction and motivate the path I take in resolving the contradiction. I provide a new amended definition of collision-less substitution which blocks the contradiction in a non-ad hoc way. (...) I elaborate on the consequences of the amended definition, namely the invalidity of the Church-Rosser theorem. I present a counterexample to the validity of the theorem in TIL with an amended definition of substitution. (shrink)

What happens when well-defined disciplines meet or are confronted with transdisciplinary discourses and concepts, where transdisciplinary concepts are analytical tools rather than specifications of a field of objects or a class of entities? Or, if disciplines reject transdisciplinary discourses and concepts as having no part to play in their practice, why do they so reject them? This essay addresses these questions through a discussion of the relationship between philosophy – the most tightly policed discipline in the humanities – and what (...) I will argue is the emblematically transdisciplinary practice of feminist theory, via a discussion of interdisciplinarity and related terms in gender studies. It argues that the tendency of philosophy to reject feminist theory in fact correctly intuited that the two defining features of feminist theory – its constitutive tie to a political agenda for social change and the transdisciplinary character of many of its central concepts – are indeed at odds with, and pose a threat to, the traditional insularity of the discipline of philosophy. It argues, further, that feminist theory operates with what we should now recognise as a set of transdisciplinary concepts – including, sex, gender, woman, sexuality and sexual difference – and that the use of these concepts in feminist philosophy has been the most far-reaching continuation in the late 20th/early 21st centuries of the critique of philosophy initiated by Marx and pursued by ‘critical theory’. This puts feminist philosophy in a difficult position: its transdisciplinary aspects open it up to an unavoidable contradiction. Nonetheless, this is a contradiction that can and must be endured and made productive. In order to draw out the specificity of the concept of transdisciplinarity at issue the essay begins with a discussion of attempts to define inter- and transdisciplinarity, particularly in gender studies. Arguing for the transdisciplinary origin of the concept of gender, it then suggests one way of understanding its function as a critical concept, before making explicit how this leads to the historical antagonism between traditional philosophy and the critical, transdisciplinary concept of gender and with feminist theory more generally. (shrink)

_The Contradictions of Modern Moral Philosophy_ is a highly original and radical critique of contemporary moral theory. Paul Johnston demonstrates that much recent moral philosophy is confused about the fundamental issue of whether there are correct moral judgements. He shows that the standard modern approaches to ethics cannot justify - or even make much sense of - traditional moral beliefs. Applied rigorously, these approaches suggest that we should reject ethics as a set of outdated and misguided claims. Rather than facing (...) up to this conclusion, most recent moral philosophy consists of attempts to find some ways of preserving moral beliefs. This places a contradiction at the heart of moral philosophy. As a resilt it is often impossible to tell whether a contemporary philosopher ultimately rejects or endorses the idea of objective right and wrong. On the basis of a Wittgenstein approach Paul Johnston puts forward an alternative account of ethics that avoids this contradiction and recognises that the central issues of ethics cannot be resolved by conceptual analysis. He then uses this account to highlight the contradictions of important contemporary moral theorists such as Bernard Williams, Alasdair MacIntyre, Thomas Nagel and Charles Taylor. (shrink)

It is argued that the result assumption of Bohm's theory, which says that particle configurations represent measurement results, contradicts the predictions of the Schroedinger equation.

Through readings of Jacques Derrida's Of Grammatology and 'The Age of Hegel', attention is given to two of the problematic types of relationships that philosophy can have with education. These engagements, alongside a reading of 'The Antinomies of the Philosophical Discipline: Letter Preface', show how Derrida’s thought can prescribe no educational programme and instead troubles educational proclamations and certainties. Throughout his life, Derrida negotiated his relationships to the educational systems and institutions to which he was responsible, these negotiations, though, were (...) not indicative of a belief in any ontologically grounded educational truth. Quite to the contrary, as I will claim, Derrida’s thought is remarkable for its deflation of the myth, stretching at least as far back to Plato’s Republic, that philosophy can discover and prescribe the practical means for its own educational good. The argument presented in this article is that Derrida’s thought is particularly fertile when it comes to educational reflection precisely because it does not close down, presuppose, or prescribe, and that these characteristics also allow for generative contradictions in Derrida's educational and philosophical thought and practice. (shrink)

Archaeological theory -- Philosophy and archaeology -- Critical realism as critique of Western philosophy -- Critical realism as philosophical underlabourer -- Diversity and impasse in current archaeological theorising -- The contradictions of archaeological theory -- The material in archaeological theory -- Critical realism, the material, and absence -- Time, scale, and the ontology of the material -- Conclusions, implications, and further research.

What is it to believe something might be the case? We develop a puzzle that creates difficulties for standard answers to this question. We go on to propose our own solution, which integrates a Bayesian approach to belief with a dynamic semantics for epistemic modals. After showing how our account solves the puzzle, we explore a surprising consequence: virtually all of our beliefs about what might be the case provide counterexamples to the view that rational belief is closed under logical (...) implication. (shrink)

Leibniz was a philosopher of principles: the principles of Contradiction, of Sufficient Reason, of Identity of Indiscernibles, of Plenitude, of the Best, and of Continuity are among the most famous Leibnizian principles. In this article I shall focus on the first three principles; I shall discuss various formulations of the principles (sect. 1), what it means for these theses to have the status of principles or axioms in Leibniz’s philosophy (sect. 2), the fundamental character of the Principles of (...) class='Hi'>Contradiction and Sufficient Reason (sect. 3), some attempts to demonstrate the Principles of Contradiction and Sufficient Reason (sect. 4), and one attempt to demonstrate the Principle of Identity of Indiscernibles (sect. 5). The main results of the chapter are summarized in a short conclusion (sect. 6). (shrink)

This article draws on data from a qualitative research study undertaken in an old UK university with the main aim of investigating the issue of the gender dimension of academic careers. It examines the idea of an individualistic academic career that demands self-promotion, which is still used as a measure of achievement by those in senior positions. However, there is a basic contradiction. While this idea is upheld, men simultaneously gain by an in-built patriarchal support system. They do not (...) have to make a conscious effort to be helped by it, thereby perpetuating the cultural hegemony of individualism. Women are not admitted to this support system, and if they are seen as needing or wanting to set up their own system, this is viewed as a weakness. The answer appears to be for women to strategically harness feminist ways of working in a collaborative and supportive way. (shrink)

Following J.-Y.Béziau in his pioneer work on non-standard interpretations of the traditional square of opposition, we have applied the abstract structure of the square to study the relation of opposition between states in superposition in orthodox quantum mechanics in [1]. Our conclusion was that such states are contraries, contradicting previous analyzes that have led to different results, such as those claiming that those states represent contradictory properties. In this chapter we bring the issue once again into the center of the (...) stage, but now discussing the metaphysical presuppositions which underlie each kind of analysis and which lead to each kind of result, discussing in particular the idea that superpositions represent potential contradictions. We shall argue that the analysis according to which states in superposition are contrary rather than contradictory is still more plausible. (shrink)

In both Metaphysics Γ 4 and 5 Aristotle argues that Protagoras is committed to the view that all contradictions are true. Yet Aristotle’s arguments are not transparent, and later, in Γ 6, he provides Protagoras with a way to escape contradictions. In this paper I try to understand Aristotle’s arguments. After examining a number of possible solutions, I conclude that the best way of explaining them is to (a) recognize that Aristotle is discussing a number of Protagorean opponents, and (b) (...) import another of Protagoras’ views, namely the claim that there are always two logoi opposed to one another. (shrink)