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)

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 ...

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)

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)

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.

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)

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)

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)

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)

Coastal protection is crucial to human development since the ocean has many values associated with the economy, ecosystem, and culture. However, most ocean protecting efforts are currently ineffective due to the burdens of finance, lack of appropriate management, and international cooperation regimes. For aiding bottom-up initiatives for ocean protection support, this study employed the Mindsponge Theory to examine how the public’s perceived economic and cultural values influence their willingness to support actions to protect the ocean. Analyzing the European-Union-Horizon-2020-funded dataset of (...) 709 respondents from 42 countries, we discovered that perceived economic values have negative effects on the tendency of ocean protection supports (i.e., food, transportation, renewable energy, oil and gas, and recreation). In contrast, certain perceived cultural values can help increase the willingness to do so (i.e., mental well-being and sense of identity). However, the effects of perceived cultural values are only moderately reliable. These findings suggest that designing cultural information delivery campaigns can help promote coastal reserve supports, such as fundraisings and preserving the oceans from the community. (shrink)

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)

Contradictions of the Welfare State is the first collection of Offe's essays to appear in a single volume in English, and it contains a selection of his most important recent work on the breakdown of the post-war settlement.

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)

Following the publication of my book The New Dialectic and Marx's 'Capital', and the symposium on it in Historical Materialism 13.2, a critique by Roberto Finelli recently appeared: 'Abstraction versus Contradiction: Observations on Chris Arthur's The New Dialectic and Marx's “Capital”' in Historical Materialism 15.2. Finelli argues that my systematic dialectic is not taken sufficiently far, in that I retain presuppositions not posited by the capitalist totality. Here, I argue against Finelli's closed totality of wholly abstract forms, not least (...) because it affords no realistic exit strategy. I reaffirm that the logic of contradiction is required to conceptualise the capital relation. (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)

This paper grapples with two objections against Max Weber’s methodology that arise because Weber borrows some ideas from Heinrich Rickert’s neo-Kantian philosophical system. The first objection (“the contradiction argument”) is raised by Julius J. Schaaf who disagrees with Weber’s claim that historical objects are constituted through retrospectively and hypothetically applied selections of value relations and that we can understand these objects. Weber’s idea that the relating ideal type constructions are also non-arbitrary—i.e., not merely subjective—and can be rectified, Schaaf maintains, (...) contradicts his own characterization of historical objects and reality. The second objection (“the incom¬patibility argument”) was made by Gerhard Wagner and Heinz Zipprian. It focuses on the conception of objective possibility. According to this, counter¬factual chains of historical events are contrived to figure out the relevant set of causes by which a certain event can be said to necessarily occur. The critics claim that it is only based on the ontological assumption of a preexisting real object that this thought-experiment can operate. That is, the pre-emptive assumption of realism is indis¬pensable for explaining the historical individual. To refute these two objections, I clarify some foundational notions and ideas of Weber’s methodology. (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.

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)

A common and much-explored thought is Łukasiewicz's idea that the future is ‘indeterminate’—i.e., ‘gappy’ with respect to some claims—and that such indeterminacy bleeds back into the present in the form of gappy ‘future contingent’ claims. What is uncommon, and to my knowledge unexplored, is the dual idea of an overdeterminate future—one which is ‘glutty’ with respect to some claims. While the direct dual, with future gluts bleeding back into the present, is worth noting, my central aim is simply to sketch (...) and briefly explore an alternative glutty-future view, one that is conservative—indeed, entirely classical—with respect to the present. The structure of the paper runs as follows. §1 briefly sketches the target gap picture of an indeterminate future yielding gappy claims at the present. §2 presents the direct dual idea—a glut picture of an overdeterminate future yielding glutty claims at present. §3 sketches the central idea, a more interesting glut picture in which the future contains contradictory states but the present remains entirely classical. §4 contains a general defence of the idea, leaving it open as to whether the gappy-future view enjoys substantive virtues over the proposed glutty-future view of §3. (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.

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)

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)

Instantaneous changes may well be thought to give rise to contradiction. If one endorses an explosive logic, where contradictions entail everything, this is entirely unacceptable. However, if one deploys a paraconsistent logic, which keeps contradictions under control, one may give perfectly coherent and precise models of such changes. In In Contradiction the author showed how and he explored the philosophical implications of the model. Here, the author revisits the issue in the light of a recent critique by Greg (...) Littmann. (shrink)

In this article, I reply to Jens Timmermann’s critical discussion of my essay “Contradiction and Kant’s Formula of Universal Law”. I first consider Timmermann’s reasons for rejecting my interpretation of the Formula of Universal Law. I argue that the self-contradiction relevant to determining a maxim’s moral status should not be sought in the imagined world in which the maxim is a universal law. I then discuss Timmermann’s suggestion that something like a volitional self-contradiction is found within the (...) will of the immoral agent. I deny this and clarify that the relevant contradiction is diagnosed counterfactually in moral reflection. Finally, I explain the differences between Timmermann’s account, Korsgaard’s Practical Contradiction interpretation, and my own Volitional Self-Contradiction interpretation. (shrink)

Contradictions of Archaeological Theory Content Type Journal Article Category Review Pages 499-506 DOI 10.1558/jcr.v11i4.499 Authors A. Martin Byers, Vanier College, Montreal Journal Journal of Critical Realism Online ISSN 1572-5138 Print ISSN 1476-7430 Journal Volume Volume 11 Journal Issue Volume 11, Number 4 / 2012.

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)

Graham Priest; VI*—Contradiction, Belief and Rationality, Proceedings of the Aristotelian Society, Volume 86, Issue 1, 1 June 1986, Pages 99–116, https://doi.or.

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)

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)

In this paper, I offer a close reading of Wittgenstein's remarks on inconsistency, mostly as they appear in the Lectures on the Foundations of Mathematics. I focus especially on an objection to Wittgenstein's view given by Alan Turing, who attended the lectures, the so-called ‘falling bridges’-objection. Wittgenstein's position is that if contradictions arise in some practice of language, they are not necessarily fatal to that practice nor necessitate a revision of that practice. If we then assume that we have adopted (...) a paraconsistent logic, Wittgenstein's answer to Turing is that if we run into trouble building our bridge, it is either because we have made a calculation mistake or our calculus does not actually describe the phenomenon it is intended to model. The possibility of either kind of error is not particular to contradictions nor inconsistency, and thus contradictions do not have any special status as a thing to be avoided. (shrink)

A dialectical contradiction can be appropriately described within the framework of classical formal logic. It is in harmony with the law of noncontradiction. According to our definition, two theories make up a dialectical contradiction if each of them is consistent and their union is inconsistent. It can happen that each of these two theories has an intended model. Plenty of examples are to be found in the history of science.

_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)

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)

A number of philosophers deny that contradictions can be believed. Are they correct? In this note, I show that even in quite weak logics, on pain of inconsistency, if there are false beliefs, either there are propositions which are true but unbelievable or contradictions are believable. Since the antecedent clearly holds, I offer some considerations in favor of the latter disjunct. Objections and variants of the main argument are considered.

The apparently paradoxical nature of self-deception has attracted a great deal of controversy in recent years. Focussing on those aspects of the phenomenon which involve the holding of "contradictory" beliefs, it is our intention to argue that this presents no "paradox" if a non-classical, "paraconsistent", doxastic logic is adopted. (On such logics, see, for example, N. C. A. da Costa, 'On the theory of inconsistent formal systems', Notre Dame J Formal Logic 11(1974), 497-510, and A. I. Arruda, 'A survey of (...) paraconsistent logic', in A. I. Arruda, N. C. A da Costa and R Chuaqui, _Mathematical Logic in Latin America, North-Holland, 1984, pp. 1-41.). (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)

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)

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)

This volume investigates what is beyond the Principle of Non-Contradiction. It features 14 papers on the foundations of reasoning, including logical systems and philosophical considerations. Coverage brings together a cluster of issues centered upon the variety of meanings of consistency, contradiction, and related notions. Most of the papers, but not all, are developed around the subtle distinctions between consistency and non-contradiction, as well as among contradiction, inconsistency, and triviality, and concern one of the above mentioned threads (...) of the broadly understood non-contradiction principle and the related principle of explosion. Some others take a perspective that is not too far away from such themes, but with the freedom to tread new paths. Readers should understand the title of this book in a broad way,because it is not so obvious to deal with notions like contradictions, consistency, inconsistency, and triviality. The papers collected here present groundbreaking ideas related to consistency and inconsistency. (shrink)

ARISTOTLE'S PROGRAM Aristotle says outright that the law of non-contradiction cannot be demonstrated: you can't prove everything, and among the things you ...

As a unique method of philosophical argument, performative contradiction attracted general attention after the change in direction of pragmatics in the twentieth century. Hintikka used this method to conduct an in-depth analysis of Descartes’ proposition “I think, therefore I am,” providing a proof which is a model in the philosophical history; Apel absorbed performative contradiction into his own framework of a priori pragmatics; and Habermas introduced it into the theory of formal pragmatics and rendered it an effective weapon (...) of debate. Wittgenstein, who had fallen into the trap of performative contradiction in Tractatus Logico-Philosophicus, later managed to extract himself from it and indeed used the methodology of performative contradiction to cure the ills of philosophy, making it a general philosophical method. Through analysis of its connotations and classic examples of its use we can see that it is crucial in refuting extreme relativism and skepticism, and hence provides methodological support for a new foundation for philosophical paradigms. (shrink)