"Paradox drives a good deal of philosophy in every tradition. In the Indian and Western traditions, there is a tendency among many philosophers to run from contradiction and paradox. If and when a contradiction appears in a theory, it is regarded as a sure sign that something has gone amiss. This aversion to paradox commits them, knowingly or not, to the view that reality must be consistent. In East Asia, however, philosophers have reacted to paradox differently. Many East (...) Asian philosophers-both in the Daoist and the Buddhist traditions-have openly embraced paradox. They have taken compelling arguments for contradictory positions to suggest that the world is-at least in some respects, and often in very deep respects-inconsistent, and that our best theories of the world will therefore be inconsistent. This book is an initial survey of the writings of some influential East Asian thinkers who were committed to paradox, and for good reason. Their acceptance of contradiction allowed them to develop important insights that evaded those who consider paradox out of bounds"--. (shrink)

The concept of organizational stigma has received significant attention in recent years. The theoretical literature suggests that for a stigma to emerge over a category of organizations, a “critical mass” of actors sharing the same beliefs should be reached. Scholars have yet to empirically examine the techniques used to diffuse this negative judgment. This study is aimed at bridging this gap by investigating Goffman’s notion of “stigma-theory”: how do stigmatizing actors rationalize and emotionalize their beliefs to convince their audience? We (...) answer this question by studying the stigma over the finance industry since 2007. After the subprime crisis, a succession of events put the industry under greater scrutiny, and the behaviors and values observed within this field began to be publicly questioned. As an empirical strategy, we collected opinion articles and editorials that specifically targeted the finance industry. Building on rhetorical analysis and other mixed methods of media content analysis, we explain how the stigmatizing rhetoric targets the origins of deviant organizational behaviors in the finance industry, that is, the shareholder value maximization logic. We bridge the gap between rhetorical strategies applied to discredit organizations and ones used to delegitimize institutional logics by drawing a parallel between these two literatures. Taking an abductive approach, we argue that institutional contradiction between field and societal-level logics is sufficient, but not necessary to generate organizational stigma. (shrink)

The writer is an engineering science technician. Based on the epistemology and methodology of materialist dialectics, understanding the thought of the universe origin of Taoist philosophy and Buddhist philosophy, and combining the modern scientific information of modern physics, system science and physical cosmology, the author has put forward a series of new ideas on the universe origin. The new scientific universe ontology calls on the scientific community to prove and explain the origin of the universe with science, solve the doubts (...) of the theoretical scientific community about quantum mechanics, realize the scientific understanding of the universe space and the existence in space, create new ideas and understanding of space and time, and create a new universe view. This is not only the inspiration and verification of modern science to the primitive thought of the universe of our ancestors, but also a new method to solve the contradiction of modern physics, which inspires human beings to think about survival and existence. (shrink)

Almost all contemporary philosophers on the subject agree that emotions play an indispensable role in the justification (as opposed to the mere causation) of other mental states and actions. However, how this role is to be understood is still an open question. At the core of the debate is the phenomenon of conflict without contradiction: why is it that an emotion need not be revised in the light of better judgment and knowledge? Conflict without contradiction has been explained (...) either by difference in content between emotion and judgment, or by a difference in the respective attitude towards content. I argue that conflict without contradiction is due to both differences, where difference in content is prior to difference in attitude. (shrink)

The Brave New World–style utilitarian dystopia is a familiar feature of the cultural landscape; Kantian dystopias are harder to come by, perhaps because, until Rawls, Kantian morality presented itself as a primarily personal rather than political program. This asymmetry is peculiar for formal reasons, because one phase of the deliberative process on which Kant insists is to ask what the world at large would be like if everyone did whatever it is one is thinking of doing. I do not propose (...) to write a Kantian Brave New World myself, but I am going to ask, of what these days is called “the CI-procedure,” what would happen if everybody followed it. I will argue that if the CI-procedure works as advertised, it exposes a practical incoherence in the commitment to having it govern one’s actions: in the Kantian vocabulary that goes with the territory, that the Categorical Imperative gives rise to a contradiction in the will. (shrink)

Critical discussion of Alan Code's paper "Aristotle's Investigation of a Basic Logical Principle: Which Science Investigates the Principle of Non-Contradiction?".

In the scholarship on Wittgenstein’s later philosophy of mathematics, the dominant interpretation is a theoretical one that ascribes to Wittgenstein some type of ‘ism’ such as radical verificationism or anti-realism. Essentially, he is supposed to provide a positive account of our mathematical practice based on some basic assertions. However, I claim that he should not be read in terms of any ‘ism’ but instead should be read as examining philosophical pictures in the sense of unclear conceptions. The contrast here is (...) that basic assertions that frame philosophical ‘isms’ are propositional such that they are subject to normal argumentative evaluation, while pictures in Wittgenstein’s sense are non-propositional—they lack a clear truth condition. They, therefore, need clarification rather than argumentation. In this paper, I provide a detailed analysis of Wittgenstein’s treatment of philosophical pictures with special focus on his argument on contradiction. I begin by explaining the problem with this trend of theoretical interpretation, taking Steve Gerrard’s otherwise excellent interpretation as a representative example and pointing out why it is problematic. Next, I will argue that those problems do not arise if we take Wittgenstein’s task as the clarification of philosophical pictures. I do this, first, by explaining Wittgenstein’s method using his argument concerning the Augustinian Picture in Philosophical Investigations and then pointing out that the same method can be identified in the crucial arguments in his philosophy of mathematics. Finally, in order to connect my interpretation with the current scholarship, I will explain the relation of my interpretation with those of New Wittgensteinian scholars. (shrink)

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)

Aristotle gave seven arguments for the law of non-contradiction. The first one is against a special case of dialetheism, the view that only some contradictions are true, and other six arguments are mostly against trivialism, the view that everything and consequently every contraction is true. Aristotle never argued that dialetheism entails trivialism. Unlike Aristotle, Avicenna, in his defense of LNC, not only considers trivialism and argues against it, but also argues that dialetheism entails trivialism. The argument that dialetheism entails (...) trivialism is called explosion. It is usually known that the first argument for explosion is given by the twelfth century logician William of Soissons. In this paper, we will meet Avicenna’s different argument for explosion and then I will demonstrate that this argument is a non-sequitur. (shrink)

It is sometimes said that there are two, competing versions of W. V. O. Quine’s unrelenting empiricism, perhaps divided according to temporal periods of his career. According to one, logic is exempt from, or lies outside the scope of, the attack on the analytic-synthetic distinction. This logic-friendly Quine holds that logical truths and, presumably, logical inferences are analytic in the traditional sense. Logical truths are knowable a priori, and, importantly, they are incorrigible, and so immune from revision. The other, radical (...) reading of Quine does not exempt logic from the attack on analyticity and a priority. Logical truths and inferences are themselves part of the web of belief, and the same global methodology applies to logic as to any other part of the web, such as theoretical chemistry or ordinary beliefs about ordinary objects. Everything, including logic, is up for grabs in our struggle for holistic confirmation. The purpose of this paper is to examine the law of non-contradiction, and the concomitant principle of ex falso quodlibet, from the perspective of the principles advocated by the radical Quine. I show that he has no compelling reason to accept either of these. To put it bluntly, neither the law of non-contradiction nor the rule of ex falso quodlibet is empirically confirmed, and these principles fare poorly on the various criteria for theory acceptance on the methodology of the radical Quine. So the radical Quine is led rather quickly and rather directly into something in the neighborhood of Graham Priest’s dialetheism. (shrink)

Midway through How to Do Things With Words, J.L. Austin’s announces a “fresh start” in his efforts to characterize the ways in which speech is action, and introduces a new conceptual framework from the one he has been using up to that point. Against a common reading that portrays this move as simply abandoning the framework so far developed, Marina Sbisà contends that the text takes the argumentative form of a proof by contradiction, such that the initial framework plays (...) an instrumental role as part of a proof in favour of the subsequent one. Despite agreeing with Sbisà’s broad instrumentalist approach, we argue that her regimentation of Austin’s narrative into a proof by contradiction ultimately fails - both as a proof and as an interpretation of Austin. Instead, we suggest that a better way of interpreting the peculiar structure of How to Do Things With Words is as a pedagogical exercise whose point is to bring a concealed alternative into view in a manner that also explains its initial concealment, and that this approach provides richer resources for supporting Sbisà’s own conventionalist understanding of illocution than that afforded by reading the text as a proof by contradiction. (shrink)

Discussion of von Wright's account of logic and time in relation to Marxist dialectics.

According to some critics, Aristotle’s elenctic defence (elenchos, elenchus) of the Law of Non-Contradiction (Metaphysics IV) would be ineffective because it viciously begs the question. After briefly recalling the elenctic refutation of the denier of the Law of Non-Contradiction, I will first focus on Filippo Costantini’s objection to the elenchus, which, in turn, is based on the dialetheic account of negation developed by Graham Priest. Then, I will argue that there is at least one reading of the elenchus (...) that might not be viciously question-begging. In doing so, I will leverage, reinterpret and adjust the distinction between two senses of epistemic dependence, offered by Noah Lemos and originally based on some thoughts about George Edward Moore’s ‘proof of an external world.’ The key point of my counter-objection to recover the elenchus is to use the distinction between a necessary-condition relation between propositions (p only if q) and a grounding relation between facts (the fact that an epistemic agent S believes that p is grounded in the fact that S believes that q), where p and q are the content of S’s beliefs. (shrink)

It has long been recognized that negation in Aristotle’s term logic differs syntactically from negation in classical logic: modern external negation attaches to propositions fully formed, whereas Aristotelian internal negation forms propositions from sentential constituents. Still, modern external negation is used to render Aristotelian internal negation, as may be seen in formalizations of Aristotle’s semantic principles of non-contradiction and of excluded middle. These principles govern the distribution of truth values among pairs of contradictory propositions, and Aristotelian contradictories always consist (...) of an affirmation and a denial. So how should we formalize a false denial? In the literature, we find that a false denial is formalized by means of two negation signs attached to a one-place predicate. However, it can be shown that this rendering leads to an incorrect picture of Aristotle’s principles. In this paper, I propose a solution to this technical problem by devising a formal notation especially for Aristotelian propositions in which internal negation is differentiated from external negation. I will also analyze both principles, each of which has two logically equivalent forms, a positive and a negative one. The fact that Aristotle’s principles are distinct and complementary is reflected in my new formalizations. (shrink)

In this paper I show that proofs by contradiction were a serious problem in seventeenth century mathematics and philosophy. Their status was put into question and positive mathematical developments emerged from such reflections. I analyse how mathematics, logic, and epistemology are intertwined in the issue at hand. The mathematical part describes Cavalieri's and Guldin's mathematical programmes of providing a development of parts of geometry free of proofs by contradiction. The logical part shows how the traditional Aristotelean doctrine that (...) perfect demonstrations are causal demonstrations influenced the reflection on proofs by contradiction. The main protagonist of this part is Wallis. Finally, I analyse some epistemological developments arising from the Cartesian tradition. In particular, I look at Arnauld's programme of providing an epistemologically motivated reformulation of Geometry free of proofs by contradiction. The conclusion explains in which sense these epistemological reflections can be compared with those informing contemporary intuitionism. (shrink)

This article provides an overview of philosophical interpretations of Dostoevsky, focusing on readings that pay particular attention to his representation of the battle between good and evil, and postulating that said representation constitutes the essence of his works. The analysis maps this history of interpretations as developing within a specific framework: the dispute between interpreters who argue that good triumphs in Dostoevsky’s works and those who maintain that nihilism prevails in the end. In this context, the article submits its own (...) thesis: that a fundamental contradiction haunts the offer, in Dostoevsky’s works, of Christian salvation, and condemns Dostoevsky to defeat at the hands of his nihilists. (shrink)

A common response to those who question the Law of Non-Contradiction is that it is impossible to debate such a fundamental law of logic. The reasons for this response vary, but what seems to underlie them is the thought that there is a minimal set of logical resources without which rational debate is impossible. This chapter argues that this response is misguided. First, it defends non-apriorism in logic: the view that logic is in the same epistemic boat as other (...) scientific theories. It then offers an account of logical theory change in terms of this epistemology. The LNC is discussed in terms of this account of logical theory change, and it is shown that rational debate over this law can, and does, proceed. Finally, arguments for and against the LNC are discussed, and how and where non-a priori considerations arise in these arguments are illustrated. (shrink)

Łukasiewicz distinguishes three formulations of the principle of contradiction in Aristotle’s works: ontological, logical, and psychological. The first two formulations are equivalent though not synonymous, but neither of them is equivalent to the psychological one, which expresses not a principle but only an empirical law. Furthermore, the principle of contradiction is neither a simple and ultimate law nor is it necessary for conducting an inference, because the syllogism is independent of it. The further explanation of this concept leads (...) Łukasiewicz to formulate the idea of a non-Aristotelian logic, that is, a logic operating without the principle of contradiction. If the principle of contradiction shall be valid, it must be proved. A proof can be supplied only on the basis of a definition of object, as something that cannot have and not have the same property at the same time. However, this definition does not hold for all objects, i.e., for contradictory objects. In virtue of its ontological character the Aristotelian principle of contradiction is then different from that of symbolic logic. (shrink)

Nietzsche s work was heavily influenced by ancient Greek philosophy. Meyer shows how Nietzsche attempted to revive the Heraclitean-Protagorean position that is critically analyzed by both Plato and Aristotle in the Theaetetus and Metaphysics IV, and establishes Nietzsche as a naturalist who believes that there are objective facts.The book not only highlights the foundations of his thought, but also restores order to Nietzsche s work.".

Le polythéisme polynésien était-il une forme métaphorique de panthéisme ?

Hume’s Treatise, with its celebrated bundle theory of the self, is a significant contribution to the embryonic Newtonian experimental philosophy of the enlightenment. But the theory is inadequate as it stands, as the appendix to the Treatise makes clear. For this account of the self, apparently, rests on contradictory principles — propositions, fortunately, that can be reconciled, according to Hume. My paper is a critical exploration of Hume’s argument for this intriguing suggestion.

The topic of this paper is Aristotle’s ‘proof by refutation’ of the Principle of Non-Contradiction (Metaphysics Γ 4, 1006a11–1007a20). I consider a worry which has often been raised in connection with this proof. The worry is that, faced with an opponent who is prepared to tolerate contradictions, the argument is dialectically powerless: it is incapable of getting them to abandon their position. In reply, I argue that the proof needs to be seen in its proper context, that is, as (...) part of Aristotle’s response to an opponent who demands a demonstration of the principle. This allows us to clarify the purpose of the argument and answer the worry about its effectiveness. (shrink)

The article analyzes and criticizes the assumptions of Peter Van Inwagen’s argument for the alleged contradiction of the foreknowledge of God and human freedom. The argument is based on the sine qua non condition of human freedom defined as access to possible worlds containing such a continuation of the present in which the agent implements a different action than will be realized de facto in the future. The condition also contains that in every possible continuation of the present state (...) of affairs, the same propositions about the ‘present past’ (the past before the present moment) are true as are true in the present state of affairs. The paper argues that Van Inwagen’s reasoning is inconclusive, it contains the type of mistake of confusing conditional impossibility with unconditional and presents a methodologically wrong method of solving a philosophical problem. It is because in the very construction of the problem determining the available solution. The article points to the possibility that the human freedom of some action is not excluded by the fact that specific past facts logically entail that this event will occur. (shrink)

Here I attempt to clarify the general sense of the question that forms the background of Hegel's section on contradiction: What is the essence of contradiction? To what extent does this question pose a philosophical problem for Hegel? By considering this problem can we come to understand contradiction as a relation pertaining to "objective logic"? Translated by Erin Flynn & Kenneth R. Westphal. Originally published as "Über Hegels Lehre vom Widerspruch," in: Dieter Henrich, ed., Hegels Wissenschaft der (...) Logik: Formation und Rekonstruktion (Stuttgart: Klett-Cotta, 1986), 107-28. (shrink)

This paper attempts to illuminate and interpret the contradictory portrait of God as both seen and unseen in the Torah. Thus Moses is commanded not to look on the face of God yet also praised for having spoken to God “face to face". We seek ways to reconcile the contradictory portraits of God through the use of the term “doubled-mindedness” in the theology of Jerome Gellman, in the logic of “thirdness” in C.S. Peirce’s semiotics, and in the use of both (...) particle and wave models in Einstein’s physics of light. The paper concludes by disusing the practical consequences of theological double-mindedness for the religious life and the philosophical meaning of redemption as the time when the contradiction of the unseen and seen God is resolved. (shrink)

On the ground of Kant’s reformulation of the principle of con- tradiction, a non-classical logic KC and its extension KC+ are constructed. In KC and KC+, \neg(\phi \wedge \neg\phi),  \phi \rightarrow (\neg\phi \rightarrow \phi), and  \phi \vee \neg\phi are not valid due to specific changes in the meaning of connectives and quantifiers, although there is the explosion of derivable consequences from {\phi, ¬\phi} (the deduc- tion theorem lacking). KC and KC+ are interpreted as fragments of an S5-based first-order (...) modal logic M. The quantification in M is combined with a “subject abstraction” device, which excepts predicate letters from the scope of modal operators. Derivability is defined by an appropriate labelled tableau system rules. Informally, KC is mainly ontologically motivated (in contrast, for example, to Jaśkowski’s discussive logic), relativizing state of affairs with respect to conditions such as time. (shrink)

Avicenna (d. 1037) and Tūsī (d. 1274) have different doctrines on the contradiction and conversion of the absolute proposition. Following Avicenna's presentation of the doctrine in Pointers and reminders, and comparing it with what is given in Tūsī's commentary, allow us to pinpoint a major reason why Avicenna and Tūsī have different treatments of the modal syllogistic. Further comparison shows that the syllogistic system Rescher described in his research on Arabic logic more nearly fits Tūsī than Avicenna. This in (...) turn has consequences for analysing Avicenna's logic, and for writing the history of a fascinating period of change and diversity in the discipline in the medieval Islamic world. (shrink)