"--David Ruelle, author of "Chance and Chaos" "This is an important book, one that should cause an epoch-making change in the way we think about mathematics.

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)

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)

"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)

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)

In 'Metaphysics' book 4 Aristotle offers several arguments in defense of the principle of noncontradiction (PNC). In this paper I want to focus on the stretch of argument from 1006a11 to 1006b34 which Aristotle calls a proof by refutation (elenktikos apodeixai), (1006a11). Contrary to Elizabeth Anscombe and others, I will argue that in this section of the defense Aristotle can defend a version of the principle that extends to nonessential predication, predication of properties, aggregates, and transcategorials.

The solution of this problem is extremely important to the process of the development of logic. Its solution is of great theoretical significance in upholding the methodology of dialectical materialism; criticizing the sophistry of metaphysics, skepticism, and relativism; developing formal logic and symbolic logic; forming the scientific system of dialectical logic in the strict sense; and conducting research to strengthen all the concrete sciences. It also has enormous significance for the criticism of "leftist" and right-wing opportunism and revisionism, and especially (...) for criticizing the counterrevolutionary revisionist line of the "gang of four.". (shrink)

Drawing on respective ideas from within both liberal political philosophy and Frankfurt School critical theory, this paper seeks to examine claims about autonomy and empowerment made on behalf of educational policies such as teacher-led codeswitching; a policy that seeks to empower students from racially marginalised groups by facilitating their proficiency in the language and cultural expressions of societally dominant groups. I set out to evaluate such claims by first sketching two competing formulations of autonomy; namely, liberal autonomy concomitant to political (...) power, and autonomy that arises out of the practice of critical self-reflection. I proceed by testing codeswitching within each formulation to reveal how – in this case – these two conceptualisations of autonomy are educationally incompatible with each other. I conclude by suggesting that educational interventions such as codeswitching may ultimately be complicit in the longer term processes of racialisation and marginalisation that they seek to diminish, not only because they carry the potential to damage minority students’ self-integrity, but also because they limit possibilities for both majority and minority students to engage in dialectical encounters that may open avenues to new principles of social and political organisation. (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)

This article examines Pauline Kleingeld’s “volitional self-contradiction” (VSC) interpretation of Kant’s formula of universal law. It begins in §1 with an outline of Kleingeld’s interpretation and then proceeds in §2 to raise some worries about how the interpretation handles Kant’s egoism example. §3 considers VSC’s handling of the false promise example comparing it in §4 with the Logical/Causal Law (LCL) interpretation, which arguably does better than its VSC competitor in handling this example. §5 deploys the LCL interpretation to consider (...) the related objections that the VSC interpretation is “superfluous” or at least “misguided” as a (formal) criterion of the permissibility of action on a maxim. These objections, it is argued, help reveal two distinct roles for contradictions in Kant’s applications of the formula of universal law – one for delivering moral judgments and one reflective of a formal coherence constraint on all deliberation having psychological significance for agents who contemplate violating duty. Disentangling these helps reveal some of the complexity in the use to which Kant puts the formula of universal law in his sample applications revealing the true significance of what Kleingeld refers to as volitional self-contradiction. In §6 is summary. (shrink)

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)

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)

This paper engages critically with Dimitri Gutas’ recent characterization of post-classical Islamic philosophy and theology as a form of paraphilosophy or intellectual activity that merely simulates philosophy. I argue that this view arises from a misguided understanding of the concept of philosophy that should provide the standard for its historiography. In order to avoid a number of problematic consequences, such as gaps in historical continuity or a disconnection from what we understand by philosophy today, we must take our cue from (...) a sufficiently uncontroversial contemporary concept of philosophy instead of any particular historical concept, such as the Peripatetic amalgam of metaphysics, theory of science, and the empirical sciences. Such a strategy provides a sound basis for the inclusion of post-classical thinkers, as well as many classical thinkers who are not falāsifa, in the history of Islamic philosophy without vicious circularity or loss of a normative concept of philosophy. (shrink)

This dissertation concerns dynamic semantics and the broader normative and epistemic consequences of theorizing with dynamic contents. Dynamic semantics deviates significantly from canonical approaches to meaning in that it treats the meanings of sentences as well as the contents of attitudes as context-change-potentials rather than propositions. While some of the consequences of this deviation have been recognized, several crucial consequences remain, heretofore, unexplained. In particular, I argue that dynamic theories not only differ from more traditional static theories with respect to (...) their preferred representational objects, but also with respect to how they must treat the normative statuses of these representational objects, their idealizing assumptions, and how content interfaces with choice and decision. In each case, I demonstrate how and why dynamic accounts differ and explore the consequences. In certain cases, I argue why these consequences ought to be embraced. In others, I provide solutions to the problems they pose. (shrink)

Peng and Nisbett put forward an influential theory of the influence of culture on the resolution of contradiction. They suggested that Easterners deal with contradiction in a dialectical manner, trying to reconcile opposite points of view and seeking a middle-way. Westerners, by contrast, would follow the law of excluded middle, judging one side of the contradiction to be right and the other to be wrong. However, their work has already been questioned, both in terms of replicability and (...) external validity. Here we test alternative interpretations of two of Peng and Nisbett’s experiments and conduct a new test of their theory in a third experiment. Overall, the Eastern and Western participants behaved similarly, failing to exhibit the cross-cultural differences observed by Peng and Nisbett. Several interpretations of these failed replications and this failed new test are suggested. Together with previous failed replications, the present results raise questions about the breadth of Peng and Nisbett’s interpretation of cross-cultural differences in dealing with contradiction. (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)

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.

Book Gamma of Aristotle’s Metaphysics contains a vigorous defense of the principle of non-contradiction (PNC). A chief part of Aristotle’s strategy is to attack those, such as Heraclitus and Protagoras, who are said to deny the principle. Commentators have found a number of logical and historical problems with Aristotle’s arguments, but none are more troubling than those he deploys against Protagoras. Midway through Gamma 4, and throughout Gamma 5, he represents Protagoras not as simply denying PNC but rather as (...) asserting the contrary of the principle. The latter, the proposition that every thing has every property and its negation, I call the strong denial of PNC. In particular, Aristotle argues that Protagoras is committed to strong denial because of ‘Protagorean’ relativism – the doctrine that if something appears to be the case, then it is the case. This paper provides a reconstruction of Aristotle’s arguments in Gamma 4 and 5, and suggests that the second argument may infact hold against the Protagorean. (shrink)