Volume 47, Issue 3, November 2018, Page 461-466.

What sorts of things qualify as first principles of reasoning and what kind of justification for them can be offered? We think of principles like that of non-contradiction as first principles of reasoning. Laurence Bloom argues that Plato’s Republic, the first text that affords us a complete statement of the Principle of Non-contradiction, offers us a powerful, complex and detailed argument for taking form—specifically that of the good—as the first principle of both knowing and being.

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

For Damascius, any attempt to grasp the first principle of all things, the Ineffable, implies the rejection of the principle of non-contradiction (PNC). The reasoning soul, using aporia, is forced to admit contradictory statements as true when it comes to cognising what lies beyond any intelligible being. Damascius shows that it is necessary to postulate a completely transcendent and unknowable Absolute which is the uncoordinated cause of all things beyond the One. This paper examines how Damascius relates (...) the rejection of the PNC and regressive arguments by distinguishing two types of reversal (peritropê) of arguments. This paper begins by analysing: i) Damascius’ first aporia, ii) his characterisation of the first principle as ineffable and iii) its unknowable nature. This leads to some comments about Damascius’ use of predicates and their negations. Finally, the paper distinguishes between regression and reversal to suggest that Damascius’ reversal of the predicates implies that the first principle lies beyond the PNC but does not involve an infinity of first principles. (shrink)

Papineau has suggested that the Principle of Non-Contradiction is a logical law that ?verificationists? are not entitled to claim as a prioritrue. The Principle, like that of Excluded Middle, is not sufficiently grounded in the ?miserly? epistemology of verificationism to be proven in ?verificationist logic?. We examine who might be challenged by this claim: who are the ?verificationists?? We defend our candidates against Papineau's criticisms and other attacks, but this leaves the verificationist open to a different criticism.

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)

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)

This paper considers the use that Plato makes of the Principle of Non-Contradiction in his engagements with eristic refutations. By examining Plato’s use of the principle in his most detailed engagements with eristic—in the Sophist, the discussion of “agonistic” argumentation in the Theaetetus, and especially the Euthydemus—I aim to show that the pressure exerted on Plato by eristic refutations played a crucial role in his development of the PNC, and that the principle provided him with a (...) much more sophisticated means of demarcating philosophical argumentation from eristic than he is generally thought to have. In particular, I argue that Plato’s qualified formulation of the PNC restricts the class of genuine contradictions in such a way that reveals the contradictions that eristics produce through their refutations to be merely apparent and that Plato consistently appeals to his qualified conception of genuine contradiction in his encounters with eristics in order to demonstrate that their refutations are merely apparent. The paper concludes by suggesting that the conception of genuine contradiction afforded by the PNC did not just provide Plato with a way of demarcating genuine from eristic refutations, but also with an answer to substantive philosophical challenges that eristics raised through their refutations. (shrink)

The aim of this paper is to present and analyze arguments provided for the Psychological Principle of Non-Contradiction which states that one cannot have, or cannot be described as having, contradictory beliefs. By differentiating two possible interpretations of PNC, descriptive and normative, and examining arguments provided for each of them separately I point out the flaws in reasoning in these arguments and difficulties with aligning PNC with the empirical data provided by research done in cognitive and clinical psychology. (...) I claim that PNC cannot be derived from any metaphysical stance regarding the mental phenomena and that having contradictory beliefs should be regarded as possible. Furthermore, I argue that interpreting a subject as having contradictory beliefs, and therefore abandoning PNC, can be more effective in explaining the phenomena of contradictory beliefs and irrational behaviour than solutions consistent with the PNC. (shrink)

Five major stances on the problems of the possibility and fruitfulness of a debate on the principle of non-contradiction (PNC) are described: Detractors, fierce supporters, demonstrators, methodologists and calm supporters. We show what calm supporters have to say on the other parties wondering about the possibility and fruitfulness of a debate on PNC. The main claim is that one can find all the elements of calm supporters already in Aristotle’s works. In addition, we argue that the Aristotelian refutative (...) strategy, originally used for dealing with detractors of PNC in Metaphysics, has wider implications for the possibility and fruitfulness of an up-to-date debate on PNC, at least in exhibiting some serious difficulties for the other parties. (shrink)

In his Metaphysics Γ.4, Aristotle defends the principle of non-contradiction (PNC). The PNC says that all contradictions are false. So if some contradictions are true, then PNC is false. Even if PNC’s contrary is false, PNC’s contradictory might still be true. But it’s been noted in the literature for over a century that Aristotle seems to be exclusively interested in attacking PNC’s contrary (‘All contradictions are true’) rather than PNC’s contradictory (‘Some contradictions are true’). So his defense of (...) PNC seems to fail. This would be a surprising error from the inventor of formal logic. It is especially puzzling because we have plenty of evidence showing that Aristotle is keenly aware of the distinction between contraries and contradictories, and because Aristotle distinguishes between PNC’s contradictory and PNC’s contrary in Γ.4. I defend Aristotle against these charges: (1) I explain that one important reason for Aristotle’s focus on PNC’s contrary is that he took it to be deeply connected to views held by thinkers such as Anaxagoras, Cratylus, Democritus, Empedocles, Heraclitus, Parmenides, Protagoras, and Xenophanes; (2) Aristotle’s defense of PNC must be a particular kind of indirect defense rather than a direct demonstration; (3) I argue that if Aristotle’s defense of PNC is read as centering around his argument for what counts as a thing that is determinate, Aristotle demonstrates the reliance of coherent communication on non-contradiction. Read this way, he gives a fairly compelling case to reject not just PNC’s contrary but also PNC’s contradictory. (shrink)

The present article deals with the not very common opinion among medieval philosophers according to which the identity principle is the true first principle, undermining the primacy of the principle of non-contradiction. Following a refutation of this position in the logical work of the Franciscan Geraldus Odonis, we intend to investigate its target as well as other cases of the same dispute in 14th century authors: Antoine Andre, John of Buridan, John of Baconthorpe and Nicolas of (...) Autrecourt. We defend that Odonis presents a successful response to this position. (shrink)

In "Metaphysics" Gamma 3 Aristotle declares that the philosopher investigates things that are qua things that are and that he therefore should be able to state the firmest principles of everything. The firmest principle of all is identified as the principle of non-contradiction (PNC). The main focus of Gamma 3 is Aristotle's proof for this identification. This paper begins with remarks about Aristotle's notion of the firmness of a principle and then offers an analysis of the (...) firmness proof for PNC. It focuses on some key assumptions of the proof and on the range and force of the proof. Aristotle closes Gamma 3 with the claim that PNC is ultimate in the sense that all other principles somehow rest on it. This, rather controversial, claim is given a defensible reading and shown to be central to the chapter's effort to establish PNC as the firmest principle of all. As such it completes the firmness proof and is not simply an appended remark. (shrink)

The discussion on the principle of non-contradiction (1946–1957) between Marxist and non-Marxist philosophers was one of the major philosophical discussions in Polish philosophy of this period. In my text, I carefully reconstruct this discussion and outline its relation to Soviet debates on the subject. I show that the change in Schaff’s position happened in the early 1950s under the combined influence of the Lvov–Warsaw School and the changes in the official Soviet position regarding formal logic. I discuss the (...) aftermath following Schaff’s change in attitude towards the analytic tradition for the development of Polish philosophy, as well as the critique of this change by Jarosław Ładosz. In my reconstruction of the latter, I focus on the problem of the historical development of science. I refer to Ilyenkov’s critique of Schaff, opposing synchronic (“positivist”) and diachronic (“dialectical”) concepts of knowledge. As I argue, these opposing concepts of science can be seen as a genuine issue at stake in the Polish discussion as well, especially in the polemic between Schaff and Ładosz. (shrink)

This article concerns the nature of reason in the work of the Twentieth Century Catholic theologian Erich Przywara and Georg Wilhelm Friedrich Hegel. The discussion centers on three interlocking issues: the question whether proper thinking submits to or transgresses the principle of non-contradiction; the relationship between reason and history; the theological concern with distinguishing the “history of reason” and the divine life. It is argued that both Hegel and Przywara give an account of reason where there are moments (...) of contradiction, and that this is a necessary feature of historical existence. Further, while Przywara and others are concerned with Hegel’s making reason’s reconciliation of contradiction in history identical with the divine life, I argue that although this is a real concern, Hegel’s account is more equivocal than normally admitted. Finally, I argue that the distinguishing feature between Przywara and Hegel is what happens after the moment of contradiction; that is where we see the most important difference between an analogical and a dialectical account of reason. (shrink)

This article concerns the nature of reason in the work of the Twentieth Century Catholic theologian Erich Przywara and Georg Wilhelm Friedrich Hegel. The discussion centers on three interlocking issues: (a) The question whether proper thinking submits to or transgresses the principle of non-contradiction; (b) The relationship between reason and history; (c) The theological concern with distinguishing the “history of reason” and the divine life. It is argued that both Hegel and Przywara give an account of reason where (...) there are moments of contradiction, and that this is a necessary feature of historical existence. Further, while Przywara and others are concerned with Hegel’s making reason’s reconciliation of contradiction in history identical with the divine life, I argue that although this is a real concern, Hegel’s account is more equivocal than normally admitted. Finally, I argue that the distinguishing feature between Przywara and Hegel is what happens after the moment of contradiction; that is where we see the most important difference between an analogical and a dialectical account of reason. (shrink)

In what follows I will say little if anything about the animadversions vis-à-vis Irwin and Lukasiewicz and Owen, because there is so much of such greater interest in what Code has told us about Aristotle, the great preponderance of which, in my opinion, is true. I will review some of this truth, specify one place where I have trouble reconciling his account with the evidence, and then try to give a better account that I think is entirely compatible with the (...) rest of what he has given us. (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.

For some years, Matthew Meyer has labored at a comprehensive interpretation of Nietzsche’s oeuvre that understands his philosophical and literary output as a revival of a particularly Greek mode of thought. This volume represents the culmination of much, but not all, of this previous work, and it serves also as a promise of future work in the same vein. The title, Reading Nietzsche Through the Ancients, is therefore a trifle misleading: Meyer is not reading all of Nietzsche through all the (...) ancients, but only some of Nietzsche through some of them. That is all for the good, so far as I am concerned, since I am usually suspicious of ambitions to resolve Nietzsche’s debt to antiquity in a single... (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)

The question of whether the Pyrrhonist adheres to certain logical principles, criteria of justification, and inference rules is of central importance for the study of Pyrrhonism. Its significance lies in that, whereas the Pyrrhonist describes his philosophical stance and argues against the Dogmatists by means of what may be considered a rational discourse, adherence to any such principles, criteria, and rules does not seem compatible with the radical character of his skepticism. Hence, if the Pyrrhonist does endorse them, one must (...) conclude that he is inconsistent in his outlook. Despite its import, the question under consideration has not received, in the vast literature on Pyrrhonism of the past three decades, all the attention it deserves. In the present paper, I do not propose to provide a full examination of the Pyrrhonist’s attitude towards rationality, but to focus on the question of whether he endorses the law of non-contradiction (LNC). However, I will also briefly tackle the question of the Pyrrhonist’s outlook on both the canons of rational justification at work in the so-called Five Modes of Agrippa and the logical rules of inference. In addition, given that the LNC is deemed a fundamental principle of rationality, determining the Pyrrhonist’s attitude towards it will allow us to understand his general attitude towards rationality. (shrink)

RECENT attempts to explain and justify Aristotle's principle of non-contradiction have focused to a great extent on the dialectical dimension of Aristotle's account. For example, T. Irwin maintains that Aristotle justifies the PNC by arguing that there is a sub-set of dialectical opinions which no one can rationally give up. J. Lear supports the importance of the dialectical dimension by summarizing Aristotle's defense of the PNC as follows: The opponent of the PNC tries to argue dialectically that one (...) should not accept it. "Aristotle's point is that there is no conceptual space in which such a rational discussion can occur." By appealing to the limits of rationally, externally, expressible discourse as the basis of the PNC, Irwin and Lear fail to take seriously the more explicitly psychological and metaphysical bases of the PNC. C. Kirwan, and most recently, R. Smith also either argue against or ignore the role of the psychological and metaphysical bases. Smith goes so far as to argue that common axioms like the PNC are simply empty statement schemata of universal validity, i.e., general verbal forms or patterns which no one can deny with intelligibility. (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)

The Law of Non-Contradiction - that no contradiction can be true - has been a seemingly unassailable dogma since the work of Aristotle. 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 discuss methodological issues that arise. The result is a balanced inquiry into a venerable principle of logic, one that raises questions at the (...) very centre of logic itself. (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)