The logical Law of Non-contradiction – that a proposition cannot be both true and false – enjoys a special, perhaps uniquely privileged, status in philosophy. Most philosophers think that finding a contradiction – the assertion of both P and not-P – in one's reasoning is the best possible evidence that something has gone wrong, the ultimate refutation of a position. But why should this be so? What reason do we have to believe it? In this paper, I address (...) these questions. (shrink)

The author provides another metaphysical argument to bolster his thesis of the logical harmony of determinism and volition. He shows how the typical mainstream and Objectivist doctrine of “libertarian” free will commits the same logical error as the Sophist attacks on the Law of Non-Contradiction—namely, an out-of-context interpretation of, respectively, the Law of Causality and the Law of Identity as being unconditional absolutes, which they are not and cannot be.

In Book Γ of the Metaphysics Aristotle states and attempts to prove what he calls the basic principle of the science of being as being: the law of non‐contradiction. In this paper I defend an interpretation of his proof, inspired by Elizabeth Anscombe's 1961 essay in ‘Three Philosophers’, though some of its features were remarked on by Lukasiewicz in 1910, according to which Aristotle is proving this principle only for substance predicates, and that it is to be understood as (...) the basic principle of metaphysics rather than of logic. It is the principle that every substance has an essential nature, and if it is of the essential nature of x to be F then it cannot be of the essential nature of x to be not‐F since then x's being F and x's being not‐F would be the same. He puts it by saying that in such a case F and not‐F would ‘signify the same’ for x. Since they do not, x cannot be both. (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)

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)

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)

Abstract. As a general theory of reasoning—and as a general theory of what holds true under every possible circumstance—logic is supposed to be ontologically neutral. It ought to have nothing to do with questions concerning what there is, or whether there is anything at all. It is for this reason that traditional Aristotelian logic, with its tacit existential presuppositions, was eventually deemed inadequate as a canon of pure logic. And it is for this reason that modern quantification theory, too, with (...) its residue of existentially loaded theorems and patterns of inference, has been claimed to suffer from a defect of logical purity. The law of non-contradiction rules out certain circumstances as impossible—circumstances in which a statement is both true and false, or perhaps circumstances where something both is and is not the case. Is this to be regarded as a further ontological bias? (shrink)

L'auteur montre que la demonstration aristotelicienne du principe de non-contradiction se joue sur le terrain de la psychologie. Le livre Gamma de la Metaphysique renvoie au traite De l'ame et c'est a une theorie de l'enonciation qu'aboutit Aristote: l'unite offerte par l'acte d'affirmer etant, selon lui, l'expression non seulement de l'unite, mais encore de l'individualite du sujet.

U Metafizici Γ. 3 počelo neproturječnosti otkriva se kao počelo mišljenja, ali i počelo svih bića. Prema tome, PN ima svoja dva aspekta – ontički i logički. Ti su aspekti izraženi različitim formulacijama počela neproturječnosti koje nalazimo u Γ. 3. Ne može se govoriti o primatu nekog od aspekata, jer su oni upućeni jedan na drugoga: mišljenje je mišljenje bića, a biće je ono što se u mišljenju misli. PN se ističe time da je najpostojanije počelo jer je ono nužno (...) najspoznatljivije. Spoznatljivost ovoga počela ne ovisi o nekim subjektivno- psihološkim uvjetima već o tome da je PN ono konstitutivno svakog spoznavanja, što proizlazi iz njegove onto logičke naravi.In Metaphysics Γ. 3 the principle of non-contradiction is revealed as the principle of thought but also as the principle of all beings. Thus, it has two aspects – ontical and logical. These aspects are expressed by different formulations of PN which can be found in Γ. 3. It cannot be said that any aspect has primacy, because each one bears necessary relation with the other: thinking is the thinking of being and being is that which is thought in the thinking. PN is distinguished as the firmest principle because it is that which is necessarily the most knowable. Knowability of this principle does not depend on some subjective-psychological conditions, but on the fact that the PN is that which is constitutive in every knowledge, and that follows from its onto-logical nature. (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)

This article focuses on the applications of philosophical logic in the discipline of philosophy of religion of both ‘Eastern’ and ‘Western’ traditions, in which the problem of apparent ontological contradictions can be found. A number of philosophers have proposed using the work of those non-classical logicians who countenance the violation of the law of non-contradiction (LNC) to address this problem. I discuss (1) whether classical or non-classical account of logic is universal in applying to all true theories, and (2) (...) whether there might be extra-logical considerations which affect what is the correct account of logic for the doctrines in question. With regard to Jc Beall’s application of non-classical (FDE) logic to the doctrine of the Incarnation, I argue using the evidence from the writings of church fathers that the meaning of negation found in the core claims of the doctrine of the Incarnation should not be interpreted in accordance with Beall’s FDE account, and that this extra-logical consideration refutes Beall’s project. Moreover, the FDE’s acceptance of the possibility of statements that are both true and false is contrary to what is allowed by the definition of negation in classical logic; therefore (contrary to Beall), Beall is in fact using a different definition of negation compared with the definition used by the classical account. I develop this point in interaction with contemporary philosophy of religion literature and explain its implications and significance for this discipline. (shrink)

Dynamic semantics violates numerous classical laws, including Non-Contradiction. Proponents of dynamic semantics have offered no explanation for this behavior, and some critics consider this result to be strong evidence against the tenability of the dynamic program. I defend and explain failures of Non-Contradiction by comparing dynamic semantics and classical, truth conditional semantics in terms of their idealizing assumptions. I demonstrate that dynamic semantics rejects context fixity, an idealizing assumption that truth-conditional semantics typically adopts. I then argue that any (...) semantics which rejects context fixity should, by the classical semanticist’s own lights, violate Non-Contradiction under certain circumstances. I then demonstrate that dynamic semantics violates Non-Contradiction in all and only those circumstances. I subsequently appeal to this insight to vindicate some of dynamic semantics’ more controversial predictions. I close by suggesting that discussion of idealizing assumptions, common in the sciences, is similarly crucial to fruitful discussion in natural language semantics. (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)

Several philosophers have argued, against the hypothesis of alternative logical mentalities, that it is not conceivable that there should be peoples who reject the law of non-contradictlon. In reply, I argue first that these philosophers are lending an unwarranted pre-eminence to this law, and second that their case is made to look stronger than it is by confusing different senses in which a logical law might be 'rejected'. Finally, I consider some remarks of Wittgenstein which suggest that 'acceptance' of contradictions (...) might not be unintelligible. (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)

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)

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)

The principle of contradiction, or non-contradiction, is traditionally included as one of the three fundamental principles of logic, together with the principle of identity and the principle of excluded middle. There is a consensus now regarding the shape of the principle of contradiction in modern formal logic. However, a deeper look at the history of its formulation reveals a much more complicated picture. We trace some of such developments from the beginning of the twentieth century when all (...) sorts of formalisms were proposed, and even the name itself was up for debate. Our focal point is the proposals made by Christine Ladd-Franklin, which we describe against the background of other attempts at the time. (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)

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)

Est‐il possible d'exposer une doctrine sans la comparer et l'opposer à d'autres doctrines, proches ou éloignées ? Et pour faire bien ressortir ce qui lui appartient en propre, ne faut‐il pas établir une utile dispute avec tels ou tels points de vue qui semblent au premier abord ne pas trop s'en écarter? La question que les trois brèves études critiques qui suivent cherchent à. mettre en lumière est des plus importante: c'est l'idée même de la cohérence de la vie intellectuelle (...) qu'elles abordent. Leur but est moins de critiquer autrui nue de s'exposer elles‐mêmes à la critique. (shrink)

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)

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)

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.

The self-visitation paradox is one paradox of time travel. As Ted Sider puts it, “Suppose I travel back in time and stand in a room with my sitting 10-year-old self. I seem to be both sitting and standing, but how can that be?” (2001, 101). So as not to beg any questions, let us label what is sitting B and what is standing C. The worry is about how B can be C in light of the looming contradiction that (...) this one person would be sitting and standing. Sider’s own approach is perdurantist, and holds that B is not C. My concern, though, is with solutions offered by, or on behalf of, endurantists–more 1 specifically, with solutions holding that B is C. The endurantist answer I shall criticize is a relativizer position maintaining that the sitting and the standing need to be relativized to the personal time or proper time of the time traveler. This manner of solution has been offered by Paul Horwich (1975, 433-435 ; 1987, 114-115) and also by Simon Keller and Michael Nelson (2001, 344). I will show that such a view has a linguistically suspect element and that there are three further reasons why relativizing only in this way falls short of solving the paradox. This will be enough to squash the relativizer position because it will not be clear how additional relativization could help, and furthermore any additional relativization would only make the linguistic matter worse. I will also present some considerations in favor of a non-contradiction endurantist alternative; this view eliminates the need for any relativization by denying that sitting and standing are contradictory properties. (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.

This chapter analyzes and criticizes the argument of Aristotle in Metaphysics, Book Gamma, against those who would violate the Law of Non-Contradiction, together with what a number of later commentators have made of them.

According to the standard account of Nicholas' views,his scepticism is constrained by his commitment to the law of non-contradiction as a basis for certain truth. Such an account fails to distinguish the views found in the "Leters to Bernard" and the "Exigit Ordo" the latter clear rejects the law of non-contradiction and propounds a full fledged scepticism.