The aim of this paper is to show that the principles of logics based on the Law of Contradiction are not universal in the sense that their use can appear to be irrelevant if premises are contradictory.

There have been many discussions on problems of logic over the past several years. While the problem of the nature of the law of contradiction, one of the laws of formal logic, has received particular attention by everyone, the question has not been posed very precisely in the arguments. Actually, the question is not whether the movement, change, and development of things can be reflected in consciousness by use of the methods of formal logic, or in distinguishing the effectiveness (...) of the law of contradiction in disputation, proofs, or theoretical systems from its effectiveness in the general process of cognition, when applied to phenomena. If the development of reality cannot at all be reflected by the use of the logical tools of formal logic, what use do they have? No one denies that formal logic does not suffice as a method of cognition. If, in disputations and proofs, or in the establishment of theoretical systems, one relies only on the logical tools of formal logic, this is also not enough. The scope of applicability of the laws of formal logic, as laws that are studied by a concrete science, is necessarily limited. It is impossible for them to be all-powerful; it is of course impossible, relying on the law of contradiction, to know and grasp the contradictions in reality — the unity and conflict of opposites. All disputations and proofs, and the establishment of theoretical systems, are, in fact, efforts to know real objects, efforts of the subjective to grasp the objective. In principle, the use of formal logic in disputations and proofs and in the establishment of theoretical systems, and its use in knowing an object, should be no different. What, then, is the question? The question should be posed as follows: can thought contravene the law of contradiction? (shrink)

Slbajiban; Can the Law of Contradiction be Stated?, Analysis, Volume 21, Issue 5, 1 April 1961, Pages 101–105, https://doi.org/10.1093/analys/21.5.101.

I propose to examine the definition of the law of contradiction, to determine its significance for systems of thought, to analyze the idealists’—especially Blanshard’s—justification for its acceptance, and to comment on the validity of that justification.

라이프니츠는 회의주의를 물리칠 수 있다고 확신하였다. 그가 제시한 해결책은 회의주의를 논박하는 데 있어 대표적이고 매우 전형적인 것으로 간주될 수 있다. 그는 모순율이야말로 가장 확실한 이성의 진리이기 때문에, 어떤 회의주의자라도 이것을 받아들일 수밖에 없다고 여겼다. 섹스투스 엠피리쿠스의 저작을 살펴보면, 섹스투스 엠피리쿠스조차 모순적인 주장을 받아들이는 것을 불가능한 일을 시도하는 것으로 보고 있음을 알 수 있다.BR 그러나 라이프니츠는 정말 승리를 거둔 것일까? 내 생각에는 그렇지 않다. 섹스투스 엠피리쿠스에게 진짜 자기 입장이란 존재하지 않는다. 그는 모든 것에 대해 긍정하지도 않고 부정하지도 않는다. 다만 독단적 주장에 (...) 대해 독단적 주장을 맞서 세움으로써 모든 독단주의를 쓸어버리려고 할 뿐이다. 섹스투스 엠피리쿠스는 라이프니츠를 물리치기 위해 분명 헤겔을 끌어들일 것이다. 모순율에 대해 모순을 대립시킴으로써 양자를 효과적으로 패퇴시키려는 회의적 전략을 그는 구사하고자 하는 것이다.BR 그렇다면 섹스투스 엠피리쿠스의 기획은 성공할 것인가? 내가 보기에, 그는 모순을 인정하지 않고 모순율만을 고집했던 라이프니츠 철학을 물리치는 데는 어려움이 없겠지만, 헤겔의 사변 철학 앞에서는 좌절할 것이다. 왜냐하면 사변 철학에서는 타자에 맞서는 타자란 존재하지 않기 때문이다. 모순율과 모순은 이제 더 이상 양립 불가능한 타자로서 맞서지 않는다. 사변 철학에서 모순율은 모순 안에 지양된 타자이고, 모순의 자기 관계 안으로 편입된 타자인 것이다.BR 섹스투스 엠피리쿠스는 라이프니츠 철학과 헤겔 철학을 포함하여 모든 철학을 무화(無化)하려 하였다. 그러나 헤겔 철학에서 무화되는 철학이란 없다. 라이프니츠 철학도 섹스투스 엠피리쿠스의 회의주의도 모두 지양된 타자로서 총체적 철학 안에 포섭되며, 이것이 바로 헤겔이 회의주의를 극복한다고 할 때 그가 의미하고자 한 것이다.BR 모순율과 회의주의와 관련해서 이 세 철학자가 전개한 논의는 단순히 이들에게만 중요한 것이 아니라, 이 주제를 다루려는 한 하나의 전범으로서의 위상을 지닌다고 나는 생각한다. (shrink)

Tradition usually assigns greater importance to the so-called laws of thought than to other logical principles. Since these laws could apparently not be deduced from the other principles without circularity and all deductions appeared to make use of them, their priority was considered well established. Generally, it was held that the laws of thought have no proof and need none, that as universal constitutive or transcendental principles they are self-evident.

Aristotle discovered the law of contradiction more than 2000 years ago. Since then, this law has been regarded as one of the basic principles of logic. Aristotle considered this principle to be 'the most indisputable of all beliefs,' but nearly half a century ago, it began to be criticized. The voice of criticism came from a philosophical logic - paraconsistent logic. This study analyses in depth the specific properties of the positive logic plus approach, non-adjunctive approach, and relevant approach (...) of paraconsistent logic and presents three definitions of the law of contradiction. It also shows that there are two types of the law of contradiction in C-logics and that the law of contradiction with classical negation is valid in them. Furthermore, this study proves that the law of contradiction with classical negation is also valid in a non-adjunctive approach and explains the reason this law cannot be deduced in some relevant logic systems. Based on these, we can clarify what type of the law of contradiction is questioned by paraconsistent logics and thoroughly reveal the exact meaning of 'the law of contradiction is invalid' in paraconsistent logics. (shrink)

A special supplement [of Kuang-ming Daily] published an article by Comrade Chu-ko Yin-t'ung entitled "Can the Law of Contradiction Be Contravened?"; in it he maintains that the law of contradiction, as well as the other laws of formal logic, must be observed in every situation. "When thinking dialectically, the laws of formal logic must always be observed." His chief argument is that "we have still not found an example in which the law of contradiction has been contravened." (...) In addition to explaining the three generally accepted judgments resulting from dialectical thinking on the definitions, etc., of mechanical motion, he asserts that they actually contain no "logical contradictions." There are, however, other arguments; and since, after the article was published, there were some who opposed it and some who agreed with it, I thought I would contribute to the discussion. (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 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)

In connection with the discussion on the problem of logic, both within our country and abroad , it has already turned from the general, comparatively abstract, and difficult-to-resolve problem of the "relationship between formal logic and dialectics" to the more concrete problem of the functional scope of formal logic. Some people have even utilized special articles to inquire about a certain law in formal logic: the functional scope of the law of identity or the law of contradiction. The purpose (...) of these philosophers or logicians is to try to define the functional scope of a certain law in formal logic as a starting point, and then to proceed to study the functional scope of formal logic in the entire thinking process of mankind. If the functional scope of formal logic in mankind's entire thinking process is clearly and precisely defined, the solution of this complicated problem of the "relationship between formal logic and dialectics" would certainly not be very difficult. The basic purpose of Comrade Chu-ko Yin-t'ung's article on the problem of "whether or not formal logic's law of contradiction can be contravened in the dialectical thinking process" of men, which appeared in issue No. 82 of the "Philosophy" supplement of Kuang-ming Daily on April 24, is like this. It should be considered as a rather practical method. But I do not quite agree with his basic points of argument and with his analysis of certain examples of dialectics. I intend to present my superficial views here and to study them with Comrade Chu-ko. (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 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)

The arguments of the dialetheists for the rejection of the traditional law of noncontradiction are not yet conclusive. The reason is that the arguments that they have developed against this law uniformly fail to consider the logic of encoding as an analytic method that can resolve apparent contradictions. In this paper, we use Priest [1995] and [1987] as sample texts to illustrate this claim. In [1995], Priest examines certain crucial problems in the history of philosophy from the point of view (...) of someone without a prejudice in favor of classical logic. For each of these problems, the logic of encoding offers an alternative explanation of the phenomena---this alternative is not considered when Priest describes what options there are in classical logic for analyzing the problem at hand. -/- The argument at heart of the case that Priest develops against the law of noncontradiction (i.e., the argument based on the paradoxes of self-reference) is then reanalyzed in light of encoding logic. After showing why the argument is inconclusive, the paper concludes both with a more general discussion of logic and predication and with the suggestion that there is no need to tamper with the logic of the traditional mode of predication if there is alternative mode of predication which is well-suited to the analysis of cases involving contradictory objects. (shrink)

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.

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)

This paper discusses some paradoxical propositions in Chinese tradition, especially the School of Names. It not only explains what Chinese philosophers mean by these propositions and why there are such paradoxes in Chinese philosophy, but also makes an attempt to formulate these paradoxical propositions in the language of symbolic logic. Meanwhile, the paper makes a comparison between Chinese views about contradiction and Aristotle?s law ot non?contradiction and explores the relation between them. It comes to the conclusion that once (...) the difference between Chinese concept of contraries and Aristotle?s is made clear, inconsistency between Chinese paradoxial propositions and Aristotle?s. law of non-contradiction disappears. (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)

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)

There is a widespread view that Buddhist philosophy embodies logical contradictions such that there would be 'true' contradictions, This article explains that this is not the case and that Buddhist philosophy, more generally the Perennial philosophy, denies all contradictions for the sake of a doctrine of Unity.

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)

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)

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)

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.

The suicidal proclivity of our time, writes the acclaimed philosopher J. Budziszewski, is to deny the obvious. Our hearts are riddled with desires that oppose their deepest longings, because we demand to have happiness on terms that make happiness impossible. Why? And what can we do about it? Budziszewski addresses these vital questions in his brilliantly persuasive new book, _The Line Through the Heart_. The answers can be discovered in an exploration of natural law—a venture that, with Budziszewski as our (...) expert guide, takes us through politics, religion, ethics, law, philosophy, and more. Natural law, the author states plainly but provocatively, is a _fact_ about human beings; as surely as we have hands and feet, we have the foundational principles of good and evil woven into the fabric of our minds. From this elemental fact emerges a natural law _theory_ that unfolds as part of a careful study of the human person. Thus, Budziszewski shows, natural law forms a common ground for humanity. But this common ground is slippery. While natural law is truly an observable part of human nature, human beings are hell-bent—quite literally—on ignoring it. The mere mention of the obligations imposed on man by his nature will send him into a rage. In this sense, _The Line Through the Heart _explores natural law as not simply a fact and a theory but also a _sign of contradiction_. While investigating the natural law and its implications, Budziszewski boldly confronts—and offers a newly integrated view of—a wide range of contemporary issues, including abortion, evolution, euthanasia, capital punishment, the courts, and the ersatz state religion being built in the name of religious toleration. Written in Budziszewski’s usual crystalline style, _The Line Through the Heart_ makes clear that natural law is a matter of concern not merely to scholars; it touches how each of us lives, and how all of us live _together_. His profoundly important examination of this subject helps us make sense of why habits that run against our nature have become second nature, and why our world seems to be going mad.__. (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)

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)