Heine introduces The Principle of Contradiction in its first English translation. Conze’s account of the history and evolution of the principle of contradiction illuminates the thought of Aristotle, Marx, and Buddha, and provides the groundwork for a new cross-cultural and interdisciplinary approach to philosophical theory and practice.

Heine introduces The Principle of Contradiction in its first English translation. Conze’s account of the history and evolution of the principle of contradiction illuminates the thought of Aristotle, Marx, and Buddha, and provides the groundwork for a new cross-cultural and interdisciplinary approach to philosophical theory and practice.

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)

This is the first English translation directly based on the original Polish ‘Zasada sprzeczności a logika symboliczna’, the appendix on symbolic logic of Jan Łukasiewicz's 1910 book O zasadzie sprzeczności u Arytotelesa (On the Principle of Contradiction in Aristotle).

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.

Leibniz was a philosopher of principles: the principles of Contradiction, of Sufficient Reason, of Identity of Indiscernibles, of Plenitude, of the Best, and of Continuity are among the most famous Leibnizian principles. In this article I shall focus on the first three principles; I shall discuss various formulations of the principles (sect. 1), what it means for these theses to have the status of principles or axioms in Leibniz’s philosophy (sect. 2), the fundamental character of the Principles of (...) class='Hi'>Contradiction and Sufficient Reason (sect. 3), some attempts to demonstrate the Principles of Contradiction and Sufficient Reason (sect. 4), and one attempt to demonstrate the Principle of Identity of Indiscernibles (sect. 5). The main results of the chapter are summarized in a short conclusion (sect. 6). (shrink)

The philosophical Framework of modern physics puts forward a philosophical solution to the contradiction between relativity theory and quantum mechanics theory, aiming to break through the restriction of material philosophy on human thought and solve the artificial contradiction generated by material philosophy. This scheme is the physical principle of natural philosophy. Newton discovered the mathematical principles of natural philosophy, he expressed the principles of the universe’s natural philosophy through mathematics, discovering universal gravitation, the mutual perception and motion (...) of material mass. This line of thought continued with the discovery of electromagnetism by Faraday and Maxwell, and quantum mechanics by Einstein, Planck, Born, Bohr, and Dirac many scientists. This represents the completion of the great natural theology of the universe, a credit to these great scientists. However, we have not recognized this as natural theology. Newton and Leibniz jointly discovered absolute space, but due to insufficient scientific information, we lost an opportunity. Today, modern physics has given us another chance; by combining scientific information with the Cosmic origin principles left by our ancestors, we can understand absolute space. Starting with an analysis of the “theoretical contradictions” in quantum mechanics and relativity, reflecting on the concept and essence of physics, and recognizing the Cosmic origin principle is the natural philosophy principle of physics. (shrink)

Peirce’s principles of excluded middle and contradiction more resembled those of Aristotle than those of contemporary logicians. While the principles themselves are simple and straightforward, many of Peirce’s comments about them have been misunderstood by commentators. In particular, his belief that the principle of excluded middle does not apply to the general and that the principle of contradiction does not apply to the vague have been mistakenly connected to his eventual rejection of the principle of (...) bivalence and development of three-valued logical connectives. An understanding of Peirce’s view of those logical principles shows that those beliefs motivated neither his rejection of bivalence nor his work in triadic logic. (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 his 1910 book On the principle of contradiction in Aristotle, Jan Łukasiewicz claims that syllogistic is independent of the principle of contradiction . He also argues that Aristotle would have defended such a thesis in the Posterior Analytics. In this paper, we first show that Łukasiewicz's arguments for these two claims have to be rejected. Then, we show that the thesis of the independence of assertoric syllogistic vis-à-vis PC is nevertheless true. For that purpose, we (...) first establish that there is no possibility to account for Aristotle's original views on syllogistic without using per impossibile deductions. At last, following an idea due to Smith 1983, we prove that there is a complete reconstruction of assertoric syllogistic using ecthesis instead of reductio ad absurdum. Contrary to what is claimed in Smith 1983, we show that Smith's system SE has to be improved for such a reconstruction. This results in an ecthetic system which is complete with respect to syllogistic arguments, not explosi.. (shrink)

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)

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)

The purpose of this dissertation is to provide a defence of Aristotle's principle of contradiction against the critique made on it by Jan Lukasiewicz in an article he wrote in 1910 which was translated and published in the March 1971 number of The Review of Metaphysics. Lukasiewicz maintains in general that the law of contradiction has no logical worth. Specifically, he charges Aristotle with having several laws of contradiction instead of one as Aristotle claims; with attempting (...) to prove the law despite his claim that this is impossible and finally with failing in the very attempt to prove the law, or at least one of its formulations. In 20 chapters, each dealing with a respective section of Lukasiewicz's article, I attempt to show that all of Lukasiewicz's allegations are unfounded. My methodology is simply to follow Lukasiewicz through his 20 sections and compare what he says with what Aristotle actually wrote. If successful, this dissertation will show, in basic agreement with Professor Joseph Owens, that the best way to read Aristotle is on his own terms and not, as in the case of Lukasiewicz, via the latest developments in symbolic logic. I reiterate, with Aristotle, that the law of contradiction is the basic principle of being qua being and has logical worth precisely because of that fact. (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)

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)

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)

Traditional interpretations of the Euthydemus find little of value in its sophistical sections. Where value is found at all it is in those aspects of the sophistic display which point to serious issues in other dialogues. This paper argues that there is methodological value intrinsic to the sophistic sections, that taken together these displays make a coherent and valuable contribution to an understanding of sophistic argumentation, and of the foundations of correct reasoning. Each of the sections deals in some way (...) with the principle of contradiction; it is the manipulation of this principle which produces the sophistic tricks, and the principle itself which reveals and organizes around itself the many sides of the sophistic display. The first display offers an apparent refutation of this principle, one based only on verbal ambiguity. In the second display the principle is denied from Parmenidean and Heraclitean perspectives, and the implications of such are analyzed. In the third display the brothers misapply this principle to relational predicates so as to work their tricks. Plato reveals here the necessity and limits of the principle of contradiction, and how its denial and misuse stand at the basis of various sophistical arguments. (shrink)

In the discussion at hand I have attempted to pave the way for such a treatment of the principle of contradiction. In a number of respects it seems to me worthwhile to relate my critical exposition to Aristotle's train of thought. Indeed, every critique must be raised against something substantial, otherwise it generally becomes the critic's leisurely game with his own cerebral phantasies. Now Aristotle's intuitions regarding the principle of contradiction are, for the most part and (...) clear down to the present day, the usual and traditional ones; and arguments for and against the principle can be found together in the Stagirite in greater completeness than in any one modern textbook of logic. My investigation will proceed with the Aristotelian text at hand and with regard to the results of symbolic logic. The most important results shall be sketched very briefly in the following. (shrink)

According to Boole it is possible to deduce the principle of contradiction from what he calls the fundamental law of thought and expresses as \. We examine in which framework this makes sense and up to which point it depends on notation. This leads us to make various comments on the history and philosophy of modern logic.

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

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)

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

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)

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 previous three articles have discussed scientific ontology, resolving the contradictions between quantum mechanics and relativity using the cosmic origin philosophical framework, and interpreting the principles of natural philosophy through physics. Aristotle established material philosophy and material science, relegating the philosophical concepts of cosmic ontology and the cosmic origin to metaphysics and theology. As a result, philosophy was divided into first philosophy and second philosophy as scientific considerations. When material science developed into the ontology of the universe, able to explain (...) the cosmic origin principle, a major issue arose: after 2500 years of development, humanity has only grasped the meaning of “matter.” Yet, what are “energy” and “information”? We still haven’t figured that out. Modern physics has brought both benefits and contradictions to humanity. To resolve these contradictions, we need to redefine the scientific consideration of “philosophy” and its philosophical concepts. This article continues to explore the contradictions between quantum mechanics and relativity using the principles of cosmic origin, reflecting on the basic concepts of philosophy and human thought. (shrink)

This is a companion article to the translation of ‘Zasada sprzeczności a logika symboliczna’, the appendix on symbolic logic of Jan Łukasiewicz's 1910 book O zasadzie sprzeczności u Arytotelesa (On the Principle of Contradiction in Aristotle). While the appendix closely follows Couturat's 1905 book L'algebra de la logique (The Algebra of Logic), footnotes show that Łukasiewicz was aware of the work of Peirce, Huntington and Russell (before Principia Mathematica). This appendix was influential in the development of the Polish (...) school of logic, directly inspiring Stanisław Leśniewski and Leon Chwistek and more widely by serving as a text of the new symbolic logic. This appendix was an important source of the dominant algebraic logic in Poland, but also indicates that Łukasiewicz appreciated Russell's axiomatic approach to logic. (shrink)

Certain Buddhist texts contain statements that are prima facie contradictions. The scholarly consensus has been that such statements are meant to serve a rhetorical function that depends on the apparent contradictions being resolvable. But recently it has been claimed that such statements are meant to be taken literally: their authors assert as true statements that are of the form ‘p and not p’. This claim has ramifications for our understanding of the role played by the principle of non-contradiction (...) in Buddhist argumentation. I argue that these make the claim less plausible. (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)

In 1910, Jan Łukasiewicz published a groundbreaking book, On the Principle of Contradiction in Aristotle. The book contained a critique of the traditional attitude to the Principle of Non-Contradiction, and a reevaluation of its significance in the light of contemporary developments in logic. In the first half of the book, Łukasiewicz produced an analysis of Aristotle’s defence of the Principle in the Metaphysics, showing its deep inadequacy. In the second half of the book, Łukasiewicz, in (...) his own terms, considers the pros and cons of the principle. The present paper provides an analysis and commentary on the second half of the book. Łukasiewicz is seen to be badly torn. Though he eventually endorses the principle, he does so, not in virtue of the evidence he considers, but in despite of it. In particular, he considers arguments against the Principle, drawn from Hegel, Meinong, and the paradoxes of self-reference, but rejects them for what appear to be patently inadequate reasons. (shrink)

In Norton(2003), it was urged that the world does not conform at a fundamental level to some robust principle of causality. To defend this view, I now argue that the causal notions and principles of modern physics do not express some universal causal principle, brought to light by discoveries in physics. Rather they merely assert that, according to relativity theory, spacetime has an invariant velocity, that of light; and that theories of matter admit no propagations faster than light.

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)