Law Of Non-contradiction Research Articles

The Law of Non-contradiction and Global Philosophy of Religion

AbstractThis 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.

On the Preconditions of Rationality

In the field of legal argumentation theory, rational justification is probably the most important part, and yet it is not fully understood by scholars even today. In several publication the author has presented already presented her theory on this, but has not discussed all the preconditions. In the present contribution this will be handed in – at least in a short version. Thus, aspects of epistemology and linguistic theory are discussed, as well as what the author calls the ‘LBA theorem’ (from ‘The Least Bad Alternative’), which relies on the law of noncontradiction and describes a criterion for when exactly an assertion is rationally justified.

Reviewing the law of non-contradiction: A Marxist reading

Karl Popper argues that (i) because dialectics fails to comply with the law of non-contradiction (LNC) and (ii) a thought system that violates the latter is destructive to scientific theorising, dialectics cannot serve as the basis for scientific theorising. In connection with Popper’s accusation, the article seeks to review evidence of dialectical thinking in Marxist literature in accordance with the LNC to clarify the former’s relation to scientific theorising. Lucio Colletti and Lawrence Wilde are notable examples who have made clear commitments to extricate dialectics from the accusation that it violates the LNC. Despite the commendable contributions made, related conclusions do not arise from a concrete analysis of examples from Marxist dialectics about the LNC. We put forward two claims as our position and hence our contribution. First, we side with Popper’s premise (ii): that any thought system that fails to take the LNC seriously cannot validly support scientific theorising. Second, we oppose the truth of Popper’s premise (i): that dialectics undermines the LNC. Consequently, because premise (i) is unfounded, we are unable to grant the soundness of Popper’s contention against dialectics. According to our method of proof, we deploy the tool of concept analysis on relevant examples from Marxist literature. In the end, our overarching purpose is to show that dialectics operationalises the LNC and therefore Marxist dialectics is not disturbed by Popper’s objection.

Seeing as We Cannot

The belief that Jastrow’s duck-rabbit (J) is both a duck-head and a rabbit-head drawing violates the Law of Non-Contradiction (LNC), as does the belief that J seems to be something independent of all the ways J can seem. Call the former belief B1 and the latter B2. I argue that B1 and B2 are rational, though contradictory beliefs, and conclude that we must reassess the LNC’s status of being a fundamental requirement for rationality. In contrast with B1 and B2, our experiences that correspond to said beliefs do comply with the LNC. That is: we cannot see J as both duck and rabbit at the same time (E1), nor does J seem something independent of the ways J can seem (E2). Since there is no satisfactory explanation for why we are not able to see J as the contradictions E1 or E2―even though our corresponding beliefs about J are the contradictions B1 and B2―I propose that the LNC is merely an empirical hypothesis concerning the limits of our perception.

BOOK REVIEW: GUYER, PAUL. Kant on the Rationality of Morality (Cambridge University Press, 2019, 73p. )

I discuss Paul Guyer’s contribution to the Cambridge Elements: The Philosophy of Immanuel Kant series. The author argues that Kant derives the fundamental principle and the object of morality from the fundamental principles of reason (the law of noncontradiction, of excluded middle and the principle of sufficient reason). I provide an overview of its chapters and discuss some of its main interpretative claims.

How to Read Both: The Logic of True Contradictions in Chaucer's World

This essay argues that medieval culture is characterized by a commitment to mutually exclusive truths, despite upholding the fundamental principle of Aristotelian logic that there can be no true contradictions. The possibility of true contradiction, known to modern philosophy as dialetheism, is explored in Troilus and Criseyde, Pearl, and Piers Plowman; in contrast, Chaucer's Pardoner is discussed as an example of lived contradiction that manifests as incoherence. The law of non-contradiction is still regarded as fundamental in philosophy, despite some celebrated challenges: Hegel's famous insistence on the contradictory nature of all things is here used to illuminate the logical difficulties created by the ineffable nature of the Trinity. Medieval theologians such as Duns Scotus, William of Ockham, Robert Holcot, and others, were faced with a particularly acute epistemological crisis as they struggled to formulate theories that could reconcile the universality of logic (without which all rational inquiry was threatened) with the unique contradictions of triune divinity. Finally, the inevitable existence of moral dialetheias, in life and in fiction, is explored in the emergence of the romance, first in the illusory moral dilemmas of Chrétien's romances, and then in the real moral crisis suffered by Thomas of Britain's Tristan. It is argued in conclusion that fiction is the prime tool for the examination of true contradiction, being in itself a lie of profound moral necessity.

The Non-Contradiction of Determinism

Abstract 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” (could-have-done-otherwise) 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.

Ambiguity and contradiction: the outlines of Jung's dialectics.

This essay explores Jung's thinking strategies, argumentation patterns, and concept formation processes, and reveals how they distinguish his work from normal present-day science. Jung doesn't much appreciate the law of noncontradiction, which is a cornerstone of classical logic, and he doesn't refrain from using openly ambiguous theoretical terms. It will be pointed out that not only specific archetypes, but the notion of archetype itself, as well as other of Jung's theoretical notions (energy, including libidinal energy, polarity, integration, wholeness, instinct, symbol, and so on), are consciously ambiguous and thus potentially contradictory. It is shown that this kind of dialectic research strategy and related contradiction-tolerant and ambiguity-tolerant methods connect his work to Post-Kantian German Idealism, Schelling's and Schopenhauer's philosophy in particular. However, it was Hegel who, in his Science of Logic, presented a systematic overview of such dialectic principles of reasoning, which were, in the 19th century, widely applied by German philosophers, theologians, and other scholars. Unfortunately, Jung decided not to study Hegel, but, instead, wrote derogatorily of his work. It will be argued that a Jungian who wants to be conscious of her own argumentation strategies and methods of concept formation should study Hegel's complex and sophisticated dialectical logic. In addition, it is suggested that Jungian depth psychology might help us to amend the phenomenological deficits of Hegel's system by providing it with a primal experiential source. This is needed because Hegel's Geist, due to its intellectual emphasis, is a self-conscious conceptual totality which advances progressively from stage to stage by guiding itself with the help of dialectical reason (Vernunft). It will be shown that if enriched with a proper kind of experiential givenness, which includes the Jungian unconsciousness (with libidinal energy, instincts, and archetypes), Hegelian metaphysics would be able to embrace a seriously aconceptual or preconceptual dimension. Aconceptual experience, which is, for Jung, mainly the instinctual layer of archetypes, remains essentially inaccessible, not only for normal scientific concepts, but for the concepts of any form of dialectics as well.

Avicenna on the Law of Non-contradiction

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.

Propositional Logic Applied to Three Contradictory Definitions of the Zeta Function

The paper discusses the following contradictions: (1) Contradictory definitions of the Zeta function. These three definitions of the Zeta function contradict each other: the Dirichlet series, Riemann’s Zeta function, and a third definition that is conditionally convergent throughout the critical strip and divergent throughout half-plane Re(s)≤0. If the Dirichlet series definition and one of the other two definitions are both true, then there is a contradiction regarding convergence/divergence of Zeta in the critical strip. If Riemann’s Zeta function and the third definition are both true, then there is a contradiction regarding convergence/divergence of Zeta in half-plane Re(s)≤0. And if only the Dirichlet series definition is true, than all theories that falsely assume that the other definitions are true are rendered logically unsound. (2) The Hankel contour’s contradiction of the preconditions of Cauchy’s integral theorem. The derivation of the Riemann Zeta function uses both of these,but the contradiction between the two renders the Riemann Zeta function invalid. (3) Conditionally convergent series. According to the Riemann series theorem, any conditionally convergent series can be rearranged to be divergent. This contradicts the associative and commutative properties of addition. It also means that all conditionally convergent series are paradoxes, and that any argument that uses a conditionally convergent series (e.g. the third definition of the Zeta function, and the definition of the Euler-Mascheroni constant) violates the Law of Non-Contradiction (LNC) in logic, and triggers Ex Contradictione Quodlibet (ECQ), also called the Principle of Explosion.

Dialetheism and the Problem of the Missing Difference

Abstract During the past few decades, Graham Priest has advocated for Dialetheism, the controversial position that some contradictions are true. Dialetheism entails that the Law of Non-Contradiction fails. In recent decades the philosophical community has begun to recognize the significant challenge posed by Priest’s arguments. Priest has primarily appealed to paradoxes of self-reference, such as the Liar Paradox, to support his position. Following Priest’s approach, I offer another argument for Dialetheism, which appeals to a self-referential paradox that has been more or less ignored in the philosophical literature on the subject: the paradox of the missing difference. When we reflect on the question ‘what is a concept?’ from the perspective of a classical model of conceptual analysis, we arrive at the paradox of the missing difference. Although contradictions may be improbable, when we reflect on the question ‘how is the domain of concepts possible?’ we are led to a startling principle: without dialetheia any theory concerning concept formation (from a classical perspective on concepts) would be impossible. Dialetheism is a necessary condition for the existence of a domain of concepts in general. As a result, Dialetheism may even be more central to philosophical reflection than even dialetheists themselves have recognized.

The Challenge of Paradox: Infinity and Contradiction in Western and Chinese Philosophy

Kant claimed that it is impossible for us to have a consistent notion of the infinite. I shall concentrate on three versions of the paradoxes of the infinite: Kant’s first antinomy, the paradoxes of Cantorian set theory, and applications of Cantorian arguments to the metaphysics of the world. I shall dare two side-glance looks at Ancient Chinese Philosophy, where analogies to the Western paradoxes can be found. I shall first discuss key passages from the Chinese sophists, and then consider the formulation of the Law of Non-Contradiction in the Moist Canons. I conclude that the paradoxes of the infinite remain a major challenge for reason.

A non-probabilist principle of higher-order reasoning

The author uses a series of examples to illustrate two versions of a new, nonprobabilist principle of epistemic rationality, the special and general versions of the metacognitive, expected relative frequency (MERF) principle. These are used to explain the rationality of revisions to an agent’s degrees of confidence in propositions based on evidence of the reliability or unreliability of the cognitive processes responsible for them—especially reductions in confidence assignments to propositions antecedently regarded as certain—including certainty-reductions to instances of the law of excluded middle or the law of noncontradiction in logic or certainty-reductions to the certainties of probabilist epistemology. The author proposes special and general versions of the MERF principle and uses them to explain the examples, including the reasoning that would lead to thoroughgoing fallibilism—that is, to a state of being certain of nothing (not even the MERF principle itself). The author responds to the main defenses of probabilism: Dutch Book arguments, Joyce’s potential accuracy defense, and the potential calibration defenses of Shimony and van Fraassen by showing that, even though they do not satisfy the probability axioms, degrees of belief that satisfy the MERF principle minimize expected inaccuracy in Joyce’s sense; they can be externally calibrated in Shimony and van Fraassen’s sense; and they can serve as a basis for rational betting, unlike probabilist degrees of belief, which, in many cases, human beings have no rational way of ascertaining. The author also uses the MERF principle to subsume the various epistemic akrasia principles in the literature. Finally, the author responds to Titelbaum’s argument that epistemic akrasia principles require that we be certain of some epistemological beliefs, if we are rational.

Above Reason Propositions and Contradiction in the Religious Thought of Robert Boyle

In this essay, I argue that Robert Boyle does not hold that true religion requires us to believe doctrines that are in violation of the law of noncontradiction or that it yields logical contradictions. Rather, due to the epistemological limitations of human reason, we are sometimes called to believe doctrines or propositions that are at first blush contradictory but, upon further inspection, not definitively so. This holds for doctrines considered singly or together and is an important qualifier to the traditional line of scholarship’s flat claim that Boyle’s limits of belief are logical contradictions. My conclusions here are at odds with Jan W. Wojcik’s claim, in her important, revisionist work on the famous natural philosopher, that he teaches that sometimes we are required to believe religious doctrines that violate the law of noncontradiction.

This Biosphere Which Is Not One: Towards Weird Essentialism

This essay uses the thought of Luce Irigaray as a very powerful way to imagine what ecological beings such as meadows and whales are like. For reasons given yet implicit in Irigaray's work, it is possible to extend what she argues about woman to include any being whatsoever. In particular, it is shown that to exist is to defy the so-called law of noncontradiction. Various paradoxes demonstrate that in order to care for beings that we consider to be ecological, such as meadows, we had better relax our adherence to this “law.” Ecological beings are, like Irigaray's woman, not one and not two. They cannot be thought as constantly, presently themselves, or as decomposable into other beings – not without violence. A side effect of the argument is that we can now use Irigaray to think a multiplicity of sexualities and gender identities.

Quantum Mechanics is not Physical Reality But Mental Potentiality Because of the Law of Non-Contradiction

Quantum mechanics have always shown great predictive successes, but also some weird aspects concerning the mathematics-reality correspondence, such as superposition of contradictory events, like a dead and alive cat. Although physicists claim that we have to live with these contradictions, a psycho-biological analysis could propose another explanation. Observation of extra-mental reality is based on direct physical contact between an object, its corresponding sense organ and its mental representation in the brain. In contrast, prediction of the future is no longer directly linked to extra-mental reality, but projects possible observations from the memory of the past into the future. Due to the uncertainty of the future, predictions require mental potentiality, meaning that it may or may not happen in extra-mental reality. Nevertheless, if past observations are regular as in classical physics, they allow predictions with high reliability, whereas if they are irregular as in quantum physics, they are limited to uncertainty and probability. Superposition in classical physics increases space or time units accordingly, whereas quantum superposition considers multiple space locations for the same object at the same time. Thus, the quantum mechanical formalism is in direct contradiction to the philosophical law of non-contradiction, which does not allow considering it as extra-mental reality. However, it has all characteristics of mental potentiality, which allows prediction of future outcomes with probability. The consideration of quantum mechanics as mental potentiality would solve the superposition problem, as well as the measurement and the non-locality problem. According to the regularity or irregularity of observation, classical or quantum mechanical formalism has to be applied for prediction of future dynamics. There is no collapse or continuation of superposition in the wave function, but simply the replacement of an uncertain prediction model by the more certain observation. With this interpretation some weird aspects could be completely eliminated.

Dialectical Contradictions and Classical Formal Logic

A dialectical contradiction can be appropriately described within the framework of classical formal logic. It is in harmony with the law of noncontradiction. According to our definition, two theories make up a dialectical contradiction if each of them is consistent and their union is inconsistent. It can happen that each of these two theories has an intended model. A number of examples of this are to be found in the history of science.

V-On Conceiving the Inconsistent

This work has been developed within the 2013–15 ahrc project The Metaphysical Basis of Logic: The Law of Non-Contradiction as Basic Knowledge (grant ref. ah/k001698/1). A version of the paper was presented in September 2013 at the Modal Metaphysics Workshop in Bratislava. I am grateful to the audiences there and at the Aristotelian Society meeting for many helpful comments and remarks.

Dialectical Leadership in a Contradictory World

Prior research suggests that the organizational context is not only full of complication but also contradiction. How do effective executives address this issue? Some scholars maintain that both cognitive complexity and behavioral complexity are required to effectively cope with endless organizational paradox. However, few have directly addressed top managers' mental assumptions and cognitive strategies behind it. Since organizational paradox has become a common phenomenon nowadays, it is worth exploring at great depths. Given that contradiction has been extensively discussed in the circle of philosophy for thousands of years, we first reviewed the literature of philosophy. It was found that Greek Dialectic proposes a cognitive strategy to attain deep truths through contradiction while Hegelian Dialectic illustrates a worldview where any evolving entity tends to contain contradiction, thus causing the thesis-antithesis- synthesis evolution. Next, through a multiple-case, inductive study of three world-class leaders, we found that effective executives tend to see contradiction in various sorts of things, rather than obeying Aristotle's Law of Noncontradiction. Second, effective executives also tend to witness the thesis-antithesis-synthesis process proposed by Hegel. Third, effective executives are inclined to adopt Socratic Method, thus arriving at higher truths through contradiction. However, effective executives use formal logic too when it comes to their principles or beliefs, which suggests that effective executives perceive two sorts of contradiction in reality, i.e. impossible contradiction and necessary contradiction. Lastly, ineffective executives may tend to perceive impossible contradiction only in their worldviews, thus losing the integrative potential that moves contradiction into synthesis.

How Does Eternity Affect the Law of Non‐Contradiction?

How Does Eternity Affect the Law of Non‐Contradiction?