Principle Of Non-contradiction Research Articles

Validity, Verifiability, and Confirmability: A Critique of Multiphase Packed Bed Modeling

The pseudocontinuum models of reactions in packed beds are complicated, and an assessment of the reliability of the predictability of their numerical solution is difficult. The predictability reliability depends on validity and verifiability, whereas the numerical solutions of models of reactions in packed beds cannot be validated or verified. Scientific acceptability cannot commence by metaphysics alone, and the truth of the speculative justifications of the results of the numerical models without robust empirical confirmation is a matter of chance occurrence. Adherence to the principles of noncontradiction and mathematical consistency seems to be the minimal criterion if a pseudocontinuum model is to demonstrate a degree of reliability in prediction, simulation, and design. This article is an exposition of the verifiability, validity, and confirmability characteristics of multiphase multidimensional models of reactions in packed beds. It addresses the difficulties of validation and the complexities of construction of models of reactions in packed beds by modeling kinetic data directly to show that often the claims of validity, verifiability, or confirmability of the results of multidimensional or even one-dimensional models of chemical reactions in packed beds, in spite of robust statistical tools, should be viewed with some degree of skepticism.

Who Needs a Proof of the Principle of Non-Contradiction?

Abstract The topic of this paper is Aristotle’s ‘proof by refutation’ of the Principle of Non-Contradiction (Metaphysics Γ 4, 1006a11–1007a20). I consider a worry which has often been raised in connection with this proof. The worry is that, faced with an opponent who is prepared to tolerate contradictions, the argument is dialectically powerless: it is incapable of getting them to abandon their position. In reply, I argue that the proof needs to be seen in its proper context, that is, as part of Aristotle’s response to an opponent who demands a demonstration of the principle. This allows us to clarify the purpose of the argument and answer the worry about its effectiveness.

Mendelssohn and the Protestant Pedants: The Skeptical Rabbis, the Principle of Noncontradiction, and Judaism’s Spiritual Dialogue

AbstractThis study explores the extent to which Mendelssohn’s Jerusalem engages with Protestant sources in its portrayal of rabbinic tradition, which will allow further light to be shed on the pivotal role of rabbinic Judaism and its representations within the emotionally charged polemics surrounding Jewish emancipation in eighteenth-century Prussia. This examination demonstrates that Mendelssohn’s idealized perception of rabbinic thought is deeply embedded in anti-rabbinic Protestant works, whose framework aids him in shaping his own unique outlook. By analyzing Mendelssohn’s deployment of the notion of contradiction, this article shows how his argumentative strategies in Jerusalem efficaciously counter well-known Protestant patterns of critique against rabbinic Judaism. By focusing on his idiosyncratic quotations and insinuations, it recovers the Christian works that he draws on and appropriates for his apologetic objectives and establishes that he uses Johann A. Eisenmenger for his depiction of the nature of rabbinic discursive practices while speaking out against “many a pedant” for their assertion that the rabbis disregarded the principle of noncontradiction. This article argues that Mendelssohn is alluding to eighteenth-century Protestant theologians who unreservedly follow Eisenmenger’s anti-rabbinic perspective and elaborates on how Mendelssohn entirely reframes this view as a conceptual strength of Judaism’s dialogical essence, thus rendering it compatible with the Enlightenment-based Weltanschauung.

Beyond the Principle of Non-Contradiction : Damascius on the Ineffable

Abstract 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.

Clearing Up Correlationism

In After Finitude, Quentin Meillassoux speculates from the principle of noncontradiction’s a priori enclosure toward a standpoint of absolute contingency. Based on his propositions, I argue that his thinking continues to reproduce a contradiction between the finitude of the subject and the infinitude of the noumenal world. Accordingly, I eschew the principle of noncontradiction in favor of a principle of contradiction derived from Hermann Levin Goldschmidt’s Contradiction Set Free. Goldschmidt formulates contradiction as an Either-And-Or whereby the two contradictory terms share a space between them in which there elapses a continuous process of negotiation. If the relation between finitude and infinitude is an Either-And-Or, then there is an interpenetration between the finite and the infinite, between bounded subject and noumenal world. Goldschmidt’s method reinvigorates the contradiction with which Meillassoux is grappling and introduces a more immanent mode of infinitude that echoes certain Spinozist and pre-Spinozist strains of Jewish thought.

The Concept of Motion in Ancient Greek Thought: Foundations in Logic, Method, and Mathematics

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Foundations of the Principles of Non-Contradiction and Identity

Aristotle finds “why a thing is itself” to be “a meaningless inquiry,” (Aristotle, 2000, VII - 17) Hume says about the propositions that express that one thing is identical with itself “we really should mean nothing” (Hume, 2019, p. 230) and, according to Wittgenstein (1922), they say nothing (5.5303). However, I would like to ask here, how can it be so obviously true for a healthy adult person, who has no idea about science, mathematics or logic, that one thing is not another one, but the thing itself? I believe that the tautology, A is not non-A, but A, or short expressed “A is A,” seems so obviously true that it may help to find the origin of so-called “the laws of thought” through the medium of the clues that are given by its self-evidence. &#x0D; The purpose of this work is to claim that the principles of non-contradiction and identity are first based not on human reasoning or thought, but on the biological foundations , namely reception, sensation and perception, which every known living being has. To begin, these principles and then their origin, the discerning faculty, will be explained from the point of view of John Locke. After that, with the help of some examples from biology, it will be indicated that not only human but also every known life form that doesn’t have cognition as human has has this fundamental faculty in its perception and thereby can discern its perceptibilia . Finally, due to this fact, the biological roots of these principles will be demonstrated.

Plato, the Eristics, and the Principle of Non-Contradiction

Abstract This paper considers the use that Plato makes of the Principle of Non-Contradiction (PNC) 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.

The Paraconsistent Brahman? Saguṇatva, Nirguṇatva, and the Principle of Non-contradiction

The Paraconsistent Brahman? Saguṇatva, Nirguṇatva, and the Principle of Non-contradiction

Ibuanyidanda and the Principle of Non-Contradiction: A Logico-Metaphysica Discourse of Asouzu’s Complementary

Ibuanyidanda and The Principle of Non-Contradiction aims at instantiating the claims of Asouzu’s Complementary Reflection that whatever exists serves as a missing link of reality. Reality has been construed within a bifurcating frame of mind, a project that was characterized by the elitist mindset of Plato and was further espoused in Aristotle’s philosophy of essence. For Aristotle, the wise is destined to rule the unwise. This divisive mentality permeates the entire Western culture. Unfortunately, Placid Tempels made some African scholars to erroneously believe and argue that the Western understanding of being is static, while that of Africa is dynamic. This anomaly, among other things, is what Ibuanyidanda as a philosophy and a method of doing philosophy sets out to address. Ibuanyidanda ontology contends that reality can be better understood from the complementary point of view. The principle of non-contradiction championed by Aristotle and the Western scholars sees the opposite of being as non-being, but Asouzu’s complementary reflection sees the opposite of being as to be alone (ka so mu di). This work holds that ibuanyidanda complementary reflection is capable of handling the problems of contradiction that are apparent in the Western mode of philosophising. Opposites do not contradict themselves, they complement each other. Ibuanyidanda philosophy and its position are contrary to the views of Aristotle’s metaphysics and open to sight ontological updating - a good recipe for the advancement of 21st-century philosophizing. Analytic, textual, contextual, and historical methods are employed in this work.

The Principle of Non-Contradiction in Plato’s Republic: an Argument for Form. By Lawrence Bloom

The Principle of Non-Contradiction in Plato’s Republic: an Argument for Form. By Lawrence Bloom

Two Formulations of the Τhesis of Protagoras in Metaphysics Γ and Plato's Theaetetus

This presentation deals with the Aristotelian interpretation of the Thesis of Protagoras (TP) in Metaphysics Γ and its connection with Plato's Theaetetus. Particular attention is paid to the dispute about the difference between two formulations of TP, which takes place among modern scholars. If the first formulation only denies Principle of Non-Contradiction, the second allows Aristotle to interpret TP in the context of the teaching of Anaxagoras.

PAL-VMEA: A Novel Method for Enhancing Decision-Making Consistency in Maintenance Management

Decision-making regarding maintenance planning has become increasingly critical. In view of the need for more assertive decisions, methods, and tools based on failure analysis, performance indicators, and risk analysis have obtained great visibility. One of these methods, the Variation and Mode Effect Analysis (VMEA), is a statistically based method that analyses the effect of different sources of variations on a system. One great advantage of VMEA is to facilitate the understanding of these variations and to highlight the system areas in which improvement efforts should be directed. However, like many knowledge-based methods, the inherent epistemic uncertainty can be propagated to its result, influencing following decisions. To minimize this issue, this work proposes the novel combination of VMEA with Paraconsistent Annotated Logic (PAL), a technique that withdraws the principle of noncontradiction, allowing better decision-making when contradictory opinions are present. To demonstrate the method applicability, a case study analyzing a hydrogenerator components is presented. Results show how the proposed method is capable of indicating which are the failure modes that most affect the analyzed system, as well as which variables must be monitored so that the symptoms related to each failure mode can be observed, helping in decision-making regarding maintenance planning.

Transcendental Philosophy, The History of Psychology Kant and Freud.

Kant is not generally recognised to be an Aristotelian hylomorphic Philosopher because of his extension of logic into Philosophical Psychology in the form of Transcendental Logic. This extension is a natural articulation of hylomorphic metaphysics. Aristotle’s 4 kinds of change, 3 principles, and 4 “causes” are all transformed into the Kantian system of categories of judgement and also transposed into the faculties of sensibility, understanding, and reason. The principles of noncontradiction and sufficient reason obviously have origins in Aristotelian logic and Metaphysics. Freud claims that he is writing the Psychology that Kant would have written had he written subsequent to the “divorce” between Philosophy and Psychology in 1870 but it is clear that Freud too must be considered a hylomorphic Psychologist. This latter claim must be true if it is the case that Kant can be regarded, a hylomorphic Philosopher. Freud regards Consciousness and psychological residues (rituals) that we find in institutions as vicissitudes of Instinct. Instinct is here of course a philosophical concept possessing an aim, an object, a bodily source and a demand for motor activity. Early vicissitudes of instincts are narcissistically based and give rise the genesis of a strong ego under favourable circumstances. Freudian theory correctly interpreted ought to give rise to ethical theory of the type we find in Kant. This is a requirement for theories that we find in the arena of transcendental psychology.

Fakhr ad-Din ar-Razi’s Criticism of the Sophists: An Analyse in the Context of the Kalam

Antik Yunan’ın siyasal ve sosyal şartları sonucunda tarih sahnesine çıkan sofistler, bir kavram olarak çeviri hareketleri ile beraber Aristoteles üzerinden İslam düşüncesi kaynaklarına girmiştir. Kelâmcılar, eserlerinin bilgi bahislerinde sofistlere geniş ölçüde yer vermiş ve sadece görüşlerini veya ortaya attıkları problemleri aktarmakla yetinmemişlerdir. Sofistleri, Lâedriyye, İnâdiyye ve İndiyye şeklinde yeni bir tasnife tabi tutan kelâmcılar, Aristoteles perspektifinden hareketle çeşitli açılımlarda bulunmakla birlikte, çelişmezlik ve üçüncü halin imkânsızlığı gibi ilkeler bağlamında çözüm üretmişlerdir. Kelâm ve felsefe uğrağında önemli bir yerde duran Fahreddin Râzî ise, kendinden önceki mirası devralarak sofistleri farklı bağlamlarda tekrar gündeme getirmiştir. Râzî’nin sofistleri ele aldığı yeni bağlam, İslam düşünce geleneğinde mezhepler arasında çıkan tartışmalar dolayımındadır. Bu çalışma, Râzî ve kelâm ilminin sofistik görüşleri işleyiş tarzlarını ve çözümlerini bağlamsal bir çerçeve kapsamında incelemektedir

Analogy after Aquinas: Logical Problems, Thomistic Answers by Domenic D’Ettore

Reviewed by: Analogy after Aquinas: Logical Problems, Thomistic Answers by Domenic D’Ettore Richard Cross Analogy after Aquinas: Logical Problems, Thomistic Answers. By Domenic D’Ettore. Washington, D.C.: The Catholic University of America Press, 2019. Pp. 224. $65.00 (hard). ISBN: 978-0-8132-3122-8. This excellent book traces the history of Thomistic accounts of analogy from the early fourteenth century to Francis Sylvestri of Ferrara and Chrysostom Javelli, writing in the 1520s and 1530s in the light of Cajetan’s magisterial De nominum analogia. D’Ettore starts with the philosopher who caused such difficulty for the logic of analogy: namely, John Duns Scotus. Scotus argued that both the principle of noncontradiction and syllogistic validity require univocal concepts, such that there is one ratio through which a name signifies reality. As the earliest Thomists saw, this directly threatens Aquinas’s denial of that very claim, in his assertion that analogy is sufficient for avoiding the fallacy of equivocation. D’Ettore argues that Aquinas’s account simply does not evince any awareness of these difficulties, and hence needs supplementation to enable it to provide answers to Scotus’s worries. A good part of the exposition is devoted to the divergent interpretations of [End Page 664] Aquinas proposed by the Thomists to shore up Aquinas’s position against the Scotist onslaught. It is fashionable in some theological circles today to urge that Scotus’s target was Henry of Ghent, and thus that his criticisms do not touch Aquinas’s account. But that was decidedly not the opinion of the early Thomists, and they were clearly right to be worried. As D’Ettore puts it, “If a Thomist insists that Aquinas’s model(s) of analogous naming demand more than one ratio, then the Thomist must explain how this model dodges Scotus’s criticism that, without one and only one ratio for a term, demonstration is impossible. If a Thomist argues instead that there is one ratio involved in analogous signification, then the Thomist must explain the difference between his own position and that of Scotus, either admitting that analogy reduces semantically to univocity or challenging Scotus’s definition(s) of univocity and analogy” (31–32). D’Ettore groups the philosophical and exegetical problems facing early interpreters of Aquinas under three useful headings: the rationes problem (whether analogous terms signify one or many rationes); the analogy-model problem (whether the theory of analogy is modeled on the relationship between one thing and another [unius ad alterum]—which D’Ettore labels the “Healthy Model”—or of two to a third [duorum ad tertium]—which he labels the “Principle Model”); and the equivocation problem (whether the use of analogous terms necessarily generates equivocation, as Scotus held). The discussion is quite dense, and the array of issues treated very complex. A helpful chart (186) aids the reader in tracking the manifold different answers offered by the subjects of this study: the early fourteenth-century thinkers Hervaeus Natalis and Thomas Sutton; the early fifteenth-century thinker John Capreolus; the late fifteenth-century philosophers Flandrensis and Socinas; and from the early sixteenth century Cajetan and the two Thomists mentioned above. All but the first three were associated with the Dominican studium in Bologna. As Joshua Hochschild convincingly argued a few years ago (The Semantics of Analogy: Rereading Cajetan’s “De nominum analogia” [Notre Dame: University of Notre Dame Press, 2010]), Cajetan has a good right to claim to have solved Scotus’s objections by appealing to the analogy of proper proportionality. As D’Ettore puts it, “Proportional unity does not eliminate diversity, but it is, nevertheless, a real form of similarity such that whatever properties belong to one thing also belong proportionally to whatever is proportionally similar to it” (139). The different rationes have some kind of unity or identity—a proportional unity or identity—and as such “whatever belongs to one, belongs also to the other proportionally” (ibid., quoting Cajetan, De nominum analogia, c. 10, n. 106). This unity allows Cajetan to circumvent Scotus’s claim that syllogisms that include terms whose significations are related merely analogously ultimately have four (or more) terms. What grounds syllogistic validity and theological reasoning is that, in...

Çelişkilere Dönüş: Łukasiewicz İtirazı

The Principle of Non-Contradiction is found and christened as “the firmest principle” by Aristotle. Since then, almost no objection has been raised against this principle and its firmness, until Łukasiewicz. By reflecting on the possibility of the emergence of new systems of logic with reference to the developments in non-Eucledian geometry, Łukasiewicz stated that the reconsideration of the principles of logic may lead to new systems. With the guidance of this idea, in his revolutionary work “On the Principle of Contradiction in Aristotle” Łukasiewicz approaches Aristotle’s account on the Principle of Non-Contradiction and analyzes it thoroughly. Starting with the identification and the comparison of three distinct definitions of the Principle of Non-Contradiction in Metaphysics, the Polish logician criticizes Aristotle’s arguments regarding the unprovability and the firmness of the principle. Even though Aristotle defended that the principle cannot be proved by direct proof but can be proved by indirect ones, i.e. elenchus, Łukasiewicz realizes that Aristotle’s aforementioned distinction is actually built on sand, since the Stagirate had stated in Prior Analytics that these two types of proof can be used interchangeably. This statement means that there is no err in using direct proofs instead of elenchtic ones and thus it appears that if the principle can be proved by elenchus, it can be proved by direct proof as well. In other words, Aristotle runs into a contradiction by trying to prove the principle that cannot be proved. Having found that there lies a contradiction in the very foundations of the Principle of Non-Contradiction regarding its unprovability, he continues with scrutinizing Aristotle’s elenchtic proofs in Metaphysics. With the discovery of fallacies appealed by Aristotle in those proofs, Łukasiewicz is ready for raising his objection to the firmness of the Principle of Non-Contradiction. Starting with stating how contradictions were defined before and by Aristotle, how the Stagirate formulated the Principle of Non-Contradiction, our study aims to examine Łukasiewicz’s objection and summarize his arguments against the Principle of Non-Contradiction.

Özdeşlik İlkesi Sorunu ve Yansımalı Olmayan Mantıklar

The principle of identity is one of the three basic principles of reason on which classical logic rests. The other two basic principles of reason are principle of noncontradiction and of the excluded middle. These principles were accepted almost unquestionably until the beginning of the twentieth century. Therefore, classical logic, which adhered to these principles, continued to prevail. Today, however, one of the most interesting debates in the field of science is whether these fundamental principles on which classical logic rests can be seen as necessary and invariable truths. With this discussion, a logic emerged in the twentieth century, rejecting the basic principles of reason. In this study, we will examine the logics -non-reflexive logics- that rejects or limits the principle of identity, from which the other two principles of classical logic are derived. First of all, we will talk about the origins of non-reflexive logic. Next, the basic assumptions of the identity principle of classical logic will be discussed. Finally, we will discuss the reasons for which non-reflexive logic rejects or limits the principle of identity, in other words, which assumptions of the identity principle are considered problematic.

Internal Negation and the Principles of Non-Contradiction and of Excluded Middle in Aristotle

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.

Heidegger on No-thing and the Principle of Non-contradiction

Heidegger’s 1929 lecture on Nothing is usually considered as a critique of logic and, more generally, of the sciences that mainly rely on it. However, it can also be interpreted as a strong attempt to overcome Western metaphysics, i.e., the metaphysics of Anwesenheit, as well as a specific interpretation of the principle of non-contradiction on which this metaphysical perspective is grounded. In this new particular philosophical framework proposed by Heidegger, Dasein’s thrownness finds its proper space — the space of Dasein’s freedom. In my paper, I will argue that Heidegger’s proposal, more than just a critique of logic, is a call to re-think some fundamental topics of philosophy and, above all, is a call to be attentive to what is. Surprisingly, this fundamental attention is also the element that discloses Dasein’s thrownness, making possible its freedom. This latter, then, assumes in Heidegger’s thought a very different character from its usual understanding: it is not recognised as a completely absolute possibility of action, i.e., untied from constraints, but rather an attuned response to Being.