Principle Of Non-contradiction Research Articles

Ben Brice, Coleridge and ScepticismColeridge and Scepticism. Ben Brice. Oxford: Oxford University Press, 2007. Pp. x+229.

<i>Ben Brice</i>, Coleridge and Scepticism<i>Coleridge and Scepticism</i>. Ben Brice. Oxford: Oxford University Press, 2007. Pp. x+229.

Aristotle’s Theory of Deduction and Paraconsistency DOI:10.5007/1808-1711.2010v14n1p71

In the Organon Aristotle describes some deductive schemata in which inconsistencies do not entail the trivialization of the logical theory involved. This thesis is corroborated by three different theoretical topics by him discussed, which are presented in this paper. We analyse inference schema used by Aristotle in the Protrepticus and the method of indirect demonstration for categorical syllogisms. Both methods exemplify as Aristotle employs classical reductio ad absurdum strategies. Following, we discuss valid syllogisms from opposite premises (contrary and contradictory) studied by the Stagerian in the Analytica Priora (B15). According to him, the following syllogisms are valid from opposite premises, in which small Latin letters stand for terms such as subject and predicate, and capital Latin letters stand for the categorical propositions such as in the traditional notation: (i) in the second figure, Eba,Aba ` Eaa (Cesare), Aba, Eba ` Eaa (Camestres), Eba, I ba ` Oaa (Festino), and Aba,Oba ` Oaa (Baroco); (ii) in the third one, Eab,Aab ` Oaa (Felapton), Oab,Aab ` Oaa (Bocardo) and Eab, Iab ` Oaa (Ferison). Finally, we discuss the passage from the Analytica Posteriora (A11) in which Aristotle states that the Principle of Non-Contradiction is not generally presupposed in all demonstrations (scientific syllogisms), but only in those in which the conclusion must be proved from the Principle; the Stagerian states that if a syllogism of the first figure has the major term consistent, the other terms of the demonstration can be each one separately inconsistent. These results allow us to propose an interpretation of his deductive theory as a broad sense paraconsistent theory. Firstly, we proceed to a hermeneutical analysis, evaluating its logical significance and the interplay of the results with some other points of Aristotle’s philosophy. Secondly, we point to a logical interpretation of the Aristotelian syllogisms from opposite premises in the antilogisms method proposed by Christine Ladd-Franklin in 1883, and we also present a logical treatment of the Aristotelian demonstration with inconsistent material in the paraconsistent logics Cn, 1 _ n _ !, introduced by da Costa in 1963. These two issues seem having not yet been analysed in detail in the literature.

Não contradição ou terceiro excluído? Avicena e o primeiro princípio da metafísica

Em sua paráfrase da Metafísica de Aristóteles, Avicena parece adotar um primeiroprincípio diferente do adotado pelo filósofo grego para essa ciência. De fato, alguns intérpretesconsideram que ele prefere o princípio do terceiro excluído em vez do princípio denão contradição. Como discordo dessa tese, proponho-me analisar aqui a formulação deAvicena do primeiro princípio.

Mereological Heuristics for Huayan Buddhism

This is an attempt to explain, in a way familiar to contemporary ways of thinking about mereology, why someone might accept some prima facie puzzling remarks by Fazang, such as his claims that the eye of a lion is its ear and that a rafter of a building is identical to the building itself. These claims are corollaries of the Huayan Buddhist thesis that everything is part of everything else, and it is intended here to show that there is a rational basis for this thesis that involves a nonstandard notion of parthood and, importantly, that does not violate the principle of noncontradiction.

The principle of noncontradiction and Descartes' god

The article analyzes the status of the principle of non-contradiction as an eternal truth in Descartes' metaphysics, and tries to answer the question is it caused. After making the difference between created and uncreated eternal truths, the reached conclusion is that the principle of non-contradiction is created eternal truth. As such, it could be applied even to God but only if we understand him as the most perfect being. The very essence of God, that is absolute power i.e. causa sui is beyond the range of this principle, because absolute power as the essence of God is the realm of absolute identity between His essence and His existence. Since man can think only in accordance with the principle of non-contradiction, even God's infinite power he must understand with regard to that principle. Nevertheless, since the principle of non-contradiction is not applicable on God's absolute identity, its absence man understands as its negation, and because of that, that identity appears to him as self-contradictory. In the end, it is shown a (partial) lack of ground of Lebniz's critique of Descartes concerning ontological argument.

Science Versus Religion?: The Insights and Oversights of the “New Atheists”

Science Versus Religion? The Insights and Oversights of the “New Atheists” Brad S. Gregory (bio) The recent “science versus religion” debate has tended to unfold in a way that reflects the angry shouting match characteristic of our debased political culture, lacking in rigor and loaded with rancor. The American media exacerbates the problem, typically staging the issue as a boxing match: in this corner, the strident religious dogmatists defensively brandishing their bibles; in the other corner, the rationalist scientific atheists confidently preaching the neo-Darwinian gospel. This media setup is presumably to the liking of the so-called New Atheists, since it parallels their portrayal of the issue in their respective books and interviews. Isn’t it obvious who wins? But to accept their characterization of the issue in dispute prejudices the matter and begs the question. As this article endeavors to show, the dichotomy as alleged by the New Atheists and parroted by the popular media is a false one. To unveil this will require a way of proceeding that differs from most contributions to this often fruitless dispute. It will require making some distinctions that are normally ignored. The “science versus religion” debate is both real and illusory. It is real insofar as the natural sciences, to the extent that they provide [End Page 17] an impressively cumulative corpus of knowledge about natural processes, clearly undermine some religious truth claims about the natural world. It is illusory insofar as all scientific findings are entirely compatible with other, different religious truth claims about God’s relationship to the natural world. The “New” Atheists (conceptually there is nothing original about them)—a group that, for the purposes of this article, includes Richard Dawkins, Daniel Dennett, Sam Harris, Christopher Hitchens, Michel Onfray, and John Allen Paulos—see the religious beliefs contradicted by scientific findings and proceed to ridicule religion and religious believers in general. In doing so, they mistakenly construe religion as though it were an undifferentiated whole. Furthermore, they are unaware of the character of their own philosophical presuppositions, uninformed about intellectual history and sophisticated biblical scholarship, and lacking in any methodological rationale or rigor in their treatment of religion. Consequently they seem not to see how their alleged refutations of the reality of God depend on their assumptions about what they think theology is. Posturing as educated intellectuals standing up for critical rationality against naive credulity, in fact they demonstrate at length how little they know about intellectual matters directly relevant to their concerns, a point that in their respective ways David Bentley Hart and Terry Eagleton have recently made with erudite panache.1 And like some of the religious believers whom they belittle, the New Atheists apparently bother to read only what confirms their personal beliefs. This article both acknowledges the insights and demonstrates a few of the most egregious oversights of the New Atheists. It shows that the findings of science do not demand an atheistic denial of God, but can instead be rationally interpreted in different terms consistent with a traditional Christian view of God and theology of creation. Antagonistic grinding back and forth leads nowhere because of parallel dubious assumptions: on the one hand, that “religion” and “faith” make truth claims about reality and yet are individual, interior, personal, private matters of the heart and so [End Page 18] beyond rational criticism or reproach; on the other hand, that all religious claims are false simply because many are demonstrably mistaken. Neither presupposing nor seeking to demonstrate God’s existence, this essay proceeds on the minimalist assumption that truth cannot contradict truth—the principle of noncontradiction is necessary for the pursuit of truth and for rationality whether in science or in religion. I Most critics of the New Atheists have not acknowledged the legitimate points that they make. This is perhaps understandable considering the antireligious loathing that pervades their works. Still, the New Atheists say some things that are true. For example, they rightly assert that the findings of science falsify many religious beliefs. To choose only one such example, widespread especially in the United States among many fundamentalist Protestants: the earth is not six thousand or so years old, nor is it and the life...

Leibniz on the Trinity and the Incarnation: Reason and Revelation in the Seventeenth Century by Maria Rosa Antognazza

BOOK REVIEWS 501 working through these studies, one must wonder how it is even possible to regard the metaphysics in Thomas's ethical writings as some sort of dispensable appendage. Perhaps the only answer is that discerning metaphysical influence takes a "metaphysical eye." Dewan has one, and the influence he sees is deep and pervasive. This is not to deny the distinctness of ethics. It has its own subject and principles, and hence its "autonomy." But it is not a self-starter, partly because of what we saw earlier: it is not its own last end. Its absolutely first principle, for Thomas, is the last end. (In some interpretations, however, even this is not too clear.) To be sure, the first principles that ethics supposes, being genuine firsts, must be indemonstrable, "self-evident." But ethics only supposes them. To determine, judge and defend them-to bring them fully into their own "evidence"-is a metaphysical exercise. That this is so for Thomas ought to be plain enough even from a glance at the first few lines of the proemium to his commentary on Aristotle's Metaphysics. In this book Dewan puts on display how it is so. These essays are certainly not just for specialists. Anyone wanting to understand Thomas's thought better will benefit immensely from them. It is not just that Dewan knows Thomas intimately and gets his meaning right. He has a way of capturing what is "happening" in the text, of "watching" Thomas philosophize and re-enacting the event, which is unusually instructive. As for the prose, it is always crystal clear, and as fresh as it is serene. The book's chief virtue, however, is simply the perennial moral wisdom that it transmits. Dewan says, "I wish to stress the lifelong use of St. Thomas's Summa theologiae secunda secundae. Moral education, self-help in spirituality, requires that we make such a book, such a treatise on human living, a constant stimulus of our reflection" (363). Clearly he has done this very thing. The results have a power to stimulate all their own. Pontficial University of the Holy Cross Rome, Italy STEPHEN L. BROCK Leibniz on the Trinity and the Incarnation: Reason and Revelation in the Seventeenth Century. By MARIA ROSA ANTOGNAZZA. Translated by GERALD PARKS. New Haven and London: Yale University Press, 2007. Pp. 348 $60.00 (cloth). ISBN: 978-0-300-10074-7. An all-too-common view of Leibniz is that ofthe metaphysician who humored his more devout correspondents with an occasional, though disingenuous, bit of theologizing. How many times have we read that Leibniz was pulling the leg of his Jesuit interlocutor Bartholomew de Bosses when he compared his notion of 502 BOOK REVIEWS the vinculum substantiale with the Eucharist? Surely, a century's worth of rationalists have informed us, the man who invented the calculus would not-could not-have taken Christianity seriously. Leibniz on the Trinity and the Incarnation, a fully revised version of the author's Trinita e Incarnazione: II rapporto tra filosofia e teologia rivelata nel pensiero di Leibniz, should drive the final nail in the coffin of this tired old story. Hardly the textbook rationalist, Leibniz emerges in Antognazza's fine work as passionate defender of the Christian mysteries, a dexterous exponent of St. Augustine's account of Trinitarian vestiges in creation, and an able apologist for the perennial value of the terms 'substance', 'nature', and 'person' in Trinitarian theology. Moreover, Antognazza makes a fine case for rereading Leibniz's metaphysics in light of his commitment to revealed theology: Although theological in origin, these Trinitarian debates were interwoven with many philosophical problems, such as the relationship between reason and revelation, knowledge and faith; the issue of the limits of human understanding, of the degrees of knowledge, and of the epistemological status of belief; the question of the scope and validity of the principle of noncontradiction; the reflection on the role and meaning of analogy; the inquiry into the concepts of 'nature,' 'substance,' and 'person'; and the theory of relations (xiii). Two conclusions emerge from Antognazza's survey of Leibniz's theological interests. On the one hand, she argues that Leibniz was "clearly convinced" that the doctrine...

Qubit Semantics and Quantum Trees

In the qubit semantics the meaning of any sentence α is represented by a quregister: a unit vector of the n–fold tensor product ⊗n ℂ2, where n depends on the number of occurrences of atomic sentences in α (see Cattaneo et al.). The logic characterized by this semantics, called quantum computational logic (QCL), is unsharp, because the noncontradiction principle is violated. We show that QCL does not admit any logical truth. In this framework, any sentence α gives rise to a quantum tree, consisting of a sequence of unitary operators. The quantum tree of α can be regarded as a quantum circuit that transforms the quregister associated to the occurrences of atomic subformulas of α into the quregister associated to α.

Aristotle on the Firmness of the Principle of Non-Contradiction

AbstractIn Metaphysics Gamma 3 Aristotle declares that the philosopher investigates things that are qua things that are and that he therefore should be able to state the firmest principles of everything. The firmest principle of all is identified as the principle of non-contradiction (PNC). The main focus of Gamma 3 is Aristotle's proof for this identification. This paper begins with remarks about Aristotle's notion of the firmness of a principle and then offers an analysis of the firmness proof for PNC. It focuses on some key assumptions of the proof and on the range and force of the proof. Aristotle closes Gamma 3 with the claim that PNC is ultimate in the sense that all other principles somehow rest on it. This, rather controversial, claim is given a defensible reading and shown to be central to the chapter's effort to establish PNC as the firmest principle of all. As such it completes the firmness proof and is not simply an appended remark.

A Curious Turn in Metaphysics Gamma: Protagoras and Strong Denial of the Principle of Non-Contradiction

A Curious Turn in Metaphysics Gamma: Protagoras and Strong Denial of the Principle of Non-Contradiction

On Partial and Paraconsistent Logics

In this paper we consider the theory of predicate logics in which the principle of bivalence or the principle of noncontradiction or both fail. Such logics are partial or paraconsistent or both. We consider sequent calculi for these logics and prove model existence. For $ \bf L_4$, the most general logic under consideration, we also prove a version of the Craig-Lyndon Interpolation Theorem. The paper shows that many techniques used for classical predicate logic generalize to partial and paraconsistent logics once the right setup is chosen. Our logic $ \bf L_4$ has a semantics that also underlies Belnap's logic and is related to the logic of bilattices. $ \bf L_4$ is in focus most of the time, but it is also shown how results obtained for $ \bf L_4$ can be transferred to several variants.

Robust Intelligibility: Response to Our Critics

Robust realism is defended by developing further the account in Inquiry 42 (1999), pp. 49-78 of how human beings make things and people intelligible. Incommensurate worlds imply a violation of the principle of noncontradiction, but this violation does not have the consequences normally feared. Given our capacities to make things intelligible, some things, like human action, are most intelligible when they are understood as contradictory (e.g. free and determined). Things-in-themselves need not have contradictory features for multiple orders of nature to make sense. We can coherently suppose that both Western and Chinese science give two incommensurable and complete accounts of the functioning of the human body. Since things do not have contradictory properties, we would then have to suppose that, in the case of bodies, there are two independent functional orders. If this can be true for bodies, it can be true for the orders of nature as a whole. John Haugeland's account of systems and interfaces shows us how to make sense of necessary functional components of the universe. Finally, multiple realism makes more sense than Rorty's deflationary pragmatism because it explains how things can matter.

The Principle of Non-Contradiction in Early Greek Philosophy

Analyse des formulations ontologiques et logiques du principe de non-contradiction dans la philosophie grecque antique de Parmenide a Aristote, en passant par Gorgias et Platon. Alors que Gorgias montre que la formulation de Parmenide non(ce qui n'est pas existe) (NC) est inconsistante avec la these G affirmant que ce qui n'est pas est ce qui n'est pas, en vertu du principe P selon lequel a est b implique a existe, l'A. montre que les quatre penseurs traitent de differentes facons de la meme triade inconsistante (NC, G, P)

The Scope of Aristotle’s Defense of the Principle of Non-contradiction

The Scope of Aristotle’s Defense of the Principle of Non-contradiction

How Nietzsche Explains and Why

How Nietzsche Explains and Why Daniel Touey It is very much a matter of debate whether we are experiencing the end of philosophy or, as others would rather say, simply enduring an aberrant period during which such extravagant claims are being inexplicably tolerated. This debate has been going on for some time now. It will generate additional inconclusive discourse as long as there are differing notions of what “philosophy” consists of, what it means to be doing it, and what it means not to be doing it. But I think that it is quite plausible that philosophy is changing its nature and that a whole group of philosophical questions has at least shifted in emphasis for our time. I would like to examine, in a speculative way, what seems to me to be a fundamental reorientation in how we ask philosophical questions and what sort of answers we expect to be able to give them. I will be mainly concerned with what may be roughly called the philosophy of explanation—with what, in our ongoing inquiries, we take to be shifting, problematic, obscure, and in need of explanation and what, in turn, we take to be stable, foundational, and known, which acts as the means through which we account for the former. But I would like also to touch upon a second aspect of this reorientation—the implications of our philosophy of explanation for an ongoing interpretive and critical assessment of society. In both of these exercises I will be relying on the philosophy of Nietzsche, who is one of those figures who announced the shift that I am claiming has overtaken philosophy and who continues to be a useful exemplar for our attempt to conceptualize it. The Structure of Explanation Aristotle makes a basic point about the structure of explanation or demonstration (apodeixis) in the Metaphysics while arguing for the priority of the principle of noncontradiction. Some thinkers demand a demonstration even of this principle, but they do so because they lack education; for it is a lack of education [End Page 485] [apaideusia] not to know of what things one should seek a demonstration and of what he should not. For, as a whole, a demonstration of everything is impossible, for the process would go on to infinity, so that even in this manner there would be no demonstration. 1 I take Aristotle’s meaning to be that in any demonstration, or explanation, we must take something as primary, as given and self-evident, before it can proceed. Elsewhere he says that the starting-point (arché) of an inquiry is “to hoti “—“the that” or the simple fact. Seeing its inherent validity is necessary for the inquiry to go on. 2 Aristotle believed that these primary assumptions which guided inquiry were not arbitrary, that they were rooted in the nature of things. But we do not have to hold that the metaphysical commitments which determine the basic structure of our inquiries are supported in such a way. Wittgenstein, who makes the same basic point about the need for privileging some things in order to make successful explanations, does not think that we have any absolute means for legitimating those choices. Can’t an assertoric sentence, which was capable of functioning as an hypothesis, also be used as a foundation for research and action? I.e. can’t it simply be isolated from doubt, though not according to any explicit rule? It simply gets assumed as a truism, never called in question, perhaps not even ever formulated. 3 Both Wittgenstein and Aristotle describe how the validity of those fundamental, operative assumptions, which cannot be demonstrated because they are means by which everything else is demonstrated, is established in practice. Aristotle says that the foundations of thought and discourse, like the principle of noncontradiction, can be doubted only in speech. Someone can make the pretense of denying them, but if we push hard enough we can show him that he is continually making use of those principles which he believes he is rejecting. 4 Of a fundamental truth Wittgenstein says that “everything speaks in its favor, nothing against it.” 5 Both suggest that we discover how deeply entrenched and indispensable...

God and the Principle of Non-Contradiction

Soulevant la question de savoir si Dieu, dans sa toute-puissance, peut refuter le principe de non-contradiction, l'A. mesure la possibilite de soutenir la these thomiste selon laquelle Dieu ne peut creer un etat de choses contradictoire, au regard des derniers developpements de la logique en matiere de calcul infinitesimal, de nombres transfinis et de traitement du paradoxe de Zenon. Examinant les arguments traditionnel et moderne de D. Goldstick, et distinguant le probleme d'une exception individuelle au principe de non-contradiction avec le probleme de la refutation du premier principe, l'A. montre que la these medievale d'un theologien naturel reste valable: Dieu ne peut considerer une contradiction comme vraie

Aristotle on ‘Signifying One’ atMetaphysicsΓ 4

I IntroductionAtMetaphysicsΓ 3, Aristotle argues that it belongs to a single discipline, which he callsfirst philosophy,to investigate both substance (οὐσία) and a special class of claims which includes among its members the principle of non-contradiction (PNC). At Γ 4, after insisting that the PNC is, strictly speaking, indemonstrable, he sets forth a series of sketches of refutative arguments intended to show how it can, nonetheless, be substantiated. Traditionally, his main refutative argument has been taken to be embedded in the passage which runs from 1006a31 tob34. In that passage, he tries to show that anyone who denies the PNC and who can then be led, by means of an artfully arranged series of questions, to agree (whether willingly or grudgingly) to a few seemingly modest theses about the signification of expressions of a certain type — which Aristotle illustrates with the general term ‘man’ (ἄνθρωπος) — is thereby logically committed to the following modal claim: ‘It is necessary, then, if it is true to say that something is a man, that it be a bipedal animal' (1006b28-30).

«Seny» and common sense in Jaume Balmes

The article deals with the common sense criteriology of the philosopher Balmes and its relationship with the Catalan conception of “seny”. Since it is a problem to explain the exact meaning of both “common sense” and “seny” in a philosophical sense we try to distinguish several possible meanings of both notions. Nevertheless, this is a large topic, therefore here it is studied in relationship with Balmesian philosophy. We begin by expounding Balmes' criteriology, where common sense is only one of three fundamental criteria of truth. Moreover, a first principle corresponds to each criterion. The criteria are 1) consciousness (first principle: the “cogito”), in whose scope all the interna1 facts of mind are included, 2) evidence, regulated by the principle of non contradiction, and 3) common sense or the natural tendency of our reason to the truth. However, this last notion is more complex and we need to distinguish its several meanings. Some of them are close to the notion of “seny”, a kind of practical wisdom. We conclude stating that in his early work Balmes conception of common sense was closer to the notion of “seny”, than in his Filosofia Funamental.

Aristotle’s Defence of the Principle of Non-Contradiction

L'A. expose sa propre interpretation de l'argumentation d'Aristote sur le principe de non-contradiction, apres avoir analyse les traductions et interpretations problematiques de Kirwan et Dancy

Gerardus Odonis O.F.M. on the Principle of Non-Contradiction and the Proper Nature of Demonstration

One of the most original works by the Franciscan Master Gerardus Odonis (Guiralt Ot) is the third part of his Logica , De principiis scientiarum.1 This treatise is not just a commentary on Aristotle's Posterior Analytics , nor is it a specialized treatment of its subject matter, which is demonstrative (or rather epistemonicla) knowledge, as is found in Ockham's Sum of Logic.2 Rather, Odonis took his treatise to be a supplement to the Aristotelian work, where the demonstrative principles proper to the different 'sciences' ( principia propria) as well as those they all have in common {principia communia) are extensively discussed by Aristotle, but less attention is paid to the most common principles of the intellect (principia communissima intellectus ), such as the twofold principle of noncontradiction.3 What Odonis means to do, then, is to discuss the