The Law of Non-Contradiction
The Law of Non-Contradiction

Author: Graham Priest

Publisher: Clarendon Press

Published: 2006-11-30

Total Pages: 456

ISBN-13: 0191548065

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The Law of Non-Contradiction-that no contradiction can be true-has been a seemingly unassailable dogma since the work of Aristotle, in Book Gamma of the Metaphysics. It is an assumption challenged from a variety of angles in this collection of original papers. Twenty-three of the world's leading experts investigate the 'law', considering arguments for and against it and discussing methodological issues that arise whenever we question the legitimacy of logical principles. The result is a balanced inquiry into a venerable principle of logic, one that raises questions at the very centre of logic itself. The aim of this volume is to present a comprehensive debate about the Law of Non-Contradiction, from discussions as to how the law is to be understood, to reasons for accepting or re-thinking the law, and to issues that raise challenges to the law, such as the Liar Paradox, and a 'dialetheic' resolution of that paradox. One of the editors contributes an introduction which surveys the issues and serves to frame the debate. This collection will be of interest to anyone working on philosophical logic, and to anyone who has ever wondered about the status of logical laws and about how one might proceed to mount arguments for or against them.

The Law of Non-contradiction
The Law of Non-contradiction

Author: Graham Priest

Publisher: Oxford University Press

Published: 2004

Total Pages: 474

ISBN-13: 9780199265176

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This book presents a comprehensive debate about the Law of Non-Contradiction (LNC), from discussions as to how the law is to be understood, to reasons for accepting or re-thinking the law, and to issues that raise challenges to the law, such as the Liar Paradox, and a 'dialetheic' resolution of that paradox.

The Law of Non-contradiction
The Law of Non-contradiction

Author: Graham Priest

Publisher:

Published: 2006

Total Pages: 0

ISBN-13: 9780199204199

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The Law of Non-Contradiction -- that no contradiction can be true -- has been a seemingly unassailable dogma since the work of Aristotle, in Book G of the Metaphysics. It is an assumption challenged from a variety of angles in this collection of original papers. Twenty-three of the world's leading experts investigate the "law," considering arguments for and against it and discussing methodological issues that arise whenever we question the legitimacy of logical principles. The result is a balanced inquiry into a venerable principle of logic, one that raises questions at the very center of logic itself. The aim of this volume is to present a comprehensive debate about the Law of Non-Contradiction, from discussions as to how the law is to be understood, to reasons for accepting or re-thinking the law, and to issues that raise challenges to the law, such as the Liar Paradox, and a "dialetheic" resolution of that paradox. The editors contribute an introduction which surveys the issues and serves to frame the debate, and a useful bibliography offering a guide to further reading. This volume will be of interest to anyone working on philosophical logic, and to anyone who has ever wondered about the status of logical laws and about how one might proceed to mount arguments for or against them.

The Principle of Non-contradiction in Plato's Republic
The Principle of Non-contradiction in Plato's Republic

Author: Laurence Bloom

Publisher: Lexington Books

Published: 2017-03-08

Total Pages: 273

ISBN-13: 0739190245

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Plato’s formulation of the Principle of Non-contradiction (PNC) in Republic IV is the first full statement of the principle in western philosophy. His use of the principle might seem to suggest that he endorses the PNC. After all, how could one possibly deny so fundamental a principle—especially when it seems difficult to deny it without relying on it. However, the endorsement in the text is qualified. Socrates refers to the principle as one that he and his interlocutors will hypothesize and warns that if it should ever be shown to be false, all that follows from it will also be refuted. Scholars who have noticed this issue have tended to assume that the truth of the hypothesis in question can be guaranteed. Laurence Bloom argues against unthinkingly accepting this claim. He suggests that what emerges from the text is more sophisticated: Plato’s concession that the PNC is hypothetical is a textual clue pointing us to a complex philosophical argument that grounds the PNC, as well as the sort of reasoning it grounds, in form. Indeed, in framing the problem in this way, we can read the Republic as providing an extended argument for form. The argument for forms that emerges is complex and difficult. It is not and cannot be a normal, discursive argument. Indeed, the argument cannot even be one that assumes the PNC; if it did so, it would fall prey to a vicious circularity. Rather, the argument rests on the very possibility of our hypothesizing the PNC in the first place. Our ability to hypothesize the PNC—and perhaps our inability not to hypothesize it—is the linchpin. When we ask questions such as “to what objects does the PNC apply?” or “how is it possible that we apply the PNC?,” we are asking questions that lead us to the existence of form. The Principle of Non-contradiction in Plato’s Republic also explores the soul of the knower—the very entity to which and by which the principle is applied in the text—and its underlying unity.

How to Sell a Contradiction
How to Sell a Contradiction

Author: Francesco Berto

Publisher:

Published: 2007

Total Pages: 0

ISBN-13: 9781904987437

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"There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the truth - viz. that the same thing cannot at one and the same time be and not be" with these words of the Metaphysics, Aristotle introduced the Law of Non-Contradiction, which was to become the most authoritative principle in the history of Western thought. However, things have recently changed, and nowadays various philosophers, called dialetheists, claim that this Law does not hold unrestrictedly - that in peculiar circumstances the same thing may at the same time be and not be, and contradictions may obtain in the world. This book opens with an examination of the famous logical paradoxes that appear to speak on behalf of contradictions (e.g., the Liar paradox, the set-theoretic paradoxes such as Cantor's and Russell's), and of the reasons for the failure of the standard attempts to solve them. It provides, then, an introduction to paraconsistent logics - non-classical logics in which the admission of contradictions does not lead to logical chaos -, and their astonishing applications, going from inconsistent data base management to contradictory arithmetics capable of circumventing Gödel's celebrated Incompleteness Theorem. The final part of the book discusses the philosophical motivations and difficulties of dialetheism, and shows how to extract from Aristotle's ancient words a possible reply to the dialetheic challenge. How to Sell a Contradiction will appeal to anyone interested in non-classical logics, analytic metaphysics, and philosophy of mathematics, and especially to those who consider challenging our most entrenched beliefs the main duty of philosophical inquiry. Francesco Berto is Lecturer in Logic and Metaphysics at the University of Venice, Italy. He has published articles in American Philosophical Quarterly, The Australasian Journal of Philosophy, Dialectica, Logique et Analyse, The European Journal of Philosophy, and the books La dialettica della struttura originaria [The Dialectics of the Basic Structure, Padua 2003], Che cos'è la dialettica hegeliana [What is Hegel's Dialectics?, Padua 2005], Teorie dell'assurdo [Theories of the Absurd, Rome 2006] and Logica da zero a Gödel [Logic, from Zero to Gödel, Rome 2007].

The Principle of Contradiction
The Principle of Contradiction

Author: Edward Conze

Publisher: Lexington Books

Published: 2016-09-30

Total Pages: 560

ISBN-13: 1498540147

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Conze’s monograph The Principle of Contradiction: On the Theory of Dialectical Materialism is his most important philosophical work and the foundation for his later publications as a Buddhist scholar and translator. The openly Marxist work was published under considerable risk to both printer and author alike in December 1932 in Hamburg, Germany. Only months later, in May 1933, almost all of the five hundred copies of the first edition were destroyed during the Nazi book burning campaign. It is only now, more than eighty years later, that Conze’s key philosophical work is made available to a broad audience in this English translation. In the work, Conze sets out to develop a detailed account of the historical and material conditions that support the emergence, production, and transmission of theoretical knowledge—as exemplified by the principle of contradiction—and, furthermore, to show that under different social and historical conditions the allegedly necessary truth and indubitable content of the principle would dissolve and be replaced by a radically different understanding of the principle of contradiction—a dialectic understanding of the principle that would compel a rejection of the Aristotelian dogma. From a Marxist perspective, the analysis and critique of the principle of contradiction is a crucial and necessary step towards a dialectical understanding of philosophical (and political) theory and practice. Conze’s monograph, which attempts to clear the ground for a deeper understanding of the very foundation of classical Marxist thought, may very well be the most comprehensive Marxist critique of the Aristotelian principle of contradiction available to this day. However, Conze’s pioneering 1932 monograph goes well beyond the constraints of an orthodox Marxist analysis. His erudite and scholarly 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.

In Contradiction
In Contradiction

Author: Graham Priest

Publisher: Oxford University Press, USA

Published: 2006-02-16

Total Pages: 351

ISBN-13: 0199263299

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Priest advocates and defends the view that there are true contradictions (dialetheism), a perspective that flies in the face of orthodoxy in Western philosophy since Aristole and remains at the centre of philosophical debate. This edition contains the author's reflections on developments since 1987.

Putting Logic in Its Place
Putting Logic in Its Place

Author: David Christensen

Publisher: Oxford University Press

Published: 2004-11-04

Total Pages: 200

ISBN-13: 0199263256

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What role, if any, does formal logic play in characterizing epistemically rational belief? Traditionally, belief is seen in a binary way - either one believes a proposition, or one doesn't. Given this picture, it is attractive to impose certain deductive constraints on rational belief: that one's beliefs be logically consistent, and that one believe the logical consequences of one's beliefs. A less popular picture sees belief as a graded phenomenon. This picture (explored more bydecision-theorists and philosophers of science thatn by mainstream epistemologists) invites the use of probabilistic coherence to constrain rational belief. But this latter project has often involved defining graded beliefs in terms of preferences, which may seem to change the subject away fromepistemic rationality.Putting Logic in its Place explores the relations between these two ways of seeing beliefs. It argues that the binary conception, although it fits nicely with much of our commonsense thought and talk about belief, cannot in the end support the traditional deductive constraints on rational belief. Binary beliefs that obeyed these constraints could not answer to anything like our intuitive notion of epistemic rationality, and would end up having to be divorced from central aspects of ourcognitive, practical, and emotional lives.But this does not mean that logic plays no role in rationality. Probabilistic coherence should be viewed as using standard logic to constrain rational graded belief. This probabilistic constraint helps explain the appeal of the traditional deductive constraints, and even underlies the force of rationally persuasive deductive arguments. Graded belief cannot be defined in terms of preferences. But probabilistic coherence may be defended without positing definitional connections between beliefsand preferences. Like the traditional deductive constraints, coherence is a logical ideal that humans cannot fully attain. Nevertheless, it furnishes a compelling way of understanding a key dimension of epistemic rationality.

The Book of Non-Contradiction
The Book of Non-Contradiction

Author: Phillip Campbell

Publisher: Createspace Independent Publishing Platform

Published: 2017-02-04

Total Pages: 202

ISBN-13: 9781542947145

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"The Book of Non-Contradiction: Harmonizing the Scriptures", by Phillip Campbell reintroduces the classical method of harmonizing difficult scriptural passages, showing how the skeptics' claim of a "Bible full of contradictions" is completely unfounded. Proceeding from the axiom that truth cannot contradict truth, "The Book of Non-Contradiction" follows in the footsteps of great Catholic exegetes like St. Augustine and Tatian who demonstrated the harmony of the Scriptural narrative.