Download or read book Contradictions from Consistency to Inconsistency written by Walter Carnielli and published by Springer. This book was released on 2018-10-13 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume investigates what is beyond the Principle of Non-Contradiction. It features 14 papers on the foundations of reasoning, including logical systems and philosophical considerations. Coverage brings together a cluster of issues centered upon the variety of meanings of consistency, contradiction, and related notions. Most of the papers, but not all, are developed around the subtle distinctions between consistency and non-contradiction, as well as among contradiction, inconsistency, and triviality, and concern one of the above mentioned threads of the broadly understood non-contradiction principle and the related principle of explosion. Some others take a perspective that is not too far away from such themes, but with the freedom to tread new paths. Readers should understand the title of this book in a broad way,because it is not so obvious to deal with notions like contradictions, consistency, inconsistency, and triviality. The papers collected here present groundbreaking ideas related to consistency and inconsistency.
Download or read book Contradictions from Consistency to Inconsistency written by Walter Alexandre Carnielli and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume investigates what is beyond the Principle of Non-Contradiction. It features 13 papers on the foundations of reasoning, including logical systems and philosophical considerations. Coverage brings together a cluster of issues centered upon the variety of meanings of consistency, contradiction, and related notions. Most of the papers, but not all, are developed around the subtle distinctions between consistency and non-contradiction, as well as among contradiction, inconsistency, and triviality, and concern one of the above mentioned threads of the broadly understood non-contradiction principle and the related principle of explosion. Some others take a perspective that is not too far away from such themes, but with the freedom to tread new paths. Readers should understand the title of this book in a broad way,because it is not so obvious to deal with notions like contradictions, consistency, inconsistency, and triviality. The papers collected here present groundbreaking ideas related to consistency and inconsistency.--
Download or read book Paraconsistent Logic Consistency Contradiction and Negation written by Walter Carnielli and published by Springer. This book was released on 2016-06-14 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical theory and offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative achievements in contemporary logic, with deep roots in philosophical questions involving negation and consistency This book offers an invaluable introduction to a topic of central importance in logic and philosophy. It discusses (i) the history of paraconsistent logic; (ii) language, negation, contradiction, consistency and inconsistency; (iii) logics of formal inconsistency (LFIs) and the main paraconsistent propositional systems; (iv) many-valued companions, possible-translations semantics and non-deterministic semantics; (v) paraconsistent modal logics; (vi) first-order paraconsistent logics; (vii) applications to information processing, databases and quantum computation; and (viii) applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning.
Download or read book Logic Epistemology and the Unity of Science written by Shahid Rahman and published by Springer Science & Business Media. This book was released on 2009-03-15 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first volume in this new series explores, through extensive co-operation, new ways of achieving the integration of science in all its diversity. The book offers essays from important and influential philosophers in contemporary philosophy, discussing a range of topics from philosophy of science to epistemology, philosophy of logic and game theoretical approaches. It will be of interest to philosophers, computer scientists and all others interested in the scientific rationality.
Download or read book Trends in Logic written by Vincent F. Hendricks and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1953, exactly 50 years ago to this day, the first volume of Studia Logica appeared under the auspices of The Philosophical Committee of The Polish Academy of Sciences. Now, five decades later the present volume is dedicated to a celebration of this 50th Anniversary of Studia Logica. The volume features a series of papers by distinguished scholars reflecting both the aim and scope of this journal for symbolic logic.
Download or read book How to Sell a Contradiction written by Francesco Berto and published by . This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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].
Download or read book In Contradiction written by Graham Priest and published by Oxford University Press, USA. This book was released on 2006-02-16 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Doubt Truth to be a Liar written by Graham Priest and published by Oxford University Press. This book was released on 2006 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book is required reading for anyone who wishes to understand dialetheism; (especially) for anyone who wishes to continue to endorse the old Aristotelian orthodoxy; and, more generally, for anyone who wishes to understand the role that contradiction plays in our thinking."--BOOK JACKET.
Download or read book Predicative Arithmetic MN 32 written by Edward Nelson and published by Princeton University Press. This book was released on 2014-07-14 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book The Law of Non Contradiction written by Graham Priest and published by Clarendon Press. This book was released on 2006-11-30 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Yablo Paradox written by Roy T Cook and published by OUP Oxford. This book was released on 2014-05-29 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Roy T Cook examines the Yablo paradox—a paradoxical, infinite sequence of sentences, each of which entails the falsity of all others later than it in the sequence—with special attention paid to the idea that this paradox provides us with a semantic paradox that involves no circularity. The three main chapters of the book focus, respectively, on three questions that can be (and have been) asked about the Yablo construction. First we have the Characterization Problem, which asks what patterns of sentential reference (circular or not) generate semantic paradoxes. Addressing this problem requires an interesting and fruitful detour through the theory of directed graphs, allowing us to draw interesting connections between philosophical problems and purely mathematical ones. Next is the Circularity Question, which addresses whether or not the Yablo paradox is genuinely non-circular. Answering this question is complicated: although the original formulation of the Yablo paradox is circular, it turns out that it is not circular in any sense that can bear the blame for the paradox. Further, formulations of the paradox using infinitary conjunction provide genuinely non-circular constructions. Finally, Cook turns his attention to the Generalizability Question: can the Yabloesque pattern be used to generate genuinely non-circular variants of other paradoxes, such as epistemic and set-theoretic paradoxes? Cook argues that although there are general constructions-unwindings—that transform circular constructions into Yablo-like sequences, it turns out that these sorts of constructions are not 'well-behaved' when transferred from semantic puzzles to puzzles of other sorts. He concludes with a short discussion of the connections between the Yablo paradox and the Curry paradox.
Download or read book Inconsistency Tolerance written by Leopoldo Bertossi and published by Springer Science & Business Media. This book was released on 2004 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inconsistency arises in many areas in advanced computing. Often inconsistency is unwanted, for example in the specification for a plan or in sensor fusion in robotics; however, sometimes inconsistency is useful. Whether inconsistency is unwanted or useful, there is a need to develop tolerance to inconsistency in application technologies such as databases, knowledge bases, and software systems. To address this situation, inconsistency tolerance is being built on foundational technologies for identifying and analyzing inconsistency in information, for representing and reasoning with inconsistent information, for resolving inconsistent information, and for merging inconsistent information. The idea for this book arose out of a Dagstuhl Seminar on the topic held in summer 2003. The nine chapters in this first book devoted to the subject of inconsistency tolerance were carefully invited and anonymously reviewed. The book provides an exciting introduction to this new field.
Download or read book Graham Priest on Dialetheism and Paraconsistency written by Can Başkent and published by Springer Nature. This book was released on 2020-01-01 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state of the art in the fields of formal logic pioneered by Graham Priest. It includes advanced technical work on the model and proof theories of paraconsistent logic, in contributions from top scholars in the field. Graham Priest’s research has had a considerable influence on the field of philosophical logic, especially with respect to the themes of dialetheism—the thesis that there exist true but inconsistent sentences—and paraconsistency—an account of deduction in which contradictory premises do not entail the truth of arbitrary sentences. Priest’s work has regularly challenged researchers to reappraise many assumptions about rationality, ontology, and truth. This book collects original research by some of the most esteemed scholars working in philosophical logic, whose contributions explore and appraise Priest’s work on logical approaches to problems in philosophy, linguistics, computation, and mathematics. They provide fresh analyses, critiques, and applications of Priest’s work and attest to its continued relevance and topicality. The book also includes Priest’s responses to the contributors, providing a further layer to the development of these themes .
Download or read book Inconsistent Mathematics written by C.E. Mortensen and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: without a properly developed inconsistent calculus based on infinitesimals, then in consistent claims from the history of the calculus might well simply be symptoms of confusion. This is addressed in Chapter 5. It is further argued that mathematics has a certain primacy over logic, in that paraconsistent or relevant logics have to be based on inconsistent mathematics. If the latter turns out to be reasonably rich then paraconsistentism is vindicated; while if inconsistent mathematics has seri ous restriytions then the case for being interested in inconsistency-tolerant logics is weakened. (On such restrictions, see this chapter, section 3. ) It must be conceded that fault-tolerant computer programming (e. g. Chapter 8) finds a substantial and important use for paraconsistent logics, albeit with an epistemological motivation (see this chapter, section 3). But even here it should be noted that if inconsistent mathematics turned out to be functionally impoverished then so would inconsistent databases. 2. Summary In Chapter 2, Meyer's results on relevant arithmetic are set out, and his view that they have a bearing on G8del's incompleteness theorems is discussed. Model theory for nonclassical logics is also set out so as to be able to show that the inconsistency of inconsistent theories can be controlled or limited, but in this book model theory is kept in the background as much as possible. This is then used to study the functional properties of various equational number theories.
Download or read book Emancipation After Hegel written by Todd McGowan and published by Columbia University Press. This book was released on 2019-05-28 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hegel is making a comeback. After the decline of the Marxist Hegelianism that dominated the twentieth century, leading thinkers are rediscovering Hegel’s thought as a resource for contemporary politics. What does a notoriously difficult nineteenth-century German philosopher have to offer the present? How should we understand Hegel, and what does understanding Hegel teach us about confronting our most urgent challenges? In this book, Todd McGowan offers us a Hegel for the twenty-first century. Simultaneously an introduction to Hegel and a fundamental reimagining of Hegel’s project, Emancipation After Hegel presents a radical Hegel who speaks to a world overwhelmed by right-wing populism, authoritarianism, neoliberalism, and economic inequalities. McGowan argues that the revolutionary core of Hegel’s thought is contradiction. He reveals that contradiction is inexorable and that we must attempt to sustain it rather than overcoming it or dismissing it as a logical failure. McGowan contends that Hegel’s notion of contradiction, when applied to contemporary problems, challenges any assertion of unitary identity as every identity is in tension with itself and dependent on others. An accessible and compelling reinterpretation of an often-misunderstood thinker, this book shows us a way forward to a new politics of emancipation as we reconcile ourselves to the inevitability of contradiction and find solidarity in not belonging.
Download or read book Handbook of Paraconsistency written by Jean-Yves Béziau and published by . This book was released on 2007 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paraconsistent logics are logics which allow solid deductive reasoning under contradictions by offering a mathematical and philosophical support to contradictory yet non-trivial theories. Due to its role in models of scientific reasoning and to its philosophical implications, as well as to its connections to topics such as abduction, automated reasoning, logic programming, and belief revision, paraconsistency has becoming a fast growing area. During the III World Congress on Paraconsistency (WCP3) held in Toulouse, France, in July, 2003, it became apparent that there is a need for a Handbook covering the most recent results on several aspects of paraconsistent logic, including philosophical debates on paraconsistency and its connections to philosophy of language, argumentation theory, computer science, information theory, and artificial intelligence. This book is a basic tool for those who want to know more about paraconsistent logic, its history and philosophy, the various systems of paraconsistent logic and their applications. The present volume is edited by Jean-Yves Beziau, Walter Carnielli and Dov Gabbay, expert logicians versed in a variety of logics.
Download or read book Complexity and Contradiction in Architecture written by Robert Venturi and published by The Museum of Modern Art. This book was released on 1977 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foreword by Arthur Drexler. Introduction by Vincent Scully.
