Pluralism in Mathematics: A New Position in Philosophy of Mathematics

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Author: Michèle Friend

Publisher: Springer Science & Business Media

ISBN: 9400770588

Category: Science

Page: 291

View: 759

This book is about philosophy, mathematics and logic, giving a philosophical account of Pluralism which is a family of positions in the philosophy of mathematics. There are four parts to this book, beginning with a look at motivations for Pluralism by way of Realism, Maddy’s Naturalism, Shapiro’s Structuralism and Formalism. In the second part of this book the author covers: the philosophical presentation of Pluralism; using a formal theory of logic metaphorically; rigour and proof for the Pluralist; and mathematical fixtures. In the third part the author goes on to focus on the transcendental presentation of Pluralism, and in part four looks at applications of Pluralism, such as a Pluralist approach to proof in mathematics and how Pluralism works in regard to together-inconsistent philosophies of mathematics. The book finishes with suggestions for further Pluralist enquiry. In this work the author takes a deeply radical approach in developing a new position that will either convert readers, or act as a strong warning to treat the word ‘pluralism’ with care.

Foundations of Logical Consequence

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Author: Colin R. Caret,Ole T. Hjortland

Publisher: Oxford University Press, USA

ISBN: 0198715692

Category: Consequentia (Logic)

Page: 357

View: 2104

This volume presents new work on a central issue in the philosophy of logic. Leading figures in the field offer ground-breaking insights into topics including the nature of logical consequence; the relation between logic and inference; the relativity of logic; and the structural properties of the consequence relation.

The Metaphysics of Logic

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Author: Penelope Rush

Publisher: Cambridge University Press

ISBN: 1316148017

Category: Philosophy

Page: N.A

View: 5231

Featuring fourteen new essays from an international team of renowned contributors, this volume explores the key issues, debates and questions in the metaphysics of logic. The book is structured in three parts, looking first at the main positions in the nature of logic, such as realism, pluralism, relativism, objectivity, nihilism, conceptualism, and conventionalism, then focusing on historical topics such as the medieval Aristotelian view of logic, the problem of universals, and Bolzano's logical realism. The final section tackles specific issues such as glutty theories, contradiction, the metaphysical conception of logical truth, and the possible revision of logic. The volume will provide readers with a rich and wide-ranging survey, a valuable digest of the many views in this area, and a long overdue investigation of logic's relationship to us and the world. It will be of interest to a wide range of scholars and students of philosophy, logic, and mathematics.

Inconsistent Geometry

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Author: Chris Mortensen

Publisher: N.A

ISBN: 9781848900226

Category: Mathematics

Page: 174

View: 1633

The Theory of Inconsistency has a long lineage, stretching back to Herakleitos, Hegel and Marx. In the late twentieth-century, it was placed on a rigorous footing with the discovery of paraconsistent logic and inconsistent mathematics. Paraconsistent logics, many of which are now known, are "inconsistency tolerant," that is, they lack the rule of Boolean logic that a contradiction implies every proposition. When this constricting rule was seen to be arbitrary, inconsistent mathematical structures were free to be described. This book continues the development of inconsistent mathematics by taking up inconsistent geometry, hitherto largely undeveloped. It has two main goals. First, various geometrical structures are shown to deliver models for paraconsistent logics. Second, the "impossible pictures" of Reutersvaard, Escher, the Penroses and others are addressed. The idea is to derive inconsistent mathematical descriptions of the content of impossible pictures, so as to explain rigorously how they can be impossible and yet classifiable into several basic types. The book will be of interest to logicians, mathematicians, philosophers, psychologists, cognitive scientists, and artists interested in impossible images. It contains a gallery of previously-unseen coloured images, which illustrates the possibilities available in representing impossible geometrical shapes. Chris Mortensen is Emeritus Professor of Philosophy at the University of Adelaide. He is the author of Inconsistent Mathrmatics (Kluwer 1995), and many articles in the Theory of Inconsistency.

Varieties of Logic

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Author: Stewart Shapiro

Publisher: OUP Oxford

ISBN: 0191025518

Category: Philosophy

Page: 240

View: 4750

Logical pluralism is the view that different logics are equally appropriate, or equally correct. Logical relativism is a pluralism according to which validity and logical consequence are relative to something. In Varieties of Logic, Stewart Shapiro develops several ways in which one can be a pluralist or relativist about logic. One of these is an extended argument that words and phrases like 'valid' and 'logical consequence' are polysemous or, perhaps better, are cluster concepts. The notions can be sharpened in various ways. This explains away the 'debates' in the literature between inferentialists and advocates of a truth-conditional, model-theoretic approach, and between those who advocate higher-order logic and those who insist that logic is first-order. A significant kind of pluralism flows from an orientation toward mathematics that emerged toward the end of the nineteenth century, and continues to dominate the field today. The theme is that consistency is the only legitimate criterion for a theory. Logical pluralism arises when one considers a number of interesting and important mathematical theories that invoke a non-classical logic, and are rendered inconsistent, and trivial, if classical logic is imposed. So validity is relative to a theory or structure. The perspective raises a host of important questions about meaning. The most significant of these concern the semantic content of logical terminology, words like 'or', 'not', and 'for all', as they occur in rigorous mathematical deduction. Does the intuitionistic 'not', for example, have the same meaning as its classical counterpart? Shapiro examines the major arguments on the issue, on both sides, and finds them all wanting. He then articulates and defends a thesis that the question of meaning-shift is itself context-sensitive and, indeed, interest-relative. He relates the issue to some prominent considerations concerning open texture, vagueness, and verbal disputes. Logic is ubiquitous. Whenever there is deductive reasoning, there is logic. So there are questions about logical pluralism that are analogous to standard questions about global relativism. The most pressing of these concerns foundational studies, wherein one compares theories, sometimes with different logics, and where one figures out what follows from what in a given logic. Shapiro shows that the issues are not problematic, and that is usually easy to keep track of the logic being used and the one mentioned.

The Legacy of Mario Pieri in Geometry and Arithmetic

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Author: Elena Anne Marchisotto,James T. Smith

Publisher: Springer Science & Business Media

ISBN: 9780817646035

Category: Mathematics

Page: 494

View: 8879

This book is the first in a series of three volumes that comprehensively examine Mario Pieri’s life, mathematical work and influence. The book introduces readers to Pieri’s career and his studies in foundations, from both historical and modern viewpoints. Included in this volume are the first English translations, along with analyses, of two of his most important axiomatizations — one in arithmetic and one in geometry. The book combines an engaging exposition, little-known historical notes, exhaustive references and an excellent index. And yet the book requires no specialized experience in mathematical logic or the foundations of geometry.

Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems

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Author: Guanrong Chen,Trung Tat Pham

Publisher: CRC Press

ISBN: 9781420039818

Category: Mathematics

Page: 328

View: 5371

In the early 1970s, fuzzy systems and fuzzy control theories added a new dimension to control systems engineering. From its beginnings as mostly heuristic and somewhat ad hoc, more recent and rigorous approaches to fuzzy control theory have helped make it an integral part of modern control theory and produced many exciting results. Yesterday's "art" of building a working fuzzy controller has turned into today's "science" of systematic design. To keep pace with and further advance the rapidly developing field of applied control technologies, engineers, both present and future, need some systematic training in the analytic theory and rigorous design of fuzzy control systems. Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems provides that training by introducing a rigorous and complete fundamental theory of fuzzy sets and fuzzy logic, and then building a practical theory for automatic control of uncertain and ill-modeled systems encountered in many engineering applications. The authors proceed through basic fuzzy mathematics and fuzzy systems theory and conclude with an exploration of some industrial application examples. Almost entirely self-contained, Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems establishes a strong foundation for designing and analyzing fuzzy control systems under uncertain and irregular conditions. Mastering its contents gives students a clear understanding of fuzzy control systems theory that prepares them for deeper and broader studies and for many practical challenges faced in modern industry.

Studies and Exercises in Formal Logic

Including a Generalisation of Logical Processes in Their Application to Complex Inferences

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Author: John Neville Keynes

Publisher: N.A

ISBN: N.A

Category: Logic

Page: 455

View: 6018

Computer Algebra in Scientific Computing

CASC '99 : Proceedings of the Second Workshop on Computer Algebra in Scientific Computing, Munich, May 31-June 4, 1999

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Author: Victor Grigorʹevich Ganzha,Ernst Mayr,Evgenii Vasilʹevich Vorozhtsov

Publisher: Springer Verlag

ISBN: 9783540660477

Category: Mathematics

Page: 509

View: 8033

This book contains papers submitted by the participants of the workshop on Computer Algebra in Scientific Computing CASC '99, as well as two invited papers. The collection of papers included in the proceedings covers various topics of computer algebra methods, algorithms and software applied to scientific computing. Moreover, applications of computer algebra methods for the solution of current problems in group theory are treated, which mostly arise in mathematical physics. Another important trend which may be seen from the present collection of papers is the application of computer algebra methods to the development of new efficient analytic and numerical solvers, both for ordinary and partial differential equations. Some papers deal with algorithmic and software aspects associated with the implementation of computer algebra methods, or study the stability of satellite and mechanical systems, or the application of computer algebra to the solution of problems in technology.

New Directions in Paraconsistent Logic

5th WCP, Kolkata, India, February 2014

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Author: Jean-Yves Beziau,Mihir Chakraborty,Soma Dutta

Publisher: Springer

ISBN: 8132227190

Category: Mathematics

Page: 552

View: 5486

The present book discusses all aspects of paraconsistent logic, including the latest findings, and its various systems. It includes papers by leading international researchers, which address the subject in many different ways: development of abstract paraconsistent systems and new theorems about them; studies of the connections between these systems and other non-classical logics, such as non-monotonic, many-valued, relevant, paracomplete and fuzzy logics; philosophical interpretations of these constructions; and applications to other sciences, in particular quantum physics and mathematics. Reasoning with contradictions is the challenge of paraconsistent logic. The book will be of interest to graduate students and researchers working in mathematical logic, computer science, philosophical logic, linguistics and physics.

Turkish Studies in the History and Philosophy of Science

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Author: G. Irzik,Güven Güzeldere

Publisher: Springer

ISBN: 9781402033322

Category: Science

Page: 308

View: 585

As an academic discipline, the philosophy and history of science in Turkey was marked by two historical events: Hans Reichenbach's immigrating to Turkey and taking a post between 1933 and 1938 at Istanbul University prior to his tenure at UCLA, and Aydin Sayili's establishing a chair in the history of science in 1952 after having become the first student to receive a Ph.D. under George Sarton at Harvard University. Since then, both disciplines have flourished in Turkey. The present book, which contains seventeen newly commissioned articles, aims to give a rich overview of the current state of research by Turkish philosophers and historians of science. Topics covered address issues in methodology, causation, and reduction, and include philosophy of logic and physics, philosophy of psychology and language, and Ottoman science studies. The book also contains an unpublished interview with Maria Reichenbach, Hans Reichenbach's wife, which sheds new light on Reichenbach's academic and personal life in Istanbul and at UCLA.

Differentialgeometrie, Topologie und Physik

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Author: Mikio Nakahara

Publisher: Springer-Verlag

ISBN: 3662453002

Category: Science

Page: 597

View: 5264

Differentialgeometrie und Topologie sind wichtige Werkzeuge für die Theoretische Physik. Insbesondere finden sie Anwendung in den Gebieten der Astrophysik, der Teilchen- und Festkörperphysik. Das vorliegende beliebte Buch, das nun erstmals ins Deutsche übersetzt wurde, ist eine ideale Einführung für Masterstudenten und Forscher im Bereich der theoretischen und mathematischen Physik. - Im ersten Kapitel bietet das Buch einen Überblick über die Pfadintegralmethode und Eichtheorien. - Kapitel 2 beschäftigt sich mit den mathematischen Grundlagen von Abbildungen, Vektorräumen und der Topologie. - Die folgenden Kapitel beschäftigen sich mit fortgeschritteneren Konzepten der Geometrie und Topologie und diskutieren auch deren Anwendungen im Bereich der Flüssigkristalle, bei suprafluidem Helium, in der ART und der bosonischen Stringtheorie. - Daran anschließend findet eine Zusammenführung von Geometrie und Topologie statt: es geht um Faserbündel, characteristische Klassen und Indextheoreme (u.a. in Anwendung auf die supersymmetrische Quantenmechanik). - Die letzten beiden Kapitel widmen sich der spannendsten Anwendung von Geometrie und Topologie in der modernen Physik, nämlich den Eichfeldtheorien und der Analyse der Polakov'schen bosonischen Stringtheorie aus einer gemetrischen Perspektive. Mikio Nakahara studierte an der Universität Kyoto und am King’s in London Physik sowie klassische und Quantengravitationstheorie. Heute ist er Physikprofessor an der Kinki-Universität in Osaka (Japan), wo er u. a. über topologische Quantencomputer forscht. Diese Buch entstand aus einer Vorlesung, die er während Forschungsaufenthalten an der University of Sussex und an der Helsinki University of Sussex gehalten hat.

Perspectives in Philosophy

Indo-Bulgarian Philosophical Studies

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Author: Rasik Vihari Joshi

Publisher: N.A

ISBN: N.A

Category: Filosofía búlgara

Page: 432

View: 8951

Assumptions of Grand Logics

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Author: J.K. Feibleman

Publisher: Springer Science & Business Media

ISBN: 9400992785

Category: Philosophy

Page: 283

View: 7701

A system of philosophy of the sort presented in this and the following volumes begins with logic. Philosophy properly speaking is characterized by the kind oflogic it employs, for what it employs it assumes, however silently; and what it assumes it presupposes. The logic stands behind the ontology and is, so to speak, metaphysically prior. One word of caution. The philosophical aspects of logic have lagged behind the mathematical aspects in point of view of interest and develop ment. The work of N. Rescher and others have gone a long way to correct this. However, their work on philosophical logic has been more concerned with the logical than with the philosophical aspects. I have in mind another approach, one that would call attention to the ontological (systematic meta physics) or metaphysical (critical ontology) aspects, whichever term you prefer. It is this approach which I have pursued in the following chapters. Since together they stand at the head of a system of philosophy which has been developed in some seventeen books, a system which ranges over all of the topics of philosophy, the chosen approach can be seen as the necessary one. But I have not written any logic, I have merely indicated the sort of logic that has to be written.

Engineering Optics

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Author: CTI Reviews

Publisher: Cram101 Textbook Reviews

ISBN: 146725925X

Category: Education

Page: 52

View: 3617

Facts101 is your complete guide to Engineering Optics. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

Kant-Studien

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Author: Hans Vaihinger,Max Scheler,Bruno Bauch,Max Frischeisen-Köhler,Arthur Liebert,Paul Menzer

Publisher: N.A

ISBN: N.A

Category:

Page: N.A

View: 1568

1904-26 (includes lists of members)