Inconsistent Geometry


Author: Chris Mortensen

Publisher: N.A

ISBN: 9781848900226

Category: Mathematics

Page: 174

View: 7108

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.

Pluralism in Mathematics: A New Position in Philosophy of Mathematics


Author: Michèle Friend

Publisher: Springer Science & Business Media

ISBN: 9400770588

Category: Science

Page: 291

View: 3876

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


Author: Colin R. Caret,Ole T. Hjortland

Publisher: Oxford University Press, USA

ISBN: 0198715692

Category: Consequentia (Logic)

Page: 357

View: 8150

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


Author: Penelope Rush

Publisher: Cambridge University Press

ISBN: 1107039649

Category: Mathematics

Page: 278

View: 6130

This wide-ranging collection of essays explores the nature of logic and the key issues and debates in the metaphysics of logic.

Varieties of Logic


Author: Stewart Shapiro

Publisher: OUP Oxford

ISBN: 0191025518

Category: Philosophy

Page: 240

View: 2858

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


Author: Elena Anne Marchisotto,James T. Smith

Publisher: Springer Science & Business Media

ISBN: 9780817646035

Category: Mathematics

Page: 494

View: 737

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


Author: Guanrong Chen,Trung Tat Pham

Publisher: CRC Press

ISBN: 9781420039818

Category: Mathematics

Page: 328

View: 3399

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.

New Directions in Paraconsistent Logic

5th WCP, Kolkata, India, February 2014


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

Publisher: Springer

ISBN: 8132227190

Category: Mathematics

Page: 552

View: 1700

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.

Studies and Exercises in Formal Logic

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


Author: John Neville Keynes

Publisher: N.A


Category: Logic

Page: 455

View: 4965

Turkish Studies in the History and Philosophy of Science


Author: G. Irzik,Güven Güzeldere

Publisher: Springer

ISBN: 9781402033322

Category: Science

Page: 308

View: 7541

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.

Über Zahlen und Spiele


Author: John H. Conway

Publisher: Springer-Verlag

ISBN: 3322889971

Category: Mathematics

Page: 205

View: 4279

Perspectives in Philosophy

Indo-Bulgarian Philosophical Studies


Author: Rasik Vihari Joshi

Publisher: N.A


Category: Filosofía búlgara

Page: 432

View: 595

Engineering Optics


Author: CTI Reviews

Publisher: Cram101 Textbook Reviews

ISBN: 146725925X

Category: Education

Page: 52

View: 6469

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.

Naive Mengenlehre


Author: Paul R. Halmos

Publisher: Vandenhoeck & Ruprecht

ISBN: 9783525405277

Category: Arithmetic

Page: 132

View: 8805



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

Publisher: N.A



Page: N.A

View: 2986

1904-26 (includes lists of members)