An Introduction to the Philosophy of Mathematics

Author: Mark Colyvan

Publisher: Cambridge University Press

ISBN: 0521826020

Category: Mathematics

Page: 188

View: 1742

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This introduction to the philosophy of mathematics focuses on contemporary debates in an important and central area of philosophy. The reader is taken on a fascinating and entertaining journey through some intriguing mathematical and philosophical territory, including such topics as the realism/anti-realism debate in mathematics, mathematical explanation, the limits of mathematics, the significance of mathematical notation, inconsistent mathematics and the applications of mathematics. Each chapter has a number of discussion questions and recommended further reading from both the contemporary literature and older sources. Very little mathematical background is assumed and all of the mathematics encountered is clearly introduced and explained using a wide variety of examples. The book is suitable for an undergraduate course in philosophy of mathematics and, more widely, for anyone interested in philosophy and mathematics.

An Introduction to Decision Theory

Author: Martin Peterson

Publisher: Cambridge University Press

ISBN: 1107151597

Category: Business & Economics

Page: 348

View: 1382

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Now revised and updated, this introduction to decision theory is both accessible and comprehensive, covering topics including decision making under ignorance and risk, the foundations of utility theory, the debate over subjective and objective probability, Bayesianism, causal decision theory, game theory, and social choice theory. No mathematical skills are assumed, with all concepts and results explained in non-technical and intuitive as well as more formal ways. There are now over 140 exercises with solutions, along with a glossary of key terms and concepts. This second edition includes a new chapter on risk aversion as well as updated discussions of numerous central ideas, including Newcomb's problem, prisoner's dilemmas, and Arrow's impossibility theorem. The book will appeal particularly to philosophy students but also to readers in a range of disciplines, from computer science and psychology to economics and political science.

An Introduction to the Philosophy of Science

Author: Kent W. Staley

Publisher: Cambridge University Press

ISBN: 0521112494

Category: Science

Page: 300

View: 4326

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This book explores central philosophical concepts, issues, and debates in the philosophy of science, both historical and contemporary.

An Introduction to Non-Classical Logic

From If to Is

Author: Graham Priest

Publisher: Cambridge University Press

ISBN: 9781139469678

Category: Science

Page: N.A

View: 1996

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This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

An Introduction to Gödel's Theorems

Author: Peter Smith

Publisher: Cambridge University Press

ISBN: 1107022843

Category: Mathematics

Page: 406

View: 2420

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A clear and accessible treatment of Gödel's famous, intriguing, but much misunderstood incompleteness theorems, extensively revised in a second edition.

An Introduction to Formal Logic

Author: Peter Smith

Publisher: Cambridge University Press

ISBN: 9780521008044

Category: Mathematics

Page: 357

View: 2654

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Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.

Introducing Philosophy of Mathematics

Author: Michele Friend

Publisher: Routledge

ISBN: 1317493796

Category: Philosophy

Page: 240

View: 9518

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What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.

An Introduction to Ethics

Author: John Deigh

Publisher: Cambridge University Press

ISBN: 052177246X

Category: Philosophy

Page: 241

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This book examines the central questions of ethics through a study of the great ethical works of Western philosophy.

Kant's 'Critique of Pure Reason'

An Introduction

Author: Jill Vance Buroker

Publisher: Cambridge University Press

ISBN: 1139458329

Category: Philosophy

Page: N.A

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In this introductory textbook to Kant's Critique of Pure Reason, Jill Vance Buroker explains the role of this first Critique in Kant's Critical project and offers a line-by-line reading of the major arguments in the text. She situates Kant's views in relation both to his predecessors and to contemporary debates, explaining his Critical philosophy as a response to the failure of rationalism and the challenge of skepticism. Paying special attention to Kant's notoriously difficult vocabulary, she explains the strengths and weaknesses of his arguments, while leaving the final assessment up to the reader. Intended to be read alongside the Critique (also published by Cambridge University Press as part of The Cambridge Edition of the Works of Immanuel Kant in Translation), this guide is accessible to readers with little background in the history of philosophy, but should also be a valuable resource for more advanced students.

Mathematics: A Very Short Introduction

Author: Timothy Gowers

Publisher: Oxford Paperbacks

ISBN: 9780192853615

Category: Mathematics

Page: 143

View: 1550

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This book aims to explain, in clear non-technical language,what it is that mathematicians do, and how that differs from and builds on the mathematics that most people are familiar with from school. It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.

Der Gödelsche Beweis

Author: Ernest Nagel,James R. Newman

Publisher: de Gruyter Oldenbourg

ISBN: 9783486597264

Category:

Page: 110

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Spätestens seit Douglas R. Hofstadters "Gödel, Escher, Bach" ist der Name Gödel auch bei Nichtmathematikern bekannt geworden. 1931 hatte Kurt Gödel unter dem Titel "Über formal unterscheidbare Sätze der Principia Mathematica und verwandter Systeme" seinen Unvollständigkeitssatz publiziert. Nagel und Newman haben das Wesentliche an Gödels Ergebnissen für Nichtfachleute dargestellt. Die vorliegende 9. Auflage ist ein unveränderter Nachdruck der längst klassisch gewordenen Ausgabe von 1958.

An Introduction to the Philosophy of Science

Author: Rudolf Carnap

Publisher: Courier Corporation

ISBN: 0486140865

Category: Science

Page: 336

View: 6620

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Stimulating, thought-provoking text by one of the 20th century's most creative philosophers makes accessible such topics as probability, measurement and quantitative language, causality and determinism, theoretical laws and concepts, more.

Reasoning and the Logic of Things

The Cambridge Conferences Lectures of 1898

Author: Charles Sanders Peirce

Publisher: Harvard University Press

ISBN: 9780674749672

Category: Philosophy

Page: 297

View: 9406

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Charles Sanders Peirce (1839-1914) was an American philosopher, physicist, mathematician, and the founder of pragmatism. Despire his importance in the history of philosophy, a unified statment of his thought has been unavailable. With this publication, readers at long last are offered the philosopher's only known, complete, and coherent account of his own work. Originally delivered as the Cambridge Conferences Lectures of 1898, Reasoning and the Logic of Things is the most accessible and thorough introduction to Peirce's mature thought to be found within the compass of a single book. Beginning with an explanation of the nature of philosophy, Peirce proceeds to illustrate his claim that mathematics provides the foundation of our logic and metaphysics. We find here the clearest formulation of an idea present in Peirce's thought since the 1860s, the distinction between three kinds of reasoning: induction, deduction, and retroduction. Then follows an introduction to Peirce's chief logical doctrines, as well as his attempts to provide a classification of the sciences, a theory of categories, and a theory of science. In conclusion, turning from "reasoning" to the "logic of things," Peirce called for an evolutionary cosmology to explain the reality of laws and described the kinds of reasoning he employed in developing this cosmology. At the urging of his friend William James, Peirce made an uncharacteristic effort in these lectures to present his ideas in terms intelligible to a general audience--those without advanced training in logic and philosophy. The introductory materials by Ketner and Putman add to the volume's lucidity. Consequently, this book will be a valuable source for readers outside of the circle of Peirce specialists.

Descartes's Meditations

An Introduction

Author: Catherine Wilson

Publisher: Cambridge University Press

ISBN: 9780521007665

Category: Philosophy

Page: 271

View: 6777

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This is a new introduction to a philosophical classic. Drawing on the reinterpretations of Descartes' thought of the past twenty-five years, Catherine Wilson examines the arguments of Descartes' famous Meditations, showing how Descartes constructs a theory of the mind, the body, nature, and God from a premise of radical uncertainty. She discusses in detail the historical context of Descartes' writings and their relationship to early modern science, and at the same time she introduces concepts and problems that define the philosophical enterprise as it is understood today.