An Introduction to the Philosophy of Mathematics

Author: Mark Colyvan

Publisher: Cambridge University Press

ISBN: 0521826020

Category: Mathematics

Page: 188

View: 8620

DOWNLOAD NOW »

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 the Philosophy of Science

Author: Kent W. Staley

Publisher: Cambridge University Press

ISBN: 0521112494

Category: Science

Page: 300

View: 2423

DOWNLOAD NOW »

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

An Introduction to Gödel's Theorems

Author: Peter Smith

Publisher: Cambridge University Press

ISBN: 1107022843

Category: Mathematics

Page: 406

View: 9823

DOWNLOAD NOW »

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

An Introduction to Decision Theory

Author: Martin Peterson

Publisher: Cambridge University Press

ISBN: 1107151597

Category: Business & Economics

Page: 348

View: 3005

DOWNLOAD NOW »

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 Logic

Author: Daniel Cohnitz,Luis Estrada-González

Publisher: Cambridge University Press

ISBN: 1108603289

Category: Philosophy

Page: N.A

View: 2931

DOWNLOAD NOW »

Philosophy of logic is a fundamental part of philosophical study, and one which is increasingly recognized as being immensely important in relation to many issues in metaphysics, metametaphysics, epistemology, philosophy of mathematics, and philosophy of language. This textbook provides a comprehensive and accessible introduction to topics including the objectivity of logical inference rules and its relevance in discussions of epistemological relativism, the revived interest in logical pluralism, the question of logic's metaphysical neutrality, and the demarcation between logic and mathematics. Chapters in the book cover the state of the art in contemporary philosophy of logic, and allow students to understand the philosophical relevance of these debates without having to contend with complex technical arguments. This will be a major new resource for students working on logic, as well as for readers seeking a better understanding of philosophy of logic in its wider context.

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: 6800

DOWNLOAD NOW »

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.

Introducing Philosophy of Mathematics

Author: Michele Friend

Publisher: Routledge

ISBN: 1317493796

Category: Philosophy

Page: 240

View: 2975

DOWNLOAD NOW »

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 Formal Logic

Author: Peter Smith

Publisher: Cambridge University Press

ISBN: 9780521008044

Category: Mathematics

Page: 357

View: 4193

DOWNLOAD NOW »

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.

An Encyclopedia of Philosophy

Author: G.H.R. Parkinson

Publisher: Routledge

ISBN: 113498815X

Category: Reference

Page: 958

View: 4949

DOWNLOAD NOW »

* Presents a broad survey of philosophical thought * Each chapter explores, and places in context, a major area of philosophical enquiry - including the theory of meaning and of truth, the theory of knowledge, the philosophies of mathematics, science and metaphysics, the philosophy of mind, moral and political philosophy, aesthetics, and religion * Annotated bibliographies for each chapter and indexes of names and subjects * Glossary of commonly-used philosophical terms * Chronological table of the history of philosophy from 1600 `It is a fine achievement and deserves the warmest praise ... Anyone interested in learning what contemporary philosophical debate is about will find this book invaluable ... for a book of this size and quality of content the cover price is modest. Every public library as well as every university, college and school library should have a copy on its shelves.' - Times Higher Education Supplement `A stimulating collection.' - Reference Reviews

Principia Mathematica to *56

Author: Alfred North Whitehead,Bertrand Russell

Publisher: Cambridge University Press

ISBN: 9780521626064

Category: Mathematics

Page: 410

View: 3710

DOWNLOAD NOW »

The great three-volume Principia Mathematica (CUP 1927) is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premises and primitive ideas, establishing that mathematics is a development of logic. This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students will of course wish to refer to the complete edition). It contains the whole of the preliminary sections (which present the authors' justification of the philosophical standpoint adopted at the outset of their work); the whole of Part I (in which the logical properties of propositions, propositional functions, classes and relations are established); section A of Part II (dealing with unit classes and couples); and Appendices A and C (which give further developments of the argument on the theory of deduction and truth functions).

An Introduction to the Philosophy of Science

Author: Rudolf Carnap

Publisher: Courier Corporation

ISBN: 0486140865

Category: Science

Page: 336

View: 1207

DOWNLOAD NOW »

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.

Kant's 'Critique of Pure Reason'

An Introduction

Author: Jill Vance Buroker

Publisher: Cambridge University Press

ISBN: 1139458329

Category: Philosophy

Page: N.A

View: 2274

DOWNLOAD NOW »

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.

Logic

Author: Paul Tomassi

Publisher: Routledge

ISBN: 1134705913

Category: Philosophy

Page: 432

View: 3346

DOWNLOAD NOW »

Bringing elementary logic out of the academic darkness into the light of day, Paul Tomassi makes logic fully accessible for anyone attempting to come to grips with the complexities of this challenging subject. Including student-friendly exercises, illustrations, summaries and a glossary of terms, Logic introduces and explains: * The Theory of Validity * The Language of Propositional Logic * Proof-Theory for Propositional Logic * Formal Semantics for Propositional Logic including the Truth-Tree Method * The Language of Quantificational Logic including the Theory of Descriptions. Logic is an ideal textbook for any logic student: perfect for revision, staying on top of coursework or for anyone wanting to learn about the subject. Related downloadable software for Macs and PCs is available for this title at www.logic.routledge.com.

Mathematics: A Very Short Introduction

Author: Timothy Gowers

Publisher: Oxford Paperbacks

ISBN: 9780192853615

Category: Mathematics

Page: 143

View: 957

DOWNLOAD NOW »

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.

Plato: Oxford Bibliographies Online Research Guide

Author: Oxford University Press

Publisher: Oxford University Press, USA

ISBN: 9780199809028

Category: Philosophy

Page: 26

View: 7918

DOWNLOAD NOW »

This ebook is a selective guide designed to help scholars and students of social work find reliable sources of information by directing them to the best available scholarly materials in whatever form or format they appear from books, chapters, and journal articles to online archives, electronic data sets, and blogs. Written by a leading international authority on the subject, the ebook provides bibliographic information supported by direct recommendations about which sources to consult and editorial commentary to make it clear how the cited sources are interrelated related. This ebook is a static version of an article from Oxford Bibliographies Online: Philosophy, a dynamic, continuously updated, online resource designed to provide authoritative guidance through scholarship and other materials relevant to the study Philosophy. Oxford Bibliographies Online covers most subject disciplines within the social science and humanities, for more information visit www.oxfordbibligraphies.com.

An Introduction to Mathematical Reasoning

Numbers, Sets and Functions

Author: Peter J. Eccles

Publisher: Cambridge University Press

ISBN: 9780521597180

Category: Mathematics

Page: 350

View: 8760

DOWNLOAD NOW »

This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.