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Philosophy of Mathematics : Structure and Ontology by Stewart Shapiro (2000, Trade Paperback)
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About this product
Product Identifiers
PublisherOxford University Press, Incorporated
ISBN-100195139305
ISBN-139780195139303
eBay Product ID (ePID)1644945
Product Key Features
Number of Pages296 Pages
Publication NamePhilosophy of Mathematics : Structure and Ontology
LanguageEnglish
SubjectHistory & Philosophy, Logic
Publication Year2000
TypeTextbook
Subject AreaMathematics, Philosophy
AuthorStewart Shapiro
FormatTrade Paperback
Dimensions
Item Height0.7 in
Item Weight15.2 Oz
Item Length9.1 in
Item Width6.3 in
Additional Product Features
Intended AudienceScholarly & Professional
Reviews"This book is an important contribution...presenting an original, structuralist philosophy and axiomatic framework in comprehensive detail, placing it in broad philosophical and historical perspective, and comparing it systematically with other approaches seen as leading structuralist alternatives to the one set forth by Shapiro himself....this is an interesting, important, and thought-provoking book."--Journal of Symbolic Logic, "Clearly and charmingly written, and provides a strong defence ofstructuralism....There is no doubt that the book represents an important andoriginal contribution to the field, and deserves to be widely read anddiscussed."--Mathematical Reviews, "This book is an important contribution...presenting an original, structuralist philosophy and axiomatic framework in comprehensive detail, placing it in broad philosophical and historical perspective, and comparing it systematically with other approaches seen as leading structuralistalternatives to the one set forth by Shapiro himself....this is an interesting, important, and thought-provoking book, sure to stimulate further work in developing structuralist philosophy in mathematics."--Journal of Symbolic Logic, "This book is an important contribution...presenting an original, structuralist philosophy and axiomatic framework in comprehensive detail, placing it in broad philosophical and historical perspective, and comparing it systematically with other approaches seen as leading structuralist alternatives to the one set forth by Shapiro himself....this is an interesting, important, and thought-provoking book."-- Journal of Symbolic Logic, "Clearly and charmingly written, and provides a strong defence of structuralism....There is no doubt that the book represents an important and original contribution to the field, and deserves to be widely read and discussed."--Mathematical Reviews, "This book is an important contribution...presenting an original,structuralist philosophy and axiomatic framework in comprehensive detail,placing it in broad philosophical and historical perspective, and comparing itsystematically with other approaches seen as leading structuralist alternativesto the one set forth by Shapiro himself....this is an interesting, important,and thought-provoking book."--Journal of Symbolic Logic, "Clearly and charmingly written, and provides a strong defence of structuralism....There is no doubt that the book represents an important and original contribution to the field, and deserves to be widely read and discussed."--Mathematical Reviews"This book is an important contribution...presenting an original, structuralist philosophy and axiomatic framework in comprehensive detail, placing it in broad philosophical and historical perspective, and comparing it systematically with other approaches seen as leading structuralist alternatives to the one set forth by Shapiro himself....this is an interesting, important, and thought-provoking book, sure to stimulate further work in developing structuralistphilosophy in mathematics."--Journal of Symbolic Logic, Extremely interesting and deserves the attention of anyone with a serious interest in the field ... a careful study of the book will be enormously rewarding to anyone with some prior exposure to the field.
Dewey Edition20
IllustratedYes
Dewey Decimal510/.1
SynopsisShapiro argues that both realist and anti-realist accounts of mathematics are problematic. To resolve this dilemma, he articulates a 'structuralist' approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle., Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians., Do numbers, sets, and so forth exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing these questions that have attracted lively debate in recent years, Stewart Shapiro argues that standard realist and antirealist accounts of mathematics are both problematic. To resolve this dilemma, he articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers, existing independently, but simply a natural structure, the pattern common to any system that follows the general laws of addition. Shapiro concludes by showing how his approach can be applied to wider philosophical questions such as the nature of an object. Clear, compelling, and tautly argued it will be of deep interest to both philosophers and mathematicians.
LC Classification NumberQA8.4
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