Philosophy of Mathematics: Structure and Ontology

Paperback | September 15, 2000

byStewart Shapiro

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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 antirealistaccounts 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 thatfollows 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.

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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 antirealistaccounts of mathematics are both problematic. To...

Stewart Shapiro is Professor of Philosophy at Ohio State University at Newark and the University of St. Andrews, Scotland.

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Format:PaperbackDimensions:296 pages, 8.9 × 5.91 × 0.91 inPublished:September 15, 2000Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0195139305

ISBN - 13:9780195139303

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"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