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Philosophy of Mathematics: Structure and Ontology

by Stewart Shapiro

2020-11-24 16:28:46

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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 argue... Read more
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. Less

Book Details

File size9.21 X 6.14 X 0 in
Print pages296
PublisherOxford University Press
Publication date July 1, 1997
LanguageEnglish
ISBN9780195094527
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Stewart Shapiro
Author
Stewart Shapiro received an M.A. in mathematics in 1975, and a Ph.D. in philosophy in 1978, both from the State University of New York at Buffalo. He is currently the O'Donnell Professor of Philosop...

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