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Philosophy of Mathematics: Structure and Ontology
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Philosophy of Mathematics: Structure and Ontology Paperback - 2000

by Stewart 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 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.

First line

For a long time, many philosophers and some mathematics believed that philosophical matters, such as metaphysics and ontology, determine the proper practice of mathematics.

Details

  • Title Philosophy of Mathematics: Structure and Ontology
  • Author Stewart Shapiro
  • Binding Paperback
  • Edition Paperback
  • Pages 296
  • Volumes 1
  • Language ENG
  • Publisher Oxford University Press
  • Publication date 2000-09-28
  • ISBN 9780195139303 / 0195139305
  • Weight 0.95 lbs (0.43 kg)
  • Dimensions 9.08 x 6.3 x 0.73 in (23.06 x 16.00 x 1.85 cm)
  • Category Science
  • Dewey Decimal Code 510.1

About the author


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

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Philosophy of Mathematics: Structure and Ontology

Philosophy of Mathematics: Structure and Ontology

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by Shapiro, Stewart

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