Overview

"Moving beyond both realist and anti-realist accounts of mathematics, Shapiro 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."

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9780195094527

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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 structuralist alternatives to the one set forth by Shapiro himself....this is an interesting, important, and thought-provoking book. --Journal of Symbolic Logic

Insightful. The Economist (UK), February 2000 Shapiro is admirably candid about the limits of structuralism in dealing with mathematical applicability ... There is a lot more in this fair, judicious, and informative book than I have been able to indicate in the scope of a short review. Whether or not the reader is persuaded by Shapiro's structuralism, one can learn a great deal about contemporary philosophy of mathematics from the book. * Mark Steiner, The Hebrew University of Jerusalem, Jerusalem Philosophy Quarterly, vol 48, July 1999 * real realists will feel, Shapiro's book is an important contribution to the philosophy of mathematics. It fills a major gap: although structuralism has seemed to many a promising idea, we have not previously had so sustained and thorough a treatment of its metaphysical and ontological implications. Everyone interested in the subject will have much to learn from this rich and intriguing book. * Keith Hossack, The Philosophical Quarterly, Vol 50, No 198 January 2000 *

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