Journals Higher Education



Published: 28 September 2000

296 Pages

6-1/8 x 9-1/4 inches

ISBN: 9780195139303

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Bookseller Code (06)


Philosophy of Mathematics

Structure and Ontology

Stewart Shapiro

Shapiro 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.