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Philosophy of Mathematics
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Philosophy of Mathematics: Structure and Ontology

Stewart Shapiro

Abstract

The philosophy of mathematics articulated and defended in this book goes by the name of “structuralism”, and its slogan is that mathematics is the science of structure. The subject matter of arithmetic, for example, is the natural number structure, the pattern common to any countably infinite system of objects with a distinguished initial object and a successor relation that satisfies the induction principle. The essence of each natural number is its relation to the other natural numbers. One way to understand structuralism is to reify structures as ante rem universals. This would be a platoni ... More

Keywords: ante rem, mathematics, modality, ontology, philosophy of mathematics, Platonism, realism, reference, reification, structuralism, universal

Bibliographic Information

Print publication date: 2000 Print ISBN-13: 9780195139303
Published to Oxford Scholarship Online: November 2003 DOI:10.1093/0195139305.001.0001

Authors

Affiliations are at time of print publication.

Stewart Shapiro, author
Ohio State University at Newark
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