Date of Original Version

8-24-2015

Type

Book Chapter

Rights Management

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-21473-3_12

Abstract or Description

This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes that we view mathematics as a system of conventions and norms that is designed to help us make sense of the world and reason efficiently. Like any designed system, it can perform well or poorly, and the philosophy of mathematics has a role to play in helping us understand the general principles by which it serves its purposes well.

DOI

10.1007/978-3-319-21473-3_12

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Published In

Mathematics, Substance and Surmise (Editors: Ernest Davis, Philip J. Davis), 235-255.