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The Nature of Mathematical Knowledge$
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The Nature of Mathematical Knowledge

Philip Kitcher

Print publication date: 1985

Print ISBN-13: 9780195035414

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0195035410.001.0001

Mathematical Reality

Chapter:
(p. 101 ) 6 Mathematical Reality
Source:
The Nature of Mathematical Knowledge
Author(s):

Philip Kitcher (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0195035410.003.0007

We can gain empirical knowledge of elementary arithmetic and elementary geometry because the primitive core of these subjects consists of truths about manipulations of reality. Full arithmetic and geometry idealize these operations. Later mathematics attributes much more extensive powers to the ideal agent who performs mathematical operations.

Keywords:   arithmetic, geometry, mathematical knowledge, mathematical reality, Platonism

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