Chapter

Mathematical Reality

Philip Kitcher

in The Nature of Mathematical Knowledge

Published in print April 1985 | ISBN: 9780195035414
Published online November 2003 | e-ISBN: 9780199833368 | DOI: http://dx.doi.org/10.1093/0195035410.003.0007
Mathematical Reality

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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

Chapter.  23626 words.  Illustrated.

Subjects: Philosophy of Mathematics and Logic

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