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Elements of Purity

Arana, Andrew

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A proof of a theorem can be said to be pure if it draws only on what is 'close' or 'intrinsic' to that theorem. In this Element we will investigate the apparent preference for pure proofs that has persisted in mathematics since antiquity, alongside a competing preference for impurity. In Section 1, we present two examples of purity, from geometry and number theory. In Section 2, we give a brief history of purity in mathematics. In Section 3, we discuss several different types of purity, based on different measures of distance between theorem and proof. In Section 4 we discuss reasons for preferring pure proofs, for the varieties of purity constraints presented in Section 3. In Section 5 we conclude by reflecting briefly on purity as a preference for the local and how issues of translation intersect with the considerations we have raised throughout this work.

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Publisher

CAMBRIDGE

Bisac Major Subject

Philosophy

Bisac Minor Subject

General

Binding Type

Paperback

Country Of Origin

Number Of Units

Length

9.0 Inches

Barcode Indicator

EAN

Width

6.0 Inches

Publication Date

1970-01-01

Height

0.18 Inches

ISBN 10

1009055895

Weight

0.28 Pounds

Book EAN

9781009055895

Target Audiance

Adults

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Elements of Purity