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Philosophy
Elements of Purity
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.
Accessories:
No Accessory
Publisher
CAMBRIDGE
Bisac Major Subject
Philosophy
Bisac Minor Subject
General
Binding Type
Hardcover
Country Of Origin
US
Number Of Units
1
Length
9.0 Inches
Barcode Indicator
EAN
Width
6.0 Inches
Publication Date
1970-01-01
Height
0.25 Inches
ISBN 10
1009539701
Weight
0.63 Pounds
Book EAN
9781009539708
Target Audiance
Adults
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