Elements of Purity

This Element is the first comprehensive discussion of a new, critical subject in the philosophy of mathematics, purity of proof.

Andrew Arana (Author)

9781009055895, Cambridge University Press

Paperback / softback, published 16 January 2025

84 pages
22.8 x 15.1 x 0.5 cm, 0.15 kg

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.

1. Purity in practice
2. A brief history of purity
3. Types of purity
4. Values of purity
5. Conclusions
References.

Subject Areas: Philosophy [HP]