Elements of Purity (Elements in the Philosophy of Mathematics) - Softcover

Arana

Softcover

ISBN 10: 1009055895 ISBN 13: 9781009055895

Verlag: Cambridge University Press, 2025

Inhaltsangabe

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.

Details zur Ausgabe

• Verlag: Cambridge University Press
• Erscheinungsdatum: 2025
• Sprache: Englisch
• ISBN 10: 1009055895
• ISBN 13: 9781009055895
• Einband: Tapa blanda
• Anzahl der Seiten: 86
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Avery; https://www.avery.fr/; ; chemin des peupliers 27; Dardilly; Frankreich