Purity of Methods

Date
2012
Journal Title
Journal ISSN
Volume Title
Publisher
Producer
Director
Performer
Choreographer
Costume Designer
Music
Videographer
Lighting Designer
Set Designer
Crew Member
Funder
Rehearsal Director
Concert Coordinator
Moderator
Panelist
Alternative Title
Department
Haverford College. Department of Philosophy
Type
Thesis
Original Format
Running Time
File Format
Place of Publication
Date Span
Copyright Date
Award
Language
eng
Note
Table of Contents
Terms of Use
Rights Holder
Access Restrictions
Open Access
Tripod URL
Identifier
Abstract
Purity of methods is the term given to the demand that mathematical proofs use methods that are in some sense appropriate to the theorem that they prove. Using Selberg’s elementary proof of the Prime Number Theorem as a case study, I argue that any philosophical account of the purity of methods must be able to establish a connection between the methods permissible in a pure proof and the historically contingent domains into which mathematical knowledge is organized. Such an account will be an account of pure solutions to mathematical problems, which are inseparably tied to our historically contingent means of conceiving them, and not of pure proofs of ahistorical theorems. This paper provides an account of the purity of methods along these lines, and shows that this account can interpret and explain common beliefs about purity. This account brings to the surface connections between purity and mathematical explanation that both explain why pure proofs are valuable, and promise insight into the nature of mathematical explanation.
Description
Citation
Collections