Purity of Methods
Date
2012
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Haverford College. Department of Philosophy
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Thesis
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Award
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eng
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Open Access
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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.