Purity in Arithmetic: some Formal and Informal Issues

In Godehard Link (ed.), Formalism and Beyond: On the Nature of Mathematical Discourse. De Gruyter. pp. 315-336 (2014)
Download Edit this record How to cite View on PhilPapers
Abstract
Over the years many mathematicians have voiced a preference for proofs that stay “close” to the statements being proved, avoiding “foreign”, “extraneous”, or “remote” considerations. Such proofs have come to be known as “pure”. Purity issues have arisen repeatedly in the practice of arithmetic; a famous instance is the question of complex-analytic considerations in the proof of the prime number theorem. This article surveys several such issues, and discusses ways in which logical considerations shed light on these issues.
PhilPapers/Archive ID
ARAPIA
Upload history
Archival date: 2019-09-19
View other versions
Added to PP index
2017-01-11

Total views
51 ( #45,247 of 53,660 )

Recent downloads (6 months)
18 ( #33,313 of 53,660 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.