Towards an Operational View of Purity

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A proof is regarded as pure in case the technical machinery it
deploys to prove a certain theorem does not outstrip the mathematical content of the theorem itself. In this paper, we consider three different proofs of Euclid’s theorem affirming the infinitude of prime numbers and we show how, in the light of this specific case study, some of the definitions of purity provided in the contemporary literature prove not completely satisfactory.
In response, we sketch the lines of a new approach to purity based on the notion of operational content of a certain theorem or proof. Operational purity is here ultimately intended as a way to refine Arana and Detlefsen’s notion of ‘topical purity’.
Original languageEnglish
Title of host publicationThe Logica Yearbook 2017
PublisherCollege Publications
Number of pages13
Publication statusPublished - 2018


  • Mathematical proofs
  • Purity of methods
  • Infinitude of primes
  • Hilbert’s 24th problem


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