Towards an operational view of purity. (English) Zbl 1418.03018

Kahle, Reinhard; Pulcini, Gabriele

Arazim, Pavel (ed.) et al., The Logica yearbook 2017. Proceedings of the 31st annual international symposium Logica, Hejnice Monastery, Czech Republic, June 19–23, 2017. London: College Publications. 125-138 (2018).

Summary: 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’.
For the entire collection see [Zbl 1398.03004].

MSC:

03A05	Philosophical and critical aspects of logic and foundations
00A30	Philosophy of mathematics

Keywords:

purity of methods; infinitude of primes; Hilbert’s 24th problem; mathematical practice