Abstract
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’.
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 language | English |
|---|---|
| Title of host publication | The Logica Yearbook 2017 |
| Publisher | College Publications |
| Number of pages | 13 |
| Publication status | Published - 2018 |
Keywords
- Mathematical proofs
- Purity of methods
- Infinitude of primes
- Hilbert’s 24th problem