Ce que New Foundations relativise, (en hommage à Ernst Specker)
Résumé
This paper presents a philosophical reading of set theory involving in particular a comparison of NF and ZF. It also proposes a philosophical interpretation of Specker's theorem (NF disproves the axiom of choice and proves infinity). This astonishing mathematical result contradicts Bernays's view according to which the presupposition of the totality of integers by arithmetic is Platonistic. This is true only in a set theory where infinity cannot be derived as a theorem but must be included as an axiom. Genuine Platonism survives only relative to a particular set theory.