Conceptions of Infinity and Set in Lorenzen’s Operationist System

Abstract In the late 1940s and early 1950s, Lorenzen developed his operative logic mathematics, a form of constructive mathematics. Nowadays this is mostly seen as precursor better-known dialogical (Notable exceptions are works Schroeder-Heister 2008; Coquand Neuwirth 2017; Kahle Oitavem 2020.), one might assume that same philosophical motivations were present in both works. However, we want to show not everywhere case. particular, claim Lorenzen’s well-known rejection actual infinite, stated (1957), was major motivation for Rather, argue shift happened treatment infinite from 1950s. His development operationism concerned with critique Cantorian notion set related questions about notions countability uncountability; it only later switches focusing on concept infinity debate potential infinity.