Vopěnka’s Alternative Set Theory as a Framework for Feasible Numbers

Abstract This paper takes feasible numbers in Yessenin-Volpin’s work and assesses how this notion could be modelled in Vopěnka’s Alternative Set Theory. The route explored also makes an attempt to model Dummett’s weakly infinite, weakly finite totalities, the coherence of which he took to be decisive of Yessenin-Volpin’s foundational conception. The outcome turns out to be negative: Alternative Set Theory can be taken as a model of some, but not quite all features of Yessenin-Volpin’s feasible numbers. Given that only one particular approach is explored here, the outcome has limited bearing on general questions surrounding ultrafinitism or modelling feasible numbers.