A note on the circularity of set-theoretic semantics for set theory
Luca Bellotti · CINECA IRIS Institutial research information system (University of Pisa) · 2010
There is a problem of conceptual circularity (though a mathematically innocuous one) in the common adoption of a set-theoretic semantics for the usual formal systems of set theory. One could think to resort to an intuitive semantics, perhaps in terms of the iterative concept of set, and to justify this choice by means of a realist philosophy of mathematics. In this note I describe the circularity of the set-theoretic semantics of set theory and the crucial problem of quantification over the universe of sets from a different point of view with respect to this form of realism, which is epistemologically problematic.