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.

A note on the circularity of set-theoretic semantics for set theory

BELLOTTI, LUCA
2010-01-01

Abstract

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.
2010
Bellotti, Luca
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/141198
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