The set-theoretic nature of the usual semantics of set theory raises a problem of circularity. A recourse to an intuitive semantics (possibly in terms of the iterative concept of set) is often deemed necessary, and a certain kind of realist philosophy of mathematics seems its best justification, taking for granted a well-determined reality of which set-theoretic statements are true. I argue that, on the contrary, this form of realism leaves one in even deeper trouble. I try to understand the circularity of the set-theoretic semantics of set theory and the related crucial problem of quantification over the universe of sets in the light of a different, 'Neo-Kantian' perspective.

On the circularity of set-theoretic semantics for set theory

BELLOTTI, LUCA
2014

Abstract

The set-theoretic nature of the usual semantics of set theory raises a problem of circularity. A recourse to an intuitive semantics (possibly in terms of the iterative concept of set) is often deemed necessary, and a certain kind of realist philosophy of mathematics seems its best justification, taking for granted a well-determined reality of which set-theoretic statements are true. I argue that, on the contrary, this form of realism leaves one in even deeper trouble. I try to understand the circularity of the set-theoretic semantics of set theory and the related crucial problem of quantification over the universe of sets in the light of a different, 'Neo-Kantian' perspective.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/565275
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