On the circularity of set-theoretic semantics for set theory
Journal title EPISTEMOLOGIA
Author/s Luca Bellotti
Publishing Year 2014 Issue 2014/1
Language English Pages 21 P. 58-78 File size 635 KB
DOI 10.3280/EPIS2014-001004
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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 settheoretic 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.
Keywords: Set theory, semantics, iterative concept of set, quantification over the universe, mathematical realism, Kreisel, Kant.
Luca Bellotti, On the circularity of set-theoretic semantics for set theory in "EPISTEMOLOGIA" 1/2014, pp 58-78, DOI: 10.3280/EPIS2014-001004