Frege’s Theory of Types

Abstract

It is often claimed that the theory of function levels proposed by Frege in Grundgesetze der Arithmetik * I would like to thank Ansten Klev, Marco Panza, Marco Ruffino, Will Stafford, Göran Sundholm, Wim Vanrie, and two anonymous reviewers for their helpful comments on early drafts of this paper. Most of the material here has been presented in different online seminars and conferences over the past three years, in particular the OCIE Seminar in the History and Philosophy of Mathematics and Logic, Logicians in Quarantine, I Colóquio NULFA-NuLFiC de Lógica e Filosofia da Matemática, and Chá das 5. I also thank Alessandro Duarte, Erich Reck, and Edward Zalta for stimulating discussions. This research was partly supported by the AFOSR grant FA9550-18-1-0120 and the Lumina quaeruntur fellowship number LQ300092101 from the Czech Academy of Sciences.