Monads and sets

on Gödel, Leibniz, and the reflection principle

pp. 33-64

in: Mark Van Atten, Essays on Gödel's reception of Leibniz, Husserl and Brouwer, Berlin, Springer, 2015

Abstract

Gödel once offered an argument for the general reflection principle in set theory that took the form of an analogy with Leibniz' monadology. I discuss the mathematical and philosophical background to Gödel's argument, reconstruct the proposed analogy in detail, and argue that it has no justificatory force. The paper also provides further support for Gödel's idea that the monadology needs to be reconstructed phenomenologically, by showing that the unsupplemented monadology is not able to found mathematics directly.