ABSTRACT
The empty set is a particular puzzle to the philosophers who want to say that sets are real, perceptible entities. Penelope Maddy, pondering on this, was forced to abandon the empty set in her attempt to ground Set Theory in reality. There have been many philosophical problems, large and small, with Set Theory. Until the formulation of the Iterative Conception of a set, for instance, there was no really intuitive understanding of the Zermelo-Fraenkel axioms. In line with her realism she should have tried to re-construct that part of Set Theory in terms of things which have a dimension, for instance intervals, but that would have likely turned her into a Finitist. Ironically, Set Theory’s main philosophical virtue, at one time, was seen to be its ‘extensionality’, by which was then meant the accessibility of sets to the senses. Questions about infinite sets very obviously arise, with Finitism, even Strict Finitism appealing to some as a solution to many problems.
