Critical Plural Logic

This chapter develops and motivates an alternative, more critical plural logic, thus exploring the third horn of the trilemma from the previous chapter. First, a liberal view of mathematical definitions is defended, according to which any objects can be used to define a set. This entails that the traditional plural comprehension scheme needs to be restricted. Some successor principles are then formulated on the basis of the idea that any plurality needs to be circumscribed. Finally, the resulting critical plural logic is shown to give rise to a natural and elegant approach to set theory.