Publisher's Synopsis
This work addresses the question of whether or not there is a single maximal interpretation of set discourse. The question is whether there is one or more places where our ensemblist discourse is interpreted. In a way, it's a reprise of the ontological question of the "universe" of mathematical objects described by the axioms of set theory. In fact, the question to which this work turns comes down to knowing, in the light of the great diversity of theoretical constructions of models, what the axioms of set theory are about. Drawing on the most recent results of post-forcing set theory, it challenges both the single maximal universe view and the large multiverse view, to defend a hybrid position of "provisional multiversism". My assumption is that philosophical reflection on mathematics should not be indifferent to mathematical practice. In particular, the question of whether there is only one maximum definite interpretation of the ensemblist discourse needs to be examined through the avenues and approaches explored by mathematical theorists.
