Universality in Set Theories: A Study in Formal Ontology

The book

discusses the fate of universality and a universal set in several set theories. Set theories

are

ontologies. They posit sets and claim that these exhibit the essential properties laid down in the set theoretical axioms. Collecting these postulated entities quantified over poses the problem of universality. Is the

collection

of the set theoretical entities itself a set theoretical entity? What does it mean if it is, and what does it mean if it is not? To answer these questions involves developing a theory of the

universal set

.

Manuel Bremer is a professor of philosophy at the University of Düsseldorf in Germany.