Abstract

This thesis explores Russell’s Paradox and the comparative analysis of Zermelo-Fraenkel set theory, von Neumann-Bernays-Gödel set theory, and Russell’s Type Theory from a mathematical Platonist perspective, focusing on the ontology of sets. Our conclusion posits that, although these theories have made significant attempts in addressing Russell’s paradox and other inconsistencies of naïve set theory, we currently lack a proper language for expressing set theory that fully captures the underlying Platonic world of sets. Consequently, it is impossible to definitively refute or accept any of the given theories as the ultimate solution the paradox.