The Significance of Quine's New Foundations for the Philosophy of Set Theory

This paper examines Quine's set theory, New Foundations (NF), in the context of contemporary philosophy of set theory. Almost unanimously, philosophers of set theory now take the iterative conception, embodied in the axioms of Zermelo-Fraenkel set theory, to be the correct account of set. NF represents a more pragmatic methodology, where set theory is developed in response to the needs of mathematics rather than in accord with some prior philosophical conception of set theory. Quine's approach provides a critique of the more metaphysical ones that have won out in the philosophy of set theory over roughly the last fifty years.