Quine, New Foundations, and the Philosophy of Set Theory

Quine's set theory, New Foundations, has often been treated as an anomaly in the history and philosophy of set theory. In this book, Sean Morris shows that it is in fact well-motivated, emerging in a natural way from the early development of set theory. Morris introduces and explores the notion of set theory as explication: the view that there is no single correct axiomatization of set theory, but rather that the various axiomatizations all serve to explicate the notion of set and are judged largely according to pragmatic criteria. Morris also brings out the important interplay between New Foundations, Quine's philosophy of set theory, and his philosophy more generally. We see that his early technical work in logic foreshadows his later famed naturalism, with his philosophy of set theory playing a crucial role in his primary philosophical project of clarifying our conceptual scheme and specifically its logical and mathematical components.

Preface; Introduction; Part I: 1. Cantor and the early development of set theory; 2. Cantor, Russell, and Zermelo and the set-theoretic paradoxes; 3. NF and the beginnings of Quine's philosophy of set theory; Part II: 4. Quine's philosophy of set theory; 5. Clarifying our conceptual scheme: set theory and the role of explication; Part III: 6. The iterative conception and set theory; 7. NF, the axiom of choice, and arithmetic; Bibliography; Index.

Sean Morris is Associate Professor of Philosophy at the Metropolitan State University of Denver. He has written extensively on Quine and the history of analytic philosophy with a particular emphasis on Quine's work in the foundations of mathematics.