Introduction

Infinity, Mathematics' Persistent Suitor

Incommensurable Lengths, Irrational Numbers

Newton and Leibniz

Go Forward, and Faith Will Come to You

Vibrating Strings

Infinity Spurned

Infinity Embraced

Sets of Points

Infinite Sizes

Infinite Orders

Integration

Absolute vs. Transfinite

Paradoxes

What Are Sets?

Russell

Cantor

Appendix: Letter from Cantor to Jourdain, 9 July 1904

Appendix: On an Elementary Question of Set Theory

The Axiomatization of Set Theory

The Axiom of Choice

The Axiom of Replacement

Definiteness and Skolem's Paradox

Zermelo

Go Forward, and Faith Will Come to You

Knowing the Infinite

What Do We Know?

What Can We Know?

Getting from Here to There

Appendix

Leaps of Faith

Intuition

Physics

Modality

Second-Order Logic

From Here to Infinity

Who Needs Self-Evidence?

Picturing the Infinite

The Finite Mathematics of Indefinitely Large Size

The Theory of Zillions

Extrapolations

Natural Models

Many Models

One Model or Many? Sets and Classes

Natural Axioms

Second Thoughts

Schematic and Generalizable Variables

Bibliography

Index

Shaughan Lavine is Associate Professor of Philosophy at the University of Arizona.