This unique book by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. Part I describes questions and issues about mathematics that have motivated philosophers since the beginning of intellectual history. Part II is an<BR>historical survey, discussing the role of mathematics in the thought of such philosophers as Plato, Aristotle, Kant, and Mill. Part III covers the three major positions held throughout the twentieth century: the idea that mathematics is logic (logicism), the view that the essence of mathematics is<BR>the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV brings the reader up-to-date with a look at contemporary developments within the discipline. <BR>This sweeping introductory guide to the philosophy of mathematics makes these fascinating concepts accessible to those with little background in either mathematics or philosophy.

This text examines a range of philosophical issues and positions concerning mathematics. Divided into sections, it looks at the role of mathematics in the theories of philosophers such as Plato and Kant, covers the major positions of the 20th century and presents contemporary work in the field.

Stewart Shapiro is Professor of Philosophy at Ohio State University at Newark and Professorial Fellow in the Department of Logic and Metaphysics at the University of St Andrews, Scotland.

Part I. Perspective

Chapter 1. What is so interesting about mathematics (for philosopher)?

Chapter 2. A Potpourri of questions and attempted answers

Part II. History

Chapter 3. Plato's Rationalism, and Aristotle

Chapter 4. Near opposites: Kant and Mill

Part III. The big three

Chapter 5. Logicism: Is mathematics (just) logic?

Chapter 6. Formalism: Do mathematical statements mean anything?

Chapter 7. Intuitionism: is something wrong with our logic?

Part IV. The contemporary scene

Chapter 8. Numbers exist

Chapter 9. No they don't

Chapter 10. Structuralism

References

Index