Thinking about Mathematics The Philosophy of Mathematics

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
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
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.
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 unique text by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. The first describes questions and issues about mathematics that have motivated philosophers almost since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in such thinkers as Plato, Aristotle, Kant, and Mill. The third section covers the three major positions, and battle lines, throughout the twentieth century: that mathematics is logic (logicism), that the essence of mathematics is the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV looks at contemporary positions and work which brings the reader up-to-date on the discipline. Thinking about Mathematics is accessible to those with little background in either mathematics or philosophy. It is aimed at students and professionals in mathematics who have little contact with academic philosophy and at philosophy students and other philosophers who forgot much of their mathematics.

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

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