Thinking About Mathematics

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.

ISBN 0192893068   Pages 322 ISBN13 9780192893062 (What's this?)   Volumes 1 Publisher Oxford University Press   Weight (grammes) 382 Imprint Oxford University Press   Published in Oxford Format Paperback   Height (mm) 216 Publication date 13 Jul 2000   Width (mm) 138 Library of Congress 00038599   Spine width (mm) 18 DEWEY 510.1   Academic level Tertiary education DEWEY edition DC21

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

"Stewart Shapiro admirably provides an accessible introduction to contemporary thinking in mathematics, while avoiding caricature of the technicalities. His ease with the subject and lucid style makes this book a succinct introduction to a fascinating intellectual discipline." Times Literary Supplement

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