Thinking About Mathematics: The Philosophy of Mathematics

Thinking About Mathematics: The Philosophy of Mathematics

Paperback

By (author) Stewart Shapiro

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  • Publisher: Oxford University Press
  • Format: Paperback | 328 pages
  • Dimensions: 137mm x 211mm x 18mm | 386g
  • Publication date: 5 October 2000
  • Publication City/Country: Oxford
  • ISBN 10: 0192893068
  • ISBN 13: 9780192893062
  • Illustrations note: 4 line figures
  • Sales rank: 182,700

Product description

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.

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Author information

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.

Review quote

"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

Table of contents

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