Thinking about Mathematics: The Philosophy of Mathematics

Paperback | July 1, 2000

byStewart Shapiro

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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 isthe 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 theirmathematics.

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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 ...

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.

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Format:PaperbackPublished:July 1, 2000Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0192893068

ISBN - 13:9780192893062

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Table of Contents

Part I. PerspectiveChapter 1. What is so interesting about mathematics (for philosopher)?Chapter 2. A Potpourri of questions and attempted answersPart II. HistoryChapter 3. Plato's Rationalism, and AristotleChapter 4. Near opposites: Kant and MillPart III. The big threeChapter 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 sceneChapter 8. Numbers existChapter 9. No they don'tChapter 10. StructuralismReferencesIndex