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Thinking about Mathematics: The Philosophy of Mathematics

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Thinking about Mathematics: The Philosophy of Mathematics Cover

 

Synopses & Reviews

Publisher Comments:

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.

About the Author

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.

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

Product Details

ISBN:
9780192893062
Author:
Shapiro, Stewart
Publisher:
Oxford University Press, USA
Author:
null, Stewart
Location:
New York
Subject:
General
Subject:
Philosophy
Subject:
Mathematics
Subject:
Logic
Subject:
PHILOSOPHY / Logic
Subject:
Philosophy | Logic and Mathematics
Subject:
Mathematics -- Philosophy.
Subject:
Philosophy | Logic & Mathematics
Series Volume:
90-21
Publication Date:
20001031
Binding:
TRADE PAPER
Grade Level:
General/trade
Language:
English
Illustrations:
4 line illus
Pages:
328
Dimensions:
8.44x5.43x.69 in. .84 lbs.

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Related Subjects

History and Social Science » Linguistics » General
Humanities » Philosophy » General
Humanities » Philosophy » Logic
Religion » Comparative Religion » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » History
Science and Mathematics » Mathematics » Logic and Philosophy
Science and Mathematics » Mathematics » Popular Surveys and Recreational

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