Download the Free Fishpond App!
Download on the App Store

Android App on Google play
Thinking About Mathematics: The Philosophy of Mathematics

Already own it?

Sell Yours
Home » Books » Science » Mathematics » General

Thinking About Mathematics

The Philosophy of Mathematics

By Stewart Shapiro

Elsewhere $70.77 $62.63   Save $8.14 (12%)
Price includes NZ wide delivery!
Ships from UK
Order now for Christmas delivery
Rating:
 
Register or sign-in to rate and get recommendations.
Format: Paperback / softback, 328 pages
Other Information: 4 line figures
Published In: United Kingdom, 13 July 2000
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.

Table of Contents

PART I. PERSPECTIVE; CHAPTER 1. WHAT IS SO INTERESTING ABOUT MATHEMATICS (FOR PHILOSOPHER)?; ATTRACTION - OF OPPOSITES?; PHILOSOPHY AND MATHEMATICS: CHICKEN OR EGG?; NATURALISM AND MATHEMATICS; CHAPTER 2. A POTPOURRI OF QUESTIONS AND ATTEMPTED ANSWERS; NECESSITY AND A PRIORI KNOWLEDGE; GLOBAL MATTERS: OBJECTS AND OBJECTIVITY; THE MATHEMATICAL AND THE PHYSICAL; LOCAL MATERS: THEOREMS, THEORIES, AND CONCEPTS; PART II. HISTORY; CHAPTER 3. PLATO'S RATIONALISM, AND ARISTOTLE; THE WORLD OF BEING; PLATO ON MATHEMATICS; MATHEMATICS ON PLATO; ARISTOTLE, THE WORTHY OPPONENT; FURTHER READING; CHAPTER 4. NEAR OPPOSITES: KANT AND MILL; REORIENTATION; KANT; MILL; FURTHER READING; PART III. THE BIG THREE; CHAPTER 5. LOGICISM: IS MATHEMATICS (JUST) LOGIC?; FREGE; RUSSELL; CARNAP AND LOGICAL POSITIVISM; CONTEMPORARY VIEWS; FURTHER READING; CHAPTER 6. FORMALISM: DO MATHEMATICAL STATEMENTS MEAN ANYTHING?; BASIC VIEWS: FREG'S ONSLAUGHT; DEDUCTIVISM: HILBERT'S GRUNDLAGEN DER GEOMETRIE; FINITISM: THE HILBERT PROGRAM; INCOMPLETENESS; CURRY; FURTHER READING; CHAPTER 7. INTUITIONISM: IS SOMETHING WRONG WITH OUR LOGIC?; 1. REVISING CLASSICAL LOGIC; 2. THE TEACHER, BROUWER; 3. THE STUDENT, HEYTING; 4. DUMMETT; 5. FURTHER READING; PART IV. THE CONTEMPORARY SCENE; CHAPTER 8. NUMBERS EXIST; GODEL; THE WEB OF BELIEF; SET-THEORETIC REALISM; FURTHER READING; CHAPTER 9. NO THEY DON'T; FICTIONALISM; MODAL CONSTRUCTION; WHAT SHOULD WE MAKE OF ALL THIS?; ADDENDUM: YOUNG TURKS; FURTHER READING; CHAPTER 10. STRUCTURALISM; THE UNDERLYING IDEA; ANTE REM STRUCTURES, AND OBJECTS; STRUCTURALISM WITHOUT STRUCTURES; KNOWLEDGE OF STRUCTURES; FURTHER READING; REFERENCES; INDEX

Promotional Information

TEXTBOOK

About the Author

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.

Reviews

"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

EAN: 9780192893062
ISBN: 0192893068
Publisher: Oxford University Press
Dimensions: 21.44 x 13.79 x 1.75 centimetres (0.50 kg)
Tell a friend

Their Email:

Sell Yours

Already own this item?
Sell Yours and earn some cash. It's fast and free to list! (Learn More.)

Review this Product

BAD GOOD
 

Related Searches

 

Webmasters, Bloggers & Website Owners

You can earn a 5% commission by selling Thinking About Mathematics: The Philosophy of Mathematics on your website. It's easy to get started - we will give you example code. After you're set-up, your website can earn you money while you work, play or even sleep!

 

Authors/Publishers

Are you the Author/Publisher? Improve sales by submitting additional information on this title.

 

This item ships from and is sold by Fishpond World Ltd.