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.

Product Details

• Amazon Sales Rank: #351349 in Books
• Published on: 2000-07-13
• Original language: English
• Number of items: 1
• Binding: Paperback
• 328 pages

Review
"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

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.

Customer Reviews

Excellent introduction to the philosophy of mathematics
I finished my Maths degree in 1975, so I confess that many of the more recent developments (references are made right up to 1997) were not always comprehensible to me, but I still got enjoyment out of dipping through this book.

If these 2 examples don't spark any interest for you in the discussion that followed, then this book is not for you :

Kant : The concept expressed by the English word 'triangle' contains the concept of being 'three-angled'. Does it also contain the concept of 'three-sided'? The German word for 'triangle' is 'Dreieck', or 'three-cornered'. Presumably, that concept includes 'three-angled', but, again, does it include 'three-sided'?

Formalism : Consider the equation 0=0. If you print this out, you cannot say that the equation says that the leftmost hunk of ink shaped like an oval is identical to the rightmost hunk of ink also shaped like an oval. Clearly, those are two different hunks of ink.

Thinking about mathematics
This is a very nice introduction to the Philosophy of Mathematics, clear and well organized. It is more philosophical than mathematical, though. People with taste for 'hard'-formal work might be disapointed. On the other hand, for this very same reason, it is accessible to grad students in Philosophy and the curious reader in general.