FOM: Two new phil maths textbooks

Jeffrey Ketland ketland at
Wed Sep 20 13:21:53 EDT 2000

Dear FOMistas

After a very long period (30 years, maybe) in which there simply didn't
exist anything like a textbook introduction to the philosophy of mathematics
(there are plenty of research monographs - Field, Chihara (x2), Maddy (x2),
Steiner (x2), Resnik, Hellman, Burgess&Rosen, Shapiro (x2), etc.), there are
now two (excellent) textbooks available.

The first of these appeared in 1999 is by James Robert Brown and the second
has just appeared this year and is by Stewart Shapiro. (Stewart and Jim - if
you're listening - I hope you don't mind my describing this to FOM list).

The books are:

[1] Shapiro, Stewart 2000: "Thinking about Mathematics" (Oxford Univ Press).
[2] James Robert Brown 1999: "Philosophy of Mathematics: An Introduction to
the World of Proofs and Pictures" (Routledge).

Shapiro's "Thinking about Mathematics" is broken into the following 10

PART I: Perspectives
 1. What is so interesting about mathematics (for a philosopher)?
 2. A Potpourri of questions and attempted answers
PART II: History
 3. Plato's Rationalism and Aristotle
 4. Near Opposites: Kant and Mill
PART III: The Big Three
 5. Logicism: Is mathematics (just) logic?
 6. Formalism: Do mathematical statements mean anything?
 7. Intuitionism: Is something wrong with our logic?
PART IV: The Contemporary Scene
 8. Numbers exist
 9. No they don't
 10. Structuralism

It also has a very nice picture on the front.

Brown's book "Philosophy of Mathematics" is broken into the following 11

1. The Mathematical Image
2. Platonism
3. Picture-Proofs and Platonism
4. What is applied mathematics?
5. Hilbert and Goedel
6. Knots and Notation
7. What is a definition?
8. Constructive approaches
9. Proofs, Pictures and procedures in Wittgenstein
10. Computation, proof and conjecture
11. Calling the bluff

(With a nice picture of the Mandelbrot set on the front).

I recommend both books highly for FOMers interested in obtaining a single
volume and easily affordable (around £14 in the UK) introduction to more or
less all the contemporary positions within modern philosophy of mathematics.

(BTW: both authors are (correctly, of course!  ;~)  ) realists about maths).

Best - Jeff

~~~~~~~~~~~ Jeffrey Ketland ~~~~~~~~~
Dept of Philosophy, University of Nottingham
Nottingham NG7 2RD United Kingdom
Tel: 0115 951 5843
Home: 0115 922 3978
E-mail: jeffrey.ketland at
Home: ketland at

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