Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. She answers the traditional questions and poses a challenging new one, refocusing philosophical attention on the pressing foundational issues of contemporary mathematics.
Author(s): Penelope Maddy
Series: Clarendon Paperbacks
Publisher: Clarendon Press • Oxford
Year: 1990
Language: English
Pages: 218
Cover......Page 1
Title Page......Page 5
Preface......Page 9
Contents......Page 13
1. Pre-theoretic realism......Page 15
2. Realism in philosophy......Page 19
3. Realism and truth......Page 29
4. Realism in mathematics......Page 34
1. What is the question?......Page 50
2. Perception......Page 64
3. Intuition......Page 81
4. Gödelian Platonism......Page 89
1. What numbers could not be......Page 95
2. Numbers as properties......Page 100
3. Frege numbers......Page 112
1. Reals and sets of reals......Page 121
2. Axiomatization......Page 128
3. Open problems......Page 139
4. Competing theories......Page 146
5. The challenge......Page 157
1. Monism......Page 164
2. Field's nominalism......Page 173
3. Structuralism......Page 184
4. Summary......Page 191
References......Page 196
Index......Page 213
