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): Maddy P.
Series: Clarendon Paperbacks
Publisher: OUP
Year: 2003
Language: English
Pages: 217
Tags: Математика;Философия математики;
Title ......Page 3
Copyright ......Page 4
Dedication ......Page 5
Preface ......Page 7
Contents ......Page 11
1. Pre-theoretic realism ......Page 13
2. Realism in philosophy ......Page 17
3. Realism and truth ......Page 27
4. Realism in mathematics ......Page 32
1. What is the question? ......Page 48
2. Perception ......Page 62
3. Intuition ......Page 79
4. Godelian Platonism ......Page 87
1. What numbers could not be ......Page 93
2. Numbers as properties ......Page 98
3. Frege numbers ......Page 110
1. Reals and sets of reals ......Page 119
2. Axiomatization ......Page 126
3. Open problems ......Page 137
4. Competing theories ......Page 144
5. The challenge ......Page 155
1. Monism ......Page 162
2. Field's nominalism ......Page 171
3. Structuralism ......Page 182
4. Summary ......Page 189
References ......Page 194
Index ......Page 211
