Mathematics As a Science of Patterns [Paperback]

This book expounds a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics asciencehe implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a scienceof patternshe expresses his commitment to a structuralist philosophy of mathematics. He links this to a defense of realism about the metaphysics of mathematics--the view that mathematics is about things that really exist.

PART ONE: PROBLEMS AND POSITIONS
1. Introduction
2. What Is Mathematical Realism?
3. The Case for Mathematical Realism
4. Recent Attempts at Blunting the Indispensability Thesis
5. Doubts about Realism
PART TWO
6. The Elusive Distinction between Mathematics and Natural Science
7. Holism: Evidence in Science and Mathematics
8. The Local Conception of Mathematical Evidence: Proof, Computation, and Logic
9. Positing Mathematical Objects
PART THREE: MATHEMATICS AS A SCIENCE OF PATTERNS
10. Mathematical Objects as Positions in Patterns
11. Patterns and Mathematical Knowledge
12. What is Structuralism? and Other Questions
Bibliography
Index

For over twenty years, Michael D. Resnik has been crafting a philosophical view of mathematics: one remarkably sensitive to the opposing tensions that make philosophizing in this domain so difficult....The resulting book is perfect for classroom use: it's extremely clear, and Resnik ensures that even the novice is with him at every stage. --Journal of Symbolic Logic

Resnik has presented an admirably clear discussion of the main issues and arguments that define the philosophy of mathematics. His excellent exposition of the issues and his exploration of new solutions constitute an important advance in the discussion. --History & Philosophy of Logic