Mathematics as a Science of Patterns

by Michael D. Resnik

Overview

Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defence of realism about the metaphysics of mathematics--the view that mathematics is about things that really exist. Resnik's distinctive philosophy of mathematics is here presented in an accessible and systematic form: it will be of value not only to specialists in this area, but to philosophers, mathematicians, and logicians interested in the relationship between these three disciplines, or in truth, realism, and epistemology.

Product Details

ISBN-13:	9780191519000
Publisher:	Oxford University Press
Publication date:	07/31/1997
Sold by:	Barnes & Noble
Format:	eBook
File size:	463 KB

About the Author

University of North Carolina, Chapel Hill

Table of Contents

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: Neutral Epistemology
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

Editorial Reviews

"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

"...the resulting book is perfect for classroom use: it is extremely clear....[The book] articulates an ambitious and forceful position...I recommend it without reservation to everyone interested in these topics."—Journal of Symbolic Logic

From the Publisher