Mathematics As a Science of Patterns

by Michael D. Resnik

Overview

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 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 defense of realism about the metaphysics of mathematics—the view that mathematics is about things that really exist.

Product Details

ISBN-13:	9780198236085
Publisher:	Oxford University Press
Publication date:	09/11/1997
Pages:	298
Product dimensions:	8.50(w) x 5.50(h) x 0.81(d)

About the Author

University of North Carolina, Chapel Hill

Table of Contents

PART ONE: PROBLEMS AND POSITIONS1. Introduction2. What Is Mathematical Realism? 3. The Case for Mathematical Realism4. Recent Attempts at Blunting the Indispensability Thesis5. Doubts about RealismPART TWO6. The Elusive Distinction between Mathematics and Natural Science7. Holism: Evidence in Science and Mathematics8. The Local Conception of Mathematical Evidence: Proof, Computation, and Logic9. Positing Mathematical ObjectsPART THREE: MATHEMATICS AS A SCIENCE OF PATTERNS10. Mathematical Objects as Positions in Patterns11. Patterns and Mathematical Knowledge12. What is Structuralism? and Other QuestionsBibliographyIndexPART ONE: PROBLEMS AND POSITIONS1:. Introduction2:. What Is Mathematical Realism? 3:. The Case for Mathematical Realism4:. Recent Attempts at Blunting the Indispensability Thesis5:. Doubts about RealismPART TWO6:. The Elusive Distinction between Mathematics and Natural Science7:. Holism: Evidence in Science and Mathematics8:. The Local Conception of Mathematical Evidence: Proof, Computation, and Logic9:. Positing Mathematical ObjectsPART THREE: MATHEMATICS AS A SCIENCE OF PATTERNS10:. Mathematical Objects as Positions in Patterns11:. Patterns and Mathematical Knowledge12:. What is Structuralism? and Other QuestionsBibliographyIndex

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