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 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 lS(
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