Mathematics as a science of patterns / Michael D. Resnik.

Format:

Book

Author/Creator:

Resnik, Michael D.

Language:

English

Subjects (All):

Mathematics--Philosophy.

Mathematics.

Mathematical analysis.

Physical Description:

1 online resource (300 p.)

Edition:

1st ed.

Place of Publication:

Oxford : Clarendon Press ; Oxford ; New York : Oxford University Press, 1997.

Language Note:

English

Summary:

Mathematics as a Science of Patterns 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 thisto a defence of realism about the metaphysics of mathematics--the view that mathematics is about things that really exist.

Contents:

Intro

Preface

Contents

PART ONE: PROBLEMS AND POSITIONS

1. Introduction

2. What is Mathematical Realism?

1. To Characterize Realism...

2. Immanent Truth

3. Realism and Immanent Truth

4. Some Concluding Remarks

3. The Case for Mathematical Realism

1. The Prima Facie Case for Realism

2. The Quine-Putnam View of Applied Mathematics

3. Indispensability Arguments for Mathematical Realism

4. Indispensability and Fictionalism about Science

5. Conclusion

4. Recent Attempts at Blunting the Indispensability Thesis

1. Synthetic Science: Field

2. Saving the Mathematical Formalism while Changing its Interpretation: Chihara and Kitcher

3. An Intermediate Approach: Hellman's Modal-Structuralism

4. What Has Introducing Modalities Gained?

5. Doubts about Realism

1. How Can We Know Mathematical Objects?

2. How Can We Refer to Mathematical Objects?

3. The Incompleteness of Mathematical Objects

4. Some Morals for Realists

5. An Aside: Penelope Maddy's Perceivable Sets

PART TWO: NEUTRAL EPISTEMOLOGY

Introduction to Part Two

6. The Elusive Distinction between Mathematics and Natural Science

1. How Physics Blurs the Mathematical/Physical Distinction

2. Some Other Attempts to Distinguish Mathematical from Physical Objects

3. Our Epistemic Access to Space-Time Points

4. Morals for the Epistemology of Mathematics

7. Holism: Evidence in Science and Mathematics

1. The Initial Case for Holism

2. Objections to Holism

3. Testing Scientific and Mathematical Models

4. Global and Local Theories

5. Revising Logic and Mathematics

8. The Local Conception of Mathematical Evidence: Proof, Computation, and Logic

1. Some Norms of Mathematical Practice

2. Computation and Mathematical Empiricism.

3. Mathematical Proof, Logical Deduction and Apriority

4. Summary

9. Positing Mathematical Objects

2. A Quasi-Historical Account

3. Mathematical Positing Naturalized?

4. Positing and Knowledge

5. Postulational Epistemologies and Realism

PART THREE: MATHEMATICS AS A SCIENCE OF PATTERNS

Introduction to Part Three

10. Mathematical Objects as Positions in Patterns

2. Patterns and their Relationships

3. Patterns and Positions: Entity and Identity

4. Composite and Unified Mathematical Objects

5. Mathematical Reductions

6. Reference to Positions in Patterns

7. Concluding Remarks on Reference and Reduction

11. Patterns and Mathematical Knowledge

2. From Templates to Patterns

3. From Proofs to Truth

4. From Old Patterns to New Patterns

12. What is Structuralism? And Other Questions

2. On 'Facts of the Matter'

3. Patterns as Mathematical Objects

4. Structural Relativity

5. Structuralist Formulations of Mathematical Theories?

6. The Status of Structuralism

7. Structuralism, Realism, and Disquotationalism

8. Epistemic vs. Ontic Structuralism: Structuralism All the Way Down

9. A Concluding Summary

Bibliography

Index

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

Z.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (p. [275]-285) and index.

ISBN:

9786611970376

1-281-97037-9

9780191598296

9780191519000

OCLC:

316196731