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Mathematics as a Science of Patterns$
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Michael D. Resnik

Print publication date: 1999

Print ISBN-13: 9780198250142

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198250142.001.0001

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Introduction

Introduction

Chapter:
(p.3) 1 Introduction
Source:
Mathematics as a Science of Patterns
Author(s):

Michael D. Resnik (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0198250142.003.0001

Mathematics has often been described as the ‘Queen of Sciences’, yet philosophical problems arise as soon as one tries to define its subject matter. Anti‐realism concerning mathematical objects has proven to be problematic, but, on the other hand, realism gives rise to well‐known epistemological problems. In this book, I offer a type of mathematical realism according to which mathematical objects exist independently of our constructions, and mathematical truths are obtained independently of our beliefs. Central to my account of mathematical objects is a sort of structuralism, according to which mathematical objects are featureless, abstract positions in structures. On the epistemological level, I reject the apriority of mathematical knowledge, and claim that our justification for believing in the truth of mathematics is derived from pragmatic and holistic considerations concerning science.

Keywords:   anti‐realism, holism, mathematical knowledge, mathematical object, mathematical truth, pragmatic justification, realism, structuralism

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