Michael D. Resnik

in Mathematics as a Science of Patterns

Published in print December 1999 | ISBN: 9780198250142
Published online November 2003 | e-ISBN: 9780191598296 | DOI:

More Like This

Show all results sharing this subject:

  • Philosophy of Mathematics and Logic


Show Summary Details


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

Chapter.  2530 words. 

Subjects: Philosophy of Mathematics and Logic

Full text: subscription required

How to subscribe Recommend to my Librarian

Buy this work at Oxford University Press »

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content. subscribe or login to access all content.