The Reality of Numbers: A Physicalist's Philosophy of Mathematics

Hardcover (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $90.31
Usually ships in 1-2 business days
(Save 17%)
Other sellers (Hardcover)
  • All (4) from $90.31   
  • New (2) from $105.82   
  • Used (2) from $90.31   


Challenging the myth that mathematical objects can be defined into existence, Bigelow here employs Armstrong's metaphysical materialism to cast new light on mathematics. He identifies natural, real, and imaginary numbers and sets with specified physical properties and relations and, by so doing, draws mathematics back from its sterile, abstract exile into the midst of the physical world.

Read More Show Less

Product Details

  • ISBN-13: 9780198249573
  • Publisher: Oxford University Press, USA
  • Publication date: 12/28/1994
  • Pages: 202
  • Product dimensions: 5.60 (w) x 8.60 (h) x 0.80 (d)

Table of Contents

Introduction 1
Part I Metaphysics
1. Mathematics and universals 11
2. Recurrence 18
Part II Mathematics
II(a) Natural Numbers
3. Pebbles and Pythagoras 31
4. Numbers as properties 38
5. Numbers as paradigms 45
6. Numbers as relations 48
7. Numbering sets 55
II(b) Real Numbers
8. Approximations 58
9. Arithmetic and geometry 62
10. Proportions 66
11. Ratios 71
12. Real numbers 76
II(c) Complex Numbers
13. Imaginary numbers 81
14. Complex proportions 89
II(d) Sets
15. From universals to sets 101
16. Sets and essences 105
17. Sets and consistency 110
Part III Truth And Existence
III(a) The Problem
18. Functions and arguments 121
19. Truth and essence 128
20. The Fox paradox 135
III(b) Wholes and Parts
21. Counterparts and accidents 139
22. Property-instances 143
23. Robinson's merger 149
24. States of affairs 154
III(c) Anyhow to Something
25. Categories of being 158
26. The second-order Fox 166
27. Platonism and necessity 174
Bibliography 179
Index 189
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)