The reality of numbers : a physicalist's philosophy of mathematics / John Bigelow.

Format:

Book

Author/Creator:

Bigelow, John, 1948-

Language:

English

Subjects (All):

Mathematics--Philosophy.

Mathematics.

Set theory.

Logic, Symbolic and mathematical.

Physical Description:

viii, 193 pages : illustrations ; 23 cm

Place of Publication:

Oxford [England] : Clarendon Press ; Oxford [Oxfordshire] ; New York : Oxford University Press, 1988.

Summary:

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.

Contents:

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.

Notes:

Includes index.

Bibliography: pages [179]-188.

ISBN:

0198249578 :

OCLC:

17210349