The Reality of Numbers
A Physicalist's Philosophy of Mathematics
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Product details:
- Publisher Clarendon Press
- Date of Publication 14 July 1988
- ISBN 9780198249573
- Binding Hardback
- No. of pages208 pages
- Size 224x144x16 mm
- Weight 405 g
- Language English
- Illustrations 43 figures 0
Categories
Short description:
This book casts new light on mathematics through its consideration of metaphysical materialism. The author identifies natural, real and imaginary numbers and sets with specified physical properties and relations.
Set theory tempts us into misunderstanding the nature of mathematics; Bigelow challenges the myth that mathematical objects can be defined into existence.
By reconstruing numbers as real, non-linguistic, physical properties or relations, mathematics can be drawn back from its sterile, abstract exile into the midst of the physical world to which we belong.
Long description:
This book casts new light on mathematics through its consideration of metaphysical materialism. The author identifies natural, real and imaginary numbers and sets with specified physical properties and relations.
However sets are construed numbers are not sets. Sets are important simply because they instantiate all the numbers and all the other properties and relations studied in mathematics. Set theory tempts us into misunderstanding the nature of mathematics; Bigelow challenges the myth that mathematical objects can be defined into existence.
By reconstruing numbers as real, non-linguistic, physical properties or relations, mathematics can be drawn back from its sterile, abstract exile into the midst of the physical world to which we belong.
'This book is written with obvious enthusiasm and a deep, and frequently expressed, conviction of the essential correctness of the view it seeks to promote.'
Bob Hale, University of St Andrews. THES
Table of Contents:
Part I - Metaphysics contains chapter on:
Mathematics and universals; Recurrence
Part II - Mathematics contains chapters on:
Natural Numbers - Pebbles and Pythagoras; Numbers as properties; Numbers as paradigms; Numbers as relations; Numbering sets
Real Numbers - Approximations; Arithmetic and Geometry; Proportions; Ratios; Real Numbers
Complex Numbers - Imaginary numbers; Complex proportions
Sets - From universals to sets; Sets and Essences; Sets and Consistency
Part III - Truth and Existence contains chapters on:
The Problem - Functions and arguments; Truth and essence; The Fox paradox
Wholes and Parts - Counterparts and accidents; Property-instances; Robinson's merger; States of affairs
Anyhow to Something - Categories of being; The second-order Fox; Platonism and necessity.
