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The Reality of Numbers John Bigelow (Senior Lecturer in Philosophy, Senior Lecturer in Philosophy, La Trobe University)

The Reality of Numbers By John Bigelow (Senior Lecturer in Philosophy, Senior Lecturer in Philosophy, La Trobe University)

Summary

The author identifies natural, real and imaginary numbers with specified physical properties and relations and challenges the myth that mathematical objects can be defined into existence.

The Reality of Numbers Summary

The Reality of Numbers: A Physicalist's Philosophy of Mathematics by John Bigelow (Senior Lecturer in Philosophy, Senior Lecturer in Philosophy, La Trobe University)

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.

The Reality of Numbers Reviews

'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
'This is what philosophy ought to be: a grand vision combined with original and careful work on the details. It is presented with lucidity and modesty and good humour, and bedazzling technicalities. An admirable book.' David Lewis, Princeton University, Australasian Journal of Philosophy
'This is what philosophy ought to be: a grand vision combined with original and careful work on the details. It is presented with lucidity and modesty and good humour, and without bedazzling technicalities. An admirable book.' David Lewis, Princeton University, Australasian Journal of Philosophy

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.

Additional information

NPB9780198249573
9780198249573
0198249578
The Reality of Numbers: A Physicalist's Philosophy of Mathematics by John Bigelow (Senior Lecturer in Philosophy, Senior Lecturer in Philosophy, La Trobe University)
New
Hardback
Oxford University Press
1988-07-14
208
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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