Russell's Unknown Logicism

A Study in the History and Philosophy of Mathematics

By: Sebastien Gandon

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Hardcover | 30 August 2012 | Edition Number 1

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278 Pages

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21.59 x 13.97 x 1.75

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In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics , meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content. Winner of The Bertrand Russell Society Book Award 2013.

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List of Figures and Tables	p. vii
Acknowledgements	p. ix
Series Editor's Foreword	p. xi
Introduction	p. 1
Projective Geometry	p. 16
Projective and metrical properties	p. 17
The status of the fundamental theorem of projective geometry	p. 24
Russell's twofold analysis	p. 30
Russell's choice	p. 36
Space as an incidence structure	p. 42
Conclusion	p. 47
Metrical Geometry	p. 49
Logicism, if-thenism and non-Euclidean geometries	p. 50
The projective definition of a metric	p. 54
Metrical geometry, distance and stretch	p. 61
Poincaré and Russell on the perception of distance	p. 66
Metrical geometry as an empirical science	p. 71
Conclusion	p. 76
Geometry, Logicism and 'If-Thenism'	p. 79
Russell's if-thenism (I): definitions	p. 80
Russell's if-thenism (II): existence-theorems	p. 84
Topic specificities and psychologism	p. 89
The types of relations and the architecture of mathematics	p. 95
The interaction between logic and mathematics: a persistent difficulty?	p. 101
Conclusion	p. 105
Quantity in The Principles of Mathematics	p. 107
Magnitude and quantity	p. 108
The concept of a measurable magnitude	p. 114
The absolutist theory and the concept of a kind of magnitude	p. 120
The relational theory of distance	p. 126
Conclusion	p. 132
Quantity in Principia Mathematica	p. 134
Dedekind, Burali-Forti and Frege on real numbers	p. 135
Russell and Whitehead's theory of numbers	p. 141
The relational theory of vector family	p. 146
Hale's Fregean axiomatic definition versus Russell and Whitehead's relational theory	p. 153
Conclusion	p. 158
Application Constraint in Principia Mathematica	p. 160
Whitehead's conception of applied mathematics	p. 162
Real analysis and real numbers	p. 166
The architectonic use of Applic	p. 170
Applic in neo-logicism	p. 173
Applic and the distinction between logical and apparent forms of propositions	p. 178
Conclusion	p. 184
Russell's Universalism and Topic-Specificity	p. 187
Pre-logicized and logicized mathematics	p. 189
Russell's positive universalism	p. 193
Logicism and the definition of the mathematical content	p. 200
Russell's logicism and practice-based philosophy of mathematics	p. 204
Conclusion	p. 210
Notes	p. 213
Bibliography	p. 245
Index	p. 259
Table of Contents provided by Ingram. All Rights Reserved.

Russell's Unknown Logicism

A Study in the History and Philosophy of Mathematics

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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