Bertrand Russell - Introduction to Mathematical Philosophy (2010).pdf

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Introduction to Mathematical
Philosophy
by
Bertrand Russell
Originally published by
George Allen & Unwin, Ltd., London. May
.
1919
Online Corrected Edition version
),
based on the “second edition” (second printing) of April
1920
:
(February
,
1
0
5
2010
, incorporating additional corrections,
marked in green .
[Russell’s blurb from the original dustcover:]
This book is intended for those who have no previ-
ous acquaintance with the topics of which it treats,
and no more knowledge of mathematics than can
be acquired at a primary school or even at Eton. It
sets forth in elementary form the logical definition
of number, the analysis of the notion of order, the
modern doctrine of the infinite, and the theory of
descriptions and classes as symbolic fictions. The
more controversial and uncertain aspects of the sub-
ject are subordinated to those which can by now be
regarded as acquired scientific knowledge. These
are explained without the use of symbols, but in
such a way as to give readers a general understand-
ing of the methods and purposes of mathematical
logic, which, it is hoped, will be of interest not only
to those who wish to proceed to a more serious study
of the subject, but also to that wider circle who feel a
desire to know the bearings of this important mod-
ern science.
Contents
Contents
. . . . . . . . . . . . . . . . . . . . .
iv
Preface
. . . . . . . . . . . . . . . . . . . . . .
vi
Editor’s Note . . . . . . . . . . . . . . . . . . .
ix
I. The Series of Natural Numbers
. . .
1
II. Definition of Number . . . . . . . . .
17
III. Finitude and Mathematical Induction
32
IV. The Definition of Order
. . . . . . .
46
V. Kinds of Relations . . . . . . . . . . .
67
VI. Similarity of Relations
. . . . . . . .
83
VII. Rational, Real, and Complex Numbers
101
VIII. Infinite Cardinal Numbers . . . . . .
124
IX. Infinite Series and Ordinals
. . . . .
144
X. Limits and Continuity
. . . . . . . .
156
XI. Limits and Continuity of Functions .
171
XII. Selections and the Multiplicative Ax-
iom . . . . . . . . . . . . . . . . . . . .
187
XIII. The Axiom of Infinity and Logical
Types
. . . . . . . . . . . . . . . . . .
210
XIV. Incompatibility and the Theory of De-
duction
. . . . . . . . . . . . . . . . .
230
XV. Propositional Functions
. . . . . . .
248
XVI. Descriptions
. . . . . . . . . . . . . .
267
XVII. Classes
. . . . . . . . . . . . . . . . .
289
XVIII. Mathematics and Logic . . . . . . . .
311
Index
. . . . . . . . . . . . . . . . . . . . . . .
331
Appendix: Changes to Online Edition . . . .
338

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