ABSTRACT

Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which Principia Mathematica provided the detailed proof, and introduced the work of Frege to a wider audience.
In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics.

part Part I|108 pages

The Indefinables of Mathematics.

chapter Chapter I|7 pages

Definition of Pure Mathematics.

chapter Chapter II|23 pages

Symbolic Logic.

chapter Chapter III|9 pages

Implication and Formal Implication.

chapter Chapter IV|11 pages

Proper Names, Adjectives, and Verbs.

chapter Chapter V|13 pages

Denoting.

chapter Chapter VI|16 pages

Classes.

chapter Chapter VII|7 pages

Propositional Functions.

chapter Chapter VIII|6 pages

The Variable.

chapter Chapter IX|6 pages

Relations.

chapter Chapter X|8 pages

The Contradiction.

part Part II|46 pages

Number.

chapter Chapter XI|6 pages

Definition of Cardinal Numbers.

chapter Chapter XII|4 pages

Addition and Multiplication.

chapter Chapter XIII|3 pages

Finite and Infinite.

chapter Chapter XIV|5 pages

Theory of Finite Numbers.

chapter Chapter XV|8 pages

Addition of Terms and Addition of Classes.

chapter Chapter XVI|6 pages

Whole and Part.

chapter Chapter XVII|6 pages

Infinite Wholes.

chapter Chapter XVIII|6 pages

Ratios and Fractions.

part Part III|42 pages

Quantity.

chapter Chapter XIX|13 pages

The Meaning of Magnitude.

chapter Chapter XX|6 pages

The Range of Quantity.

chapter Chapter XXI|8 pages

Numbers as Expressing Magnitudes: Measurement.

chapter Chapter XXII|4 pages

Zero.

chapter Chapter XXIII|9 pages

Infinity, the Infinitesimal, and Continuity.

part Part IV|60 pages

Order.

chapter Chapter XXIV|8 pages

The Genesis of Series.

chapter Chapter XXV|11 pages

The Meaning of Order.

chapter Chapter XXVI|9 pages

Asymmetrical Relations.

chapter Chapter XXVII|7 pages

Difference of Sense and Difference of Sign.

chapter Chapter XXVIII|5 pages

On the Difference Between Open and Closed Series.

chapter Chapter XXIX|6 pages

Progressions and Ordinal Numbers.

chapter Chapter XXX|7 pages

Dedekind’s Theory of Number.

chapter Chapter XXXI|5 pages

Distance.

part Part V|112 pages

Infinity and Continuity.

chapter Chapter XXXII|11 pages

The Correlation of Series.

chapter Chapter XXXIII|6 pages

Real Numbers.

chapter Chapter XXXIV|11 pages

Limits and Irrational Numbers.

chapter Chapter XXXV|9 pages

Cantor’s First Definition of Continuity.

chapter Chapter XXXVI|8 pages

Ordinal Continuity*.

chapter Chapter XXXVII|8 pages

Transfinite Cardinals.

chapter Chapter XXXVIII|13 pages

Transfinite Ordinals.

chapter Chapter XXXIX|6 pages

The Infinitesimal Calculus.

chapter Chapter XL|7 pages

The Infinitesimal and the Improper Infinite.

chapter Chapter XLI|8 pages

Philosophical Arguments Concerning the Infinitesimal.

chapter Chapter XLII|9 pages

The Philosophy of the Continuum.

chapter Chapter XLIII|14 pages

The Philosophy of the Infinite.

part Part VI|94 pages

Space.

chapter Chapter XLIV|10 pages

Dimensions and Complex Numbers.

chapter Chapter XLV|12 pages

Projective Geometry.

chapter Chapter XLVI|11 pages

Descriptive Geometry.

chapter Chapter XLVII|15 pages

Metrical Geometry.

chapter Chapter XLVIII|10 pages

Relation of Metrical to Projective and Descriptive Geometry.

chapter Chapter XLIX|8 pages

Definitions of Various Spaces.

chapter Chapter L|8 pages

The Continuity of Space.

chapter Chapter LI|11 pages

Logical Arguments Against Points.

chapter Chapter LU|7 pages

Kants Theory of Space.

part Part VII|36 pages

Matter and Motion.

chapter Chapter LIII|4 pages

Matter.

chapter Chapter LIV|5 pages

Motion.

chapter Chapter LV|6 pages

Causality.

chapter Chapter LVI|2 pages

Definition of A Dynamical World.

chapter Chapter LVII|7 pages

Newton’s Laws of Motion.

chapter Chapter LVIII|5 pages

Absolute and Relative Motion.

chapter Chapter LIX|5 pages

Hertze’s Dynamics.