ABSTRACT

First published in 1903, Principles of Mathematics was Bertrand Russell’s first major work in print. It was this title which saw him begin his ascent towards eminence. In this groundbreaking and important work, Bertrand Russell argues that mathematics and logic are, in fact, identical and what is commonly called mathematics is simply later deductions from logical premises. Highly influential and engaging, this important work led to Russell’s dominance of analytical logic on western philosophy in the twentieth century.

part |2 pages

PART I THE INDEFINABLES OF MATHEMATICS

chapter 1|7 pages

Definition of Pure Mathematics

chapter 2|24 pages

SYMBOLIC LOGIC

chapter 3|9 pages

IMPLICATION AND FORMAL IMPLICATION

chapter 4|11 pages

PROPER NAMES, ADJECTIVES AND VERBS

chapter 5|13 pages

DENOTING

chapter 6|15 pages

CLASSES

chapter 7|7 pages

PROPOSITIONAL FUNCTIONS

chapter 8|6 pages

THE VARIABLE

chapter 9|6 pages

RELATIONS

chapter 10|8 pages

THE CONTRADICTION

part |2 pages

Part II Number

chapter 11|7 pages

Definition of Cardinal Numbers

chapter 12|4 pages

ADDITION AND MULTIPLICATION

chapter 13|3 pages

Finite and Infinite

chapter 14|5 pages

THEORY OF FINITE NUMBERS

chapter 15|8 pages

ADDITION OF TERMS AND ADDITION OF CLASSES

chapter 16|6 pages

WHOLE AND PART

chapter 17|6 pages

Infinite Wholes

chapter 18|5 pages

RATIOS AND FRACTIONS

part |2 pages

Part III Quantity

chapter 19|13 pages

THE MEANING OF MAGNITUDE

chapter 20|6 pages

THE RANGE OF QUANTITY

chapter 22|5 pages

ZERO

chapter 23|10 pages

Infinity, the Infinitesimal and Continuity

part |2 pages

Part IV Order

chapter 24|8 pages

THE GENESIS OF SERIES

chapter 25|11 pages

THE MEANING OF ORDER

chapter 26|9 pages

ASYMMETRICAL RELATIONS

chapter 27|7 pages

DIFFERENCE OF SENSE AND DIFFERENCE OF SIGN

chapter 29|6 pages

PROGRESSIONS AND ORDINAL NUMBERS

chapter 30|7 pages

DEDEKIND’S THEORY OF NUMBER

chapter 31|5 pages

DISTANCE

part |2 pages

PART V INFINITY AND CONTINUITY

chapter 32|11 pages

THE CORRELATION OF SERIES

chapter 33|6 pages

REAL NUMBERS

chapter 34|12 pages

LIMITS AND IRRATIONAL NUMBERS

chapter 35|9 pages

Cantor’s First Definition of Continuity

chapter 36|8 pages

ORDINAL CONTINUITY

chapter 37|9 pages

Transfinite Cardinals

chapter 38|14 pages

Transfinite Ordinals

chapter 39|6 pages

The Infinitesimal Calculus

chapter 42|9 pages

THE PHILOSOPHY OF THE CONTINUUM

chapter 43|15 pages

The Philosophy of the Infinite

part |2 pages

Part VI Space

chapter 44|10 pages

DIMENSIONS AND COMPLEX NUMBERS

chapter 45|12 pages

PROJECTIVE GEOMETRY

chapter 46|11 pages

DESCRIPTIVE GEOMETRY

chapter 47|15 pages

METRICAL GEOMETRY

chapter 49|8 pages

Definitions of Various Spaces

chapter 50|8 pages

THE CONTINUITY OF SPACE

chapter 51|11 pages

LOGICAL ARGUMENTS AGAINST POINTS

chapter 52|7 pages

KANT’S THEORY OF SPACE

part |2 pages

Part VII Matter and Motion

chapter 53|5 pages

MATTER

chapter 54|5 pages

MOTION

chapter 55|6 pages

CAUSALITY

chapter 56|2 pages

Definition of a Dynamical World

chapter 57|8 pages

NEWTON’S LAWS OF MOTION

chapter 58|5 pages

ABSOLUTE AND RELATIVE MOTION

chapter 59|5 pages

HERTZ’S DYNAMICS