Principles of Mathematics

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.

Table of Contents

Part I The lnde.nables of Mathematics

1 DEFINITION OF PURE MATHEMATICS

2 SYMBOLIC LOGIC

3 IMPLICATION AND FORMAL IMPLICATION

4 PROPER NAMES, ADJECTIVES AND VERBS

5 DENOTING

6 CLASSES

7 PROPOSITIONAL FUNCTIONS

8 THE VARIABLE

9 RELATIONS

10 THE CONTRADICTION

Part II Number

11 DEFINITION OF CARDINAL NUMBERS

12 ADDITION AND MULTIPLICATION

13 FINITE AND INFINITE

14 THEORY OF FINITE NUMBERS

15 ADDITION OF TERMS AND ADDITION OF CLASSES

16 WHOLE AND PART

17 INFINITE WHOLES

18 RATIOS AND FRACTIONS

Part III Quantity

19 THE MEANING OF MAGNITUDE

20 THE RANGE OF QUANTITY

21 NUMBERS AS EXPRESSING MAGNITUDES: MEASUREMENT

22 ZERO

23 INFINITY, THE INFINITESIMAL AND CONTINUITY

Part IV Order

24 THE GENESIS OF SERIES

25 THE MEANING OF ORDER

26 ASYMMETRICAL RELATIONS

27 DIFFERENCE OF SENSE AND DIFFERENCE OF SIGN

28 ON THE DIFFERENCE BETWEEN OPEN AND CLOSED SERIES

29 PROGRESSIONS AND ORDINAL NUMBERS

30 DEDEKIND’S THEORY OF NUMBER

31 DISTANCE

Part V lnfinity and Continuity

32 THE CORRELATION OF SERIES

33 REAL NUMBERS

34 LIMITS AND IRRATIONAL NUMBERS

35 CANTOR’S FIRST DEFINITION OF CONTINUITY

36 ORDINAL CONTINUITY

37 TRANSFINITE CARDINALS

38 TRANSFINITE ORDINALS

39 THE INFINITESIMAL CALCULUS

40 THE INFINITESIMAL AND THE IMPROPER INFINITE

41 PHILOSOPHICAL ARGUMENTS CONCERNING THE INFINITESIMAL

42 THE PHILOSOPHY OF THE CONTINUUM

43 THE PHILOSOPHY OF THE INFINITE

Part VI Space

44 DIMENSIONS AND COMPLEX NUMBERS

45 PROJECTIVE GEOMETRY

46 DESCRIPTIVE GEOMETRY

47 METRICAL GEOMETRY

48 RELATION OF METRICAL TO PROJECTIVE AND DESCRIPTIVE GEOMETRY

49 DEFINITIONS OF VARIOUS SPACES

50 THE CONTINUITY OF SPACE

51 LOGICAL ARGUMENTS AGAINST POINTS

52 KANT’S THEORY OF SPACE

Part VII Matter and Motion

53 MATTER

54 MOTION

55 CAUSALITY

56 DEFINITION OF A DYNAMICAL WORLD

57 NEWTON’S LAWS OF MOTION

58 ABSOLUTE AND RELATIVE MOTION

59 HERTZ’S DYNAMICS

Appendices

LIST OF ABBREVIATIONS

Appendix A

Appendix B

About the Author

Bertrand Russell (1872-1970). A celebrated mathematician and logician, Russell was and remains one of the most genuinely widely read and popular philosophers of modern times.