Contents
Preface
Introduction to the Second Edition

Part I  The Indefinables of Mathematics

Chapter 1  Definition of Pure Mathematics
Chapter 2  Symbolic Logic
Chapter 3  Implication and Formal Implication
Chapter 4  Proper Names, Adjectives and Verbs
Chapter 5  Denoting
Chapter 6  Classes
Chapter 7  Propositional Functions
Chapter 8  The Variable
Chapter 9  Relations
Chapter 10  The Contradiction

Part II  Number

Chapter 11  Definition of Cardinal Numbers
Chapter 12  Addition and Multiplication
Chapter 13  Finite and Infinite
Chapter 14  Theory of Finite Numbers
Chapter 15  Addition of Terms and Addition of Classes
Chapter 16  Whole and Part
Chapter 17  Infinite Wholes
Chapter 18  Ratios and Fractions

Part III  Quantity

Chapter 19  The Meaning of Magnitude
Chapter 20  The Range of Quantity
Chapter 21  Numbers as Expressing Magnitudes: Measurement
Chapter 22  Zero
Chapter 23  Infinity, The Infinitesimal and Continuity

Part IV  Order

Chapter 24  The Genesis of Series
Chapter 25  The Meaning of Order
Chapter 26  Asymmetrical Relations
Chapter 27  Difference of Sense and Difference of Sign
Chapter 28  The Difference Between Open and Closed Series
Chapter 29  Progressions and Ordinal Numbers
Chapter 30  Dedekind's Theory of Numbers
Chapter 31  Distance

Part V  Infinity and Continuity

Chapter 32  The Correlation of Series
Chapter 33  Real Numbers
Chapter 34  Limits and Irrational Numbers
Chapter 35  Cantor's First Definition of Continuity
Chapter 36  Ordinal Continuity
Chapter 37  Transfinite Cardinals
Chapter 38  Transfinite Ordinals
Chapter 39  The Infinitesimal Calculus
Chapter 40  The Infinitesimal and the Improper Infinite
Chapter 41  Philosophical Arguments Concerning the Infinitesimal
Chapter 42  The Philosophy of the Continuum
Chapter 43  The Philosophy of the Infinite

Part VI  Space

Chapter 44  Dimensions and Complex Numbers
Chapter 45  Projective Geometry
Chapter 46  Descriptive Geometry
Chapter 47  Metrical Geometry
Chapter 48  Relation of Metrical to Projective and Descriptive Geometry
Chapter 49  Definitions of Various Spaces
Chapter 50  The Continuity of Space
Chapter 51  Logical Arguments Against Points
Chapter 52  Kant's Theory of Space

Part VII  Matter and Motion

Chapter 53  Matter
Chapter 54  Motion
Chapter 55  Causality
Chapter 56  Definition of a Dynamical World
Chapter 57  Newton's Laws of Motion
Chapter 58  Absolute and Relative Motion
Chapter 59  Hertz's Dynamics

Appendices and Index

Appendix A  The Logical and Arithmetical Doctrines of Frege
Appendix B  The Doctrine of Types
                        Index

*  Bertrand Russell, The Principles of Mathematics, vol. 1 (Cambridge University Press, 1903)