About the Book
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.
Table of Contents:
PART I. THE INDEFINABLES OF MATHEMATICS, CHAPTER I. DEFINITION OF PURE MATHEMATICS., CHAPTER II. SYMBOLIC LOGIC., CHAPTER III. IMPLICATION AND FORMAL IMPLICATION., CHAPTER IV. PROPER NAMES, ADJECTIVES AND VERBS., CHAPTER V. DENOTING., CHAPTER VI. CLASSES., CHAPTER VII. PROPOSITIONAL FUNCTIONS., CHAPTER VIII. THE VARIABLE., CHAPTER IX. RELATIONS., CHAPTER X. THE CONTRADICTION., PART II. NUMBER., CHAPTER XI. DEFINITION OF CARDINAL NUMBERS., CHAPTER XII. ADDITION AND MULTIPLICATION., CHAPTER XIII. FINITE AND INFINITE., CHAPTER XIV. THEORY OF FINITE NUMBERS., CHAPTER XV. ADDITION OF TERMS AND ADDITION OF CLASSES., CHAPTER XVI. WHOLE AND PART., CHAPTER XVII. INFINITE WHOLES., CHAPTER XVIII. RATIOS AND FRACTIONS., PART III. QUANTITY., CHAPTER XIX. THE MEANING OF MAGNITUDE., CHAPTER XX. THE RANGE OF QUANTITY., CHAPTER XXI. NUMBERS AS EXPRESSING MAGNITUDES: MEASUREMENT., CHAPTER XXII. ZERO., CHAPTER XXIII. INFINITY, THE INFINITESIMAL, AND CONTINUITY., PART IV. ORDER., CHAPTER XXIV. THE GENESIS OF SERIES., CHAPTER XXV. THE MEANING OF ORDER., CHAPTER XXVI. ASYMMETRICAL RELATIONS., CHAPTER XXVII. DIFFERENCE OF SENSE AND DIFFERENCE OF SIGN., CHAPTER XXVIII. ON THE DIFFERENCE BETWEEN OPEN AND CLOSED SERIES., CHAPTER XXIX. PROGRESSIONS AND ORDINAL NUMBERS., CHAPTER XXX. DEDEKIND'S THEORY OF NUMBER., CHAPTER XXXI. DISTANCE., PART V. INFINITY AND CONTINUITY., CHAPTER XXXII. THE CORRELATION OF SERIES., CHAPTER XXXIII. REAL NUMBERS., CHAPTER XXXIV. LIMITS AND IRRATIONAL NUMBERS., CHAPTER XXXV. CANTOR'S FIRST DEFINITION OF CONTINUITY., CHAPTER XXXVI. ORDINAL CONTINUITY., CHAPTER XXXVII. TRANSFINITE CARDINALS., CHAPTER XXXVIII. TRANSFINITE ORDINALS., CHAPTER XXXIX. THE INFINITESIMAL CALCULUS., CHAPTER XL. THE INFINITESIMAL AND THE IMPROPER INFINITE., CHAPTER XLI. PHILOSOPHICAL ARGUMENTS CONCERNING THE INFINITESIMAL., CHAPTER XLII. THE PHILOSOPHY OF THE CONTINUUM., CHAPTER XLIII. THE PHILOSOPHY OF THE INFINITE., PART VI. SPACE., CHAPTER XLIV. DIMENSIONS AND COMPLEX NUMBERS., CHAPTER XLV. PROJECTIVE GEOMETRY., CHAPTER XLVI. DESCRIPTIVE GEOMETRY., CHAPTER XLVII. METRICAL GEOMETRY., CHAPTER XLVIII. RELATION OF METRICAL TO PROJECTIVE AND DESCRIPTIVE GEOMETRY., CHAPTER XLIX. DEFINITIONS OF VARIOUS SPACES., CHAPTER L. THE CONTINUITY OF SPACE., CHAPTER LI. LOGICAL ARGUMENTS AGAINST POINTS., CHAPTER LII. KANT'S THEORY OF SPACE., PART VII. MATTER AND MOTION., CHAPTER LIII. MATTER., CHAPTER LIV. MOTION., CHAPTER LV. CAUSALITY., CHAPTER LVI. DEFINITION OF A DYNAMICAL WORLD., CHAPTER LVII. NEWTON'S LAWS OF MOTION., CHAPTER LVIII. ABSOLUTE AND RELATIVE MOTION., CHAPTER LIX. HERTZ'S DYNAMICS., APPENDIX A. THE LOGICAL AND ARITHMETICAL DOCTRINES OF FREGE., APPENDIX B. THE DOCTRINE OF TYPES., Index
About the Author :
Bertrand Russell
Review :
`Unless we are very much mistaken, its lucid application and development of the great discoveries of Peano and Cantor mark the opening of a new epoch in both philosophical and mathematical thought.' - The Spectator
`It is impossible in a short review to do justice to the subtlety and originality.' - TLS
