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Principia Mathematica Vol. 1

Principia Mathematica Vol. 1

by Alfred North Whitehead

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About this eBook

Author
Russell, Bertrand, 1872-1970
Title
Principia mathematica, vol. 1 (of 3)
Original Publication
Cambridge: University Press, 1910, copyright 1912, copyright 1913.
Credits
Richard Tonsing, Laura Natal, Michael Roe and the Online Distributed Proofreading Team at www.pgdp.net (This book was produced from images made available by the HathiTrust Digital Library.) In memoriam of Greg Newby.
Language
English
LoC Class
QA: Science: Mathematics
Subject
Mathematics -- Philosophy
Category
Text
Project Gutenberg
eBook-No. 78050
Release Date
February 26, 2026
Copyright
Public domain in the USA.

Contents

  1. 1.Untitled
  2. 2.Untitled
  3. 3.Untitled
  4. 4.PRINCIPIA MATHEMATICA
  5. 5.Untitled
  6. 6.CONTENTS OF VOLUME I
  7. 7.Untitled
  8. 8.ERRATA.
  9. 9.PREFACE
  10. 10.INTRODUCTION.
  11. 11.CHAPTER I. PRELIMINARY EXPLANATIONS OF IDEAS AND NOTATIONS. — FOOTNOTES:
  12. 12.CHAPTER II. THE THEORY OF LOGICAL TYPES. — FOOTNOTES:
  13. 13.CHAPTER III. INCOMPLETE SYMBOLS. — FOOTNOTES:
  14. 14.PART I. MATHEMATICAL LOGIC.
  15. 15.SUMMARY OF PART I.
  16. 16.SECTION A. THE THEORY OF DEDUCTION.
  17. 17.1. PRIMITIVE IDEAS AND PROPOSITIONS.
  18. 18.*2. IMMEDIATE CONSEQUENCES OF THE PRIMITIVE PROPOSITIONS. — FOOTNOTES:
  19. 19.*3. THE LOGICAL PRODUCT OF TWO PROPOSITIONS. — FOOTNOTES:
  20. 20.*4. EQUIVALENCE AND FORMAL RULES.
  21. 21.*5. MISCELLANEOUS PROPOSITIONS. — FOOTNOTES:
  22. 22.SECTION B. THEORY OF APPARENT VARIABLES.
  23. 23.*9. EXTENSION OF THE THEORY OF DEDUCTION FROM LOWER TO HIGHER TYPES OF PROPOSITIONS. — FOOTNOTES:
  24. 24.*10. THEORY OF PROPOSITIONS CONTAINING ONE APPARENT VARIABLE.
  25. 25.*11. THEORY OF TWO APPARENT VARIABLES.
  26. 26.*12. THE HIERARCHY OF TYPES AND THE AXIOM OF REDUCIBILITY. — FOOTNOTES:
  27. 27.*13. IDENTITY.
  28. 28.*14. DESCRIPTIONS.
  29. 29.SECTION C. CLASSES AND RELATIONS.
  30. 30.*20. GENERAL THEORY OF CLASSES.
  31. 31.*21. GENERAL THEORY OF RELATIONS.
  32. 32.*22. CALCULUS OF CLASSES. — FOOTNOTES:
  33. 33.*23. CALCULUS OF RELATIONS.
  34. 34.*24. THE UNIVERSAL CLASS, THE NULL-CLASS, AND THE EXISTENCE OF CLASSES.
  35. 35.*25. THE UNIVERSAL RELATION, THE NULL RELATION, AND THE EXISTENCE OF RELATIONS.
  36. 36.SECTION D. LOGIC OF RELATIONS.
  37. 37.*30. DESCRIPTIVE FUNCTIONS. — FOOTNOTES:
  38. 38.*31. CONVERSES OF RELATIONS.
  39. 39.*32. REFERENTS AND RELATA OF A GIVEN TERM WITH RESPECT TO A GIVEN RELATION.
  40. 40.*33. DOMAINS, CONVERSE DOMAINS, AND FIELDS OF RELATIONS.
  41. 41.*34. THE RELATIVE PRODUCT OF TWO RELATIONS.
  42. 42.*35. RELATIONS WITH LIMITED DOMAINS AND CONVERSE DOMAINS.
  43. 43.*36. RELATIONS WITH LIMITED FIELDS.
  44. 44.*37. PLURAL DESCRIPTIVE FUNCTIONS. — FOOTNOTES:
  45. 45.*38. RELATIONS AND CLASSES DERIVED FROM A DOUBLE DESCRIPTIVE FUNCTION.
  46. 46.NOTE TO SECTION D. — FOOTNOTES:
  47. 47.SECTION E. PRODUCTS AND SUMS OF CLASSES.
  48. 48.*40. PRODUCTS AND SUMS OF CLASSES OF CLASSES.
  49. 49.*41. THE PRODUCT AND SUM OF A CLASS OF RELATIONS.
  50. 50.*42. MISCELLANEOUS PROPOSITIONS.
  51. 51.*43. THE RELATIONS OF A RELATIVE PRODUCT TO ITS FACTORS.
  52. 52.PART II. PROLEGOMENA TO CARDINAL ARITHMETIC.
  53. 53.SUMMARY OF PART II.
  54. 54.SECTION A. UNIT CLASSES AND COUPLES.
  55. 55.*50. IDENTITY AND DIVERSITY AS RELATIONS.
  56. 56.*51. UNIT CLASSES. — FOOTNOTES:
  57. 57.*52. THE CARDINAL NUMBER 1.
  58. 58.*53. MISCELLANEOUS PROPOSITIONS INVOLVING UNIT CLASSES.
  59. 59.*54. CARDINAL COUPLES.
  60. 60.*55. ORDINAL COUPLES.
  61. 61.*56. THE ORDINAL NUMBER .
  62. 62.SECTION B. SUB-CLASSES, SUB-RELATIONS, AND RELATIVE TYPES.
  63. 63.*60. THE SUB-CLASSES OF A GIVEN CLASS.
  64. 64.*61. THE SUB-RELATIONS OF A GIVEN RELATION.
  65. 65.*62. THE RELATION OF MEMBERSHIP OF A CLASS.
  66. 66.*63. RELATIVE TYPES OF CLASSES.
  67. 67.*64. RELATIVE TYPES OF RELATIONS.
  68. 68.*65. ON THE TYPICAL DEFINITION OF AMBIGUOUS SYMBOLS.
  69. 69.SECTION C. ONE-MANY, MANY-ONE, AND ONE-ONE RELATIONS.
  70. 70.*70. RELATIONS WHOSE CLASSES OF REFERENTS AND OF RELATA BELONG TO GIVEN CLASSES.
  71. 71.*71. ONE-MANY, MANY-ONE, AND ONE-ONE RELATIONS.
  72. 72.*72. MISCELLANEOUS PROPOSITIONS CONCERNING ONE-MANY, MANY-ONE, AND ONE-ONE RELATIONS.
  73. 73.*73. SIMILARITY OF CLASSES. — FOOTNOTES:
  74. 74.*74. ON ONE-MANY AND MANY-ONE RELATIONS WITH LIMITED FIELDS.
  75. 75.SECTION D. SELECTIONS. — FOOTNOTES:
  76. 76.*80. ELEMENTARY PROPERTIES OF SELECTIONS.
  77. 77.*81. SELECTIONS FROM MANY-ONE RELATIONS.
  78. 78.*82. SELECTIONS FROM RELATIVE PRODUCTS.
  79. 79.*83. SELECTIONS FROM CLASSES OF CLASSES.
  80. 80.*84. CLASSES OF MUTUALLY EXCLUSIVE CLASSES.
  81. 81.*85. MISCELLANEOUS PROPOSITIONS. — FOOTNOTES:
  82. 82.*88. CONDITIONS FOR THE EXISTENCE OF SELECTIONS.
  83. 83.SECTION E. INDUCTIVE RELATIONS. — FOOTNOTES:
  84. 84.*90. ON THE ANCESTRAL RELATION.
  85. 85.*91. ON POWERS OF A RELATION.
  86. 86.*92. POWERS OF ONE-MANY AND MANY-ONE RELATIONS.
  87. 87.*93. INDUCTIVE ANALYSIS OF THE FIELD OF A RELATION.
  88. 88.*94. ON POWERS OF RELATIVE PRODUCTS. — FOOTNOTES:
  89. 89.*95. ON THE EQUI-FACTOR RELATION. — FOOTNOTES:
  90. 90.*96. ON THE POSTERITY OF A TERM.
  91. 91.*97. ANALYSIS OF THE FIELD OF A RELATION INTO FAMILIES. — FOOTNOTES:
  92. 92.Untitled

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