Page:Russell, Whitehead - Principia Mathematica, vol. II, 1912.djvu/11

La bibliothèque libre.
Aller à la navigation Aller à la recherche
Cette page n’a pas encore été corrigée


CONTENTS OF VOLUME II

PAGE PREFATORY STATEMENT OF SYMBOLIC CONVENTIONS IX

PART III. CARDINAL ARITHMETIC. Summary of Part III 3

SECTION A. DEFINITION AND LOGICAL PROPERTIES OF CARDINAL NUMBERS 4

  • 100. Definition and elementary properties of cardinal numbers 13
  • 101. On 0 and 1 and 2 19
  • 102. On cardinal numbers of assigned types 24
  • 103. Homogeneous cardinals 36
  • 104. Ascending cardinals 42
  • 105. Descending cardinals 52
  • 106. Cardinals of relational types 60

SECTION B. ADDITION, MULTIPLICATION AND EXPONENTIATION 66

  • 110. The arithmetical sum of two classes and of two cardinals 75
  • 111. Double similarity 88
  • 112. The arithmetical sum of a class of classes 97
  • 113. On the arithmetical product of two classes or of two cardinals 105
  • 114. The arithmetical product of a class of classes 124
  • 115. Multiplicative classes and arithmetical classes 135
  • 116. Exponentiation 143
  • 117. Greater and less 171

General note on cardinal correlators 185

SECTION C. FINITE AND INFINITE 187

  • 118. Arithmetical substitution and uniform formal numbers 193
  • 119. Subtraction 201
  • 120. Inductive cardinals 207
  • 121. Intervals 233
  • 122. Progressions 253
  • 123. No 268
  • 124. Reflexive classes and cardinals 278
  • 125. The axiom of infinity 289
  • 126. On typically indefinite inductive cardinals 293

236987