The Principles of Mathematics (1903)

Chapter VI. Classes
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Chapter VI. Classes

Table of Contents

  1. § 66. Combination of intensional and extensional standpoints required
  2. § 67. Meaning of class
  3. § 68. Intensional and extensional genesis of classes
  4. § 69. Distinctions overlooked by Peano
  5. § 70. The class as one and as many
  6. § 71. The notion of and
  7. § 72. All men is not analyzable into all and men
  8. § 73. There are null class-concepts, but there is no null class
  9. § 74. The class as one, except when it has one term, is distinct from the class as many
  10. § 75. Every, any, a and some each denote one object, but an ambiguous one
  11. § 76. The relation of a term to its class
  12. § 77. The relation of inclusion between classes
  13. § 78. The contradiction
  14. § 79. Summary

§ 66 n. 1. La Logique de Leibniz, Paris, 1901, p. 387. ↩

§ 69 n. 1. Neglecting Frege, who is discussed in the Appendix. ↩

§ 70 n. 1. A plurality of terms is not the logical subject when a number is asserted of it: such propositions have not one subject, but many subjects. See end of § 74. ↩

§ 71 n. 1. Paradoxien des Unendlichen, Leipzig, 1854 (2nd ed., Berlin, 1889), § 3. ↩

§ 71 n. 2. i.e. the combination of A with B, C, D, ... already forms a system. ↩

§ 74 n. 1. This conclusion is actually drawn by Frege from an analogous argument: Archiv für syst. Phil., 1, p. 444. See Appendix. ↩

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