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

The Principles of Mathematics was written by Bertrand Russell, and published in in 1903. It is now available in the Public Domain.