- § 133. Single terms may be either simple or complex
- § 134. Whole and part cannot be defined by logical priority
- § 135. Three kinds of relation of whole and part distinguished
- § 136. Two kinds of wholes distinguished
- § 137. A whole is distinct from the numerical conjunctions of its parts
- § 138. How far analysis is falsification
- § 139. A class as one is an aggregate

§ 135 n. 1. Which may, if we choose, be taken as Peano's ∈. The objection to this meaning for ∈ is that not every propositional function defines a whole of the kind required. The whole differs from the class as many by being of the same *type* as its terms. ↩

§ 135 n. 2. Cf. e.g. F. 1901, § 1, Prop. 4. 4, note (p. 12). ↩

§ 136 n. 1. See Part I, Chap. IV, esp. § 54. ↩

§ 137 n. 1. I.e. it is of the same logical type as its simple parts. ↩

§ 139 n. 1. Cf. Peano, F. 1901, § 2, Prop. 1 ·0 (p. 19). ↩

§ 139 n. 2. See e.g. his Algebra der Logik, Vol. I (Leipzig, 1890). ↩

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