The Principles of Mathematics (1903)

Chapter XVI. Whole and Part
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Chapter XVI. Whole and Part

Table of Contents

  1. § 133. Single terms may be either simple or complex
  2. § 134. Whole and part cannot be defined by logical priority
  3. § 135. Three kinds of relation of whole and part distinguished
  4. § 136. Two kinds of wholes distinguished
  5. § 137. A whole is distinct from the numerical conjunctions of its parts
  6. § 138. How far analysis is falsification
  7. § 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). ↩

§ 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). ↩

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