The Principles of Mathematics (1903)

Chapter I. Definition of Pure Mathematics
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Chapter I. Definition of Pure Mathematics

Table of Contents

  1. § 1. Definition of pure mathematics
  2. § 2. The principles of mathematics are no longer controversial
  3. § 3. Pure mathematics uses only a few notions, and these are logical constants
  4. § 4. All pure mathematics follows formally from twenty premisses
  5. § 5. Asserts formal implications
  6. § 6. And employs variables
  7. § 7. Which may have any value without exception
  8. § 8. Mathematics deals with types of relations
  9. § 9. Applied mathematics is defined by the occurrence of constants which are not logical.
  10. § 10. Relation of mathematics to logic.

§ 5 n. 1. On this subject, cf. Couturat, La Logique de Leibniz, Paris, 1901. ↩

§ 7 n. 1. It is necessary to suppose arithmetical addition and multiplication defined (as may be easily done) so that the above formula remains significant when x and y are not numbers. ↩

§ 8 n. 1. One-one, many-one, transitive, symmetrical, are instances of types of relations with which we shall be often concerned. ↩

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