The Principles of Mathematics (1903)

Appendix A. The Logical and Arithmetical Doctrines of Frege
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Appendix A. The Logical and Arithmetical Doctrines of Frege

Table of Contents

  1. § 475. Principal points in Frege's doctrines
  2. § 476. Meaning and indication
  3. § 477. Truth-values and judgment
  4. § 478. Criticism
  5. § 479. Are assumptions proper names for the true or the false?
  6. § 480. Functions
  7. § 481. Begriff and Gegenstand
  8. § 482. Recapitulation of theory of propositional functions
  9. § 483. Can concepts be made logical subjects?
  10. § 484. Ranges
  11. § 485. Definition of ∈ and of relation
  12. § 486. Reasons for an extensional view of classes
  13. § 487. A class which has only one member is distinct from its only member
  14. § 488. Possible theories to account for this fact
  15. § 489. Recapitulation of theories already discussed
  16. § 490. The subject of a proposition may be plural
  17. § 491. Classes having only one member
  18. § 492. Theory of types
  19. § 493. Implication and symbolic logic
  20. § 494. Definition of cardinal numbers
  21. § 495. Frege's theory of series
  22. § 496. Kerry's criticisms of Frege

§ 476 n. 1. I do not translate Bedeutung by denotation, because this word has a technical meaning different from Frege's, and also because bedeuten, for him, is not quite the same as denoting for me. ↩

§ 477 n. 1. This is the logical side of the problem of Annahmen, raised by Meinong in his able work on the subject, Leipzig, 1902. The logical, though not the psychological, part of Meinong's work appears to have been completely anticipated by Frege. ↩

§ 477 n. 2. Frege, like Meinong, calls this an Annahme: FuB. p. 21. ↩

§ 477 n. 3. Gg. p. 10. Cf. also Bs. p. 4. ↩

§ 477 n. 4. When a term which indicates is itself to be spoken of, as opposed to what it indicates, Frege uses inverted commas. Cf. § 56. ↩

§ 480 n. 1. Vierteljahrschrift für wiss. Phil., vol. XI, pp. 249-307. ↩

§ 481 n. 1. We have here a funtion whose value is always a truth-value. Such functions with one argument we have called Begriffe; with two, we call them relations. Cf. Gl. pp. 82–3. ↩

§ 482 n. 1. Not all relations having this property are propositional functions; v. inf. ↩

§ 482 n. 2. The notion of a constituent of a proposition appears to be a logical indefinable. ↩

§ 484 n. 1. I shall translate this as range. ↩

§ 484 n. 2. Ib. p. 444. Cf. supra, § 74. ↩

§ 485 n. 1. Cf. §§ 21, 76, supra. ↩

§ 485 n. 2. Neglecting, for the present, our doubts as to there being any such entity as a couple with sense, cf. § 98. ↩

§ 488 n. 1. The doctrine to be advocated in what follows is the direct denial of the dogma stated in § 70, note. ↩

§ 489 n. 1. Archiv I. p. 444. ↩

§ 489 n. 2. For the use of the word object in the following discussion, see § 58, note. ↩

§ 489 n. 3. Wherever the context requires it, the reader is to add provided the class in question (or all the classes in question) do not consist of a single term. ↩

§ 490 n. 1. Cf. §§ 128, 132 supra. ↩

§ 491 n. 1. The word predicate is here used loosely, not in the precise sense defined in § 48. ↩

§ 492 n. 2. On this notation, see §§ 28, 97. ↩

§ 494 n. 1. See Gl. pp. 79, 85; Gg. p. 57, Df. Z. ↩

§ 494 n. 2. Gl. p. 79; cf. § 111 supra. ↩

§ 496 n. 1. Kerry omits the last clause, wrongly; for not all properties inherited in the f-series belong to all its terms; for example, the property of being greater than 100 is inherited in the number-series. ↩

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