The Principles of Mathematics (1903)

Chapter VII. Propositional Functions.

Table of Contents

  1. § 80. Indefinability of such that
  2. § 81. Where a fixed relation to a fixed term is asserted, a propositional function can be analysed into a variable subject and a constant assertion
  3. § 82. But this analysis is impossible in other cases
  4. § 83. Variation of the concept in a proposition
  5. § 84. Relation of propositional functions to classes
  6. § 85. A propositional function is in general not analysable into a constant and a variable element

§ 83 n. 1. It is necessary to assign some meaning (other than a proposition) to aRb when R is not a relation.

§ 83 n. 2. A propositional function, though for every value of the variable it is true or false, is not itself true or false, being what is denoted by any proposition of the type in question, which is not itself a proposition.