The Principles of Mathematics (1903)

Chapter XV. Addition of Terms and Addition of Classes
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Chapter XV. Addition of Terms and Addition of Classes

Table of Contents

  1. § 124. Philosophy and mathematics distinguished
  2. § 125. Is there a more fundamental sense of number than that defined above?
  3. § 126. Numbers must be classes
  4. § 127. Numbers apply to classes as many
  5. § 128. One is to be asserted, not of terms, but of unit classes
  6. § 129. Counting not fundamental in arithmetic
  7. § 130. Numerical conjunction and plurality
  8. § 131. Addition of terms generates classes primarily, not numbers
  9. § 132. A term is indefinable, but not the number 1

§ 127 n. 1. Ed. Gerhardt, II, p. 300. ↩

§ 128 n. 1. Grundlagen der Arithmetik, Breslau, 1884, p. 40. ↩

§ 130 n. 1. A conclusive reason against identifying a class with the whole composed of its terms is, that one of these terms may be the class itself, as in the case class is a class, or rather, classes are one among classes. The logical type of the class class is of an infinite order, and therefore the usual objection to x∈x does not apply to this case. ↩

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