- § 124. Philosophy and mathematics distinguished
- § 125. Is there a more fundamental sense of number than that defined above?
- § 126. Numbers must be classes
- § 127. Numbers apply to classes as many
- § 128. One is to be asserted, not of terms, but of unit classes
- § 129. Counting not fundamental in arithmetic
- § 130. Numerical conjunction and plurality
- § 131. Addition of terms generates classes primarily, not numbers
- § 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

does not apply to this case. ↩`x`∈`x`

The Principles of Mathematics was written by Bertrand Russell, and published in in 1903. It is now available in the Public Domain.