§ 497 n. 1. Cf. § 203. ↩

§ 500 n. 1. It might be doubted whether the relation of ranges of propositions to their logical products is one-one or many-one. For example, does the logical product of `p` and `q` and `r` differ from that of `p``q` and `r`? A reference to the definition of logical product (§ 25) will set this doubt at rest; for the two logical products in question, though equivalent, are by no means identical. Consequently there is a one-one relation of all ranges of propositions to some propositions, which is directly contradictory to Cantor's theorem. ↩

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