Early Work on the Substitutional Theory [1905]

Here we print two texts on the substitutional theory. The first of them, 3a, which gives the earliest detailed explanation of that theory, is a letter of 15 December 1905 from Russell to G. H. Hardy. The second, 3b, entitled “On Substitution” and dated December 1905 by a note on it in Russell’s hand, is the earliest extant paper exclusively on the theory. The manuscript of 3b was originally filed in the Russell Archives with Hardy’s letters, reflecting the fact that this 1905 paper was sent to Hardy—probably early the following year. (As we see below, it was first sent to another mathematician.)