Note 99 — SUPPLEMENTARY NOTE TO CHAPTER IV.

If you consider the lines a and α, as Dr. Stout prefers to do, I should have thought two views possible. (a) There are not two lines at all, but one, the “junction” at M being merely ideal. Then there remains nothing to connect and there is no relation of “immediate connection.” Or (b), the junction may be taken as real, and then you have a perfectly ordinary case of relation, the terms being the terminated lines a and α, and the relation being one of contact at M. On every ground (a) seems to me the right view, but it is incompatible with the reduction of continuity to “immediate connection.” Thus the source of the difficulty is that (1) immediate connection can only hold between the immediately successive terms of a discontinuous series, and yet (2) cannot hold between them precisely because they are discontinuous.