ABSTRACT
In this passage, the remark: “There is that which goes before, and that which follows; there is distance or interval,” if considered as an inference, is a non sequitur; the mere fact of order does not prove that there is distance or interval. It proves, as we have seen, that there are stretches, that these are capable of a special form of addition closely analogous to what I have called relational addition, that they have sign and that (theoretically at least) stretches which fulfil the axioms of Archimedes and of linearity are always capable of numerical measurement. But the idea, as Meinong rightly points out, is entirely distinct from that of stretch. Whether any particular series does or does not contain distances, will be, in most compact series (i.e. such as have a term between any two), a question not to be decided by
argument. In discrete series there must be distance; in others, there may be-unless, indeed, they are series obtained from progressions as the rationals or the real numbers are obtained from the integers, in which case there must be distance. But we shall find that stretches are mathematically sufficient, and that distances are complicated and unimportant.
