limits the observed portion so as to set it between other portions. Thus, at all events in such cases as our own consciousness of the extended world, our process of attentive discrimination tends to become a Recurrent Process,[1] i.e. a process in which every step leads to conditions which demand, or at least appear to demand, a repetition of the very type of act that led to the step in question itself. For if I have discriminated, then, at least in this sort of instance, I have found a basis for a repetition of discriminations.
Now it is also plain, at least in case of such an object as the world of extended things, that this very recurrent character of our process of discrimination becomes to us a motive for interpreting what we take to be the “real structure” of space itself. Because we are led, upon any clear distinction of positions in space, to an observation of an interval between two positions, while this interval itself becomes the basis for new discriminations between the positions that lie once more within that interval, we find ourselves started upon a process which we can define as recurrent, that is, as capable of repeating itself indefinitely; and since we see no reason why this process should meet with any limit in the nature of extended facts, we come to the familiar postulate of the infinite divisibility of space. And because every such observed collection of spatial objects, once discriminated, and then viewed as a whole, turns out to be between still other regions of space, which its very presence leads us to discriminate from itself, this process of discrimination
