formal or concrete. For the deepest essence of the number-series lies not in its power to aid us in finding how many units there are in this or that collection, but in its expression of the notion that something is first, and something next, in any type of orderly connection that we may be capable of knowing. It is the relational system of the numbers, taken in their wholeness as one act, which here interests us. Those degrade arithmetical truth who conceive it merely as the means for estimating the cardinal numbers of collections of objects. The science of arithmetic is rather the abstract science of ordered collections. But all collections, if they have any rational meaning, are ordered and orderly. Hence, it is indeed worth while to know where it is that we first clearly learn what order means.
Now it is not very hard to see, and to say, that I first recognize order as a form of unity in multiplicity when I learn, of myself, to put something first, and something next, and self-consciously to know that I do so. That counting my fingers, or learning the names of the numbers, first sets me upon the way to attain this degree of self-consciousness, is true enough. But our question is what the concept of order, as the one transparent form of unity in manifoldness, directly implies. In following the analysis of the number-concept, we have been led to the point where this becomes an answerable question. Given, as “bare conjunction,” is what you will. The intellect, however, as Mr. Bradley well says, accepts only what it can make for itself. The first object that it can make for itself, however, is seen, as Mr. Bradley also says, to involve the seeming of an endless process. The single purpose of the intellect, in any effort at self-comprehension, proves to be recurrent precisely when it is most obvious and necessary. The infinite task looms up before us; and, in impatient weariness, we talk of “endless fission” breaking out everywhere, and are fain to give up the task; failing, however, to observe that just hereby we have already seen how the One must express itself, by the very self-movement of the intellect, as the Many. If we reflect afresh, however, we observe that what we have seen
