is due to the fact that the only systems of ideal objects which the intellect can define without taking account of “bare external conjunctions,” are systems such that to whatever object we have presupposed, another object, expressing the same intellectual purpose, must correspond, as the next object in question. This fact, however, is due to the simple necessity of the reflective process in which we are involved.
Our thought seeks its own work as its object. That is of the very essence of this effort to let the intellect express its self-movement. But making its own work its object, observing afresh what it has done, is merely reinstating, as a fact yet to be known, the very process whose first result is observed when the intellect contemplates its own just accomplished deed. Reflection, then, implies, to be sure, what, in time, must appear to us as an endless process. We are not interested, however, in the mere feeling of weariness which this endless process (in consequence of still another “bare conjunction,” of a psychological nature) involves to one of us mortals when he first observes its necessity. What interests us is the positive structure of the whole intellectual world. We have found that structure. It is the structure of a self-representative system of the type that we now have in mind. We frankly define all such systems as endless, so far as concerns the variety of their elements. But hereupon we indeed observe that, as self-representative, they are, in a perfectly transparent way, self-ordered. The trivial illustration of the map within the country mapped, has been followed by the more exact illustrations of the self-representative character of the complete number-system when once its traditional structure is accepted as something given and present in totality. With these examples of self-ordered unity in the midst of infinite diversity, we have returned to the question of the logical genesis of the very conception of order of which the number-system is the first example. We have found the answer to our question in the assertion that since a self-representative system, of the type here in question, once assumed as an ideal object, determines its own order, and assigns to its constitu-
