included in this totality. Once everything a thing needs is present, it no longer needs anything at all, and its existence must then follow. For as long as it still needs something, it does not exist; but once everything upon which its existence depends is present, and its existence no longer depends upon anything else, it must exist. Thus, by the totality of that upon which a thing’s existence depends, one should mean those things which, when present, entail the existence of the aggregate, and without all of which the aggregate does not exist.

It is clear that, if this is what is meant, that totality cannot be merely a part of the aggregate, since this would entail that some of its parts suffice for the whole. For he has defined the totality as that whose presence makes the existence of the aggregate necessary, and without which the aggregate cannot exist. If some of the parts constituted that totality, those parts would necessarily suffice to bring about the aggregate—whether they were supposed to be the agent of themselves and the rest of the totality, whether their existence were supposed to be the very existence of the aggregate, or whether any other impossible supposition were made. Whatever supposition is made, it is impossible. For the totality of that upon which the aggregate depends cannot be a part of the aggregate, however it is interpreted. This is what was to be demonstrated.

The expression “aggregate,” however, is ambiguous. It may mean merely the collective configuration, all the individual members, or all the individual members together with the collective configuration. If the first meaning is intended, there is no doubt that one of the individual members may necessitate this configuration, as in an aggregate composed of the necessary being and a contingent being, for