dependent upon anything outside itself, even though some of its parts depend upon others. This, however, is a baseless misconception. For if the totality is said to be non-contingent, we have explained in our discussion of logic that whatever is not contingent in the strict sense must be either necessary in itself or impossible. It cannot be said to be impossible, for otherwise it would not exist. It must therefore be necessary in itself. Yet if the totality is the aggregate of its individual members, and each member is contingent, then the totality is also contingent in itself. What is necessary in itself cannot possibly be contingent in itself.

If it is contingent, it must have a determining factor, since it exists. This determining factor must be either contingent or necessary. It cannot be contingent, since it would then belong to the totality. Moreover, it would follow that it determines itself, because it determines the totality, and whatever determines the totality determines its individual members, of which it is one. This is impossible. It would also follow that it is the cause of its own cause, which is an impossible circularity.

If, on the other hand, it is necessary in itself and depends upon no cause for its existence, it must be the cause either of the totality or of some part of it. If it is the cause of the totality, it must be the cause of every individual member, since the totality is the aggregate of those members. This is impossible, because it would entail each member of the supposed totality having two causes: the necessarily existent cause, and the member of the totality said to be its cause. If it is the cause of some part of the totality that has no other cause, this contradicts the hypothesis.

These impossibilities follow only from the claim that there is no end to the series; that claim is therefore impossible. How could it be otherwise? Whenever causes and effects are said to depend upon a cause that itself has no cause, the claim