as stated above. If it were necessary, then, despite the impossibility of this, that would itself establish precisely what we seek to prove. If it were contingent, it would require a determining cause. This determining cause must be either within the totality or outside it. The former cannot be maintained, for the determining cause of the totality is also a determining cause of its individual members. It would therefore necessarily determine itself, since it is one of those members. It would thereby cease to be contingent, contrary to the hypothesis. It would also determine its own cause, since that cause is among the individual members. This would make the cause an effect and the effect a cause—an impossible circularity.

If the determining cause is outside the totality, it must be either contingent or necessary. If it were contingent, it would belong to the totality, contrary to the hypothesis. Thus, the only remaining possibility is that it is necessary in itself, which is what we seek to prove.”

I say:

This, then, is the argument he presented; he offered no other argument to establish the existence of the Maker.

He then raised numerous objections to his own argument, including the following objection:

“We do not grant that anything called a totality exists in an infinite series, such that your argument would hold. Nor does the validity of this concept in a finite series, with its implication of boundedness, entail its validity in an infinite series. Let us concede that the concept of a totality applies to an infinite series and that it is contingent.