And even if it were assumed that this supposition could be established, this would constitute a counterargument, not a challenge to any of the premises. A counterargument requires a proof of its own, and we shall discuss that later.

If the objector were to say, “I challenge the validity of the division and make this the basis of my challenge,” this would not be valid. The reply is that a challenge must concern a premise for which no proof has been offered. Yet the proponent has shown that the division is self-evidently valid, so it cannot validly be challenged. If, however, the objector establishes the possibility of an existent that is neither within the world nor outside it, he is presenting an argument for the opposite of his opponent’s position. He would then be usurping the proponent’s role, for such usurpation consists in challenging a premise by establishing the opposite of the conclusion to be proved.

In effect, he is saying: “If the proponent’s proof were sound, my position would be invalid. But my position is not invalid, for such-and-such reasons.” This is usurping the proponent’s role and is therefore not accepted.

The same applies here: if he challenges the division by establishing this supposition, that supposition is itself his position. For he claims that there is an existent to which this division does not apply, and this is precisely the point at issue. If he argues for its possibility, he is usurping the proponent’s role, and this is not accepted from him. Thus, it is clear that the proof is complete.

This objection therefore amounts to saying: “If an existent is posited that is neither eternal nor originated, then the division of existents into originated and eternal is invalid. And if an existent is posited that is neither necessary nor contingent, neither subsisting in itself nor subsisting in another, then the division of existents into the necessary, the contingent, that which subsists in itself, and that which subsists in another is invalid.” And it is well known that a division which is known