must exist both on the supposition of its existence and on the supposition of its nonexistence certainly exists in reality. This is the intended conclusion.

If it is said:

“How can its existence be supposed while its nonexistence is also supposed? This combines two contradictories.”

The reply is:

“Yes. Since the supposition of its nonexistence is impossible in reality, it may entail something that is likewise impossible in reality. This further establishes its existence.

“Moreover, if supposing its nonexistence entails combining two contradictories, that supposition is impossible in reality. Thus, the supposition of its nonexistence is impossible in reality; and if its nonexistence is impossible, its existence is necessary. This is the intended conclusion.”

If it is said:

“If its nonexistence is certainly impossible in reality, and the invalidity of the objection is conditional upon its nonexistence, then the invalidity of the objection does not follow. If the objection is valid, the aforementioned proof is invalid.”

We reply: Supposing its nonexistence is part of the proof that the objection is invalid; it is not itself the invalidity of the objection. It is well known that the absence of a proof does not entail the absence in reality of what it establishes, for a proof need not hold in reverse. Even if its nonexistence in reality were, by itself, a proof that the objection is invalid, supposing the contrary of that proof would not entail that the objection is valid. How much more so when it is merely part of a proof!