If it is said:

“The invalidity of part of a proof entails the invalidity of the proof itself. Thus, the proof given for the invalidity of the objection is itself invalid.”

The reply is: The expression “part of the proof” is ambiguous. If “part” means one of the alternatives posited, this claim is false: the invalidity of one of the posited alternatives does not entail the invalidity of the proof when another alternative is valid. If, however, “part of the proof” means one of its premises, the claim is correct: when a premise of a proof is invalid, the proof is invalid. Here, however, the premise is valid, since it consists of an exhaustive division into negation and affirmation. It is well known that a division between two contradictories necessarily entails that one of the alternatives is false in reality. The premise of the proof is not the conjunction of two contradictories, for that is impossible; rather, it is the validity of the division into negation and affirmation.

The second premise is that the intended conclusion follows on either supposition. If the division is between negation and affirmation, and the intended conclusion follows from either alternative, then that conclusion is established in reality. Even if one alternative does not obtain in reality, the intended conclusion follows on the other supposition, so the failure of the former to obtain does no harm. These suppositions were mentioned only to demonstrate that the objection raised does not undermine the validity of the aforementioned proof of the Necessary Existent. Rather, the proof is valid on either of the two contradictory suppositions. This is among the finest argumentative turns in reasoning and disputation for refuting unsound objections. It is like an enemy who arrives intent on fighting