by nonexistence, that is correct, but it is not what is under discussion.
But if he means that the beginningless kind, which has always existed and will always exist, cannot be preceded by nonexistence, this is precisely what is disputed.
He has thus assumed what he seeks to prove merely by changing the wording. It is as though he had said, “Temporally originated events cannot continue perpetually.” This is like saying, “What is everlasting cannot come to an end; every individual future event comes to an end; therefore, future events cannot be everlasting.”
The answer is that it is the kind that is everlasting, not each individual instance. The same answer applies to the past. This matter has been discussed at length elsewhere.
[Third]
It may be said:
This premise is the subject of well-known disagreement among rational thinkers. Perhaps most communities of religious adherents and philosophers dispute it. As for the existence of an infinite series of causes and effects, there has been no disagreement concerning it among any known rational thinkers.
Even supposing that the disputed premise were correct, establishing the agreed-upon premise by means of a disputed one would run counter to proper teaching, exposition, and argumentation—especially since the latter is neither clearer than the former nor supported by a proof peculiar to it. A disputed premise may sometimes be introduced because it has a proof peculiar to it, or because of its clarity, or for some similar reason. Without such a reason, however, this is not a sound way to argue.