The More Than Three Persons discourse does not answer the co-paternity of the Holy Ghost quandary directly. Reply to Objection 4 says that since there is a relation of proceeding between Father and the Holy Ghost, the Holy Ghost cannot be in relation of principle even as parent. But Aquinas did not apply the same logic when the Son, though in relation of begetting with respect to the Father, is in relation of principle as spirer.
Moreover, if we know that the Father and the Holy Ghost have one and the same goodness, then it would follow that the fruit of the goodness, the Son, would be co-begotten by them.
The reply to Objection 4 would still stand, because of the fact that the infinite loop purported in Objection 4 would have to alternate between procession and filiation and therefore break, leaving the number of Divine Persons at 3.
The only part of "Reply to Objection 4" that I understand is that goodness is of the essence of God and is shared by all three Persons.
I don't understand the rest of it. I have to do more studying 8-)
But Aquinas did not apply the same logic when the Son, though in relation of begetting with respect to the Father, is in relation of principle as spirer.
Moreover, if we know that the Father and the Holy Ghost have one and the same goodness, then it would follow that the fruit of the goodness, the Son, would be co-begotten by them.
I think this is addressed in post #14.
The reply to Objection 4 would still stand, because of the fact that the infinite loop purported in Objection 4 would have to alternate between procession and filiation and therefore break, leaving the number of Divine Persons at 3.
This part I think I understand, in that goodness belongs to the essence of God. As St. Thomas says in post #14, there is no absolute difference between Persons, but only differences of relation.
Sorry that I can't be of any more help. This is a subject worth studying.