I understand that you’re not looking to create difficulties, I’m just pointing out that you seem to be looking in the wrong places if you want to understand Aquinas. Best to start with experts on Aquinas first, since they have a much better grasp of the terms being used, and the context in which they were used. If you start with those who study Aquinas in a mistaken and polemical fashion, it’s really no different than taking a course in Catholicism at a fundamentalist Baptist college.
This relates directly to what we said before about the fact that there is no difference between Divine Essence and Divine Person, in terms of points of distinction. What is there in the Divine Essence that is not in the Son? Nothing. What is in the Son that is not in the Divine Essence? Nothing. If any of the Divine Persons have anything in them that is “other” than the Divine Essence, then they would be “other than God” by definition. This is brought out in the Creed when we say “of one substance”, because they don’t merely share a nature in a general way, as humans do, but share the very same identical nature, and in terms of substance are not just “like” eachother, but identical to each other.
This is an example of the terms not being understood as Aquinas uses them. Remember that Aquinas makes it absolutely clear that, in God, relations “subsist”; they are not attributes, but rather are the Divine Essence, are God, and are therefore Personal. He is not using “relation” in God and “relation” in creatures univocally, and he makes this very clear.
So, whereas in us we might say that “humanity proceeding from Adam”, we would be saying that there are two or more distinct human beings, and not one substance. “Proceeding from Adam” is an attribute of Eve, and does not subsist in itself because “humanity proceeding” is not its own being (because “humanity” is not its own being), but rather is an attribute/accident of “this human person, Eve”. Relation, in the case of all creatures, is something less than being, and is rather a description of one being’s relation to another.
With God, however, whenever we say “God” refering properly to the Divine Nature Itself, we automatically assume subsisting being, since God fundamentally is, and is Personal (“I Am that Am” is the only proper name of God, after all). So when we say “God proceeding from the Father”, this relation automatically is, and is Personal. It’s not an accident, because it is self-subsisting by definition in being “God”. So when we say “God begotten”, it is not describing the relational attribute of the Son, but the very being and Person of the Son, whereas when we say “humanity begotten” it carries no such connotation of individual subsistence.
The knowledge of the Son is the knowledge of the Father. These are not two seperate beings who confront eachother and learn externally of eachother, nor two individual beings who come to knowledge of self by exposure to “other”, but rather two Persons who share the very same singular being and knowledge. The Son knows the Father by the Divine Essence Itself, which is the very same substance (not generally, but totally) for the Father and the Son. This is why Christ can say “nobody knows the Son except the Father, and nobody knows the Father except the Son”. The Son has all the knowledge of the Father, not as a seperate knowledge, but as one single knowledge; the difference is that this knowledge is unbegotten in the Father, and begotten in the Son. The distinction of Persons lies in their relation to eachother, not in any difference of substance in any way.
They differ from the Divine Essence only in the mind, but Aquinas never says they differ from eachother only in the mind (this was the error of Sabellius, who said that “Father” and “Son” were merely mental distinctions, like “Ghosty the typist” and “Ghosty the Thomist”). Again, these people are falling into the trap of collapsing all the terms into eachother, rather than maintaining the very precise distinctions that Aquinas has laid out. When Aquinas says that “God begotten” is the same as “God”, this is because “God begotten” neither lacks nor adds anything to “God” as an Essence. Aquinas does NOT say that “begotten is the same as begettor”. Begotten is, by definition, opposite of begettor, but begotten is in no way distinct from God. And even though both begotten and begettor do not differ in any way from God, they are distinct from eachother, so that the distinction lies between relations/Persons, and not on the level of substance. If “God begotten” in any way differed from “God”, then there would be a difference of substance between “God begotten” and “God”, and we would have two Gods, and not one.
Remember, we don’t just say we have one Divinity, but one Divine. We don’t just have one Godliness, but one God. This is not something we say of humanity and human. Neither you, nor I are the same as humanity itself; we are both human, but we are not one humanity, let alone one human. If the Son is not just Godly like the Father, but is
one God with the Father, then Father must equal God, and Son must equal God, but Father need not equal Son.
Modern (and ancient heretical) attempts to equate these Persons as A = B = C miss the entire sublety of Apostolic theology, from the Cappadocian Fathers through Aquinas. It’s attempting to put Divinity into a straightjacket of creaturely reasoning; God is reasonable, for sure, but our reasoning is limited when dealing with the Divine Infinite.