Is the Son autotheos?

On Facebook, a Catholic apologist objected to the belief that each person of the Trinity is autotheos. Before addressing his objections directly, I'd like to take a few steps back:

i) I don't have a problem with church councils. There's nothing wrong with Christian representatives getting together to produce a joint declaring that not only expresses their individual beliefs, but their shared beliefs. A public statement of common faith can be very useful in various ways. But from a consistent Protestant perspective, a council doesn't make doctrine true; rather, true doctrine makes a council true. In the classic words of the Westminster Confession:

The supreme judge by which all controversies of religion are to be determined, and all decrees of councils, opinions of ancient writers, doctrines of men, and private spirits, are to be examined, and in whose sentence we are to rest, can be no other but the Holy Spirit speaking in the Scripture (WCF 1.10).

ii) Some Protestants pay lip-service to sola scripture, but when that's put to the test, they seem to be insecure about their ultimate commitments. Some Protestants act as though God made a temporary exception to sola Scriptura by inspiring "ecumenical councils" for the first 500 years of church history. But if you can't make allowance for the possibility, in principle, that these councils could be mistaken in some particular, then you're not operating with a consistent Protestant epistemology. Rather, you're straddling the fence.  

Objecting to my position, the Catholic apologist said:

He has constantly ascribed "aseity" to each of the persons of the Trinity in their personal capacity, rather than properly limiting it to the Trinity as a whole and/or the unbegotten, unspirated person of the Father. It seems clear that he wants to apply the concept of aseity to the Son as to the Father. So, what we are left with is separate persons who are gods or separate gods, i.e., polytheism. 

Clearly there cannot be separate infinite, perfect, omnipotent gods as a logical proposition; there can only be one infinite, perfect, omnipotent God. The existence of a second such being would mean that one or the other, or both, is not perfect, infinite or omnipotent. 

The Trinity is one God; the persons of the Trinity are identical and equal, except in origin, since the Son is begotten and the Holy Spirit proceeds from the Father and the Son, and the Father is neither unbegotten and proceeds from nothing. Thus, they share the same nature and the same substance and are one God. There cannot be two different Gods having different origins with a different nature.

His objection is a bundle of confusions:

i) He doesn't actually present an argument. But he seems to have two intuitive arguments that he lacks the competence to articulate. So we have to begin by making his arguments for him before we can dispose of them. The first argument he's groping at seems to be this: If all three Trinitarian persons are autotheos, that means they have different origins. If they have different origins, that makes them separate Gods. 

And I agree with him that if the Father, Son, and Spirit each has different origins, that makes them separate Gods. But the problem with his argument is this: to be autotheos is to be unoriginate. Likewise, aseity means having no origin. 

Therefore, to say each Trinitarian person is autotheos, or to ascribe aseity to each person of the Godhead, is the polar opposite of saying each person has a different origin. Rather, it means none of the persons of the Godhead has a source of origin. So his argument is utterly confused. He has things exactly backwards.

ii) The second argument he's groping at is based on the alleged impossibility of two (or more) "infinite" beings. He doesn't turn that into an actual argument. He merely asserts the impossibility of two (or more) "infinite" beings. I'm guessing that in his inchoate intuition, he's getting carried away with a spatial metaphor. 

This seems to be what he has in mind: there can only be one infinitely large object. That's because it takes up all the available space. So there's no extra room for a second infinitely large object. One infinitely large object squeezes out the possibility of more than one infinitely large object. And perhaps he thinks that's analogous to monotheism. Assuming that's an accurate reconstruction of what he's gesturing at, it's beset by a host of problems:

iii) It presumes a theory of absolute space, where space is considered to be an empty container. That's the Newtonian view. And that was eclipsed by Einstein's relational view of space.

iv) What does he mean by "infinite"? If he means a potential infinite, then you could have two (or more) infinitely large objects inasmuch as a potential infinite is an actual finite.

v) Perhaps, though, he means an actual infinite. If so, why think the notion of an actually infinite physical object is even coherent, intelligible, or realistic? Try to imagine an infinitely large steel ball or an infinitely large cube. Is that even conceivable, much less physically possible? To be a physical object is to have boundaries, right? To have boundaries is to be finite rather than infinite.  

vi) A deeper problem is that God is not a physical object, so spatial infinitude is inapplicable to God. That's a category mistake. God doesn't literally fill the universe. But if the objection is that God is analogous to a physically infinite object, I have no idea where the point of comparison lies. 

vii) Perhaps he means God is "infinite" in the sense of unlimited. Yet there are things that God can't be and things that God can't do. God can't be ignorant. God can't scratch his head (since God has no head or hands). 

Likewise, for the argument to go through, God would have to be unlimited in a sense that precludes two unlimited beings. But that's just too vague. 

viii) The coexistence of abstract actual infinities is not only possible, but bedrock reality. Just combine mathematical realism with infinite sets. 

ix) Furthermore, if we choose to stick with the language of infinitude, there is a sense in which the Trinity does consist of three "infinite" individuals. For instance, if you define omnipotence as infinite (i.e. unlimited) power, and each person is omnipotent, then each person is infinite. Mind you, I don't think that's the best way to define omnipotence. 

To take a better example, if you define omniscience as knowing an actual infinitude of necessary truths, contingent truths, and counterfactual or hypothetical truths, and each person is omniscient, then each person is infinite. So either our Catholic apologist must deny that the Son is omniscient, or he must deny that his knowledge is actually infinite. Otherwise, he must be prepared to admit that, in this sense, monotheism is consistent with three "infinite" individuals.   

x) Indeed, it's always been a challenge for Christian philosophers and theologians to formulate the Trinity in a way that avoids modalism while avoiding the appearance of tritheism. But that's the hand we've been dealt. Those are the cards we must play. We can't burn a card to avoid the charge of "polytheism". We are duty-bound to work with what we've got. 

xi) Finally, to say the Son's existence is absolute and inderivative is a higher Christology than to say the Son's existence is derivative. (ditto: the Spirit.) It's ironic when, in the name of orthodoxy, Catholics accuse you of heresy for defending higher Christology than their own.