Andrew Hollingsworth has an interesting paper, Thomistic Simplicity and Distinguishing the Immanent and Economic Trinities (PDF), arguing that the former causes problems for the latter. Unfortunately, he makes a number of common errors. This is seen very clearly in his account of what simplicity means for Aquinas:
The DDS: (i) God lacks all composition and is made up of no parts, be those parts physical or metaphysical. (ii) There exist in God no distinctions, be those distinctions between essence and existence, act and potency, substance and attribute, essence and accident, genus and differentia, or form and matter. (iii) God is identical with all of his intrinsic features, and all of said features are identical with one another.
This is wrong in ways that end up being significant for the argument.
(i) is roughly correct, although 'physical or metaphysical' is not a genuine Thomistic distinction in this context; the doctrine in fact relies on the Thomistic account of composition, in which you have composition wherever you have act and passive potency. There are different kinds of parts, but what makes them parts is always the same, so 'physical or metaphysical' does no work in the Thomistic account. (It gets added in these contexts because people often assume that 'parts' means 'physical parts'.)
(ii) is inconsistent with the Thomistic account of simplicity. (As a side issue, 'substance and attribute' and 'essence and accident' are bad pairings -- one would expect 'substance and accident' and 'essence and existence'.) What is true is that there are in God no distinctions that imply composition (which, again implies act and passive potency). Some kinds of distinctions, like purely relative distinctions, do not necessarily do so. Hollingsworth is sloppy about this; he sometimes just says 'distinctions' and sometimes 'real distinctions', which is a very specific kind of distinction. This is actually a problem for his argument, because there is no reason whatsoever why one would think the immanent/economic distinction is a real distinction. They aren't separable; they aren't related as act and passive potency; and dividing God into two trinities would cause any number of problems. Rather, the economic Trinity just has to be the immanent Trinity considered relatively. Thus, to use the example that Hollingsworth uses, the divine missions (like the sending of the Son in the Incarnation or the sending of the Spirit to believers) are just the divine processions considered relative to a temporal effect. The Son is sent because the Son is always from the Father and creation is made to have an effect specifically linked to the Son being from the Father (the Incarnation).
(iii) is very, very wrong; this is a claim of analytic philosophers, not Thomists. Aquinas actually makes a famous distinction here: God is idem (same) with everything in God secundum rem, but not idem with everything in God secundum rationem. This is quite important, because identitas secundum rem doesn't require transitivity, which is what is usually implied in contemporary philosophy if you are talking about something being 'identical' without any qualification. Identitas in Latin does not mean 'identity' in the modern sense, although identity in the modern sense would be a kind of identitas. It means 'sameness'; its usual meaning is just generic sameness (sameness of kind), although in philosophical contexts other kinds of sameness are often in view.
There are also problems with Hollingsworth's understanding of the Incarnation, in Thomistic terms.
When applied to the Son’s submission to the Father, the problem becomes clear. According to Thomas, the Son—qua his humanity—wills to submit to the Father’s will. The Son does not—qua his divinity—will to submit to the Father. However, it does not seem to matter by which nature the Son wills to submit to the Father. Though it may be by his human will in the incarnation, the Son—nevertheless—wills something distinct from what he wills in the IT. In the Incarnation, the person of the Son is still a unified single subject, though he has two natures. But it is the Son, as a single subject, that wills submission to the Father, not the human nature apart from the person of the Son.
The supposed problem is not at all clear, however. The human will is not part of the divine substance, and therefore its distinction from the divine will does not introduce composition into God. Acts of the human will are in fact distinct from acts of the divine will, and this is true of the Son, who is a subject with a human will and a divine will. Hollingsworth seems to be baffled as to why St. Thomas doesn't affirm monothelitism; the reason he doesn't is the Third Council of Constantinople. Monthelitism is simply wrong; your account of the Incarnation should not be getting the result that the acts of the divine will and the acts of the human will are the same without distinction. But there is, again, no conflict with the doctrine of divine simplicity because the human will is not divine, and therefore it obviously implies composition and distinction from what is wholly simple. (Hollingsworth also seems to miss that Aquinas's analogies to the horse and rider and the master and servant are not depictions of the relation in the Incarnation but clarifications of the relevant principles of instrumental causality, because Aquinas holds that the human will of Christ has a necessarily subordinate and instrumental relation to the divine will, which is why the human will never conflicts with the divine will.)
But in any case, Hollingsworth gets the apparent problem he does because he assumes that (ii) is taken by Thomists to be true, as is, and, what is more, true not just of God himself but (what no one who was not a lunatic could believe) of everything attributable to God, even relatively, so that God engages in no distinguishable acts, even relatively. But God's creation of the world is (for instance) distinct from his miraculous parting of the sea for Moses, and both are distinct from God's sending of the Holy Spirit to the Church at Pentecost. But the distinction does not introduce any composition into God, because we distinguish these acts relative to things other than God (different objects and effects) and under a description, where the descriptions are not synonymous with each other. Thus there is no problem on the Thomistic account with attributing to God two distinct operations; such operations will in some sense be the same, and will not be distinct in a way that introduces composition, but they will be distinguishable.
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