This is a revised version of my argument in this earlier blog:

If God is a necessary a being and uncaused, then He must lack all passive potentiality. Whatever intrinsic properties He has (qua God), He must have necessarily. Here's the argument.

First, I will need the concept of a logical moment. If agent A causes some effect E, then we can identify two logical moments, even if the action and the effect are temporally simultaneous. If agent A causes E, then agent A acts at one logical moment M1, and the effect is first in actuality at a posterior moment M2. The relation of priority/posteriority between logical moments is transitive and asymmetric. No logical moment is prior to itself, and no moment is prior to any moment that is prior to it.
 
We have proven that there are absolutely uncaused facts. These facts must belong to logical moments that are absolutely primal—i.e., logical moments that are posterior to no logical moments.
 
Second, I need the concept of a full complement of intrinsic properties. A substance x has a full complement of intrinsic properties at moment N with respect to its nature if and only if every property P is such that, if x has P intrinsically at some logical moment in some possible world, then x has either P or its negation intrinsically at N (with respect to that same nature).
 
Now I’m in a position to propose a basic principle about causality:
 
The Completeness of Agents (COA). Necessarily, if agent x acts at logical moment M to produce some effect, then x has a full complement of intrinsic properties at M with respect to its nature.
 
The rationale for COA is this: in order to act at a logical moment, an agent must actually exist in that moment. But an agent cannot actually exist at a moment without possessing a full complement of properties at that moment. If it didn’t possess such a full complement, it would fall short of actuality and would thereby be disqualified from acting.
 
I need one further principle:
 
The Groundedness of Intrinsic Properties. Necessarily, if an individual x has property P intrinsically at logical moment M, then there are some properties Q1 through Qn such that: x’s being P at M is wholly grounded by x’s having Q1 through Qn at M, and for each Qi, x’s having Qi at M is a basic, positive fact.

Let’s suppose that God is one of the agents acting at a primal moment M. Suppose for contradiction that God has some intrinsic property P at M contingently. By GA, there must be some basic properties Q1 through Qn possessed intrinsically by God at M, and God’s having P at M is wholly grounded by His having Q1 through Qn at M. We can assume that grounding is a necessitation relation. Consequently, God must have at least one property Qi contingently at M. If He had all of them at M necessarily, then He would have to have P at M necessarily as well.
 
Since it is a basic, positive, contingent fact that God possesses Qi at M, then this fact (by the PSR or principle of causality) must have a cause. But that is inconsistent with our assumption that M is a primal moment, and so no fact at M can have a cause.
 
Hence, God cannot possess any contingent intrinsic properties at logical moment M.
 
If it is necessary that God possess P intrinsically at M, there must be some explanation of this necessity. A logical moment is not a thing in its own right, but simply a node in the causal network of the world. So, if it is necessary that God possess P intrinsically at M, this must be a result of God’s essence, and a result of God’s essence alone, since there are no prior facts to appeal to. But if God’s possessing P is a result of God’s essence alone, then He must possess P necessarily at ever logical moment in every possible world, and not just at M.
 
Suppose that God has an intrinsic property P at moment N. Since God has a full complement of properties at the primal moment M, God must either have P or its negation at M. So, God qua God must have P necessarily at all logical moments in all possible worlds. Hence, God has all His intrinsic properties necessarily at every logical moment.
 
Here’s another way to look at this. Why can’t God lack some intrinsic property P at primal moment M, such that God could gain P in some subsequent logical moment? For a thing x to lack a possible intrinsic property is for it to have an intrinsic character of a certain kind. This intrinsic character must be a positive fact about x. Either the absence of P is grounded by x’s having some contrary intrinsic property Q, or else there is some totality property T [1] of x that encompasses the fact that x’s total complement of intrinsic properties does not include P. In either case, there is a basic, positive fact about x that must be causally explained (given the PSR).

When God lacks a particular intrinsic property (with respect to His divine nature), this absence is not a mere absence but a kind of privation. Contingent privations are causable facts, and so the PSR requires that they all have actual causes (see Haldane 2007). Consequently, God cannot have (qua God) any contingent privations in the primal moment M. It is not possible for Him to subsequently gain intrinsic properties in His divine nature, since He has with necessity a full complement of intrinsic properties.
 
Since God has every intrinsic property essentially, He must be a being of pure actuality, with no passive potentiality. Consequently, He must be timeless.
 
[1] A totality property is a constituent of what David M. Armstrong (1997) called totality facts. A totality fact about some particular substance would entail that the substance lacks any intrinsic property not contained in some totality C. Totality facts are basic, positive facts that ground truths about privations.

I have argued that we can deduce that God is a being of pure actuality, without passive potentialities, from the fact that He is absolutely the First Cause. Joe Schmid has challenged me on this inference, rightly pointing out that the implication is not immediate. I will try here to make the connection more nearly evident.
 
To do so, I will have to introduce some technical machinery. First, I will need the concept of a logical moment. If agent A causes some effect E, then we can identify two logical moments, even if the action and the effect are temporally simultaneous. If agent A causes E, then agent A acts at one logical moment M1, and the effect is first in actuality at a posterior moment M2. The relation of priority/posteriority between logical moments is transitive and asymmetric. No logical moment is prior to itself, and no moment is prior to any moment that is prior to it.
 
We have proven that there are absolutely uncaused events. These events must belong to logical moments that are absolutely primal—i.e., logical moments that are posterior to no logical moments.
 
The second technical device that I need is the definition of a nature-constituted disjunction of properties. Let D be a (possibly infinite) disjunction of monadic properties. Then D is a nature-constituted disjunction for individual x if and only D is a minimal disjunction such that it is essential to x to have some property in D. That is, there is no disjunction D* whose disjuncts form a proper subset of the disjuncts of D and such that it is essential to x to have some property from D*.
 
Let’s say that an individual x has a full complement of properties at logical moment M just in case x has at M every property that is essential to x, and, for every nature-constituted disjunction  D of properties for x, x has a property from D at M.
 
Now I’m in a position to propose a basic principle about causality:
 

• The Completeness of Agents (COA). Necessarily, if agent x acts at logical moment M to produce some effect y, then x has a full complement of properties at M.

 
The rationale for COA is this: in order to act at a logical moment, an agent must actually exist in that moment. But an agent cannot actually exist at a moment without possessing a full complement of properties at that moment. If it didn’t possess such a full complement, it would fall short of actuality and would thereby be disqualified from acting.
 
I need one further principle:
 

• The Groundedness of Accidents (GA). Necessarily, if an individual x has property P as an intrinsic, natural property, then there is some nature-constituted disjunction D of x’s essence such that P is one of the disjuncts of D.

 
In order for a property to be an intrinsic and natural property of a thing, it must be determinate of some determinable property that is essential to that thing. A thing can’t just take on intrinsic properties willy-nilly. An intrinsic property must fulfill some essential role dictated by the thing’s nature. The requirements of a thing’s nature lay out the possibilities for a thing’s intrinsic character.
 
Let’s suppose that God is one of the agents acting at a primal moment. Suppose for contradiction that God has some intrinsic property P contingently. By GA, there must be some disjunction D such that D is a nature-constituted disjunction for God, and P is a disjunct of D. If D were a trivial disjunction (with only one disjunct), then P would be an essential property of God and so not contingent. So, D must be a non-trivial disjunction.
 
Let M be a primal moment at which God acts. By COA, we know that God possesses a full complement of properties, relative to the divine nature, at that primal moment M. So, God must possess some member of D at M. But every member of D is such that, if God possesses it at M, He must possess it contingently. Consequently, God must have some contingent intrinsic property at M. Call this property Q.
 
Now, either it is necessary that God possess Q at M, or it is contingent that He do so. Both are impossible.
 
If it is necessary that God possess Q at M, there must be some explanation of this necessity. A logical moment is not a thing in its own right, but simply a node in the causal network of the world. So, if it is necessary that God possess Q at M, this must be a result of God’s essence, and a result of God’s essence alone, since there are no prior facts to appeal to. But if God’s possessing Q is a result of God’s essence alone, then He must possess Q necessarily and not contingently.
 
There is a second reason for ruling out this first horn of the dilemma: a reason based on St. Thomas's First Way. Suppose that it is necessary for God to have Q at the primal moment M. Then, since Q is contingent, it must be possible for God to have some contrary property at some posterior logical moment. If so, this would mean that God is intrinsically changeable. But an intrinsically changeable being exists within time, not outside it. And a being that is inside time cannot be causally responsible for the propagation of time, as the Prime Mover must be.
 
If, alternatively, it is contingent that God possess Q at M, then this fact (by the PSR or principle of causality) must have a cause. But that is inconsistent with our assumption that M is a primal moment, and so no fact at M can have a cause.
 
Hence, God cannot possess any contingent intrinsic properties at any logical moment. He must be a being of pure actuality, with no passive potentiality.
 
There is a complication that is introduced by the fact of the Incarnation. The Second Person of the Trinity has two complete natures, one divine and one human. Hence, we must distinguish between the properties that God the Son has qua God and those He has qua man. Qua God, the Son cannot have any contingent intrinsic properties, for the reason given above. Qua man, the Son has many contingent intrinsic properties. In fact, having a human nature is one of those contingent properties that the Son has qua man. So, in this sense, and only in this sense, God can have contingent intrinsic properties, namely, by assuming a second nature.

In the Summa Theologiae Q4, a1, Thomas gives just one simple argument for concluding that God is perfect: namely, the fact that imperfection always implies some lack of actuality, and God is actuality in its absolute fullness. His reply to objection 3 is also noteworthy. Objection 3 observes that ‘existence’ seems radically imperfect, since things can exist no matter how far they are from perfection. Since God’s nature is simple, unqualified existence, He would have to be the most imperfect thing of all.
 
In the Reply, Thomas rejects this greatest common factor conception of ‘existence’. It is true that the formula ‘X exists’ can be true, no matter how minimal X’s grip on existence may be. (Thomas calls this the ‘formal principle of existence’, by which he seems to mean its logical or semantical role.) However, Thomas urges us to focus instead on the metaphysical role that is played by acts of existence (actus essendi). It is the act of existence that gives each thing whatever degree of being it has. The act is limited by the nature or essence of the thing, not vice versa. Acts of existence are the source of reality and actuality. Hence, God, as the supreme act of existence, must contain eminently every possible degree of being, so that He can give to each individual act of being all the actuality it needs to do its work, given its associated essence.
 
In article 2, Thomas argues that God possesses all the perfections had by creatures. This is the crucial point at which we depart from purely negative theology. He gives two arguments: one from God’s place as First Cause, and the other from God’s essence being His pure existence. First, since God is the cause of all the perfections in any creature (not only in the actual world, but also in any alternative possibility), God must possess in an eminent form each of those perfections. This is an appeal to the principle of proportionate causality which we’ve seen repeatedly since the First Way. As Thomas explains, the fact that the sun is the cause of heat does not entail that the sun is formally hot. But it does entail that it contains heat eminently—that it has some attribute that is, by virtue of its greater nobility of being, capable of making other things formally hot. Similarly, God is the cause of all heat, but He is not himself formally hot. How, then, is He eminently hot? He is so, as we shall see, by being an Intellect, knowing the form of heat as one of His possible creations. This is the same sense in which an architect is eminently a house.
 
So far, we have not really moved very far from a negative theology, since to say that God is eminently F is really to say little more than that He is the cause of F-ness. The second argument is, I think, the more fruitful. God’s existence is unlimited by any distinct form or essence. He is thereby a case of pure, unqualified existence. For the moment, let’s define a perfection as a property that doesn’t explicitly entail that its bearer is not God (not the First Cause, not identical to its own act of existence). So, for example, being finite, being created, having a nature, having passive potentiality—none of these would count as perfections, since they all entail explicitly that their bearer is not the First Cause. In contrast, being powerful, loving, knowing things—none of these explicitly rule out being God.
 
Say that F is such a perfection. If God lacked the possibility of being F, then being itself would lack this possibility. If F were not absolutely impossible, and if F does not explicitly rule out being God, then it would have to be possible for God to be F. There could be then no explanation of the impossibility of God’s being F: F itself does not rule this out, and God has no nature but existence, so if His nature rules it out, there must be a fundamental incompatibility between existing and being F. So, God must be possibly F.
 
But God lacks all passive potentiality. Hence, it is impossible for God to be merely potentially F. If He can be F, He must actually be F. Consequently, God must possess every perfection.
 
The basic premise of this second argument is that impossibility must have some explanation. If F and G are both purely positive, then there could be no logical inconsistency between them. Hence, is must be possible for F and G to be combined. Existence as such is purely positive. Hence, existence can be combined with any purely positive property. Since God’s nature is nothing but existence, it must be possible for God to have any purely positive property. Since God is a being of pure actuality, He must have in actuality every purely positive property.
 
We saw, when considering the Third Way, that Thomas seemed to assume that the possible existence of something that doesn’t actually exist needs to have an explanation. There is some prima facie tension between that principle and the principle relied on here. Suppose that there is no explanation for the possible existence of p, and no explanation for the impossibility of p. Is p then possible or not? The Third Way would say No, and the argument from perfection would say Yes. But p can’t be both possible and impossible.
 
The two principles can be reconciled in the following way. The Third Way appeals to the Nihil ex Nihilo principle:
 
(NEN) If x does not actually exist, then x’s existence is possible only if there is something that actually exists with the actual power to cause x to exist.
 
The second perfection argument depends on the principle that logically consistent combination is always possible:
 
(LCC) It is impossible to combine two properties only if there is some logical inconsistency between their essential internal structure or definition.
 
Are the two principles consistent? Consider some x that does not actually exist. Now consider two properties: actually existing, and being x. These are clearly not logically inconsistent in their internal structure or definition. So, by LCC, it must be possible to combine them. This means that x’s existence is possible. By NEN, it follows that something has the power to cause x to exist. But this is true: God exists and has this power. What’s interesting is that these two principles by themselves seem to entail that in every possible world, something exists with the power to cause the existence of anything that doesn’t exist in that world. This isn’t quite a proof of God’s existence, but it’s close. This does suggest that many atheists will find either NEN or LCC implausible. One could mitigate this problem by restricting LCC in such a way that it doesn’t apply to properties like being x (some particular thing). We might limit LCC to potentially general properties, properties that could in principle be instantiated by more than one thing. Then the atheist could consistently accept both principles.