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.

Does God have a Will?
Summa Theologiae I, Q19, a1, and SCG I.72
 
For Thomas, this pretty easy. Everything that has intellect also has will. Every substance is striving in some sense to perfect its own nature. If a substance is intellectual, then it moves towards its own perfection with understanding. But to move with understanding is precisely to move voluntarily, by the exercise of will. This will be especially true of God, since He understands Himself perfectly.
 
However, there is a problem: God is unmovable, immutable. So, He cannot be said to move toward His own perfection. He is essentially His own perfection. But when a substance rests in its own perfection, that perfection remains its natural end. And when an intellectual substance rests in its own perfection, that resting is resting with understanding, which is by definition the state of delight. So, God perpetually delights in His own perfection. But delight is a function of the will, so God has a will.
 
In the SCG, Thomas also points out (in paragraph 8), that God, as first agent, is supremely free. Nothing can move Him or make Him do anything. To act with free will is essential to being free, so God must have a will.
 
Does God will other things than Himself?
 
Summa Theologiae I, Q19, a2, and SCG I.75
 
So, God will His own perfection, and so He wills Himself. Does He also will other things? Given that God is essentially in a state of perfection, which is also a state of perfect happiness in which His will is at rest, is there any room for Him to will anything else? He has no needs or deficiencies to fill. He can’t be any happier than He would be if He willed nothing but Himself. No additional object of the will can add to His happiness, if ‘adding’ implies a kind of increase. (Objection 3)
 
In addition, if God willed more than His own essence, then His will would be divisible. Or, at the very least, His act of willing would be complex. But God is simple. (Objections 1 and 4)
 
Moreover, if He did will something else, it seems that the value of that other thing could be said to “move” His will by attraction. But God is immovable. (Objection 2)
 
In response, Thomas appeals to the self-dispersive nature of goodness. Good things (including especially good people) have a natural tendency to spread that goodness to others, even if doing so doesn’t add to their own happiness. To good to others is a sufficient reason in itself for acting. Since God is maximally good, this dispersive nature is especially true of Him.
 
Thomas makes the point in a slightly different way in SCG, paragraphs 3 and 4. We’ve established that God loves Himself. Whatever loves itself also loves to some degree the things that resemble. Every actual thing resembles God to some degree, so God naturally loves all actual things.
 
God wills Himself as the sole proper and immediate object of His will, but He wills other things insofar as their existence is a fitting effect of His perfect goodness. Just as He understands all possible things by understanding His own essence, so He wills all actual things by willing His own perfection. There is a single act of will in God, just as there is a single act of understanding. And these two acts are the same act.
 
In response to objection 2, Thomas argues that God is “moved” only by His own goodness, and so His immovability is not compromised.
God doesn’t will things in order to add to His happiness. He wills them simply because and insofar as it is good that they exist.
 
Thomas explains in SCG I.77 why God’s willing multiple objects is compatible with His absolute simplicity. God wills multiple things only insofar as they are included (“comprehended”) in His goodness, just as He knows multiple things by knowing Himself in His infinite power. In paragraph 5, Thomas argues that the multiplicity of objects of will is less of a threat to divine simplicity than multiple objects of understanding were, since the will acts for the sake of the goodness that is in the object, not for some value existing in itself. Hence, there is no obstacle to a simple will’s willing multiple objects

By delaying this issue until Question 11 in the First Part of Summa Theologiae (and chapter 42 in the SCG, I), Thomas is indicating that it is easier to prove that there is at least one God than it is to prove that there is no more than one. It is also important to realize that the ‘one’ that we appeal to in proving God’s unity is not the number 1, but the concept of oneness that is convertible with being. God is supremely one precisely because He is supremely a being. We don’t count gods in the same way that we can count apples or doors. As we shall see, the nature of God excludes the very possibility of there being two or more gods. At the same time, since the oneness involved is not that of the numerical one, Thomas is leaving open the door for God’s being, in some sense, a plurality or multitude. This will help in working through both the problem of God’s ideas  and the Trinity.
 
In Summa Theologiae I, Q11, article 1, Thomas explains that the focal meaning of ‘one’ in ‘there is one God’ is that of being undivided. God is supremely indivisible, and this follows from His simplicity. Thomas argues that if oneness were not convertible with being, an infinite regress would result. If oneness is not equivalent to being, then it would have to be something that is added to being. But then we can ask what makes this addition one addition, and an infinite regress follows.
 
But what about multitudes, like crowds of people? If they exist, they must also be one. And, indeed, a crowd is one crowd. But how can something be both one and many? Isn’t that inconsistent? Thomas anticipates here an answer given much later by the German logician Gottlob Frege. A multitude is one in one way, and many in another. It is, for example, one crowd but many people. Thomas elaborates this point in article 2, again distinguishing between one as the principle of number and one as convertible with being. We can ask for the number of a crowd, and this question must appeal to some way of dividing the crowd—into families, or individuals, or human cells.  At the same time, a crowd must be, like anything that exists, in some more basic sense one thing. Some more recent metaphysicians, following the work of American logician George Boolos, have suggested that multitudes can exist without being one thing at all. Very large proper classes, like the class of all sets, for example, seems to be a real multitude that is not in any sense one thing. If this is right, it could create some difficulty for some of Thomas’s proofs (in article 3) for God’s oneness. Or, it might simply point to the fact that the oneness of God is consistent with His comprising a kind of multiplicity, so long as these things are not parts or attributes of God.
 
In objection 4, Thomas addresses the problem of the definition of one as undivided. Being undivided is a negative notion, signifying the absence of division. But being is perfectly positive. So, how can being be convertible with oneness? Thomas replies that division is prior to one only in the order of our understanding. Ontologically, being undivided is prior to being divided. It’s just that we are first aware of composite things before we are aware of their simple parts.
 
In article 3, Thomas offers three arguments for the oneness of God. The first argument appeals to God’s simplicity. God is made to be God by His divine nature, and that divine nature also makes Him exist as a particular being. For there to be two gods, there would have to be two divine natures, each of the same species. But for two natures to exist with the same species, there would have to be something responsible for making each distinct from the other. So, for example, two men can be two by virtue of being combined with two packets of prime matter. Two packets of prime matter have no actual nature of their own, and so they can be fundamentally or primitively distinct. The divine nature is an actual nature (it is maximally actual), and so two divine natures cannot be fundamentally distinct. Since God is identical to His own nature, there cannot be two instances of the divine nature, just as there cannot be two instances of a single angelic species.
 
In the second argument, Thomas appeals to God’s infinity. (This is a new argument, not present in the SCG.) In fact, he appeals to the infinity of God’s perfection, by which he means that nothing can be superior to God in perfection. Suppose that there were two such maximally perfect beings. In this argument, Thomas concedes (for the sake of argument) that there could be two distinct species of god. If there were two such species, something would have to differentiate them. One would have to have something that the other did not have. But this means that one would have to have some form of perfection that was lacking in the other. But God has all perfections. So, in fact, this argument actually appeals to God’s perfection, rather than His infinity.
 
Third, Thomas appeals to the apparent unity of the world. This is one of the relatively few cases in which Thomas appeals to some form of the Fifth Way—pointing to God as the cause of the world’s systematic harmony, the fact that the active and passive powers of the world’s created substances fit together in order to make a stable, scientifically intelligible universe. Thomas gives a more detailed version of this argument in Summa Contra Gentiles 1.42, paragraph 7.
 
In Summa Contra Gentiles 1.42, paragraph 5, Thomas also appeals to some details of Aristotle’s natural philosophy, especially the assumption that the movement of the heavenly spheres are regular and continuous. It’s not clear to me whether any of this can be salvaged, given the falsity of Aristotle’s astronomy.
 
In paragraph 8, Thomas argues that if there were two gods, at least one would have to be composite. But no composite being could be necessary through itself (as established in the Third Way). It’s not obvious here why one of the gods would have to be composite, but the two arguments that Thomas gives in the Summa Theologiae support this premise: either the two gods would belong to the same species, in which case each would have to have a part that individuates it from the other, or they would belong to two species, in which case each would have to add some differentia to their common genus.
 
Paragraphs 9-11 contain another interesting argument that appeals to God’s necessity of being. This argument involves a complex dilemma: if there were two necessary beings (each necessary per se), then either (1) the two differ by something required for the completion of the necessity of being, or (2) not.
 

• Assuming (2). (Paragraph 9) If not, then they are different by something accidental. This accident must have a cause (since all accidental additions must be caused), which is either (a) the essence of the necessary thing, or (b) some external thing. We can rule out (a), since both necessary beings would have the same accident, if it is a proper accident determined by their common essence. If (b), then the existence of two necessary beings depends on the action of this third thing. But then the existence of each thing would also depend on the third thing, and so neither could be necessary in itself.
•  
• Assuming (1). (Paragraph 10) That which differentiates the two necessary beings would be either (a) something included in the common nature of necessary being, or (b) something that differentiates the two natures into two species. Case (a) is impossible because in that case, the factor will be present in both necessary beings. In case (b), the common nature must be made actual by each of the two differentiae, in which case, each necessary being would derive its existence from something else. Hence, the two things cannot be necessary in themselves, nor could each be simple and identical to its own act of existence. This complex argument seems to be mirrored in the first two arguments in the Summa Theologiae. The SCG helps us to see that these are really two parts of a single argument, based on a dilemma (either one species of god or two).

 
Paragraph 12 involves a very simple argument, based on the thesis that God is identical to His nature and to His act of existence. If there were two gods, then each god would have the same divine nature. But this divine nature would then have to be identical to two distinct acts of existence. But nothing can be identical to two distinct things.
 
Paragraphs 13 and 14 contain another complex argument.
 

1. If x is a per se necessary being, then x’s necessary being belongs to x insofar as it is x. That is, the necessity of x is grounded by x’s being x.
2. Suppose there were two per se necessary beings, x and y. Then x’s being x would also consist in x’s not being y, since if x and y are distinct, x’s being x depends on its not being y.
3. Consequently, x’s necessity would belong to it insofar as x is distinct from y.
4. This means that x’s necessity depends on the existence of y.
5. Consequently, x’s necessity would not be per se. Contradiction
6. So, there cannot be two per se necessary beings.

 
Thomas defends premise 1 in paragraph 14. If x’s necessary being depends only on x, then x’s necessary being must belong to x insofar as it is x.
 
In paragraph 18, Thomas appeals to the fact that God is supreme being. Since being is convertible with oneness, God must be supremely one, and so undivided. This applies equally well to the divine nature.
 
Thomas also appeals in paragraph 20 to the superiority of monarchy as the form of government. Since God is the perfect governor of the universe, God must be one.

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.

A central thesis of Thomas’s natural theology is the claim that God is a being of pure actuality—meaning that God is utterly lacking in passive potentiality. This follows quickly from the fact that God is absolutely the first cause, in the sense of being the cause even of other necessities. God is the only being that is necessary in Himself. In order to act as first cause, God must be in His very essence fully equipped with a complete complement of intrinsic properties. If He were not, then there would be a component of contingency or at most conditional necessity in His intrinsic state as the first cause, but any such component would require a still more primary cause, contradicting God’s status as absolutely first.
 
God lacks only passive potentialities: He possesses active potentialities (i.e., active powers) to the greatest possible degree. God can cause anything that is metaphysically causable—His active power is without limit. If it were limited, then this limit would require some cause, again contradicting God’s status as first cause.
 
God is, moreover, maximally free. He was free, in particular, to create nothing at all, or to create any cosmos that would be a fitting expression of His nature. There are many such possible cosmoses. Ours is just one. Hence, our cosmos is thoroughly contingent.
 
How is the contingent exercise of active power on God’s part consistent with His lack of passive potentiality? In Aristotelian metaphysics, there is no conflict, since the exercise of active power is an action, and an action takes place in the patient, not in the agent. God does not have to modify Himself in order to exercise His active power. He does not have to deliberate or plan, and His intentional action requires no internal representation in His mind. The truthmaker for God’s intentionally creating creature x is simply the existence of x itself. No difference internal to God is required to differentiate worlds in which God creates x from worlds in which He does not.
 
But, a critic may respond, isn’t God identical to His own action, given Thomas’s strong doctrine of divine simplicity? If so, the objection goes, since God exists necessarily, His action must exist necessarily, in which case everything that God creates must also exist necessarily.
 
It is true that Thomas embraces the thesis that God is identical to His own action. In Summa Contra Gentiles, I, chapter 45 and in Summa Theologiae I, Q14, article 4, Thomas argues that God’s act of understanding is identical to His essence. Since He is identical to His own essence, God is identical to His act of understanding. In Part II of the Summa Contra Gentiles, Thomas claims both that God’s power is identical to His own substance, and that His action is identical to His power.
 
Ordinarily, the act of a power is distinct from that power. So, if I whistle a tune, my particular act of whistling is obviously distinct from my power of whistling. However, in God’s case, His act of understanding is identical to His power of understanding, and both are identical to God Himself.
 
The act of a power is the perfection of the power. A power that isn’t exercised is imperfect. So, if God’s act were distinct from His power of understanding, then that act would perfect His power. Furthermore, the perfecting of this power would be the perfecting of God’s essence. Hence, God’s perfection would depend on something other than God, which would contradict the fact that God is infinitely perfect. God’s act must be identical to God, so that it is God who perfects Himself.
 
An act stands to a power as actuality to potentiality. So, if God were not identical to His act, then His power of understanding would have a potentiality that is actualized by His act. But God has no passive potentiality. He doesn’t stand as potential to anything else. So, He must be identical to His own act.
 
The Modal Collapse Argument
 
Many critics of Thomas argue that he is committed to God’s willing necessarily everything that He wills, because of Thomas’s strong doctrine of divine simplicity. The argument typically goes something like this:
 

1. God exists necessarily (Third Way)
2. God is identical to His act of willing (Divine simplicity – SCG I.45 and II.9)
3. God’s act of willing is identical to His act of willing to create this universe.
4. So, God’s act of willing to create this universe exists necessarily. (From 1, 2, 3 by the law of identity)
5. So, God necessarily wills to create this universe. (From 4?)

 
The argument is guilty of a fallacy of equivocation. Understood in one way, the term “God’s act of willing to create this world” picks out something that exists necessarily, namely, God Himself. Understood in a second way, the term picks out something that exists only if this world exists. On either meaning, conclusion 5 does not follow from sub-conclusion 4. On the second meaning, the phrase “God’s act of willing to create this universe” is actually a kind of quantifier: “There is something that is uniquely an act of willing by God to create this universe and…”
 
To make clear why 5 does not follow from 4 using the first meaning, the inference to 5 on that reading requires an additional assumption:
 
4b. God’s act of willing to create this universe is essentially God’s act of willing to create this universe.
 
On the first reading, assumption 4b is false. God’s actual act of willing (which is in fact an act of willing that He create this world) could have been an act of willing that He create a different world, or no world at all. Consider, for example, a parallel proposition:
 
BD. Ben’s father is essentially Ben’s father.
 
Not true—although I am in fact Ben’s father, there are possible worlds in which I have no children at all.
 
Critics of Thomas will complain that the cases are not parallel. Assumption 4b just must be true, because every act of willing has its own object essentially. My choosing a chocolate cookie for a snack could not have been my choosing an oatmeal cookie. Different objects necessarily imply different acts of will. However, this is wrong, for two reasons. First, because God is different from creatures. God does not have to undergo any kind of process of deliberation in order to make a choice. Hence, He and His act of will are exactly the same in every possible world. They have different objects in different worlds, but this difference is merely a Cambridge difference in God—it doesn’t require any internal modification. The objects of God’s choosing are immediately present to God as chosen by Him—they don’t have to be re-presented within God as chosen.
 
Second, even in the case of human actions, it is possible for the same act of human willing to have different objects in different worlds. I’m thinking of a case of spontaneous but voluntary action—acts taken without any prior deliberation, but which are nonetheless guided by the human will. Consider, for example a musician who is improvising as he plays, or a speaker who is speaking very rapidly. The notes or words that are chosen are chosen by will, and yet there need be no prior mental event guiding the action. The action has “voluntariness”, as Elizabeth Anscombe puts it, without being the product of some internal volitional event. In a different possible world in which the person chooses a different note or different word, there may be no internal difference despite the fact that a different choice was made. Consequently, there is no reason to deny that the very same act of will could exist in both worlds.
 
Let’s return to the argument and consider using the second meaning. On that interpretation, steps 4 and 5 look like this:
 
4c. There is something that is uniquely an act of willing by God to create this universe, and that thing exists necessarily.
5c. There necessarily exists something that is uniquely an act of willing by God to create this universe.
 
Again, 5c does not follow from 4c, unless we assume that anything that is in this world an act of willing by God to create a certain universe must be an act of God to create that same universe in every possible world in which it exists. Again, we have to assume that God’s act of willing is essentially an act of willing to create this universe specifically. And that Thomas will deny.

This is the crux of Thomas’s whole natural theology—it is the main conclusion toward which the first Four Ways point, and it is the fulcrum from which Aquinas moves our theology toward God’s perfection and infinity. In this respect, Aquinas’s natural theology is unique. I don’t know of anyone, earlier or later, who proceeds in the same way. Duns Scotus, for example, drops the First Way entirely and relies primarily on God’s infinity, deduced from his version of the Second, Third, and Fourth Ways.
 
In his masterful The Metaphysics of Theism, Norman Kretzmann elucidates Thomas’s arguments in Book I of the Summa Contra Gentiles. In the chapter on simplicity, Kretzmann distinguishes two “interpretations” of Thomas’s claim that God’s essence is His existence: the cautious and the bold. On the cautious interpretation, we claim only that God’s essence entails (all by itself) that God exists. On the bold interpretation, we claim that God’s essence is identical to His act of existence. Kretzmann recognizes that Aquinas clearly endorses the bold interpretation. The only question is whether his arguments support this bolder and stronger claim.
 
Kretzmann begins with the argument that he calls G6, which is a version of Aquinas’s Third Way. So, let’s assume that God is that thing which is necessary per se and not through another. Kretzmann suggests that a being whose essence entailed its existence would qualify as necessary per se. He compares the existence of God with the existence of certain mathematical entities, like the number zero or the empty set, whose nature seems to guarantee that they “exist” in some sense in every world. Yet clearly in none of these cases are the essences identical to their act of existence.
 
Kretzmann thinks that Aquinas’s strongest argument for the bolder claim is the argument from potentiality and actuality. That is, if we think of essences as representing the potential existence of something, and the act of existence as the actuality of that potential, then essences must be thought of as passively receiving existence from something else. Since a thing can’t exist until its essence has received such existence, nothing of this sort could be uncaused. Therefore, since God is uncaused, His essence cannot receive existence. So, He could exist only if His essence already was an act of existence.
 
Of course, this presupposes that we have accepted the essence/existence to potentiality/actuality correspondence. This turns, I think, on seeing Thomas’s theory as a theory of actuality. It is acts of existence that actualize possibilities. Mere essences, sans such acts, are thus mere potentialities for existence.
 
In addition, one could question Kretzmann’s claim that something could be necessary per se by having an existence that is “entailed by” but not identical to its essence. His examples are mathematical, and one could argue that such mathematical things derive their necessary existence from God. If God were not the ultimate, necessarily existing Mathematician, could things like numbers or sets really exist?
 
And, in fact, do numbers and sets exist at all, in the relevant sense. We are looking for something exists necessarily and without cause, and which exists with the causal power to create other things. Mathematical objects are causally inert. Alexius Meinong suggested that they merely “subsist” in a shadowy realm of mental objects, in contrast to the full-bored existence of God and concrete creatures. Arguably, the existence of something could be explained by an essence only by being caused by it. So, if God is uncaused, His existence cannot be explained or “entailed” by His essence, unless they are one and the same thing.
 
1. God is identical to His own Essence (SCG I.21 and STh Q3 a3)
 
The first step in Aquinas’s argument is to suggest that God is, in a way, identical to His own form, as are angels. In fact, this already follows from the fact that God contains no matter, as Thomas argues in the Summa Theologiae. Without matter, there is nothing in God to individuate Him from other things with the same kind of form. Hence, God must be identical to His form simpliciter.
 
In the SCG, Thomas also appeals to the fact that God lacks composition. If God were not identical to His own essence, then there would have to be something (matter or accidents) that have been added to His essence, resulting in His having “parts” of a kind (i.e., metaphysical parts).
 
He also argues (in par. 5) that, if something is not identical to its form, then that form is a kind of cause of the thing. The thing would then depend for its existence on the form. Since God depends on nothing, He must be identical to His own form, and so to His own essence.
 
In par. 6, he appeals to the potency/act distinction, arguing that whatever is outside an essence is a mere potentiality that is actualized by the essence (or form). I think the picture is that the parts of things (matter, accidents) that are not identical to a form receive their existence through the form. But, since God contains no passive potentialities (chapter 16), He must be pure form/essence.
 
2. God is identical to His own act of Existence (SCG I.22, STh Q3 a4, De Ente par. 80-3)
 
In the Summa Theologiae, Aquinas proves that God’s essence is identical to His existence. Since we have already established that God is identical to His essence, this entails that God is also identical to His act of existence.
 
The main argument appeals to causation. If a thing has something beyond its essence, then this thing must be caused either by that essence or by something else. So, if God has existence as something “beyond” His essence, then either that existence is caused by the essence or by something else. However, God’s existence is absolutely uncaused. So, God’s existence cannot be “beyond” his essence. As Kretzmann pointed out, this argument doesn’t show that God’s existence must be identical to His essence. It could be something entailed by His essence without being identical to it or caused by it.
 
Thomas goes on in article 4 to argue that the existence of a thing cannot be entailed by its essence, since this would mean that the thing had caused itself to exist. For the essence to do any causing, the thing would have to already exist. Hence, the essence of a thing cannot cause the existence of that very thing.
 
But could the essence “entail” the existence without causing it? Aquinas is assuming (reasonably) that something can explain or entail the existence of a concrete thing with causal power only by causing it to exist. Hence, the essence of a thing cannot be the ultimate explanation for its existence.
 
Aquinas’s second argument is the appeal to potency and act that I discussed above.
 
In his third Summa Theologiae argument, Aquinas argues that if something has existence but is not its own existence, then it enjoys only “participated” (i.e., caused) existence. This is I think an appeal to the Fourth Way. The highest form of existence would be to be simply identical to pure, unadulterated existence. This would be possible only if one’s essence was identical to one’s existence.
 
In SCG I.22, paragraph 2, Aquinas argues in the following way. First, he shows that God’s essence must be compatible with existence. Given that, Aquinas argues that there are just three alternatives: either God’s existence depends on His essence, or both depend on some third thing, or the essence must depend on the existence. One might push back: why couldn’t both the existence and essence be independent, uncaused things? I think that Aquinas would argue that, whenever essence and existence are distinct, then the two must be dependent on each other, or on some third thing. An essence depends on the existence in order to exist, and the existence depends on the essence for its identity, tied as that is to the character of the thing whose existence it is.
 
If God’s existence depended on His essence or some third thing, then God’s existence couldn’t be uncaused, contrary to the Second and Third Way. So the case to consider is that in which God’s essence depends on His existence. However, if God’s essence could depend on God’s existence, then we could make sense of God’s existence without considering His essence. Here again we have to turn to the actuality/potentiality distinction. If essence and act of existence are distinct, then the act of existence must actualize the possibility represented by the essence. The act of existence cannot both bring into being a possibility and then actualize that some possibility. An act of existence cannot do anything prior to its actualizing of an essence—it is only after actualizing an essence that it can be said to have a nature that could bring about anything.

Anthony Kenny was right (in his The Five Ways) to connect the Fourth Way with the claim (first stated by St. Thomas in the early De Ente et Essentia) that God is identical to His own act of existence. I think that he’s also right in thinking that St. Thomas did not change his theory of esse (act of existence) but did change his understanding of essence or quiddity. In De Ente, Aquinas did not distinguish between understanding the meaning of a word (like ‘phoenix’) and grasping the essence of the kind of thing that the word names. In fact, if there are no phoenixes, it is impossible for us to grasp the essence of a phoenix. This does undercut St. Thomas’s first argument for the real distinction between essence and existence in De Ente, but, in my opinion, this is no great loss. The real case for the distinction lies in the fact that there can be only one thing whose essence is its existence. Hence, the real distinction is easy to establish for everything but God.
 
Kenny approaches the problem as you would expect a mid-20th-century analytic philosopher to do so: from a grammatical-linguistic analysis of the verb ‘to be’ (and ‘est’ in Latin). Not surprisingly, he concludes that St. Thomas’s account of God is “unintelligible”. Aquinas’s strategy is to argue that we are forced to the “unintelligible” conclusion by the facts of causation and the natural world. The exceptional nature of God is a feature, not a bug. It is not surprising if the grammar of ordinary language finds it difficult to accommodate the conclusion.
 
I thought it was surprising that Kenny doesn’t mention Exodus 3 in this context, in which God tells Moses that His name is “I am that I am,” which (as St. Thomas notes) is a striking anticipation of Thomas’s theory. The phrase “that I am” clearly refers to God’s act of existence, and the phrase “I am…” in this context clearly asks for a phrase delineating God’s nature or essence.
 
The second thing that Kenny fails to take into account is that Aquinas’s theory of ‘esse’ and ‘actus essendi’ (acts of existence) is a substantive metaphysical proposal, not merely an analysis of ordinary language and thought. Aquinas is offering an interesting and attractive theory about actuality, something that philosophers have wrestled with from antiquity to the present time. How are my actual daughters different from all of the possible but not actual daughters that I could have had? There have been relatively few accounts of this fact in the history of philosophy:
 

• Actualism. There is no such thing as a non-actual daughter. Talk about such things must be paraphrased as talk about our ideas or suppositions.
• Mysterious quality. There is a special, ineffable quality that all and only actual things have.
• Kantianism. To be actual is to be connected in appropriate ways to sensations (as opposed to acts of imagination or supposition).
• Leibnizian optimism. To be actual is to be a denizen of the best possible world.
• Thomism. To be actual is to contain an act of existence (actus essendi). These acts of existence are all exactly the same, with one exception—all but God are cases of participated existence, while God is the unique case of unparticipated existence.
• Centrality. To be actual is to belong to the central portion of reality, upon which all merely potential realities depend (by being related to the powers or dispositions of actual things).

 
It’s easy to dispose of options 2, 3, and 4. We have no acquaintance with any actual-ish quality, and even if we did, it would be easy to conceive of non-actual things with that quality (disposing of 2). Kant’s attempted definition ignores the fact that it is only actual sensations that are relevant to the actuality of a physical thing, rendering his definition of ‘actual’ viciously circular (disposing of 3). Being part of the best possible world intuitively has nothing to do with being actual. If God chooses to make the best possible world actual, He must do something. Being best isn’t sufficient to make it actual on its own (disposing of 4).
 
I don’t think 6 is really a competitor with 5. Necessary beings (like God) are essentially “central” in this way, so 6 would provide some basis for identifying God as actual. However, many actual things are contingent. This means that although they are in fact metaphysically central, they could have been peripheral. We still need an explanation of what makes one contingent thing metaphysically central and another peripheral.
 
So, that leaves only 1 and 5. Aristotelians will reject 1 (actualism) on the ground that it denies the metaphysical significance of the actuality/potentiality distinction. If everything non-actual is completely unreal, then we face the Parmenidean problem of explaining how substantial change (generation and corruption of substances in nature) is possible. Even more importantly, we cannot treat active powers or passive potencies to change as aspects of reality. If something has the potential to become hot, for example, this consists in the thing’s having a real relation to a merely potential accident of heat. If there are no merely potential entities, then we would have to embrace some form of Platonic realism, understanding the potentiality for heat as a relation to the universal idea of Heat Itself.
 
Kenny puts a great deal of emphasis on Aquinas’s principle that everything receives its existence through its form. Thus, for Socrates to exist, existence must come to Socrates through his form of humanity. Consequently, Socrates cannot exist without being a living human being. Thus, for Socrates, to be is to be human, a living human being. However, Aquinas’s theory is that this is true only of creatures. God does not receive His existence from anything. Consequently, it does not have to come to Him through any limiting form. His existence is simple, unqualified, and unlimited. For God to be is simply for God to be, full stop.
 
As Kenny notes, Aquinas insists that God’s existence is not the greatest-common-factor kind of existence that is common to every actual thing (SCG I.26). That kind of generic existence is shared by both God and creatures—in God it is unlimited, in creatures it is limited by essence. God’s existence is the sort that is incompatible with any kind of limitation or restriction.