Good metaphysical arguments don’t operate in a vacuum. They occur within a theoretical framework provided by a successful, time-tested research program. The oldest and most successful research program in metaphysics is that of the so-called perennial philosophy, beginning with Plato and Aristotle, extended by the Neo-Platonists, and developed in Western scholastic philosophy. At the core of this program is the distinction between two modes of being, potential and actual, along with a commitment to a strong principle of proportionate causation, that is, the principle that the greater the effect, the greater the cause must be. Many contemporary philosophers have defended this program (myself included).
 
Another important assumption of the perennial philosophy concerns the dependent nature of time. Time is not merely a static dimension within which events and states can be located. Such a Block Universe picture of time would leave us with many inexplicable data, including the irreversible direction of time and causation, the fixity of the past and the openness of the future, the basis of the Second Law of Thermodynamics and other irreversible laws, and our universal experience of the passage of time. Aristotle provides a much more satisfying account of time in Book III of his Physics: time is simply the measure of change. Change is the more fundamental phenomenon, and the distinctive characteristics of time are derivable from the nature of change.
 
This hypothesis requires that change itself not be given a real definition in terms of time. That is, we must reject Bertrand Russell’s At-At theory of change (Russell 1922, Lecture VI), according to which a thing x undergoes change just in case it has one feature at some time t1 and a contrary feature at some later time t2. Instead, we must define change as Aristotle does. A thing x is undergoing change just in case there is some feature F of such a kind that x has a potentiality for F-ness that is in some degree of partial actualization. This definition does not make any reference to moments of time or their temporal relations of earlier and later. However, it does entail that if some entity x is undergoing change with respect to F-ness, there must be earlier and later times of such a kind that x is progressively closer to F at the successively later moments of time. Partial actualization requires at least two distinct modes of being (i.e., instants of time), one in which x is (still) only potentially F, and another in which it is actually F. In fact, there must be an infinite number of such instances, each with a different degree of actuality of x’s F-ness, with the full actualization of x’s potential for F-ness occurring in exactly one of these. The direction of time is determined by the prior direction of change: if x’s potentiality for F-ness is partially actualized, and this partial actualization corresponds to a set of moments, then the later moments in that set must be ones in which x is closer to being F.
 
Now let’s add to this picture the assumption that all change must have a cause. Another word for ‘change’ in this context is ‘passion’. Let’s assume, then, that every passion has a corresponding action. On this picture, the action of the agent is the cause; the passion of the patient is the effect. Causation always involves two or more substances. Here we will also introduce a principle of proportionate causality. It is obvious, for example, that actual change or passion can only result from actual action, involving an actually existing agent and an actually possessed active power. A merely potential event cannot be the actual cause of any actual change. A merely potential agent cannot act.
 
If we were to abandon this principle of ontologically proportionate causality, we would have no explanation for the asymmetry and irreflexivity of causation. That is, we couldn’t explain why a given passion couldn’t be its own cause, promoting itself from mere potentiality to actuality. This would be tantamount to rejecting the causal principle altogether.

It is important to recognize that accepting this Aristotelian framework does not depend on deciding the A Theory/B Theory issue. In particular, it does not depend in any way on so radical a thesis as Presentism—the view that everything that is actual is actual at the present time. It is compatible with Aristotelianism that there be infinitely many different modes of actuality, one for each moment of time, past, present and future. All that is required  is the assumption that to effect a change that is actual in mode t, the agent must have a power that is actual in that same mode, i.e., at that same time.
 
This viewpoint would not be consistent with a non-Aristotelian version of the B Theory—one in which every event at every moment of time is actual in exactly the same way. On such a Block Universe model, there is no room for defining change as the actualization of a specific potential. Such a model, as J. M. E. McTaggart long ago noted, fails to take seriously the reality of change.
 

As I have argued, Thomas proposes that every actual being has its own act of existence (actus essendi). An act of existence is a real being, although it is not a substance. In this sense, the act of existence is something like an accident, since accidents are also real but non-substantial beings. Nonetheless, an act of existence is not an accident of its substance, since it is causally prior to that substance. The act of existence gives the substance actual existence. Substances do have (by virtue of their essences) a kind of being (potential being) that is independent of the act of existence. It is potential beings that make up the structure of mere possibilities (including Leibniz's 'possible worlds').
 
Do acts of existence themselves exist, and, if so, do we face an infinite regress, with each act of existence requiring a further act to give it existence? I think acts of existence do exist, but they exist in a way that is different from the way that substances and accidents exist. They exist simply by being acts of existence, while substances and accidents require distinct acts to give them actual existence. Substances and accidents can have potential existence, which is why they can be contained in mere possibilities. Acts of existence cannot have potential existence: they are intrinsically actual. Hence, no mere possibility contains any act of existence.
 
An act of existence must give whatever actuality a thing has. Hence, acts of existence, as such, are infinite, while all substances and accidents are finite. If acts of existence as such were finite in any way, then there would be possible entities that could not be actualized. But that is a contradiction in terms: to be a possible entity is to be possibly actualized. Hence, acts of existence must have the power to actualize everything, to the outermost limits of possibility. They must be intrinsically infinite.
 
Furthermore, if any act of existence were finite as an individual, then this finitude would define a particular kind of being. In other words, the act of existence would have a kind of essence built into it. But if the act includes such an essence, then it would make sense for the act to exist only in potentiality. But, as we've seen, this is impossible. Every act of existence must be actual.
 
Finally, existence itself can have no limit, since a limit implies some possible thing beyond the limit, but nothing can exist “outside” of existence. A limit is something that receives existence, and that limits the existence it receives. Existence itself cannot be or have a limit.
 
God is a pure act of existence, without any associated essence. Hence, God is absolutely infinite. He must possess every possible perfection without any limit whatsoever.
 
Now, infinity seems to be something negative—the lack of finite boundaries or limitations. However, when infinity is combined with God’s perfection, we do get something positive. God must have each perfection to a greater degree than any possible creature.
 
Infinity is, for Thomas, a complicated matter. For Aristotle, infinity is generally a bad thing. Being not-finite means lacking sharp boundaries. A non-finite thing is somewhat amorphous and shapeless, lacking any sharp definition. Shadows, clouds, or crowds would all be examples of in-finite, somewhat vague entities. Clearly none of this applies to God. God is definitely what He is, with no vagueness or amorphousness.
 
In addition, Aristotle generally associates infinity with potentiality. Nothing in the material world is ever actually infinite. A real line segment (say, one on the surface of a box), for example, does not contain an actual infinity of points. Instead, each of its internal points exists only potentially, since the line segment can be divided in any of an infinite number of quantitatively different ways. Similarly, the future is potentially but not actually infinite. We will never reach a day that is infinitely many days after this one. God, in contrast, is pure actuality. So, it seems that God’s essence and infinity should be incompatible.
 
But, of course, God’s infinity is not a quantitative infinity. He is not infinite by having an infinite number of parts, or by filling (in a physical way) an infinite volume of space or an infinite duration of time. The kind of finitude that material substances have is itself foreign to God. My form is made finite by my matter, since my matter is quantitatively limited prior to my generation. At the same time, my matter is also made finite by my form, since it is form that gives a definite size and shape to my matter. Thus, finitude emerges in the cooperation of matter and form.
 
There is nothing corresponding to matter in God. Hence, there is nothing that can put a limit to His “form”. And, conversely, there is nothing that could be limited by His form. Hence, God is in-finite.
 
When we turn to article 2 of Question 7, we see that creatures can be “relatively” infinite, but only God can be absolutely infinite. Matter, for example, is relatively infinite, in the sense that it is capable of taking on any substantial form for a material substance. A material substance can be relatively finite with respect to its possible accidents, like shape. Angels have no matter, and yet they too can be only relatively infinite, since their being (esse) is “received and contracted into a determinate nature.” Only God is pure, absolute being, and so only He can be absolutely infinite.
 
God’s infinity is an infinity of active power and maximum nobility. He and He alone has the full power of being itself.
 
In the Summa Contra Gentiles, I I.43, Thomas talks of God having an infinite “spiritual” magnitude. We shouldn’t read too much into the word ‘spiritual’ (spiritualis). The term is used in two quite different ways in scholastic philosophy. It can mean purely intellectual substances, like God, the angels, and the separated soul. But it can also mean the more ethereal and subtle aspects of the physical world. Light, for example, is sometimes classified as spiritual. So too are the ‘animal spirits’ which scholastic philosophers took to be circulating through the body (like our modern electrical impulses of the nervous system).
 
Thomas identifies two dimensions of spiritual magnitude: active power, and the goodness or completeness (perfection) of one’s nature. Clearly, God is infinite in both these respects.
 
In natural magnitudes, as we’ve seen, infinity is a kind of privation, a lack of definition and form. In God’s case, it is a pure, non-primitive negation, a simple absence of boundaries and limits, without any implication that those boundaries and limits ought to be there.
 
Things that have limits have those limits either due to the definition of their nature (reflected in their genus and species) or from something into which they are received. So, anything whose existence and essence are distinct must have a limit: the essence will have limits due to its definition, and the act of existence will be limited by being received by something limited (the essence). God has no definition or genus, and His existence is not received into any distinct nature. Hence, God’s existence is infinite.
 
Thomas also argues that God is infinite in the sense that He cannot be exceeded by anything else. Since He has no passive potentiality, nothing can be more actual than He is. (SCG 1.43, paragraphs 6-7, 9-11) He argues, in somewhat Platonic fashion, that nothing could be better than a being that is its own goodness (par. 9). He appeals to something like Anselm’s conception of God as the greatest conceivable thing in par. 10, arguing that there must be a greatest of all intelligible beings. These are interesting, but they fall short of showing that God is infinite, as opposed to simply the greatest of all finite beings.
 
In par. 11, Thomas argues that we can think of something greater than any finite being, and yet our intellect cannot think of something greater than its own cause. So, God (our intellect’s cause) must be infinite. (This is close to one of Descartes’ arguments for God in the Meditations, a sort of hybrid of the cosmological and ontological arguments.)

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.