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.)

The heart of the Fourth Way, as I interpret it, is a simple argument:

1. In every possible world, God is the cause of the actual existence of all other actually existent things. (From the Second and Third Ways).
2. The cause of something's existence must be at least as noble, true, and good as the thing itself. (Aristotle's principle from Metaphysics 2)
3. Therefore, God is a noble, true, and good as anything could possibly be.

 
Why think that the Aristotelian principle is true? And what does it mean for something to be truer, nobler, better, or “more existent” than another? We have already seen an appeal to the proportionality of causes in the First and Second Ways. A cause must “have” what it “gives” in some way, either “formally” (by literally have the same characteristic) or “eminently”. Applying this to existence, we could say that the cause of the existence of x must exist either in the same way as x or in a “higher” way.
 
What do “higher”, “nobler” or “better” mean in this context? They must refer to a real, objective hierarchy, not just to our subjective preferences or interest. They must mean something like: having a wider array of powers and capabilities. As Kenny suggests, this corresponds to something like having a more powerful set of cognitive capacities. Despite what Kenny says, St. Thomas’s argument does not depend on everything’s lying on a strictly linear order. It’s okay if some pairs of things are not comparable in their degree of being, so long as there are some things that are strictly nobler than everything else (a common peak in the “Mountain of Being”).
 
I should say something briefly about Aristotle and Aquinas’s notion that some beings are “truer” than others. As Aquinas explains, “true” can be used in two ways: to refer to a cognition that corresponds to some reality, and to a reality that corresponds to some cognition. My idea of a triangle is true if it accurately represents triangles. A triangle is “true” (as a triangle) if it accurately corresponds to the definition of triangle. What would it be for a thing to be “truer” than another thing (as an existing thing)? It might be that it corresponds more accurately to the full, unqualified concept of Being as such. If so, the more nearly perfect or the nobler a thing is, the truer it is.

Like the Third Way, the Fourth Way consists of two principal parts. The first part establishes that there is something that is maximal in being, goodness, “truth”, and nobility. The second part reaches the conclusion that this maximal being is the cause of the being (and goodness, etc.) of all finite things. As in the case of the other Ways, St. Thomas does not suppose that he has yet proven the unity or uniqueness of God. So, we should really say that the first half involves the claim that there is some thing or things maximal in being, and the second half the claim that this thing or things is or are the cause(s) of all other things. For the sake of grammatical simplicity, I shall mostly ignore this important qualification.
 
The Big Question in interpreting the Fourth Way is this: just how Platonic is the argument? In his dialogue Phaedo (100a1-101a5), Plato has Socrates argue that he has discovered that the true cause of the beauty of things is something called Beauty Itself. Similarly, there is Justice Itself, the cause of the justice of all just things, Goodness Itself, Equality Itself, and so on. These are the so-called “Forms” or “Ideas”.
 
Anselm offered what seems to be a purely Platonic argument that parallels the Fourth Way in his Monologion. Anselm writes in Chapter 1:
 
“Necessarily, all good things are good through something, and this something is understood to be the same thing in each of the various good things…. And who would doubt that that through which all good things are good is a great good?.... That through which every good thing is good is good through itself…. The one thing that is good through itself is the one thing that is supremely good.”
 
Boethius makes a very similar argument in The Consolation of Philosophy (Book III, Chapter X). Is this exactly the argument Thomas Aquinas is making?
 
I think not, for two reasons. First, the steps of Aquinas’s argument are different. First, he establishes that there is a supreme being, and then he argues that this supreme being is the cause of other beings, which is the opposite of the Plato/Boethius/Anselm order. Second, he explicitly rejects in many places (following Aristotle) the argument from Many to One on which Plato/Boethius/Anselm rely. Human beings, for example, are each made human by his or her own human form, not by a Platonic Idea. It’s true that there is a kind of archetype of humanity (a divine idea) that was involved in our creation, but the divine idea is involved in God’s efficiently causing us to exist, which seems significantly different from the way that good things are supposed to be good “through” the Idea of the Good.
 
Kenny (in chapter 5 of The Five Ways) is pretty good on all this. He brings out the way in which a “common nature” for Aquinas is not some separate thing but rather a way of explaining the commonness of the members of a species in terms of some intimate relationship among their forms—namely, that the forms are not individual in themselves but only through their involvement with prime matter.
 
So, I think it is important to look closely at St. Thomas’s source: the end of chapter 1 of Book 2 (Alpha the Lesser) of the Metaphysics. I am also relying on some interpretive suggestions by Michael Augros in his paper, “Twelve Questions about the Fourth Way.” (The Aquinas Review, volume 12, 2005) In the Metaphysics, Aristotle argues that if something is the cause of all true things, then it must be supremely true. If we translate this into more familiar language about existence and nobility, we could say that if something of the existence of all existing things, then it must have supreme existence (likewise for nobility, goodness, and so on). This fits well with the place of the Fourth Way: we have already established that there is one existing thing that causes the existence of all other existing things (Second Way). Moreover, we know that this thing exists necessarily and causes the existence of everything else in every possible world (Third Way). The Fourth Way adds to this the conclusion that this necessary first cause must have supreme existence (nobility, etc.).
 
If this is right, then the second part of the Fourth Way is really the crucial part. The first part is simply designed to make the ultimate conclusion more plausible, by suggesting that there is something (at least, in the realm of possibility or potentiality) that has maximal existence. The second part assures us that this supreme thing actually exists, and, given the Third Way, actually exists and is supreme in existence in every possible world.
 
Alternatively, as Augros suggests, we could take the first part as simply arguing that there must be something that is, de facto, the highest thing on the scale of existence among the actually existing things. This need not, at this stage, be identified with the greatest possible being. Then the second part establishes that this de facto greatest thing must be the cause of the existence/greatness of all other things in all possible worlds, and so it must be the greatest possible being.
 
If this is right, then the standard translations of the crucial principle of the second part of the Fourth Way are misleading at best. Here’s the Latin original: “Quod autem dicitur maxima in aliquo genere est causa omnium quae sunt illius generis.” Kenny translates it as: "Now whatever is most F is the cause of whatever else is F.” The Leonine translation: “Now the maximum in any genus is the cause of all that is in that genus.” These make the principle a generalization of the form: all things that are maximal in a genus are the cause of the rest of the genus. But the Aristotelian principle in Metaphysics is the converse of this: all things that are the cause of the rest of the genus are maximal in that genus.
 
We should try to fit our translation to this Aristotelian principle, and I think it is possible, since the ‘quod’ is singular rather than general. Aquinas does not write “whatever” (omnia) is most F, as Kenny supposes, but rather “that which” (quod) is most F (or is supposed to be most F). The Leonine translation is better, if we take it to mean: the maximum in a genus and the cause of all that is in the genus (supposing that each of these exist) are one and the same thing. Ways 2 and 3 give us something that is the necessary cause of all other beings, and the first part gives us something that is a supreme in being, and the Aristotelian principle allows us to infer that the necessary cause of being is a supreme being, which is what we want. (Parenthetically, the presence of ‘dicitur’, ‘is said to be’, is some reason to prefer my reading of the first part over Augros’s: the supreme being of the first part is merely a supposed or hypothetical entity.)