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

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.

​As in Maimonides’ case, Aquinas adds a second stage to the argument. He wants to establish not only the existence of a necessary being, but of a necessary being that has existence “in and of itself”, that doesn’t derive its necessary existence from something else.  Here again Aquinas has recourse to his no-infinite-regress assumption: the chain of causation explaining why derivatively necessary beings are necessary must terminate in a thing that is non-derivatively necessary, and this being will be God (a being whose essence is its existence).
 
Here’s a way of thinking about this second stage. Let’s suppose for contradiction that there is an infinite regress of necessary beings, each of which derives its necessity from its predecessor. So, N1 is caused to be necessary by N2, N2 is caused to be necessary by N3, and so on. And let’s assume that all necessary beings belong to such a regress: nothing is necessary in and of itself (unconditionally). Now, a world in which none of N1, N2, N3, etc. exist is an impossible world, since each of these beings exists necessarily and so exists in every possible world. So, the scenario in which none of the N’s exist is an “impossible world”, if you’ll allow me to talk of it that way. Let’s call this impossible world w!.
 
Let’s assume that if a scenario S is impossible, and this scenario S can be derived from some possible world w simply by deleting entities that exist in w, then there must be some ground or explanation of S's impossibility. Let's stipulate that the impossible world w! comes from the actual world (which is possible) by deleting all of the conditionally necessary beings in the actual world. Then the impossibility of w! must be explained in one of two ways: it fails to include something that is unconditionally necessary, or it violates some constraint of conditional necessity, i.e., it contains A but not B, even though A would (if it existed) necessitate B’s existence (which it could do by necessitating B’s necessary existence). But w! is not impossible in either of these ways. There is (by hypothesis) no unconditionally necessary being, so it isn’t impossible for that reason. And it satisfies all of the conditional constraints by never including any of the N’s. Its non-inclusion of Ni is permissible, because it also fails to include N(i+1), and Ni is necessary only conditional on N(i+1)’s existence. So, w! is possible, after all, which means that none of the N’s is necessary.
 
Therefore, it is impossible for anything to be necessary unless something is necessary unconditionally. And to be necessary unconditionally is to be necessary in and of oneself.

My colleague and friend Dan Bonevac has discovered a new interpretation the Third Way that resolves the problems that have puzzled readers from medieval times. The argument seems to involve two highly problematic claims:
 

1. If it is possible for a thing not to exist, then there must be some point of time at which the thing does not exist in reality.
2. If for each thing in some class C there is some time at which it does not exist, then there is a single time at which nothing in C exists.

 
Dan proposes that we interpret the temporal adverbs in the argument (quandoque, aliquando, modo) as modal rather than temporal modifiers. Such an interpretation is quite natural in many (if not all)  languages, including Latin and English. Dan notes that St. Thomas never uses the word 'time' ('tempus') or any other explicitly temporal term. In fact, if we look at the parallel argument in the Summa Contra Gentiles (I.13, paragraph 33), we see a complete absence there of temporality. Under this interpretation, the two problematic claims become:
 

1. If it is possible for a thing not to exist, then there is some possible situation in which it does not exist.
2. If for each thing in class C, there is some possible situation in which it does not exist, then there is a single possible situation in which nothing in C exists.

 
Now principle 1 is simply a tautology of modal logic. Principle 2 is still a substantive principle, but it is a quite plausible one, as we shall see.
 
Here is the Third Way under this modal interpretation:
 
Here’s the Third Way under this interpretation:
 

1. There are contingent (non-necessary) beings (because we see things coming into and going out of actual existence).
2. That which is contingent is non-existent in some possible world. (Modal logic)
3. Suppose for contradiction that all actual beings are contingent (non-necessary).
4. Given 2 and 3, there is a possible world in which nothing exists.
5. If it were possible for nothing to exist, then nothing would exist in the actual world.
6. Since it is impossible for something that doesn’t exist to exist as a possibility except by the causal agency of something actually existing. (Nihil ex nihilo)
7. But, obviously, something exists in the actual world (namely, the contingent things mentioned in premise 1).
8. Therefore, by contradiction (of the hypothesis in line 3), some actual being is a necessary being. (From 3-7)

Now everything is crystal clear, except for premises 4 and 5. Dan shows how we can construct, using resources available to Thomas Aquinas, plausible arguments for each. He calls premise 4 the “Annihilation Lemma” and 5 “the Dead End Lemma”.
 
Proof of premise 4: the Annihilation Lemma.
 

1. Suppose that everything is contingent in the actual world, w0.
2. Necessarily, all causal chains are finite (no regresses or cycles).
3. So, there are uncaused contingent things in w0. Let the xx’s be the plurality of those things.
4. Subtraction rinciple: if a world x contains one or more uncaused contingent things, then there is a world y in which those things do not exist, and the set of uncaused things in y is a subset of the set of uncaused things in x (i.e., no additional things exist uncaused in y).
5. So, there is a world w1 in which none of the xx’s exist, and such that the set of uncaused things in w1 is a subset of those in w0.
6. Since the xx’s are all the uncaused things in w0, this means that the set of uncaused things in w1 is empty.
7. However, if all causal chains are necessarily finite, then a world with no uncaused things must be an empty world, a world in which nothing exists.
8. So, w1 is an empty world.
9. So, it is possible for nothing to exist.

 
Proof of Premise 5: The Dead End Lemma
 

1. Suppose that w1 is an empty world.
2. Something can possibly exist relative to world w only if there is something in w that can cause it to exist. (A causal principle: Nihil ex Nihilo)
3. So, nothing can possibly exist relative to world w1.
4. The actual world is necessarily possible. (Axiom B of standard modal logic)
5. So, the actual world is possible relative to world w1. (4, definition of necessity)
6. So, nothing exists in the actual world. (From 3, 5)

 
Why think the Subtraction Principle is true? Suppose that there is an uncaused thing x which, if deleted from the world, necessitated the introduction of a new uncaused thing y in its place. In that case, it seems that the existence of y in the new world would be caused by the absence of x (together with the other conditions that, jointly with the non-existence of x, necessitated the existence of y). This is doubly problematic. First, and most importantly, because we seem to have a contradiction: the existence of y would be both caused and uncaused. And, second, because it doesn’t seem that the existence of anything could be wholly caused (or explained) by the non-existence of something else.
 
This version of the argument requires two causal principles: (i) necessarily, every causal chain is finite, and (ii) necessarily, it is impossible for something to exist unless (a) it actually exists, or (b) it could be caused to exist by something that actually exists. The second principle (Nihil ex Nihilo) is pretty strong. It would imply (given S5 modal logic) that every contingent thing in the actual world has a cause in the actual world. Here’s the proof. Suppose for contradiction that x is contingent and uncaused in w0 (the actual world). Consider any possible world w1 in which x does not exist. The existence of x is possible but not actual in w1 (by axiom B), so by Nihil ex Nihilo there must be some y that exists in w1 and is capable of causing x to exist. This plausibly entails that, in any world w in which x does exist, x is caused to exist by some y that also exists in w. Hence, since x exists in the actual world w0, x must be caused to exist in this world, contrary to our original assumption.
 
An interesting question: could we do without the first causal principle (namely, no infinite regresses or cycles)? Here’s a possible way of doing so. Suppose that there are infinite series or cycles of contingent things. We could plausibly strengthen our subtraction lemma, so that it allows for the simultaneous subtraction of all uncaused contingent things and all infinite contingent series and cycles, without requiring the addition of any new uncaused things or any new infinite series. If so, we could run the original argument without the first principle

The Third Way is clearly building on the Second Way. It adds an important component to the conclusion: we reach the conclusion that the uncaused cause of things must be a necessary being, in contrast to the contingent beings that are familiar to us. This immediately raises the question of what Aquinas means by 'necessary'. There are a range of possible interpretations:
 

1. Logically necessary. Its non-existence “entails a contradiction.” Or, perhaps, its non-existence is not ideally conceivable. Or, perhaps, its existence is an “analytic” truth (true by virtue of the meanings of the terms involved).
2. Metaphysically necessary. The narrowest form of real necessity. Not relative to a system of logic, and not epistemically or semantically defined.
3. Naturally necessary. Necessary given the metaphysically contingent order of nature within creation. Its existence is necessitated by the existence of anything or any kind of thing found in the actual creation.
4. Actually existing at every time.
5. Naturally incorruptible.
   

         a. Actually exists at some time and cannot naturally be corrupted.
         b. Actually exists at all times and cannot naturally be corrupted.
 
We can set aside meaning 1, since the argument has nothing to do with logical deducibility, analyticity, or conceivability.
 
Anthony Kenny argues (in his book, The Five Ways) that the Third Way must intend ‘necessary being’ in sense 5a or 5b. This is based on Aquinas’s assertion in the Summa Contra Gentiles (Book II, chapter 30) that the heavenly spheres are “necessary beings,” despite being created by God. However, this evidence does not rule out 3 or 4 either, although it does rule out 2.
 
​The next point of complexity concerns the distinction between things that are necessary per se (in and through themselves) and those whose necessity is caused by another. Are each of the four relevant categories of necessity (2, 3, 5a, and 5b) divided into two sub-categories by this distinction, or can some forms of necessity exist only per se or only when caused by another?
 
Now, suppose that the distinction cuts across all four meanings. Suppose, further, that Aquinas intended ‘necessary’ to correspond to meaning 3, 5a, or 5b. If so, the only result that Aquinas could reach would be that God is an incorruptible being that exists at all times or with merely natural (created) necessity. God is certainly incorruptible, but it wouldn’t make sense to attribute to Him existence in and through time, or merely natural necessity.
 
So, we must assume either that Aquinas intended meaning 2 throughout, or that he intended ‘necessary’ to include things that are necessary in senses 2, 3, 5a, or 5b, but he believed that only things with necessity in sense 2 (metaphysical necessity) could be necessary per se. Given his affirmation of created, metaphysically contingent beings (like the heavenly spheres) as ‘necessary’ in SCG II.30, the second assumption seems most likely. So, we can assume that necessary beings include all beings that are either metaphysically or naturally necessary, and that only metaphysically necessary beings are necessary per se. This leaves open the question of whether there could be metaphysically necessary beings (meaning 2) whose necessity is caused by something else. The most plausible candidates would be the divine ideas, although Aquinas never says that the necessary being of the divine ideas is caused (Summa Th. I q15, a1 and a2). He suggests instead that each divine idea is in some sense “identical” to the divine essence, despite the existence of many ideas.
 
The safest interpretation might be that only God is metaphysically necessary and only God is necessary per se (so those two categories coincide). Consequently, all of the merely naturally necessary beings have their necessity caused by God.
 
We still have to consider meanings 5a and 5b, which were favored by Kenny. I would rule out 5a immediately, since Aquinas never, as far as I know, labels the human soul as ‘necessary’, even though it is certainly incorruptible. It is true that Aquinas states (in Summa Theologica I q75 a6 ad 2) that the human soul has no ‘potentiality for non-existence’ but it isn’t clear that that is the same as necessary being.
 
The heavenly spheres are necessary beings in both sense 3 and 5b. So, the acid test will be to see which meaning makes most sense of the premises of the first part of Thomas’s argument. I will turn to this problem next week.