In Jose Benardete’s paradox, we are to suppose that there is an infinite number of Grim Reaper mechanisms, each of which is engineered to do two things: first, to check whether the victim, Fred, is still alive at the Grim Reaper’s appointed time, and, second, if he is still alive, to kill him instantaneously, and, if he is already dead at the appointed time, to do nothing. The last Grim Reaper (Reaper 1) performs this dual task at exactly one minute after noon. The next-to-last Reaper, Reaper 2, is appointed to perform the task at exactly one-half minute after noon. In general, each Reaper number n is assigned the moment 1/2^(n-1) minutes after noon. There is no first Reaper: for each Reaper n, there are infinitely many Reapers who are assigned moments of time earlier than Reaper n’s appointment.
 
It is certain that Fred does not survive the ordeal. In order to survive the whole ordeal, he must still be alive after one minute after twelve, but, we have stipulated that, if he survives until 12:01 p.m., then Reaper 1 will kill him. We can also prove that Fred will not survive until 12:01, since in order to do so, he must be alive at 30 seconds after 12, in which case Reaper 2 will have killed him.  In the same way, we can prove that Fred cannot survive until 1/2^(n-1) minutes after 12, for every n. Thus, no Grim Reaper can have the opportunity to kill Fred. Thus, it is impossible that Fred survive, and also impossible that any Reaper kill him! However, it seems also to be impossible for Fred to die with certainty and yet to do so without any cause.
 
The original Grim Reaper paradox requires some assumption about causality: that Fred cannot die unless someone or something kills him. I would like to eliminate that dependency. Consider the following variation: the Grim Placer. In place of asking whether a pre-existing victim Fred is dead or alive, we will focus instead on the question of whether or some Grim Placer has issued a death warrant. Let’s say that each Grim Placer #n can issue a death warrant by placing a particular kind of point-sized particle in a designated position, at exactly the distance of d/2^n meters from a plane P. Each Grim Placer #n checks to see if a particle is already at a distance of d/2^i  meters from plane P, for some i > n: that is, he checks to see if any earlier Placer has issued a “warrant”. If a particle has already been placed in one of the designated spots, then the Grim Placer #n does nothing, other than maintaining the status quo.
 
If there is no particle in an appropriate location, then the Grim Placer #n issues his warrant, placing a particle exactly d/2^n meters from P. We can now prove both that at 12:01 that some particle is located within d meters of the plane, and that no particle is located there. Suppose that there is no particle at any location d/2^i meters from plane P, for any i. This is impossible, since if there were no particle d/4 meters from P, then Grim Placer #1 would place a particle in the position d/2 meters from P.
 
Thus, there must at 12:01 pm be some particle in an appropriate position. Suppose that the particle is located at that time in position d/2^n meters from P, for some n. This means that every Grim Placer whose number is greater than n did nothing, contrary to our hypothesis. Thus, this option is also impossible.

​As Alexander Pruss has observed (Pruss 2009), the Grim Reaper paradox suggests not only that no finite time period can be divided into infinitely many sub-periods but also that it is impossible that there should exist infinitely many time periods, all of which are earlier than some event. It seems to provide grounds for thinking that time must be bounded at the beginning: that there must be a first period of time. If not, we could simply construct a new version of the Grim Placer paradox. As in the original version, we postulate the possibility of a Grim Placer, who creates a particle and places it at a designated spot, if and only if no particle is already located at a spot corresponding to any earlier Placer. In this version, Placer 1 is set to act at the first moment of 1 B.C., Placer 2 at the first moment of 2 B.C., and so on ad infinitum. Once again we can generate the contradiction: some particle must be placed within d meters of the plane, but there is no finite distance from the plane such that a particle could have been placed there.

The Kalam argument for God’s existence, which was pioneered by John Philoponus (490-570), developed by Islamic philosophers such as al-Kindi and al-Ghazali, and championed in recent years by William Lane Craig (Craig 1979) and by me (Koons 2014), is an attempt to prove that the universe must have had a cause, a role which God seems best suited to fit. The argument typically takes the following form:
 
1. Whatever begins to exist must have a cause.
2. The universe began to exist, because time itself is bounded in the past.
Therefore, the universe had a cause.
 
The first premise has a great deal of intuitive appeal, and there are severe epistemological costs to countenancing the idea of uncaused origins. For instance, the skeptical scenario popularized by Bertrand Russell—How do we know that the universe didn’t simply appear 5 minutes ago?—would be a live possibility in the absence of an a priori causal principle similar to premise 1. So, let’s focus on premise 2.

The typical Kalam strategy for defending premise 2 is to argue that time past is not eternal, that is, that there is some finite temporal bound to all past events. Now, it is not immediately obvious that a finite bound to the past entails that the “universe” began to exist. First, it is not obvious that there is such a thing as the universe: perhaps the plurality of things that exist at a time t do not compose a single whole at t. We might try to avoid this composition question by modifying premise 2 into 2.1:
 
2.1 There is a time t such that everything existing at t began to exist at t, and nothing existed at any time prior to t.
 
In order to get the desired conclusion, we would also have to modify premise 1 as follows:
 
1.1 If some things xx began to exist at time t, then there must be some thing y or things yy not among the xx such that y (or the yy) caused the xx to begin to exist at t. (I am using double letters as plural variables, following George Boolos’s plural quantification (Boolos 1984). One should read ‘yy’ as ‘the y’s (plural)’.)
 
We will also have to rule out the possibility that the things coming into existence at the first moment of time might have been caused by things existing at later times:
 
3. If the yy cause the xx to exist at t, then the yy exist at t or at some time earlier than t or eternally.

Form 1.1, 2.1, and 3, we can reach the conclusion that something that exists eternally caused the beginning-to-exist of all the things that existed at the first moment of time (if there is such a first moment).
 
There is, however, a further lacuna to fill: from the fact that the past is finite in extent or duration, it does not follow that there is a first moment of time. For example, it could be that no event occurs 14 billion or more years ago, but for every length of time L years less than 14 billion years, there are events that occurred exactly L years ago. That is, there might be a finite bound on the past, with past moments that approach arbitrarily close to that boundary, but no moment that reaches it, i.e., no absolutely first moment. (Think of the set of positive real numbers, which approach arbitrarily close to zero without actually including it.)

Instead of looking for proof of the finitude of the past, we should look instead for support of what Alexander Pruss (2016) has called causal finitism. If we can show that every event has a finite causal history (i.e., no causal loops and no causal infinite regresses), then we can infer that there are uncaused events. If we can further assume that everything that begins to exist at a time must have a cause and that every non-eternal or fully temporal thing must have begun to exist at some time (because the past is finite), then we can conclude that all uncaused things must be eternal in nature (i.e., existing “outside” or “beyond” time itself). At that point, we might be able to show that such an eternal cause of temporal events must be relevantly godlike.
 
Here is a version of this Pruss-inspired argument:
 
P1. Every event has a finite causal history (no causal loops or infinite regresses).
P2. For everything that begins to exist (at some point in time), the event of its beginning to exist must have a cause.
P3. Every non-eternal thing began to exist at some point in time (since the past of each non-eternal thing is finite in length).
P4. If the yy cause the xx to begin to exist at t, then the yy exist at t or at some time earlier than t or eternally. [Premise 3 above]
Therefore, every non-eternal thing is ultimately caused to exist by some eternal (godlike) thing.

This proof assumes (in premise 3) that, for anything that begins to exist, there is a first moment of its existence. That seems pretty reasonable. In addition, one could probably derive this from causal finitism. Suppose, for contradiction, that some x has a finite past but no first moment of existence. Then it seems that there must an infinite regress of periods of x's existence, each caused by its predecessor, in contradiction to the principle of causal finitism.

But suppose one doesn't buy either of these moves. Then there would have to be a single initial period P of x's existence, a period which lacks a first instant. In that case, premises P2 and P4 (suitably modified) would entail that there must be some cause of x's beginning to exist, a cause that is either timeless or active at a time t that is prior to and adjacent to period P. And so the proof will go through.

The proof is pretty simple. Suppose x is some non-eternal thing. By P2 it begins to exist, and by P3 its beginning to exist must have a cause. By P4, this cause must either exist eternally or at the same or earlier time than that of the beginning of x's existence. If the cause is an eternal being, we're done. If the cause is a non-eternal being, then it must have a beginning of its existence. Premise P1 rules out an infinite regress of temporal causes. So, there must be an eternal cause.

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.

 
Summa Theologiae I, Q22, and SCG III.71-74
 
God’s providence means that God is intelligently ordering all things toward their ultimate end. To do this, it is not sufficient that He simply create things—He must also order their interactions. Since God is the cause of the whole creation, He necessarily moves the whole creation to its ultimate end, which consists in good overall order.
 
Agents order their actions to some ends. Since God’s action extends all the way to every detail of creation, every such detail must be ordered to God’s ends. God’s knowledge and agency extend to particular things, and not just to general kinds of things. And, as we saw last time, His agency always produces definite effects.
 
In reply to objection 1 of article 2, Thomas embraces the radical conclusion that there is nothing that happens by chance in relation to God, since all the eventualities are foreseen by God. It seems to me that this moves too fast. It is true that all coincidences are foreseen by God, but it doesn’t seem to follow that they cannot happen by chance. If a coincidence is the result of God’s moving two or more things toward distinct ends, and neither of the ends entails the coincidence, then it seems that we could call the coincidence a matter of chance, even if God foresees that it would happen. God can foresee something as happening without intending it either as a means or an end.
 
In his reply to objection 2 in the same article, Thomas argues that God permits all of the defects in creation for the sake of some good of the universe as a whole. For example, lions would cease to exist if there were no slaying of animals. I don’t think that this entails (or is meant to entail) that this is the best of all possible worlds—merely that there must be some reason for the existence of all of the privations within creation. As Augustine said, God is able to bring (some) good from evil, but it doesn’t follow that each evil is necessary in order to maximize total goodness.
 
I question whether Thomas has established that there is such a thing as the “good of the universe.” The universe, or the totality of creation, is not a single substance. Consequently, we can’t be sure that it has its own final cause or natural end. Created things have a common end – which is God’s glory, the manifestation of His self-diffusive goodness, but that doesn’t imply that they collectively have a single end, as Thomas seems to assume.
 
There are three plausible candidates for a global good or end: justice in the distribution of benefits, the variety of modes of participating in God, and the overall beauty of the universe. On the first point, it seems plausible to think that things must already form a unity or a system of some kind, before the question of justice can even arise. If there are rational animals in the Andromeda galaxy, for example, does it make sense to ask whether God has exercised distributive justice in giving goods to them and to us? Can we ask whether God has exercised distributive justice between me and a vein of coal in Pennsylvania? On the second point, I’m not sure that variety as such is a good. It seems to like the finitude and definition that is generally required of goods—there is no maximum degree of variety that the world could contain. Perhaps it is better to say that God created each kind of thing simply because it is good for such things to exist, with variety as a mere by-product. And in the case of beauty, it seems that something must possess a certain kind of unity in order to count as beautiful. I will grant that a plurality of substances can be collectively beautiful, like the stars in the earth’s sky, but there must be at least a unified standpoint from which the collective can be considered, and I’m not sure that there is such a thing with respect to the universe as a whole.
 
The question of whether the universe as a whole has its own end or value is important. Thomas infers that God’s providence consists in a kind of unified plan or blueprint for the entire cosmos, rather than a library of plans or intentions for each substance and unified system of substances. One might respond: if God has multiple plans or intentions, must He not coordinate them, to avoid internal conflict in His intentions? Yes, but coordination isn’t the same thing as consolidation. We can imagine, I think, a plurality of divine plans existing in a degree of mutual contingency and independence from one another.
 
If God has a single, unified plan for creation, then it must have been in effect from the very first moment of creation. Since God’s plan is necessarily effective, and if (as St. Thomas teaches) the plan is complete in every detail, it is hard to see how this can be compatible with genuine contingency in the future. In contrast, if God has multiple, mutually compatible plans, then there is no reason that such plans could not come “on line” at different points in history. Such a plan goes into effect as soon as its earliest elements are actualized, but not before that point. Prior to actualization, the plan would be contingent relative to the events so far realized. Of course, all the plans are equally in effect from the perspective of God’s eternity, but that should be compatible with a changing status relative to the progress of time.
 
William of Ockham introduced a useful distinction concerning future facts. Some of these are hard facts and others are soft. So, for example, let’s suppose that it is genuinely a matter of contingency whether the Astros win their pennant this year. Let’s suppose that in fact they won’t. Then the truth of the statement ‘The Astros won’t win the pennant in 2021’ is a soft fact about the future. In contrast, let’s suppose that God has determined that one day the Anti-Christ will emerge. Then the truth of the statement ‘The Anti-Christ will emerge’ is a hard fact about the future. All facts about the present and past are now hard facts. So, it is now a hard fact that dinosaurs once lived or that the Astros won the 2017 World Series. Similarly, Ockham argues, facts about God’s will and knowledge concerning the future can be either hard or soft. As time passes, some of these facts harden. This does not involve any real change in God, since His act of will and knowledge is not internally modified by their objects.
 
In the reply to objection 4, Thomas considers the problem of reconciling human freedom with divine providence. He argues that human freedom consists in the fact that human beings are not naturally determined to a unique course of action in each circumstance. This lack of determinism applies only within the created order—it does not exclude God’s unique mode of causality (primary causation). “Everything happening from the exercise of human freedom must be subject to divine providence.” God’s providence extends in a “more excellent way” to the just than to the wicked. He can be said to have “abandoned” (dimittere) them, although they are not altogether excluded from His Providence, since that would mean their annihilation.
 
Reply 5: “Since a rational creature has, through its free will, control (dominium) over its actions, it is subject to divine providence in an especial manner (speciali modo).” I think this means that God’s agency does not exclude our own “control” or dominion over our actions. Instead, as I suggested before, we exercise a kind of joint dominion, neither excluding the other. When we do wrong, this is imputed to us and not to God as fault, because of the difference in our respective intentions. Compare Genesis 50:20 (Joseph to his brothers): “But as for you, you meant evil against me [by selling me to the Egyptians], but God meant it for good, in order to bring it about as it is this day, to save many people alive.”
 
In article 4, Thomas explains that at times God governs the creation through intermediaries. This reflects God’s strength and not His weakness. It is not that He needs such intermediate causes, but that He further enhances the glory of His creation by bestowing on creatures the dignity of real causality.
 
The role of secondary causes in explaining evil is explained by Thomas in SCG I, chapter 71. A defect that is produced by some secondary or instrumental cause is not always attributed to the primary cause. Think of a skilled artisan using a flawed tool.
 
But isn’t God responsible for any defect in His secondary agents? No, because all creatures are necessarily “defective” or imperfect in some respect. No rational creature, for example, can take into account every possibly relevant factor. Moreover, the excellence of creation requires that creatures exist at a variety of levels or grades of excellence.
 
The goodness of God’s government of creation requires that He allow things to work according to their own, limited nature. Otherwise, creation would be a kind of sham, a world of mere shadow-boxing.
 
It is interesting that Thomas never appeals in these articles (as far I can tell) to God’s timelessness, in the way that Boethius does in The Consolation of Philosophy. Neither does Thomas bring to bear the implications of his strong doctrine of creation—namely, the fact that the content of God’s will and knowledge are extrinsic to His own being. He does insist that God’s causality of future things does not take away their real contingency in the circumstances, but he does seem to think that future contingencies are already in some way certain and immutably fixed. However, I don’t think that this follows. From our point of view, within the flow of time, future events are really and not just apparently contingent and indeterminate. It is true that for God (in eternity) all things happen “at once”, past, present, and future, but that does not contradict that fact that at the present time the past is fixed and the future is largely “open”. If a future event is really now contingent, then so is God’s eternal knowledge and will with respect to that event. As time passes, God’s will gradually shifts (in its objects) from contingency to necessity, but this is merely a Cambridge change in God, with no intrinsic modification required.
 
God can make certain future events necessary, by promising them to us or by inspiring prophets with infallible foreknowledge of them. So, for example, Judas’s betrayal and Peter’s denials were fixed in advance by prophecy, as was Cyrus’s decree to allow the Jews to return to Canaan. Similarly, the future advent of the Anti-Christ, and the Second Coming of Christ are fixed and certain. But much of the future is genuinely open to alternatives, depending on our choices and chance events.
 
To clarify this point, let’s look at Peter van Inwagen’s consequence argument for the incompatibility of free will and determinism. I will modify van Inwagen’s argument to make it apply to God’s Providence, conceived of as a fixed and comprehensive plan for the future.
 
1.God has (in eternity) a Plan according to which I will do x tomorrow (where x is some arbitrary free action of mine).
2.It’s not currently up to me whether God has such a plan.
3.Necessarily, if God has such a Plan, then I will do x tomorrow. (God’s providence is infallibly effective).
4.Therefore, it’s not currently up to me whether I will do x tomorrow. (By 1-3 and van Inwagen’s transfer principle)
 
I think we should deny that premise 2 is generally true. Whether I do x tomorrow can be both up to me and up to God, and there is no determinate divine Plan already in effect that settles the matter one way or the other. To think that God has to plan ahead in order to govern the creation with coherent providence is to be guilty of a kind of anthropomorphism. God is infinite in wisdom, and so He can do whatever “planning” is needed on the fly, so to speak.
 
Presumably, God has some plans about creation that are not currently up to me. For example, His eternal plans about what happened in the past are currently beyond my control. Let Plan-Minus stand for the sum total of God’s plans that are currently beyond my control. Here’s another version of the consequence argument:
 
1.It’s not currently up to me what God’s Plan-Minus contains. (By definition of Plan-Minus)
2.Necessarily, if God has Plan-Minus, then His comprehensive Plan for all of history must include my doing x tomorrow. (Any initial segment of God’s Plan entails all of its successive elements.)
3.Necessarily, if God’s comprehensive Plan for all of history includes my doing x tomorrow, then I will do x tomorrow. (God’s providence is infallibly effective).
4.Therefore, it’s not currently up to me whether I will do x tomorrow. (By 1-3 and van Inwagen’s transfer principle)
 
Once again, I think we should deny 2. This is where it is crucial to determine whether God has simply a single Plan, each part of which requires all of the other parts, or whether God has multiple partial plans that are mutually contingent. If the latter, then we can ask when a particular partial plan has become the external object of God’s will. We can ask, for example, when a particular person became elect or reprobate, and we can ask what contingent events contributed to this fact.

Summa Theologiae, I, Q49, a1 and a2; I-II, Q9, a6; I-II, Q75, a3; I-II Q79, a1
 
In Part I, Q49, a1, Thomas explains that evil has no per se efficient cause, but it does always have a per accidens efficient cause. Every evil act or situation is good insofar as it exists, and something must cause per se that element of goodness. However, there need be no per se cause of the deficiency that is evil in the thing. When something good causes something bad, there is always some pre-existing deficiency of some kind, either in the agent or the patient, or both.
 
Since there is no defect in God, when God causes something that is evil, there must be some pre-existing defect in the patient. As Thomas puts it in reply 2, “And, likewise, whatever there is of being and action in a bad action, is reduced to God as the cause; whereas whatever defect is in it is not caused by God, but by the deficient secondary cause.”
 
When Thomas explains, in I-II Q9, a6, how God moves the human will, he points to two ways. First, God causes our nature, which includes the free will and its natural inclinations. And, second, God is absolute goodness—so every apparently good thing that moves the will does so because of its apparent participation in God’s goodness. In neither of these ways is God responsible for our sin.
 
In I-II Q75, a3, Thomas insists that nothing external to the will can necessitate sin. God is the cause of the movement of the will that is sin, but God (in His essence) does not necessitate that the will choose badly.
 
In I-II Q79, a1, “Whether God is a cause of sin,” Thomas summarizes his conclusions:
 
“Now God cannot be directly the cause of sin, either in Himself or in another, since every sin is a departure from the order which is to God as the end: whereas God inclines and turns all things to Himself as to their last end, as Dionysius states (Div. Nom. i): so that it is impossible that He should be either to Himself or to another the cause of departing from the order which is to Himself. Therefore, He cannot be directly the cause of sin.”

Summa Theologiae I, Q19, a4
 
Here Thomas is primarily interested in proving that God causes the universe by Will, and not by the necessity of His nature. His target is the Neo-Platonic tradition, who talked about finite things as “proceeding” from the One, rather than being intentionally created by God. Thomas argues that the first agent must act by intelligence and will and not simply by the necessity of His nature. Like all agents, God acts for the sake of an end. Since no end demands His choice, beyond His own existence, this means that all finite creatures are freely chosen for the sake of the proliferation of divine goodness.
 
Thomas appeals to Question 7, article 2, to the effect that God’s effects cannot be undetermined and indefinite. Thomas here anticipates a view recently defended by Notre Dame philosophy Peter van Inwagen. Van Inwagen proposes that God wills indeterminate facts, which the creation makes definite by chance. E.g., God could dictate that a certain coin should land either Heads or Tails, without choosing either option. When the coin falls one way or another, the determinate effect will exceed God’s intention in specificity. Similarly, van Inwagen imagines that the early history of the universe might be the result of chance filling in the indefiniteness of God’s decree. In Question 7, Thomas denies that God could give any created thing an indeterminate nature, since forms (both substantial and accidental) are always definite, and all forms come from God.
 
Is the Will of God always Fulfilled?
 
Summa Theologiae I, Q19, a6
 
No effect can escape the scope of God, who is the universal cause.
 
But, doesn’t God desire for all men to be saved? (Objection 1, appealing to I Timothy 2:4) Thomas’s best response is to distinguish between God’s “antecedent” and “consequent” will. Take some particular man, like Judas Iscariot. Does God want Judas to be saved? Yes—other things being equal, it is always better for a human to be saved rather than damned. But, things are not always equal. So, God’s antecedent will (His will about some result considered by itself, in isolation, other things’ being equal) is for all to be saved, but His consequent will (all things considered, with things not being equal) is only for the salvation of the elect.
 
What God wills antecedently need not happen, but what He wills consequently always happens.
 
Does God’s Will Abolish Contingency from the Created World?
 
If everything happens according to God’s will, in what sense can things be “contingent” in the created world. Things that God creates are absolutely contingent, in the sense that He could have chosen not to create them. But, given that He does will that a certain event or action happens, it is necessary that it should happen (as we saw in the last section). We might put it this way: our creaturely actions ever contingent in their actual circumstances (this is sometimes called historical contingency)? Is there any room for the creature to make its own contribution to what happens, a contribution that is in some sense independent of God’s will?
 
There is an important sense in which my action is free and undetermined in its actual circumstances (historically contingent). If I exercise free will, then my choice is not determined by the whole history of the world up until that point, including my current psychological state at the moment of acting. There are possible worlds in which exactly the same events and conditions obtain as obtain in the actual world, and in which I make a different choice. This doesn’t require changing the natures, powers, potentialities, or accidents of anything in creation, including myself.
 
But, of course, this does not make my free choice independent of God’s will. I cannot choose in a way that is contrary to the way that God wills that I choose. Doesn’t that make me unfree? I don’t think so. God’s will about my choice is also undetermined by the past. At the moment of my choice, both God’s will and my will are undetermined. They are jointly contingent—either of us could make either choice. My choice is necessarily caused by God’s will, but God’s will is not necessitated by the past. God’s will is free to cause me to act in either way that is open to me.
 
Of course, it is impossible for God to will that I choose A and for me to choose B, or vice versa. However, there are two live options: (i) I choose A and God wills that I choose A, or (ii) I choose B and God wills that I choose B. Is the choice between these two options in any sense “up to me”? I think it is. It is also up to God. The choice is 100% up to me and 100% up to God. The relation between God’s will and the will of a creature is a unique sort of relation, quite different from the relation between any two creatures. Crucially, although my choice of A (if I do choose A) is contingently caused by God’s will, but it isn’t caused by the fact that God wills that I choose A. The fact that I chose A and the fact that God willed that I choose A are the very same fact, looked at from two different perspectives. Facts cannot cause themselves, so my choice is not caused by God’s choice, nor is God’s choice caused by my choice.
 
Is my choice nonetheless explained asymmetrically by God’s choice? In some cases, Yes, and in other cases No. It may be that my choice plays some important role in God’s providence, in which case my free choice will be explainable in terms of that role (think of Mary’s sinlessness or Judas’s betrayal). But in most cases, God wills that I make a certain choice simply because that is the sort of choice that I would be inclined to make from time to time. God’s permissive willing is a kind of fiduciary willing: He wills what, putting Himself in our place, it makes sense for us to choose freely.
 
An analogy that I like to use is the relationship between a human author, like J. R. R. Tolkien, and one of his fictional characters, like Frodo. Does Frodo act with free will? Yes, I think he does. Does this make him independent of Tolkien’s choices? No. It’s not as if Tolkien had to go into a trance and let the spirit of Frodo move his pen or his typewriter in order to exercise his free will. Frodo decided freely to accept the One Ring, and Tolkien willed that Frodo should so decide. The two cases of free agency are compatible.
 
Article 12 is quite relevant to this point. In that article, Thomas distinguished five ways in which God wills things: prohibition, precept, counsel, operation, and permission. The most relevant distinction at this point is between operation and permission. If I choose to sin, God does not operationally will that I do so—instead, He permissively wills so. This does not mean that God wills only that I should sin or not sin, and then leave the result up to me. God cannot will something indefinite or indeterminate. Instead, God permissively wills that I sin, and He does not will consequently that I not sin. He does will antecedently that I not sin (He wills antecedently that each person abstain from sin on every occasion), but His antecedent will is not effective. His consequent will, even when that will is permissive, does necessitate the result.
 
The other three forms of God’s will, like His antecedent will, are not universally effective. God expresses what we ought to do and not do by way of prohibition, precept, and counsel. It is still up to us (and to God’s consequent, permissive will) whether we do what God commands.

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

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

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

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

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

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

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.

 All of Aquinas's Five Ways depend, in one way or another, on ruling out the possibility of infinite causal regresses. In the version of the First Way (the argument from motion) in the Summa Contra Gentiles (I.13), Aquinas follows Aristotle in offering two separate arguments against the causal regress. In the first three ways in the Summa Theologiae, he offers just one of the two Aristotelian arguments: an argument that depends on what I call the No-Intermediate-Real-Cause thesis. This is a thesis that states that if x is a cause of y, and y is a cause of z, then y is not really a cause in the strict sense but only secundum quid (only in a manner of speaking). An intermediate link in a causal chain is not in any sense the source of the reality of the ultimate effect--it is merely a conduit through which the first cause acts. Therefore, an infinite regress is impossible, because (as Aristotle and Aquinas note) every link in the regress would be only an intermediate cause. Hence, such a regress cannot contain any real causation.
 
This is a plausible argument, despite the fact that it is often dismissed as based on a fallacy of equivocation. The standard objection (going back at least to Cajetan, I believe) is that Aquinas equivocates on the phrase "removing the first cause." If we have a finite chain and we hypothetically remove the first cause from the series, it is obvious that none of the intermediate causes can act. Aquinas asserts that if we consider any infinite regress, we have a situation from which we have (in a sense) "removed the first cause". But, as critics point out, in this case there never was a first cause to be "removed", and so the cases are incomparable. However, Aquinas real point is simply to claim that intermediate causes are never causes in their own right but are always wholly parasitic on the first cause. Given that assumption, infinite causal regresses are indeed impossible.
 
The other strategy for dealing with infinite regresses was invented by Avicenna, followed by Scotus, Leibniz, and many subsequent thinkers (including me in 1997). This is the Aggregation Strategy. The Aggregation Strategy concedes, for the sake of argument, that infinite regresses are possible. However, the Strategy insists, if a regress consists entirely of contingent (or finite) things, then we can aggregate the whole series into a single entity and insist on a cause for it. Start now with a single finite thing, and consider all of the finite causes of that thing (whether immediate or remote). Either this series terminates in an uncaused thing, or else it constitutes an infinite regress. In the latter case, we can demand a cause for the whole series. This cause must be infinite, since any finite cause of the series would be a cause of the original entity and so would already be included in the series itself. A member of the series cannot cause the whole series. An infinite thing cannot be caused. And so we reach an uncaused first cause.
 
Aquinas was aware of this strategy, through his close reading of Avicenna. Why didn't he adopt it? I think he was worried that not all infinite series can be aggregated into a single entity. If an infinite series consists of entities of the same species (or a finite number of species), then it has the characteristic that Aquinas labels being accidentally infinite. An accidentally infinite series can be aggregated and must be caused as a whole. This is why Aquinas can concede that accidentally infinite series might exist without losing the force of his first cause argument. However, if an infinite series consists of entities of an infinite number of species, with the species climbing progressively higher and higher in the Great Chain of Being, the Aggregation Strategy could not be convincingly applied. Aquinas would call such a series essentially infinite, and he must (if the Second or Third Way is to work) deny the metaphysical possibility of such a series. This is why he appeals to Aristotle's argument and what I call the No-Intermediate-Real-Cause thesis, which should now be applied only to series that rise "vertically" through the ontological order of species.