God, Über-God, and Unter-God

Abstract

I examine two related arguments for the claim that if God is omnipotent, God cannot lack abilities such as the ability to do evil or to act irrationally. Both arguments concern the idea that omnipotence is inconsistent with being dominated with respect to abilities. I raise new issues in the formulation of such dominance principles about ability, and attempt to solve them. I also discuss and reject existing objections to these arguments. I conclude that these arguments are promising but not conclusive, and that important work remains to be done in formulating the relevant dominance principles.

The scope of omnipotence

There is an important question about the demandingness of the concept of omnipotence, as it figures in the classical theistic religions: what abilities must an agent possess to qualify as omnipotent? An answer to this question would not only tell us much about the kind of being posited by classical theism, but would also have important implications for several issues in contemporary philosophy of religion.

For example, the traditional paradox of the stone threatens to show that the concept of omnipotence is so demanding as to be internally contradictory.¹ The paradox says that an omnipotent agent must possess an ability that itself rules out omnipotence, such as the ability to make a stone that the omnipotent agent cannot lift. At least partly in response to this sort of puzzle, it is now widely held that omnipotence does not require the ability to do just anything at all.² The inability to bring it about that 2 + 2 = 5 does not seem to preclude omnipotence. Similarly, perhaps, for the ability to make a stone that an omnipotent agent cannot lift.

But another issue concerns whether omnipotence is too demanding to fit with other attributes that have traditionally characterized God. A very old theological problem concerns how omnipotence can be reconciled with necessary moral perfection.³ It seems that if an agent is omnipotent, then that agent must be able to kill an innocent person for no morally significant reason. After all, many ordinary humans possess (and, unfortunately, exercise) this ability.⁴ But if an agent also had necessary moral perfection, then it would be impossible for it to perform such an immoral action. So there is tension between God's alleged possession of both omnipotence and necessary moral perfection.

Hill (2014) recently pointed out that this puzzle extends to a wide variety of other traditional divine attributes. Here I will focus on just two (in addition to necessary moral perfection): necessary omniscience and necessary rational perfection. Many ordinary humans are able to believe falsely (e.g. intentionally deceive themselves) and act irrationally. There is some pressure, then, to think that an omnipotent agent must be able to believe falsely and act irrationally as well. But these acts would be impossible for a necessarily omniscient and perfectly rational agent to perform. So the same general form of argument reveals a tension between omnipotence and necessary omniscience and necessary rational perfection.

A popular response to the argument that omnipotence contradicts other divine attributes builds on the standard response to the paradox of the stone. Not only does omnipotence not require the ability to do just anything at all, but it never requires the ability to do the metaphysically impossible.⁵ Since it is impossible for God to act immorally, irrationally, or have false beliefs, God can be omnipotent despite lacking the ability to do these things, as omnipotence does not require being able to do the impossible. I will label this popular response ‘The Metaphysical Impossibility Response’ (MIR). It consists of three schematic claims that stand in the following logical relationship:

The Metaphysical Impossibility Response (MIR)

1. (1) Omnipotence does not require the ability to do the metaphysically impossible.

2. (2) It is metaphysically impossible that God Φs.

Therefore it is consistent that:

1. (3) God is both omnipotent and unable to Φ.

This article examines two arguments against MIR. Both of these arguments already exist in embryonic form, but in this article I hope to improve on existing formulations and discuss new problems for these arguments and how they might be solved. Although my focus is specifically on the question about the required scope of God's omnipotence, several lessons can be generalized about what omnipotence demands in general.

First, however, a quick word about analyses of omnipotence. Recent philosophical discussion about omnipotence has been dominated by proposed analyses of omnipotence and critical discussion thereof.⁶ Moreover, these analyses are often put forward in explicit service of vindicating the coherence of omnipotence with itself and other divine attributes. Such analyses purport to give a fully general account of the scope of omnipotence. One could survey these analyses in an attempt to show that those that vindicate MIR fail to be adequate analyses of omnipotence, as Hill (2014) recently does.⁷ But this article does not adopt this methodology. Instead, I aim to abstract away from some of these details about the analysis of omnipotence, by examining general arguments for the claim that God's having omnipotence would require the ability to act immorally, etc. If these arguments succeed, then they show that there is something wrong with any analysis of omnipotence that entails that God is omnipotent even though God is unable to act immorally, etc.

The Über-God Argument

At the centre of the concept of omnipotence is the idea of maximal power. Oppy (2005, 78–82) develops an argument from this conception of omnipotence to the claim that God (as orthodoxly conceived) is not omnipotent. The theoretical core of the argument is expressed in the following passage:

If you can do everything that I can do, and more besides, then it seems to me to be evidently true that you are more powerful than I. But it is simply an analytical truth that nothing can be more powerful than an omnipotent being.

Let's separate the two principles indicated above:

Maximality: ◻∀x(◊∃y(y is more powerful than x) → x is not omnipotent)

Dominance: ◻∀x∀y(If y's abilities are a proper subset of x's, then x is more powerful than y)

Both of these principles are extremely attractive. Maximality follows from the conception of omnipotence as maximal power. As for Dominance, it is hard to imagine better grounds for having superior power to another than being able to do all that they can and more.

Now consider God. At least according to the metaphysical impossibility response, God is a being with certain essential limitations in ability. God cannot act immorally, irrationally, or believe falsely, by virtue of the essential divine attributes. Now we may imagine an agent just like God with respect to abilities, but who is not necessarily omniscient or rationally and morally perfect. Call this being ‘Über-God’. Über-God may now have some abilities that God lacks, particularly abilities to act immorally, irrationally, and believe falsely. It appears that Über-God now dominates God with respect to abilities. Our Über-God thought experiment, together with the above principles, lead to the following argument:

The Über-God Argument

The Über-God Argument threatens to show that God cannot be both omnipotent and yet lack the ability to act immorally, irrationally, and believe falsely. While the Über-God Argument is specifically about God, the form of the argument applies quite broadly. What it appears to demonstrate is that any agent for whom we can imagine another agent that dominates it in abilities, that agent is not omnipotent.⁸

In what follows, I discuss some under-examined issues that the Über-God Argument faces. I begin with a discussion of Dominance.

Specifying dominance

I introduced Über-God as having all of God's abilities and some more. But on closer inspection, this appears impossible. For each agent, there are many abilities such that it is logically necessary that only that agent has them. For any agent A, only A can write A's autobiography, and only A can make it the case that A Φs without being made by anyone else to Φ. So Über-God cannot have all of God's abilities and more, speaking unrestrictedly.

There are now two challenges for the Über-God Argument. First, we must specify some particular set of abilities with respect to which Über-God dominates God. And second, dominance with respect to this set of abilities must be sufficient for being more powerful overall. In other words, once we give up the claim that God's abilities are a proper subset of Über-God's abilities speaking unrestrictedly, we must employ a strengthened dominance principle in order to render the Über-God Argument valid.

We might begin by noting that the problem cases I pointed to earlier involve ineliminable reference to specific particulars. Other examples of these kinds of abilities include the ability to ride that particular bike, or the ability to cross the Delaware River. These abilities are to be contrasted with abilities that can be ascribed without ineliminable reference to specific particulars, such as the ability to ride a bike and the ability to cross a river wider than 30 ft. Call the former kinds of abilities ‘non-qualitative abilities’ and the latter ‘qualitative abilities’.⁹ Even though God has some non-qualitative abilities that Über-God lacks, perhaps Über-God dominates God with respect to qualitative abilities.

Unfortunately, this restricted qualitative dominance thesis is still not quite correct. The reason is that God has various qualitative properties that Über-God lacks. This allows us to construct, admittedly rather contrived, qualitative abilities that God has that Über-God lacks. For example, God has the ability to lift a stone while being necessarily omniscient, but Über-God does not. We must therefore search for an even more refined set of abilities such that Über-God dominates God with respect to that set, and which is still sufficient for being more powerful.

Here we might appeal to the distinction between basic and non-basic actions.¹⁰ Non-basic actions are those one does by doing something else; such as turning on the light, which one does by flicking the switch. Basic actions are not non-basic; such as perhaps moving my finger. Now apply this basic/non-basic distinction to abilities – basic abilities are abilities to perform basic actions, non-basic abilities are abilities to perform non-basic actions. It is plausible that the ability to lift a stone while being necessarily omniscient is non-basic, since one performs this action by doing something else, namely lifting a stone.

Our new proposal is that Über-God dominates God with respect to basic, qualitative abilities. Über-God has the ability to choose to play a devious trick for fun, whereas God, being essentially morally perfect, lacks this ability. Moreover, it is plausible that choosing to play a devious trick for fun is a basic ability – one does not do it by doing something else.

Unfortunately, even if this new dominance thesis is correct, it is of no help. The problem is that dominance with respect to basic, qualitative abilities is not sufficient for being more powerful overall. Imagine two embodied agents, Tip and Tap, whose basic abilities consist only of motor skills, like moving their limbs in particular ways. Moreover, Tip and Tap have all the same motor skills, with one small exception – Tap can wiggle their toe in a particular way that Tip can't. Both Tip and Tap are trapped in rooms that are qualitatively similar, but whereas Tap's room is bare, Tip's room has a variety of switches that Tip can push to turn on the lights, turn on air conditioning or heat, and many other effects. None of these are basic actions, since Tip does them only by moving their finger in a certain way. But Tap shares this basic ability, being able to move their finger in that way, even though Tap is unable to turn on the lights or even flick a switch. It appears that Tap dominates Tip with respect to basic, qualitative abilities since they both can move their bodies around in all the same ways, except Tap can wiggle their toe in a particular way that Tip can't. But Tip seems far more powerful overall, since Tip has considerable control over their environment in a way that Tap does not.

What this seems to indicate is that basic, qualitative abilities are not sensitive to external circumstances, preventing them from being sufficient indicators of overall power. The appeal to basic abilities will therefore not work in formulating the Über-God Argument.

The intuitive impression remains that Über-God does dominate God in some important sense, and that this shows that Über-God is more powerful than God. That God has certain abilities like the ability to lift a stone while being necessarily omniscient is intuitively irrelevant. However, we have not been able to locate the relevant dominance thesis. There is therefore the following unresolved challenge for the Über-God Argument:

Specifying Dominance: The Über-God Argument requires that there is some set of abilities S such that (a) Über-God dominates God with respect to S; and (b) dominance with respect to S is sufficient for being more powerful overall.

Dimensions of ability

Suppose that we successfully narrow in on the desired set of abilities S described above. There are still a few complications for formulating a true dominance principle in terms of S. We have been assuming that dominance with respect merely to the range of one's abilities is sufficient for being more powerful, but this assumption is a simplification, as there are several dimensions along which our abilities can be assessed. Our range of abilities is merely one of these dimensions, so dominance with respect to that dimension isn't always enough.

Our abilities also differ in their reliability. Having an ability does not require surefire success. That a golfer missed a putt once does not entail that they were not able to make the putt.¹¹ In fact, according to one prominent theory of abilities, S's having the ability to Φ merely requires that it be possible that S Φs (holding fixed some contextually salient facts). At the other end of the spectrum, the most reliable kind of ability would be something like what Pearce and Pruss (2012, 407) call ‘perfect efficacy of will’:

X has perfect efficacy of will if and only if for all P, necessarily if X were to try to bring it about that P, then X would intentionally bring it about that P.

Having perfect efficacy of will guarantees that all of one's abilities (or at least all of one's abilities to act intentionally) are surefire.

The fact that A has a strictly greater range of abilities than B does not entail that A is more powerful than B if B's abilities are more reliable than A's. For example, suppose that A can throw four kinds of pitches (two-seam fastball, slider, change-up, and curveball), whereas B can throw just three of these ( B has no slider). But suppose B's pitches are far more reliable than A's, so that B succeeds in throwing these three pitches nearly every time B tries, whereas A succeeds in throwing their four pitches only about half of the time. A dominates B with respect to the range of pitches they can throw, but this does not show that A is more powerful as a pitcher than B, since B's pitches are better along another dimension.

Another dimension along which abilities are assessed is their robustness. By this I mean the range of relevant facts that can be held fixed when truly ascribing that ability. To illuminate this notion, consider the sense in which Lewis says he can truly be ascribed the ability to speak Finnish.¹² This sense can be invoked by comparison with an ape – ‘an ape can't speak Finnish, but I can’ sounds true. Lewis identifies this sense with the fact that his speaking Finnish is compossible with facts about his larynx and nervous system (whereas an ape's speaking Finnish is not compossible with corresponding facts about the ape larynx and nervous system). However, this sense is clearly less robust than the sense in which Noora, a native Finnish speaker, is able to speak Finnish. We can truly say that Noora is able to speak Finnish even holding fixed facts about her training and upbringing, something that we cannot do with respect to Lewis; Lewis's speaking Finnish is not compossible with his lack of training.¹³ In this sense, an ability is more robust to the extent that truly ascribing it does not require failing to attend to various facts about the agent's actual circumstances. While the notion of robustness can be usefully explicated on Lewis's compossibility framework, any adequate theory of ability ascriptions will also be able to elucidate this distinction. For example, on broadly counterfactual analyses, we can understand robustness in terms of how distant a world we must consider in evaluating a true ability ascription. A less robust ability requires more counterfactual suppositions about an agent's actual circumstances when being ascribed. We must consider more distant counterfactual circumstances if there is any true sense in which Lewis can speak Finnish. These would be worlds where the facts about Lewis's larynx and nervous system are the same, though facts about his training differ. By contrast, there is less distance needed to evaluate the counterfactual that makes true the claim that Noora can speak Finnish.¹⁴

Having introduced the dimension of robustness, consider another pitching example. Pitchers A and B might both be able to throw a change-up, but B's ability to do so might be more robust. B might be able to do so even holding fixed strong winds or low temperatures or the fact that it is the bottom of the 9th inning with bases loaded, whereas truly ascribing this ability to A requires abstracting away from these conditions. Again, if A merely dominates B with respect to the range of pitches A can throw but not with respect to the robustness of those abilities, A is not thereby a more powerful pitcher than B.

A final dimension that I will mention is quality. Two people may have the ability to Φ, but the quality of their performances may differ considerably. What determines quality may vary considerably depending on the nature of the ability in question. In the case of the ability to throw a curveball, some of the relevant factors may be the speed at which it can be thrown, the amount of movement on the pitch, and the degree of control that the pitcher has over it. It is obvious that dominance with respect to the range of pitches that one can throw does not indicate being a more powerful pitcher if the quality of the pitches is allowed to differ.

I have proposed that there are at least four dimensions along which our abilities may be assessed – range, reliability, robustness, and quality. Each of these dimensions matters in assessing how abilities contribute to power. There may be more, but that will not matter for our purposes.

There is an interesting question about whether some of these dimensions are more fundamental than others. Some might propose to reduce all of them to just the range of abilities. Perhaps all of these dimensions can be accounted for by just being more fine-grained in attributing abilities. Consider, for example, the ability to throw a curveball. Maybe quality is captured by nothing more than having the ability to throw a X-mph curveball that breaks Y-ft in direction D. Robustness can be described as the ability to throw a curveball in circumstances C. And reliability is the ability to throw a curveball X% of the time.

While this question is important, I intend to remain neutral on it in what follows. Even if some dimensions of ability are more conspicuously described as constructions based on others, all should recognize some phenomena corresponding to each of the dimensions I have mentioned.

I propose to amend Dominance in the following way:

Dominance_dimensions: ◻∀x∀y(If x's S-set of abilities dominates y's S-set with respect to at least one dimension of ability and is at least equal with respect to every other dimension, then x is more powerful than y.)

This principle assumes that there is some way of satisfying the Specifying Dominance challenge which will allow us to centre in on some restricted type of abilities, S, with respect to which we can accurately compare arbitrary agents. Given that, it then says that if A is better than B along one dimension and at least equal in all others with respect to S, then A is more powerful than B.

Notice that this principle is neutral with respect to how many dimensions there really are. It allows us to avoid the kinds of counterexamples we canvassed above. For example, if pitcher A throws more pitches than B but throws all of them with lower quality and reliability, Dominance_dimensions will not give the false result that A is a more powerful pitcher than B. While A dominates B with respect to the range of relevant abilities, A falls far short with respect to other dimensions.

Our question now is how to conceive of Über-God, given these distinctions we have made. We originally claimed that Über-God dominates God with respect to range of abilities, since Über-God has abilities that God lacks, like the ability to do evil. But it is not obvious that these abilities will be of the kind that will be required for the the Über-God Argument, or in other words that they will be part of God's S-set of abilities. For example, we examined the suggestion that the S-set is the set of all basic, qualitative abilities. If this were the S-set, then the ability to do evil or act irrationally would not be part of the S-set, since these abilities are not basic. One does evil by doing something else, some more basic action that is evil, like killing an innocent. But this is still not basic. Eventually one gets back to something like moving one's finger (for example, to thereby pull a trigger on a gun aimed at an innocent) or perhaps trying to move one's finger. Assuming God is not embodied, God's basic actions would have to be more like tryings or willings. So perhaps the basic ability Über-God has that God lacks is the ability to try to pull that trigger.

But now there is a potential problem. It may be argued that God does have the ability to try to pull that trigger. There may be worlds where God does pull that trigger. These worlds must be worlds where pulling that trigger is not an evil act (e.g. the gun is not aimed at anyone). But this possibility, so goes the objection, is sufficient for God's being able to pull that trigger.

We may concede that God has the ability to pull that trigger. The important moral I wanted to draw from this line is that some of Über-God's abilities are more robust than God's. Even if God has the ability to pull that trigger, this ability is less robust than the corresponding ability of Über-God's. For it remains true that Über-God is able to pull that trigger even when you hold fixed all of the past and present facts that make it wrong to pull that trigger. By contrast, according to the metaphysical impossibility response, it cannot be true that God is able to pull that trigger if you hold these facts fixed when evaluating the ability ascription.¹⁵ Therefore, even if there is a sense in which God is able to (try) to pull that trigger, this sense is less robust than the sense in which Über-God is able to (try) to pull that trigger.

My point here has not been to further explore the idea that the S-set should be the set of basic abilities, as we saw earlier that this idea will not work. Rather, it has been to point out that some of Über-God's abilities are more robust than God's corresponding abilities. This gives us more flexibility when attempting to meet the challenge of Specifying Dominance. By Dominance_dimensions, it suffices that the S-set is such that Über-God dominates God with respect to at least one dimension of those abilities, and they at least match along all other dimensions. We have identified two possible dimensions along which such dominance might occur: range and robustness.

The distinctions we have made in this section allow us to make Specifying Dominance more specific:

Specifying Dominance: The Über-God Argument requires that there is some set of abilities S such that (a) Über-God dominates God along at least one dimension and at least matches God along all other dimensions with respect to S; and (b) Dominance_dimensions is true when formulated in terms of S.

In this section, I argued that it is not just the range of one's abilities that contributes to overall power, but also the reliability, robustness, and quality of one's abilities. Elucidating these notions leads to useful theorizing about abilities. It also allows us to become clearer about just what the Specifying Dominance challenge requires. Moreover, doing so showed that Über-God has a range of abilities that are more robust than God's corresponding abilities. This allows for more options in meeting the Specifying Dominance challenge. Finally, it allowed for an improvement to our dominance principle that avoids a wide range of counterexamples.

Modality and Maximality

In the last two sections we precisified and explored the challenges required to formulate a dominance principle about abilities that would sustain the Über-God Argument. The desired dominance principle would entail that our hypothetical Über-God is more powerful than plain old God. Yet there remains a potential objection to the Über-God Argument which raises issues about the modal status of Maximality.

Theists may regard Über-God as a metaphysical impossibility, and insist that this somehow blocks the Über-God Argument. This response has been proffered by several theists in response to arguments similar to the one I have formulated.¹⁶ In this section, I reconstruct the best version of this objection that I can and critically assess it.

By our reasoning from the previous section, we know that Über-God must at least match God with respect to reliability of abilities for the Über-God argument to succeed. Now theists can claim that God has the highest degree of reliability, namely what Pearce and Pruss (2012, 407) labelled ‘perfect efficacy of will’. But there is an argument for the claim that there cannot be two beings with perfect efficacy of will, which I adopt from Baillie and Hagen (2008):

1. (1) If there were two agents A and B with perfect efficacy of will, then it would be possible for A and B to have a conflict of will.

2. (2) If A and B have a conflict of will, then either A wills that P but P is false or B wills that not-P but not-P is false.

3. (3) So either the counterfactual ‘if A were to will that P, then A would intentionally bring it about that P’ would be false or ‘if B were to will that not-P, then B would intentionally bring it about that not-P’ would be false.

4. (4) So either A or B would not have perfect efficacy of will.

5. (5) Therefore there cannot be two agents with perfect efficacy of will.

Having argued for the impossibility of two agents with perfect efficacy of will, the theist then claims that God exists with metaphysical necessity, and that therefore the existence of any other agent with perfect efficacy of will is metaphysically impossible. Since Über-God would have to at least match God with respect to reliability, Über-God is therefore metaphysically impossible. The objector finishes by claiming that omnipotence is ruled out only if there is a metaphysically possible agent that is more powerful overall, and so the Über-God Argument fails.

I do not find this objection persuasive, but examining it will shed some light on Maximality, so it is worth discussing. I will first argue, non-concessively, that the argument for the metaphysical impossibility of Über-God does not work. This is important, since many have held that there cannot be two omnipotent agents on the basis of this kind of argument. Second, I will argue, more concessively, that even if Über-God is metaphysically impossible, the Über-God Argument is still promising given a strengthened version of Maximality.

On the first point, I dispute (1), which claims that two agents with perfect efficacy of will must lead to the possibility of conflicts of will, in which one wills that P and the other wills that not-P. Two agents with perfect efficacy of will could harmonize, so that their wills never conflict. It is not even implausible that God and Über-God would never have conflicts of will, although Über-God is not necessarily morally perfect. For suppose that Über-God was not perfect, but was essentially very good. If Über-God only made a few minor mistakes here and there, there is no reason to suppose God would possibly will to prevent Über-God's willings. God allows many creatures leeway to make even very significant moral mistakes. Thus, it is perfectly possible for there to be both a necessary God and an Über-God which never have any possible clashes of will.¹⁷

But suppose that for some reason Über-God was metaphysically impossible. Would this overturn the Über-God Argument? That depends. Maximality is formulated with a possibility modal ‘◊’. Suppose we take this modal to express metaphysical possibility. In that case, what Maximality says is that, necessarily, an agent fails to be omnipotent if, in some metaphysically possible world, there is another agent that is more powerful. So construed, the Über-God Argument does require that Über-God is metaphysically possible.

But suppose we instead took ‘◊’ to express conceptual possibility. Maximality is, after all, plausibly a conceptual truth about the very concept of omnipotence.¹⁸ If it is even conceptually possible that an agent is less powerful than another, that agent is not omnipotent, no matter what restrictions are placed on what is metaphysically possible by the necessary existence of God. By analogy, suppose that necessitarianism were true, so that this was the only metaphysically possible world. Further, suppose that humans are the most powerful agents that actually exist. Still, the mere conceptual possibility of agents far more powerful than humans is sufficient to show that no human Is omnipotent, even if those agents are somehow not metaphysically possible.¹⁹

What Maximality would then say is that, necessarily, if there is some merely conceptually possible world where Über-God is more powerful than God, then God is not omnipotent. The objector must now claim that Über-God is not even conceptually possible. Some theists may be inclined to believe this, perhaps on the basis of some sort of ontological argument to show that God's existence is conceptually necessary, together with the above argument showing that the conceptual necessity of one perfectly efficacious agent would rule out the conceptual possibility of any others. But I tend to think it would be a hard line to sustain. (The most promising versions of the ontological argument, I believe, appeal to the metaphysical essence of God, not to the concept God.)²⁰

Lembke (2012, 432) argues that the conceptual version of the maximality principle is not true. Implicitly, by assuming that Über-God might be conceptually possible despite being metaphysically impossible, I have been assuming that conceivability might outstrip metaphysical possibility. On that sort of view, it seems plausible that certain mathematical truths are metaphysically but not conceptually necessary. Perhaps geometrical truths are synthetic a priori, à la Kant. Or certain mathematical axioms or independent hypotheses such as the Continuum Hypothesis could be metaphysically necessary, despite their negation being conceivable. If that's right, then it is also conceivable for someone to prove these mathematical truths. So it is conceivable that there is an Über-God that, in addition to its other abilities, is able to prove the Continuum Hypothesis. It follows that it is conceptually possible that there is an agent that is more powerful than God, or Über-God sans the extra mathematical abilities. According to the conceptual maximality principle, this should entail that Über-God sans mathematical abilities is not omnipotent. But this entailment seems wrong, and furnishes a counterexample to the conceptual maximality principle.

I suggest that Über-God is conceivable in a stronger sense than the truth of the Continuum Hypothesis is conceivable. The Continuum Hypothesis is conceivable only in the sense of ‘negative conceivability’.²¹ In other words, one cannot detect a contradiction in the proposition that the Continuum Hypothesis is true, or that there is an agent that proves the Continuum Hypothesis. On the other hand, Über-God is not only negatively conceivable, but also positively conceivable²² – one can clearly and distinctly imagine the existence of Über-God. What the counterexample shows is that mere negative conceivability of something more powerful does not rule out omnipotence. But I still hold that the positive conceivability of something more powerful does.

This section assessed an objection to the Über-God Argument based on the alleged metaphysical impossibility of Über-God. My response was twofold. First, I challenged the argument for the metaphysical impossibility of Über-God. Second, I argued that even if Über-God were metaphysically impossible, the Über-God Argument could still succeed as long as Über-God is positively conceivable. This is because we can understand the possibility modal in Maximality as expressing positive conceptual possibility.²³

Abilities and liabilities

There is one final important objection to dominance principles. This objection is the claim that the possession of some abilities does not contribute to power but rather decreases it. Therefore, merely being dominated with respect to the range of one's abilities does not entail being less powerful, as the extra abilities could be ones that do not contribute to overall power.

Some proposed examples of abilities that do not contribute to power are the ability to find something difficult to do,²⁴ the ability to be killed,²⁵ and (most relevantly) the ability to do evil.²⁶ I will call alleged examples of abilities that detract from overall power ‘weakening abilities'. My response to the challenge of weakening abilities is twofold. Some weakening abilities, I argue, are not abilities in the relevant sense of ‘ability’ used in dominance principles. The rest of the weakening abilities, I argue, tend to decrease power only because they normally come along with a lack of other abilities. Because of this feature, they cannot constitute counterexamples to dominance principles.

Take the following weakening abilities: the ability to be killed and the ability to involuntarily become completely impotent.²⁷ Notice that these refer not to actions – things that are actively done by the agent – but rather to things that simply happen passively to the agent. The English expression ‘able to’ is not sensitive to this active/passive distinction. In other words, ‘able to’ can be used both to express abilities, namely capacities for actively performing actions, and liabilities, namely capacities for passively being affected by events. When I use ‘abilities' in the context of Dominance_dimensions, I intend only to refer to abilities in this active sense. Therefore, examples of this kind, which involve liabilities rather than abilities, are not potential counterexamples to our dominance principle.

The rest of the weakening abilities, I maintain, do intrinsically contribute to overall power, but tend to be associated with a lack of power because they tend to come along with a lack of other abilities. The ability to find something difficult to do normally comes along with an inability to find that thing easy to do.²⁸ Similarly, some argue that the ability to do evil does not contribute to power because those with the ability to do evil are unable to ensure that they do not exercise this ability.²⁹ Notice that in order to constitute a counterexample to Dominance_dimensions, we need two agents A and B, such that A has strictly more abilities than B (and at least equals B along all other dimensions of ability), but is not more powerful than B. There are two ways in which these weakening abilities might be used to try to construct such a counterexample.

First, we could give A the extra weakening ability without giving A any associated lack of ability. But then it seems to me that A really is more powerful than B. An agent with the ability to do something with difficulty and with ease is more powerful than the agent only able to do it with ease, all else equal.³⁰ Similarly, an agent able to do evil and with perfect control over the exercise of this ability is more powerful than the agent who is unable to fall into sin only because of a lack of the ability to sin entirely, all else equal.

Second, we could give A the weakening ability and the associated lack of ability, but then we must also give B the associated lack of ability, so that A actually dominates B with respect to range of abilities. But then again it seems that A is more powerful than B. An agent able to do something with difficulty and unable to do it with ease is more powerful, all else equal, than an agent unable to do it with difficulty or with ease. Better to be able to do something with difficulty than not to be able to do it at all.

I have argued that the proposed weakening abilities are either not weakening or not abilities, and therefore do not constitute counterexamples to our dominance principle. But perhaps the real issue is not that the ability to do evil is a counterexample to dominance principles, but that this ability necessarily comes along with a lack of another ability. If that were correct, then the concept of Über-God would be incoherent. For Über-God is meant to have all of God's abilities and more, including the ability to do evil. But God is able to ensure that God remains sinless, whereas, some may argue, Über-God cannot have this ability and have the ability to do evil. In response, there is nothing conceptually impossible about an agent that has the ability to do evil and also has perfect control over the exercise of the ability, lacking any inclination to exercise it. This merely requires that someone can have the ability to do evil and the ability to never be tempted to sin.

I conclude that these considerations do not pose any new, significant challenge to the Über-God Argument.

Prospects for the Über-God Argument

We have formulated the Über-God Argument, an argument that aims to show that God cannot be omnipotent and lack certain kinds of abilities, therefore taking aim at the heart of MIR. The argument goes that if God lacks the relevant abilities, God could be dominated with respect to the range of abilities by Über-God, and therefore could not be omnipotent. We then subjected the Über-God Argument to four serious objections:

1. (1) That Über-God cannot have all of God's abilities and more, and that there is no relevant sense in which Über-God dominates God with respect to abilities.

2. (2) That dominance with respect to range of abilities is not sufficient for being more powerful, since there are other dimensions of ability.

3. (3) That Über-God is not possible and that this undermines the argument.

4. (4) That dominance with respect to range of abilities is not sufficient for being more powerful, since some abilities detract from power.

My assessment after reviewing these objections is that the Über-God Argument is still quite promising. The third and fourth objections can be refuted fairly persuasively. The second objection proved useful for refining our dominance principle, but did not prove to be an insurmountable obstacle. The first objection is the most basic, but also the most difficult and serious. We made several attempts to locate the relevant sense in which Über-God dominates God, and attempted to show that dominance in this sense is sufficient for being more powerful overall. While we were not ultimately successful, some progress was made in working towards what the solution might look like. And I remain confident that it can be done, because there does seem to be an intuitive sense in which an agent can dominate another with respect to ability. To finish the task of defending the Über-God Argument, we must locate the relevant dominance thesis. Doing so promises not only to yield insights in this area of philosophy of religion, but also to be a rich source of insights about the nature of abilities and power.

The Unter-God Argument

The Über-God Argument is a deductive argument against the claim at the heart of MIR, that God can be both omnipotent and unable to do various things like sin or act irrationally. By contrast, the Unter-God Argument is best viewed as an explanatory challenge for MIR.³¹ The challenge begins by imagining an agent just like God with respect to abilities, but for whom it is metaphysically impossible to move red objects. Call this agent ‘Unter-God’. It seems clear that Unter-God is not omnipotent, on account of their inability to move red objects. However, the challenge points out that a generalized version of MIR would appear to rule out this conclusion:

The Generalized Metaphysical Impossibility Response (GEN-MIR)

1. (1) Omnipotence does not require the ability to do the metaphysically impossible.

2. (2) It is metaphysically impossible that A Φs.

Therefore it is consistent that:

1. (3) A is both omnipotent and unable to Φ.

If the line of reasoning schematized by GEN-MIR is sound in general, then it would also show that the inability to move red objects does not rule out Unter-God's claim to omnipotence. So it cannot be that this sort of reasoning is sound in general.

The proponent of MIR therefore seems to bear the burden of explaining why MIR should be accepted for the relevant instances of ‘Φ’ even though GEN-MIR should be rejected for various instances of ‘A’ and ‘Φ’. One instance of this challenge would be to explain why Unter-God's inability to move red objects rules out Unter-God's claim to omnipotence, even though God's inability to do evil does not rule out God's claim to omnipotence. The proponent of the Unter-God Argument claims that the proponent of MIR either cannot or does not discharge this explanatory burden, and that this is a cost of the view.

Attempts to meet the explanatory burden

In this section we will briefly consider two attempts to discharge the explanatory burden represented by the Unter-God Argument. Such an explanation would consist of a plausible, principled necessary and sufficient condition for when any arbitrary inability rules out omnipotence, plus an argument that the relevant inabilities that apply to God do not meet this condition.

One account that is plausible appeals to dominance considerations. Perhaps an inability A rules out being omnipotent just in case an agent with A could be dominated in ability. Unfortunately, this account will probably not be of much help to the proponent of MIR. The account gets the desired results only if Unter-God can be dominated by God, but God cannot be dominated by Über-God. Showing the former dominance claim would require solving the main problem with the Über-God Argument. Namely, it would require specifying the exact sense in which one agent can dominate another with respect to abilities, and showing that the corresponding dominance principle is true. Thus, it would involve rebutting the Unter-God Argument only by vindicating the Über-God Argument.

Another account with some plausibility is that an inability A is consistent with omnipotence just in case possession of omnipotence conceptually entails possession of A. In other words, being maximally powerful requires having all the abilities that are consistent with being maximally powerful. This account succeeds at explaining why Unter-God cannot be omnipotent – omnipotence does not conceptually entail the inability to move red objects, so an omnipotent being cannot possess this limitation. This account too, however, appears unfriendly to the proponent of MIR. To finish discharging the explanatory burden, the proponent of MIR must now argue that omnipotence conceptually entails the inability to do evil, act irrationally, believe falsely, and all of the other inabilities they posit God has.³² But the problem is that, if God has these inabilities, this seems to be due to God's necessarily being perfectly good, perfectly rational, omniscient, and so on. They do not seem to be due to God's omnipotence. But this is exactly what the proponent of MIR must claim.

One could attempt to sustain the claim that omnipotence conceptually entails all the relevant inabilities as follows. Pearce and Pruss (2012, 409–411) argue that omnipotence entails perfect freedom of will, and that perfect freedom of will entails both perfect rationality and omniscience. And if morality is somehow derived from rationality (a big ‘if’, to be sure), then perhaps perfect rationality and omniscience together entail perfect goodness. Now one can argue that each of these properties entails a corresponding inability – perfect rationality entails being unable to act irrationally, perfect goodness entails being unable to do evil, and so on. So all of the relevant inabilities are allegedly derived from omnipotence.

But there are at least two serious problems with this line of reasoning. First, the perfections in question do not entail the relevant inabilities. Being perfectly rational does not entail the inability to act irrationally, for example. Even if perfect rationality involves the disposition to choose a rational option in any possible situation, it does not follow that one is unable, in any situation, to choose a less than perfectly rational option. It may still be that if one were to try to choose an irrational option, one would succeed. If anything entails these inabilities it is not the mere possession of these perfections, but rather the necessary possession of these perfections. So, at best, necessary omnipotence entails the inabilities. But this does not show that these inabilities are compatible with omnipotence, according to the account we are considering. Instead, this account, plus the claim that necessary omnipotence entails these inabilities, entails that necessary omnipotence is impossible. The second problem is that it is far from clear that perfect freedom of will entails perfect rationality. Pearce and Pruss (2012, 411) do not really argue for this claim, so much as assert it. Many or perhaps all theories of free will do not seem to support this entailment. For example, if perfect freedom was just always having the ability to do otherwise, then it would not at all seem to entail perfect rationality. However, there is no room for a sufficiently thorough examination of the relation between freedom and rationality here.³³

Prospects for the Unter-God Argument

The Unter-God argument is less ambitious than the Über-God Argument. It concludes only that there is a cost to accepting MIR. I have not argued that this cost is overwhelming or conclusive. The cost could also be discharged by meeting the explanatory challenge generated by The Unter-God Argument. I have not argued that the explanatory challenge cannot be met. All that I suggest is that the challenge seems quite difficult to meet, and that the attempts just examined do not work.

But because the Unter-God Argument is less ambitious than the Über-God Argument, it is also more tractable. There is a difficult theoretical obstacle still outstanding to complete the Über-God Argument, namely figuring out the proper dominance thesis and principle. No comparable obstacle stands in the way of the Unter-God Argument. This shows that accepting the MIR to resolve the conflict between omnipotence and the necessity of other divine attributes comes with a cost. Whether a more definitive conclusion about MIR can be reached remains to be seen.