Looking back and ahead

Intuitively, of course, omnipotence is the ability to do anything. But this might suggest something like the following analysis:

Here and in what follows, let an ‘agent’ be any non-abstract and causally efficacious entity: be it atomic or complex, material or non-material, personal or non-personal. So, if he satisfies (D1), A can not only create the universe ex nihilo and instantaneously cure all diseases, but he can also draw pictures of square circles, step over living corpses, and have a beer with married bachelors. On this account, then, A can do absolutely ‘everything that can be expressed in a string of words that makes sense’ (Geach (Reference Geach1977), 7) – even if that sense is self-contradictory. As Peter Geach says: ‘You mention it, and God can do it’ (ibid.) – a claim that Geach himself, of course, does not endorse. A towering figure in the history of philosophy who did endorse it, however, was René Descartes.Footnote ¹ This fact singlehandedly warns us not to dismiss (D1) too hastily.

Suppose, however, that (D1) is true. Thus, at one stroke, all conceivable theological difficulties and potential self-contradictions disappear into oblivion. Take, for example, the problem of evil. If God is omnipotent according to (D1), then obviously it is within his power to ensure that whatever is objectively a moral outrage is nevertheless objectively morally all right; that whatever is evil is in fact not evil but good; that no suffering has as a matter of fact ever occurred; in short, that everything is and has always been in a state of sublime happiness. Moreover, as has been pointed out rather ingeniously by Harry G. Frankfurt, it is likewise (on this account) in God's power to create a stone too heavy for him to lift, for

Thus, having created a stone too heavy for him to lift, he then lifts the stone that is too heavy for him to lift! In like manner, God can perform any action that is not performed by God, like writing a novel that has the property of not being written by God. All in all, then, if indeed omnipotence is to be defined in line with (D1), it is utterly futile to advance any charges of logical inconsistency against it, for its point is precisely that omnipotence is not bound by any logical constraints.

In a way, then, (D1) is congenial to theism. Yet it comes with a price that almost no philosopher is willing to pay: abandonment of rationality and, with it, coherence of theistic ideas. That which transgresses logical laws cannot be logically discussed – except by one who is omnipotent à la (D1), of course. So, since to accept (D1) as a true analysis of omnipotence is to reject the possibility of further analysis altogether, almost all philosophers agree in concluding that (D1), although pre-philosophically somewhat intuitive, and even if ‘unscrupulous logicians could fadge up a case for this view’ (Geach (Reference Geach1977), vi), is false. Purported actions like stepping over living corpses and drawing square circles are ‘pseudo-tasks’ which are impossible to perform, wholly regardless of one's powers, and thus ‘are not objects of power at all’ (Mavrodes (Reference Mavrodes1963), 223).Footnote ² Also, as Jordan Howard Sobel says, even if (D1) is pre-philosophically somewhat intuitive, it is still the case that ‘no well speaker, innocent of philosophy, who said that an omnipotent could do anything would mean that an omnipotent would be capable of changing the past, or making three less than two, or anything else that is impossible’ (Sobel (Reference Sobel2004), 346).Footnote ³ So, as generally affirmed, ‘it seems reasonable not to require of an omnipotent being that he be able to bring about a state of affairs that it is logically impossible to bring about’ (La Croix (Reference La Croix1977), 181).

Now, if (D1) is false, there is another account that immediately suggests itself:

According to this definition, omnipotence does not involve the ability to perform pseudo-tasks but only the ability to perform such tasks that are logically possible to perform: that is, tasks whose linguistic descriptions are not self-contradictory. Unfortunately, in spite of whatever advantage over (D1) it may have, (D2) runs into a very serious difficulty. Take, for example, the action of writing a novel that is not written by A. Obviously any novelist except A is able to write such a novel; hence the action in question is perfectly performable. It is just that A cannot perform it. But clearly the ‘inability’ on A's part to write a novel that is not written by A is no reason to think that A's literary creativity is somehow flawed or limited. Similarly, the ‘inability’ of A to perform an action that is not performed by A clearly does not tell against A's omnipotence. After all, no-one is able to do an action that he or she does not do. In fact, if (D2) is true, omnipotence is an impossible property: one that cannot be exemplified in reality. To dismiss omnipotence on this condition, however, is premature. Why not rather conclude that (D2) is false, since it states a seemingly unreasonable criterion?

Trying to evade this difficulty, a third candidate analysis readily presents itself:

Note that the modality in question has changed from ‘logical’ to ‘metaphysical’. (Logical impossibilities, as I use the terms, form a sub-class of the class of metaphysical impossibilities; not every linguistic description of a metaphysical impossibility involves a logical contradiction.) Nonetheless, this account is certainly no improvement. To see this, consider Alvin Plantinga's creation, Mr McEar,Footnote ⁴ an abnormal man who, ‘for unspecified reasons’ (Wielenberg (Reference Wielenberg2000), 40), is capable only of ‘scratching his ear’ (Plantinga (Reference Plantinga1967), 170). Absurdly, given (D3), it turns out that McEar, this ‘notorious weakling’ (Flint and Freddoso (Reference Flint, Freddoso and Freddoso1983), 84), is omnipotent, since he is able to perform the one action that it is metaphysically possible for him to perform. Hence (D3) should be rejected. Whatever omnipotence is, it is perfectly clear that it is not possessed by McEar.

Here an early lesson might be drawn. Despite his severe disabilities, McEar is consistently causing trouble to those who may attempt to relativize omnipotence to God. Remember, God (or at least the God of traditional Christian theism) is by stipulative definition essentially impeccable. As we shall discuss in detail in the next section, this means that he cannot possibly do what is morally wrong. So, if (D3) is suggested as an account of omnipotence so as to allow for the essential properties of God to limit the scope of actions that an omnipotent being must be able to perform, the drawback of this suggestion is that creatures like McEar threaten to come out as omnipotent as well.

A more promising response to the difficulty posed by (D2) is this:

Rather than being stated in terms of the ability to perform actions, (D4) is stated in terms of the ability to actualize (or bring about) certain possible states of affairs.Footnote ⁵ By this apparent circumlocution, a defender of omnipotence may hope to sidestep the fact that all agents except A are able to perform actions that are not performed by A. For, whereas all agents except A are able to perform actions that are not performed by A, no agent is able to actualize the state of affairs consisting in A's performing an action that is not being performed by A. Accordingly, A's own ‘inability’ to actualize this state of affairs ought not to count against his claim to omnipotence – nor does it on (D4)'s account.

Yet there is a serious problem with (D4). Defenders of omnipotence are often defenders of libertarian freedom as well: a view according to which agents act freely only insofar as their choices of actions are not determined, either by external forces or internal compulsions. Now consider, say, the state of affairs consisting in Jane's freely reading a text on metaphysics. Suppose someone other than Jane actualizes this state of affairs. Then it surely seems as if Jane's freely reading a text on metaphysics becomes something of a contradiction. To actualize a state of affairs s, or to bring it about that s obtains, is presumably to ensure or determine somehow that s is made real. But if Jane's reading is thus determined by an external force, it apparently follows that Jane's reading is not, after all, a result of her own free choice. Conversely, if there is such a thing as Jane's freely reading a text on metaphysics, then this state of affairs cannot be actualized by anyone other than Jane. That is to say, if libertarian freedom exists, (D4) is false.

To sidestep this problem, one may attempt to make a distinction between ‘strong’ and ‘weak’ actualization: the former kind being exemplified whenever someone directly and determinately causes a certain state of affairs to obtain, and the latter kind being exemplified when someone arranges things so as to ensure (in some incompatibilistically acceptable sense) that someone else will freely act in a certain way. As an example of the latter kind, Thomas P. Flint and Alfred J. Freddoso suggest that ‘a mother might actualize her child's freely choosing to have Rice Krispies for breakfast by limiting his choices to Rice Krispies and the hated Raisin Bran’ (Flint and Freddoso (Reference Flint, Freddoso and Freddoso1983), 86). Thus, if it is insisted that ‘an analysis of omnipotence … be construed broadly to include both strong and weak actualization’ (ibid.),Footnote ⁶ one may then argue that, even if no-one distinct from Jane can strongly actualize the state of affairs consisting in Jane's freely reading a certain text, it is still possible for someone distinct from Jane to weakly actualize this state of affairs.

Unfortunately, as Flint and Freddoso show, this last line of argument seems doomed; on their view, it should rather be concluded that, even if the distinction between strong and weak actualization is accepted, ‘there will be some state of affairs … which even an omnipotent agent is incapable of actualizing’ (ibid., 95). Nevertheless, according to Flint and Freddoso,

Now be this as it may, here is where we reach a point of seemingly no return: that state of elusiveness described in the introduction in which there is no consensus left to be found. In fact, the sheer complexity of some contemporary accounts of omnipotence is a source of bewilderment.Footnote ⁸ As Wes Morriston notes,

Thus we seem to be back to where we started: a place that is unsatisfactory for everybody involved.

Still, on a preparatory note, I think we are able to draw a modest and philosophically largely uncontroversial conclusion – yet one that is pre-philosophically somewhat unintuitive. Whatever omnipotence is, it does not involve the ability to perform every performable action. To be sure, this conclusion presupposes that (D2) is false; but as we have seen there is a strong if not conclusive reason to think that this is indeed the case. A second conclusion that might be drawn so far, one that is conditional in kind, is this: If compatibilism regarding determinism and free will is true (i.e. if it is possible to act freely even if one is determined to act as one does), or if free will simply does not exist, then (D4) appears to be quite a plausible analysis. Yet again, many defenders of omnipotence are not ready to accept either of these ifs; hence this second conclusion is of somewhat limited interest.

Some problems of compossibility

As we have seen, a clever argument against the compossibility (or the possibility of one individual's simultaneous possession) of omnipotence and some other divine attribute, especially essential impeccability, has resurfaced during the last three decades or so.Footnote ⁹ In its basic version, it goes something like this. Ordinary people are able to murder, lie, and cheat, but one who is essentially impeccable is necessarily unable to do any of these things. Yet one who is omnipotent must by any reasonable account, regardless of its details, be able to do what ordinary people are capable of doing all the time. As W. R. Carter says, ‘a being [who] not only does not but cannot do many things (murder, rape) that ordinary humans can do … has no claim at all to being judged omnipotent’ (Carter (Reference Carter1985), 54). Hence, since God by definition is both essentially omnipotent and essentially impeccable, it follows that, necessarily, there is no God: in no possible world does God exist.

Let us try to spell out this basic argument in a little more detail. After all, given our preparatory conclusion that an omnipotent being need not be able to perform every performable action, the alleged fact that God by nature is unable, say, to act cruelly is not by itself sufficient evidence that he cannot be omnipotent. So here is a first attempted specification. If indeed God is essentially impeccable, then God is not as powerful as possible. For, suppose that there is a being, Potentia, who is able to do all that God is able to do but who in addition is able, say, to act cruelly. Thus, however powerful God may be, he is not as powerful as Potentia. But, as Graham Oppy says, ‘it is simply an analytical truth that nothing can be more powerful than an omnipotent being’ (Oppy (Reference Oppy2005), 78),Footnote ¹⁰ and, as Brian Leftow concurs, ‘[w]e can agree in advance of any detailed account of omnipotence that an omnipotent being is as powerful as it is possible to be’ (Leftow (Reference Leftow, Flint and Rea2009), 183). Consequently, if Potentia is so much as possible, it follows that God, who by definition exists by necessity, cannot be essentially omnipotent, precisely because one who is omnipotent must be a maximally powerful agent in any world in which he exists. As a result, since God by definition is (among other things) essentially impeccable and essentially omnipotent, it follows that God cannot possibly exist.

The crucial clause in this line of reasoning is this: if Potentia is so much as possible, it follows that God cannot exist. Note that the reverse conditional is equally true: if God is so much as possible, it follows that Potentia cannot exist. That is, the possibility of either being entails the impossibility of the other; hence the above argument does not establish the impossibility of God unless it is accompanied by an argument to the effect that Potentia, unlike God, is possible. But for all I know, no-one has ever attempted to present such an argument; hence, thus interpreted, the compossibility argument against divine omnipotence seems at best to be a radically unfinished business.

As one would suspect, however, it may be possible to specify the argument differently. Although its proponents may not always have been as explicit on this subject as one would have wished, the compossibility objection can be couched purely in terms of conceivability. Perhaps the leading voice of this version is Morriston. As he points out, it is ‘simply too easy’ to conceive of (someone like) Potentia not to compare the idea (or notion) of Potentia with that of God (Morriston (Reference Morriston2001a), 18). Indeed, if compared with each other, the idea of Potentia will distinguish itself as a better conceptual candidate for omnipotence than will the idea of God. In other words: in theory, Potentia is more powerful than God. But this suffices to conclude that God, however powerful, is not omnipotent, for to qualify meaningfully as omnipotent one must be as powerful as conceivable. Thus Morriston:

The underlying idea is this. In order to determine whether some agent A qualifies as omnipotent or not, ‘[w]e should first decide what we think omnipotence is’ (ibid.). But this is a purely conceptual procedure which can be carried out whatever the limits of metaphysical possibilities may be. Hence, what omnipotence comes down to is a matter of conceivability, not possibility; even if A might, for all we know, be more powerful than any other possible being, he may still not be powerful enough to qualify as omnipotent.Footnote ¹¹ Accordingly, given that the notion of Potentia entails more wide-ranging capabilities than does the notion of God, ‘it is natural enough to conclude that a God of the Anselmian type could not be omnipotent’ (ibid., 10). Thus, to drive the point home,

As Morriston concludes, then, ‘I think we have a reason of some weight for not saying that possessing maximal power is sufficient for being all powerful’ (ibid.).

Thus interpreted, I think this is an important argument against divine omnipotence, yet one that only partly gets it right. What is right, I think, is the very last conclusion: being maximally powerful may not, for all we know, be sufficient for being omnipotent (or all powerful, or almighty).Footnote ¹² That is to say, it is conceivable that analyses such as

or

are false. Pace Morriston, however, I do not think that possession of the greatest conceivable power is necessary for being omnipotent. That is to say, I think that an analysis such as

is false too – a claim to be much qualified, however, in what follows. In preliminary support of this latter claim, imagine two candidates for omnipotence: X and Y. Suppose that, all else being equal, X is (for some esoteric reason) essentially unable to prove or disprove Goldbach's conjecture (the mathematical claim that every even number greater than 2 is the sum of two primes). Y, on the other hand, has no such essential limitations; hence it is at least conceivable that Y is able to prove or disprove Goldbach's conjecture. On Morriston's view, this would seem to mean that Y is a better candidate for omnipotence than X; indeed, that X's essential limitation regarding Goldbach's conjecture suffices to rule out her candidacy for omnipotence. But I disagree. Y's candidacy can be said to be conceptually stronger than X's only if we already know (or at least have a good reason to think) that it is mathematically possible either to prove or to disprove Goldbach's conjecture. If this is not the case, then the cognitive happenstance that we may still, ‘without absurdity’ (Morriston (Reference Morriston2001a), 18), conceive of Y as being able to prove or disprove Goldbach's conjecture is irrelevant as to whether Y is a better candidate for omnipotence than X. As a result, possession of the greatest conceivable power is not necessary for being omnipotent.

More on this later. In the rest of this section, I will pursue a different line of thought. Indeed, contrary to the conclusion just reached, let us grant for argument's sake that possession of the greatest conceivable power – call it ‘C-omnipotence’ – is necessary for being omnipotent simpliciter. I will argue that it is at least far from clear that God cannot, due to his other essential characteristics, be C-omnipotent. Our main focus will be on the compossibility of C-omnipotence and essential impeccability, but we will look into several other issues of divine compossibility as well.

To begin, consider C-omnipotence itself. God has all of his defining properties essentially; thus, insofar as God is C-omnipotent at all, he is necessarily C-omnipotent; he cannot possibly exist without being C-omnipotent. By contrast, suppose that Potentia is merely accidentally C-omnipotent; that is, although as a matter of fact Potentia is C-omnipotent, she is not necessarily C-omnipotent; it is possible for her to cease being C-omnipotent and yet continue to exist. Now, then, as a conceptual exercise, who is the more powerful being: Potentia or God?

It should first be noted that Potentia is able to do at least one action that God is essentially unable to do, namely, to relinquish her C-omnipotence. But this may give her at least a prima facie stronger claim to C-omnipotence than God. On the other hand, it is not prima facie clear that the ability to abandon one's C-omnipotence is a sign of strength and not rather of weakness.Footnote ¹³ After all, if she abandons her C-omnipotence, it is not at all clear (indeed, it is highly unlikely) that she will then be able to regain it; thus the action of relinquishing one's C-omnipotence might be described as rather fateful. Is it then the case that Potentia is, conceivably, more powerful in this respect than God?

Here it is interesting to note that opinions vary quite considerably – even among those who otherwise are in agreement that C-omnipotence is the only omnipotence worth its name. Notably, whereas Sobel takes an uncompromising point of view, arguing in effect that God ‘would not be omnipotent’ precisely because he ‘would be incapable of diminishing [his] power’ (Sobel (Reference Sobel2004), 362),Footnote ¹⁴ Morriston suggests instead that, ‘once the case is fully understood’, we do not ‘run foul of any strong pre-philosophical intuition’ if we concede that God's inability to give up his omnipotence ‘is not inconsistent with maximal power’ (Morriston (Reference Morriston2001b), 156).Footnote ¹⁵ Whatever the case may be, then, it is at least not obvious that the ability to relinquish one's omnipotence is a necessary condition for being C-omnipotent.

In fact, I think Potentia's claim to C-omnipotence is weaker than God's. The alleged fact that Potentia is merely accidentally C-omnipotent seems to suggest that not only is she able to relinquish her C-omnipotence, but she is also able to lose it – involuntarily perhaps, by sheer metaphysical coincidence. If indeed she is merely accidentally C-omnipotent, then (whether she likes it or not) it is in any case conceivable that she might suddenly lose her C-omnipotence, never more to be regained. Just as God due to his essence cannot either relinquish or otherwise lose his omnipotence, Potentia can, due to her essence, do both – or so it would seem, anyway. But this would suggest that Potentia, despite being enormously powerful, suffers from a rare kind of metaphysical vulnerability. Indeed, for all we know, she might one day find herself completely impotent. But whatever else we may say in this regard, the ‘ability’ involuntarily to become completely impotent cannot be a necessary condition for being C-omnipotent; in fact, it would rather seem to be a sufficient condition for not being C-omnipotent.

But then perhaps it is also conceivable that Potentia is somehow able to guarantee that she will never unwillingly lose her C-omnipotence. In addition, perhaps it is conceivable that she is somehow able to guarantee that she will never stupidly (but willingly) abandon it herself. If so, however, then our present conceptual exercise rather seems to suggest that the conceivability criterion of omnipotence is anything but clear. What is clear, however, is that God cannot ever either abandon or otherwise lose his omnipotence. That is to say, God's powerfulness is not in any conceivable way threatened, either by external forces or internal deterioration. And this, I think, suggests that God, being essentially omnipotent, has a stronger claim to C-omnipotence than Potentia.

Next, by parallel reasoning, consider immortality. By stipulative definition, God is essentially immortal (and hence essentially alive). Now, for purposes of comparison, let Potentia be merely accidentally immortal. Thus, unlike God, Potentia can cease being immortal and yet exist. Again, this means that Potentia is able, should she become mortal, to do at least one action that God is essentially unable to do: namely, to kill herself. Hence it might be argued that Potentia is overall more powerful, since she is potentially able to do one more action, than God. On the other hand, it is by no means obvious that the potential ability to commit suicide, and thus to cease to exist, is a necessary condition for being C-omnipotent. In fact, I think it can be plausibly argued that the requisite property in question, that is, the property of being potentially mortal, makes Potentia a weaker candidate for C-omnipotence than God. To be potentially mortal (which anyone who is accidentally immortal is) is not only to be potentially able to kill oneself but also to be potentially able to die for some other reason. It is at least conceivable that one who is potentially mortal will someday be killed. But it would be absurd to suggest that the capacity for being killed is a necessary condition for being C-omnipotent. Again, it might also be conceivable that Potentia, despite being merely accidentally immortal, is somehow able to eliminate the possibility of her being killed, or of stupidly (but willingly) killing herself, but this is all very obscure. What is not obscure is that one who is essentially immortal cannot ever die, either by his own hand or by anyone else's; and again I think this counts in favour of, rather than against, the alleged C-omnipotence of God. Likewise with respect to incorruptibility: the essential possession of such an attribute does not tell against the owner's being as powerful as conceivable.

What about omniscience? God is essentially omniscient; by contrast, let Potentia not be omniscient at all. Now this means that there is at least one thing that Potentia but not God is able to do: to learn. According to Thomas Metcalf, this inability to learn counts against God's being omnipotent. For, whereas Potentia ‘can perform every task’ that God can perform, ‘plus one more task’ that God cannot perform, God has no ‘power-granting analogue in His repertoire’ (Metcalf (Reference Metcalf2004), 293). Thus, Metcalf argues, the inability to learn is sufficient to disqualify God's claim to C-omnipotence.

This argument, however, strikes me as misconceived; I think Sobel, for one, would agree. Discussing the ability to ‘stand up’, Sobel says that someone who is ‘always standing’ and hence ‘can never stand up’ should not be disqualified from ‘the title “omnipotent” as naturally deployed’ (Sobel (Reference Sobel2004), 348). Likewise, then, I think that the inability of God, who already knows all there is to know, to learn, should not be taken to suggest that he cannot be omnipotent. Moreover, and I think more importantly, Metcalf does not discuss the conceivable possibility of Potentia's forgetting what she in fact knows. Not being essentially omniscient, it is at least conceivable that Potentia might suddenly suffer from some kind of metaphysical stroke that makes her forget all that she knows. Once again, it may also be conceivable that, despite not being essentially omniscient, she is somehow able to secure that which she knows from ever being forgotten – and so we are once again faced with seemingly conflicting conceivabilities. But this much is clear: one who is essentially omniscient cannot ever forget anything. And this too, I think, counts in favour of, rather than against, the alleged C-omnipotence of God.

But now we come to the crux of the matter, or at least to that which most frequently has been held forward as a decisive reason to disqualify God from considerations of C-omnipotence. By stipulative definition, God is essentially impeccable: in no possible world does God do anything that is morally wrong. Indeed, as Nicholas Everitt clarifies, it is not merely that an essentially impeccable being ‘never has done or never will do anything immoral, but that he cannot do anything immoral’ (Everitt (Reference Everitt2004), 264).Footnote ¹⁶ By contrast, Potentia, let us suppose, can do what is immoral. For example, she can torment disabled children. She might as a matter of fact never do so, but – and this is what matters here – she is able to. God, on the other hand, is not able to torment disabled children; hence there is something that Potentia but not God is able to do. Of course, this conclusion can be generalized: there are innumerable actions that God, in virtue of being essentially impeccable, cannot perform; hence it would seem as if Potentia in this case has a considerably larger range of actions available to her than God has. Prima facie, then, it seems that Potentia has a stronger claim to C-omnipotence than God.

In response to this argument, I wish to make two points. First, let us introduce a third character: Peccatia, a being who is essentially unable to do anything moral. Whereas God is capable of doing (roughly) whatever is morally indifferent and whatever is morally right, Peccatia is capable of doing (roughly) whatever is morally indifferent and whatever is morally wrong. Now, who has the strongest claim to C-omnipotence: God or Peccatia? On a little reflection, it seems clear enough that Peccatia has a significantly weaker claim than God. After all, to be unable to do what one ought to do is surely a graver limitation on one's powers than to be unable to do what one ought not to do anyway.Footnote ¹⁷ But this is a telling asymmetry. If indeed God has a stronger claim than Peccatia to C-omnipotence, then it is at least not obvious that he has a weaker claim than Potentia. There is something about the ability to do evil that makes it dubious as far as power enhancement is concerned. Anselm tries to pinpoint what it is by arguing that the more one can do what one ought not to do, ‘the more power misfortune and wickedness have over him, and the less he has over them’ (Anselm (Reference Williams1995), 103);Footnote ¹⁸ and Aquinas likewise argues that ‘[t]o sin is to fall short of a perfect action; hence to be able to sin is to be able to fall short in action, which is repugnant to omnipotence’ (Aquinas (Reference Aquinas2007), 138).Footnote ¹⁹ As Morriston sums up, ‘the ability to choose evil [according to these lines of reasoning] is not an active power, but a liability – a liability that is due either to ignorance or to weakness’ (Morriston (Reference Morriston2001b), 157).

Let us dwell on this point for a while and see if it can be somehow illuminated. Consider the relation between morality and reason. As Alan Gewirth says, ‘[t]he most important and difficult problem of philosophical ethics is whether a substantial moral theory can be rationally justified’ (Gewirth (Reference Gewirth1978), 9). Philosophers who have sought to provide answers in the affirmative include Plato, Aristotle, Kant, and Mill; those who have rather attempted to answer in the negative include Hume, Marx, and Nietzsche. Suppose, however, that the following is true: necessarily, to act immorally is to act irrationally (or contrary to reason). Thus Potentia's ability to torment disabled children is ipso facto an ability to act irrationally. Now, is really this – the ability to act irrationally – a necessary condition for C-omnipotence? Or to put it somewhat provocatively: is one who is able to act idiotically really more C-powerful than one who necessarily acts in accordance with reason? At the very least, I think it is far from clear that the ability to act utterly ridiculously is a necessary condition for being C-omnipotent. This, it seems, might better be conceived of as a sufficient condition for not being C-omnipotent at all – and something like this is what Anselm, Aquinas, and others seem to have had in mind.

However, this argument, or rather these argumentative indications, is of course dependent on an affirmative answer to that ‘most important and difficult problem of philosophical ethics’. Yet it is certainly conceivable that immorality entails irrationality – albeit the denial of this proposition is conceivable as well. What seems to be the case, then, is that yet again we end up with conflicting conceivabilities, and thus again we are reminded of the rather imprecise character of C-omnipotence. Is it, or is it not, required of one who is C-omnipotent that she be able to torment disabled children? I find it difficult to give a decisive answer.

The second point I wish to make is this. Since Potentia is not essentially impeccable, it is conceivable that she will one day actually torment a disabled child. By contrast, of course, it is inconceivable that God will do such a thing. But then consider this act: the act of guaranteeing, with absolute certainty, that one will never torment any disabled child. Is this an act that Potentia is able to perform? Well, she must be, surely, if she is to count as C-omnipotent – God is perfectly capable of doing it, anyway. But she can do it only if she knows that, as a matter of fact, she will never torment any disabled child. Hence we seem to have the following predicament on our hands. In the first place it is being argued (by Morriston and others) that the capacity to do what is wrong is necessary for being C-omnipotent. Still, to be capable of guaranteeing with absolute certainty that one will actually never do what is wrong, one needs to know that one will actually never do what is wrong – that is to say, one needs to know that one will never exercise one's ability to do what is wrong. Hence, to be C-omnipotent, at least according to this line of thought, it seems to be necessary, not only that one can torment disabled children, but also that one will never exercise this ability. But then if indeed the exercise of one's ability to do what is wrong would disqualify one's candidacy for C-omnipotence, it surely seems that the mere possession of the selfsame ability is of no significance in this regard. Thus, if this predicament is correctly analysed, I think the correct lesson to be drawn is that God's essential inability to do what is immoral does not tell against his C-omnipotence after all.

To sum up thus far, I find it far from clear that God, due to his essential nature, cannot be C-omnipotent. Hence, even if it is granted for the sake of argument that possession of the greatest conceivable power is necessary for being omnipotent simpliciter, I find it far from clear that God still cannot qualify as such. As already pointed out, however, I do not think that one should grant this assumption in the first place. In the next section I will try to elaborate on this point.

What (I think) omnipotence is

Earlier in the foregoing section it was argued that the mere conceivability of X being able to prove or disprove Goldbach's conjecture is of no significance with regard to X's candidacy for omnipotence, unless it is mathematically possible that Goldbach's conjecture can be proved or disproved. Hence it was concluded that possession of the greatest conceivable power is not necessary for being omnipotent. Here we may add a few more examples in support of this result. Perhaps in some sense it is conceivable that X is able to alter the past, or pop in and out of existence, or arbitrarily but legitimately decree what is right and wrong, but surely none of these conceivabilities (if such they are) gives us any reason to think that X has a better claim to omnipotence than someone who is essentially unable to do these things – unless there is some independent reason to think that these abilities are metaphysically possible. Indeed, in some sense Descartes and others might even have found it conceivable that X (read: God) is able to draw square circles, but precisely because we know (or think we know) that this ‘ability’ is metaphysically impossible we can safely discard whatever conceivability it may enjoy. Hence, to repeat, possession of the greatest conceivable power is not necessary for being omnipotent.

On the other hand, following Morriston, it was also concluded that possession of the greatest possible power may not, for all we know, suffice for being omnipotent. This latter conclusion, however, needs to be clarified. What it wants to capture is this: it is not the case that a maximally powerful being X is omnipotent, no matter exactly how powerful X is. If, as a matter of metaphysical fact, X is insufficiently powerful to be adequately entitled ‘omnipotent’, then – it goes without saying – X is not omnipotent. For all we know, of course, X's degree of power may be such that X is adequately entitled ‘omnipotent’ in every possible world in which he exists. Hence it is conceivable, both that maximal powerfulness is sufficient, and that it is not sufficient, for being omnipotent. It all depends on how powerful a maximally powerful being really is.

To get a better hold of this issue we may consider Yujin Nagasawa's strategy in ‘A new defence of Anselmian theism’. According to this strategy, Anselmian theists need not be committed to the classical ‘omniGod’ thesis; rather, they only need to accept the ‘maximalGod’ thesis: a thesis according to which ‘God is the being that has the maximal consistent set of knowledge, power and benevolence’ (Nagasawa (Reference Nagasawa2008), 586). In Nagasawa's view, then, Anselmian theists need only affirm that God is overall as great as possible – not that he is ‘omniperfect’ in every respect (ibid., 596). Accordingly, lest they be guilty of attacking a straw man, the compossibility objectors to Anselmian theism should only assume as much. But then, as Nagasawa concludes, it will be ‘significantly more difficult’ for these objectors to accuse Anselmian theism of conceptual incoherence (ibid.).

But here is the problem: if Nagasawa is right then Anselmian theism is necessarily coherent; it will then not only be ‘significantly more difficult’ but hopelessly futile to accuse it of incoherence. If God is whatever is as great as possible then God exists in at least one possible world; but if God exists in at least one possible world then the notion of God simply cannot be inconsistent. Hence, despite its cleverness, Nagasawa's strategy is dialectically powerless. For, unless we know how great a maximally great being is, the metaphysical tautology that a maximally great being is possible does nothing to justify the conclusion that the Anselmian notion of God is coherent. For all we know, as Oppy notes, ‘it may turn out that a maximally overall excellent being is very, very far from being a perfect [or Anselmian] being’ (Oppy (Reference Oppy2011), 135). Likewise with respect to omnipotence in particular; as Morriston says, although having ‘maximal power’ sounds ‘grand and godlike’, it may not be sufficient for being ‘all powerful’ in an adequate sense (Morriston (Reference Morriston2001a), 14).

This, then, is what we might say. Possession of the greatest possible power, which may be metaphysically sufficient for being omnipotent, is not conceptually sufficient for being omnipotent. Our knowing that a being X has the greatest possible power does not by itself legitimize our inferring that X is omnipotent; and in this sense maximal power is not sufficient for omnipotence.

This claim can be supported from another angle. Envision two beings: X and Y. Suppose that X is maximally powerful and that Y is less powerful – but only infinitesimally so. That is to say, Y is, to all intents and purposes, as powerful as X. But then it is gravely inadequate to call X ‘omnipotent’. Whatever omnipotence is, it excludes competition; as Geach says, ‘no creature can compete with God in power, even unsuccessfully’ (Geach (Reference Geach1977), 4). So, since X and Y are seemingly capable of an all but endless struggle for dominance, neither of them has any legitimate claim to omnipotence. Thus again: even if X is maximally powerful, our knowing this does not by itself legitimize our inferring that X is omnipotent.

But now I need to regroup and hazard an account of my own. Without further ado, then, this is what I think ‘omnipotent’ is:

For the remainder of this article I will try to illuminate and defend this claim. However, to try to understand the reasoning that underlies it, we might as well begin by considering another and perhaps more intuitive definition:

Note that ‘agent’ might signify an individual being or a collective unit. To simplify matters, (D9) says that A is omnipotent if and only if A is incomparably more powerful than any other possible agent (of which A is not a part).

I think (D9) too is true – but too vague. It tries to capture the intuitively reasonable idea, only just brought up, that no-one or nothing can compete in power, ‘even unsuccessfully’, with one who is omnipotent. To be omnipotent is not only to be more powerful than all other metaphysically possible beings but to be absolutely beyond challenge as far as power is concerned – indeed, to be beyond the possibility even of being troubled. Crucially, the adverb ‘incomparably’ is utilized for the purpose of capturing this idea: the idea of a greater-than relation that cannot be expressed in terms of ratios or percentages. Thus, by mathematical analogy, if an agent A is incomparably more powerful than an agent B, then A's being greater in power than B is like an infinite set being greater in size (or cardinality) than a finite set. The differences in power and size, respectively, are infinite rather than enormous, limitless rather than vast.

By way of somewhat less lofty analogies, consider Michelangelo's artistic abilities as a sculptor. In a perfectly good sense he is incomparably better at sculpting than, say, all possible chimpanzees put together. The fact that certain Senegalese specimens have been observed to sharpen tools in a spear-like manner to be used for hunting, thereby indicating ‘the kind of foresight and intellectual complexity that most likely typified early human relatives’ (Pruetz & Bertolani (Reference Pruetz and Bertolani2007), 414), or the fact that a Swedish zoo chimpanzee has gained international fame by preparing and compiling stones to be used as missiles against spectators (Osvath (Reference Osvath2009)), merely goes to prove the point: the idea of comparing Michelangelo's artistic abilities as a sculptor with those of chimpanzees is meaningless more than misleading. And so is the idea of comparing a newborn baby's abilities as a boxer with those of Muhammad Ali, or of comparing a cow's capacity for swimming with that of a mackerel. Indeed, cows are able to swim, but mackerels' ability to swim is not merely superior but distinctively different. We might generalize: if an agent A is incomparably better than an agent B with respect to an ability F, then the difference between A's being F and B's being F is a matter of kind (species or genus) rather than degree.

Still, these analogies merely go to exemplify different cases in which we might reasonably describe something as being incomparably greater in some respect than something else – they do nothing to clarify why, or in virtue of what, A is incomparably more powerful than any other possible agent. But this is precisely where (D8) comes into play. If indeed A is such that the very possibility of any other agent (and hence of any action not performed by A) is metaphysically created by A, then certainly A has a very strong claim to being incomparably more powerful – or more able to do things – than any other possible agent. After all, which is the more impressive: B's ability, say, to build a tower, or A's ability to ‘possibilize’ B's ability to build a tower?Footnote ²⁰ Indeed, if B and whatever action he might do are possible solely because A makes them so, I find it rather obvious that A's power is incomparably greater than B's. So, since what goes for B's ability to build a tower can be generalized, I conclude that (D8) succeeds in identifying what it takes for an agent to be incomparably more powerful than any other possible agent – and this is why I think that (D8) is true.

Now, if indeed A is thus able to create metaphysical space, A can be said to be a ‘delimiter of possibility’ (Morris (Reference Morris1985), 266). That which A does not will to be possible cannot possibly be. In line with this interpretation, (D8) can be said to radicalize the ‘non-negotiable element of orthodox western theism’ that says that ‘no created thing can remain in existence for any interval of time without being directly conserved by God throughout that interval’ (Freddoso (Reference Freddoso and Morris1988), 81). As Geach points out, ‘God is … the source of all power; any power a creature has comes from God and is maintained only for such time as God wills' (Geach (Reference Geach1977), 4f.). The radicalization, then, consists in this: rather than claiming that other agents are actual only if they are being infused with actuality by one who is omnipotent, (D8) claims that other agents are possible only if they are being willed into possibility by such a being – if such there is.

Here, however, is a drawback of the present proposal: As far as I can see, (D8) cannot be semantically formalized in terms of possible worlds. Consider, for example, this attempt:

This will not do; (D10) entails that every agent in the actual world (which too is a possible world) is created by A; but there are many agents in the actual world that are created by us, such as machines, fireworks, liquor, drugs, and, at least to some extent, human offspring. Nor will it do to try to exempt the actual world from consideration thus: ‘for any possible agent B and any possible but not actual world W…’ If the actual world is thus exempted from consideration, the resulting analysis is obviously of no actual interest.

This drawback, however, need not force us to retract. If we assume, pace David Lewis's ‘genuine’ (Divers (Reference Divers2002), 43), or rather ‘extreme’ (Pruss (Reference Pruss2001), 169), modal realism, that the difference between our world and other possible worlds is not merely a matter of indexicality, then we shall have to conclude that the semantics of possible worlds is patently unable to tell us what it is for a world to be actual rather than merely possible. Yet (D8), my preferred analysis, requires there to be an ontological difference between them: whether or not A actualizes (strongly or weakly, directly or indirectly) another possible agent B, A possibilizes B in the first place – the latter of course being a metaphysical prerequisite for B's actuality. Thus its inability to be formulated in semantic terms of possible worlds need not tell against (D8), because the semantics of possible worlds is itself incapable of making a real distinction between what is actual and what is merely possible.

Now it may be objected that, whatever its merits may be, (D8) does not succeed in identifying a sufficient condition for omnipotence. To see this, imagine that A (our candidate for being omnipotent) is essentially unable to do anything except to possibilize other agents. Suppose, for example, that A is essentially unable to actualize things. Surely (the objection goes) this is all we need to know in order to rule out A's candidacy, for whatever an omnipotent being must be capable of doing, he must be capable of actualizing something – not merely of possibilizing anything.

In reply, I think the crucial assumption of this objection is not even remotely plausible. Why should we think that A, a delimiter of possibility, a creator of metaphysical space, one whose willing there to be other possible agents besides himself is both necessary and sufficient for the possibility of these agents, is not necessarily able to actualize a myriad of diverse things? Why should we think that there is even a single possible world W in which A, despite being the exclusive metaphysical prerequisite for the very possibility of other agents in W, is unable to actualize some of these beings? Indeed, I find such an idea highly implausible. If (D8) is true, surely it entails, metaphysically if not conceptually, that A is able to do a very great deal besides to possibilize other agents. Exactly what it entails I cannot profess to know – nor will I attempt to disclose it. Suffice it to reiterate our preparatory conclusion that omnipotence does not involve the ability to perform every performable action.

Finally, (D8) sidesteps a number of other objections usually directed at attempted analyses of omnipotence. For example, whether or not A is able to create a stone too heavy for him to lift, or write a novel that is not written by A, or sit down, or learn, or forget, or relinquish his abilities, or act wrongly, or behave ridiculously – all this is beside the point. Off the mark, too, is Mr McEar; one who is capable only of scratching his ear is obviously incapable of possibilizing anything. As for Potentia and Peccatia, our earlier acquaintances of morally complex and depraved character, respectively, the jury may still be out. This, I think, is as it should be. For, while it is satisfiable only by one, (D8) is not relativized to anyone in particular.Footnote ²¹