"Maximal Power" (with Thomas P. Flint), pp. 81-113 in Alfred J. Freddoso, ed., The Existence and Nature of God (Notre Dame, IN: University of Notre Dame Press, 1983). 

Maximal Power

Thomas P. Flint and Alfred J. Freddoso


Christians profess that God is almighty. He has created the world and conserves it in being. Whatever can or does occur is within his control. His great power guarantees the fulfillment of his providential designs. 

Theologians and philosophers have typically commenced their explications of divine power with the assertion that God is omnipotent, i.e., that in some sense or other God can do everything. But Peter Geach has recently charged that this assertion is wrongheaded:

    When people have tried to read into 'God can do everything' a signification not of Pious Intention but of Philosophical Truth, they have only landed themselves in intractable problems and hopeless confusions; no graspable sense has ever been given to this sentence that did not lead to self-contradiction or at least to conclusions manifestly untenable from the Christian point of view.1
Geach goes on to argue that in all probability any philosophically adequate analysis of omnipotence will have the consequence that in order to be omnipotent an agent has to be able to act in morally reprehensible ways. For instance, it seems reasonable to think that any omnipotent being must have the power, whether or not it is in fact exercised, to perform actions which constitute the breaking of his previously made promises. Yet Christians have traditionally believed that God is impeccable, /82/ i.e., absolutely incapable of such behavior. Once God has promised to send his Son, for example, it appears that he no longer even has the power not to send him. But this could not be true if God were omnipotent. In short, omnipotence on any plausible construal turns out to be incompatible with impeccability. 

Nelson Pike had earlier reached the same conclusion by a somewhat different route.2 Accepting the common view that an omnipotent being is one who can bring about any consistently describable state of affairs, Pike argues that some consistently describable states of affairs are necessarily such that anyone who brings them about is morally blameworthy for so doing. So any agent capable of bringing about such a state of affairs is also capable of acting in a morally reprehensible way and hence is not impeccable in the sense specified above. 

Pike responds to this dilemma by urging us to abandon the belief that the person who is God lacks the ability to act in a morally blameworthy fashion. But Geach testily (though correctly, we believe) dismisses this suggestion as patently unorthodox. He counsels us instead to jettison the belief that God is omnipotent. We must simply be careful to distinguish the suspect proposition that God is omnipotent from the theologically central proposition that God is almighty. The latter entails, for instance, that God has power over all things, that he is the source of all power, and that his intentions cannot be thwarted; but it is compatible with the evident truth that there are many things that an agent with all of God's attributes--including, most notably, impeccability--cannot do. 

At first Geach's "way out" seems little more than a verbal ploy. After all, it is hardly self-evident that being almighty differs from being omnipotent, or that having power over all things differs from having the power to do all things (or, as we prefer to say, having maximal power). Nonetheless, further reflection reveals that Geach's position does not essentially depend on the dubious claim that the terms 'almighty' and 'omnipotent' are normally used to express two distinct concepts. Bather, it depends only on the more plausible claim that there are two distinct concepts to be expressed. And here, we believe, Geach is correct. 

The term 'almighty', as he uses it, expresses a properly religious /83/ concept, i.e., a concept whose explication is subject to overtly theological constraints. To say that God is almighty is to attribute to God all the power that a being with his nature can have.3 This way of characterizing God's power is not very informative, since it gives one no more insight into the nature of God or the extent of his power than is had antecedently from the sources of revelation. However, there is no danger that the belief that God is almighty will engender any pernicious theological consequences. Most importantly, we can know a priori that it is possible for an agent to be both almighty and impeccable, since this possibility is already explicitly packed into the notion of being almighty.

The term 'omnipotent', on the other hand, is used by Geach to express what we might call a properly secular concept, i.e., one whose explication is subject only to those nontheological constraints which emerge from a careful consideration of the ordinary notion of power and of the relation of power to other properties. It is clear, for instance, that an analysis of omnipotence should not be constructed so as to ensure that there cannot be a morally imperfect omnipotent agent, or a non-omniscient omnipotent agent, or an agent who is only contingently or perhaps even only temporarily omnipotent. But God cannot be an agent of any of these types. So even if God has all the power that a being with his nature can have, there is no a priori guarantee that he has maximal power, absolutely speaking. If Geach is right, then all our evidence points to just the opposite conclusion, viz., that God does not have, indeed cannot have, maximal power. 

We concur with Geach that almightiness and omnipotence are distinct properties. However, we will argue in what follows that an orthodox believer need not for this reason give up the hallowed belief that God is omnipotent. For, pace Geach, an adequate analysis of maximal power will show that God can be both almighty and omnipotent; and, pace both Geaeh and Pike, such an analysis will show that it is possible for an agent--even a divine agent--to be both omnipotent and impeccable. We will begin by proposing five conditions of philosophical adequacy for an account of maximal power, indicating in the footnotes which of these conditions are not satisfied by one or another of the. numerous recent attempts to explieate omnipotence. /84/ Then we will present an analysis which meets all five conditions and argue that it is both philosophically adequate and theologically benign.


I

1. Our first condition of adequacy is that an analysis of maximal power should be stated in terms of an agent's power to actualize or bring about states of affairs. (Since we are assuming that there is an exact isomorphism between states of affairs and propositions, we can also speak equivalently of an agent's power to make propositions true.) Though this condition is now widely accepted, some writers have employed the alternative strategy of casting their accounts of omnipotence in terms of an agent's ability to perform tasks, where a task is expressed linguistically by the nominalization of a verb phrase rather than, like a state of affairs, by the nominalization of a complete declarative sentence. The problems with this alternative strategy are well known. Suppose we claim that an agent S is omnipotent just in case S can perform any logically possible task, i.e., any task which is possibly such that someone performs it. This proposal rules out Smith as omnipotent simply on the ground that Smith cannot perform the logically possible task of saying something which is (at the same time) being said only by Jones. Yet it is clear intuitively that this fact about Smith in no way points to a lack of power on his part. Moreover, when we attempt to amend our analysis by claiming that S is omnipotent just in case S has the power to perform any task that it is logically possible for S to perform, we find that we are forced to count as omnipotent the notorious weakling Mr. McEar, who is capable of scratching his left ear but essentially incapable of performing any other task.4

Such difficulties are obviated by our first condition. For the state of affairs of Smith's saying something which is being said only by Jones is logically impossible and thus unproblematically not within anyone's power to actualize, whereas the state of affairs of Jones's (or: someone's) saying something which is being said only by Jones may well be one which agents other than Jones can actualize and which we should expect an omnipotent being to have the power to actualize. /85/

Nevertheless, even though our first condition is commonplace today, few writers on omnipotence have explicitly entertained the following question: Is it possible for one agent to actualize (and hence to have the power to actualize) a state of affairs consisting in or at least involving in some way the free actions of other agents? If we assume a compatibilist account of freedom, the answer to this question is uncontroversially affirmative. For it is obviously possible for a suitably powerful and aptly situated agent to bring it about that another agent has desires or needs and also opportunities that are together causally sufficient for his behaving freely (in this compatibilist sense) in a specified way. So on this view of freedom, bringing about the free actions of others is not relevantly different from actualizing states of affairs that in no way involve the free actions of others. In both sorts of cases the agent in question simply does something which, in conjunction with other operative causal factors, is sufficient for the obtaining of the state of affairs in question. 

However, we believe along with many others that there are good reasons for rejecting this account of freedom in favor of the position that every free action must involve the occurrence of an event for which there is no antecedent sufficient causal condition--an event, that is, which has only an agent and no other event as its cause. Given this libertarian conception of freedom, there is a clear and familiar sense of 'actualize' in which it is logically impossible for one agent to aetualize another agent's free actions. Following Alvin Plantinga, we call this sense of actualization strong actualization.5 Roughly, an agent S strongly actualizes a state of affairs p just when S causally determines p's obtaining, i.e., just when S does something which in conjunction with other operative causal factors constitutes a sufficient causal condition for p's obtaining. Since an agent's freely performing (or, perhaps better, freely endeavoring to perform) a given action cannot have a sufficient causal condition, it follows straightforwardly that no such state of affairs can be strongly actualized by anyone other than the agent in question. 

But even granted the libertarian conception of freedom, there is a weaker sense of actualization--discussed in rather different contexts by both Plantinga and Roderick Chisholm6--in which one agent can actualize (and hence can have the power /86/ to actualize) the free actions of another. In such cases the agent in question, by his actions or omissions, strongly brings it about that another agent S is in a situation C, where it is true that if S were in C, then S would freely act in a specified way. For instance, 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. Or she might bring it about that the child freely donates his allowance to a relief agency by telling him poignantly of the plight of those who do not have enough to eat. In short, it is a familiar truth that one agent may contribute causally to the free actions of another in any number of ways which stop short of being incompatible with the other's acting freely. In such cases it seems perfectly legitimate to say that the one has actualized the other's acting freely in the way in question. Again adopting Plantinga's terminology, we will call this sense of actualization weak actualization. Further, it is not only the free actions of another which a given agent may weakly actualize. In addition, an agent S may weakly actualize a state of affairs p through the mediation of the free actions of another agent S*. This occurs when S weakly actualizes S*'s freely acting in such a way as to bring about p. Thus, in the second of the above examples, the mother weakly actualizes not only her son's freely donating his allowance to a relief agency but also--among others--the state of affairs of someone's hunger being alleviated. 

We want to insist that in an analysis of omnipotence the term 'actualize' (or 'bring about') should be construed broadly to include both strong and weak actualization. For it is intuitively evident that a person's power is normally judged in large measure by his ability to influence the free actions of others in one or another of the ways intimated above, e.g., by restricting their options, or by providing them with information or opportunities, or by commanding them, or by persuading or dissuading them, etc. So an omnipotent being should be expected to have the maximal amount of this sort of power. This underscores nicely the impressive nature of maximal power, extending as it does even to the free actions of others. On the other hand, even though the use of this liberal sense of actualization helps us to capture the pervasiveness of an omnipotent agent's power, it also points to an almost universally ignored limitation on that power. We will discuss this limitation below.7 /87/
 

2. Our second condition is that an omnipotent being should be expected to have the power to actualize a state of affairs p only if it is logically possible that someone actualize p, i.e., only if there is a possible world W such that in W someone actualizes p. We take this claim to be self-evident. 

One generally acknowledged consequence of this condition of adequacy is that the scope of an omnipotent agent's power is limited to logically contingent states of affairs, where a logically contingent state of affairs is one that possibly obtains and also possibly fails to obtain. However, it should be obvious that an analysis of maximal power will not by itself determine just which states of affairs are logically contingent and which are not. Indeed, one could trivialize the consequence in question by espousing the extreme view, sometimes attributed to Descartes, that every state of affairs is logically contingent. Or one might weaken it considerably by embracing the slightly more modest position--and perhaps this is what Descartes actually had in mind--that many allegedly paradigmatic necessary truths, e.g., logical laws or simple mathematical truths, are in fact logically contingent. We do not endorse such views, but nothing we say about maximal power itself will rule them out. Their truth or falsity must be decided independently. 

Also, we will explicitly assume below that all states of affairs (and propositions) are tensed. If this assumption is correct, then it is reasonable to think that at least some logically contingent past-tense states of affairs are not possibly such that someone actualizes them.8 For instance, one might hold that even though it is logically possible for someone to bring it about that Jones will someday be in Chicago, it is logically impossible that anyone ever bring it about that Jones has already been in Chicago. Again, however, an account of maximal power will not by itself decide whether such a claim is true.9
 

3. Many contemporary philosophers not only have accepted our first two conditions of adequacy but also have taken them to be sufficient by themselves. This is evident from the widespread acceptance, until fairly recently, of analyses equivalent to the following:

    (A) S is omnipotent if and only if for any state of affairs p, if there is a world W such that in W someone actualizes p, then S has the power to actualize p. /88/
However, philosophers at least as far back as Aristotle have realized that if the past is in some sense necessary, then there are further, purely temporal, restrictions on the power of any agent. The medievals, in fact, had a moderately well articulated theory of temporal (per accidens) modality, from which it follows that at any given time there are states of affairs which meet the condition specified in (A) and yet are such that they cannot be within the power of any agent to actualize. Interestingly, even those like Aquinas, who held that God is not "in time," recognized this sort of restriction on God's power. 

So, for instance, suppose that Jones played basketball two days ago. Then, the claim goes, not only is it true now that Jones once played basketball, but it is also necessary now that Jones once played basketball. That is, in any possible world just like ours prior to the present moment t, it is true at t and at every moment after t that Jones once played basketball. And from this it follows that no one can now have the power to actualize the following state of affairs:

    (1) Its being the case that it will be true at some time that Jones has never played basketball.
For it is a minimal and noncontroversial constraint on any agent's having the power at a time t to actualize a state of affairs p that there be a possible world W just like ours prior to t such that at t in W someone actualizes p.10 But, the argument continues, there is no such world in the case of (1). Nevertheless, (1) satisfies the condition laid down in (A), since it is easy enough to conceive of a possible world in which someone actualizes it. Such an agent might, for example, prevent Jones's coming into existence or arrange for him not to play basketball for a long time after his birth. So it is logically possible for some one to have the power to actualize (1), even though it is logically impossible that both (a) the world have the history it has had until now and (b) someone now have the power to actualize (1). Furthermore, there are any number of states o£ affairs which are like (1) in these respects. So any adequate account of omnipotence must be relativized to a time. In addition, these purely temporal restrictions on power may vary not only from moment to moment but also from possible world to possible world. And so an account of omnipotence should also be relativized to a possible world. Hence, our analyzandum should be /89/ "S is omnipotent at t in W," and we should incorporate into our analysis the purely temporal restrictions on any agent's power. 

This argument rests on two metaphysical presuppositions. The first is that states of affairs (and propositions) are tensed. We find this claim both natural and defensible, and so we accept it. (However, it may be possible for the friends of "tenseless" propositions to recast the argument in their own idiom.) One important consequence is that some logically contingent states of affairs may obtain at some times and not at others within the same possible world. For instance, the state of affairs of Jones's having played basketball does not obtain before Jones plays basketball for the first time but always obtains afterwards. Again, the state of affairs of its being the ease that Jones will play basketball may obtain now, but it will not obtain after Jones plays basketball for the last time. Further, some states of affairs may first obtain, and then not obtain, and still later obtain again. An example is the present-tense state of affairs of Jones's (now) playing basketball. 

The second metaphysical presupposition is that it is logically impossible that someone travel into the past. This claim, though eminently reasonable, has been challenged of late by several writers, who have asserted in effect that there are no purely temporal restrictions on any agent's power.11 These philosophers would say that in the case alluded to above it is at least conceivable that someone now travel backwards two days into the past and find himself in a position to prevent Jones from playing basketball. Assuming that Jones has played basketball just this one time, our time traveler would have it within his power to actualize (1). If such a scenario is coherent, it may not be incompatible with our analysis of maximal power, since our third condition of adequacy is simply that an account of omnipotence should accommodate the (epistemic) possibility that there are purely temporal restrictions on the power of an omnipotent agent. We will satisfy this condition by claiming that an omnipotent agent should be expected to have the power at t in W to actualize p only if there is a world W* such that (i) W* shares the same history with W at t and (if) at t in W* someone actualizes p. Perhaps a proponent of the eonceivability of time travel can find a plausible interpretation of the notion of two worlds sharing the same history that allows him to accept this third condition while maintaining that it adds no restrictions on /90/ power beyond those already embodied in our second condition of adequacy. (We will return shortly to the notion of sharing the same history.) On the other hand, it may be that any theory of time travel is incompatible with our suggestion for satisfying the third condition. If this is the case, then so much the worse for time travel.

Two points of clarification should be made here. First, we assume that it is logically possible for agents to actualize future-tense states of affairs. For instance, an agent may bring it about at t that Jones will be in Chicago within two hours or that Jones will be in Chicago two hours after t. (Below we will claim that an agent brings about a future-tense state of affairs by bringing it about that a given present-tense state of affairs will obtain at the appropriate future time. So someone brings it about at t that Jones will be in Chicago within two hours by bringing it about that the present-tense state of affairs of Jones's being in Chicago will obtain within two hours after t.) Some may even go so far as to say that where p is a present-tense state of affairs, it is not possible for any agent S to bring it about at t that p obtains at t. That is, S's actualizing p cannot be simultaneous with p's obtaining but must rather precede p's obtaining. If this is so, then every instance of actualization involves the actualization of a future-tense state of affairs. In any case, it is reasonable to expect that an agent who is omnipotent at t will have extensive control over what can happen at any time after t--subject to the restriction which will be set down by our fourth condition of adequacy discussed below. 

Second, it should be noted that our third condition of adequacy does not by itself rule out the possibility that someone have the power to bring about (as opposed to alter) the past. This is a separate issue which, as noted above, falls under our second condition of adequacy. So, for example, if it is logically possible that someone now, given the history of our world, brings it about that Carter was elected president in 1976, then an omnipotent agent now has the power to actualize this past-tense state of affairs. Given that Carter was in fact elected in 1976, the argument presented at the beginning of this section does not by itself rule out such backward causation. Again, this is an issue that must be decided independently. We claimed above that an omnipotent being should be expected to have the power at t in W to actualize p only if there /91/ is a world W* such that (i) W* shares the same history with W at t and (ii) at t in W* someone actualizes p. But so far we have said nothing about what it is for two worlds to share the same history at a given time. Perhaps it is not fair to demand that one who gives an analysis provide an exact characterization of each concept used in that analysis, especially when those concepts are tolerably clear on their own. Nevertheless, in this case we feel obligated to say something more, since the concept in question is open to seemingly acceptable eonstruals which would undermine the adequacy of our account of maximal power. 

Consider, for instance, the following "natural" explication of sharing the same history:

    (2) W shares the same history with W* at t if and only if for any state of affairs p and time t* earlier than t, p obtains at t* in W if and only if p obtains at t* in W* .
Since we are assuming that states of affairs are tensed, if we take (2) together with the analogue of the law of bivalence for states of affairs, the net effect is that W can share the same history with W* at t only if W also shares the same present and future with W* at t, i.e., only if W is identical with W*. For among the states of affairs that obtain at any time prior to t in W are future-tense states of affairs which specify exactly what will be true in W at and after t. Moreover, even if we deny that the law of bivalence holds for so-called "future contingent" states of affairs, so that no such state of affairs ever obtains, (2) will still be unacceptable. For on the most popular construal of the notion of a future contingent, a state of affairs is a future contingent at a given time only if it is future-tense and not causally necessary at that time. So even when we make an exception for future contingents, it still follows from (2) that W and W* share the same history at t only if they share at t what we might call their causally necessitated futures. Such a result is particularly unwelcome when one is trying to explicate maximal power, since it is generally conceded that an agent who is omnipotent at t has the power at t to bring about events whose occurrence is in some sense contrary to nature.12

Our own account of two worlds sharing the same history at a given time, which is Ockhamistic in inspiration, has been set out in detail in another place.13 So we will simply outline it rather broadly here. The basic insight involved is that what is /92/ temporally independent--or, to use Chisholm's phrase, rooted in the present--at any given time can be specified in terms of the present-tense (or, as we prefer to say, immediate) states of affairs which obtain at that time. All nonimmediate, or temporally dependent, states of affairs that obtain at a time t obtain at t only in virtue of the fact that the appropriate immediate states of affairs did or will obtain at moments other than t. So, for instance, the nonimmediate state of affairs of Jones's having played basketball obtains now in virtue of the fact that the immediate state of affairs of Jones's playing basketball obtained at some past time. Likewise, the nonimmediate state of affairs of its being the ease that Jones will play basketball obtains now in virtue of the fact that Jones's playing basketball will obtain at some future time. This is why it is reasonable to believe that an agent brings it about that Jones will play basketball only by bringing it about that Jones's playing basketball will obtain. 

Our claim is that for any moment t in a world W there is a set k of immediate states of affairs which determines what obtains at t in a temporally independent way, i.e., what obtains at t but does not obtain at t in virtue of what occurs at moments other than t. We call k the submoment of t in W and say that k obtains in W when and only when each of its members obtains in W. Then W and W* share the same history at t if and only if they share all and only the same submoments, obtaining in exactly the same order, prior to t. Since no future-tense state of affairs is immediate or, consequently, a member of any submoment, it follows that W and W* may share the same history at t even if their futures are radically diverse at t--and this diversity may extend even to their laws of nature at and after t or to events contrary to the laws of nature that they share at or after t

Given this general picture, the most pressing task is to provide a plausible characterization of the distinction between immediate and nonimmediate states of affairs. However, our account of this distinction is much too complicated to be presented in passing here. Since it has been worked out in sufficient detail elsewhere, we will simply note one result which will become relevant below. As far as we can tell, this is the only consequence of what we say about the purely temporal restrictions on power that may prove troublesome for our claim that even a divine being may have maximal power. /93/

According to our explication of immediacy, states of affairs involving present-tense propositional attitudes directed at future-tense propositions, e.g.,

    (3) Jones's believing that Smith will arrive at 2:00 P.M. and 

    (4) Jones's promising that Smith will receive a gift,

are immediate unless they entail the future-tense propositions which they involve.14 On the other hand, if these entailments do hold, then such states of affairs are nonimmediate and hence not members of any submoment. But now consider the following states of affairs:
    (5) God's believing that Smith will be saved and

    (6) God's promising that Smith will be saved.

Since (5) and (6) both entail that Smith will be saved, each is on our account nonimmediate and hence not eligible for membership in a submoment. This is a welcome result in the ease of (5), since it enables us to reconcile divine foreknowledge with human freedom. In short, even if (5) has already obtained, there may still be a world W such that (i) W shares the same history with our world at the present moment and yet (ii) Smith is never saved in W. So even if it has already been true that God believes that Smith will be saved, Smith may still have it within his power to bring it about that he will never be saved. However, this same result is somewhat more troublesome in the ease of (6)--for reasons that we will discuss in some detail at the end of this essay.15
 

4. Some might suspect that what we have already said is sufficient for explicating maximal power. For at this point we have the resources to formulate the following analysis:

    (B) S is omnipotent at t in W if and only if for any state of affairs p, if there is a world W* such that
      (i) W* shares the same history with W at t, and 
      (ii) at t in W* someone actualizes p
      then S has the power at t in W to actualize p.
Though this analysis is surely appealing, we believe that it is nonetheless inaccurate. Its insufficiency can be traced to one primary deficiency: such an analysis fails to take account of the way in which the free actions (and dispositions to free action) /94/ of other beings would necessarily limit the power of any omnipotent being. Let us now show how this limitation arises. 

As noted above in our discussion of actualization, there seems to be good reason to think that the libertarian analysis of freedom is correct. If so, it follows that not even an omnipotent being can causally determine the free actions of another agent. This fact, of course, was what accounted for the distinction between strong and weak actualization, a distinction which allows that a being can bring about a state of affairs in two distinct ways. 

However, if libertarianism is true, it has a second and equally significant impact on the analysis of omnipotence. To see this, let us imagine the following situation. Suppose that at a time t a nonomnipotent being named Jones is free with respect to writing a letter to his wife. In that case Jones has the power at t to actualize 

    (7) Jones's freely deciding at t to write a letter to his wife
and he also has the power at t to actualize
    (8) Jones's freely deciding at t to refrain from writing a letter to his wife.
From this it follows that there is a world W, sharing the same history with our world at t, such that at t in W someone (viz., Jones) actualizes (7); and it also follows that there is a world W*, sharing the same history with our world at t, such that at t in W* someone (viz., Jones) actualizes (8). So given (B), any agent who is omnipotent at t in our world must have at t both the power to actualize (7) and the power to actualize (8).

However, on the assumption that libertarianism is true it is fairly easy to show that no one distinct from Jones--not even an omnipotent agent--can have at t both the power to actualize (7) and the power to actualize (8). Let C stand for the circumstances in which Jones finds himself at t. If libertarianism is true, then C includes the fact that there is a temporal interval beginning before t and including t, in which there is no causally sufficient condition either for Jones's deciding at t to write the letter or for his deciding at t not to write the letter. But now consider the following counterfactua1:16

    (9) If Jones were in C at t, he would freely decide at t to refrain from writing a letter to his wife. /95/
Like any proposition, (9) is either true or false. Furthermore, since (9) tells us what Jones would do if left free in a certain situation, no one other than Jones can simply decide to make (9) true or false, for no one other than Jones can determine how Jones would freely act. Therefore, not even an omnipotent being can decide by himself to make (9) true or false; its truth-value is something he is powerless to affect. 

The consequence of this inescapable powerlessness is that, regardless of whether (9) is true or false, there will be a state of affairs which, despite meeting the conditions set down in (B), cannot be actualized at t by any being other than Jones--even if that being is omnipotent at t. For suppose (9) is true. In that case, even an agent who is omnipotent at t does not have the power at t to actualize (7). He cannot, of course, strongly actualize (7), for he cannot causally determine Jones's acting freely in a certain way. But neither can he weakly actualize (7). He can, perhaps, arrange things so that Jones is in C at t. But if he does so arrange things, then (9) tells us that Jones will freely refrain from writing the letter and thereby actualize (8) rather than (7). On the other hand, if (9) is false, then our omnipotent agent cannot at t weakly actualize (8). The most he can do in an attempt to bring about (8) is to bring it about that Jones is in C at t. But if (9) is false, then it is not the case that if Jones were in C at t, he would strongly actualize (8). And no one weakly actualizes (8) unless Jones strongly actualizes it. So if (9) is in fact false, then not even an omnipotent agent has the power at t to actualize (8).17

Therefore, whether or not (9) is true, there will be some state of affairs satisfying the conditions specified in (B) which even an omnipotent agent is incapable of actualizing. And since this inability results solely from the logically necessary truth that one being cannot causally determine how another will freely act, it should not be viewed (as (B) does view it) as a kind of inability which disqualifies an agent from ranking as omnipotent. 

It follows, then, that an adequate analysis of omnipotence must acknowledge the logically inescapable limitations which counterfactuals such as (9) would place on an omnipotent agent. Now it should be obvious that there are many counterfactuals which, like (9), tell us how beings would freely act. In fact, since there are presumably an infinite number of circumstances /96/ in which a being can find himself, there will be an infinite number of such counterfactuals for any free agent. Nor can we limit our consideration exclusively to actual free beings. For though an omnipotent agent might well have the power to create free beings who are not now actual, he would nonetheless be limited by the counterfactuals relating to the free actions of these beings as well. Hence, our analysis of omnipotence must recognize the importance of counterfactuals of freedom regarding not only actual beings but possible beings as well. If we believe that, strictly speaking, there are no possible but non-actual beings, we can make this last point by saying that the relevant counterfactuals relate not to individuals but to individual essences, where P is an individual essence if and only if P is a property which is such that (i) in some possible world there is an individual x who has P essentially and (ii) there is no possible world in which there exists an individual distinct from x who has P. is An individual x will thus be said to be an instantiation of individual essence P just in case x has P

Now suppose we call a complete set of such counterfactuals of freedom a world-type. If the law of conditional excluded middle were true--i.e., if it were the case that for any propositions p and q, either p counterfactually implies q or p counterfactually implies the negation of q--then a world-type could be defined as a set of counterfactuals indicating, for every individual essence and every possible set of circumstances and times in which it could be instantiated and left free, how an instantiation of that essence would freely act if placed in those circumstances. 

However, many philosophers reject the law of conditional excluded middle, for they feel there are at least some cases in which p counterfactually implies neither q nor its negation.19 Hence, it would probably be wiser for us to provide a more general definition of a world-type which does not presuppose the truth of this law. Let us say, then, that a world-type is a set which is such that for any counterfactual of freedom--i.e., any proposition which can be expressed by a sentence of the form "If individual essence P were instantiated in circumstances C at time t and its instantiation were left free with respect to action A, the instantiation of P would freely do A"--either that counterfactual or its negation is a member of the set. (To obviate certain esoteric technical problems, we might also stipulate that for any two members of the set, the conjunction /97/ of those two members is a member of the set as well.) Let us also say that a world-type is true just in case every proposition which is a member of it is true. (Since we are assuming an exact isomorphism between propositions and states of affairs, we may take a world-type to be, alternatively, a set of counterfactual states of affairs.) 

Now any free being will have some say in determining which world-type is true. For example, since Jones is free to decide whether or not to write that letter to his wife, it is up to him whether the true world-type includes (9) or its negation. However, the vast majority of the counterfactuals which go to make up a world-type relate to beings other than Jones, and Jones, of course, is powerless to make such counterfactuals true or false. So for any free agent x there will be a set of all and only those true counterfactuals of freedom (or true negations of such counterfactuals) over whose truth-value x has no control. Since such a set will clearly be a subset of the true world-type and will be characteristic only of x, let us refer to it as the world-type-for-x.20

So it is a necessary truth that every being is in a sense simply presented with a set of counterfactuals whose truth-values he is powerless to control. That is, for any agent x the world-type-for-x will remain true regardless of what x does. So it is logically impossible for x to bring about any state of affairs which is inconsistent with the truth of the world-type-for-x with which he happens to be confronted. That is, it is logically impossible for him to bring about any state of affairs which does not obtain in any world in which that world-type-for-x is true. And since it is also logically impossible for any agent to escape this type of limitation, we cannot allow such a limitation of power to disqualify a being from ranking as omnipotent. Hence, if we allow "Lx" to stand for the true world-type-for-x, then x should not be required, in order to rank as omnipotent, to possess the power to actualize any state of affairs that does not obtain in any world in which Lx is true. We can consider this as our fourth condition for an adequate analysis of omnipotence. 

So the power of any being x will necessarily be limited by the set of counterfactuals of freedom which constitute the true world-type-for-x. Moreover, since these counterfactuals do relate to the free actions of agents, none of them will be logically necessary truths. Even if (9) is true in the actual world, it could /98/ not be a necessary truth, for Jones could not be free regarding letter writing if there were no world in which he does decide to write in the circumstances in question. So though the true world-type-for-x (where x is distinct from Jones) in our world may include (9), there are other worlds in which the true world-type-for-x includes the negation of (9). Hence, different world-types-for-x may be true in different worlds. And this gives further support to the claim, made above, that an analysis of omnipotence must be relativized to a possible world.21
 

5. If our first four conditions of adequacy were pedantically specific, our fifth and final condition is refreshingly vague. Simply stated, it is that no being should be considered omnipotent if he lacks the kind of power which it is clear an omnipotent agent ought to possess. Such a requirement might appear redundant at this point. However, it is actually needed to rule out an analysis like the following, which satisfies our first four conditions:

    (C) S is omnipotent at t in W if and only if for any state of affairs p and world-type-for-SLs such that p is not a member of Ls, if there is a world W* such that 
      (i) Ls is true in both W and W*, and 
      (ii) W* shares the same history with W at t, and 
      (iii) at t in W* S actualizes p
      then S has the power at t in W to actualize p.22
Instead of furnishing us with an analysis of absolute maximal power, the right-hand side of (C) merely provides an analysis of the maximal amount of power that can be had at t in W by any being with S's nature. As such, it may be satisfied by a being obviously lacking omnipotence, e.g., the infamous Mr. McEar. To avoid this result we will satisfy our fifth condition by insisting that to count as omnipotent, a being should have the maximal amount of power consistent with our first four conditions.23


II

Though we are aware of no previously offered analysis which satisfies each of these five conditions, it seems to us that an /99/ acceptable analysis of omnipotence can be formulated. For consider:

    (D) S is omnipotent at t in W if and only if for any state of affairs p and world-type-for-SLs such that p is not a member of Ls, if there is a world W* such that 
      (i) Ls is true in both W and W*, and 
      (ii) W* shares the same history with W at t, and 
      (iii) at t in W* someone actualizes p
      then S has the power at t in W to actualize p.
(D) appears to satisfy each of our desiderata. It is stated in terms of actualizing states of affairs and does not presuppose that an omnipotent being would have to strongly actualize every state of affairs he brings about; in other words, it leaves a place for weak aetualization. The inability of even an omnipotent being to actualize necessarily unactualizable states of affairs is acknowledged by (iii), while his inability to change the past is recognized by (ii) and (iii) together. Furthermore, by employing the notion of a world-type-for-S, (D) satisfies our fourth condition. And, finally, (D) requires that an agent who is omnipotent at t in W have the power to actualize any state of affairs (other than a member of Ls) which any agent actualizes at t in any world satisfying conditions (i) and (ii). Consequently, it seems to us that (D) does provide a philosophically adequate analysis of maximal power. 

(D) also appears to be immune to the so-called paradoxes of omnipotence. Suppose that Sam is omnipotent at t in our world. Does (D) require that Sam have the power at t to actualize the state of affairs

    (10) Its being the case that there will be a stone which Sam, though he exists, cannot move?
The answer depends upon what further properties Sam has. If Sam is essentially omnipotent, then he cannot at t actualize (10). But (D) does not require that he have this power, since in that case (10) is a logically impossible state of affairs and thus not possibly such that anyone actualizes it. On the other hand, if Sam is only contingently omnipotent, then (D) might well require that he have the power at t to actualize (10). But there is no paradox here. By actualizing (10) Sam would merely bring it about that at some future time he will be nonomnipotent.24 /100/ 

Again, take the following state of affairs:

    (11) Its being the case that a completely uncaused event will occur.
Does (D) require that Sam have the power at t to actualize (11) ? If one can actualize (11) only by causing the event in question, then (D) does not require that Sam be able to actualize (11). For in that case it is logically impossible for anyone to actualize (11), even if (11) is a logically contingent state of affairs. On the other hand, if (11) is possibly actualized by someone, then Sam must have the power at t to actualize it. In neither ease is there a paradoxical result. 

But what of this state of affairs:

    (12) Someone is actualizing p, and Sam, though omnipotent, is not actualizing p,
where p is a state of affairs which even nonomnipotent agents can normally actualize? Must Sam have the power at t to bring it about that (12) will obtain? One might have doubts about whether it is logically possible for any agent to actualize (12). However, anyone who holds a fairly liberal position with respect to the diffusiveness of power might plausibly contend that it is logically possible. For instance, a nonomnipotent being could bring it about at t that (12) will obtain at t* by bringing it about that he will be actualizing p at t*, when in fact it is true that Sam will not be actualizing p at t*. But then, by the same token, it appears that Sam too may have the power at t to bring it about that (12) will obtain at t*. Sam would do this by bringing it about that he will not be actualizing p at t*, when in fact it is true that someone else will be actualizing p at t*

Of course, it is plausible to think that if Sam is an essentially divine (i.e., eternally omnipotent, omniscient, and provident) being, then he weakly or strongly actualizes at any time t every state of affairs (other than a member of the true world-type-for-Sam) which anyone actualizes at t. In that case Sam would never have the power to bring it about that (12) will obtain. But neither would any other agent ever have this power in any world containing an essentially divine being. So (D) would not in this case require that Sam have the power at t to bring it about that (12) will obtain. In short, (12) seems to present no /101/ serious problem for our analysis of omnipotence. Perhaps there are other states of affairs which would present a problem, but we have not been able to think of any.

Furthermore, our analysis has not been "corrupted" by theological considerations. Indeed, (D) appears to be quite neutral with regard to what additional properties an omnipotent being might conceivably have. Given (D), there is no obvious conceptual requirement that an omnipotent agent be eternal, necessary, essentially omnipotent, uniquely omnipotent, omniscient, or morally impeccable--a being could conceivably lack any or all of these attributes at a time t in a world W and yet still be omnipotent at t in W. Of course, for all that (D) tells us, an omnipotent being could equally well possess any or all of these attributes (leaving open for now the question of moral impeccability, which will be discussed below). In short, it appears that (D) neither requires nor forbids an omnipotent being to possess the theologically significant properties mentioned above and thus does exhibit the kind of independence from religious matters which we would presumably prefer our analysis to exhibit.


III

So it appears that (D) meets our conditions for philosophical adequacy. But what of its theological adequacy? Does (D) allow the traditional religious believer to consider God both omnipotent and incapable of acting reprehensibly? That is, does it permit one to evade the Geachian abandonment of divine omnipotence without endorsing the Pikean rejection of divine impeccability? In attempting to answer these questions, we would perhaps be well advised to begin by noting that, given our analysis of omnipotence, there is no conceptual problem with an omnipotent agent's being impeccable. For though our analysis does apparently require that an omnipotent being have the power at a given time t to actualize many evil states of affairs, e.g.,

    (13) An innocent child's being maliciously tortured,
it does not require that our omnipotent being also possess omniscience at t. Indeed, it does not require that he be very /102/ knowledgeable at all. He could conceivably be utterly ignorant of the consequences of his actions and hence bring about evil states of affairs such as (13) unintentionally. Provided that his own ignorance is not a state for which he is himself culpable, it would seem to follow that he could not be held morally blameworthy for those evil states of affairs which he might unintentionally actualize at t. Hence, the ability to actualize such states of affairs at t does not entail the ability to act in a morally reprehensible fashion at t. The possibility of an omnipotent but impeccable being is thus left open by our analysis. 

Of course, this demonstration of the compatibility of omnipotence and impeccability lends little assistance to the traditional theist who professes belief in a God who, in addition to possessing both of these attributes, is omniscient as well. How, one might ask, could an impeccable God who knew with certainty the ramifications of any action he might take have the power to actualize evil states of affairs such as (13)? 

Troubling though such a question might appear, it would seem that our analysis provides the theist with a rather obvious response, a response which should sound familiar to those conversant with theistic replies to the atheological argument from evil. The analysis of omnipotence which we have proposed does not require an omnipotent being to have the power to strongly actualize states of affairs like (13); the ability to weakly actualize them is sufficient to satisfy the conditions laid down by (D) . Once this is recognized, it no longer appears strange to contend that God, while remaining impeccable, might well have the power to actualize a state of affairs such as (13). For (13) could be part of some world W which is itself such that God's actualizing it might be morally justifiable. Perhaps the actuality of (13) in W leads to greater good than would have occurred had (13) not obtained; perhaps it leads to less evil. In any event, it is surely conceivable that God recognize that his allowing one of his creatures freely to torture an innocent child would as a matter of fact result in a world so good that this allowance was morally acceptable--and this despite the fact that the actual torturing would remain an evil state of affairs and the torturer would remain blameworthy. Hence, since even an impeccable God could have the power to weakly actualize worlds such as W which contain moral evil, and since in actualizing such worlds he must weakly actualize the evil states of affairs such /103/ as (13) which they contain, it follows that God can indeed remain impeccable even though he has the power to actualize evil states of affairs. 

Now it might be thought that this response is still inadequate. It might be thought that there are some states of affairs which are so evil that no possible world containing them is a world that anyone could be morally iustified in actualizing. Hence, since no divine being could ever have the power even to weakly actualize these states of affairs, no such being could rank as omnipotent. (We are willing to accept the assumption, made by this objection, that a being who is divine at t at least weakly actualizes any state of affairs [other than a member of the true world-type-for-him] that is actualized by anyone at t.) 

Though this objection might well be potent against the theist who views Yahweh, the person who is in fact God, as a contingently divine being, it lacks efficacy against one who holds the more traditional belief that Yahweh is an essentially divine--and so essentially impeccable--being. For on this view no state of affairs of the sort just described obtains (or, consequently is actualized by anyone) in any possible world in which Yahweh exists. Hence, (D) does not require that in order to be omnipotent Yahweh must ever have the power to actualize any state of affairs which is necessarily such that anyone who even weakly actualizes it is morally reprehensible for so doing. In fact, if we go one step further and adopt the Anselmian claim that Yahweh is a necessary being as well as an essentially divine being, it follows that no such state of affairs obtains (or, as a result, is actualized by anyone) in any possible world. Some such states of affairs might be conceivable, but they are not, according to the Anselmian, logically possible.25

However, even for the Anselmian, Geach's challenge to the notion of an omnipotent God remains to be met. If God is essentially impeccable, there is no world in which he fails to fulfill a promise he has made. But if this is so, does it not follow that by making a promise God limits his ability to act in the future and thus renders himself less than omnipotent?

It appears at first that we have a straightforward answer to this question, viz., that by making a promise to his creatures God indeed limits his power, but not in a way which compromises his omnipotence. For suppose, to use one of Geach's examples, that God has already promised that Israel will be /104/ saved.26 And assume that from this it follows that God does not now (at t) have the power to actualize

    (14) Its being the case that Israel will never be saved.
Can we conclude, given (D), that God is not now omnipotent? A close look at (D) reveals that the answer to this question is negative. For in any possible world which shares the same past with our world at t, an essentially divine being who is essentially incapable of breaking his promises has promised prior to t that Israel will be saved. So in every such world Israel is saved. Hence, no one actualizes (14) at t in any such world. So (D) does not require that in order to be omnipotent now, God must now have the power to actualize (14). 

This solution to Geach's problem is extremely attractive, and if all else should fail, we will resort to using it. However, we can adopt it only if we abandon the account sketched above of what it is for two worlds to share the same history at a given time. For on that account the state of affairs

    (15) God's promising that Israel will be saved 
is nonimmediate, since it entails the future-tense proposition that Israel will be saved. Hence, (15) is not a member of any submoment, i.e., it does not count as part of what is temporally independent at the time at which it obtains. And from this it follows that a world W might share the same history (in our sense) with our world now at t even if (15) has already obtained in our world but never obtains prior to t in W. So given our official interpretation of condition (ii) in (D), it may very well be the case that in order to be omnipotent, God must now have the power to actualize (14). But this seems to entail the theologically odious conclusion that God now has the power to break a promise and so is not impeccable. 

Still, we are reluctant to scrap our explication of what it is for two worlds to share the same history at a given time, and this reluctance itself is in part motivated by theological concerns. For our explication of this notion allows us to avoid the deterministic claim that if

    (16) God's believing (the future-contingent proposition) that Israel will be saved /105/
now obtains, then it is now no longer within the power of the children of Israel to lead, without exception, lives heavily laden with moral turpitude. Rather, we can say that God's present belief that Israel will be saved is temporally dependent on the fact that the children of Israel will freely accept his grace and live accordingly.27 So it is conceivable that (16) never obtains in a world which shares the same history with our world at the present moment t, since in that world God believes at t that the children of Israel will freely reject his grace and choose to separate themselves from him. 

Of course, philosophers have devised other, non-Ockhamistic, strategies for dealing with the problem of foreknowledge and freedom. Some argue in effect that (16) is a logically impossible state of affairs, either because a future-contingent proposition can be neither true nor false, or because--as Prior would have it--a future-contingent proposition expressible by a sentence of the form "It will be the case that p" cannot be true.28 However, if one accepts this way out of the deterministic problem, then it seems to follow that (15) is logically impossible as well. For it obtains at a time t only if it is true at t that Israel will be saved. So on this view one cannot make sense of the central religious claim that God makes promises (or gives assurances) which in some way or other guarantee the truth of contingent propositions about the future. 

Geach himself employs the alternative tactic of claiming that statements ostensibly about the future are really about present intentions, dispositions, tendencies, or trends.29 So (16) obtains just in case God believes that things are presently tending toward Israel's salvation. But this is compatible with the freedom of the children of Israel, since they may by their free actions reverse this trend, in which case at some future date (before the Judgment) it would turn out to be true that Israel will not be saved. Their freedom is preserved, however, only at the expense of the traditional belief that God now knows exactly what will happen at every future moment. It is sufficient, Geach contends, that God, like a grand chess master, knows all the possible moves we might freely make and also knows exactly how he would counter each of those moves in order to accomplish his purposes.30 Nevertheless, it is difficult to see how /106/ an orthodox Christian can accept this emasculation of the notion of divine providence. Like the promise to save Israel, many of God's promises seem to presuppose foreknowledge of exactly how his creatures will freely act. Once we deny such foreknowledge, as Geach does, then we open up the possibility that God makes promises which he will not and cannot fulfill. For even Geach insists that God cannot cause his creatures to act freely in the way he desires them to act. And suppose that they all freely reject his grace. Will he than save them? Will his kingdom then come? The answer, it is clear, is no. But if God does not have foreknowledge, then he cannot discount this possibility when deciding what to promise. The grand chess master cannot accomplish his purpose if, unbeknown to him, his opponent will refuse to move according to the rules or will simply decline his invitation to play. So, given Geach's view, either God cannot in good conscience, as it were, promise that Israel will be saved--which is false according to faith; or it is logically possible that God's promise to save Israel go unfulfilled--which is also false according to faith.

So our disinclination to abandon a broadly Ockhamistic account of divine foreknowledge stems in large part from a consideration of the theological consequences of the alternative accounts. Now it may be, of course, that even within an Ockhamistic framework one could find some acceptable reason to count (15) as immediate while counting (16) as nonimmediate. For perhaps it is plausible to think that while God's beliefs about the future depend on what will happen, his promises with respect to the future are by contrast efficacious. However, we can see at present no way to formulate a general account of immediacy which preserves this asymmetry between God's promising and God's believing without producing other unacceptable consequences--especially in cases like (15) where God promises to actualize future-tense states of affairs whose actualization depends in part on the free actions of his creatures. Moreover, there are theological reasons for thinking that God's beliefs about the future are in some sense or other causally efficacious.

Instead of pursuing this line of inquiry, we will close with a very tentative sketch of an alternative strategy for reconciling, within the parameters of our Ockhamistic account of sharing the same history, God's omnipotence with his impeccability. /107/ But we wish to reiterate that if this strategy turns out to be irremediably defective, then we will jettison our account of what it is for two worlds to share the same history at a given moment. In that case the previously noted "straightforward" response to the promising problem would, at the cost of some vagueness in our analysis of omnipotence, become available to us. 

Now it is not unreasonable to think that some of God's promises to us reflect necessary truths about how God treats his creatures. For example, perhaps it is a necessary truth that any sinful free creature whom God creates is offered divine forgiveness. Suppose that this is so, and suppose further that God has promised that Jones, a sinful free creature of God's who now exists, will be offered divine forgiveness. Given this scenario, even though the state of affairs

    (17) God's promising that Jones will be offered divine forgiveness
is nonimmediate, it is still the case that there is no possible world W sharing the same history with our world at the present moment t such that at t in W someone brings it about that Jones will never be offered divine forgiveness. For in any such world Jones is a sinful free agent created by God, and so he is offered divine forgiveness. Let us call promises of this sort God's standing promises. It should be obvious that (D) does not require that God ever have, in order to be omnipotent, the power to break a standing promise. 

It is also reasonable to believe that many of God's promises to us reflect at least in part his beliefs about how he and his free creatures will freely choose to act in the future. For instance, his promise that Israel will be saved presumably depends in part on his belief that the children of Israel will, under the influence of grace, freely act in the ways appropriate for their salvation. And perhaps his promise never again to destroy the world by flood reflects his knowledge of his own present, but constant, intentions and hence his foreknowledge of his own future free actions. Let us call promises of this sort God's conditioned promises. 

Now suppose that God's promise to save Israel is indeed a conditioned promise, and suppose that he has already made this promise. Since (15) is nonimmediate, it may follow from our account of omnipotence (given the Ockhamistic construal of /108/ condition [ii] in [D]) that God now has the power to bring it about that Israel will never be saved. Suppose that this does in fact follow. Does it follow further that God has the power to break a promise or to act in a morally reprehensible way? The answer, it should be clear, is no. For take a world W which shares the same history (in our sense) with our world now at t and in which Israel is never saved. Since in W God knows that the children of Israel will reject his grace, he never promises in W that Israel will be saved. So it is compatible with all the assumptions made above that there is no possible world in which God breaks a previously made conditioned promise. That is, even if God now has the power to bring it about that Israel will never be saved, it does not follow that God now has the poxver to act in a way which is such that if he were to act in that way, he would have broken a promise. For if he were to bring it about now that Israel will never be saved, then in those possible worlds most similar to ours in which Israel is never saved, God never promises to save Israel, where the relevant notion of two worlds being similar at t is at least partially defined in terms of the notion of two worlds sharing the same history at t. (We are, for present purposes, assuming a standard possible-worlds account of the truth conditions for counterfactuals.) 

While this line of thought admittedly requires further elaboration and defense, we believe that even this brief sketch shows it to have some merit. If some such account of God's promises is indeed correct, then to complete our argument we have only to add the claim that necessarily, any promise made by God is either a standing promise or a conditioned promise. Since neither of these types of promises undermines the claim that God is both omnipotent and impeccable--or even the stronger claim that God is both essentially omnipotent and essentially impeccable--our analysis of omnipotence does not succumb to Geach's objection even if (D) is construed Ockhamistically.

Hence, we conclude that (D) does provide the type of analysis of the concept of omnipotence which Geach and Pike held to be impossible. The theist does not need to choose between divine omnipotence and divine impeccability. And neither, fortunately, does God.31 /109/


NOTES

1. Peter Geach, Providence and Evil (Cambridge, 1977), p. 4. The chapter entitled "Omnipotence" first appeared as an article by the same name in Philosophy 48 (1973): 7-20. 

2. Nelson Pike, "Omnipotence and God's Ability to Sin," American Philosophical Quarterly 6 (1969): 208-16. In fairness to Pike we should point out that he distinguishes three senses of the claim that God cannot sin: viz., (a) that it is logically impossible that someone both is God and sins; (b) that the person who is God is incapable of sinning; and (c) that the person who is God "cannot bring himself" to sin even though he is capable of sinning. Pike accepts (a) and (c) but rejects (b) as incompatible with the claim that the person who is God is omnipotent. Our response is that (b) expresses the correct understanding of the claim in question--and it is (b) which we hope to show, pace Pike, to be compatible with the claim that the person who is God is omnipotent. Later we will endorse the stronger, Anselmian thesis that the person who is God is essentially incapable of sinning, which again, given our analysis of omnipotence, is compatible with that person's being omnipotent. Hence, we admit Pike's contention that God is not morally praiseworthy for not sinning. But we hasten to add that God is still morally praiseworthy, since he performs many supererogatory acts, e.g., sending us his only begotten Son. 

3. Jerome Gellman contends that omnipotence should be explicated in this way, so that an omnipotent agent is one who has all the power that an essentially perfect being can have. See Jerome Gellman, "Omnipotence and Impeccability," The New Scholasticism 51 (1977): 21-37. In support of this analysis Cellman argues for the dubious thesis that omnipotence is conceptually inextricable from the other properties (e.g., impeccability) a perfect being must have. In effect, then, he assimilates omnipotence to almightiness. By contrast, in The Coherence of Theism (Oxford, 1977), pp. 158-61, Richard Swinburne admits that God cannot be omnipotent in the strongest sense, but he goes on to claim, pace Geach, that it is perfectly appropriate to use the term 'omnipotent' in a weaker sense in which omnipotence is compatible with impeccability. We believe that these moves made by Gellman and Swinburne are undesirable and, as we will argue, unnecessary. 

4. To the best of our knowledge, McEar makes his first contemporary appearance in Alvin Plantinga's God and Other Minds (Ithaca, 1967), pp. 168-73. But a similar difficulty was recognized at least as early, as the later Middle Ages. For instance, the following note /110/ was added by an anonymous writer to one of the manuscripts of Ockham's Ordinatio I, distinction 42: "Nor is a being said to be omnipotent because he can do all things which are possible for him to do... since it would follow that a minimally powerful being is omnipotent. For suppose that Socrates performs one action and is not capable of performing any others. Then one argues as follows: 'He is performing every action which it is possible for him to perform, therefore he is omnipotent'." See Gerald Etzkorn and Francis Kelly, eds., Ockham: Opera Theologica, vol. 4 (St. Bonaventure, N.Y., 1979), p. 611. 

5. See Alvin Plantinga, The Nature of Necessity (Oxford, 1974), pp. 172-73. 

6. Plantinga's discussion of weak actualization is in the place cited in note 5. Chisholm's discussion occurs in Person and Obiect (LaSalle, Ill., 1976), pp. 67-69. (Chisholm takes as basic the concept of causally contributing to a state of affairs rather than the notion of actualizing a state of affairs.) It is no mean feat to formulate an exact analysis of weak actualization, but an intuitive grasp of this notion will suffice for our purposes in this paper. 

7. For some analyses of omnipotence not stated in terms of actualizing states of affairs, see Richard Francks, "Omniscience, Omnipotence and Pantheism," Philosophy 54 (1979): 395-99; Jerome Gellman, "The Paradox of Omnipotence, and Perfection," Sophia 14 (1975): 31-39; and (though less explicitly) J. L. Mackie, "Evil and Omnipotence," Mind 64 (1955): 200-12. 

8. We say "at least some," since those who espouse an Ockhamistic response to the problem of future contingents might want to insist that we can have the power to actualize certain "future-infected" past-tense states of affairs. See Alfred J. Freddoso, "Accidental Necessity and Power over the Past," Pacific Philosophical Quarterly 63 (1982): 54-68. 

9. Despite what we have said, it may be the case that Descartes is an offender rather than just a trivializer of our second condition. See Harry Frankfurt, "Descartes on the Creation of the Eternal Truths," Philosophical Review 86 (1977): 36-57. 

10. This condition on power, despite first appearances, is consistent even with compatibilism. The compatibilist would, however, deny the libertarian claim that we can add the further condition that W and our world continue to share the same laws of nature (with no violations) at t itself. 

11. See, for instance, Jack W. Meiland, "A Two-Dimensional Passage Model of Time for Time Travel," Philosophical Studies 26 (1974): 153-73; and David Lewis, "The Paradoxes of Time Travel," American Philosophical Quarterly 13 ( 1976): 145-52. 

12. For a dissenting view cf. Dennis M. Ahern, "Miracles and Physical Impossibility," Canadian Journal of Philosophy 7 (1977): 71-79. /111/ Our own inclination, on the other hand, is to believe that laws of nature specify the causal powers or dispositions of natural substances. Hence, such a law, e.g., that potassium has by nature a disposition to ignite when exposed to oxygen, might remain true even when the manifestation of the disposition in question is prevented solely by the action of a supernatural agent. 

13. See Alfred J. Freddoso, "Accidental Necessity and Logical Determinism," The Journal of Philosophy 80 (1983): 257-278. This paper argues for our account of sharing the same history on purely philosophical grounds rather than on the theological grounds suggested below. 

14. A state of affairs p may be said to entail a proposition q just in case it is logically impossible that p obtains and q does not. And p may be said to involve q just in case p is necessarily such that whoever conceives it conceives q

15. Many recent philosophers have failed to recognize explicitly that any being's power is necessarily limited to states of affairs which are "temporally contingent." In addition to Francks, Gellman, and Mackie, see George Mavrodes, "Defining Omnipotence," Philosophical Studies 32 (1977): 191-202; Nelson Pike, "Omnipotence and God's Ability to Sin"; and Richard Purtill, Thinking about Religion (Englewood Cliffs, N.J., 1978), p. 31. 

16. Throughout this essay we shall follow David Lewis's practice of not presupposing that the term "counterfactual" is to be applied only to conditionals with false antecedents. See David Lewis, Counterfactuals (Cambridge, Mass., 1973), p. 3. 

17. The argument here is little more than a variant of Alvin Plantinga's argument against the thesis that God must have the ability to actualize any possible world. See Plantinga, The Nature of Necessity, pp. 180-84. 

18. The definition of an individual essence is taken from Plantinga, The Nature of Necessity, p. 72. 

19. For a discussion of conditional excluded middle see Lewis, Counterfactuals, pp. 79-82. We wish to note in passing, however, that even if the law of conditional excluded middle is false, there may be a weaker analogue of that law which is true and would be sufficient for our present purposes if we chose to invoke it. For the antecedents of the counterfactual conditionals which concern us here are all of the form "Individual essence P is instantiated in circumstances C at time t, and P's instantiation is left free with respect to action A." Now suppose we stipulate that the substituend for "C" must be a complete description of the past at t along with a clause specifying that the same laws of nature continue to hold at t. In that case there seems to be good reason to believe that where p is a proposition expressed by a sentence of this form, then for any proposition q, either p counterfactually implies /112/ q or p counterfactually implies the negation of q. However, a complete defense of this position is impossible here, and so we will proceed on the assumption that there is no acceptable version of the law of conditional excluded middle. 

20. The relationship between the world-type-for-God and divine freedom is discussed at length in Thomas P. Flint, "The Problem of Divine Freedom," American Philosophical Quarterly 20 (1983): (forthcoming). One terminological point suggested there might also be noted in passing here: God's knowledge of the world-type-for-God is identical with what is generally referred to as God's middle knowledge. The Molinist thesis that God has middle knowledge of contingent propositions whose truth-values he cannot control is hotly contested in traditional theological discussions of grace, providence, and predestination. We cannot pursue the matter here but simply wish to note our belief that it is only by adopting some version of Molinism that one can preserve a suitably strong understanding of both (a) the doctrine of divine providence and (b) the thesis that human beings are free. 

21. Among authors discussed previously, Francks, Gellman, Mackie, Pike, and Purtill all fail to satisfy this fourth condition. In addition see Gary Rosenkrantz and Joshua Hoffman, "What an Omnipotent Agent Can Do," International Journal .for Philosophy of Religion 11 (1980): 1-19; James Ross, Philosoptiical Theology (Indianapolis, 1969), p. 221; and Douglas Walton, "Some Theorems of Fitch on Omnipotence," Sophia 15 (1976): 20-27. 

22. The stipulation that p not be a member of Ls is required if we assume that by their free actions agents actualize the corresponding counterfactuals of freedom. In the example used above, this assumption would amount to the claim that by actualizing (8) Jones also actualizes (9). If, on the other hand, we deny that a counterfactual of freedom can properly be said to be actualized by anyone, then the stipulation in question is, though superfluous, completely harmless. So we have added it just to be safe. 

23. Despite Richard Swinburne's protestations to the contrary, the conceivability of McEar disqualifies his analysis. See Richard Swinburne, "Omnipotence," American Philosophical Quarterly 10 (1973): 231-37. For much the same reason an analysis offered tentatively by Plantinga must also be deemed unacceptable. On this analysis a being S is viewed as omnipotent at time t in world W if and only if (1) there are states of affairs S can strongly actualize at t, and (2) for any state of affairs p such that there is a possible world which shares the initial world-segment prior to t with W and in which S at t strongly actualizes p, S can at t strongly actualize p

24. This response to the stone paradox conforms to that given by Rosenkrantz and Hoffman in "What an Omnipotent Agent Can Do." /113/

25. The Anselmian response to Pike was first formulated by Joshua Hoffman in "Can God Do Evil?" Southern Journal of Philosophy 17 (1979): 213-20. 

26. In his comments on this essay William Wainwright argued that if our account of freedom is correct, then God cannot make promises like the alleged promise to save Israel. For a "promise" of this sort would be such that God could not fulfill it on his own, as it were, since he does not have the poxver to determine causally the free actions of his creatures. At best, Wainwright contends, God could (in virtue of his foreknowledge) "assure" some creatures that they would be saved. But he could not "promise" this. We are not completely convinced by this argument, since it may be that God, in virtue of his knowledge of the future free acts of his creatures, can make promises where nonomniscient beings can only give assurances. But even if Wainwright is correct, it seems that an orthodox believer could comfortably construe talk of God's promises as talk about God's assurances, at least in those cases where free human actions are involved. Indeed, as Wainwright himself notes, we often give assurances by using the expression "I promise you that." One who is sympathetic to Wainwright's argument should simply construe our talk below of "conditioned promises" as talk about assurances. 

27. We acknowledge that this way of speaking is infected with (some might say "infested" with) Molinist assumptions about the relation between grace and freedom. See note 20 above. 

28. See A. N. Prior, "The Formalities of Omniscience," in Papers on Time and Tense (Oxford, 1968), pp. 26-44. 

29. Geach, Providence and Evil, ch. 2, esp. pp. 44-54. 

30. The image of God as a grand chess master, first popularized by William James in his essay "The Dilemma of Determinism," is in many ways reminiscent of Jacques Maritain's image of God as an almighty stage manager who incorporates our improvisations into his providential play. See Maritain's God and the Permission of Evil (Milwaukee, 1966), p. 79. "The Dilemma of Determinism" is found in William James, The Will to Believe and Other Essays in Popular Philosophy (New York, 1897, 1956), pp. 145-83. 

31. We wish to thank William Wainwright, our commentator at the conference, along with Nelson Pike and Philip Quinn for their helpful comments on an earlier version of this essay.