Omniscience and the Identification Problem - Florida Philosophical Review

Robert Bass, Coastal Carolina University

I once came across a Mark Twain story in which a character said something to the effect that the one thing God didn’t know was that he was not all-knowing. As an argument against omniscience, Twain’s one-liner doesn’t amount to much. Thinking about it, however, led to the kind of puzzles I explore here. Some puzzles about omniscience are connected to other issues, such as whether all claims about the future presently have truth-values. Those in turn are connected to deep issues in the metaphysics of time. (Is the future real, and, if so, in what sense?) Others are connected to questions about knowledge by acquaintance ¹ —such as whether God must, in order to be omniscient, know what it is like, say, to be guilty or to have a limited perspective, and whether God can know such things without actually beingguilty or having a limited perspective.

My concern is with a different kind of puzzle, having to do with propositional knowledge, knowledge of facts that can be represented by that-clauses in sentences such as ‘John knows that the world is round.’ I shall focus upon questions about a supposedly omniscient being who propositionally knows the truth about all current states of affairs. ²I shall argue that there is no such being.

Since we are speaking about a being who supposedly knows all facts, it is useful to say something about knowledge. We can do this sufficiently for present purposes, despite the absence of a consensus among philosophers on a general account of knowledge. For there are two points upon which there is a consensus or near-consensus—that knowledge is more than true belief and that the ‘more,’ whatever its precise character, makes the belief non-accidentally right. The difference between the knower and the one who truly believes the same fact is not just a matter of luck. It is no accident that the knower got it right; it is an accident that the one who merely believes the truth got it right.

Omniscience Alone

With that background, consider omniscience. We can abstract from questions about the relation of omniscience to other divine attributes by considering what omniscience would mean for an otherwise unremarkable being. We can return later to questions about God’s omniscience. For now, let us speak of the supposedly omniscient Todd.

We can begin with a simple statement of the supposition about Todd:
(1) Todd is omniscient.
If Todd is omniscient, then, for any proposition, p, the following conditional must be true: (2) If p, then Todd knows that p.

That is, for any truth, Todd knows it. Now consider hiders, whose defining property is that they are capable of perfectly concealing their existence from any other being. When a hider conceals its existence, it is in hiding. Plainly, if there are any hiders in hiding, Todd is not omniscient, for then there is a fact that Todd does not know, namely, that there is at least one hider in hiding. ³ He does not know that there is any hider in hiding because he cannot distinguish the state of affairs in which there are no hiders from the state of affairs in which there are hiders in hiding.

Further, if hiders are even possible, Todd is not omniscient, for again he would be unable to distinguish between the non-existence of hiders and the existence of hiders in hiding. The possibility of hiders implies that there may be hiders in hiding. Since hiders in hiding are perfectly concealed from Todd, there will be a fact that Todd does not know, namely, whether there are any actual hiders or not.

Still further, even if hiders are impossible, if Todd does not know they are impossible, then he is not omniscient. First, there will then be a fact that he does not know, namely, that hiders are impossible, and second, given that he does not know they are impossible, they will be possible as far as he can tell. He will not be able to distinguish their unknown impossibility from their possibility, and so, will not know whether there are hiders or not.

Thus, if Todd is omniscient, he must know that hiders are impossible, for only if hiders are impossible, and known by Todd to be impossible, can it be the case that Todd is, and knows that he is, omniscient. If hiders exist, or are possible, or are not known to be impossible, then some of Todd’s beliefs will be, at best, accidentally true, and therefore not cases of knowledge. Thus, we have

(3) If Todd does not know that hiders are impossible, then Todd is not omniscient, and its contraposition,

(4) If Todd is omniscient, then Todd knows that hiders are impossible. Finally, given (1), that Todd is omniscient, the following can be derived: (5) Todd knows that hiders are impossible.

Of course, that argument can be run in reverse. If hiders are either possible, or else impossible in some way that Todd doesn’t know, then Todd doesn’t know hiders are impossible. If he doesn’t know that hiders are impossible, then Todd is not omniscient. The question that faces us here is how Todd knows—if he does—that hiders are impossible.

Since, if Todd is omniscient, he must know that hiders are impossible, there are two matters to be clarified, having to do with how hiders might be impossible and with how some being might know of that impossibility. ⁴ We can begin with the impossibility of hiders. They might be impossible in either of two ways. They might be intrinsically impossible, in the way that round squares are. Alternatively, hiders might be impossible, given some other fact or facts—that is, extrinsically impossible. The existence of hiders might be excluded by some other fact, in the way that irresistible forces are impossible in worlds containing immovable objects. On the first alternative, hiders could not adequately be characterized in a non-contradictory way, and thus there would be no hiders in any logically possible world. On the second alternative, though hiders would be logically possible, and therefore present in some possible worlds, there would be some proper subset of possible worlds in which some fact or set of facts ⁵ excludes the existence of hiders. There will be no hiders in any of the worlds within the subset.

If hiders are intrinsically impossible, that will only be of use to Todd if he knows of their intrinsic impossibility. If hiders are, in some possible worlds, extrinsically impossible, that will be of use to Todd only if he knows that he is in one of those worlds. So, are hiders either intrinsically or extrinsically impossible? And, if so, how does Todd know?

Before proceeding further, consider Todd’s knowledge. If Todd knows that hiders are impossible, that knowledge will be either inferential or non-inferential. Could Todd non- inferentially know that hiders are impossible? There are two reasons for suspicion. First, so far as Todd’s non-inferential knowledge is being modeled upon ours, plausible cases of non-inferential knowledge typically yield less than certainty. I do not infer from premises that the person with the familiar profile and gait that I see walking across campus is my friend, David. But, upon catching up with him, I can be surprised to discover that it is someone else entirely. Further, even where non- inferential processes appear to yield certainty, as in the case of whether two straight lines can enclose a space, the certainty may turn out to be only certitude, the state of feeling certain that something is so, which may not in fact be so. If the normal products of non-inferential belief-forming mechanisms deserve to be called knowledge, that is due to the fact that those mechanisms are generally reliable. General reliability is not enough for Todd to rule out the existence of hiders, however. For if he reaches the belief that hiders are impossible only through a generally reliable mechanism, and if he also knows, as he must if he is omniscient, that the way in which he comes to the belief is only generally reliable, it will remain possible that, though his belief that hiders are impossible was the product of a generally reliable belief-formation mechanism, it is still mistaken. ⁶

Perhaps, however, it is not fair to model the non-inferential knowledge of a being who is supposedly omniscient upon ours. There is still reason for suspicion about claims that Todd has non-inferential knowledge of the impossibility of hiders, if nothing else is provided. This derives from the nature of the case. We are speaking of whether hiders are intrinsically or extrinsically impossible. If hiders are intrinsically impossible, there are no hiders in any logically possible world. If hiders are extrinsically impossible in some world, then that world has some hider-excluding feature. That is, it is not logically possible for there to be a hider in that world, given some other fact that obtains there. If hiders are logically impossible in either way, that will be the kind of thing that can be set out in an explicit argument, and, if Todd is omniscient, that argument will be available to him. Whether or not he is somehow capable of non-inferentially reaching the conclusion that hiders are impossible, there will be available, in principle, an explicit proof of their impossibility, and so, the non-inferential access to the truth that hiders are impossible will not be necessary for Todd’s knowledge.

On the face of it, no such proof is available. There is no overt inconsistency, nor does there appear to be any covert inconsistency buried in the notion of a being capable of concealing itself from all others. Though it might be said that the inconsistency is buried too deeply for us to unearth it, that is surely a desperate move, for it amounts to saying that, so far as we can tell, the notion is consistent. (And further, the idea of an inconsistency buried too deeply to be unearthed bears as much against omniscience as against being a hider.)

Matters seem no different if we focus upon extrinsic impossibility. It is not that there is some difficulty in conceiving of some fact which is both distinct from and incompatible with the existence of hiders. For example, there might be finders, from which no being can successfully hide. If there are any finders, there can be no hiders. More to the point, if there are any omniscient beings, there can be no hiders. The problem with these is that if Todd is to know that there are any finders or any omniscient beings, he must already have ruled out the existence of hiders. Appealing to the existence of finders or omniscient beings in the attempt to show that there are no hiders

would beg the question, at least, unless there is some independent proof of their existence. But no independent proof could be satisfactory that did not rule out the existence of hiders. ⁷ That leaves us with an exacerbated version of the earlier problem: It appears that the existence of something incompatible with the existence of hiders can only be known if it is already known that there are no hiders—which leaves us, in order to show that hiders are extrinsically impossible, trying to show that they are impossible in some other way—that is, presumably, that they are intrinsically impossible. But if that could have been shown, we would never have needed to explore the question of their extrinsic impossibility at all.

God’s Omniscience and the Identification Problem

It appears, then, that Todd does not know that he is omniscient and therefore is not omniscient. Do matters change if we consider God rather than Todd, that is, if we suppose a being with the characteristics, other than omniscience, traditionally ascribed to God? Will a being who, in addition to vast knowledge, is omnipotent, self-existent, and so on be able to rule out the possibility of hiders?

Much remains the same. There is still the fact that the conception of a hider appears consistent, and if it is, hiders are not intrinsically impossible. Perhaps, however, there is something God knows that would enable him to show that hiders are extrinsically impossible. One suggestion derives from consideration of God’s role as creator. The argument would be that there could be hiders only if God had created them, but since he did not, and knows that he did not, there are none. The problem with this is that, according to orthodox conceptions of God, there is at least one thing that exists without having been created by God, namely, God himself. God cannot argue that it is impossible for there to be anything uncreated by God because that would rule out his own existence. And that means that hiders might be beings uncreated by God and, being in hiding, unknown to God.

Perhaps a revision of this line of thought will succeed. God is self-existent—that is, does not depend for his existence upon anything else. If God had a proof that there could be only one self-existent being, he could argue that if hiders exist without being his creations, then they would have to either be self-existent or the creations of some other self-existent being. But since there are no other self-existent beings—which, ex hypothesi, has been proven—there is no way for hiders to exist.

Let’s set this attempt aside, for the moment, to consider another. Suppose that some (modal) version of the ontological argument is sound. Then, it will be necessarily true that God exists with the full set of theistic attributes. That being than which no greater can be conceived will be omniscient, omnipotent, perfectly good, self-existent, and so on. But if the ontological argument is sound, God will understand that it is, and therefore will have a proof that there is an omniscient being and hence that there are no hiders. ⁸

Both of the foregoing attempts depend upon proofs which have not actually been given, and, in the absence of the proofs, it is difficult to be confident of the solution. In addition, however, they share another feature—both are susceptible to the identification problem. In each case, we are supposing that there is a proof of the existence of some being with one or more of the traditional attributes of God. Then, the conclusion of that proof is used as a premise for a further argument to rule out the existence of hiders. But what about the being considering the proof? What is to identify that being—call it the Arguer—as the one proved to exist?

To spell out the problem, let us call the being supposedly proved to exist a God-like being. Then, the general form of both arguments—and, so far as I can see, of any others to similar effect— is this:

(1) There is a God-like being.
(2) If there is a God-like being, it knows that it is omniscient.
(3) If some being knows that it is omniscient, then it is omniscient. (4) The Arguer is the God-like being.
(5) Therefore, the Arguer is omniscient.

That is valid, so let us consider whether the premises can be known to be true. For the first premise, we are supposing that there is an independent proof. The second may require the satisfaction of additional conditions, for example, that the God-like being has not created any hiders, but let us suppose that whatever conditions are needed for it to be true are also satisfied. The third premise is analytic, given that a minimum condition for knowledge is truth. The fourth premise, however, raises the identification problem. How would the Arguer know that he is the God-like being? If the Arguer does not know that, he does not know the conclusion (and, of course, the conclusion would then not be true). More concretely, the problem can be illustrated from the two arguments considered above that depend upon demonstrations of the existence of a God-like being.

Consider first the proof of the uniquely self-existent being. How will the Arguer know that he is himself the uniquely self-existent being? Perhaps, he could have a memory of an infinite past, but that is not enough. Even if there is a uniquely self-existent being, the Arguer might have always been dependent upon and, unknown to itself, sustained in existence by some other being. And if so,

the real uniquely self-existent being might be both a hider and the one upon whom the Arguer depends.

Or consider the ontological argument. The conclusion of the ontological argument, if it is sound, guarantees that there is an omniscient being and therefore that there are no hiders. But what is to certify to the Arguer that he is the omniscient being proved to exist? One suggestion is that the Arguer might know himself to possess some other property, also proven by the ontological argument to uniquely characterize God. But that leads to a dead end for two reasons. First, whatever the ontological argument can prove, it is not clear that it proves that a being than whom no greater can be conceived has no equals in any respect. ⁹ There seems no logical impossibility in omniscient God creating omniscient Todd, provided, of course, that omniscience itself is logically possible. And if the divine attributes can be exemplified in part by other beings, it will not be possible for the Arguer to mount a sound argument that, because he has divine attribute A, he must also possess the other divine attributes, B, C, and so on.

Second, there is a generalized version of the identification problem. In addition to the problem involved in a being knowing herself to be omniscient, it is not clear how she could know herself to have any of the divine attributes. How, for example, would an all-powerful being know that she was all-powerful? It might, of course, be that she had never found any difficulty in executing her will, but that does not show that she is all-powerful, as distinct from never having tried anything that exceeded her powers. For that matter, the experience of never being frustrated in executing her will does not even show that she has not alreadyattempted something beyond her power, for she may have been the beneficiary of concealed assistance. There is no apparent way for an all-powerful being to know that she is all-powerful, for an omnipresent being to know that she is omnipresent, for a perfectly good being to know that she is perfectly good, for an indestructible being to know that she is indestructible, and so on. What that means is that the attempt to use knowledge of the set of traits allegedly proven to exist in combination by the ontological argument as a solution to the identification problem is not going to work: The identification problem will have to be solved for the other traits, too.

Thus, the omniscience problem, rather than being solved by appeal to the ontological argument, actually provides evidence that the ontological argument is not sound. For, if it were sound, then there would be an omniscient being, and therefore hiders would be, and could be known to be, impossible. But it appears that any being considering this argument and faced with the identification problem would have to recognize that he might not be the omniscient being supposedly proved to exist. That is to say, he would not know himself to be omniscient, and, therefore, would not be. If that is correct, then there is no omniscient being, and hence no sound argument, ontological or otherwise, for the existence of an omniscient being. ¹⁰

Two Objections

This conclusion is reinforced by consideration of two objections, one pertaining to the relation between omniscience and the logical possibility of error and the other to the modal status of the logical possibility of hiders.

First, I did not mean for my argument to depend upon a contentious conception of knowledge. I claimed that we only need to agree that knowledge is more than true belief and that the ‘more’ includes non-accidental correctness. My argument might be challenged, though, by questioning whether something more demanding is needed. In particular, it is often supposed that omniscience differs from ordinary knowledge at least in the respect that it logically excludes, not just error, as does any true knowledge claim, but also the logical possibility of error. ¹¹But then, the objection runs, it might be that I am tacitly importing an assumption to which my uncontentious conception does not entitle me.

Elaboration is in order. In ordinary cases, we agree that if Susan knows something, she must not simply have gotten matters right by accident, but we do not insist that her grasp of the facts be necessary. Susan may know, while being fallible. Her knowledge must exclude error, but need not exclude the logical possibility of error. She can know that it is raining, without being able to rule out the possibility that she is being deceived by a special-effects team dispatched from a movie studio. Her belief may still be non-accidentally true, given that she formed it responsibly and with adequate attention to relevant evidence. Thus, the sense in which her belief is non-accidentally correct is not equivalent to its being necessarily correct.

This is important to sort out, for I have tried to show that there are facts which no being could know. My argument has been that it would not be possible to distinguish states of affairs in which one of those facts obtained from others in which it did not obtain. Thus, any being is at most only supposedly, rather than actually, omniscient. But that description suggests that my argument may rest upon the confusion of non-accidental with necessary correctness. To put the objection briefly, can my argument be defused if an omniscient being is non-accidentally right about everything, though possibly mistaken about some things? Could Todd (or God) know every fact, including the non-existence of hiders, without being able to rule out their logical possibility? If so, my argument fails.

In this case, it is the objection that fails. Note first that if Todd cannot rule out the possibility of hiders, then, if Todd is omniscient, they must be possible. Thus, the objection presupposes that hiders are logically possible. But, given that their defining property is that they are capable of perfectly concealing their existence from any other being, they cannot be known, by some other being, either to exist (if they are in hiding) or not to exist (if they do not). They could only be known not to exist if they were in some way impossible. The objection fails because it presupposes the possibility of hiders, but there can only be an omniscient being if hiders are impossible. Whether or not there is room for an omniscient being to know something while being possibly mistaken about it, he cannot be possibly mistaken about hiders and know that there are none.

A second objection questions the claim that hiders are logically possible. The core of my argument has turned upon the claim that hiders are possible and therefore that no being is omniscient. Some theists might reply, however, that what I have shown is at most that hiders are narrowly logically possible—roughly, that they cannot be shown to be impossible with our actual formal calculi—but have not shown that they are broadly logically possible. ¹²Since narrow logical possibility does not entail broad logical possibility, it may be that hiders are broadly logically impossible, even if we do not have the formal logical machinery to prove it. Thus, no conflict has been demonstrated between the possibility of hiders and the actuality of omniscience, for hiders may only be narrowly logically possible, but broadly logically impossible. ¹³

I accept this point. I have not shown hiders to be broadly logically possible. Thus, it may be, so far as I have shown, that hiders are broadly logically impossible and thus do not constitute a barrier to the possibility of omniscience. Of course, it might instead be that it is omniscience that is broadly logically impossible. Since the broad logical possibility of omniscience entails the broad logical impossibility of hiders, and the broad logical possibility of hiders entails the broad logical impossibility of omniscience, and since we cannot show which of the respective possibility- impossibility pairs obtains, it might be suggested that the only recourse is to faith.

In this case, recourse to faith is premature. Even if hiders are broadly logically impossible, the objection does not address the identification problem. If we suppose that some Arguer has in hand a proof that there is an omniscient being, and so, knows that hiders are broadly logically impossible, that does not enable the Arguer to identify herselfas the omniscient being. To draw the conclusion that the Arguer is omniscient, some premise will be needed to the effect that the Arguer possesses some characteristic that only an omniscient being could possess, but that premise, it appears, will be just as doubtful as that the Arguer is omniscient. Even if, say, only an omniscient being could be omnipotent, there seems to be no way for any but an omniscient being to know her

own omnipotence. The argument will be circular, so the Arguer cannot know herself to be omniscient.

Other versions of this objection are equally infected by the identification problem. For suppose that there is some proof that hiders are impossible that does not entail the existence of an omniscient being. Then, two further steps will be necessary. First, the proof that hiders are impossible will at most show that it is possible for there to be an omniscient being, not that there actually is one. Some further reason will be needed for thinking that there actually is an omniscient being. Then, with that reason in place, the Arguer will still need some reason for identifying herself with the omniscient being. For the same reasons as above, the argument will be circular.

In the end, the identification problem undermines the original supposition that there is some proof of the existence of an omniscient being. Since no Arguer can identify herself as omniscient, any supposed proof to the contrary must have been unsound.

Conclusion

Let’s take stock. Consider the following argument:

(1) If any being is omniscient, then it knows that it is omniscient.
(2) No being knows that it is omniscient, because there is no being that knows hiders to be

impossible and who can solve the identification problem. (3) Therefore, no being is omniscient.

That is certainly valid, and the first premise seems beyond question, so it is sound if the second premise is also true. Let’s rephrase the second premise as the conjunction of (2a) and (2b):

(2a) If hiders are not known to be impossible or if the identification problem is not solved, then no being knows that it is omniscient.

(2b) Hiders are not known to be impossible, or the identification problem is not solved.

(2a) seems to be correct. There are several ways to challenge (2b), but, as I have argued, even if it were possible to adequately address the first disjunct, none of them provides an adequate response to the identification problem, so it appears that (2b) is also true. In my judgment, then, the argument is sound. So we have

(1) If any being is omniscient, then it knows that it is omniscient.
(2a) If hiders are not known to be impossible or if the identification problem is not solved, then no

being knows that it is omniscient.
(2b) Hiders are not known to be impossible, or the identification problem is not solved. (3) Therefore, no being is omniscient.

Thus, we appear to have a sound argument that shows that there is no omniscient being and, further, one that provides a novel line of criticism of the ontological argument.

Though I take it to be sound, I do not claim to be able to see that my premises are necessary truths. Still, though not necessary so far as I can tell, the premises seem uncontentious and obvious. For those who think the conclusion mistaken, the indicated course is to question the truth of the premises. To the extent that I am correct that the premises are uncontentious and obvious, my argument at least raises the stakes. It shows how much has to be given up to reject its conclusion. ¹⁴

References

Plantinga, Alvin. The Nature ofNecessity. Oxford: Oxford UP, 1974.

Russell, Bertrand. The Problems ofPhilosophy. New York: Oxford UP, 1978.

Swinburne, Richard. The Coherence of Theism. Oxford: Clarendon Pr, 1977.

See Bertrand Russell, The Problems of Philosophy (New York: Oxford UP, 1978) 46ff.
I shall not be concerned with other conceptions of omniscience. In particular, I exclude Swinburne’s conception, according to which God knows all that can be known, but which allows that there may be unknowable truths (e.g., Richard Swinburne, The Coherence of Theism [Oxford: Clarendon Pr, 1977]). That conception may have other problems—I suspect it does—but it is immune to the argument I develop here.
Since hiders are defined as able to conceal their existence from all others, the same being might be both omniscient and a hider. For simplicity, I assume that we are speaking of hiders distinct from the supposedly omniscient being.
Since hiders are defined in terms of their ability to conceal themselves from other beings, it may be unclear whether there are any hiders in possible worlds with no other cognizing beings. In such worlds, should we say that there are no hiders or that everythingis a hider? Since we are interested in the possibility of omniscience, and therefore in that subset of possible worlds that contain at least one cognizing being, we need not settle this. It represents no loss of generality to exclude from consideration those unclear cases in which there are no cognizing beings from which to hide.
I mean to include here the possibility of disjunctive facts. It may be that there are no hiders in worlds α or β because the disjunctive fact, p or q, holds in both, that p is incompatible with hiders, that q is incompatible with hiders, that p and not-q holds in α, and that q and not-p holds in β.
I do not mean to be denying reliabilism here, though I have serious doubts about how one might reliably but not conclusively determine that hiders are impossible. That need not be sorted out here, however, since we are addressing only the question of whether Todd might have reliable non- inferential knowledge of the impossibility of hiders. As argued in the next paragraph, if hiders are impossible, then that fact must be inferentially knowable as well. There will be some sound argument that hiders are impossible from premises that Todd knows to be true.
I further consider the issues raised by independent proofs of an omniscient being below.
I speak of a modal version of the ontological argument because that, particularly as worked out by Alvin Plantinga in The Nature of Necessity (Oxford: Oxford UP, 1974), seems to me the most philosophically interesting. However, the intricacies of Plantinga’s version are not essential to my discussion. What is essential for my purposes is that the being supposedly proved to exist is maximally or unsurpassably great, and that such unsurpassable greatness entails propositional knowledge of all facts.
The ontological argument also does not seem to prove that the set of traits definitive of maximal greatness is uniquely exemplified. Perhaps, there are several tied at the top. It still might be true of each one that no greater can be conceived.
It might be objected that if omniscience is not a possible property, its non-existence cannot be an objection to the ontological argument, for the most that the argument might be supposed to prove is that there is some being with the maximum possible knowledge. This response supposes that there is a coherent conception of maximum possible knowledge. There may not be, however, any more than there is a largest integer. The ontological argument is usually understood to underwrite the attribution of omniscience to God on the grounds that, in order to be unsurpassably great, God must be noetically unsurpassable, but would not be noetically unsurpassable if his knowledge were limited in any way. His noetic greatness could be surpassed by a being that was not so limited. But it might be that each and every degree of noetic greatness is itself limited and thus surpassable. If so, there will be no such thing as unsurpassable noetic greatness. To illustrate the point in the present context, it may be that there are relative hiders—those relative to human faculties, whose existence cannot be detected by human beings. Martians may be less limited and able to detect the human-relative hiders, but unable to detect Martian-relative hiders. Jupiterians may be able to detect Martian-relative hiders, but not Jupiterian-relative hiders. And so on. I would like to thank Renée Smith for encouraging greater clarity on this point.
I take no stand on this question. I suspect that omniscience does not admit the logical possibility of error, but, since the present objection can be addressed without settling that question, I will reserve that argument for some other occasion.
See Plantinga 1-2 for the distinction. As Plantinga characterizes it, narrowly logical necessity comprises the “truths of propositional logic and first order quantification theory.”
The objection is stated in a way that involves minimal commitment on the theist’s part—only to the proposition that something that is broadly logically necessary makes the existence of hiders broadly logically impossible. The most straightforward way for the theist to hold this is to maintain that hiders are broadly logically impossible because of the existence of a maximally great being, one who is maximally perfect—omniscient, omnipotent, perfectly good, etc.—in all possible worlds. See Plantinga Chapter X. That amounts to a commitment to one form of the ontological argument. Since that raises additional questions beyond my purview here, I shall not pursue it.
I would like to thank Gayle Dean, Carter McCain, Renée Smith, and four anonymous referees for insightful comments and discussion.