Int J Philos Relig DOI 10.1007/s11153-017-9645-y ARTICLE
Omnipotence Michael Wreen1
Received: 20 April 2017 / Accepted: 27 September 2017 Springer Science+Business Media B.V. 2017
Abstract If asked to define ‘omnipotence,’ the man on the street would probably say that it’s the ability to do anything. That’s about it, he’d think; nothing more needs be said. Philosophers are never so easily satisfied. They take it as matter of professional duty to find serious problems in important concepts, and to suggest that the concept be rejected or that solutions are at hand. This paper falls into the latter camp. Beginning with a relatively simple definition of ‘omnipotence,’ increasingly complex definitions are proposed, problems are found with them, and newer, refined definitions are offered. In all, seven unsatisfactory definitions are examined before an adequate one is arrived at. Both traditional and new problems are addressed, and novel solutions are advanced. The definition argued to be adequate is itself novel, but also very much in keeping with our pre-reflective understanding of omnipotence. On the basis of the definition it’s concluded not only that an adequate definition of ‘omnipotence’ is possible, but that various problems alleged to attend attributing the notion to God can also be solved. Keywords Contradiction approach Extensional equivalence Fine-grained act individuation Heavy stone Metaphysical impossibility Metaphysical necessity Omnipotence Power/capacity
& Michael Wreen
[email protected] 1
Department of Philosophy, Marquette University, Box 1881, Milwaukee, WI 53201-1881, USA
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I Many philosophers hold that even if God can’t do certain things, that doesn’t show that he isn’t omnipotent.1 Consider the following statement form: A can x, where ‘A’ ranges over persons or personal beings, and ‘x’ over actions, considered as individual, datable occurrences, regardless of how complexly described. Aquinas and many others reject (N) A is omnipotent if and only if, for every x, A can x, a principle Descartes seems to hold. Rather, they think that a more restricted principle is correct, or at least closer to the mark, namely (P) A is omnipotent if and only if, for every ‘x’ that does not entail a contradiction, A can x. The justification for rejecting (N) in favor of (P) is that an omnipotent being shouldn’t be required to be able to do what can’t possibly be done. The concept of an ideal student doesn’t fall apart if we imagine the student being required to be able to correctly answer a multiple-choice question that has no correct answer. Rather, the requirement is illegitimate and should be dropped. Neither, for the same reason, does the concept of an omnipotent being fall apart if we imagine the being being required to be able to do what can’t be done. The requirement is at fault, not the
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Three important points about what follows. First, written as a stand-alone piece, this paper is intended to be comprehensible independently of acquaintance with the literature on omnipotence. To ensure such self-containment and accessibility, references to the literature are virtually non-existent, and a number of issues that could be critically explored at greater length—alternative definitions of ‘omnipotence,’ the distinction between a power and a capability or capacity, different solutions to the paradox of the stone, for example—are bypassed or no more than brushed upon. Space limitations, clarity, and coherence would dictate such limitations, even if the desire for ready accessibility didn’t. Second, given the long history of discussions of omnipotence, not all of the many positive or negative arguments that follow are wholly original, a fact to be expected in this context, especially in light of the treatment accorded omnipotence here. A fair number of them are, however, and both sorts of argument are seamlessly interwoven into what follows. Third, some meta-level remarks. The general view expressed in the preceding two paragraphs is unusual in philosophy, given that most journal literature is steeped in responses and counter-responses to numerous particular points, large, small, and in-between, in previous journal literature. But my sentiments are shared by some others (as well as being exemplified in other papers of my own). John Kekes’ remarks about his work on well-being, for example, need only slight adjustment to describe this paper: ‘‘This… is about [omnipotence], not about what others have written about [omnipotence]. I have, of course, read and learned from the work of others, but I have decided, for better or worse, not to engage in detailed discussions of what is called ‘the literature.’… I wanted to make what I have to say accessible to the nonspecialist readers who are likely to be interested in [omnipotence], rather than how I arrived at my views about it. This has led me to avoid detailed discussions of the works of others. I came to think of such discussions as the scaffolding without which no structure can be built, but which should be removed once the structure is completed. I hope that the end product will be judged on the basis of its merits, not on the basis of the scaffolding necessary for building it.’’ Kekes, (2010, pp. 5–6). That said, I should add that the bibliography of the scaffolding necessary for building this paper is available from the author upon request. It covers a great many, even if not quite all, of the issues surrounding omnipotence.
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notion of an omnipotent being. Omnipotence requires being able to do all that can be done, not all that can be and can’t be done. (See Sect. VII for more on the point.) To illustrate what (P) rules out: Suppose that ‘x’ is ‘draw a square circle.’ ‘x’ then entails a contradiction, since ‘draw a square circle’ entails ‘existence of a square circle,’ and that’s a contradiction in terms. Drawing a square circle thus can’t possibly be done. In accordance with (P), then, the fact that a being can’t draw a square circle doesn’t show that it isn’t omnipotent. Similar reasoning, many think, shows that God’s inability to create a stone too heavy for Him to lift doesn’t show that He isn’t omnipotent. The argument is basically this. Entailed by the very concept or word ‘God’ is ‘a being able to lift any object, no matter how heavy.’ Thus ‘create a stone too heavy for Him—God—to lift’ entails ‘create a stone too heavy to lift by a being able to lift any object, no matter how heavy.’ But the latter concept entails a contradiction, since it entails ‘existence of a stone too heavy to lift by a being able to lift any object, no matter how heavy.’ The problem here is akin to one regarding Russell’s famous barber. (I modify Russell’s example slightly, to make the point clear.) If a barber is hirable only on the condition that he shave all and only those people who don’t shave themselves, no one would ever man the empty chair. The barber would have to shave himself if and only if he didn’t shave himself. What that really shows is not that the notion of a hirable barber harbors a contradiction, but that the requirement placed upon application of the concept is illegitimate. Note, incidentally, that the supposed problem with God’s omnipotence can’t be recovered simply by omitting ‘for Him’ in the action description. Presumably, it would then mean ‘create a stone too heavy for any being to lift,’ which entails the original description. In accordance with (P), then, the fact that God can’t create a stone too heavy for Him to lift doesn’t count against His omnipotence. Removing the stone as a possible barrier to God’s omnipotence is thus possible, and without invoking any of His other defining properties, such as goodness or perfection.
II So far, so good—or at least seemingly so. (P) does handle the challenge of the too heavy stone as it has traditionally been posed. But the problem can come back in new form, and in a way that (P) can’t take care of it. Suppose that the last personal being David thought about is God. Now consider (G) God can create a stone too heavy for the last personal being David thought about to lift. The truth of (G) would mean that God could create a stone too heavy for the last personal being David thought about—that is, God—to lift. I take it that defenders of God’s omnipotence would claim that (G) is false, since the existence of such a stone would mean that God isn’t omnipotent: there would be something that God couldn’t do: lift the stone in question. But the problem with taking (G) to be false is that doing so also seems to lead to God’s not being omnipotent. That’s because ‘create a
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stone too heavy for the last personal being David thought about to lift’ doesn’t entail a contradiction. ‘M is P and M is not-P’ entails a contradiction—in fact, is a contradiction—but ‘M is P and N is not-P’ doesn’t entail a contradiction. That’s true even if M is N. Made fully explicit, the argument is this. Consider (G). For the reasons just mentioned, defenders of God’s omnipotence would say that (G) is false. And in accordance with principle (P), the falsity of (G) shows that God isn’t omnipotent unless the ‘x’ in question, ‘create a stone too heavy for the last personal being David thought about to lift,’ entails a contradiction. But it doesn’t entail a contradiction. God thus isn’t omnipotent. Principle (P) may have pushed the stone out the front door, but it’s rolled in the back. What the argument of the preceding paragraph really shows, defenders of God’s omnipotence would probably say, is not that God isn’t omnipotent, but that principle (P) isn’t really correct as it stands. It needs to be modified to be completely adequate. How, then, should it be? One way, a way suggested by Aquinas and made explicit by others, is in terms of a being’s nature: (Q) A is omnipotent if and only if, for every ‘x’ that does not entail a contradiction and every action x that is compatible with A’s nature, A can x. The reason that (G) arises as a counterexample to God’s omnipotence is that (P) doesn’t take into account the fact that God can be identified in an infinity of ways. Very few of these ways entail a contradiction when embedded in ‘x.’ The exclusive focus on contradiction thus opens the door for alternative ways of identifying God that don’t entail a contradiction, and therefore the specification of actions that, on (P), tell against His omnipotence but really shouldn’t. However, since God’s nature is what it is independently of how He is identified, and independently of any contradiction or lack thereof in ‘x,’ this defect can be remedied in the way indicated in (Q). In fact, once A’s nature is taken into account, mention of ‘x’ entailing a contradiction is really superfluous, since the performance of a ‘contradictory’ action is incompatible with every agent’s nature.
III Unfortunately, if (P) is too restrictive, not even allowing the possibility of attributing omnipotence to God, (Q) is too permissive, not allowing nearly enough to count against an attribution of omnipotence to God or anyone else. I can’t yodel for 1000 years or leap as high as Mount Everest, and my inability to do so is due to my nature as a human being and the limitations it imposes. Many of the things I can’t do are due to my nature: running faster than the speed of sound, lifting up The Rock of Gibraltar with a single hand, swimming underwater for 10 days without taking a breath. On (Q), that’s neither here nor there as far as my being omnipotent is concerned. Surely it shouldn’t be; surely those limitations demonstrate that I’m not omnipotent. A better solution is to amend (P) very differently and attack the ‘alternative identifications’ problem as such, and at its root. The idea is to pick up the benefits of
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the ‘contradiction approach,’ but to extend it in such a way as to cover alternative identifying descriptions as well. (R) A is omnipotent if and only if, for every ‘x’ such that neither it nor any ‘y’ extensionally equivalent to it entails a contradiction, A can x. (R) relaxes the unwanted strictness of (P) while making sure that the fact that I can’t float in mid-air at will does count, and definitively, against my being omnipotent. It thus ensures that I’m not omnipotent while leaving it open whether God, at least as traditionally conceived, is. And (R) also has the advantage of avoiding talk of ‘logically possible actions,’ a notion that mixes together concerns of logic and metaphysics.
IV A problem similar to that pursued in the last three sections also arises with the entire construction ‘A can x.’ Consider one of Kim Il Sung’s limitations: he can’t travel to a place where Kim Il Sung is not. The ‘x’ here, ‘travel to a place where Kim Il Sung is not,’ isn’t contradictory, nor is any phrase co-extensive with it. Mr. Sung’s inability thus isn’t ‘excused’ under the exceptions built into (R). For the reasons mentioned in Sect. I, however, this shouldn’t count against the Great Leader’s omnipotence. Not only is A’s being required to do the impossible illegitimate, so is A’s being required to do what is impossible for A to do if—and I would add only if—that impossibility is rooted in metaphysical necessity and not A’s more mundane limitations. The fact that others may be able to do what A can’t isn’t to the point here. It’s impossible for Kim Il Sung to travel to a place where Kim Il Sung is not, even though I take such trips on a regular basis. My ability to do what Kim Il Sung can’t tells naught against the Great Leader’s omnipotence, though. The general point here—that in some cases A may be able to do what B can’t and yet that doesn’t count against B’s omnipotence—is also applicable in any number of other cases, including some mentioned above. The fact that I can create an object too heavy for the creator (me) to lift, and God can’t create an object too heavy for the creator (Him) to lift, doesn’t tell against God’s omnipotence. To return: one way to handle the problem at hand is to require ‘A can x’ not to be contradictory. That’s good as far as it goes, but for reasons similar to those advanced in Sect. II, it doesn’t go far enough. Kim Il Sung can’t travel to a place where the Great Leader is not, but the corresponding positive claim, ‘Kim Il Sung can travel to a place where the Great Leader is not,’ isn’t contradictory. Speaking of Mr. Sung’s nature also is of little moment. Rather, a better way to salvage the possibility of the Great Leader’s omnipotence is to amend the definition in terms of extensional equivalence, in a way similar to that found in definition (R). (S) A is omnipotent if and only if, for every ‘x’ such that neither it nor any ‘y’ extensionally equivalent to it entails a contradiction, and every statement ‘A can x’ such that neither it nor any statement extensionally equivalent to it entails a contradiction, A can x.
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The extensional equivalence spoken of here has to do with the substitutivity of co-referring terms, not the mere sameness of truth values of propositions or sentences. There are problems with this solution to the problem, however. Suppose that the only thing Simms can do is sharpen pencils, and he’s the only person so restricted in his abilities. Simms can then be re-described as ‘the man who can only sharpen pencils.’ Let ‘x’ be ‘perform an action other than sharpen pencils.’ ‘A can x’ is thus: ‘The man who can only sharpen pencils can perform an action other than sharpen pencils.’ That’s contradictory, and so on (S) Simms’ inability to perform actions other than sharpen pencils—his inability to walk, talk, or squawk, for example—doesn’t count against his omnipotence. Since similar but much more complicated descriptions applicable to only a single person can be fadged up for every single individual, everyone is exempt from being able to perform every single action he/she can’t perform. Adjusting the definition a la (S) so that Kim Il Sung’s inability to travel to a place where the Great Leader is not doesn’t count against his omnipotence has opened the door far too wide. Everyone’s now omnipotent. One way to handle this problem is to insist that in this context, if no other, actions are to be individuated in an extremely fine-grained manner, namely, in terms of property exemplifications. Abilities to act would therefore also be so individuated. This needn’t entail that actions are property exemplifications, only that as far as a determination of omnipotence is concerned, they’re to be treated as such. On this approach, performing an act other than sharpening pencils is (taken to be) a different act from talking, walking, or squawking, for the property exemplified is different. Being able to perform an act other than sharpen pencils could then be exempted as a requirement for omnipotence, for doing so would be innocuous. Simms would still be required to be able to talk, walk, and squawk in order to be omnipotent. And since if a person walks, talks, or squawks he necessarily performs an act other than sharpen pencils, the exemption is purely nominal. In reality, Simms would be exempt from nothing of obvious relevance as far as omnipotence is concerned. The same holds mutatis mutandis for the rest of us. But if this solves the problem at hand, it also seems to bring back the original problem. Suppose that the last act that Decker thought about is traveling to a place where Kim Il Sung is not. Let ‘A’ be ‘Kim Il Sung’ and ‘x’ be ‘perform the last act that Decker thought about.’ ‘A can x’ would then be ‘Kim Il Sung can perform the last act that Decker thought about.’ If acts are individuated in a fine-grained way, the act in question wouldn’t be the same act as traveling to a place where Kim Il Sung is not, and thus the Great Leader would be required to be able to perform it in order to maintain his omnipotence. But clearly such a requirement is illegitimate. The problem here is illusory, however, for the argument of the above paragraph banks on a false premise. ‘The last act Decker thought about’ is a description coextensive with ‘traveling to a place where Kim Il Sung is not.’ The act in question is thus already exempted under the ‘any statement extensionally equivalent to ‘‘A can x’’’ clause of (S). The exemption is allowed because extensional equivalence, ushered in with ‘the act,’ holds sway and determines the act as traveling to a place where Kim Il Sung is not. The point is underscored by reading names and
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descriptions referentially in (S). (In speaking of reading names and descriptions referentially, I refer to the referential/attributive distinction, as drawn by Donnellan and developed by others.) In other words, despite the fine-grained individuation of acts, the last act Decker thought about is (the act of) traveling to a place where Kim Il Sung is not. There’s nothing comparable in the case of Simms sharpening pencils. There, the act in question was ‘an act other than,’ and the definite description which generated the problem of everyone being omnipotent concerned the re-description of Simms, not the act. But that’s just not good enough, according to Teddy Shim. Individuating acts in a fine-grained way, he says won’t, by itself, prevent the Simms problem from returning in strengthened form. Suppose that Amadio alone can perform only acts a, b, c,… z, where the number of acts is finite and relatively small. Let ‘A’ be ‘the man who can perform only acts a, b, c,… z,’ and ‘x’ be ‘perform an act other than a, b, c,… z.’ ‘A can x’ would then be: ‘The man who can perform only acts a, b, c,… z can perform an act other than a, b, c,… z.’ That’s contradictory, so Amadio’s being omnipotent isn’t compromised by his not being able to perform acts a1, b1, c1, and so on, bona fide acts that don’t figure on the list of acts that he can perform. Since all of us are like Amadio in being severely limited in just the way that he is—since a similar list of actions could be drawn up for every one of us—everyone is once again omnipotent. Individuating acts in a fine-grained way won’t alleviate the problem, for in this case (as opposed to the Simms case) there’s no definite description to hang onto in the act description, by which the extensional equivalence clause of (S) can be invoked to save the day.2 I fail to see the problem here, however. Amadio is simply Simms with a few more abilities, and the extensional equivalence clause of (S) denies Amadio omnipotence as surely as it does Simms. Suppose that I’m wrong about this, however. Even so, the problem can be alleviated by insisting on a point mentioned two paragraphs back: reading definite descriptions and names referentially. In effect, the troublesome statement in question then becomes: ‘That man (the one who [it seems] can in fact perform only acts a, b, c,… z) can perform an act other than a, b, c,….’ As this isn’t contradictory, Amadio is required to be able to perform acts other than a, b, c,… z in order to be omnipotent. In fact, if ‘A,’ as a name or definite description, and ‘x,’ if it is or contains a definite description picking out an act or range of acts; if both and any other definite description or name that occurs in ‘A can x’ are read referentially, then individuating acts in terms of property exemplifications isn’t needed, even as an assumption-for-sakeof-omnipotence-determination. The assumption becomes superfluous, because names and descriptions are, in effect, read through to the objects they refer to, even though it’s contradictoriness, and therefore conceptual content, that determines whether the inability to perform a given act precludes an attribution of omnipotence.
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My thanks to Cara Wreen for bringing this objection to my attention.
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V On to a very different point. A man can shoot the gun he’s carrying with great accuracy, and a small, innocent child is in front of him. No external barrier prevents him from shooting the child. Within his power, then, is shooting an innocent child. However, he’s also a man of high and very steadfast moral principles, and under no circumstances would he ever shoot an innocent child: he simply ‘couldn’t do it.’ In a sense, then, he’s not capable of shooting an innocent child. Call the sense of the term ‘can’ in which he can shoot the child, the power sense, and call the sense in which he can’t the (internal) capability sense. In speaking and thinking about what a person can do, or is able to do, we frequently waver between the two: sometimes not just power but capability is required—in essence, the agent must be able not just to perform the action but to will it as his or her own as well—and sometimes only power is required—the bare ability to do it is all that’s necessary. If our interest in omnipotence is, as it should be, in the complete range of what an omnipotent being can do, then both power and capability should be included in an explication of the concept. (S), then, needs further refinement. There are other things people can do that an omnipotent being shouldn’t be required to be able to do, at least if ‘be able to do’ is understood in the sense of ‘be able to will and efficaciously carry out.’ If God can’t, in the sense in question, rob a bank, misspell a word, incorrectly add a column of numbers, drive recklessly, or survey the wrong lot, that shouldn’t count against His omnipotence. This isn’t special pleading on God’s behalf, or due to His supposed perfection. The inability to perform defective actions also shouldn’t count against any human being who otherwise satisfies (S). If Walter can run faster than Rin Tin Tin, for example, bark at the moon for days on end, leap tall fences in a single bound, and so on, he would qualify as omnipotent, even if he lacked the ability, in the sense in question, to steal bones from butcher shops. Nor, perhaps surprisingly, need this be due to Walter’s being infinitely good or perfect in any very meaningful sense of the term. Perhaps he has a neural peculiarity that makes defective actions mysteriously but strongly repellant (a fact he himself may be baffled about); perhaps he has been subjected to extensive operant conditioning; perhaps he’s simpleminded but utterly steadfast in his adherence to God’s endless stream of commands, just as an obedient dog might be. At least as many people conceive it, omnipotence requires the ability (the capability) to perform neutral and positive actions, but not the ability to perform actions that are deficient or defective in some way. And rather than this being due to a being’s perfection or goodness, as many philosophers would have it, the qualification is founded on the deep but non-theistic intuition that omnipotence shouldn’t, and doesn’t, require limitations of positive qualities of other sorts, cognitive, moral, prudential, or otherwise. The points here are important to note, for although a number of philosophers have recognized that God’s inability to perform actions that are morally defective doesn’t entail lack of omnipotence, few have extended this to defective actions in general, and all seem to think the restriction is due to God’s possessing other properties, especially goodness or perfection. Duly revised, then, the new definition is:
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(T) A is omnipotent if and only if, for every ‘x’ such that neither it nor any ‘y’ extensionally equivalent to it entails a contradiction, and every statement ‘A can x’ such that neither it nor any statement extensionally equivalent to it entails a contradiction, A can x (in that A has the power to perform x); and for every x which A has the power to perform and is not a defective action, A can x (in that A is capable of performing x). Note that (T) doesn’t say that an omnipotent being can’t perform, isn’t capable of performing, defective actions. Maybe Walter can bite mailmen or maybe he can’t. But it does say that the fact that a being lacks the ability to perform such actions doesn’t count against its omnipotence. The same holds when it comes to powers, that is, for ‘contradictory’ actions that can’t possibly be performed. Suppose that somehow a being could perform such actions, for example, getting six questions wrong on a five-question test, or being at a place that he is not. That doesn’t disqualify him as less than omnipotent. One implication of this is that there may be two beings such that the first can perform all (or almost all) the actions that the second can, but the second not all that the first can, yet both are omnipotent. (Because of Kim Il Sung-like self-referential actions, it could never be the case that one human being can [has the power to] perform all the actions that a second can, even if both are omnipotent. Even supposing that both Mao and Kim Il Sung are omnipotent, Mao can travel to a place where Kim Il Sung is not, but Kim Il Sung can’t; and Kim Il Sung can travel to a place where Mao is not, but Mao can’t. I’ll ignore this largely irrelevant complication in what follows, however.) This is somewhat odd, but not all that uncommon a phenomenon. Anyone who gets above a certain score is an ‘A’ student; anyone who is over six feet six inches tall is tall; anyone who earns less than a certain amount isn’t required to pay income tax. Even with ‘all-‘or ‘infinity-laden’ properties, such as omnipotence, the situation isn’t unprecedented. The cardinality of the sets of whole numbers greater than one and of prime numbers is the same, aleph-null, and yet the first set contains the second as a proper sub-set. Note, though, that this is not to say that omnipotence is a degree concept. The definition of omnipotence advanced below, in Sect. VII, is either satisfied or it isn’t; it can’t be satisfied to various degrees. Being omnipotent is like being a qualified lifeguard: a person either is or is not a qualified lifeguard, though qualified lifeguards may differ greatly in their swimming abilities. In any case, the introduction of the concept of a defective action means that, perhaps contrary to first impression, ‘omnipotence’ is a value-laden notion to some extent.
VI It’s also worth noting that the explication of omnipotence tendered above hasn’t been fashioned with any tendentious purpose in mind, either pro-theistic or antitheistic. It has been developed in the context of traditional debates about God’s omnipotence, but more strongly, more importantly, and perhaps surprisingly,
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without God really in mind at all. The notion is explicated so as to be equally applicable (or inapplicable) to both God (if He exists) and human beings, with no qualifications or adjustments made in (T) in light of theistic concerns. This is how it should be. The explication is supposed to tell us something about the range of action-performing powers and capabilities that is required of a person or personal being in order to be omnipotent, and whether the person or personal being is human or non-human, or has or doesn’t have other omni-properties, thus should be beside the point. Non-persons and non-personal beings, however, are beside the point. An extremely large and powerful animal, a vast cosmic storm, or even the universe as a whole needn’t be considered as a candidate for omnipotence, no matter what they can ‘do.’ In other words, no special tailoring of the notion in light of possible application to candidates already in mind (such as God), either to show that he is or is not omnipotent, should be made, and thus none has been made in (T). This might not be acceptable to some philosophers, however. Explicating omnipotence in this way, they think, is unfairly loading the concept so that God isn’t omnipotent. To be more concrete: the worry is that God can’t possibly perform actions that require having a body—eating a hot dog, say, or walking up a flight of stairs—so explicating omnipotence with people and personal beings in mind, but without God specifically in mind, will result in God’s very quickly being declared not omnipotent. Surely I wouldn’t be omnipotent if I couldn’t eat a hot dog or walk up a flight of stairs. The quick response to this is that a major premise in the argument is wrong, and no barrier to God’s omnipotence has been erected. God can presumably become embodied at will, and did so in the person of Jesus Christ—I assume the traditional Christian perspective here; the claim would be roundly rejected by Muslims and Orthodox Jews.3 Eating a hot dog or walking up a flight of stairs is within the range of possible actions for Him, then. But secondly, that point aside, special pleading for an exemption for God respecting embodied actions invites special pleading for an exemption for humans respecting physically difficult actions, such as juggling a thousand toothpicks. A bad precedent would be set if either plea were taken seriously. A second objection to explicating omnipotence in a studiously neutral manner is that doing so treats the concept as univocal. This is not correct, it could be argued, for ‘power’ is predicated of humans literally, but of God analogically. A neutral explication makes this impossible. One response to this is to insist on a further specification and defense of the idea of analogical predication—in other words, to note that the burden of proof really rests on the shoulders of the advocate of analogical predication, not the person who thinks a notion is used univocally. A request of this sort wouldn’t be out of place: a presumption, though one of different strengths in different contexts, is that terms are used univocally, and if not, new and unusual uses must be explained and defended. (Indeed, the fact that there is a philosophical problem of analogical predication testifies to the fact.) A less confrontational reply is simply that (T) explicates omnipotence in almost wholly formal terms, except for the concepts of ‘power,’ 3
My thanks to an anonymous referee for reminding me of as much.
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‘action,’ ‘defect,’ and ‘capability.’ Even if all predicates are applied to God analogically, the first two notions just mentioned are barely, if at all, analogical when predicated of God, and the other two only slightly more so.
VII Still, even if all this is acceptable, further amendment is needed. Two problems come to mind. The springboard for the first is objects and events that existed in the past or will exist in the future. I can’t shake hands with Napoleon at the Battle of Waterloo now, or meet the 1000th President of the United States for lunch today, and presumably neither can God. But neither ‘shake hands with Napoleon at the Battle of Waterloo now’ nor ‘meet the 1000th President of the United States for lunch today’ nor any phrase co-designative with either harbors a contradiction. Time travel is impossible, or at least I take it to be such (although, like everything else of interest in philosophy, there are philosophers who think otherwise), but statements that entail as much don’t entail a contradiction. The problem here isn’t necessarily confined to time. There may be other statements, in addition to those mentioned above and their kin, that are necessary but whose denials don’t entail a contradiction. ‘Gold has the atomic number 79,’ ‘Churchill was born of humans,’ ‘This desk is made of wood,’ ‘Water contains oxygen,’ ‘Lightning is an electrical discharge,’ and others have been offered as likely candidates. Such statements concern an object’s, or a kind of object’s, nature or essential properties. If we exempt an omnipotent being from being able to create a square circle, because being required to be able to do what can’t be done is illegitimate, then, for exactly the same reason we should also exempt an omnipotent being from being able to perform actions that require the falsity of metaphysically necessary truths. Such actions couldn’t possibly be performed. If there are such metaphysically necessary truths, then, the fact that a being can’t create a chunk of lead with the atomic number 15, drink acetone that contains no carbon, or arrange conditions such at that Stalin is born of a clam doesn’t count against its omnipotence. The easiest way to adjust (T) to take this into account is to add a clause to the effect that x isn’t metaphysically impossible, with ‘x being metaphysically impossible’ simply meaning that the nature of the act itself doesn’t necessitate an impossible state of affairs obtaining. The Battle of Waterloo being long past and the 1000th President not yet existing make it impossible to do anything at that battle or with that president today; gold (supposedly) having the atomic number of 79 essentially makes it impossible to create, find, melt down, or run electricity through a piece of gold having an atomic number other than that; Leibniz (supposedly) having humans as his parents essentially makes it impossible that he was born of a horsehair sofa. If x-ing is metaphysically impossible, then A’s x-ing is as well. Thus not only is drinking acetone that contains no carbon metaphysically impossible, so is Mr. Rogers’ drinking acetone that contains no carbon. But, as noted in Sect. IV, there are ‘x’s that aren’t contradictory and corresponding ‘A can x’s that are. The Great
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Leader showed us as much. Is there anything comparable here, where the issue is metaphysical impossibility, not logical contradiction? In other words, are there x-ings that are metaphysically possible, with matching A’s x-ings that aren’t? I can think of none, or at least none that aren’t already picked up by the logical contradiction of the corresponding statement ‘A can x’ (or an extensional equivalent of it). I’m thus inclined to think that, aside from metaphysical impossibilities picked up by such contradictions, A’s x-ing is metaphysically impossible if and only if x-ing is. Even if I’m right about this, however, the best thing to do is to build a clause respecting the metaphysical impossibility of A’s x-ing into a revised definition, and not one respecting the metaphysical impossibility of x-ing. The argument for doing so is this. (1) As mentioned at the beginning of the last paragraph, if x-ing is metaphysically impossible, so is A’s x-ing. (2) Thus if the bi-conditional statement embedded in the last sentence of the last paragraph is correct, no harm is done by speaking only of A’s x-ing in the definition, as all relevant impossibilities, including those respecting x-ings, would have been picked up as proper exemptions. (3) However, if the bi-conditional isn’t correct and there are A’s x-ings that are metaphysically impossible without the corresponding x-ings being so, that’s all to the good as far as the definition is concerned. This is because relevant impossibilities, currently unthought of, would then be included under it, as proper exemptions. Since x-ings that are metaphysically impossible entail A’s x-ings that are, with ‘A’s x-ing’ built into the definition such x-ings would also be included as proper exemptions. Another fact needs to be taken into consideration, though a small one. An agent might be omnipotent at one time but not another. Perhaps Walter acquires and then loses his omnipotence, just as many people acquire a single power or ability—the power to walk, say—and then lose it. The acquisition and/or loss of omnipotence could be sudden and recur. Such possibilities need to be taken into account. They easily are, by adding ‘at time t’ after both ‘is omnipotent’ and ‘can x’ in (T). The upshot is this: with ‘A’ ranging over persons or personal beings and ‘x’ over actions, individual, datable occurrences, no matter how complexly described: (U) A is omnipotent at time t if and only if, for every ‘x’ such that neither it nor any ‘y’ extensionally equivalent to it entails a contradiction, and every statement ‘A can x’ such that neither it nor any statement extensionally equivalent to it entails a contradiction, and for every x such that A’s x-ing is not metaphysically impossible, A can x at t (in that A has to power to perform x at t); and for every x which A has the power to perform at t and is not a defective action, A can x at t (in that A is capable of performing x at t). As mentioned in Sect. IV, names and descriptions are to be read referentially, not attributively. If ‘x’ or some ‘y’ extensionally equivalent to it entails a contradiction, x-ing is metaphysically impossible, and so A’s x-ing is metaphysically impossible. Strictly speaking, then, the phrase ‘for every ‘‘x’’ such that neither it nor any ‘‘y’’ extensionally equivalent to it entails a contradiction’ is redundant in (U). Similarly, if ‘A can x’ or some statement extensionally equivalent to it is contradictory, A’s
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x-ing is metaphysically impossible. Thus, strictly speaking, the second major qualification in the definiens is also redundant. For some purposes, however, it’s probably best to retain both, and especially the first, while realizing that, in the letter of the law, neither belongs. Leaving the qualifications in place helps to forestall objections of the sort raised in Sects. II and IV, as well as to address some of the problems discussed in the next section. There’s one more wrinkle to consider. It comes, curiously enough, from the other side of impossibility. Suppose a given x includes a metaphysically necessary state of affairs, say, two plus two being four, or (as many people think) water’s being H2O. Although the matter is somewhat controversial, especially among theistic philosophers, I take it that no one brings about, or could bring about, such states of affairs. There are at least two arguments for thinking that this is so. The first is that necessary states of affairs obtain regardless of the actions or existence of anything else, including an omnipotent being. That suggests that their obtaining has nothing to do with the agency of anyone, including such a being. There are, however, two possible objections to this argument. The first is that its premise doesn’t seem to hold if an omnipotent being is itself included in a necessary state of affairs. And this, it could be argued, is exactly the case. For if all metaphysically necessary truths entail each another—that is, it’s impossible for one to be true and another false—then God is included in the necessary state of affairs consisting in the conjunction of all necessary states of affairs.4 But I reply in kind, by rejecting a key premise of the objection. The necessary state of affairs of potassium’s having the atomic number 19—supposing that it is a necessary state of affairs—doesn’t entail the necessary state of affairs of Leibniz’s being born of Catharina Schmuck5—again, supposing this to be a necessary state of affairs. Necessary states of affairs whose conceptual descriptions are logically independent don’t entail each other. In fact, as I understand them, states of affair as such, and whether necessary or not, don’t entail anything at all. It’s sentences or propositions that have entailments, not states of affairs. Moreover, even considering just sentences or propositions, the view that every necessary truth entails every necessary truth is an artifact of standard first-order logic. While first-order logic is an inferential system of great convenience in many cases, it also has its share of anomalies, one being that the proposition that seven plus five equals twelve entails the proposition that only widows are women—that is, every necessary truth entails every necessary truth. Metaphysics need not bow before logic, no matter how useful and revered logic may be. The second objection directly attacks the conclusion. It’s at least arguable that God is the ground of necessary moral truths, such as ‘necessarily, it is prima facie wrong to torture innocent children.’ If so, the conclusion is false, and so there must be something wrong with the argument.6
4
I am again grateful to an anonymous referee for bringing a relevant objection to my attention.
5
Empiricists will no doubt seize on this necessary state of affairs as evidence for empiricism’s superiority to rationalism.
6
Once again I am indebted to an anonymous referee for bringing a relevant objection to my attention.
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My reply is, first, the claim that God is the ground of morally necessary truths is a highly contentious one, and second and much more importantly, even if God is the ground of such necessary truths, his being so is based on his all-goodness, not his omnipotence. Oddly enough, the second argument begins with the reminder that an omnipotent being isn’t required to be able to bring about a metaphysically impossible state of affairs. As mentioned in Sect. I, that’s because it’s illegitimate to require any being to bring about what can’t possibly be brought about. Intuitively, however, the illegitimacy of being required to bring about what can’t possibly be brought about has a deeper root, and is founded on the fact it’s metaphysically necessary that the impossible can’t be brought about. It’s this metaphysical necessity, a kind of ontological restriction at the deepest level, that ultimately gives force to the claim of illegitimacy. Thus, as a principle, metaphysical necessity is prior to omnipotence as a concept, and as realities, metaphysically necessary states of affairs are prior to omnipotent beings as existents. If that’s so, no being, not even an omnipotent one, could bring about a necessary state of affairs, for its obtaining would be ontologically, though not necessarily temporally, prior to the existence of any such being. It’s in light of such considerations, among others, that some philosophers think that necessary states of affairs bring themselves about, and others that the whole idea of their being brought about doesn’t arise, or doesn’t make sense. Be that issue as it may, all that’s of moment here, and all that’s been argued for, is that an omnipotent being shouldn’t be required to be able to bring about a metaphysically necessary state of affairs, because it’s impossible for any person or personal being to do so. The clarifying proviso of several paragraphs back being understood, then, and the redundancy built into the definition being duly noted, I propose that (O) A is omnipotent at time t if and only if, for every ‘x’ such that neither it nor any ‘y’ extensionally equivalent to it entails a contradiction, and every statement ‘A can x’ such that neither it nor any statement extensionally equivalent to it entails a contradiction, and for every x such that A’s x-ing is not metaphysically impossible and x-ing doesn’t include a metaphysically necessary state of affairs obtaining, A can x at t (in that A has the power to perform x at t); and for every x which A has the power to perform at t and is not a defective action, A can x at t (in that A is capable to performing x at t). In essence, despite the relatively modern and slightly technical terminology, and despite the sorts of problems and complications noted above, some of which have never been aired in the literature, (O) is continuous with, but a further development of, traditional definitions of ‘omnipotence.’ Basically, it says that a person or personal being is omnipotent if and only if the only limitations on its powers, if there are any at all, are imposed by metaphysical impossibility (A’s x-ing’s being metaphysically possible) and metaphysical necessity (x-ing not including bringing about a necessary state of affairs), and the only acceptable limitations on its capabilities, if any exist at all, are due to the possession of other positive character and personality traits (powers to perform defective actions needn’t be capabilities). The limitation due to metaphysical necessity is itself subsumable under that of
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metaphysical impossibility, if the arguments of a few paragraphs back are correct, and it’s impossible to bring about a necessary state of affairs. Since many would question those arguments, however, it’s best to err on the side of caution and assume that they’re not sound, and, more strongly, that it’s not metaphysically impossible to bring about a necessary state of affairs. Even so, it’s anomalous to require an omnipotent being to be able to bring about what would obtain even if it didn’t bring it about, and what it couldn’t change or make otherwise even if it wanted to, such as two plus two equaling four. Thus if circumspection dictates that the arguments of a few paragraphs back not be taken as probative—and it’s best to assume as much— there’s at least some reason to think that the clause respecting metaphysical necessity should be retained in the definition.
VIII How would (O) handle the God’s apparent inabilities (a) to destroy Himself, (b) to make Himself ignorant of one or more truths, or (c) to divest Himself of one or more of his powers or capabilities to perform neutral or positive actions? Some philosophers think that (a), (b), and/or (c) show that God isn’t omnipotent. This is doubtful, however. If ‘eternal’ (or ‘everlasting’) is entailed by ‘God,’ ‘destroy God’ is contradictory, since it entails ‘non-existence of a being that always exists (or exists out of the flow of time).’ Similar considerations hold for ‘make God ignorant of a truth,’ at least if the ‘omniscience’ that figures in the definition of ‘God’ is short for ‘ever omniscient.’ The same holds for ‘strip God of a power or capability to perform neutral or positive actions,’ on the assumption that ‘omnipotence’ is short for ‘ever omnipotent.’ But even if the ‘ever’ were missing in the latter two cases, and ‘destroy God’ weren’t contradictory, God’s omnipotence wouldn’t be compromised. All three proposed actions are valuationally defective. Destroying a being like God certainly is; making a being more ignorant is; limiting a being’s powers to perform neutral or positive actions is. (A word about this last point and valuationally neutral actions. I take the power or ability to x to be valuationally neutral if and only if x-ing is valuationally neutral. The abilities to walk and to turn one’s head are valuationally neutral, while the abilities to murder and to steal are not. The limitation or loss of a neutral ability, such as the ability to walk or to turn one’s head, is obviously a bad thing, however, so limiting or destroying the ability to perform valuationally neutral acts is itself valuationally defective.) The case of God’s inability (d) to create an object He can’t destroy is similar but slightly different. If destroying an object is, as such, a defective action, then, as (O) has it, God’s inability to destroy an object doesn’t count against His omnipotence; but if it isn’t a defective action, then it’s arguable that ‘create an object that God can’t destroy’ is contradictory in much the same way that ‘create a stone too heavy for God to lift’ is. Entailed by the phrase is ‘create an object that can’t be destroyed by a being that can destroy anything,’ which itself entails ‘existence of an object that can’t be destroyed by a being that can destroy anything.’ That’s contradictory in much the same way that the original stone example is. Either
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interpretation—as a defective action or as non-defective action—thus yields the same result. Last, consider the ability (e) to create an object which the creator can’t subsequently control. Mackie thinks that if God has this ability there’s something He can’t do: control the object in question. But if He lacks this ability, there’s something He can’t do: create the object in question. The way to handle this problem, Mackie thinks, is to distinguish between first order omnipotence (omnipotence (1)), that is unlimited power to act, and second order omnipotence (omnipotence (2)), that is unlimited power to determine what powers to act things shall have. Then we could consistently say that God all the time has omnipotence (1), but if so no beings at any time have to power to act independently of God. Or we could say that God at one time had omnipotence (2), and used it to assign independent powers to act to certain things, so that God thereafter did not have omnipotence (1). But what the paradox shows is that we cannot consistently ascribe to any continuing being omnipotence in an inclusive sense.7 But there’s really no need to embrace either horn of the dilemma here, and thus no need to deny ‘‘continuing omnipotence’’ to God in any sense worth worrying about. As stated, the problem is identical with that of the too heavy stone, and should be accorded the same treatment. The particular ability Mackie actually has in mind, however, may make his case more convincing: the ability to create beings—agents—who then act in ways that can’t be controlled by God—act freely, understood in a libertarian sense. According to orthodox Christianity, God not only has this ability, but exercised it in creating us. If so, it seems that there’s something God can’t do: control us.8 The problem here, however, is generated by quick trafficking between ‘control us’ and ‘control our actions’ on the one hand, and ‘control free beings’ and ‘control free actions’ on the other. God can control us and our actions, but under pain of contradiction He can’t control free beings (other than Himself) or free actions (other than His own). Insofar as He controls a being other than Himself or an action other than His own, that being or action isn’t free, for a free being or a free action controlled by another isn’t, on a libertarian understanding of freedom, really free at all. In short, God is able to control others and their actions—but not others or their actions insofar as they’re free. God’s inability on that count, though, doesn’t tell against His omnipotence, since the descriptions in question, ‘create a free being other than God but controlled by God’ and ‘create a being other than God whose free actions are controlled by God,’ harbor contradictions. Thus there seems to be a problem with God’s omnipotence only because two action descriptions are juggled but not kept track of.
7
Mackie (1955, 2001, p. 273.)
8
My thanks to an anonymous referee for reminding me that my statement needs to be qualified: Not all orthodox Christians are libertarians.
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IX There may be other reasons, besides those mentioned above, for denying God’s omnipotence; and (O) may well stand in need of further refinement in order to best capture the notion of omnipotence. But I conclude, at least tentatively, that (1) despite its technical terminology, (O) reasonably well captures the range of actions that many people take an agent to be required to be able to perform in order to be regarded as omnipotent, (2) God’s omnipotence has survived intact, and (3) at the very least, (N), (P), (Q), (R), (S), (T), and (U) stand in need of important amendment in order to cast neither too wide nor too narrow a net to haul in omnipotence.9
References Kekes, J. (2010). The human condition. Oxford: Oxford University Press. Mackie, J.L. (1995). Evil and omnipotence. Mind 64:200–212. (Reprinted in Philosophy of religion: Selection readings, 2nd ed., pp. 263–273, by M. Peterson, H. William, R. Bruce & B. David, Ed., 2001, Oxford: Oxford University Press).
9
My thanks to Teddy Shim, Cara Wreen, and an anonymous referee for a large number of useful comments on an earlier draft of this paper.
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