Paradox of Omnipotence and Perfection

THE PARADOX OF OMNIPOTENCE, AND

PERFECTION

JEROME GELLMAN*

We may state the "Paradt)x of Omnipotence" as follows (where A is any action the doing of which would diminish God's power or his ability to control a being): 1

(1) Either God can do A or he cannot.

(2) If God can do A, then it is possible for his power to become diminished.

(3) If God's power can become diminished, then God is not omnipotent.

So, (4) If God can do A, he is not omnipotent. (2,3)

(5) If God cannot do A, then there is something he cannot do.

(6) If there is something God cannot do. he is not omnipotent.

So, (7) If God cannot do A, he is not omnipotent. (5,6) Therefore, (8) God is not omnipotent. (1,4,7)

Presumably this argument constitues a paradox in that each of its premisses if true is necessarily true, and, so, the conclusion is also necessar i l y true. So, despite appearances the concept of "God being omnipotent" is logically defective. So we are faced with a paradox: we have a concept that seems coherent on the one hand, but logically blemished at the same time.

The "Mavrodes-Plantinga solution" (so-called because of its essential resemblance to the respective solutions of George Mavrodes and Alvin Plantinga z) shows how God's omnipotence

* University of the Negev, Beer sheva. Israel. 1 See J. I.. Maekie, "Evil and Omnipotence" Mind, 64, r 210. z George Mavrodes. "Some Puzzles Concern ing Omnipotence , " Philo-

sophieal Review, 72 (1963~, 221-223, Alvin P lant inga , God and Other Minds (Cornell, 1967), pp. 163-173.

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can be maintained without lapsing into logical absurdity. For, supposing God is omnipotent, either (a) God cannot logically possibly exist without being omnipotent (in which case we shall say God is omnipotent essential ly) or (b) God can possibly exist without being omnipotent (in which case he is omnipotent materially).

If (a), God's doing A is logically impossible. Hence, in accordance with the theological tradition that omnipotence does not extend to the doing of the impossible, his inability to do A does .not detract from his omnipotence. Premiss (6) is true for rational theology only if understood as

(6') If there is something logically possible for God to do that God cannot do, he is not omnipotent.

and (7) follows from (6') and (5) only if the latter is inter- preted as

(5') If God cannot do A, then there is something logically possible for God to do that e~mnot do.

which is patehtly false, on (a) where God is omnipotent essentially.

If (b), then God's doing A is logically possible. So, God can do A. since he is omnipotent materially. But that fails to entail that God does A and that his power is actually diminished. If God does A (and he can, since he is omnipotent materially), he will then lose power and no longer be omnipotent. But he is (now) omnipotent. So, if (b), then premiss (3) is false.

On the assumption that God is omnipotent, either (a) or (b) is true, and so either premiss (5) or premiss (3) is false. The paradox is thereby resolved.

The Mavrodes-Plantinga solution gives rise, however, to what I shall call the "Paradox of Essential Omnipotence." I will first state the paradox, and then show how the premisses may be defended on the basis of the Mavrodes-Plantinga solution to the first paradox:

(9) Either God can do.A or he cannot.

(10) If God can do A, then it's possible for his power to become diminished.

(11) If God's power can become diminished, then God is not omnipotent essentially.

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THE PARADOX OF OMNIPOTENCE, AND PERFECT ION

So, (12) If God can do A, he is not omnipotent essentially. (10, 11)

(13) If God cannot do A, there is something that he cannot do that a material ly omnipotent being can do.

(14) If God cannot do what a material ly omnipotent being can do, God is not omnipotent.

So, (15) If God cannot do A, God is not omnipotent. (13, 14)

So, (16) If God is omnipotent, tie is material ly omnipotent. (12, 15, 9)

So, (17) God is not omnipotent essentially.

The problem with (17) is that it is a f irmly entrenched doctrine of ortodox rational theology not only that God is omnipotent, but that he is omnipotent essentially. If the premisses of this argument are true, they are necessari ly true. So if the argument is sound, the concept of God's essential omnipotence is logically defective.

I pass over steps (9) - - (12) as being unproblematic. (13) must surely be accepted by the Mavrodes-Plantinga solution, since the latter partly turns on its admission that

(18) A material ly omnipotent being can do A.

and (13) follows directly from (18). What of (14)? Conceivably, a defender of the Mavrodes-Plantinga solution might argue that (14) to be acceptable must be equivalent to

(14') If there is something that God cannot do which is logically possible for him to do and which a material ly omnipotent being can do, then God is not omnipotent.

which is true even without reference to the capacities of a material ly omnipotent being in the antecedent. But (14) as it stands, he might say, is not true. For if what God cannot do is such that he logically can't do it, he remains omnipotent even if a material ly omnipotent can do that very thing. Accepting (14'), then, we would have' to change (13) to

(13') If God cannot do A, then there is something he cannot do which is logically possible for him to do and which a material ly omnipotent being can do.

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But (13') does not follow from (18) at all; and its acceptance amounts to a begging of the very question against God's essential omnipotence.

This reply, however, will not do. To see why, let us consider what concept of omnipotence could justify the rejection of (14) as it stands. The following definition of omnipotence:

(D1) X is omnipotent iff x can do whatever it is logically possible for him to do.

would justify the rejection of (14). For even if God cannot do what a material ly omnipotent being can, he can still be omnipotent, as long as his inability is a logical one. In the case of the doing of A, for example, if God is omnipotent essential ly he remains omnipotent though he cannot do A, and though (18) is true. And we must of course consider the possibil ity of essential omnipotence, otherwise we beg the question at issue. As is known, however, (D1) is not a sat isfactory definition. According to it, no matter how logically enfeebled, a being may be omnipotent provided it can per form each logically possible act left for him to perform. But surely, such a concept of omnipotence is absurd.

Suppose, now, an opponent of (14) proposes instead this definition:

(D2) X is omnipotent iff x can do whatever it is logically possible for him to do and x's logical possibilities are restr icted (if at all) only with regard to the diminishing of his power (as well as by what is logically impossible for any being whatever).

On (D2) a severely logically handicapped being is not omnipotent, since his abilities are not restr icted only by the im- possibility of losing power. And any being who is in any way logically restricted in addition to the restriction on losing power will not be omnipotent. But God, who can do everything except A, if he is omnipotent essentially, qualifies as omnipotent on (D2).

But (D2) fails as well. It is a favored doctrine of rational theology that God possesses his omniscience, goodness, etern~ ality, etc. likewise in an essential manner. So, it is logically impossible for God to forget, for example. But on (D2). God is therefore not omnipotent. But this can be patched-up as follows;

(D3) X is omnipotent iff x can do whatever it is

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THE PARADOX OF OMNIPOTENCE, AND PERFECTION

logically possible for him to do, where the logical restrictions on x (if any) are only that he cannot lose his power nor do what an essentially eternal, incorporeal, omniscient, all- good being cannot do (as well as what is logically impossible for any being whatever).

On (D3), pretty clearly (14) is false.

However, the intuitive notion of omnipotence we are work- ing with here depends, roughly, on the number of acts per- formable. Hence (D3), is utterly unconvincing, given the truth of (18); for that a being cannot do A (even if a logical cannot) ought to count against his omnipotence, since a material ly omnipotent being can do A. The logic of the situation is no different than in the case of a being logically restricted in some other way. Essential omnipotence, I am saying, ought to count as a restriction on omnipotence, since an essentially omnipotent being cannot do something that a material ly omnipotent being can do. (D3), however, entails that it doesn't matter to his omnipotence if x can or cannot do A. But this is surely unacceptable. Admitting the possibility of a material ly omnipotent being and given (18), a being who cannot do (A) is less than omnipotent. So, (D3) is counter-intuitive. On the other hand, if our reasoning against (D3) is correct, (14) appears quite plausible.

The upshot is, I believe, that (14) can be defended in the wake of the Mavrodes-Plantinga solution to the paradox of omnipotence. But in that case, the "solution" succeeds only by plunging us into another paradox for rational theology.

I I

The paradox of essential omnipotence arises from:

(18) A material ly omnipotent being can do A.

I want to argue, however, that (18) is no part of rational theology, and is indeed rejected therein. So, the paradox of essential omnipotence collapses. Also, then, the Mavrodes- Plantinga solution to the first paradox is unacceptable for rational theology, since that solution depends on (18). But once we reveal the reasons for rejecting (18), we will be able to solve the original paradox easily and without reference to material and "essential omnipotence.

Initially, the God-concept in rational theology is the unanalyzed concept of the perfect being, or most perfect being, or that than which none greater can be conceived. Divine

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attributes such as omnipotence and omniscience relate explic- atively to the fundamental unanalyzed concept of God. Omni- potence, that is, is introduced in partial answer to the question, "What are the attributes or perfections of the most perfect being?" Anselm's way of doing rational theology in the Proslogion exemplifies this approach paradigmatically. He begins, in his famous Ontological Argument, with an unanalyzed concept of God, and attempts to establish God's existence, on what may be construed a partial analysis, reveal- ing that the God-concept entails existence. In ensuing chapters of Proslogion Anselm provides a fuller philosophical explic- ation of what is meant by "that than which none greater can be conceived". This explicative task leads to God's omnipotence, as well as to other attributes.

Given the context in which omnipotence arises, perhaps a better term for the power of God would be "perfect power." Now this latter term could be understood analogously with "perfect cr ime" or "perfect coincidence." In this non-normative nonsense of perfect (Sense I) that x is a perfect F does not entail that x, or anything else, possesses a perfection in the moral sense of perfection or that to that extent x, or anything else. is worthy of worship. But surely, this is not the meaning of "perfect power" apt for rational theology. In the desired normative sense of perfect (Sense II), that x is perfect F entails that x has a moral perfection or is to that extent worthy of worship. That God is perfectly powerful, is to be taken in this second sense.

It should be noted further, that sometimes it is only by failing to be perfectly F in Sense I that one can be perfectly F in Sense II. Perfect truth-telling, for example, in Sense I (e.g. telling the truth no matter what the context or con- sequences, perhaps better described as: omni-truth-telling) is destructive of perfect truth-telling in Sense II (the moral virtue, perhaps better described as: perfection with regard to truth-telling).

In light of the above considerations, it is wrong for philosophers to seize upon the "omni-" in "omnipotence" as though it captured the basic intuition of rational theology, and squeeze it for all its worth, without regard for its explicative role for the concept of "most perfect being." If philosophers insist that the term omnipotence necessari ly encompasses the ability to do A, then the rational theologian ought to just give up that particular term as misleading or not adequately explicative of the previous notion of perfect being. For, the ability to do A, need not count as an aspect of perfection

THE PARADOX OF OMNIPOTENCE. AND PERFECTION

(Sense I I) , but as an aspect of inperfection with respect to power. The following words of Anselm are directly relevant here:

"But how art thou omnipotent, if thou art not capable of all things? Or, if thou canst not be corrupted, and canst not lie, nor make what is true, fa l se . . , how art thou capable of all things? Or else to be capable of these things is not power, but impptence . . . When one is said to have power of doing or experiencing what is not for his good, or what he ought not to do, impotence is understood in the word power. For, the more he possesses this power, the more powerful are adversity and perversity against him, and the more powerless is he against them. 3''

I believe that in this passage Anselm means to endorse the following meaning of omnipotence:

(D4) X is omnipotent if and only if x can do any logically possible action the doing of which does not logically result in an imperfect ion in x, and only such actions.

That God lies entails an imperfect ion in him; so (D4) does not require and even prohibits God's being even capable of lying in order to qualify as omnipotent. And the same applies to God's being corrupted, forgetful, or mistaken. He needn't be, indeed on (D4) cannot be, capable of any of these to be omnipotent. But the very same reasoning applies to the doing of A: if God does A, he experiences a diminution in power, which is an imperfection. So, to be omnipotent, on (D4), God must not be even capable Of doing A.

This definition helps explain, what was noted earlier, why God's essential omniscience, eternality, incorporeality, etc. do not infringe on his omnipotence. These are not ad-hoc qualifications, but follow f rom the logic of omnipotence. Since these attributes are perfections (Sense I I ) , they impose no imperfection - - entailing limitations on omnipotence.

If I am right about (D4)'s reflecting the concept of omnipotence in rational theology/ it follows that (18) is false for rational theology: no being can be both omnipotent and capable of doing (A). But if (18) is not accepted, neither is premiss

s Ansem, Proslogion, Chapter 7. T rans la t ion of S. N. Dearie, St. Anselm: Basic Writ ings (Open Court. 1962). pp. 12-13.

a For a view s imi lar t,o Anse lm s. see Aquinas ' Summa Theologica, 1, 25. 3. where he says, "To sin is to fal) short of full activity. Hence to be able to sin is to be able to fail in doing, wh ich cannot be reconci led wi th omnipotence." I would add that for s imi lar reasons to be able to do A cannot be reconci led wi th omnipotence .

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(13) of the paradox of essential omnipotence acceptable. For it is not the case that a material ly omnipotent being can do A; so, it is false that if God cannot do A, then there is something He cannot do that a material ly omnipotent being can do. Hence, the paradox of essential omnipotence disappears.

But now the original paradox of omnipotence disappears also. For consider:

(6) If there is something God cannot do, he is not omnipotent.

To be true, it should be taken as:

(6") If there is something God cannot do the doing of which does not entail an imperfection in God, then he is not omnipotent.

But in order for (5) and (6") to produce:

(7) God cannot do A, he is not omnipotent.

(5) must be reinterpreted as:

(5") If God cannot do A, then there is something he cannot do the doing of which does not entail an imperfection in God

which is false. That God does A entails a loss of power in God, and a loss of power in an imperfection. So even if (5")'s antecedent is true, its consequent needn't be true. So, understood as a necessary truth, (5") is false. With the falsity of its premisses, the paradox of omnipotence collapses.

My solution to the paradoxes accepts as true:

(19) The doing of A entails an imperfection the doer.

in

where an implicit universal quantification over power-curtail- ing acts (i.e.., "A's") is understood. Now one might argue that (19) is false, For there may be acts which curtail one's power in ways wholly irrelevant to one's worshipful status. Perhaps if God creates one tiny stone he cannot move, yet can do all else he previously could, he ought to count as just as worshipful as before. The act, A, in this case is neutral with respcct to perfection in the normative sense, And if this is so, then the paradoxes return in full force with the range of 'A' restricted to such perfection-neutral acts. (5") will indeed be true, and so will (13) (since a material ly omnipotent being can do A, under the restricted interpretation).

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THE PARADOX OF OMNIPOTENCE, AND PERFECT ION

Now I myself believe that (19) is true and that there are no power-curtail ing actions that do not result in an imperfection. Fortunately, however, we need not decide the matter in order to solve the paradoxes. For when 'A' is restricted to perfection-neutral acts, neither is (11) nor ~s (3) any longer necessari ly true. God's power could indeed become diminished without at all retracting f rom his omnipotence, since by omnipotence is meant the power of a perfect being, in the normative sense. So, indeed, the loss of a power not affecting the perfection of its possessor is compatible with omnipotence. True, there are fewer things that God can do now he has lost a power, but God is not thereby reduced in perfection, by the hypothesis of the restricted range of 'A'. So by (D4), God can do A and is omnipotent. Hence, neither (11) nor (3) is true. Finally. consider any action, B, that God cannot now do as a result of having done A and curtai led his power. God cannot do B. However if the doing of A indeed entails no imperfection, then neither does the inability to do B entail an imperfection. And if the inability to do B does not entail an imperfection then it is not incompatible with omnipotence.

In sum, whether we assert (19) or not, the paradoxes of omnipotence do not arise. I admit that a full t reatment of the subject would require a closer inspection of the concept of "perfect ion" in its theological setting, but what we have said here is correct, I believe, as far as we have considered it. And there is no reason to believe that a fuller analysis would substantial ly change our findings. 5

5 I wish to thank my colleague, Dr. Alan Zaitchik, l'or helpI'ul crit icism of an earlier draft of this paper.

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Paradox of Omnipotence and Perfection

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