God’s Omnipotence And Sovereignty – Part Five
Once voluntarism is rejected, it is necessary to specify more precisely what saying that an omnipotent being could do anything means. One natural way of doing this is to define the form:
S is omnipotent =df S can perform any action A such that C
Where C specifies some conditions, A must satisfy. Such theories of omnipotence may be conveniently referred to as act theories. The most straightforward (non-voluntarist) act theory is:
(1) S is omnipotent =df S can perform any action A such that A is possible
This act theory deals with the problem of drawing a round square and making 2 x 4 = 9: these are not possible actions. There is some difficulty in saying which acts should count as possible, which threatens to weaken the condition. For instance, a Being who could perform only physically possible actions would not be omnipotent. The usual response, dating back to Aquinas, is that an action is possible, in the relevant sense, if and only if it is consistent, that is, if it is not self-contradictory.
The Stone Paradox is most effective against act theories. Making a stone one cannot lift is a possible action, so, to count as omnipotent according to (1), a being must be able to perform it. However, if any being performs this task, then there is a possible task which that being cannot perform immediately afterward, namely, lifting the stone one has just made.
It might object that this task is impossible for the being in question, but this qualification is not permitted (1). Definition (1) requires that an omnipotent being should be able to perform any logically possible action, that is, any action that could possibly be performed by any being at all, in any circumstances at all. It is clearly possible that some being performed the action of lifting the stone one have just made, so, according to (1), a being who had just performed the action of making a stone one cannot lift could not possibly be omnipotent. It is not a problem for a being who is only contingently omnipotent: such a being might perform the first task, thereby ceasing to be omnipotent, and so be unable to perform the second task, or the being might refrain from performing the first task, and so continue to be omnipotent. However, the Paradox shows that no being could be necessarily omnitemporally omnipotent in the contemplated theory. It has sometimes been thought that this problem could be solved simply by recognizing that creating a stone an omnipotent being cannot lift is an impossible action. Therefore an omnipotent being need not be able to perform it. [xiv]
However, this line of objection fails to recognize that, in addition to the impossible action of creating a stone an omnipotent being cannot lift, there are also such possible actions as creating a stone one cannot lift and creating a stone its creator cannot lift. There are further problems. Possible actions also include coming to know that one has never been omnipotent, which, since no one can know falsehoods, no omnipotent being could do. Additionally, this kind of view causes problems for various traditional religious views, such as the assertion by the author of the Epistle to the Hebrews that it is “impossible for God to lie” (Hebrews 6:18) since lying is a possible action. Before Aquinas, medieval philosophers often attempted to deal with this problem by claiming that an omnipotent being could perform any action which does not require a defect or infirmity. However, there was little success in spelling out this assertion’s meaning (Ross 1969: 196-202). Here is a definition that captures the basic idea of these medieval analyses:
(2) S is omnipotent =df S can perform any action A, so it is logically possible that S does A. It is similar to the Medieval suggestion since, according to classical theology, God is necessary without defect or infirmity, so if action A requires a defect or infirmity, (2) does not require that God, to count as omnipotent, should be able to do it. However, (2) runs into the famous ‘McEar’ counter-example (Plantinga 1967: 170; La Croix 1977: 183). Suppose it is a necessary truth about a particular being, known as McEar, that the only action he performs is scratching his ear. It follows that if McEar can scratch his ear, he is omnipotent, despite his inability to do anything else. This result is unacceptable.
One response, considered by Alvin Plantinga and advocated by Richard La Croix, is to claim that an otherwise God-like being who satisfied this definition would be omnipotent. If the concept of God is otherwise coherent, then this claim is probably valid. It also has the benefit of being guaranteed not to create any inconsistencies, for it is built into the definition that God has the power only to perform those actions such that he may perform them. However, to adopt this strategy is to give up on the project of providing a general analysis of omnipotence.
Furthermore, this claim, on its own, does not answer the question of the Stone Paradox: is it possible for God to create a stone he cannot lift? Although not everyone agrees that La Croix’s response is satisfactory, it is widely held that the prospects are not suitable for a consistent general definition or analysis of omnipotence in terms of acts. [xv]
The main alternatives to act theories of omnipotence are the result theories. Theories analyze omnipotence in terms of the results an omnipotent being would bring about. These results are usually thought of as states of affairs or possible worlds. A possible state of affairs is the way the world could be. Philosophers also sometimes recognize impossible states of affairs, ways the world could not be.
For instance, the sky’s blue is a possible state of affairs, and John’s being a married bachelor is an impossible state of affairs. A possible world is a maximally consistent state of affairs, a complete way the world could be. Equivalent, or approximately equivalent, result theories can be stated in terms of either state of affairs or possible worlds. The simplest (non-voluntarist) result theory can be stated, in terms of possible worlds, as follows:
(3) S is omnipotent =df S can bring about any possible world.
In other words, for any comprehensive way the world could be, an omnipotent being could bring it about that the world was that way. This omnipotence account was first clearly laid out and endorsed by Leibniz, who pioneered the philosophical use of the notion of a possible world (Leibniz 1985: sects. 7-8, 52, 416). More recently, James Ross has advocated a similar account, though Ross prefers a formulation in terms of states of affairs (Ross 1969: 210-213):
(4) S is omnipotent =df for every contingent state of affairs p, whether p is the case is logically equivalent to the effective choice, by S, that p, since every state of affairs must either obtain or not, and since two contradictory states of affairs cannot both obtain, an omnipotent being would have to will some maximal consistent set of contingent states of affairs (Ross 1980: 614). That is, someone possibly would. Ross’s definition, therefore, entails Leibniz’s.
The Leibniz-Ross theory neatly handles all of the objections raised against act theories. First, the Stone Paradox depends on the existence of reflexive actions, the actions whose descriptions refer back to the actor. Although states of affairs can refer to agents, a state of affairs does not have an actor. Thus, the phrase ‘there being a stone one cannot lift’ fails to specify a state of affairs since there is no actor for “one” to refer to. To specify a state of affairs, it is necessary to replace “one” with some expression that defines which agent or agents cannot lift the stone. However, there being a stone an omnipotent being cannot lift is clearly not a possible state of affairs. An omnipotent being could, therefore, not bring it about.
On the other hand, there being a stone its creator cannot lift is a possible state of affairs. And could be brought about by an omnipotent being, under the Leibniz-Ross theory, for an omnipotent being could bring it about that some other being created a stone that that being could not lift. Therefore, the Stone Paradox is not a problem for the Leibniz-Ross theory.
The Leibniz-Ross theory is likewise invulnerable to the objection regarding coming to know that one is not omnipotent. In this theory, an omnipotent being must be essentially omnipotent, and it is impossible that an omnipotent being should come to know that it is not omnipotent. Therefore, as in the stone case, the omnipotent being could bring about someone’s coming to know that she is not omnipotent, but not an omnipotent being’s coming to know that it is not omnipotent.
Finally, no analog to the McEar objection arises for the Leibniz-Ross theory. While no apparent contradictions are involved in the Leibniz-Ross theory, there are many metaphysical consequences that some have thought odd and absurd. First, the Leibniz-Ross theory implies that an omnipotent being exists necessarily. According to Leibniz’s formulation, an omnipotent being would be able to actualize any possible world. Still, it is absurd to suppose that an omnipotent being should actualize a world in which it never existed. It follows that no such world is possible. In Ross’s formulation, obtaining any state of affairs is equivalent to being chosen by an omnipotent being. Therefore, obtaining the state of affairs of no omnipotent being is logically equivalent to an omnipotent being effectively choosing that no omnipotent being should ever exist. Still, if no omnipotent being ever exists, then no omnipotent being ever chooses. As a result, the state of affairs of no omnipotent being ever existing cannot possibly obtain. [xvi]
Leibniz and Ross are both proponents of the Ontological argument for God’s existence. So they both regard this as a benefit of this theory of omnipotence. Others have, however, found it implausible. However, many people find it intuitive to suppose that there are possible worlds in which there is no omnipotent being, the Leibniz-Ross theory of omnipotence rules out this possibility.
The Leibniz-Ross theory may narrow the space of possible worlds even further, for God, the being Leibniz and Ross believe omnipotent, is also supposed to be necessarily morally perfect. Some worlds intuitively seem possible, which a necessarily morally perfect being could not, it seems, create–for instance, worlds in which the only sentient creatures suffer excruciating pain throughout every moment of their existence. According to the Leibniz-Ross theory, if the omnipotent being could not create these worlds, then these worlds are impossible. Furthermore, the Leibniz-Ross theory entails that an omnipotent being not only cannot create beings; it cannot control but cannot create beings; it does not control[xvii]. In the Leibniz-Ross theory, an omnipotent being must choose every state of affairs to obtain, including all of the choices of its creatures. It is often thought to be a severe threat to human freedom—all of the concerns with the Leibniz-Ross theory point in the same direction.
The suggestion that there are logically possible states of affairs that is nevertheless logically impossible that an omnipotent being, or an omnipotent being who also has the other traditional divine attributes, should actualize. This line of reasoning led Plantinga to dub the view that God can actualize any possible world “Leibniz’s Lapse.” [xviii There is disagreement about exactly which, or how many, an omnipotent being cannot possibly bring about possible states of affairs. For instance, philosophers disagree about whether the claim that an omnipotent being exists is necessarily valid, false, or contingent.
Suppose it is a contingent matter whether an omnipotent being exists. In that case, the state of affairs of no omnipotent being ever existing is possible but cannot possibly be brought about by an omnipotent being. Perhaps the most widely accepted examples and those Plantinga focuses on are statements about creatures’ free choices. Plantinga believes that it is logically impossible that any being other than Caesar should bring about the possible state of affairs, such as Caesar’s freely choosing not to cross the Rubicon. If Caesar’s not crossing the Rubicon had been brought about by some other being (for example, God), then Caesar would not have freely chosen. If it is accepted that there are some possible states of affairs that it is impossible that an omnipotent being should bring about, a more complicated analysis of omnipotence is needed. An obvious candidate is:
(5) S is omnipotent =df S can bring about any state of affairs p such that it is logically possible that S brings about p
However, this brings back the McEar objection, which the Leibniz-Ross theory had escaped. It is essential to McEar that he never brings about anything other than scratching his ear. It is, therefore, impossible that McEar brings about some other state of affairs. As a result, this definition, once again, wrongly counts McEar as omnipotent, provided that he can scratch his ear. Some philosophers have responded by arguing that there could not possibly be such a being as McEar.[xix] Others have given up on the project of giving a general analysis of omnipotence. [xx] Still others have advocated theories of omnipotence, which make unique accommodation to creaturely freedom. [xxi]
Erik J. Wielenberg (2000) advocated a different approach to the problem. According to Wielenberg, omnipotence cannot be analyzed simply by considering which states of affairs an omnipotent being could or could not bring about. Instead, it is necessary to consider why the being could or could not bring them about. Wielenberg proposes the following analysis:
(6) S is omnipotent =df; there is no state of affairs p such that S cannot bring about p at least partially due to lack of power.
The analysis avoids attributing omnipotence to McEar since McEar’s limitation seems to be partially due to a lack of power. It also solves the problem of the consistency of God’s inability to do evil with omnipotence since God’s inability to do evil is not due to a lack of power. Finally, according to Wielenberg, if it is true that even an omnipotent being could not bring about Caesar’s freely choosing not to cross the Rubicon, then this must be due not to a lack of power but the logic of the situation. Wielenberg’s account’s chief limitation is that it uses some unanalyzed notions whose analysis philosophers have found quite harrowing. These are the notion of lack of power and the notion of one state of affairs obtaining partially due to another state of affairs obtaining. Without analyses of these notions, it is hard to tell whether Wielenberg’s analysis is self-consistent and whether it is consistent with other traditional divine attributes.