God’s Omnipotence And Sovereignty – Part Four

The Self-Consistency of Omnipotence:

The Paradox of The Stone

Could an omnipotent being create a stone too heavy for it to lift? More generally, could an Omnipotent Being create something it could not control? [i] This question is known as the Paradox of the Stone, or the Paradox of Omnipotence. It appears that answering either “yes” or “no” will mean that the being in question is not omnipotent after all. For suppose that the being cannot create the stone. Then it seems that it is not omnipotent, for there is something that it cannot do. But suppose the being can create the stone. Then, again, there is something it cannot do, namely, lift the stone it has created.

Although the argument is usually initially stated in this form, as it stands, it is not entirely valid. Because a particular being can create a stone it cannot lift, it does not follow that there is something that that being cannot do. It only follows that if the being were to create the stone, there would be something it could not do. As a result, the Paradox is a problem only for necessary omnitemporal omnipotence; that is, for the view that there is a Being who exists necessarily and is necessarily omnipotent at every time. [ii] There is no problem for a Being who is only omnipotent at certain times because the being in question might very well be omnipotent prior to creating the stone (but not after). Furthermore, the stone paradox provides no reason to suppose there could not be a contingently omnitemporally omnipotent being. All the being in question would need to do is decide not to create the stone, and then it would be omnipotent every time.

Nevertheless, the Stone Paradox is of interest because necessary omnitemporal omnipotence has traditionally been attributed to God. The Stone Paradox has been the main focus of those attempting to specify precisely what an omnipotent being could, and could not, do. However, some questions arise even for those who do not wish to insist on necessary omnitemporal omnipotence. Could an omnipotent being draw a square circle? Descartes notoriously answered “yes.” However, at least since Aquinas, Western philosophical and theological traditions have almost universally given the opposite answer. The Paradox of the stone has prompted several responses that employ different techniques to address the apparent Paradox. [iii]

One comes from George Mavrodes, who argues that the supposed Paradox is spurious since the notion of a stone that is too heavy for God to lift is contradictory; hence, the lifting of such a stone involves a logically impossible state of affairs. A person might make an object too heavy for the person to lift. Still, on the assumption that God is omnipotent, the phrase “a stone too heavy for God to lift” means “a stone that cannot be lifted by Him whose power is sufficient for lifting anything.” [iv]

Mavrodes suggested that comparing God’s lifting power and creating power could see the contradictory nature of “a stone too heavy for God to lift.” Suppose one takes the Paradox seriously and thinks that it forces some limitation on God’s omnipotence. In that case, one might maintain the full power of God’s infinite ability to lift things and restrict God’s ability to create, admitting that God cannot create such a stone. In such a case, has one given up anything? Mavrodes thinks not. Since God’s power to lift is infinite, God’s ability to create is still infinite. God can still create everything possible to lift; therefore, God is not limited to lifting or creating power. [v]

The main difficulty with Mavrodes’s solution to the Paradox of the stone is that it proceeds based on the assumption that God is omnipotent; however, as Richard Swinburne points out, the main thrust of Savage’s Paradox is to call into question the coherence of the very notion of omnipotence. [vi] Mavrodes’ claim the phrase “a stone too heavy for God to lift” is self-contradictory and hinges upon God’s being omnipotent. Still, one can hardly use the notion of omnipotence to resolve the Paradox until the Paradox has been resolved. Whereas Mavrodes’s response to the Paradox of the stone assumes that God cannot do logically impossible things, Harry Frankfurt takes a different line in “The Logic of Omnipotence” by arguing that a response to the Paradox does not require such an assumption. [vii]

Frankfurt points out that if we reject the principle that God cannot do logically impossible things, a solution to the Paradox comes very easily. If God can do logically impossible things, then if God can create the stone, he can just as easily lift it; that is, doing one logically impossible thing, he can do another. [viii] Frankfurt’s response to the Paradox of the stone, which relies upon the principle that God can do logically impossible things, gives away too much since it amounts to abandoning logic altogether. Suppose the main force of the Paradox is to attack the notion of omnipotence as logically incoherent. In that case, this “response” seems to strengthen the Paradox instead of solving it by apparently admitting that the notion of omnipotence is fundamentally paradoxical and even contradictory. Richard Swinburne has also responded in length to the Paradox of the stone. After considering several different formulations of the notion of omnipotence, Swinburne finally settles upon the following (which is [D] in his scheme):

[D]: a person P is omnipotent at a time t if and only if he can bring about any logically contingent state of affairs after t, the description of which does not entail that P did not bring it about at t.[ix] Swinburne relies upon [D] to defuse the Paradox. When one introduces temporal operators into the definition of omnipotence; then one can no longer talk of omnipotence simpliciter. But one must talk of omnipotence relative to a particular time. [D] logically allows a person to be omnipotent at one time, not at another. Swinburne maintains that “in the ordinary sense of ‘person,’ “a person may choose to exercise his omnipotent ability in such a way to make himself case to be omnipotent at some future time. [x]

So, if God exercises his ability to make the stone at t, he will cease to be omnipotent after t. While Swinburne sees his temporal-referenced, modified account of omnipotence as nonrestrictive, it is questionable that [D] retains a notion of omnipotence that would be acceptable to traditional theists. In the first place, there is no “ordinary sense of ‘person’ “according to which it makes sense to talk about a person being omnipotent. It is only in an extraordinary sense and only in God’s unique case that omnipotence is even associated with the notion of personhood, which suggests that there must be something logically unique about the property. The view that an omnipotent being could do absolutely anything, even the logically absurd, is known as “voluntarism.” Simply rejecting voluntarism does not answer the Stone Paradox.

Creating a stone too heavy for its creator to lift is a possible task. Another possible task that an omnipotent being can not perform is knowing that one has never been omnipotent. For human beings, this is a reasonably simple task, but for an omnipotent being, it would seem to be impossible. The general problem is this: The fact that it is logically possible that some being performs a specified task (the task itself does not contain a contradiction) does not guarantee that it is logically possible for an omnipotent being to perform that task. Coming to know that one has never been omnipotent is an example of a single task that is logically possible for some being to perform, but which is logically impossible for an omnipotent being to perform.

The Stone Paradox provides an example of two tasks (creating a stone its creator cannot lift and lifting the stone one has just created) such that each task is logically possible. Still, it is logically impossible for one task to be performed immediately after the other. It is necessary to say something more precise to meet these challenges than to affirm that an omnipotent being would be able to do whatever is possible. These more precise theories can be divided into two classes: ‘act theories,’ which say that an omnipotent being would be able to perform any action, and ‘result theories,’ which say that an omnipotent being would be able to bring about any result.

 Voluntarism

René Descartes, almost alone in the tradition of Western theology, held that God could do anything. Even affirming, “God could have brought it about … that it was not true that twice four make eight.” [xi] If this doctrine is adopted, then the Stone Paradox is dissolved: If an omnipotent being could make contradictions accurate, then an omnipotent being could make a stone too heavy for it to “lift and still lift it.” [xii] However, this doctrine is of questionable coherence. To cite just one difficulty, it would seem to follow from the claim that God could make 2 x 4 = 9 that possibly God makes 2 x 4 = 9. However, it is a necessary truth that if God makes 2 x 4 = 9, then 2 x 4 = 9. In standard modal logics, possibly p and necessarily if p, then q together entail possibly q, so it seems to follow that possibly 2 x 4 = 9. Descartes does not accept this consequence, but it is unclear how he can avoid it. It has been suggested that he may be implicitly committed to rejecting one or more widely accepted modal axioms. [xiii]. These absurdities have led to philosophers’ and theologians’ nearly universal rejection of voluntarism.

Notes

•   [i] Mackie 1955: 210
• [ii] Swinburne 1973; Meierding 1980
• [iii] In addition to the responses discussed here, see Alvin Plantinga, God and Other Minds (Ithaca, N.Y.: Cornell University Press, 1976). 168-73.
• [iv] George Mavrodes, “Some Puzzles Concerning Omnipotence,” Philosophical Review, 72, 1963, 221-23.
• [v] Mavrodes, 114.
• [vi] Richard Swinburne, The Coherence of Theism, 158.
• [vii] Harry Frankfurt, “The Logic of Omnipotence,” The Philosophical Review, Vol. 73, 1964, 262-63. Reprinted in Philosophy of Religion: An Anthology, edited by Louis Pojman (Belmont, Calif.: Wadsworth, 1998), to which the page numbers here refer.
• [viii] Frankfurt, 282
• [ix] Richard Swinburne, The Coherence of Theism, 156.
• [x] Swinburne, 161. For a discussion of temporal considerations in the notion of omnipotence as well as a distinction concerning different levels of omnipotence (“first-order” and “second-order” omnipotence), see J.L., Mackie, “Evil and Omnipotence,” Mind, Vol 64, 1955, 200-12
• [xi] Descartes 1984-1991: 2:294
• [xii] Frankfurt 1964.
• [xiii] Curley 1984