Omnipotence does not mean breaking the laws of logic

Statement

A common response from philosophers is that the paradox assumes a wrong definition of omnipotence. Omnipotence, they say, does not mean that God can do anything at all but, instead, that he can do anything that is logically possible; he cannot, for instance, make a square circle. Likewise, God cannot make a being greater than himself, because he is, by definition, the greatest possible being. God is limited in his actions by his nature. The Christian Bible, in passages such as Hebrews 6:18, says it is "impossible for God to lie".

A good example of a modern defender of this line of reasoning is George I. Mavrodes. Essentially, Mavrodes argues that it is not a limitation on a being's omnipotence to say that it cannot make a round square. Such a "task" is termed by him a "pseudo-task" as it is self-contradictory and inherently nonsensical. Harry Frankfurt—following from René Descartes—has responded to this solution with a proposal of his own: that God can create a stone impossible to lift and also lift said stone.

For why should God not be able to perform the task in question? To be sure, it is a task—the task of lifting a stone which He cannot lift—whose description is self-contradictory. But if God is supposedly capable of performing one task whose description is self-contradictory—that of creating the problematic stone in the first place—why should He not be supposedly capable of performing another—that of lifting the stone? After all, is there any greater trick in performing two logically impossible tasks than there is in performing one?

If a being is accidentally omnipotent, it can resolve the paradox by creating a stone it cannot lift, thereby becoming non-omnipotent. Unlike essentially omnipotent entities, it is possible for an accidentally omnipotent being to be non-omnipotent. This raises the question, however, of whether the being was ever truly omnipotent, or just capable of great power. On the other hand, the ability to voluntarily give up great power is often thought of as central to the Christian doctrine of incarnation.

If a being is essentially omnipotent, it can also resolve the paradox. The omnipotent being is essentially omnipotent; therefore, it is impossible to be non-omnipotent. Further, the omnipotent being can do what is logically impossible—just like the accidentally omnipotent—and has no limitations except the inability to become non-omnipotent. The omnipotent being cannot create a stone it cannot lift.

The omnipotent being cannot create such a stone because its power is equal to itself, thus removing the omnipotence, for there can only be one omnipotent being, but it nevertheless retains its omnipotence. This solution works even with definition 2, as long as we also know the being is essentially omnipotent rather than accidentally so. However, non-omnipotent beings can compromise their own powers, which presents the paradox that non-omnipotent beings can do something (to themselves) which an essentially omnipotent being cannot do (to itself). This was essentially the position Augustine of Hippo took in his The City of God:

For He is called omnipotent on account of His doing what He wills, not on account of His suffering what He wills not; for if that should befall Him, He would by no means be omnipotent. Wherefore, He cannot do some things for the very reason that He is omnipotent.

Thus, Augustine argued that God could not do anything or create any situation that would, in effect, make God not God.

In a 1955 article in the philosophy journal Mind, J. L. Mackie tried to resolve the paradox by distinguishing between first-order omnipotence (unlimited power to act) and second-order omnipotence (unlimited power to determine what powers to act things shall have). An omnipotent being with both first and second-order omnipotence at a particular time might restrict its own power to act and, henceforth, cease to be all-powerful in either sense. There has been considerable philosophical dispute since Mackie about the best way to formulate the paradox of omnipotence in formal logic. More recently, Budaev trivialized the paradox of the stone by converting it to an arithmetic form: "Can a person make such a big number that he/she cannot imagine a number greater than that?", apparently resulting in a solution similar to that by Savage: "One can imagine any number and always make an even bigger number".

God and logic

Although the most common translation of the noun "Logos" is "Word" other translations have been used. Gordon Clark (1902–1985), a Calvinist theologian and expert on pre-Socratic philosophy, famously translated Logos as "Logic": "In the beginning was the Logic, and the Logic was with God and the Logic was God". He meant to imply by this translation that the laws of logic were derived from God and formed part of Creation, and were therefore not a secular principle imposed on the Christian world view.God obeys the laws of logic because God is eternally logical in the same way that God does not perform evil actions because God is eternally good. So, God, by nature logical and unable to violate the laws of logic, cannot make a boulder so heavy he cannot lift it because that would violate the law of non contradiction by creating an immovable object and an unstoppable force.This raises the question, similar to the Euthyphro Dilemma, of where this law of logic, which God is bound to obey, comes from. According to the theologians Norman Geisler and William Lane Craig, this law is not a law above God that he assents to but, rather, logic is an eternal part of God's nature, like his omniscience or omnibenevolence.