“Can God create a stone he cannot lift?” Queries of this form are intended to present a fatal dilemma to the notion of omnipotence: either there is a stone God cannot lift or a stone He cannot create. Let’s consider the predicate logic of the statement “God cannot create a stone he cannot lift”:

Let:

• C(x) refer to that which God can create, and
• L(x) refer to that which God can lift

~∃x[C(x) ∧ ~L(x)] 

≡ ∀x~[C(x) ∧ ~L(x)] (via equivalence)

≡ ∀x[~C(x) ∨ L(x)] (via De Morgan’s Law)

≡ ∀x[C(x) → L(x)] (via equivalence)

In other words, the statement “there is no such x that God can create but cannot lift” is logically equivalent to “if God can create x then He can lift x”.

The important lesson to take away is that it is no embarrassment of omnipotence that God should not be capable of contradictory or otherwise impossible things. God cannot, for example, kill or create Himself. He cannot lie, cheat, steal, or erase His own memory. What the logic of these kinds of attempts reveals is that there is a more fundamental reading of their claims. A reading that, far from posing a dilemma for omnipotence, rather serves as a restatement of God’s omnipotence in action—it is not simply that God cannot create a stone that he cannot lift, but that God can lift all created stones.

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