Can God make a stone so heavy that He Himself cannot lift it?
If He cannot, then He is not omnipotent since there is something (namely, this) which He cannot do. If, on the other hand, He can do this, He is not omnipotent since there is something else (namely, lift everything) which He cannot do. So in any case He cannot, it would seem, be omnipotent. (331)
In order for God to create something He cannot lift, since nothing exceeds Him in power, He has to create an essentially unliftable stone (EULS). The EULS is an object described by the proposition, "No one can lift it." If God can make the EULS, then the power to lift it is not a possible power which could be instantiated in any being.
This is simply because the conjunction "No one can lift this stone" & "God can lift this stone" is a self-contradiction.
Conversely, if God cannot make an EULS, then of this stone, it will be true that "No one can make it." Since a similar contradiction can be constructed, the power to make what cannot be made is not a possible power and cannot inhere in God.
Still, if God can make an EULS, then He is a strong maker but weak lifter: there is an object that is not subject to His lifting power. Otherwise, God is a weak maker but strong lifter: there is a limit to His creativity, because an EULS is beyond His power to make.
Cowan gives the following example. He, Cowan, is able to make something he cannot lift. E.g., Cowan can make A, B, and C but out of these can lift only A and B. Perhaps Cowan is a real estate developer and can build a house that he cannot lift unaided. A certain Smith is able to lift anything he can make. Smith can lift X, Y, and Z but out of these can make only X. "But no one," Cowan says, "not even God, can do both what I can do and what Smith can do. ... So either Smith or I, although we cannot be logic alone say which, can do something even God cannot do. Thus God cannot be omnipotent." (335)
In this matter at least, humans are seemingly more powerful than God! But that's an illusion: God's power to lift is limited only by something crazy like an EULS. Cowan's power to lift is limited by, say, 200 pounds. Hence God's power to lift infinitely exceeds Cowan's. Furthermore, the EULS that God (by stipulation) can create is itself a testament to His power. Cowan cannot make anything like that.
Again, if God cannot make an EULS, then His creativity is limited only by the fact that His power extends fully to everything He can make, such that no creature can fail to be subject to His will. Smith's power to make is limited to any object that weighs less than, say, 300 pounds. Again, God's power to make is infinitely greater than Smith's. Furthermore and analogously to the previous case, the fact that God's power reaches the innermost depths of every object it encounters is a great-making property in itself.
God's power both to make and lift is infinite at first glance, and it is only by pitting these infinities against each other that a paradox arises. Either answer makes God such that no greater can be conceived. But one must choose one or the other.
We can come up with more apparent problems for omnipotence:
1. Cowan gives an example of the employer's power to hire and fire. Suppose that an employer can fire anyone at will at any time. Then he cannot contract to hire a person with a provision that he must employ him for no less than 6 months. The courts would refuse to uphold such a contract on the grounds that it would constitute a limitation on the power to discharge. If, on the other hand, he can make a contract that, say, gives a professor tenure, then he cannot fire him at his pleasure. (335ff)
2. Can God condemn someone He predestined to salvation? If He can, then predestination is a sham, like the contract to hire in the previous example. If He cannot, then that's a limitation on God's power to convict. Either way one or the other power cannot be possessed by God at the same time.
3. "Is it that God cannot completely control every universe He can create, or that He cannot create a universe He cannot completely control?" (348)
4. "Has the almighty being the power to achieve something which is immune to his later interference? If he has this power, then there are limits to his might and he is no longer almighty; if he lacks this power, he is by virtue of this fact alone not almighty." (Mises, HA, 69-70)
Therefore, Cowan is right: "We cannot have everything, but must be content with the best of all possible gods." (336)