The omnipotence paradox is generally summed up by the phrase or some form of the phrase "Can God create a rock so heavy that he can't lift it?". Either God can or can't create the rock. If he can create a rock so big he can't lift it then he's not omnipotent because he can't lift it. If he can't create a rock that big in the first place then he's still not omnipotent.
Accidental vs. Essential Omnipotence
The omnipotence paradox may be resolved by stating that God is either accidentally or essentially omnipotent.
An accidentally omnipotent God could resolve the paradox by creating a rock so heavy that he can't lift it and thus, ceases to be omnipotent. However, one could argue that it's hard to tell if a god of this sort was ever truly omnipotent or just in possession of great power. One way to reconcile this is to suggest that the God is really omnipotent. But just as many of us will not want to drive a knife through our eyes, God too may not choose to make himself not omnipotent anymore, although he has the ability to do so. Again, the point that God is not truly omnipotent can be raised. This point, however, commits the No true Scotsman fallacy. Put simply, an accidentally omnipotent God IS omnipotent and can thus make himself not omnipotent anymore.
Essential omnipotence states that it is impossible for the god to be non-omnipotent. Some theists may argue that God is not "absolutely omnipotent" but is merely "omnipotent". This is an extremely dishonest use of words, for omnipotence is suppose to be the highest possible attainable state of power in which the being can acheive anything, and adding the term "absolutely" means nothing. One can say that God is "absolutely absolutely absolutely omnipotent", which gives a similar empty effect. Nonetheless, according to Peter Geach, if Y is absolutely omnipotent, then Y "can do everything absolutely. Everything that can be expressed in a string of words even if it can be shown to be self-contradictory," Y "is not bound in action, as we are in thought by the laws of logic." (See Wikipedia: Omnipotence Paradox) On the other hand, being merely "omnipotent" means that Y will be subjected to the laws of logic. "Absolute omnipotence" will put Y in a precarious position of falling straight into the omnipotence paradox. Mere "omnipotence", however, shows that Y is unable to acheive everything anymore, as there is something that Y cannot do, which is to defy the laws of logic which it has supposedly created formerly. The term "omnipotence" used to described Y will then be very misleading.
Even if we grant that God can do all things except those which are "logically impossible", there still seem to be limits on God's abilities in practice, though not prohibited by logic. Can God act in a way that is evil? By definition, God is supposed to be omnibenevolent, so the answer should be no. Yet people can do many things that are evil, so clearly being evil is logically possible, but God supposedly cannot do it.
God's Free Will
Apologists may respond to the above argument by stating that it isn't that God can't do evil, it's just that he always uses his perfect free-will to choose not to. This, of course, raises the question of why God didn't create humans the same way. It would be a good solution to the problem of evil.
Another answer to the above argument is the assertion that being good is "God's nature," and He can only do things that aren't against His own nature. At this point, the concept of omnipotence starts to get completely fuzzy. "God's nature" appears to be defined as "the things that God is capable of doing." In this case, the claim of omnipotence is nothing more than the tautological statement, "God can do all things that God can do." Under this usage, people are also "omniscient."
The fundamental problem may be that the concept of being all-powerful is ill-defined and lends itself to equivocation.
Standard of Morality
A third answer to the above: Because God is the defining standard of morality, anything that God does is good, regardless of how horrendous the same action would be if it were conducted by a human. This neatly resolves the omnibenevolence issue, but does not address omnipotence.
Omnipotence vs omniscience
An omnipotent god is further confused when it is also granted omniscience, that is knowledge of all things past, present and future. If a god knows what is going to happen in the future, it is not able to omnipotently change that future because it is limited to what it knows will happen. If a god can omnipotently change that future then that god can not of known the future in the first place and is therefore not omniscient.
For example, the omnipotent and omniscient God at Time X speculates that Scenario A will occur 10 minutes later. 5 minutes later, one then wonders whether this God can cause Scenario B, instead of A, to occur after another 5 minutes. If he can, then he is no longer omniscient; if he cannot, then he is no longer omnipotent.
One must note that omnipotence can easily lead to omniscience. An omnipotent god has the ability to do anything with the unlimited power of his, that is, he can gain the knowledge of all things past, present and future. As such, this may be considered as another form of the omnipotence paradox.
Richard Swinburne invented the following definition of omnipotence in an attempt to define this paradox out of existence:
- "A person P is omnipotent at a time t if and only if he is able to bring about any logically contingent state of affairs x after t, the descriptions of which does not entail that P did not bring x about at t. This is subject to the restriction that a person is no less omnipotent for being unable to bring about a state of affairs if he believes that he has overriding reason not to bring it about. So, God is omnipotent even if he is unable to do what he believes wrong. The paradox of the stone has false premises."
Swinburne's argument depends on linear time, or at least the ability to describe events in a linear fashion. Furthermore, the concept of a "Logically contingent state of affairs" presumes that person P is subject to the laws of logic - as the alleged creator of the universe that contains these laws, one would presume that God also created these laws and retains the ability to alter them.
The premise of the stone-paradox is not whether god chooses to do only what he considers right. The paradox is arises when determining whether god is CAPABLE of performance. Performance is inconsistent with the logic of this universe. God could not simultaneously maintain the laws of this universe AND break the paradox.
Expanding this argument, we can further state that God cannot create even a single atomic particle without violating the logic of this universe, and thus demonstrating a flaw in his alleged omnipotence.