This argument is a favorite among folks who like to stump their Sunday school teachers:
Can God create a burrito so hot that even he cannot eat it?
Can God create a rock so big that even he cannot lift it?
Here are some responses that the teacher shouldn't give.
- Definition: God is omnipotent.
- Definition: An omnipotent object can do anything.
- Conclusion: If God exists, he can create an uneatable burrito.
- Conclusion: If God exists, he can eat any burrito.
- Conclusion: If God exists, there can exist a burrito that is both eatable and uneatable.
- Definition: An object that is uneatable is not eatable.
- Conclusion: God does not exist.
Yes, this is a valid and rigorous proof, spelled out as thoroughly as I could make it. Did you notice anything about the argument? There are no premises. This is somewhat unusual in a logical proof. It means that there is no way to question the original assumptions of the proof, because there are no original assumptions.
What you can question, however, are the definitions. It's not that the definitions are wrong per se. In logic, one definition is about as good as another. What's wrong is that these definitions do not necessarily match the definitions we use in everyday language. Who's to say that God is omnipotent? Who's to say that omnipotence really means capable of doing everything?
I mean, who really cares if God can't make uneatable burritos? Who cares if he can't make round squares? As long as God can create universes, answer prayers, and manifest himself in human form, I think most people will be satisfied.
And so, any serious thinker would simply modify the definition of God or of omnipotence to get around the burrito argument. That modification is: the definition of "omnipotence" does not allow for any logically impossible action. It's a rather trivial modification, that doesn't change anything else about God in any way whatsoever. And it's not even like this is a new development for theology or anything--it dates at least as far back as St. Agustine in the 5th century.
It's quite common to include a whole host of other exceptions to the definition of omnipotence. God can't sin. God can't contradict his own will. God can't change his mind. God can't cause himself to lose omnipotence (we can add a further exception to this exception so that God can make part of himself human). God can't contradict free will. Etc. Etc. Just about any omnipotence paradox you can think of can be fixed by a trivial exception. No, it's not really special pleading, not anymore than "You can't divide by zero" is special pleading.
With all these exceptions, you might ask, "How can you still call God omnipotent?" Easy. He's still more omnipotent than you are, right? More omnipotent than anything else imaginable? That is sufficient.
I might add that the free will exception allows for an interesting variation on the burrito paradox, to which the answer is a straightforward "yes":
Can God create a being with will so free that even he cannot control it?But I wouldn't read too much into it.