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The "pizza" argument against the existence of an all-powerful being goes something like this:

Suppose for a contradiction that there exists an all-powerful being. Then there cannot exist a pizza so big, that He cannot eat it. Therefore, this being cannot create a pizza so big, that He cannot eat it. Therefore, there exists something that this being cannot do. Therefore, this being is not all-powerful, a contradiction.

I don't like calling this the "pizza argument", since it really has nothing to do with pizza. What is this argument actually called?

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    Interesting that you checkmarked the rock answer. Question: Why are rocks better than pizzas in this scenario? – user4894 Mar 4 '15 at 1:07
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    Not better, that's just the traditional form of it, so its the closest to a "name" as we could get. – Cort Ammon Mar 4 '15 at 3:32
  • @user4894 I identified his argument as being of the omnipotence paradox form, with the paradox of the stone being just one example. – Five σ Mar 4 '15 at 19:08
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It looks like a version of the classic omnipotence paradox to me.

For instance, the paradox of the stone:

Could an omnipotent being create a stone so heavy that even he could not lift it? If he could lift the rock, then it seems that the being would not have been omnipotent to begin with in that he would have been incapable of creating a heavy enough stone; if he could not lift the stone, then it seems that the being either would never have been omnipotent to begin with or would have ceased to be omnipotent upon his creation of the stone

One way of getting around this sort of paradox is by noting that omnipotence is with reference to acts that are logically possible. I.e. God cannot perform logical absurdities.

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