Divine omnipotence and impossible tasks: An intensional analysis

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Atheists are frequently content to argue God's nonexistence using contingent premises concerning the existence of evil or, more plausibly, concerning the enormous quantity of evil in the world. But sometimes they are more aggressive. They may try to argue that God cannot exist because the very concept God (taken here as including the properties of being omnipotent, omniscient, and perfectly good) is logically self-contradictory or inconsistent. This takes some doing since the conception is certainly not obviously inconsistent. One collection of arguments in this vein focuses on the concept of omnipotence and attempts to show that it is incoherent to suppose the conception actually applies to something. A typical example of this sort is the "Paradox of the Stone." Can God make a stone which even He cannot lift? Yes? Then there is something which He cannot do, viz., lift said stone. No? Then there is something which He cannot do: make such a stone. In either case, God is not omnipotent. Hence, of necessity, God cannot be omnipotent. Hence, He cannot exist. Well, what is or at least should be the standard reply is that omnipotence does not require the impossible and creating a stone which an omnipotent being cannot lift is impossible. This is pretty much the answer given by St. Thomas Aquinas ([26], Question 25, Article 3), George Mavrodes ([13]), Alvin, Plantinga ([19]) and others. Actually the argument as stated contains a logical gap (see Section I below), so that if the theist wanted to be strict about it, he could reject the thing after pointing out its invalidity. However, it is relatively easy to fill the lacuna and give the atheist his due. But when this is done, the reasoning is still subject to the objection just explained.