  Related to the classic paradoxes of logic and set theory is the Paradox of the Stone. One begins by granting the basic dilemma, as an evident instance of LEM: either God is omnipotent or God is not omnipotent. With omnipotence, He can do anything, and in particular He can create a stone, call it s, that is so heavy even He cannot lift it. But then there is something He cannot do, viz. (ex hypothesi) lift s. But this is a violation of LNC: God can lift s and God cannot lift s.  This paradox, and the potential challenge it offers to either LNC or the possibility of omnipotence, has been recognized since Aquinas, who opted for retaining the Aristotelian law by understanding omnipotence as the capacity to do only what is not logically impossible.  (Others, including Augustine and Maimonides, have noted that in any case God is “unable” to do what is inconsistent with His nature, e.g. commit sin.) For Descartes, on the other hand, an omnipotent God is by definition capable of any task, even those yielding contradictions. Mavrodes (1963), Kenny, and others have sided with St. Thomas in taking omnipotence to extend only to those powers it is possible to possess; Frankfurt (1964), on the other hand, essentially adopts the Cartesian line: Yes, of course God can indeed construct a stone such that He cannot lift it—and what's more, He can lift it! (See also Savage 1967 for a related solution.)