The omnipotence of god and the paradoxes it creates were attempted to be solved by Rene Descartes he theorised that god is completely omnipotent and there is nothing that cannot do e.g. create a stone too big for him to lift. Descartes would then go on the say that although he has created a so called object that he cannot lift he would be able to lift because of his omnipotence no matter how logically impossible the instance. This form of omnipotence is similar to the first version of Peter Geach’s theory of omnipotence of the absolutely omnipotent where god can perform any action even if it breaks the laws of logic however the key difference between the two is that Descartes stands by his theory whilst Peter Geach dismisses the notion of an Absolutely Omnipotent God.
Peter Geach’s solution to the paradoxes that arise to god omnipotence allow him to create 4forms of omnipotence and on form of the almighty he then dismisses the 4 versions of omnipotence and sticks to almighty this that God is not just more powerful than any creature; no creature can compete with God in power, even unsuccessfully. In this account nothing like the omnipotence paradox arises, but perhaps that is because God is not taken to be in any sense omnipotent. On the other hand, Anselm of Canterbury seems to think that almightiness is one of the things that makes God count as omnipotent.
If Descartes’ theory of omnipotence is correct, then any attempt to disprove God’s existence using logic is hopeless. If God can do the logically impossible, then he can both create a stone so heavy that he cannot lift it, and lift it, and so can do all things. Yes, there’s a contradiction in this, but so what? God can, on this understanding of omnipotence, make contradictions true.
Thomas Aquinas had a narrower conception of omnipotence. According to Aquinas, God is able to do anything possible; he can part the red sea, and he can restore the dead to life, but he cannot violate the laws of logic and mathematics in the way that Descartes thought that he could.
Aquinas’ understanding of omnipotence, which is more popular than that of Descartes, also survives the paradox of the stone. For if God exists then he is a being that can lift all stones. A stone that is so heavy that God cannot lift it is therefore an impossible object. According to Aquinas’ understanding of omnipotence, remember, God is able to do anything possible, but not anything impossible, and creating a stone that God cannot lift is something impossible.
Aquinas can therefore answer the question "No" without compromising divine omnipotence.
Alvin plantinga argued that god doesn’t have to has omnipotence as a quality of god as he could choose to limit his power to protect logic and the free will of the human race.
In conclusion god’s omnipotence is logically coherent until god omnipotence attempts something illogical and the it becomes incoherent and completely depends on what way you interpret the omnipotence of god.