Omnipotence and Classical Theism
Classical theists like Aquinas never understood omnipotence to mean God can just do anything. Because God is incorporeal, God cannot just do anything, like eat salmon or float in the Atlantic. This is why Aquinas couched omnipotence in God’s ability to produce whatever is inherently producible: “Whatever can have the nature of being falls within the range of things that are absolutely possible, and it is with respect to these that God is called all-powerful.” (De Potentia I, 1, 7).
Brian Davies phrases it as God can make to be anything which can be thought of as able to be.
This understanding of omnipotence sidesteps several (but not all) concerns raised by contemporary philosophers. Can God lift a stone to heavy to lift? That depends. Is a stone that God is unable to lift capable of being? Most classical theists — in fact, most theists in general — say no, that is not actually something that could exist. Any stone, by nature, is inherently liftable. In which case, God not being able to produce such a stone does not count against God’s omnipotence.