Overview
A common modern version of the omnipotence paradox is expressed in the question: "Can create a stone so heavy that it cannot lift it?" This question generates a dilemma. The being can either create a stone which it cannot lift, or it cannot create a stone which it cannot lift. If the being can create a stone that it cannot lift, then it seems that it can cease to be omnipotent. If the being cannot create a stone which it cannot lift, then it seems it is already not omnipotent.
The problem is whether the above question is ad hoc, or, instead, is inherently required by the concept of omnipotence. If it is ad hoc, then the concept of omnipotence does not include being subject to be exceeded. If it is inherently required, then there is no way to exclude answering the question in either the affirmative or the negative, and, thus, no way to determine whether an omnipotent being is logically possible or impossible. But, if the question is inherently required by the concept of omnipotence, then it seems the logic which allows it to be inherently required is a paradox since the particular concept of omnipotence which requires it is a paradox. In short, the act of seeming to find omnipotence to be a contradiction-of-terms is founded on the act of conceiving something against which to construct the contradiction: prior to any ‘act’, omnipotence is conceived as coherent both with itself and with the possibility of knowledge (which begs the question of what is the knowledge that constitutes the identifiability of omnipotence-as-a-paradox?).
But, whether the concept of omnipotence itself is a material paradox, or is simply too obscure to us to preclude being construed by paradoxical thinking, the central issue of the omnipotence paradox is whether the concept of the 'logically possible' is different for a world in which omnipotence exists from a world in which omnipotence does not exist. The reason this is the central issue is because our sense of material paradox, and of the logical contradiction of which material paradox is an expression, are functions of the fact that we presuppose that there must be something which exists which is inherently meaningful or logical, that is, which is concretely not a compound of other things or other concepts. So, for example, in a world in which exists a materially paradoxical omnipotence, its very paradoxicality seems either to be a material-paradox-of-a-material-paradox, or to be a non-paradox per the proposition that it exists (i.e., if it exists, then nothing has inherent meaning, including itself). Whereas, a world in which exists non-paradoxical omnipotence, its own omnipotence is coextensive with whatever is the concrete basis of our presupposition that something must be inherently meaningful.
The dilemma of omnipotence is similar to another classic paradox, the irresistible force paradox: What happens when an irresistible force meets an immovable object? One response to this paradox is that if a force is irresistible, then, by definition, there is no truly immovable object; conversely, if an immovable object were to exist, then no force could be defined as being truly irresistible. Some claim that the only way out of this paradox is if the irresistible force and the immovable object never meet. But, this way out is not possible in the omnipotence case, because the purpose is to ask if the being's own inherent omnipotence makes its own inherent omnipotence impossible. Moreover, an object cannot in principle be immovable, if there is a force which may move it, regardless of whether the force and the object never meet. So, while, prior to any task, it is easy to imagine that omnipotence is in state of coherence with itself, some imaginable tasks are not possible for such a coherent omnipotence to perform without compromising its coherence.
Read more about this topic: Omnipotence Paradox