This is a sufficient definition and from human POV; that is, if something like what is described existed, we would call it omnipotent.
Let U be a closed universe, or something very near closed. Closed means that the things inside it can’t get to or sense the outside, and hence are unlikely to know anything about it. Let G be an undefined entity (you can read it as God if you really want to).
G is omnipotent with regards to U if G can shape U into whatever native form it could encompass. So, for example, in our universe an omnipotent G could create and remove physical objects at will, but it would not be necessary for G to be able to create things fundamentally beyond our understanding (I have a few problems with trying to create examples for certain reasons), because they are not part of our universe as is.
From this basis, a theorem: G must be outside the conception of time (or entropy or another measure of change, with apologies to everyone who knows physics for probably misusing “time” and “entropy”) that exists in U.
If this was not the case, G could first (within the dominant measure of change) create the indestructable wall and then create a cannonball that destroys everything it touches, third make them touch, which results in impossible outcome, and hence is not true. This does not happen when G is outside the conception of change as it applies in U, because then G would both create something and cancel it at the same time, which amounts to not creating the thing to start with, which leads to no paradox, because G didn’t actually create one of the conflicting absolutes after all.
The definition also assumes G is omniscient, but when talking about omnipotence, that is kinda trivial.
This is a semiformal proof. A formal one would be hard to understand without pictures and would require me checking out the English translations of a number of words, which I am not inclined to do.
A square is defined as an ordered set of four points, no three of which are on the same line, and further that the angles thus created are all right (there is a bit more, but it is not too relevant). Circle is defined as a set of points that are from given distance (radius) from a given point. Because a square does not exist in hyperbolic geometry, it is sufficient to think about Euclidean geometry. Assume that there is a square circle. Let A and B be two points of the circle that are part of the same edge (i.e. that edge does not go through the circle’s center). Let C be a point that is between A and B. Distance from The center of the circle to C is lesser than the distance to A or B, so it is also lesser than the radius. Accordin to one axiom I am a bit too lazy to check out, it is possible to find D so that D is behind C when observed from the circle’s center and D’s distance from the center is the circle’s radius. Hence D is part of the circle. D is not anyof the original points that defined the circle, because if it was either of the unnamed ones, the definition of rectangle would get messy, and if it were A or B, C would also be A or B, which contradicts the choice of C. Hence, there are no square circles. Qued est demonstratum.
This diversion due to another discussion.
Mathematics is the art of proving p.
Philosophy is the art of justifying p.
A proof is almost always a justification.