Omnipotence

In "Anselm and Actuality", David Lewis presents an interpretation of the ontological argument. He argues that while it is a valid argument, it isn't sound; according to Lewis, one of the premises is false because the actual world is not unique. What he means by this is that all possible worlds are equally concrete, just like the world around us; that is, they are dynamic spatiotemporal expanses of energy and mass. To my mind, the actual world is unique; even if there were spatiotemporally distinct cosmoses from ours, that doesn't mean they are entire actual worlds individually. It's just that the actual world would consist of two or more spatiotemporally distinct dynamic expanses of energy and mass.

So, with that in mind, let's continue on to the argument itself. The argument consists of three premises: the Consistency Premise, the Possibility Premise, and the Actuality Premise. It's the Actuality Premise which Lewis argues is false. Some philosophers may argue that the Possibility Premise is (also) false because they think that there are metaphysical principles in addition to the minimal constraint of logical consistency; I can't think of any way of verifying supposed metaphysical principles beyond seeing if they are logically necessary or at least consistent. Also, some philosophers may argue that the Consistency Premise is false, based on "rock heavier than an omnipotent being can move" objections; my counterobjection to this is that the concept of something heavier than can be moved by an omnipotent being is inconsistent, that is, such a thing is literally impossible, which means that an omnipotent being doesn't have to be able to do it. That is, an omnipotent being only needs to be able to do all possibilities; this is so-called logical omnipotence.

1. Consistency: The concept of the omnipotent is logically consistent.
2. Possibility: Logical consistency implies metaphysical possibility.
3. Actuality: Something actual is more powerful than something merely possible.
Conclusion: The omnipotent is actual.

Another presupposition of this argument is that the concept of omnipotence is comprehensible. Perhaps omnipotence is so far beyond our finite capacities that even our best understanding of it fails woefully short of truly grasping the nature of omnipotence. I would counter that we have developed finitely long sentences which intuitively express the nature of infinity and the transfinite hierarchy. In a meta-predicate logic, there are propositions which intuitively express simple infinity, such as that of the natural numbers (0, 1, 2 ...). Beyond that, you can prove that there are infinities which are bigger than simple infinity; for instance, the real numbers (such as pi, e, etc.) are more numerous than the natural numbers. You can also prove that for each infinity, there's at least one other one which is strictly larger than it. So, the question becomes, how many possible powers are there?

A power is an ability to bring about some possible state-of-affairs. So, how many possible states-of-affairs are there? Even if the physical is all there is and is necessarily finite, there's no logical limit on how big it can be; that is, it is finite, but arbitrarily large. There may be limits on how much energy you can stuff into a particular volume of spacetime (the amount that would cause a black hole to form in that volume), but there seemingly is no logical limit on how big spacetime can itself get (the rate of cosmic expansion is accelerating currently, in fact). That means, there are at least a simple infinity of possible states-of-affairs that are consistent with the laws of nature; but there's seemingly no logical necessity to the laws of nature. Given that there can be spatiotemporally distinct regions of the actual world, there could be other universes out there that operate under different laws of nature; each set of laws would generate at least a simple infinity of possible states-of-affairs. So, the physical cannot be all there is, since it is necessarily finite, but something infinite, namely, possibility itself exists given that the physical exists (which it apparently does). So, the number of possible states-of-affairs is at least simply infinite, which means there are at least a simple infinity of powers. So, given that the omnipotent exists and has all powers, it is not a finite being; if the physical is necessarily finite, then the omnipotent is non-physical.