The Limits of Omnipotence
As my class in Kant took its course through the "Ideal of Pure Reason", the third and final chapter of the second book of the Transcendental Dialectic in Kant's Critique of Pure Reason, I was once again catapulted into the subspace of Metaphysics concerning God. This is by far one of the most interesting parts of philosophy, in my humble opinion. During the class discussion it was brought to my attention that most of the philosophically-trained population regards the realm of metaphysical possibility to be properly contained in the realm of logical possibility. That's philosophese for "God can't do anything that's not logically possible".
The realm of metaphysical possibility is generally regarded as those effects that an omnipotent being could cause. The realm of logical possibility contains every effect that does not imply a logical contradiction (A and not A). For example, it would be logically impossible for an apple to be red-all-over and green-all-over at the same time, because obviously if an apple that was red-all-over had even the slightest bit of green on it, it would fail to be red-all-over, which would contradict our assumption. Of course, properly contained within these is the realm of physical possibility (what we can do in the external world), and within that the realms of economic possibility (what we can afford), legal possibility (what the law allows), political possibility, moral possibility, etc etc. These lesser realms are all overlapping each other, at it would seem that none properly contains any other. Of course, you can come up with realms of possibility and reason about how they fit in with the others as much as you like, but I shall leave that as an exercise for the reader.
So anyway, during the class discussion, my professor and I agreed that the proposition that "the realm of metaphysical possibility is properly contained within the realm of logical possibility" is, in short, total crap. But before we get into exactly why that is, let us review some basic properties of arguments (a.k.a. "proofs", for the loose-of-tongue).
The basic components of an argument are the premises, a logical progression, and a conclusion. All arguments aim to "prove" that the conclusion is true by following a logical progression from the premises. An argument is said to be "valid" if all the steps in the logical progression are correct - that is, if they do not contain any invalid moves, called "fallacies". This is analogous to the steps of algebraic manipulation, how each algebraic step follows from the previous one by some theorem or another. An argument is said to be "sound" if it is valid AND all of its premises are true. One can show that the argument fails to establish its conclusion by finding a logical fallacy or by showing one or more premises to be false. It's important to note that this is quite far from showing that the conclusion is false, and instead only shows that the argument presented is insufficient to prove that it is true. Asserting that a conclusion is false is a much stronger claim, which requires showing its negation to be true - another whole argument with its own premises and logical progression.
There are many logical fallacies out there that everyone commits from time to time, often without realizing it until someone else points it out. The fallacy we're going to concern ourselves with here is that of "Begging the Question". The fallacy of Begging the Question is one in which the argument uses the conclusion itself as a premise that is then used to establish the conclusion. This is often considered to be a form of circular reasoning. In it's simplest formulation, an argument that begs the question takes the form "Assume p. Aha! Therefore, p!" In a strict sense of "valid", this argument is completely valid - there is nothing wrong with the logic here. After all, given p we definitely have p, right? However, it makes no progress to establishing p on its own, and requires some outside argument to save it. If no outside argument exists that could save it, we're stuck not knowing the truth-value of the conclusion. For a powerful example of Begging the Question with profound consequences, please see David Hume's Problem of Induction.
So what does all this have to do with the limits of omnipotence? Recall the original claim: "the realm of metaphysical possibility is properly contained within the realm of logical possibility", or, equivalently: "an omnipotent being (God) can't do anything that's not logically possible". The question that's just begging to be asked is really quite simple: "Why is the power of God bound by logic?" Take a moment to ponder that question. After long enough you'll come to realize that any argument aiming to establish that logic limits the power of God - any argument at all - must use logic. A core component of every argument is reasoning governed by rules for rational thought (precisely what logic is). Without logic, there is no argument - there is no reasoning. Thus any argument to establish that God is bound by logic must assume that God is bound by logic in order to use logic to show that God is bound by logic. Sound familiar? You guessed it: that's a pretty serious case of begging the question. In fact, unless some premise of mine is unsound or I've committed some logical fallacy, we've just established that there is no possible argument capable of showing God's power to be bound by logic. We simply do not have the intellectual capacity to put limits on God's power. For all we can tell, it is well within God's power to create a boulder heavier than God can lift and then proceed to lift it, or to microwave a burrito hotter than God can eat and then proceed to eat it. It may never make sense to us, but it doesn't seem like there's any way around it. It would appear that, just as anything outside of space or outside of time is beyond the realm of our possible experience, anything outside of the realm of logical possibility is beyond our possible understanding.
Thanks Kant!
Jack