The omnipotence of GOD
One of the fundamental qualities of GOD is His omnipotence- which can be defined as infinite power, the ability to do anything. This would mean that there is nothing GOD cannot do, and it implies that GOD is above everything.
Certainly, we understand that GOD is the highest and greatest- He is above and beyond everything. So, when we talk of GOD not being able to do something, this superficially sounds like GOD is not all-powerful.
There are understood to be two things that GOD cannot "do". These are:
1. GOD cannot go against His own nature.
2. GOD cannot do anything that is logically impossible.
The issue with saying that there are things GOD cannot "do" is obvious- we have just said that GOD is omnipotent, so how can there be anything He can't do?
The first is easier to refute than the second, so let's address that first:
- GOD cannot go against His own nature
Effectively, what's being said here is: GOD cannot be, or do, anything that contradicts His own character- His traits of being perfect, omniscient, omnipotent, omnipresent, omnibenevolent, eternal, unchanging etcetera.
When you think about it, it's quite obvious. Take one of his characteristics- omnipotence- if GOD could not be omnipotent at any point, then of course He's not omnipotent to begin with! All-powerful implies that GOD is eternally all-powerful, otherwise if GOD possessed the potential to lose power, then that in itself would be a weakness, meaning that He was not all-powerful to begin with, since He has the weakness of potentially losing power.
GOD cannot not be perfect- at any point. GOD is consistent with Himself at all times. This is because GOD is eternal and unchanging (Hebrews 13:8) and thus cannot at any time or place be anything but all-powerful, all-knowing and all-loving. In fact, by the very definition of these infinite qualities, they must be constant at all times- eternal- as eternity is an infinite quality. As mentioned before, if, at any moment, GOD could not be all-powerful, then by definition, He would not be all-powerful, since the ability to lose power would actually be a weakness- all-powerful means that He has no weaknesses.
In order for GOD to be perfect, all-powerful and infinite, He must be eternally unchanging and consistent. Otherwise He would not be perfect, and could not be trusted. Think about it anyway- if there were the possibility that GOD at some unpredictable moment could be unloving and evil, then how could He be trusted? As it happens, that is not GOD's nature, for GOD is perfect.
In order for a being to be perfect- it cannot change. Think about it- "change" means to "become different". When things change, they can change to become better or worse. But if an entity is already perfect, it is as high as it can be- so it cannot change to become better, by definition. You do not want a perfect entity to change, for then it would be imperfect- it cannot change for the better, only for the worse, and thus become imperfect.
So, then, a perfect entity cannot change, for if it had the potential to change, that would mean it would have the potential to become imperfect, and would therefore be imperfect (since if it has the potential to be imperfect, then it is not perfect), therefore a perfect entity must not be able to change. In this sense, "change" is an imperfection, a negative quality, not a good or perfect one.
This goes to show how GOD's qualities are all in perfect necessary harmony- eternal, unchanging, omnipotent, absolute. This makes GOD's omnipotence necessary and absolute- GOD cannot be anything but Himself.
Summed up: If GOD were able to go against His own nature, He would not be GOD
Moving onto the second thing GOD "can't do":
- GOD cannot do anything that is logically impossible.
The second criticism is a bit harder to refute, because many insist that any omnipotent being would be able to do things like make square circles or 2 + 2 = 5. In reality, however, these things are necessarily impossible. There is no possible reality that exists, or can exist, where the laws of logic are different from the ones here. Otherwise, if logic could be violated, then something would both exist and not exist at the same time, since the law of non-contradiction would no longer apply.
But, when we talk of logically impossible actions, what do we really mean? The term "impossible" is actually a misleading one- it implies that what it's referring to is an action, just one that cannot be done. However, it is understood by many Christian philosophers, like Richard Swinburne, that logically impossible "actions" are not even actions at all. In fact, the term "logically impossible" is really wrong, since, as I mentioned, "impossible" does refer to an undo-able action, thus implying it falls under the category of "action". This is misleading, simply because:
Logically impossible "things" do not actually exist
Anything that is "beyond logic" is non-existent. It is simple. It is like saying "beyond truth", "beyond reality" or "beyond existence". It makes no sense to talk of something existing beyond logic- that sentence is inconceivable, and illogical itself. Logic is not a "thing" that you can exist separately from, it refers to human reasoning and laws that we can utilize to determine truth. "Logic" isn't something that you can exist beyond, or that exists beyond anything. It is a word, referring to the abstract process of human reasoning. Perhaps, instead of saying "logically impossible", we should just say "non-existent" since saying "impossible" implies that it's some kind of action that just can't be done.
In theology and philosophy, it is understood that "illogic" is actually non-existent. There is no such thing, effectively, as "illogic". It's like "non-truth" (or lies) or "non-existence" are not actually true or real. That's why they're lies.
This would mean, since logically impossible "things" are not things, since they don't exist and are inconceivable, then logically impossible "actions" are not actions! They don't exist.
So saying that an omnipotent being cannot do anything logically impossible, is nothing more than saying an omnipotent being can't do something that is non-existent, because if it could, it's "power" would have to be non-existent. Or it's like saying a being that can only tell the truth, can't tell a lie. The "ability" to "do" something logically impossible is not an ability, and does not exist anyway.
If omnipotence included the ability to violate logic, then it would not be omnipotence, since this would also mean that it would contradict itself- and thus not being omnipotent at the same time. Omnipotence thus cannot violate logic, or it would not be omnipotence. It would escape it's own definition and cease to exist.
In summary: "Logically impossible" is a misleading term, as "impossible" denotes an "action" that cannot be "done", while in reality, logically impossible things are not actions and do not exist anyway.
(And the reason I keep putting "do" in quotations is simple- these things are not actually "doings" in the first place, they are non-actions, since they are non-existent).
So then, this may beg the question:
If GOD cannot do anything logically impossible, then does this not mean that GOD is limited by a higher authority (logic)?
You're making what I call a "conceptual mistake". You are personifying "logic" as if it's some kind of being. Words are used to produce concepts in the mind. Thing is, people use the word "logic" to refer to it as an abstract concept, almost as if it is a person, when it's not. I have already stated- logic refers to abstract human reasoning. It is not an entity or a person. "Logically impossible" is nothing but a fallacious term, since "impossible" gives us a concept of an action that can't be done, when logically impossible "actions" or "things" are neither actions nor things- it is non-existent.
It's a bit like asking: "Since GOD is above and beyond everything, and created the laws of everything, then He is above existence itself and made truth". Again, your question is fallacious- it doesn't make any sense and you are making a conceptual mistake. If GOD were beyond existence, and "invented" truth, it must mean He is beyond the truth- and hence non-existent and untrue Himself! In reality, however, your question makes a conceptual fallacy, because you are talking of "existence" and "truth" as if they are things like GOD or other entities, in which it is possible to exist above and beyond. We talk of GOD being outside of space and time and full comprehension, but not outside logic, truth, reality or existence.