On the Omnipotence Paradox: The Laws of Thought are Beyond God's Power

Addressing the counterarguments

In my prior article, I argued that a truly omnipotent God is impossible. This article will now respond to the counterarguments I've received to this conclusion. Remember, the question is, "Is an omnipotent God possible?" I will answer, "No, because omnipotence is not a coherent concept in either a structured or chaotic world."

If there is any doubt that a truly omnipotent God does not exist, please let me know if there are any arguments I may have missed. Yet otherwise, we can continue philosophy without an all-powerful God and successfully move past the fictional being that has preoccupied far too much of humanity’s mental energy.

As a reminder of the prior argument, you can only choose 2!

(1) The Principle of Sufficient Reason (PSR) is true.

(2) There are no true contradictions.

(3) An omnipotent God exists as a brute fact.

If you choose (1) and (2): God is powerless (if the world is structured, God cannot control it, making him powerless).

If you choose (1) and (3): God is meaningless (If there are true contradictions, then all randomness can exist, making God's truth trivial and meaningless since God cannot control a truly random world).

If you choose (2) and (3): God cannot exist (Because (2) and (3) can never both be true, God could not exist).

The Argument

Like everyone else, God cannot do the impossible. He can only perform actions that are logically possible because logic (not God) governs all. When God's will and logic conflict, logic always prevails.

Theists often respond by acknowledging that God cannot change necessary truths of logic, arguing that Omnipotence is limited to the ability to change contingent truths. However, everyone can affect contingent truths. While God may be capable of changing many contingent truths, these changes must still be grounded in logical truths. To use a metaphor, God may be a powerful player in the game, but like all players, He must obey the rules.

Yet God cannot create a contradiction, and all of His powers to change the world must have an explanation. He is not truly "magic," and any unexplained abilities would be inexplicable. If God's powers were genuinely brute and ungrounded by explanation, such powers would present a contradiction—which even God cannot create.

Every one of these powers must have an explanation; otherwise, they would lead to a contradiction, which we have established God cannot create. God's powers must comply with the laws of nature, and if they were to "amend" those laws, God would be obligated to provide a logical explanation for that amendment. God must always operate within a system.

God's power is not entirely infinite. He is completely powerless with respect to necessary truths and is bound by what is logically possible—just like all of us. God can only perform actions within His capability, just as we can. Therefore, God's powers, in this sense, are rather trivial.

For example, I cannot jump to the moon, teleport to another galaxy, or travel back in time without encountering a contradiction somewhere. The physical limitations of my body make such actions logically impossible. Similarly, since God can only do what is possible, He cannot perform true miracles without providing an explanation for His actions, or else it would lead to a contradiction.

Under the Principle of Sufficient Reason (PSR), contingent truths supervene on necessary truths. Therefore, if God cannot change necessary truths, He cannot change contingent truths either.

In summary, since necessary truths govern contingent truths and God has no power over necessary truths, it follows that God would have no power over contingent truths. Because God lacks power regarding both necessary and contingent truths, God is powerless.

The following premises clarify this argument further:

(P1): Reason exists as a necessary truth (true by the facts of logic).

(P2): Reason exists independently of God.

(P3): True contradictions do not exist.

(P4): God exists as an omnipotent being.

(P5): "Omnipotent" means either (a) holding all power or (b) holding all possible powers.

(P6): The ability to change Reason is a power.

(P7): God cannot change Reason.

(C1): Therefore, God cannot be omnipotent according to (P5)(a).

(P8): "Omnipotence" should be understood in terms of (P5)(b).

(P9): All contingent truths are explained by causation.

(P10): Causation can be explained by Reason.

(C2): Thus, contingent truths are explained by Reason (Principle of Sufficient Reason).

(P11): A coherent universe without God is conceivable.

(P12): Because of (P11), God's existence is contingent.

(C3): Consequently, based on (P2) and (P12), God's existence is explained by Reason.

(P13): Because of (C2), God cannot change contingent truths.

(C4): Therefore, God is powerless because He cannot change either necessary or contingent truths.

The Counterarguments

The responses I have received to the above argument are discussed below, with the hope that they will be taken in good faith. I welcome the opportunity to address and build on any responses based on what has been provided.

(A1): "God is a necessary being. Your argument assumes that He is contingent, which Theists do not typically believe."

My argument claims that God can only exist as a brute fact. Some have objected to this claim by asserting that God exists necessarily rather than contingently. However, assuming that God is "necessary" begs the question. We cannot answer the question "Does God exist?" simply by asserting His necessary existence. The Theist must first demonstrate that God is necessary, meaning that He must exist in every possible world. If God is necessary, then even the possibility of His non-existence would be a contradiction. However, as I hope to demonstrate, it is the possibility of His existence that is contradictory.

If we accept that the truths of logic are necessary (i.e., those truths that arise from the laws of thought, such as 2+2=4), they would exist in every possible world and could not be changed by anyone. Regardless of how powerful a being may be, it would be incapable of changing these necessary truths, as worlds in which 2 plus 2 equals anything other than 4 are truly inconceivable (in the most literal sense, not in the “The Princess Bride” sense).

God is not necessary because it is conceivable that a world could exist without Him. Therefore, God does not have to exist, implying that He cannot be considered necessary. If God's existence is dependent on something higher, then He cannot be truly omnipotent. A true "God" would not be contingent.

Thus, the only way to salvage the concept of God would be to consider Him a brute fact—contingent, yes, but not explained by anything else, as that would make Him a subject. By definition, a truly omnipotent being cannot be the subject of anything. This is why God could only exist as a brute fact. However, under the PSR, brute facts do not exist—so, neither can God.

(A2) "God's nature is logical. He cannot change logic because he cannot change his nature."

Many accept that God has limitations regarding logical truths, such as mathematics. They may say, "God can't alter the laws of thought because they reflect His nature."

However, this already concedes that God has a "nature" that He cannot change. God is unable to will anything that is illogical; He is restricted by logic and operates only as an agent of eternal truths. It is generally acknowledged that God Himself is subject to the same laws of logic as we are. Like us, God has a nature that He was born with and laws that He must follow in relation to that nature.

If God cannot perform an act because it is immoral, it implies that morality exists independently of God. For instance, God cannot torture babies for fun, nor could He even desire to do so. While this may suggest that God is moral, it does not imply that He is omnipotent, since the higher truths of morality still bind him. Asserting that God would never torture babies addresses the Euthyphro dilemma, indicating that metaphysical properties such as "piety" and "morality" exist outside of God's will and are binding upon Him. If God lacks the power to change their will, we also admit that such God is subject to Reason.

(A3) "Sure, God can be subject to a logical system. But logic is merely a system. God is the author of our system, even though He Himself is subject to a higher one."

Some may accept that God is simply part of a larger set of system—he is the author of our current system, the system he is on is authored by an even “greater God” and we might author systems below us and become their “God.” However, for all practical purposes, He is still considered God because He is the immediate authority over us, the creator of this particular system. This acknowledgment means He is subject to a higher authority, and therefore, He is no longer the "ultimate" being. If a greater system dictates God's nature, then He is not omnipotent. Even though He has control over our system, that "control" actually stems from His being governed by this larger system.

We should not deceive ourselves into believing that the author of our system is omnipotent, as that author himself is subject to still a higher system. It is merely a series of systems all the way up, with a "God" just above each one. The meta-rules of these systems govern everything, not "God."

(A4) "Violating logic isn't a power within Omnipotence. Omnipotence means the ability to do all logically possible things, not all things."

Premises (P5) and (P8) of my above argument each use both definitions of Omnipotence.

God can do all things" or God "can do all possible things" in P5 and P8, respectively. In either case, God is powerless because these definitions aren't truly distinct once we accept the PSR.

Assuming the PSR, if you can't change logic, then you cannot change causation, and therefore you cannot change contingent facts.

Allow me to use an illustration to show how, without the ability to change logical (necessary) truths, God cannot alter contingent truths, for what I'll call the "Chain and Lock Scenario."

Imagine that God is bound by chains that restrict his movement. However, if God were omnipotent, then God could break out of that chain, as an omnipotent being's movement cannot ever be restricted.

Yet these chains are themselves bound by locks. These locks bind God to the chains, and even the chains themselves are "grounded" by the locks. The locks determine the movement of both the chains and God. The chains and God cannot move without any slack the locks give to this movement— otherwise, the chains can't move outside of the fixed boundaries established by the locks.

God could, therefore, only break the chains by first breaking the locks that bind the chains. However, if God cannot break these locks, then he cannot break the chains. Sure, if these chains didn't have locks on them, God may be able to break them. But because the chains do have locks, God's actions cannot affect the chain. God may be able to move the chains to the extent the locks allow it, but God can't free the chains (or himself) from the locks. Since God can't break the locks, he can't break the chains, and therefore cannot move unless the locks let him.

For this analogy to apply to God's power over the physical world, we’d need to answer the following questions: (A) Do these metaphorical "locks" exist? (B) Can God break these locks? (C) Do these locks control the "chains"? (D) Can God control the chain without having to break the locks?

We have already established (A) in the affirmative because necessary truths exist (1+1=2), and these truths govern the “chains” (i.e., contingent truths), and we have established (B) in the negative because God cannot change these truths (God can't make 1+1=3). We have also established (C) in the affirmative since causation is logically structured under the PSR. To summarize, these locks exist in the form of Reason, God can't break these locks, and these locks govern the chains (contingent truths). So can God control the chains notwithstanding the locks?

Theists may be tempted to argue yes. But under the PSR, all causation is logical, and brute facts can't exist. God can't control the chains without controlling the locks. So by accepting the PSR, we can establish (D) in the negative. We can think of God as being bound by the locks of logic—if he can’t break these locks of logic, he can’t truly do anything.

Theists try to exclude God's powerlessness over necessary truths from the definition of "omnipotence," which is limited to God's control over contingent truths. But as shown by the "Chain and Lock Scenario", God cannot actually control contingent truths without first controlling necessary truths.

This argument often fails to be appreciated because we can imagine that God can do the impossible. But once we understand what "doing the impossible" means, imagination is revealed to be a poor guide into Omnipotence. Because "doing the impossible" actually means violating the laws of logic, and because we accept that God cannot violate the laws of logic, we'd have to conclude that God cannot do the impossible.

For instance, we can imagine me teleporting to the Andromeda galaxy or becoming a character in "The Simpsons" by running headfirst into my TV screen. Yet, notwithstanding their possibility in imagination, given the nature of my physical state, these actions are logical impossibilities. They are just as logically impossible as making 5+7=13, for to do those impossible acts would imply a contradiction somewhere along the chain of causation, as logic could not explain such an inconsistency.

Theists may respond by stating that God can change the laws of nature, yet this is to misunderstand these laws. Laws of nature aren't governed by an omnipotent agent or by physical things that the agent manipulates. Rather, the physical world is governed by a set of principles of causation that we can even explain with algorithms. It's possible to change this algorithm, but this would require an algorithm of its own. It's algorithms all the way down.

The lowest unit of analysis that governs the cosmos isn't the atom or the quark but the principles and rules of logic, or "Reason," as I have been calling it. As we've already established, God can't change "Reason."

Just because we can imagine a God who re-arranges the laws of physics (so that such acts are conceivable) doesn't mean that its logically possible to change these laws, any more than the conceivability of me teleporting into a fictional TV show makes that cartoon-like ability possible. We may be able to imagine God changing the boiling point of water from 212°F to 212,000°F, but God can only do so within the laws of logic. If that action were logically impossible, then God would have no power to do it. Otherwise, there would be a contradiction, which would be impossible to create (even for God).

The same principles of Reason apply to both us and God. If God changes the laws of physics, then such a power would need an explanation bound by Reason on pain of contradiction, which is also true for all of us.

(A5) "Are you saying that Reason causally explains the physical world?"

No! Reason doesn't play a causal role for contingent facts, but an explanatory role. The facts of the physical world are grounded in causation, and causation is grounded in logic, as provided by the PSR. Causation isn't a sequence of randomly occurring events, but a logically structured series of events where cause X necessarily causes the effect Y.

As soon as you flip a coin, whether the coin lands head or tails has already been determined because the established present facts logically entail future facts. The forces imposed on the coin would logically fix what side it will land on, and the physics can even be expressed mathematically, allowing the future event to be accurately predicted. Since the physical world can, in theory, be explained through the logic of mathematics, the physical world is grounded in logic.

Just because we do not understand all physical phenomena at this point doesn't mean that it is theoretically impossible to express the events of the universe through mathematics.

(A6) "But what if causation is not logical, as suggested by [insert unresolved issue in physics], so that logic can’t explain the physical world?"

Unexplained phenomena in physics may question the belief that the world is grounded in logic. Couldn’t it be possible for events to occur that truly lack any explanation?

There are multiple problems with this response. First, it assumes we understand the world completely, to the point that we can judge unexplained events to be unexplainable, rather than simply undiscovered. Over history, many believed they lived in a time when all the universe's questions were known. This response is to repeat this same naivete and the “God of the Gaps” fallacy.

Second, we shouldn’t confuse not having an explanation with there not being an explanation. When I see a magic trick I can't explain, I don't suddenly believe in magic and throw out what I understand to be fundamental about the world. Moreover, I don't even update my belief that magic is true, because I have another background belief that says "Magicians are in their line of work because they can create illusions which appear to be magic, but this has nothing to do with the existence of magic."

Similarly, when we have unexplainable events in science, we should be mediated from denying logical truths by our background belief that "Past researchers also made radical conclusions from events that they didn't yet fully understand. So I should reserve judgment on such conclusions like the world being random until I understand it better."

David Hume argued that just because we see a miracle doesn't mean we should discard all of our developed experience. A single data point doesn't justify discarding the laws of nature. The same is true for unexplained events. Just because we aren't able to explain phenomena doesn't mean we're warranted discarding our logic. Let's hold off until we fully understand the matter before making radical conclusions.

The very goal of science is to develop coherent explanations to understand the physical world. We should never admit that a feature of the world is beyond explanation just because we don't yet understand it. The limitations of our knowledge should be viewed as challenges for us to overcome, rather than proof of the futility of knowledge. We should continue studying the world and searching for explanations until we have very good evidence that this assumption is untrue. And if this assumption is false, then we'd have to abandon science entirely, as what good is science's search for explanations that do not exist? As long as we believe science is worth pursuing, we assume underlying explanations exist and are discoverable.

(A7) "You are still changing the definition of Omnipotence. It cannot mean the ability to do all things, or even logically possible things, but only all possible things. Doing the impossible is meaningless."

This argues that requiring God to be capable of changing logic isn’t part of the definition of Omnipotence, since such acts are impossible. While He can't change logical truths, His ability to do the possible and change contingent truths still makes Him God, as it is impossible to change necessary truths. For instance, when responding that God can't make a "square circle," a Thiest may state that a square circle is simply inconceivable and would fall outside of true “omnipotence.”

While a common response, this argument has a few major problems. First, we recognize that the ability to do the impossible is still an ability. Reason is a limitation from doing the truly impossible, like creating a square circle or a "married bachelor." If someone could do the impossible, being unbound from the laws of logic, then we'd call that ability a power. In fact, the "only" power God could have that would make him God is the ability to do the impossible (anyone can only do the possible). As this article argues, if God can't do the truly impossible, then he is not God, just another subject of the logically possible.

Second, we do not accept this redefinition argument in other contexts. If an ability is incoherent, but someone still claims to possess this incoherent ability, then the burden is still on them to show that they truly have this ability (you can't redefine an impossible trait, just because its impossible).

For instance, being "all-knowing" requires disproving global skepticism (by proving that one is not a brain in a vat or is being manipulated by an evil demon). But if it is not logically possible to be “all-knowing” (as the debate around global skepticism has proved) we can’t just lower the standard for being truly omniscient.

Take the below dialogue between the “Know-it-all” and the “Skeptic” as an illustration:

Know-it-all: I am omniscient! I know everything! My mind contains all the truths of reality, which I know with 100% certainty!:

Skeptic: OK, then are you a brain and in a vat? And, how do you know?

Know-it-all: That is not what omniscient means! Omniscient means knowing all the truths that it is possible to know. I can't possibly know that I'm not a brain in a vat because all knowledge is compatible with the truth or falsity of being a brain in a vat. I'm still omniscient!

Skeptic: The imposibility of knowing whether you are a brain in a vat is your problem, since you're the one claiming to be omniscient. If (1) you're the one saying that you're omniscient and know all the facts of the world, and (2) whether you're a brain in a vat is a fact of the world, you should be able to confirm whether you are or you are not a brain in a vat since you know everything.

Know-it-all: How could I possibly know whether I'm a brain in a vat? There is no actual evidence I can point to which would affirmetly determine my "brain in vat"-ness. Even if I was somehow able to see I am a brain in a vat, even seeing a brain in a vat labeled “Know-it-all's brain,” and I was given evidence that the actions of this brain determined my experience, such visual "proof" could just be an illusion and I still wouldn't know with 100% certainty that I'm a brain in a vat. And you certainly can't confirm you're not a brain in a vat since any such evidence would be consistent with being a brain in a vat. It's not a possibility that could ever be ruled out. No one can know that.

Skeptic: This is to only demonstrate that true omniscience is nonsense, for there are truths that we cannot possibily know. And the burden is still on you to prove that you're omniscient, which you've shown is an impossible task.

Know-it-all: That's a meaningless requirement of omniscient then. I can't even conceive of evidence for not being a brain-in-vat. You're redefining knowledge to include logically impossible things for me to know. I'm still all-knowing since being able to know that I'm not a brain in a vat, or being controlled by an evil demon, isn't knowledge. But fine, I know all things that it is possible for me to know. Happy now?

Skeptic: So you admit you can't rule out the possibility of a brain in a vat, but still claim certainly over the facts in the world. How could you know all those possible facts without first ruling out the possibility that you're a brain in a vat? You can't say you know anything with 100% certainty because there is always that possibility hanging over all your supposed "knowledge" that you're only a brain in a vat and everything you think you know are only from illusions in your head. To know anything about the world, you'd need to first know you're not a brain in a vat. Since you don't know you're not a brain in a vat, you don't know anything!

Know-it-all: Knowing that I'm not a brain in a vat is nonsense, I don't even know what evidence for that fact would even look like since everything is consistent with being a brain in a vat. And we have no problem claiming knowledge without first proving that we are a brain in a vat. Especially since proof that one is not a "brain in a vat" is conceptual nonsense. Again, I don't even know what that would be. It's like a square circle, it just doesn't exist.

Skeptic: The fact that it doesn't exist is, again, your problem, as well as for anyone else who claims to be truly omniscient. All your knowledge is now suspect because you cannot prove that you are not a brain in a vat. You try to separate the fact that you don't know you're a brain in a vat from the other knowledge you claim to have, as if the former is unrelated to the latter. But really, you can't possibly know anything about the external world without first concluding that you aren't a brain in a vat. Ignoring this connection would be actually to redefine knowledge.

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We can’t just lower the standard only because the standard set was impossible to begin with. If (1) one claims to know everything and (2) knowing that one is not a brain in a vat is to know something, then (3) an "all-knowing" being must be able to show that he is not a brain in a vat. If knowing that one is not a brain in a vat is impossible, then too bad for whoever claims to be omniscient.

But even if we reject the Skeptic's characterization, we are relegated to omniscience redefined as meaning "knowing everything that one can possible know," which is a tautology. For not knowing everything it is possible for you to know would be a contradiction. You can only know what it is possible for you to know; you cannot know anything more or less than that.

We can apply this paradox of omniscience to that of omnipotence. If one claims to do everything and if holding the ability to change Reason is an ability someone can do, then someone who claims to be able to do anything should be able to change the laws of logic. If you can’t change the laws of logic, you aren’t omnipotent.

Moreover, it is the Theist who is redefining the term "Omnipotence." Once you use Omnipotence in the most ultimate sense possible (a supreme deity who controls all truths), then any contradiction involved with that most ultimate level of power becomes the Theist's problem.

And even if the Theist's definition of "omnipotence" is adopted and we define it as "the ability to do anything that's possible for one to do," then we've just made a tautology—the Theist's redefinition of Omnipotence would be meaningless. God wouldn't be any more "omnipotent" than we are, as we also could only do what is logically possible.

I can only do what's possible for me to do, for being able to do anything more or less than that would imply a contradiction somewhere in the chain. And it would be impossible for me to do what's beyond my possibility. God may have more possibilities than me, but he is ultimately still bound by the possible.

Overall, either necessary truths control the world, and God is bound by necessary truths, in which case God is powerless. Or the world is chaotic and God is also subject to this chaotic state, in which case God is powerless.

(A8): "The world isn’t logical or structured, it’s all random and under God’s control."

This response believes that an omnipotent God and true randomness can exist. But true randomness would make God just as impotent as true structure. And there is no space in between fundamental randomness or structure where God could exist.

To adopt the "Chain and Lock Scenario" used above, if the chains aren't bound by the locks, such that the movement of the chains would be purely random, then the chains can only break due to randomness. God wouldn't be able to break the chains here either, since his chains are also subject to randomness. God would be powerless over true chaos unless his powers somehow impose logical structure. And, in this case God's power would still be restricted to the logical. Like in the free will debate, neither deterministic causation nor randomness can count as agency.

Let's say causation is truly random; the structure of the world can never be explained because the foundations of reality are in unpredictable flux. Then it can't be controlled by an omnipotent being because if it could, it would not be truly random. So either the world is structured, and God is powerless, or the world is random, and God is powerless. So the unexplained cannot save omnipotence, since a true lack of explanation would also mean that omnipotence can’t then be an explanation.

(A9) "But God can change the laws of thought. God can make 1+1=3."

This response asserts that true contradictions exist and the laws of thought are wrong. But if true contradictions are possible, then so would everything. Both God existing and God not existing would be possible, as would every other proposition. Just a single contradiction comes with an explosion of possibilities (and the Liar's Sentence offers no protection for this view), making the possibility of God’s existence trivial (i.e., meaningless).

(A10) "God can make true contradictions without the principle of explosion."

You cannot create a contradiction without explosion. Any being who is claimed to do so cannot exist. Accepting a contradiction without explosion for the sake of God is to abandon logic for the sake of God. A God who can create contradictions without explosion could never be grounded in reason.

(A11) "God is beyond our understanding, and speaking of any of his qualities is misguided."

"Whereof one cannot speak, thereof one must be silent."

- Ludwig Wittgenstein

Final Thoughts

If God is bound by Reason, then he can't do the impossible. If he can't change necessary truths, and these necessary truths govern the contingent world, then God does not govern the contingent world. Necessary truths rather than God would govern contingent truths.

Moreover, God wouldn't be able to change necessary truths. These include the truths of mathematics, logic, and philosophy, which must exist independently of God. If God can only change contingent truths, like features of the physical world, his power is the same as ours.

God's power differs from our own only as a matter of degree rather than kind. We all have the power to affect contingent truths, and some of us can change more contingent truths than others, but God can only affect a large number of contingent truths.

The omnipotence paradox has not been fully appreciated. Once you understand the implications of God's inability to violate the laws of logic, then you can see how Omnipotence is impossible.

If you accept the PSR, then you’d have to accept that the PSR would bind God, as all of his actions and even his very existence would owe logic an explanation. Otherwise, you accept a contradiction if you don’t accept the PSR.

While the PSR does have necessitarian implications (which some are uncomfortable with), necessitarianism is generally consistent with the deterministic implications of science-based physicalism.

Even if you aren't sold on the principles of causation governing the natural world, only note that we have come to understand the physical world because of these principles. All of our advances in knowledge and technology have come about from applying the fundamentals of nature, rather than random trial and error. We haven't just been lucky, but owe our progress to humanity's discovery of the laws of nature.

The world is already ordered. Therefore, God cannot impose order onto the world, which then becomes the subject of his mind. As such, God's mind must be bound by Reason. If God's mind is not bound by Reason but is instead chaotic, then he's powerless over himself as he lacks control over his own being. Admitting a chaotic world is admitting God's lack of omnipotence.

Although "omnipotence" is a meaningless concept, we mean something when we refer to "God," as I had explained when discussing the "meaning paradox." The next article will discuss the nature of non-existent beings like God.