God Does Not Exist (or else he is powerless or meaningless)

On the Principle of Sufficient Reason

TL;DR:

You can only choose two!

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

(2) There are no true contradictions.

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

The Principle of Sufficient Reason (PSR), represented as (1) above, which states that everything has a reason for its being, along with (2) above, that there are no true contradictions, are both true. As such, this article will show how, as a result of those two beliefs, (3) cannot be true because an omnipotent God cannot change the necessary truths of logic, and these necessary truths of logic allow the PSR to play an explanatory role for all truths. Because the PSR asserts an underlying logic to all truths, and God cannot change logic, then God cannot change truth, making God powerless. Therefore, the existence of an omnipotent God would be a contradiction, violating (2) above. And if (2) and (3) above are both true, God would be meaningless. God, therefore, either does not exist, is powerless, or is meaningless.  

This article will argue that because God cannot change the necessary laws of logic, he cannot truly be omnipotent. And more than that, because the necessary laws of logic govern the physical world, God can't govern the physical world. If everything has an explanation, then God's actions and even his very existence would require an explanation. God cannot change either logical or physical truths since physical truths are subject to logical truths. Where God and logic conflict, logic always wins. For God to truly have any abilities would be a logical contradiction. And if such logical contradictions are true, everything, including God, would be meaningless.

Theists are often the ones to put into play arguments for God's existence, forcing atheists to go on the defense. In contrast, atheists' arguments against God are frequently lacking and can be dispelled by a committed enough theist. Atheists tend to be more agnostic rather than atheistic, failing to posit positive arguments against God and instead remaining open to his possibility based on future evidence.¹

The "Problem of Evil" is often viewed as the strongest argument against God's existence, which states that the current evil in the world is incompatible with a benevolent, all-powerful God. But even this argument falls short. The theists' creator can be said to work in complex enough ways that are beyond human understanding, which nonetheless still create a moral universe. But what is logically incompatible with God is logic itself, as this article will explain.

Is God Compatible with Necessary Truth?

An unstoppable force and an immovable object cannot both exist. Either the force can move the object (making the object movable), or the immovable object can stop the force (making the force stoppable). But their mutual existence would be a contradiction—only one or the other can be actualized. Therefore, the existence of one would prove the non-existence of the other.

Analogously, an omnipotent being and unchangeable truths cannot both exist. If we understand omnipotence to mean "having unlimited power; able to do anything," and if we understand necessary truths as "those truths that exist necessarily," then either God can change or eliminate these necessary truths (in which case these truths wouldn't be necessary), or God can't change these truths (in which case God isn't omnipotent). God is the alleged unstoppable force, whereas necessary truths are the immovable object. Therefore, if we show that necessary truths do exist, which can't be changed, we can show that an omnipotent God doesn't exist, necessarily.

"1+1=2" is necessarily true. There is no possible world where 1+1 could equal anything other than 2. Creating such a world would be beyond God's capabilities, as would creating a “square circle” or a “married bachelor.” Hopefully, this facetious demonstration conveys that "having unlimited power" is contradicted by God's "not having the power to change some truths." Even though these are truths of logic, it is important that we first accept that God lacks the power to change logic.

But some try to salvage God by defining "omnipotence" as having unlimited powers except for those unchangeable truths (still admitting that these truths are beyond God's power). God has power over everything physical (i.e., contingent truths), but not in anything logical (i.e., necessary truths). We imagine God as a magical giant who can create or destroy any aspect of existence.

This creates a dichotomy between truths under God's complete power and those completely outside of God's power. We are meant to care about God's power over the former rather than the latter.

Yet, this dichotomy between God's absolute power over truths of the universe (we can call these "contingent truths") and powerlessness over truths of logic (we can call these "necessary truths") is a false one. Contingent truths are grounded in necessary truths, as affirmed by the Principle of Sufficient Reason (PSR), which states that all contingent truths have an explanation (to use its weaker version). And because the structure of causation is logical, these contingent truths can be explained by the necessary truths of logic.

There is a logical structure to reality's causation that we could even express as algorithms. If the logic of this causal logic can't be changed, then neither can its causal effects. Once we accept that the physical world is deterministic and we understand "causation" as being the logical entailment of events, we can understand how reality has a logical structure. Not even God can make this structure illogical. This is why the laws of physics can be explained through the logic of mathematics.

As Galileo Galilei said, "The book of nature is written in the language of mathematics." The foundations of reality aren't physical, but mathematical. The rules of Reason govern our world.

The physical makeup of reality doesn't matter, either. Why would we care about the lowest level of physical matter when higher-order rules of logic govern anyway? We can imagine universes composed of barticles, marciles or schmarticles (whatever name we give to the smallest unit of matter). But no matter what, those universes must contain logical, necessary truths. 5+7=12 must be true in that world, and the events in that world can be explained using logic. Logical rules, not tiny materials or God, govern reality. Necessary truths determine contingent truths.

By understanding that these truths govern everything, as provided by the PSR, we can conclude that God is powerless. He cannot control necessary truths, so he cannot control contingent truths; therefore, God does not control any truths. God would be subject to the same laws we are, making him our equal in our shared slavery to the logic of necessity.

There are many types of these “necessary truths.” In no universe could there be a colorless red object. In no universe could there be an even prime number greater than 2. In no universe could a sadistic torturer be morally upright.² These would violate the necessary truths of language, mathematics, and morality, respectively. We couldn't even imagine any of these universes where the above statements are true. I'll refer to such necessary and truly universal truths of logic as "Reason."

In summary, the unchangeable truths of Reason are true in all possible worlds. A truly omnipotent God would have all powers, including the power to change these truths, but God cannot. Therefore, God cannot be omnipotent. Even more so, because Reason exists in all possible worlds, an omnipotent god cannot exist in any world! Omnipotence is antithetical to logic (at least, not without contradiction). The truths of Reason then govern the physical world, not God.

As God cannot change Reason, and Reason governs the world (according to the PSR), then God cannot change the world. God is powerless.

This argument is a form of the "Omnipotence Paradox," and it's the strongest argument that would show either God's non-existence or impotence. But it's also the most misunderstood atheistic argument. This article seeks to clarify it properly.

To simplify the Omnipotence Paradox: God cannot be truly omnipotent, as he lacks power over Reason. God could never make 5+7=11, no matter how hard he willed.³ Not only could God not change Reason, but his actions are governed by Reason. Therefore, God is subject to the same truths of Reason that we all are.

This argument is horribly misunderstood by those who are familiar with it. "Can God create a stone that he cannot pick up?" These questions are often dismissed, usually due to a misunderstanding of the argument as trivializing God's limitations. Its detractors can ignore it as a “troll” atheist argument. But we should understand the true implications of God's powerlessness to Reason.

The PSR states that everything has a reason or cause that explains it. Accordingly, there are no true "brute" facts—all facts have some kind of explanation.

So God cannot do the impossible and change the necessary truths of Reason. Reason exists necessarily—we cannot imagine a world where Reason does not exist. Just try imagining a world where 1+1=3. You may be able to imagine people saying "1+1=3" and being told they are correct, or university-level textbooks printing that "1+1=3," but you couldn't really imagine a world where 1+1=3.

Reason must exist in all possible worlds, but God doesn't have to. It's easy for us to conceive of a world without God, as even committed theists could admit that such a world is possible, at least in theory. And because God is only a possibility, God is only a contingent truth (not a necessary one), and God's ability to change contingent truths requires a logical explanation. As the PSR states, he (like us) owes us a logical explanation for his actions. Not even God can violate the laws of logic.

This is not to say that Reason itself has causal powers over the physical world. This argument only states that "causation" can be explained through Reason. There is a logic to causation that allows Reason to play an explanatory role. And an explanatory role is a grounding role—Reason is fundamental to the world because the world possesses logical consistency (as our discoveries on the laws of nature are confirming). There is, according to the PSR, an explanation for everything. A logically consistent universe may seem like a bold claim in this overly skeptical age where truly every premise in philosophy is subject to question, but it is a fundamental truth that should inform philosophy.

We tend to believe that there is some explanation for the phenomenon of our physical world. And our science operates under this assumption (otherwise, why would science bother to look for explanations).

True contradictions are never fully accepted when we study the world. Not even the most committed dialetheist would be satisfied when asked, "Am I pregnant?" with a response saying, "Both yes and no." The same goes for all facts in the world. We continue to seek explanations for mysterious phenomena until we stumble upon their logic. What appears to be a mysterious contradiction today can be entirely explained tomorrow.

Without contradictions, we can fully accept logical, necessary truths. If necessary truths govern contingent truths, and God has no power over necessary truths, then God would have no power over contingent truths. Because contingent truths do supervene on necessary truths, God has no power with respect to either necessary or contingent truths, making him powerless.

The premises below hopefully 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 holding all power

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

(P7): God cannot change Reason

(C1): God cannot be omnipotent

(P8): "Omnipotence" instead means "all possible powers."

(P9): All contingent truths are explained by causation

(P10): Causation can be explained by Reason

(C2): 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): Because of (P2) and (P12), God's existence is explained by Reason

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

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

The above argument shows that an omnipotent being is not logically possible and that God is powerless even under a limited definition of omnipotence.

Reason is the only true "brute fact" of the world because Reason is self-justifying. The logical truths of Reason are true by necessity (mathematics and logic) and do not require any further grounding. These fundamental truths structure causation so that all contingent truths are determinable through Reason. Without Reason, contingent truths wouldn't have explanations, and we would only have brute facts, ungrounded and without foundation. But Reason does exist, and God has no power over it.

Separately, it doesn't even matter whether God was in fact the first mover. Because Reason grounds all, God's initial movement must have been grounded in Reason. If God simply "popped" into existence, with all the powers over the universe he is claimed to have, then this would be violating the PSR and accepting a true contradiction, since you have an action without a logical explanation.

The assumption of God's unexplained movement may seem innocent enough (it is only "one" violation of the PSR), but it is nevertheless a contradiction—you would be accepting inconsistency. True brute facts and the PSR cannot both be true. One or the other has to give.

Rejecting the PSR and Accepting Contradictions

As argued above, believing in God requires rejecting the PSR and accepting true contradictions. If things do not need an explanation, then neither do God or his powers. God wouldn't be subject to Reason because nothing would be. We can allow the world to have logical inconsistency.

However, by rejecting the PSR, we not only allow for the existence of God, but also the existence of everything. Once you allow contradictions, everything is allowed. This is known as the principle of explosion. Because contradictions are allowed to be true, which not only allows for the existence of God but of everything, leading to trivialism. God's existence would be true, but so would everything else, making the truth of God's existence meaningless.

Without the PSR, we are left with "brute facts"—facts that do not need a logical explanation. When contradictions are allowed, we can have unlimited brute facts, even when these facts contradict one another (this is why some have described the PSR as a fourth law of logic).

The thiest is left trying to explain certain "brute facts," or how things can exist without explanation, while also establishing a limiting principle to prevent “explosion.” But once you accept true contradictions, this goal becomes impossible. Any sort of limiting principle to limit explosion rests on sand, as the possibility of that principle's opposite is still in play.

Some have tried to use the uncertainty of quantum mechanics to show the existence of true contradictions and, therefore, the possibility of God. But this argument rests on two faulty assumptions.

First, it assumes that we have all the available information and understanding where we would be able to make such a powerful conclusion—that just because we do not understand a phenomenon, we conclude that it cannot be understood. More likely, our understanding of quantum mechanics is limited, and we shouldn't make radical conclusions based on this incomplete knowledge. We should reserve judgment until our understanding improves and admit that we're not so much more enlightened than those who have come before us (and who were similarly confident in their knowledge).

Second, and more importantly, citing quantum mechanics' indeterminacy does not help support the conclusion of God's powerlessness. If truly chaotic action exists, then God is equally subject to these truths and would still have no power over any truths. Randomness can't free God from causation, even chaotic causation.

The Thiest would need to believe that things "pop" into existence, which, if true, would allow for the existence of anything. No explanation needs to be given for anything since everything can exist without an explanation; only pure randomness would exist.

And just because an action is conceivable doesn't make it logically possible (a popular misunderstanding). I can conceive of myself jumping onto my TV screen and becoming a character in the show I'm currently watching ("The Simpsons"). Such an action may be conceivable if we could imagine it (we may have seen that "Charlie and the Chocolate Factory" scene of that happening), but it would be logically impossible. The same is true for other actions that we could conceive but which are still logically impossible, like a physical being traveling faster than the speed of light or backward time travel—but that doesn't stop these events from being imagined and illustrated in popular media.

A proponent of PSR could understand that such conceivable actions (even if they are shown to have taken place on a TV screen) are nonetheless impossible based on logic. However, a denier of the PSR could not accept the impossibility of anything, as unbelievable events could be a brute fact. Once you reject the PSR, you're forced to accept everything, regardless of any explanation—demanding an explanation for your beliefs is akin to admitting the PSR.

We can conceive of God violating the laws of nature. However, if the PSR is true, God cannot truly violate such natural laws. He may be able to amend them, but these amendments must still be logical. God's actions must obey the rules and remain logical in some fundamental sense, even when performing "miracles,” as even miracles must obey the PSR. We can imagine God as only a player in a game governed by Reason. He may be the most valuable player, but like us, he is still only a player and must abide by the game’s rules, as set by Reason.

As a summary, the PSR argues that causation is bound by logic. An event must not only have a cause but be logically warranted from that cause. Therefore, if God cannot change logic, he cannot affect causation. If Reason did not apply, God would still have no control because the world would be truly chaotic; he would only be a part of this chaotic world and not a true agent.

All events have logical explanations grounded in Reason, which no agent can change. God can't make 2+2=5 any more than he can repeal the second law of thermodynamics. If God creates two apples and then makes two more, he can't do anything to prevent four apples from being created. Two apples and two apples necessarily cause four apples. All physical world actions can be explained by Reason, and science and mathematics aim to discover those rules of Reason that explain our world.

Conclusion

God, like us, is a subject of Reason. Whereas Reason exists in all worlds, God can only exist if allowed to by Reason. But being a subject is antithetical to being a truly omnipotent God. Moreover, because Reason governs all, there is no room for God's power. Once we accept the PSR, an omnipotent God becomes inconceivable. God's actions and even his very existence must be subject to the laws of Reason and causation. And even if we say that Reason doesn't govern, implying that the world is chaotic and full of contradictions, then God would be subject to such chaos and would become meaningless. A contradiction would create an "explosion," where all becomes true and, therefore, trivial.

The next article will discuss possible counterarguments to this argument and how they fall short of proving even the possibility of an omnipotent God.

1. I have no idea what evidence would be satisfactory. A magical man who performs unexplained miracles and confirms the literal truth of the gospels? This sounds much more like a con than actual evidence for Christianity.

2. Readers may be reminded of the "Euthepho dilemma," which asks whether an act is pious because the divine made it so, or because it is pious independent of the divine.

3. Some theists even say that it's not possible to will such a thing, giving God even less power.