Gödel, Epistemic Limits, and the Logical Constraints on God
Introduction
This essay examines the logical and epistemic limitations of the concept of an all-powerful, all-knowing, and omnibenevolent God. It argues that absolute truth, in its strictest sense, is unknowable and possibly non-existent, which in turn necessitates the logical limitation of God if such a being were to exist within any conceivable framework of reality. The claim that God exists as an absolute truth is problematic because absolute truth itself is neither provable nor epistemically accessible. Any claim of absolute truth requires that all underlying assumptions be absolute, with zero theoretical gaps. However, human knowledge is fundamentally limited—our understanding is bounded by perception, cognition, and probabilistic reasoning. If humans are epistemically limited, then there is no way to verify absolute truth.
This creates a paradox: absolute truth could theoretically exist, but could also theoretically not exist, and we have no means of verifying either claim. This essay explores this paradox and demonstrates how it undermines theological claims of absolute certainty regarding God. If absolute truth is unknowable, then God's existence as an absolute truth collapses under scrutiny.
Practical Certainty vs Theoretical Uncertainty
In everyday life, we rely on practical certainty—we assume certain truths to function and make decisions, but this does not mean we have absolute certainty. For instance, if a car is speeding toward me, I step aside because I am practically certain that the car is real and that it will hit me if I do nothing. However, theoretically, there is a non-zero probability that the car is a hologram, a hallucination, or part of a simulation.
This distinction is important because many theological arguments conflate practical certainty with absolute truth. The assumption that an omnipotent being must exist as an absolute truth is based on the false equivalence between what we assume to be true for practical purposes and what can be verified as objectively and fundamentally true.
Absolute truth, if it existed, would require a zero probability of being false. But all knowledge, including mathematical and logical reasoning, is ultimately assumption-based.
The Limits of Mathematical and Logical Truths: Gödel's Incompleteness and the Epistemic Paradox
Mathematics is often regarded as the closest thing to absolute truth due to its precision, consistency, and ability to describe the fundamental workings of reality. It governs the structure of the universe, from quantum mechanics to relativity, and is embedded in natural patterns such as the Fibonacci sequence in biological growth, fractal formations in nature, and the orbital mechanics of celestial bodies. Even within human physiology, mathematical principles regulate neural activity, the heart's rhythmic oscillations, and sensory perception. The sheer predictive power and applicability of mathematics suggests that it is objectively true from a practical standpoint—it is observable in nature, reproducible, and provides an unparallelled framework for describing reality.
However, despite its extraordinary utility, mathematics still rests on foundational assumptions, and this introduces the possibility of theoretical gaps at the most fundamental level. Mathematics is built on axioms—statements assumed to be true without proof. The Peano axioms define the basic properties of numbers, but they are still assumptions rather than self-evident, absolute truths. This becomes even more apparent in geometry: in Euclidean geometry, the sum of the angles in a triangle is always 180 degrees, but in non-Euclidean geometries, such as on curved surfaces (Riemannian geometry), this no longer holds. The mathematical description of space itself depends on the axioms chosen, demonstrating that mathematical truth is framework-dependent, rather than universally absolute.
This same principle applies beyond mathematics. Newtonian mechanics was once considered the fundamental truth of motion, but it was later revised by Einstein's theory of relativity, which introduced a more accurate model of spacetime. Similarly, Schrödinger's equation provides a probabilistic framework for quantum mechanics, governing the behaviour of particles at microscopic scales. While these equations work remarkably well within their respective domains, they are still built upon assumptions about the nature of space, time, and measurement, meaning that even our most reliable physical laws may not be absolute truths in a fundamental sense.
The idea that mathematics could be both essential to reality and yet incomplete presents a deep epistemic paradox, which is formalized in Gödel's incompleteness theorems. Gödel proved that in any sufficiently complex mathematical system:
- There will always be statements that are true but unprovable within the system.
- The system cannot prove its own consistency using only its internal rules.
This means that even in the most rigorous logical structures, there will always be truths that cannot be fully verified within the system itself. If mathematics itself is incomplete, then all human knowledge is also necessarily incomplete. This presents an epistemic paradox: absolute truth could theoretically exist, but we lack the means to verify it. Any formal system attempting to describe absolute truth would itself be incomplete.
So, mathematics appears to be the closest thing to an absolute truth within our practical and epistemic framework, as it is observable in nature, predictive, and objectively verifiable within our current models of reality. However, whether mathematics is truly, fundamentally absolute is theoretically unknowable, because its foundational assumptions could themselves be incomplete. To claim that mathematics is absolute truth would require proving that its axioms are absolutely and universally valid, with zero probability of them being false. Given that our understanding of reality is constantly evolving, and that even the most fundamental physical laws are subject to revision based on new evidence, the notion of fundamental absolute mathematical truth remains an open question rather than a certainty.
The Expanding Universe and the Non-Existence of Absolute Truth
If absolute truth existed, then knowledge would eventually reach a fixed, complete state. However, this contradicts the fundamental nature of the universe. The universe is expanding. If knowledge were absolute, it would imply a fixed and finite reality, which contradicts modern physics. Quantum mechanics shows that reality is fundamentally probabilistic, challenging the idea of fixed, unchanging truths. Knowledge is constantly evolving. Even scientific principles once considered immutable have been overturned.
If reality itself is in flux, then the idea of absolute truth existing as a fixed entity becomes increasingly untenable.
The Fallacy of "God is Beyond Human Logic"
The paradox of omnipotence is a well-known philosophical problem. Can God create a rock so heavy that even he cannot lift it? If yes, then there is something God cannot do (lift the rock). If no, then God's omnipotence is already limited. This paradox exposes a fundamental contradiction: omnipotence, when taken to its logical extreme, collapses under its own weight, rendering itself impossible.
Some argue that God exists beyond human logic, meaning he is not constrained by paradoxes. However, this presents a major problem. If God exists within the universe, then he must conform to logical constraints to interact with reality. If God exists outside logic, then nothing meaningful can be said about him, because all human reasoning relies on logic.
Someone could argue that if axioms such as the Peano axioms are human assumptions, then God exists beyond such assumptions. However, this leads to another paradox. If God exists beyond mathematical and logical principles, then he exists beyond the very structure that allows humans to comprehend anything, including God himself. This again renders any claims about God's nature, morality, or purpose entirely meaningless, as they would be beyond all forms of human understanding.
If God is beyond logic, then all theological statements about God are meaningless—including claims of omnipotence, omniscience, and omnibenevolence. If logic does not apply to God, then we cannot discuss him meaningfully. If God cannot be both good and evil simultaneously, then he is bound by classical logic, where A cannot be ¬A. This means he must exist within a definable framework rather than as an absolute truth, making his existence conditional on the very logical structures that define truth and falsehood.
The issue is not just with how God is described, but with the claim itself—if he is bound by logic, then he is not truly infinite or absolute. If absolute truth is epistemically unknowable, then so is any claim that God necessarily exists. The most rational position is epistemic humility: acknowledging that while absolute truth could theoretically exist, human limitations make it impossible to verify. In that light, any claim of absolute certainty regarding the existence of God is not just unproven; it is, by its very nature, epistemically unjustifiable.
Conclusion: The Limits of Absolute Truth and God's Epistemic Constraints
This essay does not argue that absolute truth does not exist—rather, it asserts that if absolute truth does exist, it remains fundamentally unverifiable within our epistemic framework. Any claim that depends on absolute truth as its foundation collapses because it requires an impossible level of certainty.
Similarly, this essay does not argue that a god does not exist, but rather that any claim of an omniscient, omnipotent, or omnibenevolent god must be examined within the same logical and epistemic constraints we use to understand anything else. If a god must necessarily possess omni-traits to be considered a god, then such a god does not exist, because the very concept of omnipotence, omniscience, or infinitude leads to contradictions. However, if a god can exist without these traits—meaning a limited god—then such a being could theoretically exist, even if the probability remains extremely low.
As a result, the issue is not just how God is described—it is the claim itself. If God is bound by logic, then he is not truly infinite or absolute. If God exists beyond logic, then he is beyond meaningful discussion. If someone argues that "God cannot be evil," they are inherently accepting that God is bound by classical logic. But if they then argue that an omni-god is beyond logical constraints, they contradict themselves—because the same logical framework they used to define God is the one that renders an omni-god impossible. You cannot selectively apply logic to construct an argument for God's nature while dismissing it when it refutes the notion of an omnipotent or infinite being.
At this point, the discussion inevitably turns to evidence. And there is, quite simply, more evidence that a god does not exist than that a god does. That does not mean that a god definitively does not exist, but it does mean that any claim that a god must be infinite, omnipotent, or an absolute truth is epistemically unjustifiable. The only logically consistent position is that any coherent definition of a god must be constrained in some way within our epistemic framework.
Some might invoke apophatic theology, arguing that God's nature is beyond human categories. But this leads to an even deeper problem: if God's nature is beyond our understanding, then any claim about his attributes—goodness, love, justice—becomes meaningless. "God is good" could mean "God is not good" under his own framework. If anything can be theoretically argued for God, then we must also accept that I could argue that a unicorn caused my lack of motivation this morning. Theoretically possible? Sure. Valid? Not at all. The mere theoretical possibility of something does not give it any epistemic weight.
The most rational position, then, is epistemic humility—acknowledging that absolute truth could exist, but we lack the means to verify it. Likewise, a god could exist, but if that god is to be defined within the same logical and epistemic framework used to discuss him, then he must be limited in some way. Ultimately, any claim that a god exists as an infinite or absolute truth collapses under the same logical framework that was used to define him.