The Beauty of Imperfection
Even mathematics, the most rational and abstract field, is fundamentally incomplete. So, when it comes to something as complex and context-dependent as ethics, we should be even less likely to believe in the existence of a completely perfect moral system.
Gödel’s incompleteness theorems, located at the crossroads of philosophy and mathematics, are not only milestones in formal logic but also serve as a source of inspiration for ethics, particularly the dispute between absolute and relative morality.
I. Gödel’s Incompleteness Theorems in Brief
In 1931, Kurt Gödel proposed two key theorems:
- Any sufficiently complicated formal system capable of expressing fundamental arithmetic will always contain claims that cannot be proven true or incorrect within the system itself (First Incompleteness Theorem).
- A system cannot prove its own consistency from within (Second Incompleteness Theorem).
This means that a self-consistent system is fundamentally incapable of demonstrating all truths or validating its own validity from within.
A significant aspect of Gödel’s proof was creating a self-referential statement that essentially said, “This statement cannot be proven within the system.” If it could be confirmed, the system would be inconsistent; if it cannot be shown yet remains true, the system is incomplete. This paradox demonstrates a profound truth: when functioning within a system, certain self-referential truths—no matter how intuitively obvious—may always remain beyond formal demonstration.
Stephen Hawking once remarked that Gödel’s theorems not only had a significant impact on mathematics and logic, but they also called into question the idea of a “Theory of Everything”—a single, all-encompassing model understanding the universe. He argued that, just as mathematical systems cannot guarantee their own completeness, physics may never produce a totally complete theoretical framework. This idea provides a powerful comparison for considering the boundaries of moral systems.
II. Absolute vs. Relative Morality
In ethics, absolute morality asserts that moral truths are universal and unchanging, independent of culture, time, or individual belief. Relative morality, by contrast, sees moral standards as human constructs, varying with context and cultural perspective.
In reality, absolute morality provides stability and consistency, but it might appear rigid and insensitive to contextual complexity. Relative morality promotes tolerance and diversity, but it can also lead to moral relativism, which makes distinguishing between right and wrong difficult or even impossible.
Even if we accept that some moral principles are largely constant—such as “do not take another’s life without cause”—we must equally acknowledge that such rules are frequently changed by technological and societal changes. For example, in a future in which human consciousness can be stored, replicated, or revived at will, is murder still the ultimate moral crime? If a person may be “resurrected,” can the act of taking their own life still be assessed by today’s absolute standards? When “death” ceases to be definitive, must we also redefine “killing”?
III. Ethical Lessons from Gödel’s Theorems
- The Limits of Systems: Boundaries of Moral Judgment Gödel’s theorems reveal the limitations within any formal system. Applied to ethics, this means that even the most logically consistent moral framework may face “unsolvable” dilemmas or internal contradictions in real-world situations, such as those found in bioethics (e.g., euthanasia or abortion), which frequently defy resolution by a single moral standard.
- The Need for an External Perspective: Transcendence and Reflection in Ethics Gödel’s insight implies that in order to evaluate a system’s soundness, one must walk outside of it. In ethical philosophy, this implies that we should analyze our values from views other than our cultural or personal frameworks—possibly even perspectives other than the human. Cross-contextual thinking promotes humility and a greater appreciation for others.
- Rejecting Absolutism Without Falling Into Nihilism Gödel’s work denies the possibility of completeness but not the existence of truth itself. This can inspire a balanced ethical stance: we can affirm the value of certain relatively stable moral principles (like respect for life and honesty) while accepting that, in different contexts, the application of those principles may justifiably vary.
IV. Seeking Within Limits
Gödel’s theorems remind us that both logic and morality are bound by the limits of human systems. But limitation doesn’t imply futility. On the contrary, it is precisely this incompleteness that calls for greater reason, empathy, and openness. Uncertainty should inspire ongoing reflection and deeper understanding. The path of ethics lies not in reaching perfect answers but in continually asking, “Could I be wrong?”—and in seeking coexistence and mutual respect amid diversity and conflict.
I still remember learning about Gödel’s theorems in high school and couldn’t help but ask my math and physics teachers how they viewed these ideas. I wasn’t questioning the value of studying systems that can’t be complete—I asked them what they thought about the theorems themselves. Their responses have stayed with me: precisely because logic is incomplete, we are driven to innovate and push the boundaries of theory. That, they said, is the beauty of mathematics and physics—the beauty of imperfection.
Gödel shattered the myth of formal systems with formal logic. In ethics, we must also let go of the illusion of absolute correctness and embrace the complexity and incompleteness of human judgment. That humility, perhaps, is where true moral goodness begins — and it is often flawed beauty that touches the heart the most.
Acknowledgement
This article was inspired by Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter, as well as a conversation with Jeremy Bleakley on absolute and relative morality at church on May 10.