Here's a puzzle that's bothered me: the three major ethical traditions (virtue ethics, utilitarianism, deontology) have been treated as competing theories for centuries.
Philosophers spend careers defending one against the others. But what if they're not actually competing? What if they're just different tools for the same underlying thing?
I've been playing with a mathematical metaphor that makes this suddenly obvious: life works through multiplication, not addition.
In a multiplicative system, virtue ethics optimizes your daily multipliers, utilitarianism calculates across all the products, and deontology prevents catastrophic zeros.
They're complementary, not contradictory.
This is one of those frameworks that, once you see it, keeps showing up everywhere. It explains why small habits compound exponentially (1.01^365 vs 0.99^365). Why some harms feel categorically different. Why recovery from rock bottom is so hard. Even why Hume's is-ought gap might be a false problem.
I'm still figuring out how much weight this metaphor can bear, so I'm putting it out there to see what breaks when other people push on it.
A parent promises their child they will attend her recital, but a work meeting is inadvertently booked at the same time, and the parent chooses the meeting instead. Something feels wrong about this, but why? The promise that was broken ripples outward: the child's trust is diminished, the parents' integrity is eroded, and the relationship itself is weakened. Each person who learns of the broken promise adjusts their own expectations slightly downward. Small actions compound like interest, and life is the accumulated product.
The Mathematics of Mattering
Picture every living system (from a single cell to an entire civilization) as a product of crucial factors:
Metabolism × Reproduction × Information Transfer × Cooperation × Trust × Communication × ...
The fact that the factors are multiplicative means that if any essential factor reaches zero (total metabolic failure, complete breakdown of trust, or absolute communication collapse), the entire product is rendered useless and cannot recover. Zero is forever. Soft setbacks such as war, recession, or organ injury can sometimes be reinflated by outside energy, but a hard zero is final.
In this multiplication metaphor, different factors affect our course:
- Less than 1 (×0.9), contracts or degrades the system,
- Equal to 1 (×1.0), maintains it, and
- Greater than 1 (×1.1) expands or amplifies it.
A thriving forest, a healthy body, or a vibrant city typically maintains multipliers above one, such that its total product snowballs over time.
If our experience is metaphorically a number beginning at 1, unable to hit 0, and changing with each interaction, then every experience becomes a multiplier, increasing or decreasing our number.
For example, actions such as promise-breaking (×0.9), deception (×0.95), or violence (×0.85) act as fractional multipliers, each reducing trust and cooperation factors, nudging systems toward collapse. While actions such as reliable communication (×1.1), altruism (×1.2), and creativity (×1.25) enhance these multipliers, pushing systems toward flourishing.
Though it’s important to note here that the specific reference to numbers (×0.9 for betrayal, ×1.1 for trust) is purely illustrative. They represent the direction and relative magnitude of the effects rather than precise measurements. Think of them as conceptual placeholders showing that some actions degrade (multipliers less than 1) while others enhance (multipliers greater than 1) our systems. Actual impacts would depend on context and culture, and factors often trade off. Though even without the precision, the framework should align with our moral intuitions: betrayal feels fundamentally destructive yet categorically different from mere disappointment.
Living systems face constant multiplicative pressures. Not all factors need to be optimal; a few suboptimal multipliers (0.99 × 0.97 × 0.96) won't necessarily end a system. It's only when critical factors approach zero that existential collapse becomes a threat. This resilience allows for complexity and trade-offs, but long-term flourishing requires keeping multipliers collectively above one.
Why Good and Evil Are Directions, Not Properties
Could evil exist without life? Could good? From a naturalist perspective, both emerge from and depend upon life itself. Hume’s is-ought problem (Hume, 1739/2019) asks how we can move from descriptive facts of what “is” (such as “breaking promises causes distrust") to normative claims involving values (such as "you ought not break promises").
However, any normative claim (you ought to do “x”), including arguing “we shouldn't value persistence”, can only be made by a system maintaining itself above zero. The system is underpinned by a value structure that ensures persistence. Moral reasoning requires metabolic processes, as well as neural activity, linguistic competence, and social communication, each of which must be maintained at a level above zero for reasoning to occur. In this sense, we don't derive ought from is; rather, both emerge together from the lived reality of being self-maintaining systems.
In Principia Ethica (Moore, 1903), G.E. Moore argued that goodness must be a non-natural property, since we can always ask, "But is X really good?" The multiplication metaphor suggests that good isn't a property at all; it's a directional orientation, moving away from zero. Moore’s classic response would be to ask the open question, "Is moving away from zero really good?", but the question seems nonsensical; it’s like asking, "Is upstream really up?" Both mistake directions for properties. Good and bad (perhaps not evil) are the directions we embody: enhancement or degradation, flourishing or decay.
The Natural Drag of Needs
Maslow's theory of motivation (1943) reveals a truth about why maintaining our multipliers is challenging. Our basic needs function as natural fractional multipliers that continuously degrade our state if unmet. Meaning we don't start each day at neutral, we start with built-in degradation:
- Unresolved hunger (×0.95)
- Thirst (×0.8 and decreasing rapidly)
- Safety concerns (×0.98)
- Social isolation (×0.9)
These needs create unpleasant sensations, acting as an alarm system that orients us to address critical factors before they threaten survival. They're not bugs but features. If we did nothing and our needs remained unmet, their multipliers would compound downward until they eventually reached zero.
But these needs point to something deeper. As social animals, our multipliers aren't just about individual persistence. To persist, a life form must continuously solve problems; we also must solve problems, but our problems scale from survival to purpose. Existing in a web of meaning, where individual members are constantly solving their own, but also others' problems. In doing so, we find purpose and make persistence worthwhile. When these self-actualization and self-transcendent needs go unmet, we experience not just discomfort but a degradation of significance.
The Asymmetry of Decay and Growth
Systems can degrade rapidly and recover slowly. Broken trust, damaged health, or lost hope can be catastrophic to a system (×0.1), instantly devastating decades of growth. Recovery from a low base (0.1) requires sustained effort; there aren’t often any magic pills. Rather, to build back up requires consistent virtuous actions (×1.01, ×1.03, ×1.05) to compound gradually.
This dovetails nicely into Aristotle's emphasis on the importance of habituation in acquiring virtue (NE 1093a). No behaviour is truly neutral (equal to 1) in a multiplicative system; our daily practices compound exponentially. A 1% daily improvement compounds to 38 times the initial value over a year (1.01³⁶⁵ ≈ 37.8), while a 1% daily decline leaves you with 3% of where you started (0.99³⁶⁵ ≈ 0.03). The gap between 0.99 and 1.01 may seem negligible on a daily basis, but it proves existentially decisive over time.
This metaphor also extends to explain why some solutions work, while others merely appear to do so. Genuine multipliers, courage (×1.03), justice (×1.05), and wisdom (×1.04) create sustainable, compounding growth. They are addressing underlying needs and building a systems capacity. Whereas false multipliers such as escapism (×0.8), addiction (×0.7), or mindless consumption (×0.95) simulate the feeling of being above 1 while actually degrading the system. They offer temporary relief from low states but require escalating doses while eroding underlying factors. It’s very similar to a term used in AI called reward hacking, where a “reinforcement learning (RL) agent finds loopholes or shortcuts in its environment to maximize its reward without actually achieving the goal envisioned by its developers.”. It’s the same process for humans; when we binge-watch TV, or succumb to alcohol, sugar, or drug addictions, we’re essentially reward hacking. The system doesn’t benefit, but we experience the evolved mechanisms (pleasure) as if it did.
Individual Zeros, Collective Multiplication
It’s essential to acknowledge that individual systems don't exist in isolation. Morality is the navigation between ourselves and others, presents and futures, with respect to our shared pasts, toward mutual flourishing. With that in mind, understanding the full moral landscape requires distinguishing two fundamental modes: multiplication within systems and addition between them.
Within a system (such as your body, a community, or an ecosystem), factors multiply (trust × cooperation × communication). One essential factor hitting zero collapses the whole. Between systems, however, the relationship is additive. Individuals sum to form humanity; species sum to form ecosystems. When one human dies, humanity loses one member, but it doesn't collapse.
Take, for example, self-sacrifice: a soldier jumping on a grenade zeroes their own multiplication but merely subtracts one from humanity's sum. Paradoxically, their sacrifice can actually multiply trust and cohesion within their unit, enhancing the group's product while losing one member. The metaphor captures what pure self-interest cannot, how individual zeros can create collective multiplication.
It also reveals genocide's unique evil. Murder subtracts individuals from the sum. Genocide attempts to zero an entire multiplicative system, not just killing people but destroying the cultural, linguistic, and social multiplication that constitutes a people. Once that collective product reaches zero, it cannot be multiplied back. This matches our moral intuition that genocide represents a categorically different evil than even mass murder.
The metaphor illuminates why we admire sacrifices where individuals accept severe personal multiplication downward to prevent societal degradation. But unlike simple utilitarian calculus, it also explains why we shouldn't mandate such sacrifices, forcing individuals to zero for collective benefit destroys the trust multipliers that make society worth preserving.
Virtue ethics, utilitarianism, and deontology have long been seen as competing moral theories. Although the multiplication metaphor suggests that they are more like complementary strategies for maintaining life's multiplication away from zero, than competing theories for how to derive right from wrong.
Virtue Ethics as Character Multiplication
Virtues within the metaphor can be defined as character traits that reliably maintain multipliers above 1.
- Courage, for example, protects systems from threats that could zero out essential factors.
- Temperance would prevent self-degradation through excess, combating the system's tendency to reward hack.
- Justice maintains cooperation multipliers in communities.
- Wisdom optimizes resource allocation and decision-making.
The Aristotelian emphasis on habituating virtues makes mathematical sense: small, daily virtuous acts compound into flourishing, while slight vices inevitably lead to eventual collapse. Virtue ethics identifies the character traits that create sustainable multiplication within individuals and between individuals within societies.
Utilitarianism as System-Wide Calculation
Utilitarianism, on the other hand, solves a different problem. The aim of the greatest good or the least suffering (Negative Utilitarianism) for the greatest number is calculating effects across all systems. Take, for example, the famous trolley problem: killing one to save five seems like simple arithmetic: -1 + 5 = +4. But deliberately sacrificing someone degrades trust multipliers throughout society. People who fear being sacrificed "for the greater good" become less cooperative (×0.9), less trusting (×0.85), and more defensive. The metaphor allows utilitarians to calculate both additive effects between systems AND multiplicative effects within them, revealing why our intuitions resist simple numerical trades of human life.
Deontology as Zero-Prevention Firewalls
Then there is Immanuel Kant's “categorical imperatives” (Kant, 1785), which the Stanford encyclopedia explains as:
“an objective, rationally necessary and unconditional principle that all rational agents must follow despite any desires they may have to the contrary” (Johnson & Cureton, 2022).
Within the multiplication metaphor, these Categorical Imperatives function as absolute protections for factors that cannot approach zero without systemic collapse.
- "Never lie", for example, protects an important function of information transfer; if this principle is compromised, communication collapses.
- "Don't kill" prevents zeroing individuals and degrading security multipliers.
- "Keep promises" maintains trust above critical thresholds.
The universalizability test, “act only in accordance with that maxim through which you can at the same time will that it become a universal law” (G 4:421), essentially asks: would this behaviour, if universalized, drive any essential multiplier toward zero? So rather than competing with Utilitarianism and Virtue Ethics, Deontology's absolutism reflects mathematical reality: some factors are so essential that any degradation risks catastrophic collapse.
What this points at is that all three approaches (Virtue Ethics, Utilitarianism, Deontology) address the same underlying reality from different angles:
- Virtue Ethics cultivates traits that maintain a greater than 1 multiplier over time,
- Utilitarianism optimizes the total sum across all systems while accounting for multiplication, and
- Deontology establishes hard boundaries preventing factors from approaching zero.
They seem to form a complete ethical toolkit. Use deontological rules to avoid catastrophic zeros. Develop a virtuous character for sustainable multiplication. Apply utilitarian calculation for system-wide trade-offs. The deontologist warns, "trust approaching zero would be catastrophic." The virtue ethicist notes, "Daily trust-building compounds into flourishing". The utilitarian calculates, "We must maximize total trust across all systems." All examine the same mathematical reality from complementary perspectives.
Sophie’s choice
Critics might ask, “But what about when all available multipliers fall below 1?”.
Sophie's Choice (from William Styron's novel) presents this ultimate test. Where a mother is forced to choose which child dies. Within the metaphor, all options lead to catastrophic multiplication:
- Choose child A: Child B dies (x0), trust in justice (×0.1), will to live (×0.2)
- Choose child B: Child A dies (x0), trust in justice (×0.1), will to live (×0.2)
- Refuse to choose: Both children die (x0), plus moral agency (×0.1)
The metaphor doesn't pretend such situations have "good" answers. Instead, it reveals why they're tragic: when external forces constrain all multipliers to be below 1, the system faces degradation regardless of the choice. Importantly, the framework locates evil in the creation of such situations, not in how victims navigate them. The Nazi forcing the choice commits a moral atrocity by engineering a context where all paths lead downward. Sophie bears no moral culpability; she didn't choose from a standard possibility space but from one where flourishing was systematically excluded.
Consider another hard example, where a patient has a terminal illness with intractable pain. Their options might be:
- Continue living: Physical agony (×0.2) × Cognitive decline (×0.3) × Loss of autonomy (×0.1), where their multiplier moves further away from one each day. Or,
- A Peaceful death: Where the Individual multiplier becomes zero (they pass away), but their loved ones' relief from witnessing their suffering is aleviated, they choose death with dignity, preserving meaning.
If there is a chance of life, it might change the options. What this hopefully highlights is that although life (above zero) is fundamental, the metaphor doesn't mandate persistence at any cost. When all paths lead inexorably toward zero, choosing the timing and manner can be a final multiplicative act. Transforming inevitable degradation into meaningful closure. We distinguish between suicide from temporary despair (where positive paths remain) and rational end-of-life decisions (where only degradation remains).
These hard cases reveal a profound principle: ethics involves preserving possibility spaces for multiplication greater than 1. Coercion and oppression are wrong because they artificially constrain multipliers below 1. Education and opportunity are beneficial because they expand access to opportunities for flourishing.
The framework's philosophical validity doesn't require decimal-place precision. What matters is directional accuracy: Does betrayal degrade (multiplier less than 1) or enhance (multiplier greater than 1) human flourishing? The answer constrains possible values to a range that, while not precise, suffices for moral reasoning.
We don't need to know water freezes at exactly 32.000°F or 0.000°C to understand that ice forms below freezing. Similarly, we don't need to know that betrayal equals x0.85 precisely to understand that it degrades trust and pushes systems toward zero.
There has been extensive research in behavioral economics and social psychology that points to this reality, including work on trust games and reciprocity by Ernst Fehr and colleagues (2000), which confirms these directional patterns. Trust builds slowly but breaks quickly; cooperation requires reliability, violence degrades social cohesion. The exact multipliers may vary, but the directions remain consistent across cultures and contexts.
The Choice That Defines Us
We began asking whether good and evil could exist without life. The multiplication framework reveals they cannot, not because life is inherently valuable, but because life generates value through multiplicative persistence. Good and evil aren't properties we discover but directions we embody: enhancement or degradation, flourishing or decay.
This metaphor aims to dissolve some of these philosophical puzzles by exposing flawed premises. The is-ought gap assumes that facts and values occupy separate realms; however, they are inseparable within the multiplicative structure of life. Moore assumed that good must be a property, but it’s likely a directional orientation. The three ethical traditions often seem incompatible, whereas they are likely complementary strategies for the same mathematical reality.
The framework explains why ethics feels both objective and culturally variable. Directional constraints are universal; no sustainable system treats betrayal as enhancement. Yet specific values vary with context, explaining diversity within unity. We're all navigating the same game: keeping our multiplication above zero.
The mathematical metaphor illuminates why moral life is difficult. We begin each day with built-in degradation from unmet needs. Small choices compound exponentially. Recovery from harm requires sustained effort against asymmetric odds. Sometimes, all paths lead downward, making the preservation of positive possibility spaces a fundamental imperative.
But perhaps the deepest insight is that asking whether we should value persistence is like asking whether we should value having values. The question can only be posed by beings already embodying the answer. We are not observers contemplating life's multiplication from outside. Rather, we are life's multiplication, temporarily organized in patterns complex enough to recognize ourselves.
Every conversation either builds or erodes trust. Every small kindness compounds. Every betrayal multiplies outward. We are not observers of life's mathematics; we are the calculations themselves, constantly computing whether to move toward or away from zero. The choice, like the mathematics, is elegantly simple: enhance or degrade, flourish or decay.
Zero is forever. Everything else is a possibility.
References:
Aristotle. (1966). Ethics : the Nichomachean ethics. Penguin Books.
Fehr, E., & Gächter, S. (2000). Cooperation and punishment in public goods experiments. American Economic Review, 90(4), 980-994.
Foot, P. (1967). The Problem of Abortion and the Doctrine of the Double Effect. In Virtues and Vices (pp. 19–32). Oxford Review. https://doi.org/10.1093/0199252866.003.0002
Hume, D. (2019). Treatise of Human Nature. Digireads Com. (Original work published 1739)
Johnson, R., & Cureton, A. (2022). Kant’s Moral Philosophy. Stanford Encyclopedia of Philosophy; Stanford University. https://plato.stanford.edu/entries/kant-moral/
Kant, I. (1785). Groundwork for the Metaphysics of Morals. Oxford University Press.
Maslow, A. H. (1943). A theory of human motivation. Psychological Review, 50(4), 370-396.
Moore, G. E. (1903). Principia Ethica. Cambridge University Press.
Styron, W. (1979). Sophie's Choice. Random House.