Against moral arithmetic

By Leandro Castelluccio

In our society, we are often compelled to make complex decisions regarding fundamental aspects such as the distribution of resources, the allocation of healthcare, the administration of justice, and even determining who deserves to live or die in contexts of warfare or self-defense. We are confronted with ethical dilemmas where we are asked to assign quantitative values to human lives, as if they were interchangeable commodities on a scale.

However, this numerical approach disregards the inherent complexity of each human life, particularly in relation to the person making the evaluation and the specific circumstances surrounding them. In this article, I challenge the deeply ingrained belief that we can reduce the value of a human life and compare it to others through some form of mathematical equation, a notion steeped in consequentialist morality, which I aim to refute here. The goal is to free ourselves from this view and uncover a more positive perspective, one that acknowledges the uniqueness of each existence.

To address this topic, English philosopher Peter Singer has highlighted the morality of our decisions in his work “Practical Ethics,” where he argues that ethics should focus on maximizing overall well-being. However, Singer also acknowledges the complexity of individual value in his critique of utilitarianism, asserting that human life cannot be reduced to numbers on a scale, as each life is unique and irreplaceable (Singer, 1993). This statement supports the idea that lives cannot be exchanged like goods.

I argue that any attempt to establish a hierarchy of human lives based on seemingly objective criteria is inherently problematic and ethically questionable, as individual well-being is non-transferable and indivisible from a personal perspective. Rather than resorting to a simplistic arithmetic logic, I propose a deeper reflection on ethical values and the way we assess the dignity of individuals.

Throughout this essay, I will examine the limitations of arithmetical morality and the implications of this approach for consequentialist ethics, while advocating for a more humane and compassionate stance in the ethical decisions we face as a society, recognizing the importance of the personal perspective of those who make the evaluations.

To introduce the topic at hand, it is relevant to reference the famous trolley dilemma, a thought experiment widely debated in the fields of ethics and moral philosophy. This exercise presents a hypothetical situation in which a runaway trolley is speeding towards five people tied to the tracks, unable to escape. Faced with this scenario, you have the option to intervene: you could pull a lever to divert the trolley onto a secondary track, where only one person is tied down, or choose to do nothing and allow the trolley to continue on its path, which would result in the death of the five people. The dilemma, therefore, revolves around the decision to actively intervene, sacrificing one person to save five, or not intervene and let the five die.

This thought experiment raises fundamental ethical questions, as well as inquiries about the nature of our moral decisions when confronted with painfully difficult choices. It is often used to illustrate and debate various ethical theories, such as consequentialism, deontology, or utilitarianism, each of which offers different responses to the problem.

The trolley dilemma has been central to philosophical reflection, prompting thinkers to propose different solutions and ethical frameworks. For example, consequentialism, which evaluates actions based on their outcomes, often prioritizes general well-being. A consequentialist might argue in favor of pulling the lever, reasoning that sacrificing one life to save five maximizes the collective good. This approach aligns with utilitarianism, a branch of consequentialism that holds that actions should aim to maximize happiness or minimize suffering. In this case, utilitarianism would justify the death of one person as a necessary evil to achieve a greater reduction in total harm. However, critics argue that this reasoning can lead to morally questionable decisions, as it could legitimize the sacrifice of innocent individuals for the sake of a greater benefit.

On the other hand, deontological ethics, associated with philosophers like Immanuel Kant, evaluates actions according to their adherence to moral principles, regardless of the consequences. A deontologist might argue that pulling the lever is morally unacceptable, as it involves deliberately causing harm, which would be intrinsically wrong, regardless of the resulting benefits. Kantian deontology defends the view that individuals must be treated as ends in themselves, not as means to achieve other ends. Under this principle, pulling the lever would amount to instrumentalizing one person’s life to save others, which would violate a fundamental ethical imperative. However, critics of deontology argue that its rigidity can lead to morally unsatisfactory conclusions, especially in extreme situations like the trolley dilemma.

Virtue ethics, unlike consequentialism or deontology, focuses on the development of moral character and the cultivation of virtues such as courage, compassion, and justice. In the context of the trolley problem, a proponent of this approach would not analyze the rules to follow or the direct consequences, but rather consider how the decision reflects the virtuous character of the individual making it. Thus, a virtue ethicist might argue that both the action of pulling the lever and the choice to refrain should be guided by the courage to face difficult decisions and the compassion to reduce suffering. Nonetheless, critics of this approach point out that virtue ethics can lack clear guidelines for action in specific situations, making it difficult to discern which choice best embodies the necessary virtues.

The Greek philosopher Aristotle, in his work Nicomachean Ethics, argued that virtue lies in the mean and that ethics should focus on the character of the moral agent. This suggests that moral decisions are deeply personal and should be evaluated based on virtue and the intention behind the action, not solely by their outcomes. This perspective aligns with the critique of the utilitarian approach, where the complexity of human emotions and relationships is lost in the cold calculation of “moral arithmetic.”

To overcome the limitations of strictly consequentialist or deontological approaches, some philosophers have proposed hybrid theories. One example is rule utilitarianism, which combines the flexibility of utilitarianism with the adherence to deontological principles. This approach suggests that decisions should be based on rules that, when applied universally, lead to the greatest good. In the case of the trolley dilemma, a rule utilitarian might argue that it is always preferable to pull the lever, as this general rule would, in most cases, result in better overall outcomes. Thus, it attempts to reconcile utilitarian pragmatism with the moral security offered by following established rules.

Another interesting perspective is contextual ethics, which emphasizes the importance of the specific circumstances in ethical decision-making. Instead of applying rigid frameworks, a contextual ethicist argues that each situation has unique characteristics that must be considered. In the Trolley Problem, a proponent of this view might point out that the correct decision depends on factors such as the identities of the people involved, the reasons they are on the tracks, or the broader context of the action. This approach highlights the nuanced nature of moral dilemmas, criticizing the rigidity of more traditional theories. However, critics warn that contextual ethics can become overly subjective, lacking clear guidelines for moral action in complex situations.

At the heart of the decision-making process in the Trolley Problem is an essential evaluation of the relative importance of a group of people versus a single individual. I believe that consequentialist ethics has captured the attention of most thinkers when reflecting on these dilemmas. This evaluation reflects the ethical principles and priorities to which individuals adhere, often aligning with broader philosophical stances on morality.

The assessment of the comparative importance of multiple lives versus one is a central aspect of decision-making within the Trolley Problem. Different ethical frameworks offer distinct criteria for this evaluation, whether they aim to maximize collective well-being, uphold moral principles, foster virtues, or draw on personal values and cultural contexts.

From a utilitarian perspective, the predominant criterion is the maximization of general well-being. In the context of the Trolley Problem, this means valuing the lives of a greater number of people over a single individual. Utilitarianism holds that the morally correct action is the one that generates the greatest net benefit for the majority.

The utilitarian evaluation involves a quantitative calculation of the value of each life, justifying the decision to pull the lever under the premise that sacrificing one person to save several is, overall, the most favorable option. This stance prioritizes numbers and aggregate well-being over individual particularities.

Philosopher Judith Jarvis Thomson, in her article The Trolley Problem (1985), argued that ethical decisions should not be simplified to a utilitarian calculation. She maintained that the act of intervening and causing harm, even for a greater good, raises a set of moral questions that go beyond merely calculating lives lost and saved. This reflection is crucial for understanding why trolley ethics expose fundamental flaws in utilitarian logic: moral principles cannot be sacrificed for the sake of a quantitatively favorable outcome.

In contrast, a deontological approach gives primacy to adherence to moral principles and duties, regardless of the consequences. From this perspective, favoring several lives over one may be seen as a violation of the principle of treating each individual as an end in themselves, rather than as a means.

Deontological ethics, particularly within the Kantian tradition, emphasizes the intrinsic value of each human being, meaning that the sacrifice of one life to save many is considered morally unacceptable. This approach focuses on the dignity and respect owed to individual life, without subordinating it to numerical calculations.

In addition to these philosophical frameworks, personal values and cultural influences also shape the evaluation process. Individuals may draw on their own moral intuitions, beliefs, and cultural norms to decide between the importance of several lives or one.

For example, cultures that emphasize collectivism tend to prioritize group well-being, while those that highlight individualism usually place greater importance on autonomy and individual rights. These cultural influences underscore the subjective nature of the valuation process, emphasizing the diversity of ethical approaches.

Beyond this specific dilemma, I believe consequentialist morality has firmly established itself as the dominant framework in many of our ethical reflections and decisions. In various areas of life, it is used as a criterion for evaluating moral situations, even if implicitly, inevitably blending with other principles as people weigh right and wrong.

From this perspective, I find that the various ethical currents seeking to resolve this dilemma share a common issue: the tendency to weigh the relative importance of five people against one, or vice versa, which could be described as a form of “moral arithmetic.” This type of calculation, in my view, is inadequate and unjustifiable, as it involves assigning an objective value to human lives based on quantitative criteria.

For example, it might seem reasonable to claim that five lives carry more weight than one, especially if we consider the greater well-being affected by the loss of those five lives and the social and emotional consequences it brings. However, if we knew that the sacrificed person would have discovered the cure for a disease affecting millions, their relative importance would change. Despite this scenario, the underlying criterion remains the same: to seek the maximization of overall well-being.

Now let’s consider another situation: someone kills John. Instinctively, we would label this act as morally wrong, a condemnable act. But if we reflect more deeply, let’s suppose John was destined to commit a crime of unimaginable magnitude, such as the extermination of millions of people. In this context, would we still judge the act of ending John’s life as morally wrong? The answer is not so clear.

If John’s death prevented genocide and, in turn, avoided a global war, the moral question becomes even more complex. Imagine that, despite the tragedies this war might bring, it led to a technological innovation that ultimately saved humanity from a greater catastrophe. Faced with this scenario, how would we then assess the original action of taking John’s life? Would it still be seen as immoral, or would its evaluation change when considering the long-term implications?

This thought experiment confronts us with a crucial issue within consequentialist ethics: as we expand the possible repercussions of an act, it becomes nearly impossible to discern whether that act is truly beneficial or harmful. We cannot know its ultimate purpose (if it has one) or foresee all its long-term consequences, leading us to the paradox of judging acts whose final effects are beyond our reach.

This illustration reveals that, given our human condition and cognitive limitations, it is impossible to determine with certainty the goodness or badness of an act based on the search for purpose or meaning in events, or by judging solely on the basis of its consequences. The possible existence of a purpose that transcends our capacities of anticipation or projection confronts us with the fact that we cannot foresee the multiple and inevitable future ramifications of our actions.

The philosopher David Hume emphasizes the uncertain nature of consequences in his work A Treatise of Human Nature, asserting that we cannot foresee all the ramifications of our actions. This reinforces the critique of consequentialist approaches, where the evaluation of an act depends on a series of assumptions that may not materialize. In this sense, the limited knowledge we have about the future strengthens the need to adopt a moral framework that does not rely solely on consequences.

Even if a higher purpose exists, we do not know whether our actions are contributing positively or negatively to its fulfillment. As the thought experiment shows, something that seemed negative in the past may, with time, be interpreted as beneficial. Clinging to a single interpretation of an event is therefore mistaken and may distort a more objective understanding of the circumstances. In this regard, a deontological morality, based on principles and which views human beings as ends in themselves, becomes more relevant by offering a more stable and ethical guide for our moral judgment.

To illustrate the fundamental flaws of consequentialism, let’s consider an extreme scenario. Suppose someone has the ability to completely erase another person’s memory, leaving no physical or mental trace. Now, imagine that this individual, after exercising such power, subjects their victim to physical and emotional torment, committing heinous acts of abuse. They then erase all memory of these events, both from the victim’s mind and their own.

Consider the darkest scenario possible: a victim subjected to physical and emotional torture, even sexual abuse, for a few minutes, after which all trace of the act vanishes. Is it justifiable for the perpetrator to indulge in their sadistic impulses, knowing there will be no negative consequences for either themselves or their victim? What objections could be raised from a consequentialist point of view if no lasting harm remains?

If this act occurs only once and the perpetrator erases all evidence of the event, does that mean the action has no moral significance? Is the torture justified simply because there are no future consequences?

The only applicable consequentialist argument would be that suffering is generated in the moment of the abuse. However, to claim that inflicting suffering is wrong regardless of future repercussions seems more aligned with a principle-based approach than with consequentialism. This example suggests that consequentialist morality does not capture the full truth, and that what we truly value are certain universal and inalienable principles, beyond immediate or long-term consequences.

Our final thought experiment on “moral arithmetic” reveals the profound limitations of a consequentialist approach in addressing complex ethical dilemmas. Imagine John is faced with a morally wrenching decision: a young man, armed, has broken into his home with the intention to rob. Inside the house is John’s grandmother, an elderly, vulnerable person. John has the option to defend his grandmother and neutralize the intruder, but this might mean risking the young man’s life.

From a strict consequentialist perspective, one could argue that the young intruder’s life has more value than that of John’s grandmother. The young man has his whole life ahead of him, filled with opportunities for change, redemption, and contributions to the world, while the grandmother, having lived most of her life, might have a more limited future in terms of contribution and well-being. However, this logic leads us to a morally unacceptable conclusion.

If we adhere to this moral arithmetic to the letter, we might justify that John should allow his grandmother to die in order to save the young intruder. Even if the young man intends to kill her, the consequentialist stance could suggest that John should refrain from acting, since, in this cold calculation, the young man, with his life ahead of him, would have more value than an elderly woman in her final years. This reasoning is not only disturbing but also profoundly immoral. How could we justify the sacrifice of a vulnerable and innocent person (the grandmother) in favor of another who has invaded the home with violent intentions?

This is precisely where the limitations of consequentialism become evident. Human life cannot be reduced to a numerical equation where values are exchanged based on age, life expectancy, or potential contributions. Every person possesses an intrinsic dignity, a value that transcends any attempt at quantitative evaluation. It is not ethically acceptable to equate one person’s life with another’s under the cold logic of maximizing aggregate well-being.

This example also forces us to reconsider the notion of subjective well-being. Each individual is a unique being, with experiences, values, and affections that are neither interchangeable nor reducible to a simple calculation of collective “happiness.” A person’s happiness and well-being are intransferrable. They cannot be added to others’ to create some form of “aggregate happiness” that would justify sacrificing an individual. What is morally right for one person is not necessarily right for another, and vice versa.

Let’s imagine an even more harrowing scenario: John is at home with his young son when a group of children, indoctrinated to carry out acts of violence, bursts into his home intending to kill his child. These children are not directly responsible for their actions; they have been manipulated and trained to believe that killing is their duty. However, for John, the dilemma is immediate and devastating: if he does not act to protect his son, the boy will die. The only way to prevent this is by confronting the attackers, even if it means harming them or, in the worst case, ending their lives.

From a purely consequentialist perspective, one might argue that the lives of the child attackers hold more “potential” than John’s son. After all, there are several of them, and over time, they could be rehabilitated and contribute to society. This reasoning would lead to the absurd conclusion that John should allow them to kill his son in the hope that the attackers might someday amend their ways. However, such logic is not only cold but profoundly immoral.

John’s right to protect his child and ensure his safety cannot be subordinated to a calculation of potential future benefits for others. While the child attackers are victims of the circumstances that led them to this situation, this does not diminish John’s responsibility to defend his son’s life, as he is completely innocent and depends on his father for survival.

This example also serves as an analogy for the ethical dilemmas nations face in times of war. Civilians are often used as tools by hostile forces, creating tragic dilemmas. Ideally, efforts are made to minimize harm to civilians, but when a nation is attacked, it has the right to defend itself, even if this involves decisions that result in the deaths of innocents. Soldiers fighting to protect their countries also have families, rights, and dignity; they are not mere pawns to be sacrificed in a larger narrative.

The problem with “moral arithmetic” is that it attempts to quantify the unquantifiable. Asking John to value the lives of the child attackers above his son’s, based on factors like their “future potential,” is unreasonable. His son’s dignity is non-negotiable, and his moral duty as a father is to protect him, even if that means making painful decisions.

Reducing ethical dilemmas to a mathematical calculation oversimplifies the complexity of morality. Human lives are not interchangeable numbers; each person has a unique and irreplaceable value. This mathematical approach fails to recognize that, for John, his son represents an entire universe of love, hope, and responsibility. Demanding that he sacrifice his child to save the attackers would deny him his right to happiness and his moral obligation to protect what he loves most.

This thought experiment not only exposes the limitations of consequentialism but underscores the need for an ethics that respects human dignity in all its forms. While ethical decisions in extreme situations are never perfect or devoid of pain, genuine morality must acknowledge the right of every individual to defend their own life and the lives of their loved ones, even in the most heart-wrenching circumstances.

These arguments about extreme ethical dilemmas also resonate in everyday situations, albeit less dramatically. For instance, in public spaces, we often tolerate behaviors that violate norms of coexistence, justifying them on the grounds that those engaging in such behaviors are marginalized, vulnerable, or caught in unfavorable social dynamics. While these circumstances undoubtedly deserve empathy and humane solutions, they should not justify demanding that the rest of society sacrifice their quality of life and rights in the name of a misunderstood “tolerance.”

Let’s consider the case of prostitution and drug use in public spaces. These phenomena are often linked to poverty, exploitation, and lack of access to opportunities. However, their presence in areas inhabited or frequented by families, especially children, creates an unsafe and deteriorated environment that undermines the quality of life for those trying to raise their children in a healthy and protected space.

Parents have the right to demand that the streets of their communities not be marked by activities that expose their children to physical, psychological, or moral risks. While it is essential to address the root causes of prostitution and drug use, such as homelessness, poverty, and addiction, this cannot mean that the rest of society must resign itself to sharing its everyday spaces with these issues without a visible path to resolution.

Similarly, tolerance for uncivil behaviors, such as neglecting cleanliness in public spaces or vandalism, is often justified by pointing to the social difficulties of those who commit them. However, accumulated filth, damaged infrastructure, or disorder in parks, squares, and streets negatively impact everyone’s quality of life, especially children who need safe and pleasant environments to thrive. It is neither fair nor reasonable for empathy toward certain marginalized groups to come at the expense of the broader community’s right to functional and clean public spaces.

Each citizen’s subjective well-being is non-transferable and cannot be sacrificed under an approach that disproportionately prioritizes those who violate norms due to personal or structural challenges. As in previous examples, there is a clear ethical boundary: while we must work to reduce the inequalities and marginalization that lead to these behaviors, the rest of society should not be forced to live in degraded environments that diminish their quality of life and their right to a safe and dignified community.

This issue becomes particularly pressing when considering the impact of these environments on future generations. Children need to grow up in spaces where they can develop without being exposed to violence, drug use, or exploitation. Denying them this right in the name of a misunderstood tolerance prioritizes the struggles of a few over the well-being of the many.

This is not about adopting punitive stances or denying the need for policies that address the roots of marginalization. On the contrary, it is crucial to work on comprehensive solutions that include rehabilitation, access to basic services, and opportunities for social reintegration for vulnerable individuals. However, these policies must coexist with a firm commitment to ensuring that public spaces remain safe and enjoyable for all citizens.

Defending a dignified and secure environment is not incompatible with empathy for the struggles of marginalized groups. But just as John has the right to protect his child in the earlier example, communities have the right to preserve the quality of their spaces and safeguard the well-being of all their members.

Returning to the previous analogy, in the case of John, his decision to protect his grandmother or child is one that, from his perspective, holds incalculable value. For him, his grandmother or child is irreplaceable, and the love and loyalty he feels compel him to do whatever it takes to save them, even if it means confronting the attacker and taking their life. Such decisions cannot be judged as morally wrong based on a numerical calculation of potential future consequences.

This example highlights the inherent flaws of consequentialism, which attempts to determine the morality of an action solely by its potential consequences. This approach fails to grasp the complexity and uniqueness of fundamental ethical decisions. People are not numbers in an equation, and their lives cannot be weighed as interchangeable commodities.

Ultimately, this thought experiment invites us to question the very idea that one life can be considered more valuable than another based on external criteria such as age or circumstances. Who are we to determine the intrinsic worth of a life based on such factors? Human dignity, by definition, is inalienable and indivisible. To reduce it to a calculation of future or potential contributions is to deny the true nature of morality, which is grounded in the unreserved respect for each individual as an end in themselves, regardless of their particular situation or potential utility.

Every individual has the same right to live their life and seek their happiness as anyone else. However, we often forget this fundamental principle, which lies in the fact that each person is an end in themselves. A society that builds its well-being on the sacrifice of a few is nothing more than a dystopia, for those few have the same right to live in fullness and happiness as the rest. No matter how much pleasure or benefit the majority derives from their suffering, the torture and sacrifice of others can never be morally justifiable, because every human being deserves respect and dignity, regardless of the circumstances.

True morality does not arise from the cold calculation of consequences but from the unconditional respect for human dignity and the recognition of each person’s right to pursue their subjective well-being. In this sense, John has every right to defend his grandmother’s life, and no argument claiming that the aggressor’s life is “more valuable” can undermine this right. The value of life is not measured by external qualities such as age, potential, or future life expectations.

This thought experiment exposes the fallacy of attempting to apply an “arithmetic of values” to assess human lives. The moral judgment of a situation or a person cannot be reduced to external, objective factors; instead, it must be grounded in the subjective, individual experience. Classic ethical dilemmas, like the trolley problem, fail by suggesting that human value can be evaluated mathematically, and their consequentialist conclusions underestimate the complexity of real moral decisions.

As the philosopher Martha Nussbaum points out in her book The Fragility of Goodness, human dignity is not something that can be negotiated or weighed; it is a fundamental principle that must guide our ethical decisions. Nussbaum argues that every person has the right to a dignified life and that the value of each human life must be respected in its singularity. This approach is essential to challenging the logic of “moral arithmetic,” which attempts to rank lives according to external and utilitarian criteria.

Five lives are not inherently more important than one, nor is one life more valuable than five. Judgments about the value of life can only be valid from the personal perspective of those making them. What is significant for one person may not be for another, and no external evaluation can replace this subjective dimension. Therefore, any attempt at objectivity in morality must be grounded in the defense of each individual’s subjective well-being, recognizing that every human being is a universe unto themselves, and their life and well-being cannot be exchanged or subordinated to others through any external moral calculation.

Sources:

Singer, P. (1993). Practical Ethics (2nd ed.). Cambridge University Press.

Thomson, J. J. (1985). The trolley problem. Journal of Philosophy, 96(6), 204-224.

Aristóteles. (2004). Nicomachean Ethics (R. Crisp, Ed. & Trans.). Cambridge University Press. (Original work published ca. 350 B.C.E.).

Hume, D. (1739). A Treatise of Human Nature (L. A. Selby-Bigge, Ed. & P. H. Nidditch, Trans.). Oxford University Press. (1978).

Nussbaum, M. C. (2006). Frontiers of Justice: Disability, Nationality, Species Membership. Harvard University Press.