Obligations & Permissions
Human life is riddled with obligations and permissions. We pay taxes, wait at red lights, and occasionally pretend we enjoy balut (we really don’t). On the surface, this seems straightforward: do what you must, avoid what you must not, and enjoy what you may. Yet when philosophers tried to turn these “common-sense rules” into formal logic, things got weird. In this work, I will tackle some counterintuitive aspects of deontic logic (where “ought” collides with the cold, unforgiving rigor of symbols).
Deontic logic is a branch of modal logic dedicated to modeling duties, permissions, and prohibitions (think of it as a philosopher’s version of a GPS, except it sometimes gives directions straight into a paradoxical swamp). In this system, “O P” reads as “It is obligatory that P,” “P P” as “It is permitted that P,” and “F P” as “It is forbidden that P.” On paper, this looks simple and elegant. In practice, it can produce conclusions so counterintuitive that you start questioning not just morality, but reality itself.
Take the Ross paradox (and no, Ross from Friends is not involved, although that might explain some things). One of the earliest and most famous examples is the Ross paradox, named after the philosopher W.D. Ross. Consider a simple obligation: mailing a letter. Classical deontic logic allows the inference that if mailing the letter is obligatory, then “mailing the letter or burning it” is also obligatory. The formal reasoning follows straightforwardly: from “M,” one can infer “M ∨ B.” Yet clearly, burning the letter is not what anyone intends as an obligation. The paradox demonstrates that deontic logic, unlike everyday reasoning, treats disjunctions mechanically, sometimes producing obligations that appear morally absurd. This illustrates the tension between formal consistency and intuitive moral understanding. In real-life situations, societies handle similar challenges by contextualizing obligations. Laws are rarely read in isolation; rather, legal interpretation relies on intention, precedent, and social norms to prevent absurd obligations, ensuring that the spirit of a rule aligns with its practical application.In real life, lawyers and judges avoid this absurdity by looking at context and intent (because if we actually obliged people to mail-or-burn letters, the postal service would file a formal complaint).
Another counterintuitive feature arises in contrary-to-duty scenarios, exemplified by Chisholm’s paradox. Suppose a person has an obligation to help a friend. That obligation is clear and intuitive. Now imagine that they fail to help. Common sense suggests a secondary obligation emerges: the person ought to apologize or otherwise remedy the harm. Formalizing this situation in classical deontic logic, however, produces difficulties. If one encodes the primary obligation as O H (obliged to help) and then acknowledges the violation ¬H (did not help), the logic struggles to capture what ought to be done after the violation. Naive formulations can imply that the person is now obliged to do the impossible or even to commit further violations, a result that feels paradoxical. In everyday life, such situations are managed through the concept of remedial obligations or corrective duties. Ethical frameworks and legal systems explicitly recognize that obligations after violations are distinct and context-dependent, rather than mechanically derived from the original duty.In other words, humans are better at common sense than symbolic logic, at least until someone invents computer systems that can feel guilt.
Another oddball phenomenon arises when obligations collide with impossibility. Suppose a rule says you must always prevent harm, but suddenly there is no way to do so (maybe you’re stuck in a traffic jam while the world burns metaphorically — or literally). Standard deontic logic still insists you are obliged (O P), which is absurd. Human society handles this with doctrines like “impossibility” in law, or practical forgiveness in ethics (we don’t blame people for failing to lift impossibly heavy moral boulders). The lesson: logic is literal, humans are pragmatic, and sometimes pragmatism wins.
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These paradoxes highlight the core tension of deontic logic (think of it as a debate between the strict robot in your head and the messy human in your heart). Logic demands consistency and mechanical inference; human morality cares about context, capacity, and consequences. Yet deontic logic is not useless. By exposing hidden contradictions (like “mail the letter or burn it”) and potential conflicts, it teaches us to pay attention to rules’ implications before we end up in absurd ethical cul-de-sacs.
Consider the law, which is basically a giant, slow-moving exercise in applied deontic logic (and the occasional comedy of errors). Obligations like “file taxes” or “drive on the right” might seem simple, but legal reasoning must account for context, exceptions, and intent. Courts routinely avoid Ross-style absurdities by interpreting laws in light of purpose rather than formal derivation (and also because nobody wants to see a courtroom filled with people trying to mail-or-burn letters simultaneously).
Healthcare ethics provides another stage for deontic oddities. A doctor might have obligations to care for patients, maintain confidentiality, and avoid harm. Conflicts arise constantly: one patient wants a risky procedure, another needs immediate attention. Deontic logic can formalize these conflicts (bringing clarity) while real-world ethics resolves them with prioritization, guidelines, and sometimes professional judgment (and yes, occasional coffee-fueled improvisation).
Even mundane life offers glimpses of deontic logic at work (though less formally). You promise to support a friend but fail to do so. Formal logic might infer an impossible or absurd secondary obligation, but we humans handle it by apologizing, making amends, or otherwise exercising discretion. Obligations exist in networks (not isolation), and understanding those networks helps avoid both moral chaos and social awkwardness.
Modern philosophers and computer scientists have tried to tame these paradoxes. Conditional and dynamic deontic logics allow rules like “If A occurs, it is obligatory to do B”, which handles remedial duties and conflicts more gracefully (and avoids telling you to do the impossible). Deontic logic, paradoxes and all, provides a blueprint — but practical judgment fills in the gaps (thankfully).
Ultimately, deontic logic is a lesson in humility. Obligations, permissions, and prohibitions are not just statements; they are structured, interacting, and sometimes hilariously counterintuitive. Ross, Chisholm, and impossible obligations remind us that logic can be both enlightening and absurd. Real-life applications (e.g., law, medicine, technology, and everyday moral reasoning) show how humans navigate these complexities: we interpret, prioritize, contextualize, and occasionally shrug at the impossible. Deontic logic gives us the map; human judgment decides whether to follow it, wander off, or start laughing at the absurdity of formal obligations.
