Deontic Logic
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When in 1978 I started to work at the Law School of Leiden University, I met a new colleague: Bob Brouwer. Bob had been in Salzburg, with Ilmar Tammelo, and there he had been infected with an interest in legal and deontic logic. It did not take long before Bob had passed this infection to me. I never lost my interest in legal and deontic logic, but my relation to researchers in the field, especially that of deontic logic, has been problematic. The real 'experts' in deontic logic typically did not appreciate what I did, and - frankly - that lack of appreciation was often mutual. It seemed that deontic logic was one branch of logic in their hands, and a different branch in my hands. As this website contains an overview of my research, I will present deontic logic as I see it. But the reader should be warned that my view of deontic logic is somewhat excentric in the eyes of many other researchers.
Deontic logic deals with facts regarding what an agent must, or must not do. It also deals with the issue of what an agent is permitted to do. It does not deal with the evaluation of acts or facts as good or bad.
Sometimes the notion of 'deontic' is associated with the notion of 'ought', but that can lead to mistakes. There is an important distinction between 'ought-to-do' and 'ought-to-be'. An ought-to-be judgement expresses that a particular state of affairs ought (not) to be the case. For example, the fences before cottages ought to be white, or lunatics ought not to be armed. An ought-to-be is a kind of evaluation, and does not indicate what ought to be done. That is the reason why I (in contrast to most deontic logicians) exclude ought-to-be judgements from the field of deontic logic. Ought-to-do judgments, on the contrary, belong to the core of deontic logic. These judgements express what an agent ought to do, for instance 'Jaap ought to peel the potatoes'.
Logic is usually seen as the theory of valid inference, where inference is a relation between two sets of sentences. One set is the set of premises, and the other set is the set of conclusions. The latter set often contains only one sentence: the conclusion of the argument. The sentences in valid arguments are particularly interesting if they are true, that is: if they express facts.
The truth or falsity of the premises and the conclusion of an argument are not directly relevant for the validity of the argument (but only for their soundness). Nevertheless, people are usually interested in logic to determine whether the conclusion of an argument is true, on the assumption that the premises are true. In other words, the practical relevance of logic deals with what the facts are, given other facts.
Because of this close relation between the truth of the propositions (sentences) in an argument, and the facts that the argument establishes on the basis of other facts, I have started to interpret logic, not so much as a theory about relations between sentences, but as a theory about the relations between facts, Logic is, to state this in other words, an ontological theory dealing with the question of what the facts must be, given the existence of other facts.
It is customary in deontic logic to work with 'deontic operators' which are used to express deontic sentences. The usual operators are O, P, and F, which stand for, respectively, Ought, Permitted, and Forbidden. For several reasons, I find this infelicitous. One reason has to do with the technical meaning of an operator. An operator is a function that maps (one or more) elements of a domain to (one or more) elements of the same domain. For example, the +-operator in arithmetic maps a pair of numbers (e.g. 3 and 6) on a third number (here: 9). Now suppose that the letter O stands for a deontic operator and that Op is a well-formed sentence. If Op is a sentence, and if O is an operator, p must also be a sentence. This means that p cannot be a term that stands for an action type, or for an act token.
If p is to stand for an action type, and Op means that it is obligatory to perform this type of action (e.g. save drowning persons), then O is not an operator, but a predicate that has one parameter which stands for an action type.
Although it is not impossible to work with predicates that operate on action types, it is not very practical either. It is much more natural to have a two-place predicate that operates on an agent and an action type. For instance: Jaap (agent) ought to (deontic predicate) peel the potatoes (action type).
Only action types can be obligatory for agents. Act tokens have already been performed (by definition) and it makes little sense to prescribe (or forbid) them.What we do is to evaluate act tokens by saying that they were right or wrong. Right and wrong are one-place predicates that operate on act tokens. They do not need to mention the agent, because the agent is given with the act token.
Another reason why the use of a set of deontic operators is infelicitous is that the deontic vocabulary of natural languages is much richer than obligation, prohibiton and permission. A satisfactory account of deontic reasoning must somehow deal with this richess. One example of the richer vocabulary of natural language is the distinction between duties and obligations. This distinction mainly plays a role in law. Following the Roman law tradition, an obligation is a relation between (usually) two legal subjects, according to which the one subject (the debtor) must do something and the other subject (the creditor) has a right against the debtor that (s)he will do it. Typical examples of such obligations are contractual obligations and obligations to compensate damage. Obligations, such as contractual obligations, are the results of events to which the law attaches the existence of the obligation. The content of the obligation, such as what the debtor must do, is typically also determined by this event.
Whereas obligations (in the sense defined above) are always directed to some other agent, duties are not. Duties involve that an agent must do something, but although others may have an interest in what the duty holder does, they do not have a right that the duty-holder will do it. Examples of such duties are the duty to halt for a red traffic light, or the duty for public officers not to accept bribes. Duties are usually connected to roles, such as the role of a car driver, or to status, such as the status of being a parent. Otherwise than obligations they are not the outcome of some event. Moreover, the content of a duty is determined by the law, and not by an event. Duties are typically enforced through public law, while obligations are typically enforced through private law.
From here on I will restrict myself to duties and ignore ought-to-do's. If agent A has the duty to do X, this does not mean that A ought to do X. Duties are factors that determine what an agent ought to do, but they are not a weak form of ought-to-do. Duties can conflict with each other in the sense that an agent cannot comply with all his or her duties. Ought-to-do's cannot conflict in this way. If two duties conflict, at most one of them can determine what the agent ougt to do.
The distinction betwen what an agent has the duty to do and what the agent ought to do was introduced in Foundations and Building Blocks of Law (2018), p. 151/2. It was elaborated in Deontic Logic for Lawyers (2025).
All duties exist for a reason. This reason can be a single event, such as the command to stop issued by a police officer. It can also be that a duty-imposing rule applies to a case, for instance if a car driver approaches a red traffic light. More in general, the step from 'ordinary' facts to the existence of a duty is a very common transition from non-deontic to deontic facts. The other common step to this effect is from an event that generates an obligation to the existence of the obligation.
The steps in deontic reasoning are elaborated most extensive in:
If an agent has the duty to do something or to refrain from something, this is a reason why the agent ought (not) to do it. This reason may have to be balanced against other reasons, but it is not a matter of logic what these other reasons might be.
An ought-to-do always belongs to a point of view, and the three most relevant points of view in this connection are those of morality, law, and prudence. If, for instance, the issue at stake is what an agent legally speaking ought to do, the answer can be found by balancing all reasons for what the agent legally ought to do.
In the 1990s it was still widely held desirable that a system of logic would include the model-theoretic semantics (MTS) for the logic. That explains why I tried to develop such a model-theoretic semantics for RBL. At present, I do not believe in the usefulness of MTS anymore, except perhaps for exceptional cases. But my attempts to create MTS for RBL gave me more insight in what MTS is all about and gave me reasons to depreciate the role of semantics for logic.
An argument is deductively valid if it is logically impossible that all the premises of the argument are true while the conclusion is false. But what is logically impossible? MTS is a tool to specify just that. I will explain this for propositional logic, because that is easier than MTS for predicate logic, but the underlying intuition is in both cases the same. For my argument, I assume that the reader is familiar with propositional logic and the role in it for truth tables. Truth tables are the version of MTS that is used for propositional logic.
Propositional logic (PL) distinguishes between elementary and compound propositions. It assumes that the truth values of all elementary propositions are independent from each other. In contrast, the truth values of compound propositions are determined by the truth values of the elementary propositions from which they are constructed and the definitions of the logical operators (NOT, AND, OR, IF...THEN ) used for their construction. This means two things:
Truth tables are a useful tool in PL, but there is a 'minor' problem: why are the logical operators in PL precisely the operators that are actually used? The operators determine which arguments count as logically valid, and if other operators are used, other arguments turn out to be (in)valid. Moreover, why are only the logical operators considered in determining what is logically (im)possible?
In my attempts to develop MTS for RBL, I needed to assign a logical role to sentences stating that some rule is valid. In PL this logical role was confined to the logical operators and was extended to quantifiers in predicate logic. The use of that technique (assigning a logical role to full statements, and not merely to logical operators and quantifiers, made it clear to me that the determination of what counts as logically (im)possible is rather arbitrary. Because the logical (im)possibility of sentences being simultaneously true or false determines the logical validity of arguments in which these sentences play a role, it is possible to manipulate the logical validity of arguments by adapting the definition of what is logically possible. It turns out that it is not cast in stone what arguments are logically valid. As Quine had already pointed out earlier, logical relations are what count as logical relations. Since 'counts as'-relations are a matter of social reality, logic is a matter of social reality.
While writing the above paragraph, I suddenly realised that predicate logic with identity also uses full sentences (namely statements of identity) in a logical role by allowing the substitution of terms that stand for the same individual (Leibniz's law). I never realised before that this constituted a separate logical technique.
If logic is a part of social reality, the study of logic is a part of the study of social reality. I only became aware of what this implied for logical theory when I was doing research on social reality in the 2020s. I am still thinking about the precise implications, but my present hunch is that social reality, including logic, depends on a coherent reconstruction of facts and rules that were broadly adopted for no reason (conventional facts and rules). In the end it is all coherentism, and - to become even mere speculative - cognitive consonance for social groups. But I guess I have lost most readers now.
Deontic logic is sometimes defined as the logic of norms, and if that is done, it is usually a sign of misunderstanding. The notion of a norm. is perhaps the most confusing one in deontic logic. Many different things, such as all rules, speech acts that impose duties, duties themselves, and more, have been called norms ... There has been a time that I saw this confusion as a reason not to use the notion of a norm anymore (Studies in Legal Logic (2005, Chapter 6)) and to use more precise words, such as 'rule', or 'duty'. At other occasions (Of Norms, 2018; Foundations and Building Blocks of Law (2018), Chapter 8), I proposed a precise meaning namely 'duty-imposing rule'. In the course of the years, I have experienced how hard it is to eradicate the obscure use of the word 'norm'. The most recent example is that an author (not myself) found it difficult to get a paper accepted for a journal if he would not use the word 'norm' for rules.
I do not want to waste more words on norms here, except for repeating my long-standing view that the word ' norm' should not be used at all, or that it should be given a clear and unambiguous meaning before it is used.
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