McNamara, Paul and Frederik Van De Putte, "Deontic Logic", The Stanford Encyclopedia of Philosophy (Fall 2022 Edition), Edward N. Zalta & Uri Nodelman (eds.), URL = <https://plato.stanford.edu/archives/fall2022/entries/logic-deontic/>.
- permissible (permitted)
- impermissible (forbidden, prohibited)
- obligatory (duty, required)
- omissible (non-obligatory)
- optional
- non-optional
- must
- ought
- supererogatory (beyond the call) [직무 이상으로 일하는]
- indifferent / significant
- the least one can do
- better than / best / good / bad
- claim / liberty / power / immunity
- responsibility
- blame / praise
- agency / action
You are obligated to return your friend’s car by noon, and the least you can do is return it on time with the same level of battery charge it had when you borrowed it, but it is beyond the call to buy your friend a dinner on top of that.
Various things seem to follow: It is impermissible to not return your friends car by noon; it is obligatory to return your friends car, it is optional to return it with a full charge, and doing the least you can do precludes buying dinner. For deontic logic, the aim is to develop accounts of the logical contribution made by the key concepts listed above.
Although we need to be cautious about making too easy a link between deontic logic and practicality, many of the notions listed above are typically employed in attempting to regulate and coordinate our lives. For these reasons, deontic logics often directly involve topics of considerable practical significance such as morality, law, social and business organizations (their norms, as well as their normative constitution), and security systems. To that extent, studying the logic of notions with such practical significance adds practical significance to deontic logic itself. However, in this entry we will focus on deontic logic itself, rather than its applications and practical relevance.
1. Informal Preliminaries and Background
Deontic logic has been regularly influenced by reflection on the logic of modal notions, such as necessity (in varying senses of the term). In particular, analogies between alethic (truth-implicating) modal notions and deontic notions were noticed before the fourteenth century in Europe, where we might say that the rudiments of formal (though not symbolic) deontic logic experienced its initial European stirrings. In Islamic thought, such analogies go back at least as far as the tenth century.
Although interest in what can be arguably called formal aspects of deontic logic continued off and on, the trend toward studying logic using the symbolic and exact techniques of mathematics began primarily in the nineteenth century, and became dominant in the twentieth century. Work in twentieth century symbolic modal logic provided the explicit impetus for von Wright (1951a, 1951b), the central early figure in the emergence of deontic logic as a full-fledged branch of symbolic logic in the twentieth century. However, we note that prior to von Wright 1951a, there was one significant earlier episode in symbolic deontic logic, namely Mally 1926.
1.1 Some Informal Rudiments of Alethic Modal Logic
Alethic modal logic is the logic of necessary truth and related notions. Consider six basic alethic modal notions, expressed as sentential operators—constructions that, when applied to a sentence, yield a sentence (as does “it is not the case that”)
- it is necessary (necessarily true) that
- it is possible that
- it is impossible that
- it is non-necessary that
- it is contingent that
- it is non-contingent that
Although all of the above operators are generally deemed definable in terms of any one of the first four, the necessity operator, usually symbolized as a box, ◻, is typically taken as primitive and the rest defined accordingly. Where “¬”, “&” , and “∨“ denote classical negation, conjunction, and disjunction, the definitions are as follows:
- It is possible that
- It is impossible that p
- It is non-necessary that
def= ¬◻p- It is contingent that p
def= ¬◻p & ¬◻¬p- It is non-contingent that