Ontological commitment

An ontological commitment of a language is one or more objects postulated to exist by that language. The 'existence' referred to need not be 'real', but exist only in a universe of discourse. As an example, legal systems use vocabulary referring to 'legal persons' that are collective entities that have rights. One says the legal doctrine has an ontological commitment to non-singular individuals. In information systems and artificial intelligence, where an ontology refers to a specific vocabulary and a set of explicit assumptions about the meaning and usage of these words, an ontological commitment is an agreement to use the shared vocabulary in a coherent and consistent manner within a specific context. In philosophy, a "theory is ontologically committed to an object only if that object occurs in all the ontologies of that theory." The sentence “Napoleon is one of my ancestors” apparently commits us only to the existence of two individuals (i.e., Napoleon and the speaker) and a line of ancestry between them. The fact that no other people or objects are mentioned seems to limit the “commitment” of the sentence. However, it is well known that sentences of this kind cannot be interpreted in first-order logic, where individual variables stand for individual things. Instead, they must be represented in some second-order form. In ordinary language, such second-order forms use either grammatical plurals or terms such as “set of” or “group of”. For example, the sentence involving Napoleon can be rewritten as “any group of people that includes me and the parents of each person in the group must also include Napoleon,” which is easily interpreted as a statement in second-order logic (one would naturally start by assigning a name, such as G, to the group of people under consideration). Formally, collective noun forms such as “a group of people” are represented by second-order variables, or by first-order variables standing for sets (which are well-defined objects in mathematics and logic).