In formal semantics, 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."
Background 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). Since these variables do not stand for individual objects, it seems we are “ontologically committed” to entities other than individuals — sets, classes, and so on. As Willard Van Orman Quine puts it,
the general adoption of class variables of quantification ushers in a theory whose laws were not in general expressible in the antecedent levels of logic. The price paid for this increased power is ontological: objects of a special and abstract kind, viz. classes, are now presupposed. Formally it is precisely in allowing quantification over class variables α, β, etc., that we assume a range of values for these variables to refer to. To be assumed as an entity is to be assumed as a value of a variable. (Methods of Logic, 1950, p. 228) Another statement about individuals that appears “ontologically innocent” is the well-known Geach–Kaplan sentence: Some critics admire only one another.
Quine's criterion Willard Van Orman Quine provided an early and influential formulation of ontological commitment:
If one affirms a statement using a name or other singular term, or an initial phrase of 'existential quantification', like 'There are some so-and-sos', then one must either (1) admit that one is committed to the existence of things answering to the singular term or satisfying the descriptions, or (2) provide a 'paraphrase' of the statement that eschews singular terms and quantification over so-and sos. Quine's criterion can be seen as a logical development of the methods of Bertrand Russell and G.E. Moore, who assumed that one must accept the existence of entities corresponding to the singular terms used in statements one accepts, unless and until one finds systematic methods of paraphrase that eliminate these terms. The purpose of Quine's strategy is to determine just how the ontological commitment of a theory is to be found. Quine argued that the only ontologically committing expressions are variables bound by a first-order existential quantifier, and natural language expressions which were formalized using variables bound by first-order existential quantifiers. Attempts have been made to argue that predicates are also ontologically committing, and thus that subject-predicate sentences bear additional ontological commitment to abstract objects such as universals, sets, or classes. It has been suggested that the use of meaningful names in nonexistence statements such as "Pegasus does not exist" brings with it an ontological commitment to empty names like Pegasus, a quandary referred to as Plato's beard and escaped by using quantifiers. This discussion has a connection to the Carnap–Quine argument over analytic and synthetic objects. Although Quine refers to 'ontological commitment' in this connection, in his rejection of the analytic/synthetic distinction he does not rely upon the formal translation of any particular theory along the lines he has suggested. Instead, Quine argues by using examples that although there are tautological statements in a formal theory, like "all squares are rectangles", a formal theory necessarily contains references to objects that are not tautological, but have external connections. That is, there is an ontological commitment to such external objects. In addition, the terms used to interpret the application of the theory are not simply descriptions of sensory input, but are statements in a context. That is, inversely, there is an ontological commitment of these observational objects to the formal theory. As Ryan puts it: "Rather than being divided between contingent synthetic claims and indubitable analytic propositions, our beliefs constitute a continuous range from a periphery of sense-reports to interior concepts that are comparatively theory-laden and general." Thus we end up with Quine's 'flat' ontology that does not see a distinction between analytic and synthetic objects. Quine further made a distinction between the ontological commitments of a theory (what the theory says exists) and the ideological commitments of a theory (those concepts, logical or non-logical, that are expressible within the theory).
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