An ontological commitment refers to a relation between a language and certain objects postulated to be extant 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, then 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). 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 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 p. 228)
Another statement about individuals that appears “ontologically innocent” is the well-known Geach–Kaplan sentence: Some critics admire only one another.
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 use in statements one accepts, unless and until one finds systematic methods of paraphrase that eliminate these terms.—Michael J. Loux & Dean W. Zimmerman, The Oxford Handbook of Metaphysics, p. 4
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 fictional objects 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 proposition's, our beliefs constituent 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.
Whatever process one uses to determine the ontological commitments of a theory, that does not prescribe what ontological commitments one should have. Quine regarded this as a matter of epistemology, which theory one should accept. "Appeal is made to [concerns of] explanatory power, parsimony, conservatism, precision, and so on".
Ontological parsimony can be defined in various ways, and often is equated to versions of Occam's razor, a "rule of thumb, which obliges us to favor theories or hypothoses that make the fewest unwarranted, or ad hoc, assumptions about the data from which they are derived." Glock, regards 'ontological parsimony' as one of the 'five main points' of Quine's conception of ontology.
Following Quine, Baker states that a theory, T, is ontologically committed to items F if and only if T entails that F′s exist. If two theories, T1 and T2, have the same ontological commitments except that T2 is ontologically committed to F′s while T1 is not, then T1 is more parsimonious than T2. More generally, a sufficient condition for T1 being more parsimonious than T2 is for the ontological commitments of T1 to be a proper subset of those of T2. 
These ideas lead to the following particular formulation of Occam's razor: 'Other things being equal, if T1 is more ontologically parsimonious than T2 then it is rational to prefer T1 to T2.' While a common formulation stipulates only that entities should not be multiplied beyond necessity, this version by contrast, states that entities should not be multiplied other things being equal, and this is compatible with parsimony being a comparatively weak theoretical virtue.
The standard approach to ontological commitment has been that, once a theory has been regimented and/or "paraphrased" into an agreed "canonical" version, which may indeed be in formal logical notation rather than the original language of the theory, ontological commitments can be read off straightforwardly from the presence of certain ontologically committing expressions (e.g. bound variables of existential quantification). Although there is substantial debate about which expressions are ontologically committing, parties to that debate generally agree that the expressions they prefer are reliable bearers of ontological commitment, imparting ontological commitment to all regimented sentences in which they occur. This assumption has been challenged.
Inwagen has taken issue with Quine's methodology, claiming that this process did not lead to a unique set of fundamental objects, but to several possible sets, and one never could be certain that all the possible sets had been found. He also took issue with Quine's notion of a theory, which he felt was tantamount to suggesting a 'theory' was just a collection of sentences. Inwagen suggested that Quine's approach provided useful tools for discovering what entities were ontological commitments, but that he had not been successful. His attempts are comparable to an "attempt to reach the moon by climbing ever higher trees..."
It has been suggested that the ontological commitments of a theory cannot be discerned by analysis of the syntax of sentences, looking for ontologically committing expressions, because the true ontological commitments of a sentence (or theory) are restricted to the entities needed to serve as truthmakers for that sentence, and the syntax of even a regimented or formalized sentence is not a reliable guide to what entities are needed to make it true. However, this view has been attacked by Jonathan Shaffer, who has argued that truthmaking is not an adequate test for ontological commitment: at best, the search for the truthmakers of our theory will tell us what is "fundamental", but not what our theory is ontologically committed to, and hence will not serve as a good way of deciding what exists.
It also has been argued that the syntax of sentences is not a reliable guide to their ontological commitments because English has no form of words which reliably functions to make an existence-claim in every context in which it is used. For example, Jody Azzouni suggests that "There is" does not make any kind of genuine existence-claim when it is used in a sentence such as "There are mice that talk". Since the meaning of the existential quantifier in formal notation is usually explained in terms of its equivalence to English expressions such as "there is" and "there exist", and since these English expressions are not reliably ontologically committing, it comes to seem that we cannot be sure of our theory's ontological commitments even after it has been regimented into a canonical formulation. This argument has been attacked by Howard Peacock, who suggests that Azzouni's strategy conflates two different kinds of ontological commitment – one which is intended as a measure of what a theory explicitly claims to exist, and one which is intended as a measure of what is required for the theory to be true; what the ontological costs of the theory are. If ontological commitment is thought of as a matter of the ontological costs of a theory, then it is possible that a sentence may be ontologically committed to an entity even though competent speakers of the language do not recognize the sentence as asserting the existence of that entity. Ontological commitment is not a matter of what commitments one explicitly recognizes, but rather a matter of what commitments are actually incurred.
- Burkhard Schäfer (1998). "Invariance principles and the community of heirs". In N Guarino, ed. Formal Ontology in Information Systems: Proceedings of the 1st International Conference June 6-8, 1998, Trento, Italy. pp. 108 ff. ISBN 9051993994.
- Nicola Guarino (1998). "Formal ontology and information systems". Formal Ontology in Information Systems: Proceedings of the First International Conference (FIOS'98), June 6-8, Trento, Italy. IOS Press. pp. 3 ff. ISBN 9051993994.
- Robert Audi, ed. (1999). "Ontological commitment". The Cambridge Dictionary of Philosophy (Paperback 2nd ed.). p. 631. ISBN 0521637228. A shortened version of that definition is as follows:
- The ontological commitments of a theory are those things which occur in all the ontologies of that theory. To explain further, the ontology of a theory consists of the objects the theory makes use of. A dependence of a theory upon an object is indicated if the theory fails when the object is omitted. However, the ontology of a theory is not necessarily unique. A theory is ontologically committed to an object only if that object occurs in all the ontologies of that theory. A theory also can be ontologically committed to a class of objects if that class is populated (not necessarily by the same objects) in all its ontologies.
- Quine, W. V. (1948). "On What There Is". Review of Metaphysics 2: 21–38.. Reprinted in From a Logical Point of View: Nine Logico-philosophical Essays (2nd ed.). Harvard University Press. 1980. pp. 1–19. ISBN 0674323513. See Wikisource.
- Michael J. Loux, Dean W. Zimmerman (2005). "Introduction". In Michael J. Loux, Dean W. Zimmerman, eds. The Oxford Handbook of Metaphysics. Oxford Handbooks Online. ISBN 0199284229.
- Willard Van Orman Quine (1983). "Chapter 22: Ontology and ideology revisited". Confessions of a Confirmed Extensionalist: And Other Essays. Harvard University Press. pp. 315 ff. ISBN 0674030842.
- Of course, this description is not understandable unless one knows what first-order existential quantifiers are and what is meant by saying they are bound. An approachable discussion of these matters is found in Jan Dejnožka (1996). "Chapter 1: Introduction". The Ontology of the Analytic Tradition and Its Origins: Realism, Possibility, and Identity in Frege, Russell, Wittgenstein, and Quine. Rowman & Littlefield. pp. 1 ff. ISBN 0822630532.
- Robert J Fogelin (2004). The Cambridge Companion to Quine. Cambridge University Press. p. 36. ISBN 0521639492.
- Frank X Ryan (2004). "Analytic: Analytic/Synthetic". In John Lachs, Robert B. Talisse, eds. American Philosophy: An Encyclopedia. Psychology Press. pp. 36–39. ISBN 020349279X.
- Quine, W. V. (1951). "On Carnap’s views on ontology". Philosophical Studies 2: 65–72. Reprinted in Willard Van Orman Quine (1976). "Chapter 9: On Carnap's views on ontology". The Ways of Paradox (2nd ed.). Harvard University Press. pp. 203–211. ISBN 0674948378.
- Willard Van Orman Quine (1980). "Chapter 2: Two dogmas of empiricism". From a Logical Point of View: Nine Logico-philosophical Essays (2nd ed.). Harvard University Press. pp. 20 'ff. ISBN 0674323513. See this
- Jonathan Schaffer (2009). "On What Grounds What Metametaphysics". In Chalmers, Manley, and Wasserman, eds. Metametaphysics. Oxford University Press. pp. 347–83. ISBN 0199546045. Reprinted by Philosopher’s Annual 29, eds. Grim, Charlow, Gallow, and Herold; also reprinted in Metaphysics: An Anthology, 2nd edition, eds. Kim, Korman, and Sosa (2011), 73-96: Blackwell.) Contains an analysis of Quine and proposes that questions of existence are not fundamental.
- See for example, Hilary Putnam (2001). "The analytic and the synthetic". In Dagfinn Fllesdal, ed. Philosophy of Quine: General, reviews, and analytic/synthetic, Volume 1. Taylor & Francis. pp. 252 ff. ISBN 0815337388.
- Alex Orenstein (1998). "Quine, Willard Van Orman". In Edward Craig, ed. Routledge Encyclopedia of Philosophy 8. pp. 8 ff. ISBN 0415073103. See also Choice of a theory.
- Kaila E Folinsbee et al. (2007). "Quantitative approaches to phylogenetics; §5.2: Fount of stability and confusion: A synopsis of parsimony in systematics". In Winfried Henke, ed. Handbook of Paleoanthropology: Primate evolution and human origins: Volume 2. Springer. p. 168. ISBN 3540324747.
- Hans-Johann Glock (2004). "§1: Ontological commitment and ontological parsimony". Quine and Davidson on Language, Thought, and Reality. Cambridge University Press. pp. 41–47. ISBN 1139436732.
- Willard Van Quine (1981). Theories and Things (3rd ed.). Harvard University Press. pp. 144 ff. ISBN 0674879260. Cited by Alan Baker.
- This section is a slightly modified version of the discussion by Baker, Alan (Feb 25, 2010). "Simplicity". In Edward N. Zalta, ed. The Stanford Encyclopedia of Philosophy (Summer 2011 Edition).
- Alex Ornstein (2008). "Quine vs. Quine: Canonical notation, paraphrase, and regimentation". In Chase B Wrenn, ed. Naturalism, Reference and Ontology: Essays in Honor of Roger F. Gibson. Peter Lang Publishing, Inc. p. 171. ISBN 1433102293.
- Marion David (2008). "Quine's Ladder: Two and a half pages from the Philosophy of Logic". In Peter A. French, Howard Wettstein, eds. Midwest Studies in Philosophy, Truth and its Deformities (Volume XXXII). Wiley-Blackwell. pp. 274 ff. ISBN 1405191457.
- Mark Colyvan (2001). "§4.2 What is it to be indispensable?". The Indispensability of Mathematics. Oxford University Press. pp. 76 ff. ISBN 0198031440.
- Peter Van Inwagen (1998). "Meta-ontology". Erkenntnis 48: 233–250.
- Peter van Inwagen (2008). "Chapter 6: Quine's 1946 lecture on nominalism". In Dean Zimmerman, ed. Oxford Studies in Metaphysics : Volume 4. Oxford University Press. pp. 125 ff. ISBN 0191562319. "Quine has endorsed several closely related theses that I have referred to, collectively, as his "meta-ontolgy". These are...those of his theses that pertain to the topic "ontological commitment" or "ontic commitment"."
- Heil, J. (2003). From an ontological point of view. Oxford: Oxford University Press.
- Shaffer, Jonathan. "Truthmaker Commitments".
- Azzouni, Jody (2004). Deflating Existential Consequence: A Case for Nominalism. Oxford: Oxford University Press.
- Peacock, Howard (2011). "Two Kinds of Ontological Commitment". The Philosophical Quarterly 61 (242): 79–104.