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What is Ontological Commitment?
I can infer some understanding from its usage in philosophical texts, but I would like to have a definitive answer to be able to confidently use the notion on my own. Other (for me) helpful formulations would be: What things bear ontological commitment?, When is one committed to an ontological claim?
In philosophy[,] a "theory is ontologically committed to an object only if that object occurs in all the ontologies of that theory[.]"
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.
[I think, but cannot verify:] Robert Audi, ed. (1999). "Ontological commitment". The Cambridge Dictionary of Philosophy (Paperback 2nd ed.). p. 631.
I wonder if your uncertainty is over what ontology is. One's ontology is one's theory of what sorts of objects have reality. For instance, most everyone agrees that physical objects are real--perhaps, in some ways, Buddhist, Plato, and Cartesian skeptics might be excepted from this group. Therefore such people have an ontological commitment to the reality of physical objects. Mathematical realists have an ontological commitment to the reality of numbers, so that they exist in the way that (most people assume) physical objects do.
I doubt that one can effectively characterize the sorts of theses that would entail ontological commitments. Obviously, theses about the ways in which we may make inferences based on evidence can carry with it theological ontologies or their lack. On the other hand, it is debated whether correspondence theory of truth applied to mathematical objects implies an ontological commitment to numbers.
