Metaontology is the branch of metaphysics that deals with the nature of ontology and ontological questions. The term owes its popularization to Peter van Inwagen's 1998 paper of the same name. However, the subject itself is much older, going back at least to Rudolf Carnap's distinction, introduced in 1950, between internal and external questions. Some basic metaontological questions are:
Answers to these questions split up philosophers into different camps.
Ontological questions are questions of the form "Are there Fs?"--for example: "Are there universals?", "Are there electrons?", "Are there gods?", etc. Carnap argued that such questions are ambiguous. They may be understood either from within a given conceptual framework, in which case they are to be answered by appeal to the rules of the framework, and typically they will have obvious or trivial answers, or else they may be understood from outside a framework, as asking whether there are "really" any such things, granted that they exist within the framework. Carnap, however, argued that this "external" question is tantamount to asking whether one should adopt the framework in question, and this is a question to which there is no objectively correct answer, though there may be pragmatic considerations for or against such an adoption. For example, take the framework of standard arithmetic. In standard arithmetic it is a theorem that there are prime numbers greater than 1000, from which it follows that there are prime numbers, from which it follows that there are numbers. Thus, the question "Are there numbers?" has an obvious answer if intended internally—obviously, there are numbers in standard arithmetic. On the other hand, if we say, "Yes, but are there really such things as numbers?", we are stepping outside the framework of arithmetic and asking a question about that framework—as Carnap argues, we are asking whether to adopt the framework in question. This is a practical question, a question about what to do, not about the nature of the world. Neither the internal nor the external question can be taken to be a philosophical question about the nature of the world. Hence, if Carnap is right, there are no objective ontological questions for philosophers to investigate, and ontology is an empty discipline.
Against this, Quine argued that the internal/external distinction, like the distinction between analytic and synthetic truths, is untenable, and thus ontological questions are not ambiguous in Carnap's sense. On the contrary, he held that there is a single meaning to ontological claims, and this is captured by the backwards-E existential quantifier of formal logic. Consequently, to give the answers to ontological questions, one need only translate the relevant theory (whatever the relevant area of human knowledge is) into the notation of standard logic and see whether a sentence of the relevant form is part of the translated theory.