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Ontological CommitmentIn the philosophy of language and metaphysics, an ontological commitment is a statement in which the existence of one thing is presupposed or implied by asserting the existence of another. We are "committed" to the existence of the second thing, even though we may not have expected it, and may have thought we are asserting the existence only of the first. The kind of entities in question are typically abstract objects such as universals, sets, fictional objects or classes. Background The sentence "Napoleon was one of his ancestors" asserts only the existence of at least one particular ancestor, namely Napoleon, and of all of the persons ancestors in general. That seems to limit the "commitment" made by the sentence. However, it is well known that such sentences cannot be interpreted in so-called first-order logic, where individual variables stand in for individual things, and must be represented in some second-order form. Such forms in ordinary language use grammatical plurals, or terms such as "set of ", "group of" and so on. For example: "any of people that include y, and which include any of the parents of those people, also include x". In logic, such collective noun forms are represented by so-called second-order variables, or by first-order variables standing for sets. Since these variables do not stand in for individual objects, it seems we are "ontologically committed" to entities other than individuals, such as sets, classes and so on. Quine writes - 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 sets, are now presupposed. Formally it is precisely in allowing quantification over class variables "alpha", "beta" &c, that we assume a range of values for these variables to refer sic to. To be assumed as n entity is to be assumed as a value of a variable" (Methods of Logic p. 228)
Another sentence that appears "ontologically innocent" is the well-known Geach Kaplan sentence "Some people admire only each other". Ontological Innocence Many philosophers dispute whether we are committed to such entities at all. They argue that all assertions are "ontologically innocent": they are committed only to the existence of the entities they assert. There is a considerable and growing body of literature on so-called plural reference and plural quantification. It seems counter-intuitive that a sentence such as "some people admire only each other" commits us to the existence of anything but people. Advocates of ontological innocence see in the grammatical plural simply another way to refer to exactly the same things that the singular form commits us to. Interpretations of negative existential statements have proved more difficult. See empty names for an overview of the problem. References Quine, W.V.O. Methods of Logic, London 1952
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