Quantification

In the philosophy of metaphysics, an ontological commitment is said to be necessary in order to make a proposition 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 intended to assert only the existence of the first. The kind of secondary entities in question are typically abstract objects such as universals, sets, classes, or fictional objects.

The sentence “Napoleon is one of my ancestors” asserts only the existence of two individuals 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.

For example, the sentence 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. 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.

Many philosophers dispute whether we are committed to such associated entities at all. They argue that all assertions are committed only to the existence of the entities which they actually assert. There is a considerable and growing body of literature on plural reference and plural quantification, and it seems counter-intuitive that a sentence commits us to the existence of anything other than what it states. Some see in the grammatical plural simply another way to refer to exactly the same things that the singular form commits us to.

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