Ontological commitment
Encyclopedia
In the philosophy of language
and 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 object
s such as universal
s, sets, classes
, or fictional objects.
, 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,
Another statement about individuals that appears “ontologically innocent” is the well-known Geach–Kaplan sentence: Some people admire only each other.
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 name
s for an overview of the problem.
Philosophy of language
Philosophy of language is the reasoned inquiry into the nature, origins, and usage of language. As a topic, the philosophy of language for analytic philosophers is concerned with four central problems: the nature of meaning, language use, language cognition, and the relationship between language...
and metaphysics
Metaphysics
Metaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...
, an ontological commitment is said to be necessary in order to make a proposition
Proposition
In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...
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 object
Abstract object
An abstract object is an object which does not exist at any particular time or place, but rather exists as a type of thing . In philosophy, an important distinction is whether an object is considered abstract or concrete. Abstract objects are sometimes called abstracta An abstract object is an...
s such as universal
Universality (philosophy)
In philosophy, universalism is a doctrine or school claiming universal facts can be discovered and is therefore understood as being in opposition to relativism. In certain religions, universality is the quality ascribed to an entity whose existence is consistent throughout the universe...
s, sets, classes
Class (philosophy)
Philosophers sometimes distinguish classes from types and kinds. We can talk about the class of human beings, just as we can talk about the type , human being, or humanity...
, or fictional objects.
Background
The sentence “Napoleon is one of my ancestors” asserts only 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 logicFirst-order logic
First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic...
, where individual variables stand for individual things. Instead, they must be represented in some second-order
Second-order logic
In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory....
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
Well-defined
In mathematics, well-definition is a mathematical or logical definition of a certain concept or object which uses a set of base axioms in an entirely unambiguous way and satisfies the properties it is required to satisfy. Usually definitions are stated unambiguously, and it is clear they satisfy...
objects in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
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
Willard Van Orman Quine
Willard Van Orman Quine was an American philosopher and logician in the analytic tradition...
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 quantificationQuantificationQuantification has several distinct senses. In mathematics and empirical science, it is the act of counting and measuring that maps human sense observations and experiences into members of some set of numbers. Quantification in this sense is fundamental to the scientific method.In logic,...
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 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” — that they are committed only to the existence of the entities which they actually assert.There is a considerable and growing body of literature on so-called plural reference and plural quantification
Plural quantification
In mathematics and logic, plural quantification is the theory that an individual variable x may take on plural, as well as singular values. As well as substituting individual objects such as Alice, the number 1, the tallest building in London etc...
. 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 name
Empty name
In the philosophy of language, an empty name is a proper name that has no referent.The problem of empty names is that empty names have a meaning that it seems they shouldn't have. The name "Pegasus" is empty; there is nothing to which it refers. Yet though there is no Pegasus, we know what the...
s for an overview of the problem.