In philosophy and linguistics, the denotation of a word or expression refers to its exact or literal meaning. For example, the English word "warm" denotes the quality of having a high temperature. Denotation is different from other parts of meaning, such as connotation. For instance, the word "warm" might make people think of calmness, comfort, or kindness (like the warmth of a person's personality), but these ideas are not part of the word's denotation. Similarly, the denotation of an expression is separate from meanings that depend on context. For example, describing something as "warm" often suggests it is not hot, but this idea is not included in the word's denotation.
Denotation is important in many areas. In the study of meaning and philosophy of language, denotation is a key part of understanding how words work. In mathematics and computer science, assigning denotations to expressions is an essential step in creating formal languages that can be understood. A major goal of formal semantics is to figure out the system that connects expressions in natural languages to their denotations.
In linguistic semantics
In natural language semantics, denotations are the results of the meaning part of grammar. For example, the denotation of the word "blue" is the quality of being blue, and the denotation of the word "Barack Obama" is the person known by that name. Phrases also have denotations, which are determined by the principle of compositionality. This means the meaning of a phrase is built from the meanings of its individual words. For instance, the verb phrase "passed the class" refers to the quality of successfully completing the class. Depending on the theory used, denotations may be linked to terms' extensions, intensions, or other structures like context change potentials.
When spoken in a conversation, expressions can sometimes carry additional meanings that are not directly calculated by grammar and are not part of their denotation. For example, saying "I ran five miles" might imply that exactly five miles were run and no more. This extra meaning is not included in the sentence's denotation but is instead a result of using social understanding to interpret the sentence's meaning.
Denotation, meaning, and reference
The study of differences between denotation, meaning, and reference began with the work of Ferdinand de Saussure, especially in his theory of semiotics found in his book Course in General Linguistics. Philosophers Gottlob Frege and Bertrand Russell also made important contributions to this topic.
Although denotation and reference are similar, they are not the same. A reference is a specific person, place, or thing that a speaker points to when using a word. John Searle’s speech act theory helps explain this relationship. According to this theory, the action of identifying a person, place, or thing is called "referring." The actual person, place, or thing being identified is called the "referent." Reference describes the connection between the referent and the word or phrase used. For referring expressions, the denotation of the phrase is likely the same as the referent. For content words, the denotation of the word can apply to any real or imagined object.
In his work On Sense and Reference, philosopher Gottlob Frege separated the German terms Sinn (translated as "sense") and Bedeutung (translated as "reference" or "denotation") when analyzing words like "Morgenstern" (morning star) and "Abendstern" (evening star). Translations of these terms have varied over time, but today, "meaning" is often used to describe Bedeutung. Author Thomas Herbst uses the words "kid" and "child" to show this idea. Herbst explains that these words have the same denotation because they refer to the same group of people. However, "kid" is often used in informal situations, while "child" is more commonly used in formal situations.