Connotation and denotation
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The distinction between connotation and denotation is commonly associated with the philosopher John Stuart Mill, though it is much older. It is intended to reflect the different ways in which a common name may be significant. The connotation of the name is the attribute or attributes implied by the name. The denotation of the name is any object to which the name applies.
For example, the word "city" connotes the attributes of largeness, populousness. It denotes individual objects such as London, New York, Paris.
It should not to be confused (though it often is) with the distinction between sense and reference, though it has some affinity with his distinction between concept and object. Contemporary philosophers employ the terms intension and extension for connotation and denotation respectively.
Mill's definition of the term "connotation" is altogether different from that used by Scholastic logicians. In scholastic logic, a "connotative" term was originally what would now be called an adjective, "signifying an attribute as qualifying a subject". For example, "brave", as used to say or imply of some particular person that they are brave. By contrast, the abstract noun "bravery" was thought to signify something independent of the subject, an "independent entity", thus is non-connotative. The distinction is connected with the metaphysical one between substance and attribute.
Linguistics
There is a related distinction in linguistics between the objective meaning or denotation of a word such as "vulgar", and the positive or negative association or connotation we attach to such a word. "Vulgar" derives from the Latin word for "common" and literally means ubiquitous, found everywhere, and was its original meaning. The word has now acquired the negative connotation of "gross" or "crudely obscene" (also of showy ostentatiousness). The process of acquiring a negative connotation is known as pejoration.
Connotations often give insight into the associations of the real usage of a word.