Logical Approaches and Rules of Use of Connotation and Extension of Lexical Items

Traditional logic holds that the connotation of a lexical item is the sum of the essential attributes of the object reflected in the item, i.e., the reflection of the unique properties of the thing. For example, the connotation of "commodity" is "products of labor produced for exchange"; the extension of the term refers to all the objects with the essential attributes reflected in the term, i.e., the category composed of things referred to by the term. For example, the extension of "commodity" is the category composed of various commodity objects. Let P be a genus and S a species. Thus, the extension of "P" is wider than that of "S", and the extension of "S" is narrower than that of "P"; The connotation of "P" is shallower than the connotation of "S", and the connotation of "S" is deeper than the connotation of "P". This is the so-called inverse relationship between connotation and extension of terms in traditional logic. But this is not a strict mathematical law. For example, the extension of "human" is narrower than the extension of "animal", because all human beings are animals and animals are not human; the connotation of "human" is deeper than the connotation of "animal". The connotation of "human" is deeper than the connotation of "animal", that is to say, the unique attributes of human include animals, while the unique attributes of animals do not include human.