Logical methods and usage rules of word connotation and extension

According to traditional logic, the connotation of a word is its meaning, that is, its concept, which reflects the unique attributes of things. For example, the connotation of "commodity" is "labor products produced for exchange". The extension of a term is the kind of thing that a term refers to. For example, the extension of "person" is the kind that everyone has been making up through the ages.

According to whether there is overlap between the extensions of concepts, they can be divided into two categories: compatible relationship and incompatible relationship. There may be four kinds of compatible relationships, namely, the same relationship (same relationship or overlapping relationship), true inclusion relationship (genus relationship), true inclusion relationship (species relationship) and cross relationship. There may be two incompatible relationships, namely, contradictory relationship and antagonistic relationship.

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It refers to things that are reflected in concepts and have unique attributes reflected by concepts. For example, the extension of the concept of "biology" is something unique to nature. All kinds of animals, plants and microorganisms in nature are embodied in this concept.

Connotation refers to the sum of the unique attributes of the thinking object summarized by a concept. For example, the connotation of the concept of "state" includes: it is a unique political entity in class society, an irreconcilable product of class contradictions, a tool for the ruling class to rule and oppress the ruled class, a violent ruling machine composed of the army, police, prisons, courts, legislative bodies and administrative bodies, and so on.