What are the logical meanings of "extension" and "connotation"?

Extension refers to all objects with essential attributes reflected by terms, that is, classes composed of things referred to by terms. For example, the extension of "commodity" is a class composed of various commodity objects.

Connotation refers to the sum of the essential attributes of objects reflected by words, that is, the reflection of the unique attributes of things. For example, the connotation of "commodity" is "labor products produced for exchange.

Extended data

Let P be a genus and S a species. In this way, 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 that of "S", while the connotation of "S" is deeper than that of "P". This is the inverse relationship between the connotation and extension of words in traditional logic. But this is not a strict mathematical law.

For example, the extension of "people" is narrower than that of "animals", because all people are animals, and some animals are not people; However, the connotation of "human" is deeper than that of "animal", that is to say, the unique attributes of human beings include animals, while the unique attributes of animals do not include people.

In traditional logic, reducing the connotation of a word item to expand its extension, so as to transition to a word item with a wider extension, is called generalization, such as extending "person" to "creature"; Increasing the connotation of a word to narrow its extension, so as to transition to a word with a narrow extension, is called restriction, such as narrowing "animal" to "human".