Types of Definitions
Definitions can be classified into two types, based on their purpose. First, there are descriptive definitions whose purpose are to explain the way in which some symbols have been or are used by some actual people. A descriptive definition is a form of history as it refers to the actual past. It tells what certain people meant by a certain symbol at a certain more or less specified time and place. This means that a descriptive definition always involves three persons: first the definer who is explaining the meaning of the symbol, secondly the hearer to whom the meaning is defined, and thirdly the people who have used the symbol and thereby given it its meaning. This third person must always be there because the meaning of a symbol is what it means to some person or persons. So, when asking for a descriptive definition, one should not ask "What does this symbol mean?" but rather "What do (or did) certain persons use this symbol to mean?"
The second type of definitions consists of the stipulative definitions whose purpose are to set up, or legislate, the meaning of a symbol. People use stipulative definitions when they want to introduce a new symbol that has never been used before, or when they want to temporarily change the meaning of an established symbol. When someone makes a stipulative definition, he chooses himself the meaning of the symbol and does not record its previous use. A stipulative definition, therefore, involves only two persons: the definer who assigns a meaning to the symbol and the hearer to whom the meaning is defined. There is no third person involved as in a descriptive definition. So, when asking for a stipulative definition, the correct question is neither "What does this symbol mean?" nor "What do these people mean by this symbol?" but "What have you decided this symbol to mean?"