Aristotle has claimed that all problems and propositions come from four categories of topics. These are definitions, property, genus and accident. Now Aristotle is going to explain what definitions are. He does this in Topics, Book 1.
We must now say what are definition, property, genus, and accident. A definition is a phrase signifying a things essence. It is rendered in the form either of a phrase in lieu of a name, or of a phrase in lieu of another phrase- for it is sometimes possible to define the meaning of a phrase as well. People whose rendering consists of a term only, try it as they may, clearly do not render the definition of the thing in question, because a definition is always a phrase of a certain kind. One may, however, call definitory such a remark as that the beautiful is the becoming, and likewise also of the question, Are perception and knowledge the same or different? For argument about definitions is mostly concerned with questions of sameness and difference. In a word we may call definitory everything that falls under the same branch of inquiry as definitions- and that all the abovementioned examples are of this character is clear on the face of them. For if we are able to argue that two things are the same or are different, we shall be well supplied by the same turn of argument with lines of attack upon their definitions as well- for when we have shown that they are not the same we shall have demolished the definition. But the converse of this last statement does not hold- for to show that they are the same is not enough to establish a definition. To show, however, that they are not the same is enough of itself to overthrow it.
Aristotle now begins his explanation of what definition, property, genus and accident are. A definition is a phrase that says what something is. We can define something that is usually given a name or a phrase. You cannot define something with a single word, because all definitions are in the form of a phrase. However, certain kinds of phrases do help us find definitions. Consider the phrases the beautiful is the becoming and Are perception and knowledge the same? These help us because they claim or ask whether two things are the same or not. Sameness and difference is what arguments about definitions are all about. Anything that helps us in arguments about definitions, we can call definitory. This understanding of definitions will help us when arguing about definitions. If a supposed definition is not the same as the thing it is supposed to be about, then it is not a proper definition. Therefore, arguing that the definition of a thing is different from the thing is an argument that the definition is incorrect. The reverse of this is not true though. Simply having the definition of a thing be the same as the thing does not mean that it is a good definition.
Our modern understanding of definitions is different from that of Aristotles. We often tend to claim that if a definition of a thing is the same as that that thing, then the definition is correct. We do this because we do not distinguish between a definition and a property. Any further discussion of this will have to wait until we have read Aristotle on properties.
Aristotle will discuss properties next.