Aristotle has described how differences in comparisons indicated multiple meanings. Now he continues his discussion of the second tool by describing how differentia can indicate multiple meanings. He does this in Topics, Book 1.
Now since of genera that are different without being subordinate one to the other the differentiae also are different in kind, e.g. those of animal and knowledge (for the differentiae of these are different), look and see if the items falling under the same term are differentiae of genera that are different without being subordinate one to the other, as e.g. sharp is of a sound and a body. For being sharp differentiates sound from sound, and likewise also one body from another. Sharp, then, is homonymous- for it forms differentiae of genera that are different without being subordinate one to the other.
Again, see if the items falling under the same term themselves have different differentiae, e.g. colour in bodies and colour in tunes- for the differentiae of colour in bodies are dispersing the eye and compressing the eye, whereas colour in melodies has not the same differentiae. Colour, then, is homonymous- for things that are the same have the same differentiae.
Moreover, since the species is never the differentia of anything, look and see if one of the items falling under the same term is a species and another a differentia, as (e.g.) clear as applied to a body is a species of colour, whereas in the case of a sound it is a differentia- for one sound is differentiated from another by being clear.
What we use to distinguish various kinds of something is called the differentia. What makes various kinds of animals different from each other and what makes various kinds of knowledge different are different. So knowledge and animals have different differentia. This is because knowledge is not a kind of animal, nor are animals a kind of knowledge. So if a word is used as a differentia for two unrelated genus, then that word has different meanings. For example, there are sharp objects and sharp sounds, but sounds and objects are unrelated kinds of things. But sharp tells what kind of thing the object or sound is. Therefore, sharp has multiple meanings.
It is also possible to ask what the differentia of the objects that are contain the term are. For example, what makes various clear arguments different from each other is their topic. What makes various clear objects different from each other is what kind of thing they are. Since the differences are different, clear is used in more than one way.
Finally, it is possible that a word is used as both a species and a differentia. For example, clear is a kind of appearance when applied to objects. This makes it a species of appearance. But when clear is applied to sounds, it is a differentia. Therefore, clear has multiple meanings.
Next, Aristotle will discuss which differences between things need investigation.