Aristotle has already shown that differences help us find differentia of things. He continues his explanation of the tools of argument by discussing one of the purposes of finding similarities between things. He does this in Topics, Book 1.
The examination of likeness is useful with a view both to inductive arguments and to hypothetical deductions, and also with a view to the rendering of definitions. It is useful for inductive arguments, because it is by means of an induction of particulars in cases that are alike that we claim to induce the universal; for it is not easy to do this if we do not know the points of likeness. It is useful for hypothetical deductions because it is a reputable opinion that among similars what is true of one is true also of the rest. If, then, with regard to any of them we are well supplied with matter for a discussion, we shall secure a preliminary admission that however it is in these cases, so it is also in the case before us; then when we have proved the former we shall have proved, on the strength of the hypothesis, the matter before us as well; for we have first made the hypothesis that however it is in these cases, so it is also in the case before us, and have then produced the demonstration.
There are three reasons for discovering the similarities between various things. The first two ways are for constructing inductive arguments and hypothetical arguments. Inductive arguments argue for a universal from various particulars. If various particulars are the same in some way, then that is a universal. So finding the sameness makes these kinds of arguments easy. Most people believe that what is true of one thing will also be true of something similar. This allows someone to use a hypothetical argument from similar things. A hypothetical argument is one that uses ‘if’ and ‘then’. This allows us to argue in the following way: A and B are very similar, so whatever is true with A is also true of B. A is like this. Therefore, B is like this. Once we have shown that A and B are similar, the argument has been completed.
In Aristotle, ‘particular’ just means this thing or that thing. So this horse is a particular and so is that man. A universal is anything that is true of more than one particular. So whiteness is a universal because more than one thing can be white. So is humanity, because more than one particular can be human.
Next, Aristotle shows us that similarities help us construct definitions.