Aristotle has just finished discussing how something may be mistaken for an accident usually a genus. Now continues explaining the rules of argument by showing one way to examine whether or not a universal statement is properly applied. He does this in Topics, Book 2.
Another rule is to examine all cases where a predicate has been said to belong to all or none of something. Look at them species by species, and not in their infinite multitude- for then the inquiry will proceed more directly and in fewer steps. You should look and begin with the primitives, and then proceed in order down to those that are not further divisible: e.g. if a man has said that the knowledge of opposites is the same, you should look and see whether it be so of relative opposites and of contraries and of terms opposed as privation and possession, and of contradictory terms. Then, if no clear result is reached so far in these cases, you should again divide these until you come to those that are not further divisible, and see (e.g.) whether it is so of just deeds and unjust, or of the double and the half, or of blindness and sight, or of being and not-being- for if in any case it is proved that the knowledge of them is not the same we shall have demolished the problem. Likewise, also, if the predicate belongs in no case. This rule is convertible for both destructive and constructive purposes- for if, as we proceed with the division, the predicate appears to hold in all or in a large number of cases, we may then claim that the other should actually assert it universally, or else bring an objection to show in what case it is not so- for if he does neither of these things, a refusal to assert it will make him look absurd.
There is a way to check whether or not a predicate is true of a genus or not. Examine the kind by dividing it into its species and asking whether or not the predicate is true of the species. If the species is also a genus of something, then divide each of them into species as well. Continue to divide the species until they cannot be divided further. If the predicate is true of every one of these species then it will be true of the genus as well. For example, suppose we wanted to know whether or not by knowing one thing, we also know its opposite. Well, there are various species of opposites: contraries, relative terms, privation and contradictories. If we are unsure that any of these has an clear answer on whether knowledge of one is knowledge of the opposite, then we should divide them further. For example, one could divide contradictories into kinds of contradictories such as just and unjust- relative terms into double and half- privation into blindness and sight. If we even once find that knowledge of one thing is not also knowledge of the opposite, then the universal predication will be false. This also applies if we are trying to disprove something universal. If we find even one case in which it is true, then our disproof has failed. Finally, suppose we cannot find a disproof. In that case, the opponent must either mention such a case or agree that we have proven our argument. Refusal to do either is absurd.
Next, Aristotle discusses how definitions can help determine the truth of a universal predication.