Aristotle has just finished discussing universal and particular problems. He continues his explanation of how to use the various tools of argument by showing why naming an object based on an accident is problematic. He does this in Topics, Book 2.
The conversion of an appropriate name which is derived from an accident is an extremely precarious thing; for in the case of accidents and in no other it is possible for something to be true in a certain respect and not universally. Names derived from definition and property and genus are bound to be convertible; e.g. if being a two-footed terrestrial animal belongs to something, then it will be true by conversion to say that it is a two-footed terrestrial animal. Likewise, also, if derived from the genus; for if being an animal belongs to something, then it is an animal. The same is true also in the case of a property; for if being capable of learning grammar belongs to something, then it will be capable of learning grammar. For none of these attributes can possibly belong or not belong in part; they must either belong or not belong absolutely. In the case of accidents, on the other hand, there is nothing to prevent an attribute (e.g. whiteness or justice) belonging in part, so that it is not enough to show that whiteness or justice belongs to a man in order to show that he is white or just; for it is open to dispute it and say that he is white or just in part only. Conversion, then, is not a necessary process in the case of accidents.
Naming something based on an accident it has is extremely dangerous. It is possible that it might be true of some and not others. This is only true of accidents though. Naming something based on a genus, definition or property do not have this problem. For example, if something is a rational animal right now, then we can say that it is a rational animal. This is true of genus because animals are animals as well. If someone is capable of learning grammar, then we can say that they are a creature capable of learning grammar. All of these things, if true, are always true and could not have been false. They belong to every instance of their kind. This is not true of accidents. Just because some men are just does not mean that all men are just. So showing that one man is just does not prove that a different man is just. Therefore, we cannot call men, just creatures because it is possible for a man not to be just.
This is part of Aristotle’s discussion of universal and particular problems. Accidentals are only particular problems, while non-accidentals are universal. This also makes a difference in what sort of rules apply.
Next, Aristotle talks about the two kinds of errors in problems.