Aristotle has just finished discussing dialectical propositions in his effort to discuss the various kinds of arguments we use. He now is moving on to discuss various dialectical problems. He does this in Topics, Book 1.
A dialectical problem is a subject of inquiry that contributes either to choice and avoidance, or to truth and knowledge, and does that either by itself, or as a help to the solution of some other such problem. It must, moreover, be something on which either people hold no opinion either way, or most people hold a contrary opinion to the wise, or the wise to most people, or each of them among themselves. For some problems it is useful to know only with a view to choice or avoidance, e.g. whether pleasure is to be chosen or not, while some it is useful to know merely with a view to knowledge, e.g. whether the universe is eternal or not- others, again, are not useful in themselves for either of these purposes, but yet help us in regard to some such problems- for there are many things which we do not wish to know in themselves, but for the sake of other things, in order that through them we may come to know something else. Problems also include questions in regard to which deductions conflict (the difficulty then being whether so-and-so is so or not, there being convincing arguments for both views)- others also in regard to which we have no argument because they are so vast, and we find it difficult to give our reasons, e.g. the question whether the universe is eternal or no- for into questions of that kind too it is possible to inquire.
A dialectical problem is a problem that would help us make right choices or avoid bad choices or it will help us find the truth and gain knowledge. It does that either on its own or by helping us find the solution to a different problem. As mentioned before, not every problem is a dialectical problem. Dialectical problems must be ones in which no person has an opinion, whether positive or negative or they must be one in which people disagree. Either experts disagree with most people or people disagree among themselves. Problems are also useful for various purposes. Some problems only help us understand what we should do. For example, is pleasure something that we should aim for or not. Some problems only help us understand the world. For example is the universe eternal or not. Some problems are not useful for either of those purposes, but help us answer other problems. There are also certain problems that fit into these categories but deserve special mention. One class of problems is those in which there are convincing arguments for both sides even convincing deductions. Another class of problems involve ones that we do not have arguments for because it is a big topic and it is difficult to explain our reasons for believing it. For example, is the universe eternal or not is such a problem. All of these problems are dialectical.
Next, Aristotle discusses what the thesis is.