Problems, then, and propositions are to be defined as aforesaid. A thesis is a paradoxical belief of some eminent philosopher- e.g. the view that contradiction is impossible, as Antisthenes said- or the view of Heraclitus that all things are in motion- or that what exists is one, as Melissus says- for to take notice when any ordinary person expresses views contrary to mens usual opinions would be silly. Or it may be a view contrary to mens usual opinions about which we have an argument, e.g. the view maintained by the sophists that what is need not in every case either have come to be or be eternal- for a musician who is a grammarian is so without ever having come to be so, or being so eternally. For even if some do not accept this view, a man might do so on the ground that it has an argument in its favour.
A thesis is a seemingly contradictory or absurd belief. It may be of an expert, such as the philosopher Antishenes who says that contradiction is impossible, Heraclitus who says that absolutely everything changes or Melissus who says that absolutely everything is one thing. If the ordinary person said such a thing, we would ignore it because these sorts of views sound rather silly. This belief may also be one that we have an argument for. For example, sophists argue that some things are not eternal but have no cause for their existence. They argue this on the basis of this argument: a musician who becomes a grammar expert is not eternally a grammar expert and did not become a grammar expert because he was a musician. It is possible that someone could accept this view because there is an argument for the position.
There are many positions that scientists and philosophers promote today that are theses. For example, physicists claim that elementary particles are like waves and particles. They claim that no technology can measure the position and energy of a particle accurately. Some philosophers claim that abstract objects like numbers exist. Others claim that we obtain all of our knowledge by way of science. So discussion of this point is important today, just as it was then.
Next, Aristotle discusses the difference between problems and theses.