I mean by hypothesis what the geometricians often do in dealing with a question put to them; for example, whether a certain area is capable of being inscribed as a triangular space in a given circle: they reply—I cannot yet tell whether it has that capability; but I think, if I may put it so, that I have a certain helpful hypothesis for the problem, and it is as follows: If this area The problem seems to be that of inscribing in a circle a triangle (BDG) equal in area to a given rectangle (ABCD). is such that when you apply it to the given linei.e., the diameter (BF). of the circle you find it falls shorti.e., falls short of the rectangle on the diameter (ABFE). by a space similar to that which you have just applied, then I take it you have one consequence, and if it is impossible for it to fall so, then some other. Accordingly I wish to put a hypothesis, before I state our conclusion as regards inscribing this figure in the circle by saying whether it is impossible or not. In the same way with regard to our question about virtue, since we do not know either what it is or what kind of thing it may be, we had best make use of a hypothesis in considering whether it can be taught or not, as thus: what kind of thing must virtue be in the class of mental properties, so as to be teachable or not? In the first place, if it is something dissimilar or similar to knowledge, is it taught or not—or, as we were saying just now, remembered? Let us have no disputing about the choice of a name: is it taught? Or is not this fact plain to everyone—that the one and only thing taught to men is knowledge?

I agree to that.

Then if virtue is a kind of knowledge, clearly it must be taught?

Certainly.

So you see we have made short work of this question—if virtue belongs to one class of things it is teachable, and if to another, it is not.

To be sure.

The next question, it would seem, that we have to consider is whether virtue is knowledge, or of another kind than knowledge.