We have but two sorts of people in the house, and both under the whip, that's fools and madmen; the one has not wit enough to be knaves, and the other not knavery enough to be fools. (44 – 47)
Fools, according to Lollio, are people lacking in `wit' (intelligence, understanding). As they are intellectually deficient, they are incapable of being `knaves' on that score. Madmen, however, cannot be knaves because they suffer from a different kind of brainsickness; therefore they would not be foolish enough to embark on a sexual relationship with Alibius's wife, Isabella.
The sub-plot offers us both a counterfeit fool and someone who pretends to be a madman. The fact that both characters put on roles gives us a clear notion of what the authors mean by `fools' and `madmen'. Antonio is the `fool', Franciscus the `madman'. Both are interested in Isabella (which implies, according to Lollio's concept of things, that neither is a real fool or madman); she, however, is neither foolish nor mad in any sense.
Antonio demonstrates to us, in his role as a fool, what such a person is like by answering certain questions correctly, on a simple principle, without realizing that the same simple principle cannot be applied to a somewhat different situation. Thus, in III.iii, Lollio ask him `how many is five times six', to which he replies: