9. It must therefore be granted that in the things of which we first spoke, such as knowing and doing (active being), there is an actualization, an habituation, and an actualizing reason; while in the other things there is a participation in form and reason. For indeed, if the bodies were the only essences, the relative habituations would bear no reality. If, on the contrary, we assign the first rank in existence to incorporeal things, and to the reasons, and if we define the habituations as reasons that participate in the forms, we should say that what is double has the double for its cause, and what is half, has the half as its cause; and that other things are what they are named because of the presence of the same, or of the contrary form. Now either two things simultaneously receive one the double, and the other the half, and one greatness, and the other smallness; or contraries such as resemblance and dissimilarity are to be found in each thing, as well as identity and difference; and everything finds itself simultaneously similar and dissimilar, identical and different. It might be objected that if one object were ugly, and another uglier still, they are such because they participate in a form. Not so; for if these two objects be equally ugly, they are equal in the absence of the form. If they be unequally ugly, the least ugly is such because it participates in a form which does not sufficiently subdue matter, and the uglier is such because it participates in a form which does so still less. They could, besides, be judged from the standpoint of deprivation, comparing them to each other as if they contained some form. The sensation is a form that results from two things (of that which feels, and that which is felt); so also with knowledge. In respect to the thing possessed, possession is an act which contains, which has a kind of efficacy. As to mensuration, which is an actualization of measure, in respect of the measured object, it consists in a reason. WHILE SOME ARISTOTELIAN CATEGORIES ARE LOGICALLY POSSIBLE, THE OBJECTS SUBSUMED ARE IMPOSSIBLE.