Section 6

With regard to the difficulty which we have described 1 in connection with definitions and numbers, what is the cause of the unification? In all things which have a plurality of parts, and which are not a total aggregate but a whole of some sort distinct from the parts, there is some cause ; inasmuch as even in bodies sometimes contact is the cause of their unity, and sometimes viscosity or some other such quality.

But a definition is one account, not by connection, like the Iliad , but because it is a definition of one thing.

What is it, then, that makes man one thing, and why does it make him one thing and not many, e.g. animal and two-footed, especially if, as some say, there is an Idea of animal and an Idea of two-footed?

Why are not these Ideas man, and why should not man exist by participation, not in any man, but in two Ideas, those of animal and two-footed? And in general man will be not one, but two things—animal and two-footed. Evidently if we proceed in this way, as it is usual to define and explain, it will be impossible to answer and solve the difficulty.

But if, as we maintain, man is part matter and part form—the matter being potentially, and the form actually man—, the point which we are investigating will no longer seem to be a difficulty. For this difficulty is just the same as we should have if the definition of X 2 were round bronze; for this name would give a clue to the formula, so that the question becomes what is the cause of the unification of round and bronze?

The difficulty is no longer apparent, because the one is matter and the other form. What then is it (apart from the active cause) which causes that which exists potentially to exist actually in things which admit of generation? There is no other cause of the potential sphere’s being an actual sphere; this was the essence of each. 3

Some matter is intelligible and some sensible, and part of the formula is always matter and part actuality; e.g., the circle is a plane figure. 4 But such thing 5 as have no matter, neither intelligible nor sensible, are ipso facto each one of them essentially something one; just as they are essentially something existent: an individual substance, a quality, or a quantity. Hence neither existent nor one is present in their definitions. And their essence is ipso facto something one, just as it is something existent.

Hence also there is no other cause of the unity of any of these things, or of their existence; for each one of them is one and existent not because it is contained in the genus being or unity, nor because these genera exist separately apart from their particulars, but ipso facto.

It is because of this difficulty that some thinkers 6 speak of participation, and raise the question of what is the cause of participation, and what participation means; and others speak of communion; e.g., Lycophron 7 says that knowledge is a communion of the soul with knowing; and others call life a combination or connection of soul with body.

The same argument, however, applies in every case; for being healthy will be the communion or connection or combination of soul and health; and being a bronze triangle a combination of bronze and triangle; and being white a combination of surface and whiteness. The reason for this is that people look for a unifying formula, and a difference, between potentiality and actuality.

But, as we have said, 8 the proximate matter and the shape are one and the same; the one existing potentially, and the other actually. Therefore to ask the cause of their unity is like asking the cause of unity in general; for each individual thing is one, and the potential and the actual are in a sense one. Thus there is no cause other than whatever initiates the development from potentiality to actuality. And such things as have no matter are all, without qualification, essential unities.