Question 11: Are being and unity the substances of things?

11. The hardest and most necessary inquiry for knowledge of the truth is whether being and unity are the substances of things

Is each of them, without being anything else, is being or unity respectively?

What is the nature of being and unity?

Some people think they are of being. Others think they are of unity. Plato and the Pythagoreans thought being and unity were nothing else, but this was their nature, their essence being just unity and being.

But the natural philosophers take a different line; e.g. Empedocles-as though reducing to something more intelligible-says what unity is; for he would seem to say it is love= at least, this is for all things the cause of their being one.

Others say this unity and being, of which things consist and have been made, is fire, and others say it is air. A similar view is expressed by those who make the elements more than one; for these also must say that unity and being are precisely all the things which they say are principles.

• a. If we do not suppose unity and being to be substances, it follows that none of the other universals is a substance

for these are most universal of all, and if there is no unity itself or being-itself, there will scarcely be in any other case anything apart from what are called the individuals. Further, if unity is not a substance, evidently number also will not exist as an entity separate from the individual things; for number is units, and the unit is precisely a certain kind of one.

• b. If there is a unity-itself and a being itself, unity and being must be their substance

for it is not something else that is predicated universally of the things that are and are one, but just unity and being. But if there is to be a being-itself and a unity-itself, there is much difficulty in seeing how there will be anything else besides these,-I mean, how things will be more than one in number. For what is different from being does not exist, so that it necessarily follows, according to the argument of Parmenides, that all things that are are one and this is being.

There are objections to both views.

For whether unity is not a substance or there is a unity-itself, number cannot be a substance. We have already said why this result follows if unity is not a substance.

If it is, the same difficulty arises as arose with regard to being. For whence is there to be another one besides unity-itself?

It must be not-one; but all things are either one or many, and of the many each is one.

If unity is indivisible, according to Zeno’s postulate, it will be nothing. For that which neither when added makes a thing greater nor when subtracted makes it less, he asserts to have no being, evidently assuming that whatever has being is a spatial magnitude.

If it is a magnitude, it is corporeal; for the corporeal has being in every dimension, while the other objects of mathematics, e.g. a plane or a line, added in one way will increase what they are added to, but in another way will not do so, and a point or a unit does so in no way.

His theory is of a low order. An indivisible thing can exist in such a way as to have a defence even against him (for the indivisible when added will make the number, though not the size, greater),-yet how can a magnitude proceed from one such indivisible or from many? It is like saying that the line is made out of points.

But even if number proceeds from unity-itself and something else which is not one, none the less we must inquire why and how the product will be sometimes a number and sometimes a magnitude, if the not-one was inequality and was the same principle in either case. For it is not evident how magnitudes could proceed either from the one and this principle, or from some number and this principle.