of points. But even if one supposes the case to be such that, as some say, number proceeds from the 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.[1]
Chapter 5
A question connected with these is whether numbers and bodies and planes and points are substances or not. If they are not, it baffles us to say what being is and what the substances of things are. For modifications and movements and relations and dispositions and ratios do not seem to indicate the substance of anything; for all are predicated of a subject, and none is a 'this'. And as to the things which might seem most of all to indicate substance, water and earth and fire and air, of which composite bodies consist, heat and cold and the like are modifications of these, not substances, and the body which is thus modified alone persists as something real and as a substance. But, on the other hand, the body is surely less of a substance than the surface, and the surface less than the line, and the line less than the unit and the point. For the body is bounded by these; and they are thought to be capable of existing without body, but the body cannot exist without these. This is why, while most of the philosophers and the earlier among them thought that substance and being were identical with corporeal matter, and that all other things were attributes of this, so that the first principles of bodies were the first principles of being, the more recent and those who were held to be wiser thought numbers were the first principles. As we said, then, if these are not substance, there is no substance and no being at all; for surely it is not proper to call the accidents of these
- ↑ With 1001a4-b25 cf. 996a4-9. For the answer cf. z. 1040b16-24, 1. 2, m. 1083a20-5a2.
