Metaphysics

​The difficulty next to these is whether numbers, bodies, planes, and points are certain substances or not. For if they are not, it escapes us what being is and what the substances of existing things are; for affections, movements, relations, dispositions, and ratios do not seem to signify the substance of anything (for all of them are said of some underlying subject, and none is a “this”); but as for the things which would most of all seem to signify substance, water, earth, fire, and air, from which composite bodies are constituted, of these, heat, cold, and such affections are not substances, but only the body which has suffered these persists as something that is and as being a certain substance. Yet indeed, body is less of a substance than surface, and surface than line, and line than monad and point; for by these the body is bounded, and they seem to be capable of existing without body, while body is impossible without them. Therefore, the many and the earlier thinkers thought that substance and being were body, and other things the affections of this, so that the principles of bodies were the principles of existing things; but the later and those who seemed to be wiser than these thought that numbers were. Just as we said, then, if these are not substance, there is absolutely no substance and no being; for indeed it is not right to call the accidents of these things “beings”. —But indeed, if this is agreed, that lengths of bodies and points are more of a substance, yet we do not see of what kind of bodies they could be (for it is impossible for them to be among sensible things), there would be no substance at all. Further, all these appear to be divisions of the body, one in width, another in depth, and another in length. In addition to these, any shape whatsoever is equally present in a solid; so that if Hermes is not in the stone, neither is the half of the cube in the cube in such a way as being defined; therefore, neither is a surface (for if any surface whatsoever were, that which defines the half would also have been present), and the same argument applies to a line, a point, and a monad. So that, if body is most of all a substance, and these are more so than body, and yet these do not exist nor are certain substances, it escapes us what being is and what the substance of existing things is. For in addition to what has been said, the things concerning generation and destruction result in absurdities. For substance seems, if it is now when it was not before, or is not later when it was before, to undergo these changes along with being generated and destroyed; but it is not possible for points, lines, and surfaces either to be generated or to be destroyed, though they are at one time and are not at another. For when bodies touch or are divided, simultaneously they become one when touching, and two when being divided; so that when they are put together they do not exist but have been destroyed, and when they are divided they exist which were not before (for surely the indivisible point was not divided into two); and if they are generated and destroyed, from what are they generated? And it is much the same also concerning the “now” in time; for neither is it possible for this to be generated and destroyed, but nevertheless it always seems to be other, without being a certain substance. And it is clear that it is the same also concerning points, lines, and planes; for the same argument applies; for all of them are in like manner either limits or divisions.