Do forms exist?

14. Are numbers, bodies, planes, and points substances?

If they are not, then what is being and what are the substances of things?

Modifications, movements, relations, dispositions, and ratios do not indicate the substance of anything. 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 than the line, and the line 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 body incapable of existing without these.

This is why, while most of the philosophers and the earlier among them thought that substance and being were identical with body, and that all other things were modifications of this, so that the first principles of the 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 the accidents of these it cannot be right to call beings.

But if lines and points are substance more than bodies, but we do not see to what sort of bodies these could belong (for they cannot be in perceptible bodies), there can be no substance.

Further, these are all evidently divisions of body,-one in breadth, another in depth, another in length.

Besides this, no sort of shape is present in the solid more than any other; so that if the Hermes is not in the stone, neither is the half of the cube in the cube as something determinate; therefore the surface is not in it either; for if any sort of surface were in it, the surface which marks off the half of the cube would be in it too.

The same account applies to the line and to the point and the unit. Therefore, if on the one hand body is in the highest degree substance, and on the other hand these things are so more than body, but these are not even instances of substance, it baffles us to say what being is and what the substance of things is.

For besides what has been said, the questions of generation and instruction confront us with further paradoxes.

For if substance, not having existed before, now exists, or having existed before, afterwards does not exist, this change is thought to be accompanied by a process of becoming or perishing; but points and lines and surfaces cannot be in process either of becoming or of perishing, when they at one time exist and at another do not.

For when bodies come into contact or are divided, their boundaries simultaneously become one in the one case when they touch, and two in the other-when they are divided; so that when they have been put together one boundary does not exist but has perished, and when they have been divided the boundaries exist which before did not exist (for it cannot be said that the point, which is indivisible, was divided into two).

[1002b1] they exist sometimes as one when they touch, and sometimes as two when they are divided.

Consequently, they do not exist when they are joined, but have perished, and when they are divided, they exist though they did not exist before (for surely the indivisible point was not divided into two), and if they come into being and [5] perish, from what do they come into being?

The case is similar concerning the ’now’ in time: for it is not possible for this either to come into being and perish, and yet it always seems to be different, though it is not some substance. It is similarly clear that the case is the same concerning points, lines, and planes: for the [10] same account applies: for all are equally either limits or divisions.