Metaphysics

​And if these exist, there will also be animals, since there are also senses. Furthermore, some universal propositions are proved by mathematicians, which extend beyond these substances. There will therefore be some other separate substance between the Ideas and the intermediates, which is neither number nor points nor magnitude nor time. But if this is impossible, it is clear that those too cannot exist separated from sensible things. In general, the opposite of the truth and of what is usually believed happens if one posits the objects of mathematics to exist in this way as certain separate natures. For it is necessary, on the account of their existing in this way, that they should be prior to sensible magnitudes, whereas in truth they are posterior; for the incomplete magnitude is prior in generation, but posterior in substance, as the inanimate is to the animate. Furthermore, by what and when will mathematical magnitudes be one? For the things here are one by soul or a part of soul or some other thing, reasonably enough (and if not, they are many and are dissolved); but for those things, which are divisible and are quantities, what is the cause of their being one and holding together? Furthermore, generations show this. For first it comes to be in length, then in breadth, and finally in depth, and has its limit. If, then, that which is posterior in generation is prior in substance, body would be prior to plane and length. And in this way it is also more complete and a whole, because it becomes animate; but how could there be an animate line or plane? For the assumption would be beyond our senses. Furthermore, body is a kind of substance (for it already has completeness in a way), but how are lines substances? For they are neither like a form and a kind of shape, as the soul is if indeed it is such, nor like matter, as body is; for nothing appears to be able to be composed of lines or planes or points, whereas if they were some kind of material substance, they would appear to be capable of undergoing this. Let them, then, be prior in definition, but not everything that is prior in definition is also prior in substance. For those things are prior in substance which, when separated, excel in being; and those are prior in definition whose definitions are made up of the definitions of others; and these two do not belong together. For if attributes do not exist apart from substances, as for example a moving thing or a white thing, ‘white’ is prior in definition to ‘white man’, but not prior in substance; for it cannot exist separated, but is always together with the concrete whole (and by ‘concrete whole’ I mean the ‘white man’), so that it is clear that neither is that which is by abstraction prior, nor that which is by addition posterior; for ‘white man’ is said of ‘white’ by addition. That they are, then, neither substances to a greater degree than bodies, nor prior in being to sensible things, but only in definition, nor is it possible for them to exist separated anywhere, has been sufficiently stated. But since they could not exist in sensible things either, it is clear that they either do not exist at least at all, or they exist in a certain way, and therefore do not exist in an unqualified sense; for we speak of being in many ways.