Metaphysics

Indeed, the wide is not the genus of the deep either; for if it were, body would be a kind of plane. Further, from what will the points be present in them? Plato indeed used to fight against this class of things as being a geometrical dogma, and rather called the ‘indivisible lines’ the principle of a line—and this he often posited. Yet these must have some limit; so that by the same argument that a line exists, a point also exists. —But on the whole, although wisdom searches for the cause of visible things, we have abandoned this (for we say nothing about the cause from which the principle of change begins). And while we think we are speaking of their substance, we assert that there are other substances, but how those are the substances of these, we speak in vain; for ‘participating’, as we said before, is nothing. Nor do the Forms touch in any way upon that cause which we see to be the cause in the sciences, through which every intellect and every nature acts—not even upon this cause, which we say is one of the principles. Instead, philosophy has become mathematics for modern thinkers, although they say that mathematics should be studied for the sake of other things. Further, one might suppose that the underlying substance as matter is rather mathematical, and is predicated of and is a difference of substance and of matter, rather than being matter itself. For example, ‘the great and the small’, just as the natural philosophers speak of ‘the rare and the dense’, saying that these are the primary differences of the substrate; for these are a kind of excess and defect. And as for movement, if these are to be movement, it is clear that the Forms will be moved; but if not, where did movement come from? For the whole study of nature is done away with. And what seems to be easy, namely to show that all things are one, does not follow. For by exposition all things do not become one, but rather some ‘one-itself’ is formed, even if one grants all premises; and not even this follows, unless one grants that the universal is a genus, which in some cases is impossible. Nor is there any explanation for the lengths, planes, and solids which come after numbers, either as to how they exist or will exist, or what power they possess. For these can neither be Forms (for they are not numbers), nor the intermediates (for those are the mathematical objects), nor destructible things; rather, this appears to be some other, fourth class. On the whole, to search for the elements of existing things without distinguishing them, when they are spoken of in many ways, makes it impossible to find them, especially when one searches in this way for the elements out of which they are composed. For out of what elements ‘acting’ or ‘being acted upon’, or ‘the straight’, are composed is surely impossible to grasp; but if it is possible, it is possible only for substances. Therefore, either to search for the elements of all existing things, or to think that one has them, is incorrect. And how could one learn the elements of all things? For it is clear that it is not possible to have any prior knowledge. For just as one who is learning geometry may know other things beforehand, but knows nothing beforehand of the things with which the science is concerned and which he is about to learn, so it is also with other things; so that if there is a science of all things, such as some say exists, he who learns it would have no prior knowledge at all. Yet all learning is through things previously known, whether all or some, both that which is by demonstration and that by definition (for the elements from which the definition is made must be known beforehand and be familiar); and similarly also that which is by induction. But indeed, even if it should happen to be innate, it is wonderful how we are unaware of possessing the greatest of sciences. Further, how will one know what elements it consists of, and how will it be clear? For this also presents a difficulty. For one might dispute about it, just as about certain syllables; for some say that the syllable ‘za’ is composed of s, d, and a, while others say it is a different sound, and not any of the familiar ones. Further, how could one know the objects of sense without possessing the sense? Yet they ought to, if indeed the elements of which all things consist are the same, just as composite sounds are made of their own proper elements.