Metaphysics

​It is with good reason also that people are puzzled as to which parts are parts of the form and which are not, but rather parts of the concrete whole. And yet, if this is not clear, it is not possible to define each thing; for definition is of the universal and of the form. Therefore, what sort of parts are as matter and what sort are not, if they are not clear, the formula of the thing will not be clear either. Now, as for those things which appear to supervene upon things different in form, such as a circle in bronze, in stone, and in wood, these seem to make it clear that the bronze or the stone is no part of the substance of the circle, because of their being separated from them; but as for those things which are not seen to be separated, there is nothing to prevent them from being in the same case as these, just as if all circles were seen to be of bronze; for the bronze would none the less be no part of the form; yet it would be difficult to abstract this in thought. For example, the form of man always appears in flesh and bones and parts of this kind; are these then also parts of the form and of the formula? Or are they not, but rather matter, and is it only because it does not supervene upon other things as well that we are unable to separate them? Since, then, this seems to be possible but it is unclear when, some are already puzzled even in the case of the circle and the triangle, on the ground that it is not fitting to define them by lines and by the continuous, but that all these too should be spoken of in the same way, just as flesh and bones of man, and bronze and stone of the statue; and they reduce all things to numbers, and say that the formula of a line is that of the number two. And of those who assert the ideas, some make the dyad the line-itself, and others the form of the line; for they say that in some cases the form and that of which it is the form are the same (such as the dyad and the form of the dyad), but in the case of the line this is no longer so. It turns out, then, that there is one form of many things whose form appears to be different (which also happened to the Pythagoreans), and it is possible to make one self-substantial form for all things, and to say that the others are not forms; and yet in this way all things will be one. That the matters concerning definitions, therefore, involve some puzzle, and for what reason, has been stated; and for this reason, to reduce all things in this way and to abstract the matter is superfluous; for some things are perhaps this in this, or these things in such-and-such a state. And the comparison in the case of the animal, which the younger Socrates was accustomed to state, is not well; for it leads away from the truth, and makes one suppose that it is possible for man to exist without his parts, just as the circle can exist without the bronze. But the cases are not similar; for the animal is something sensible, and it is not possible to define it without motion, and therefore not without its parts being in a certain state. For it is not in any state whatsoever that a hand is a part of man, but only when it is able to fulfill its function, so that it is animate; but when not animate, it is not a part. But in the case of mathematical objects, why are the formulae not parts of the formulae, for example, the semicircles of the circle?