Commentary Aristotle Metaphysics
But in the mathematical sciences no demonstration is made by saying that something is so because it is better for it to be so, or worse if it were not so—as if one were to say that the angle in a semi-circle is a right angle because it is better that it should be so than be acute or obtuse. And because there can be, perhaps, another way of demonstrating by means of the final cause (for example, if one were to say that if an end is to be, then what exists for the sake of an end must first be), he therefore adds that in the mathematical sciences no one makes any mention at all of any of those things that pertain to the good or to the final cause.
And for this reason certain sophists, as Aristippus, who belonged to the Epicurean school, completely disregarded any demonstrations which employ final causes, considering them to be worthless in view of the fact that in the servile or mechanical arts, for example, in the art of building, that is, in carpentry, and in that of cobbling, all things are explained on the grounds that something is better or worse. But in the mathematical sciences, which are the noblest and most certain of the sciences, no mention is made of things good and evil.
376. But on the other hand. Here he interjects another question.
First, he states this question, which has two parts.
The first part of the question is this. If different causes are considered by many sciences, so that a different science considers a different cause, then which of these sciences should be called the one that is being sought, that is, first philosophy? Is it the one which considers the formal cause, or the one which considers the final cause, or the one which considers one of the other causes?
The second part of the question is this. If there are some things that have many causes, which one of those who consider those causes knows that subject best?
377. For it is possible. He clarifies the second part of the question by the fact that one and the same thing is found to have every type of cause. For example, in the case of a house, the source of motion is the art and the builder; the reason for which, or the final cause of the house, is its function, or its use, which is habitation; its material cause is the earth, from which the walls and floor are made; and its species or form is the plan of the house, which the architect, after first conceiving it in his mind, gives to matter.
378. Therefore, from the things. Here he takes up again the question as to which of the aforesaid sciences we can call wisdom on the basis of the points previously established about wisdom at the beginning of this work—namely, whether it is the science which considers the formal cause, or the one which considers the final cause, or the one which considers one of the other causes.
And he gives, in order, arguments relating to each of the three causes, saying that there seems to be some reason why each one of the sciences (that is, any one which proceeds by means of any cause at all) should be called by the name of wisdom.
First, he speaks of that science which proceeds by means of the final cause. For it was stated at the beginning of this work that this science, which is called wisdom, is the most authoritative one, and the one which directs others as subordinates.
Therefore, inasmuch as wisdom takes precedence, or is prior in the order of dignity and more influential in its authoritative direction of the other sciences (because it is not right that the others should contradict it but they should take their principles from it as its servants), it seems that that science that deals with the end and the good, that is, the one which proceeds by means of the final cause, is worthy of the name of wisdom. And this is true because everything else exists for the sake of the end, so that in a sense the end is the cause of all the other causes.
Thus the science which proceeds by means of the final cause is the most important one. This is indicated by the fact that those arts which are concerned with ends are more important than and prior to the other arts. For example, the art of navigation is more important than and prior to the art of ship-building. Hence, if wisdom is preeminent and regulative of the other sciences, it seems that it proceeds especially by means of the final cause.
379. But insofar as wisdom. Here he introduces the arguments relating to the formal cause. For it was said in the prologue of this work that wisdom is concerned with first causes and with whatever is most knowable and most certain.
And according to this it seems to be concerned with substance; that is, it proceeds by means of the formal cause. For among the different ways of knowing things, we say that he who knows that something exists knows more perfectly than he who knows that it does not exist.
Hence in the Posterior Analytics the Philosopher proves that an affirmative demonstration is preferable to a negative demonstration. And among those who know something affirmatively, we say that one knows more perfectly than another.
But we say that he knows more perfectly than any of the others who knows what a thing is, and not he who knows how great it is, or what it is like, or what it can do or undergo. Therefore, to know a thing itself in the most perfect way absolutely is to know what it is, and this is to know its substance. But even in knowing other things (for example, a thing’s properties), we say that we know best every single thing about which there are demonstrations when we also know the whatness of their accidents and properties. For whatness is found not only in substance but also in accidents.
380. He gives the example of squaring—that is, squaring a surface of equally distant sides which is not square but which we say is squared when we find a square equal to it. But since every rectangular surface of equally distant sides is contained by the two lines which contain the right angle, so that the total surface is simply the product of the multiplication of one of these lines by the other, then we find a square equal to this surface when we find a line which is the proportional mean between these two lines. For example, if line A is to line B as line B is to line C, the square of line B is equal to the surface contained by C and A, as is proved in Euclid’s Elements 6.
381. This becomes quite evident in the case of numbers. For six is the proportional mean between nine and four; for nine is related to six in the ratio of one to one and a half, and so also is six to four. Now the square of six is thirty-six, which is also produced by multiplying four by nine, for four times nine equals thirty-six. And it is similar in all other cases.
382. But with regard to processes. Here he gives an argument pertaining to the cause of motion. For in processes of generation and actions and in every change, we can say we know a thing when we know its principle of motion, and that motion is nothing else than the act of something mobile produced by a mover, as is stated in Physics 3. He omits the material cause, however, because that cause is a principle of knowing in the most imperfect way, for the act of knowing is not caused by what is potential but by what is actual, as is stated below in book 9.
383. Then after having given those arguments which pertain to the second question, he introduces an argument which is based on the same reasons as were given above in reference to the first question—namely, that it is the office of a different science to consider all these causes, because in different subject matters different causes seem to have the principal role. For example, the source of motion has this in mobile things, the quiddity in demonstrable things, and the end in things directed to an end.
384. However, we do not find that Aristotle explicitly solves this question later on, though his solution can be ascertained from the things that he establishes below in different places. For in book 4 he establishes that this science considers being as being, and therefore that it also belongs to it (and not to the philosophy of nature) to consider first substances, for there are other substances besides mobile ones. But either every substance is a being of itself (granted that it is only a form) or it is a being by its form (granted that it is composed of matter and form).
Hence inasmuch as this science considers being, it considers the formal cause before all the rest. But the first substances are not known by us in such a way that we know what they are, as can be understood in some way from the things established in book 9. Thus in our knowledge of them the formal cause has no place. But even though they are immobile in themselves, they are nevertheless the cause of motion in other things after the manner of an end.
Hence inasmuch as this science considers first substances, it belongs to it especially to consider the final cause, and also in a way the efficient cause. But to consider the material cause in itself does not belong to it in any way, because matter is not properly a cause of being, but of some definite kind of being, namely, of mobile substance. However, such causes belong to the consideration of the particular sciences, unless perhaps they are considered by this science inasmuch as they are contained under being. For it extends its analysis to all things in this way.
385. Now when these things are seen it is easy to answer the arguments which have been raised.
First, nothing prevents the different causes in this science from belonging to a single existing thing, even though they are not contraries, because they are reducible to one thing—being in general—as has been stated.