LESSON 10

The Relative Excellence of Actuality and Potency

  Chapter 9: 1051a 4-1051a 33

             801. Furthermore, that actuality is also better and more excellent and more honorable than good potency is evident from the following: all things which are spoken of as potential are alike capable of contrary determinations; for example, what is said to be capable of being well is the same as what is capable of being ill, and simultaneously has both capabilities; for it is the same potency that is capable of being well and being ill, and of being at rest and in motion, and of building and demolishing, and of being built and being demolished. Therefore the capacity for contrary determinations belongs to the same thing at the same time; but it is impossible for contrary determinations to belong to the same thing at the same time, for example, being well and ailing. Hence one of these must be good; but the potency may be both alike or neither; and therefore the actuality is better.

             802. And also in the case of evil things the goal or actuality must be worse than the potency; for it is the same potency that is capable of both contraries.

             803. It is clear, then, that evil does not exist apart from things; for evil is by its very nature subsequent to potency.

             804. Hence in those things which exist from the very beginning and are eternal, there is neither evil nor wrong nor corruption; for corruption belongs to evil things.

             805. And it is also by activity that geometrical constructions are discovered, because they are discovered by dividing. For if they had already been divided, they would be evident; but they are now present potentially. Why, for example, are the angles of a triangle equal to two right angles? Because the angles grouped around one point are equal to two right angles. Hence, if the line next to the one side were extended, the answer would be clear to anyone seeing the construction. Again, why is an angle in a semicircle always a right angle? Because, if its three lines are equal, two of which form the base and the other rests upon the middle point of the base, the answer will be evident to anyone who sees the construction and knows the former proposition. Hence, it is evident that constructions which exist potentially are discovered when they are brought to actuality; and the reason is that the intellectual comprehension of a thing is an actuality. Hence the potency proceeds from an actuality, and it is because people make these constructions that they attain knowledge of them. For in a thing numerically one and the same, actuality is subsequent in the order of generation.

COMMENTARY

             1883. Having compared actuality and potency from the viewpoint of priority and posteriority, the Philosopher now compares them from the viewpoint of good and evil; and in regard to this he does two things.

             First (801:C 1883), he says that in the case of good things actuality is better than potency; and this was made clear from the fact that the potential is the same as what is capable of contrary determinations; for example, what can be well can also be ill and is in potency to both at the same time. The reason is that the potency for both is the same--for being well and ailing, and for being at rest and in motion, and for other opposites of this kind. Thus it is evident that a thing can be in potency to contrary determinations, although contrary determinations cannot be actual at the same time. Therefore, taking each contrary pair separately, one is good, as health, and the other evil, as illness. For in the case of contraries one of the two always has the character of something defective, and this pertains to evil.

             1884. Therefore what is actually good is good alone. But the potency may be related "to both" alike, i.e., in a qualified sense--as being in potency. But it is neither in an absolute sense--as being actual. It follows, then, that actuality is better than potency; because what is good in an absolute sense is better than what is good in a qualified sense and is connected with evil.

             1885. And also (802).

             Second, he shows on the other hand that in the case of evil things the actuality is worse than the potency; and in regard to this he does three things.

             First, he proves his thesis by the argument introduced above; for what is evil in an absolute sense and is not disposed to evil in a qualified sense is worse than what is evil in a qualified sense and is disposed both to evil and to good. Hence, since the potency for evil is not yet evil, except in a qualified sense (and the same potency is disposed to good, since it is the same potency which is related to contrary determinations), it follows that actual evil is worse than the potency for evil.

             1886. It is clear, then (803).

             Second, he concludes from what has been said that evil itself is not a nature distinct from other things which are good by nature; for evil itself is subsequent in nature to potency, because it is worse and is farther removed from perfection. Hence, since a potency cannot be something existing apart from a thing, much less can evil itself be something apart from a thing.

             1887. Hence in those (804).

             Third, he draws another conclusion. For if evil is worse than potency, and there is no potency in eternal things, as has been shown above (792:C 1867), then in eternal things there will be neither evil nor wrong nor any other corruption; for corruption is a kind of evil. But this must be understood insofar as they are eternal and incorruptible; for nothing prevents them from being corrupted as regards place or some other accident of this kind.

             1888. And it is (805).

             Having compared potency and actuality from the viewpoint of priority and posteriority and from that of good and evil, he now compares them with reference to the understanding of the true and the false. In regard to this he does two things. First (805:C 1888), he compares them with reference to the act of understanding; and second (806:C 1895), with reference to the true and the false ("Now the terms").

             He accordingly says, first (805), that "geometrical constructions," i.e., geometrical descriptions, "are discovered," i.e., made known by discovery in the actual drawing of the figures. For geometers discover the truth which they seek by dividing lines and surfaces. And division brings into actual existence the things which exist potentially; for the parts of a continuous whole are in the whole potentially before division takes place. However, if all had been divided to the extent necessary for discovering the truth, the conclusions which are being sought would then be evident. But since divisions of this kind exist potentially in the first drawing of geometrical figures, the truth which is being sought does not therefore become evident immediately.

             1889. He explains this by means of two examples, and the first of these has to do with the question, "Why are the angles of a triangle equal to two right angles?" i.e., why does a triangle have three angles equal to two right angles? This is demonstrated as follows.

Figure 1 (ABC)

Let ABC be a triangle having its base AC extended continuously and in a straight line. This extended base, then, together with the side BC of the triangle form an angle at point C, and this external angle is equal to the two interior angles opposite to it, i.e., angles ABC and BAC. Now it is evident that the two angles at point C, one exterior to the triangle and the other interior, are equal to two right angles; for it has been shown that, when one straight line falls upon another straight line, it makes two right angles or two angles equal to two right angles. Hence it follows that the interior angle at the point C together with the other two interior angles which are equal to the exterior angle, i.e., all three angles, are equal to two right angles.

             1890. This, then, is what the Philosopher means when he says that it may be demonstrated that a triangle has two right angles, because the two angles which meet at the point C, one of which is interior to the triangle and the other exterior, are equal to two right angles. Hence when an angle is constructed which falls outside of the triangle and is formed by one of its sides, it immediately becomes evident to one who sees the arrangement of the figure that a triangle has three angles equal to two right angles.

             1891. The second example has to do with the question, "Why is every angle in a semicircle a right angle?" This is demonstrated as follows.

Figure 2 (ABCD)

Let ABC be a semicircle, and at any point B let there be an angle subtended by the base AC, which is the diameter of the circle. I say, then, that angle B is a right angle. This is proved as follows: since the line AC is the diameter of the circle, it must pass through the center. Hence it is divided in the middle at the point D, and this is done by the line DB. Therefore the line DB is equal to the line DA, because both are drawn from the center to the circumference. In the triangle DBA, then, angle B and angle A are equal, because in every triangle having two equal sides the angles above the base are equal. Thus the two angles A and B are double the angle B alone. But the angle BDC, since it is exterior to the triangle, is equal to the two separate angles A and B. Therefore angle BDC is double the angle B alone.

             1892. And it is demonstrated in the same way that angle C is equal to angle B of the triangle BDC, because the two sides DB and DC are equal since they are drawn from the center to the circumference, and the exterior angle, ADB, is equal to both.

Figure 2

Therefore it is double the angle B alone. Hence the two angles ADB and BDC are double the whole angle ABC. But the two angles ADB and BDC are either right angles or equal to two right angles, because the line DB falls on the line AC. Hence the angle ABC, which is in a semicircle, is a right angle.

             1893. This is what the Philosopher means when he says that the angle in a semicircle may be shown to be a right angle, because the three lines are equal, namely, the two into which the base is divided, i.e., DA and DC, and the third line, BD, which is drawn from the middle of these two lines and rests upon these. And it is immediately evident to one who sees this construction, and who knows the principles of geometry, that every angle in a semicircle is a right angle.

             1894. Therefore the Philosopher concludes that it has been shown that, when some things are brought from potency to actuality, their truth is then discovered. The reason for this is that understanding is an actuality, and therefore those things which are understood must be actual. And for this reason potency is known by actuality. Hence it is by making something actual that men attain knowledge, as is evident in the constructions described above. For in numerically one and the same thing actuality must be subsequent to potency in generation and in time, as has been shown above.