Lecture 25 — How something is said to be "possible" and "impossible"

178 This being so, we must ask what we mean by 'possible' and 'impossible'.

179 For in its most proper use the predicate 'indestructible' is given because it is impossible that the thing should be destroyed, i.e. exist at one time and not at another. And 'ungenerated' also involves impossibility when used for that which cannot be generated, in such fashion that, while formerly it was not, later it is. An instance is a commensurable diagonal.

180 Now when we speak of a power to move or to lift weights, we refer always to the maximum. We speak, for instance, of a power to lift a hundred talents or walk a hundred stades—though a power to effect the maximum is also a power to effect any part of the maximum—since we feel obliged in defining the power to give the limit or maximum. A thing, then, which is within it. If, for example, a man can lift a hundred talents, he can also lift two, and if he can walk a hundred stades, he can also walk two. But the power is always of the maximum.

And a thing said, with reference to its maximum, to be incapable of so much is also incapable of any greater amount. It is, for instance, clear that a person who cannot walk a thousand stades will also be unable to walk a thousand and one.

182 This point need not trouble us, for we may take it as settled that what is, in the strict sense, possible is determined by a limiting maximum. Now perhaps the objection might be raised that there is no necessity in this, since he who sees a stade need not see the smaller measures contained in it, while, on the contrary, he who can see a dot or hear a small sound will perceive what is greater.

183 This, however, does not touch our argument. The maximum may be determined either in the power or in its object. The application of this is plain. Superior sight is sight of the smaller body, but superior speed is that of the greater body.

246. After pointing out the various senses of "generated" and "ungenerated," "destructible" and "indestructible," the Philosopher here explains the meaning of what is called possible and impossible.

First, he reveals his intention;

secondly, he executes his plan, at now when we speak of a power (281a7; [248]).

About the first he does two things.

First he states what his intention is concerned with (281a1), and says that since the situation is thus with regard to the meanings of "generated" and "ungenerated," "destructible" and "indestructible," it is necessary to consider how something is said to be possible and impossible.

247. Secondly, at for in its most proper use (281a3) he gives the reason for his intention, namely, that possible and impossible are included in the definition of the aforesaid. For, as has been said above, that is most appropriately called "indestructible" which not only cannot be destroyed but can in no way exist at one time and later not exist. Similarly, "ungenerated" is appropriately applied to what is impossible, namely, to be and not to be, and which cannot come to be in any way such that previously it does not exist and later does exist. Thus, for the diagonal of a square to be symmetric, i.e., commensurate, to the side, is ungenerated, because it never can begin to be.

248. Then, at now when we speak of a power (281a7), he shows how something is described as possible and impossible. And it should be noted that, as the Philosopher says in Metaphysics V, possible and impossible are said in one way absolutely, namely, because in themselves they can be true or cannot be true by reason of the relationship existing between the terms; in another way a thing is said to be possible or impossible to something, namely, what it is able for with respect to its active or passive power. And it is in this sense that "possible" and "impossible" are taken here, namely, as what is, or is not, within the power of an agent or patient—for this is the meaning that is most appropriate to natural things.

First, then, he shows how something is said to be "possible" or "impossible";

secondly, he excludes an objection, at this point need not trouble us (281a18; [251]).

With respect to the first he does two things:

first he manifests how some thing is said to be "possible";

secondly, how something is called "impossible," at and a thing said (281a15; [250]).

249. To explain the first (281a7) he says that if a thing is capable of something great, for example, if a man can walk 100 stades or can lift a great weight, we always determine or describe his power in terms of the most he can do. For example, we say that the power of this man is that he can lift a weight of 100 talents or can walk a distance of 100 stades, even though he is capable of all the partial distances included in that quantity, since he can do what exceeds. But his power is not described by these parts—we do not determine his power as being able to carry 50 talents or walk 50 stades, but by the most he can do. Consequently, the power of each thing is described with respect to the end, i.e., with respect to the ultimate, and to the maximum of which it is capable, and with respect to the strength of its excellence. Thus, too, the size of a thing is determined by what is greatest—for example, in describing the size of something that is three cubits, we do not say that it is two cubits. Similarly, we assign as the notion of man that he is rational, not that he is sensible, because what is the ultimate and greatest in a thing is what completes it and puts upon it the stamp of its species. Consequently, it is plain that one who can do what exceeds, necessarily can do what is less. For example, if a person can carry 100 talents, he can also carry two, and if he can walk 100 stades, he can also walk two; yet it is to what is excelling that the virtue of a thing is attributed, i.e., the virtue of a thing is gauged in terms of what is most excellent of all the things that can be done. This is what is said in another translation, the virtue is the limit of a power, because, namely, the virtue of a thing is determined according to the ultimate it can do. And this applies also to the virtues of the soul: for a human virtue is that through which a man is capable of what is most excellent in human actions, i.e., in an action which is in accordance with reason.

250. Then, at and a thing said (281a15), he tells how something is said to be impossible to a thing. And he says that if some amount is impossible to someone if one takes what excels, it is plain that it will be impossible for him to carry or do more. For example, a person who cannot walk 100 stades clearly cannot walk 101. Hence, it is plain that just as the possibility is determined by the greatest that a thing can do—which determines its virtue—so what is impossible is determined by the least that it cannot do, and this determines its weakness. For example, if the most that someone can do is to go 20 stades, the least that he cannot go is 21—and it is from this that his weakness is to be determined, and not from his inability to walk 100 or 1,000 stades.

251. Then, at this point need not trouble us (281a18), he excludes an objection.

First he proposes it;

secondly, he solves it, at this, however, does not touch (281a23; [252]).

He says therefore first (281a18) that nothing should disturb us in connection with the fact that what is properly called "possible" is determined according to the limit of excellence. Someone could, indeed, object that what has been said is not necessary in all matters—for there seems to be an objection in the case of sight and other senses. For a person who sees some large quantity, for example, something a stadium long, cannot for that reason see magnitudes of smaller size contained below that quantity. Rather it is more the opposite that occurs—for one who can see a point, i.e., some smallest thing perceptible to sense, or hear a faint sound, can sense what is greater.

252. Then, at this, however, does not touch (281a23), he answers this objection and says that what was stated does not affect the argument whereby it is shown that the possible is determined by excellence. For the excellence according to which the virtue of a thing is measured can be determined according to the virtue, or according to the thing. According to the thing, when there is an excellence right in it, as was said about the 100 stades or the 100 talents. According to this excellence the active virtue is determined, because whatever can act on a greater thing can act on a lesser. But with respect to virtue, there is excellence when something which is not outstanding in quantity requires an excellence of virtue. And this is seen to occur especially with passive powers—for the more a thing is passible, the more it can be moved by what is less. And since the senses are passive powers, it happens in sensible things that one who can sense what is less can sense what is greater. What he has just said he explains as follows: a vision capable of perceiving a smaller body excels in virtue; hence the excellence in this case is an excellence in the virtue and not in the thing. But that speed is more excellent which is of a greater magnitude—for that is speedier which can traverse a greater distance in the same time—and such excellence is an excellence not only in the virtue, but also in the thing.