Lecture 28 — Generated and corruptible, ungenerated and incorruptible, follow on each other

198 This is clear too from the definition of the terms. Whatever is destructible must be generated; for it is either ungenerated, or generated, but, if ungenerated, it is by hypothesis indestructible.

199 Whatever, further, is generated must be destructible. For it is either destructible or indestructible, but, if indestructible, it is by hypothesis ungenerated.

200 If, however, 'indestructible' and 'ungenerated' are not coincident, there is no necessity that either the ungenerated or the indestructible should be eternal.

201 But they must be coincident, for the following reasons. The terms 'generated' and 'destructible' are coincident;

202 this is obvious from our former remarks, since between what always is and what always is not there is an intermediate which is neither, and that intermediate is the generated and destructible. For whatever is either of these is capable both of being and of not being for a definite time: in either case, I mean, there is a certain period of time during which the thing is and another during which it is not. Anything therefore which is generated or destructible must be intermediate.

203 Now let A be that which always is and B that which always is not, C the generated, and D the destructible. Then C must be intermediate between A and B. For in their case there is no time in the direction of either limit, in which either A is not or B is. But for the generated there must be such a time either actually or potentially, though not for A and B in either way. C then will be, and also not be, for a limited length of time, and this is true also of D, the destructible. Therefore each is both generated and destructible. Therefore 'generated' and 'destructible' are coincident.

204 Now let E stand for the ungenerated, F for the generated, G for the indestructible, and H for the destructible. As for F and H, it has been shown that they are coincident. But when terms stand to one another as these do, F and H coincident, E and F never predicated of the same thing but one or other of everything, and G and H likewise, then E and G must needs be coincident. For suppose that E is not coincident with G, then F will be, since either E or F is predictable of everything. But of that of which F is predicated H will be predicable also. H will then be coincident with G, but this we saw to be impossible. And the same argument shows that G is coincident with E.

267. After proving his proposition above on the part of what is eternal, the Philosopher now proves the same thing on the part of the generated and ungenerated, the destructible and indestructible.

First, he proves it from a supposition;

secondly, with necessity, at but they must be coincident (282b7; [271]).

About the first he does two things:

first, on the supposition that ungenerated and indestructible are convertible terms, he proves that generated and destructible are convertible;

secondly, he shows whence the conversion of ungenerated and indestructible is to be supposed, at if, however, 'indestructible' (282b5; [270]).

268. He says therefore first (282b1) that what we are pursuing can be made clear from their determination, i.e., from the way these terms are distinguished one from the other and related one to the other. First he shows that "generated" follows upon "corruptible," in such a way that if something is corruptible, then necessarily it was generated. For the corruptible must be either generated or ungenerated, because one of these two must be predicated of anything that exists. If, therefore, something is destructible which was not generated, it follows that it is ungenerated. But we are assuming that "ungenerated" and "indestructible" are convertible, i.e., that if something is ungenerated, it will be indestructible. Consequently, if there exists a destructible thing that was not generated, it follows that something destructible is indestructible.

269. Secondly, at whatever, further, is generated (282b1), he proves in the same way that if something is generated, it is necessarily destructible. For what is generated must be either destructible or not. But we are supposing that if something is indestructible it is ungenerated, because these are convertible. It follows, therefore, that there is something generated which is ungenerated, which is impossible. Thus is proved that whatever is destructible is generated and vice versa, on the supposition, of course, that ungenerated and indestructible are convertible terms.

270. Then, at if, however, 'indestructible' (282b5), he shows why this must be supposed. And he says that if "indestructible" and "ungenerated" do not follow one upon the other, then "to be eternal" will not necessarily follow upon being ungenerated and being indestructible. But it has been proved above that it does.

271. Then, at but they must be coincident (282b7) he proves his proposition from necessity.

First he shows that "generated" and "destructible" are convertible;

secondly, from this he further shows that "ungenerated" and "indestructible" are also convertible, at now let E stand for (282b23; [275]).

Concerning the first he does three things:

first he reveals his intention, and says that from what will be said, it will be plain that the foregoing things follow one upon the other. It will first be shown that generated and destructible follow one upon the other.

272. Secondly, at this is obvious (282b9) he presents an argument to prove this, and says that just as the convertibility of "indestructible" and "ungenerated" is plain from what was previously said, so, too, the convertibility of "generated" and "destructible." For between "always existing" and "always not existing" there is a middle (as was said above), namely, that which follows neither, i.e., what neither always is nor always is not. Now such are the "generated" and "destructible," because both are able to be and not to be with respect to some determinate time, in such a way, namely, that for some finite time both exist and for some other finite time both do not exist. If then there is something which is generated or is destructible, such a thing must be a middle between what always exists and what is always non-existent. Consequently both terms will apply to the same thing and they are found to follow one upon the other.

273. Thirdly, at now let A (282b15) he manifests the foregoing argument by using terms, and says: Let Abe something that always exists, and B something that is always non-existent, whereas G is something generated and D something destructible. Then G is necessarily intermediate between A and B, i.e., between what always exists and what always is non-existent; for in regard to A and B there is no time at either terminus, i.e., either before or after, in which A, which is always existing, does not exist, or B, which is always non-existent, exists. But in regard to the generated, there must be some time in which it does not exist, either at both termini or at one of them, and likewise some time in which it does, and this either actually or potentially; but with regard to A and B there can be no opposite time in either way, i.e., either actually or potentially. That is left, therefore, is that the generated G exists for some definite time and for some definite time does not exist; and the same goes for D. It follows, therefore, that both are generated and destructible, i.e., in such a way that the generated thing is both, and the destructible is both. Thus it is plain that "generated" and "destructible" follow one upon the other.

274. But this argument does not seem to be valid: for it is not necessary that a middle between two contraries be one and the same thing. For the middle between white and black is indeed something neither white nor black; yet this is said of many different things which do not follow one upon the other. For red and pale and any of the intermediate colors are neither white nor black, and yet they do not follow one upon the other. Consequently, someone could say that the intermediate between "always existing" and "always not existing" is something which neither always exists nor always does not exist, but that this belongs to the "destructible" in one way and to the "generable" in some other way: for the "generated" has no existence before it exists, while the "destructible" has no existence after it has existed. But this objection is excluded by the very fact that he says that it is in some definite time that each of them exists and does not exist. Thus both of them have to have existence after non-existence, and before non-existence. And this will be made clearer in the following lecture.

275. Then, at now let E stand for (282b23), he shows from the foregoing that "ungenerated" and "indestructible" are also convertible, saying: Let E be ungenerated, Z generated, I indestructible and T destructible. Since it has been shown that "generated" and "destructible" follow upon each other, it is plain that Z and T follow upon each other. Now supposing that Z and T follow upon one another, namely, "generated" and "destructible," and assuming that E and Z, i.e., the "generated" and "non-generated," are not present in the same subject, but that one of them must be present in every subject, and the same for T and I, i.e., the "destructible" and "indestructible," namely, that they are not both present in any same subject, but one of them must be present in any subject, then, such suppositions having been made, it is necessary that I and E, i.e., the "non-generated" and "indestructible," follow one upon the other. This he proves by leading to an impossibility. For if E, which is to be non-generated, does not follow necessarily upon I, which is to be indestructible, it will follow that Z, which is generated, can co-exist with I, which is indestructible, because it has already been established that of everything is predicated either E, i.e., non-generated, or Z, i.e., generated. Moreover it has been stated that whatever is Z, i.e., generated, is also T, i.e., destructible. Consequently, it will follow that T, i.e., destructible, is found in that which is I, i.e., indestructible. But that is contrary to the assumption that T and I are never present in the same thing—for nothing is destructible and indestructible. And the same reasoning shows that I, i.e., indestructible, follows upon E, i.e., non-generated, because the non-generated, E, is related to generated, Z, in the same way as indestructible, I, is related to destructible, T.

Thus it is plain from the foregoing that whatever is destructible was generated and vice versa; and that what is indestructible is non-generated and vice versa.