Lecture 26 — Everything eternal is indestructible and ungenerated

184 Having established these distinctions we can now proceed to the sequel. If there are things capable both of being and of not being, there must be some definite maximum time of their being and not being; a time, I mean, during which continued existence is possible to them and a time during which continued non-existence is possible. And this is true in every category, whether the thing is, for example, 'man', or 'white', or 'three cubits long', or whatever it may be. For if the time is not definite in quantity, but longer than any that can be suggested and shorter than none, then it will be possible for one and the same thing to exist for infinite time and not to exist for another infinity. This, however, is impossible.

185 Let us take our start from this point. The impossible and the false have not the same significance. One use of 'impossible' and 'possible', and 'false' and 'true', is hypothetical. It is impossible, for instance, on a certain hypothesis that the triangle should have its angles equal to two right angles, and on another the diagonal is commensurable. But there are also things possible and impossible, false and true, absolutely.

186 Now it is one thing to be absolutely false, and another thing to be absolutely impossible. To say that you are standing when you are not standing is to assert a falsehood, but not an impossibility. Similarly to say that a man who is playing the harp, but not singing, is singing, is to say what is false but not impossible. To say, however, that you are at once standing and sitting, or that the diagonal is commensurable, is to say what is not only false but also impossible.

187 Thus it is not the same thing to make a false and to make an impossible hypothesis, and from the impossible hypothesis impossible results follow.

188 A man has, it is true, the capacity at once of sitting and of standing, because when he possesses the one he also possesses the other; but it does not follow that he can at once sit and stand, only that at another time he can do the other also.

189 But if a thing has for infinite time more than one capacity, another time is impossible and the times must coincide. Thus if a thing which exists for infinite time is destructible, it will have the capacity of not being. Now if it exists for infinite time let this capacity be actualized; and it will be in actuality at once existent and non-existent. Thus a false conclusion would follow because a false assumption was made, but if what was assumed had not been impossible its consequence would not have been impossible. Anything then which always exists is absolutely imperishable.

190 It is also ungenerated, since if it was generated it will have the power for some time of not being. For as that which formerly was, but now is not, or is capable at some future time of not being, is destructible, so that which is capable of formerly not having been is generated. But in the case of that which always is, there is no time for such a capacity of not being, whether the supposed time is finite or infinite; for its capacity of being must include the finite time since it covers infinite time. It is therefore impossible that one and the same thing should be capable of always existing and of always not-existing. And 'not always existing', the contradictory, is also excluded. Thus it is impossible for a thing always to exist and yet to be destructible. Nor, similarly, can it be generated. For of two attributes if B cannot be present without A, the impossibility A of proves the impossibility of B. What always is, then, since it is incapable of ever not being, cannot possibly be generated.

253. After explaining the meanings of the words proposed in the question, the Philosopher here begins to argue on the question proposed, namely, whether something can be generated and indestructible, or ungenerated and destructible.

First he shows with general arguments that this is impossible;

secondly, with arguments proper to natural science, at considerations also (L. 29; 283b17; [286]).

About the first he does two things:

first he shows what follows from the preceding with respect to the present question;

secondly, he begins to argue to his proposition, at let us take our start from this point (281b2; [255]).

254. He says therefore first (281a28) that, the preceding having been determined as to the meanings of certain words, it is now time to state what follows in this treatment. For it has been said above that the "possible" is described in terms of something definite—for example, someone's power to run is described in terms of 100 stades. But there exist in external reality some things that can both exist and not exist. Therefore it is necessary according to the foregoing that there be determined some maximum time both affecting existence, such that it is not possible to exist for a greater time, and affecting non-existence, such that it is not possible not to exist for a greater time. And lest this be understood as applying only to substantial existence, he adds that, when we say that it is possible or not possible for a thing to exist, or that which is able not to exist, such expressions can be understood with regard to any predication, i.e., with regard to any predicament: for example, that a man exist or not exist, which pertains to the genus of substance; or that white exist or not exist, which pertains to the genus of quality; or that "two cubits" exist or not exist, which pertains to the genus of quantity; or any other similar thing. That when something is said to be able to be or not be, that expression must be understood in terms of some determinate time, he now proves by leading to an impossibility. For, as he says, if there is not a time of determinate quantity in which it could be or not be, but a time greater than a given time is always assumed (for example, if it can be for fifty years and then more and again still more), and no limit is reached with respect to which every time in which it can be is less, then, since it is the same thing that can be and not be, as was said, it follows that the same thing can be for an infinite time, and not be for an infinite time, because the same reasoning applies to the non-existence as applies to the existence. This does not mean that the time in respect to which something is able not to be, and which was concluded to be infinite, is the same as the time in respect to which the thing is able to be—because then the same thing would be able to be and not be during the same time, which is impossible, as will be said below. It means rather that there is one infinite time for the thing as non-existing, and another for it as existing. Now this is impossible: for there cannot be two infinite times, because then two times would be simultaneous. But this impossibility follows from saying that the possibility to be or the possibility not to be are not reckoned with respect to some determinate time. Therefore the first thing that must be clear is that the possibility of being is said with respect to a determinate time, and similarly the possibility of not being. And this agrees with what has been already laid down about the meaning of possible.

255. Then, at let us take our start from this point (281b2), he begins to argue to his proposition.

About this he does two things:

first he argues to it with general reasons;

secondly, with an argument proper to natural science, at considerations also (L. 29; 283b17; [286]).

About the first he does two things:

first he shows the truth, namely, that indestructible and unproduced follow one upon the other; and likewise, destructible and generated;

secondly, he disproves the contrary of this, at to say then (L. 29; 283a4).

Regarding the first he does two things:

first he proves his proposition by showing how what is eternal is related to the ungenerated and indestructible, and to the generated and destructible;

secondly, how they are related to one another, at this is clear too from the definition of the terms (L. 28; 282b1).

About the first he does three things:

first he shows that everything eternal is indestructible and ungenerated;

secondly, that nothing eternal is generated or destructible, nor conversely, at but since the contradictory (L. 27; 282a4);

thirdly, he concludes that everything ungenerated and indestructible is eternal, at surely then whatever is ungenerated (L. 27; 282a25; [265]).

About the first he does two things:

first he presents some needed pre-notes;

secondly, he argues to his proposition, at but if a thing (281b18; [257]).

256. He says therefore first (281b2) that in order to prove the proposition, it is necessary to start from the fact that impossible and false do not mean the same. Regarding this he posits four reflections.

The first is that both "possible" and "impossible," as well as "true" and "false," are used in two ways. In one way, conditionally, i.e., in the sense that a thing must be true or false, possible or impossible, if certain things are assumed; for example, a triangle must in fact have three angles equal to two right angles, but nevertheless such a property is impossible if certain things are assumed—thus, if we should suppose a triangle to be a square, it would follow that a triangle would have four right angles. In like manner, it will follow that the diagonal of a square is commensurate to the side if certain assumptions are true—for example, if we should assume that the square of the diagonal is 4 times the square of the side—for then it will always follow that the ratio of the diagonal to the side is a numerical proportion, which is a commensurable ratio. In a second way things are said to be simpliciter, i.e., absolutely and in themselves, "possible" and "impossible," "false" and "true."

The second he gives at now it is one thing (281b8), and he says that to be false simpliciter, i.e. absolutely, and to be impossible absolutely, are not the same. For if I say that you are standing, whereas you are not standing but sitting, then what is said will be false but not impossible; likewise it will be false and not impossible if I say that the person playing the harp is singing, whereas he is not singing. But for someone to be standing and sitting at the same time, or for the diagonal to be commensurable with the side, is not only false, but impossible as well.

The third he gives at thus it is not (281b14) and he concludes it from the foregoing. For since the false and the impossible are not the same, it follows that it is not the same thing to assume what is false and to assume what is impossible: from the false there does not follow the impossible, but from the impossible there follows the impossible.

He gives the fourth at a man has, it is true (281b15). And because it has been said that to stand and sit at the same time is impossible, he concludes that, although something may have at the same time the power to do the opposite things—for example, to sit and to stand—in the sense that now one power is actualized and now the other, nevertheless nothing has the power to have both simultaneously (for example, to stand and sit at the same time) but this must be at different times.

257. Then, at but if a thing (281b18), he proves the proposition, namely, that everything eternal is indestructible and ungenerated.

First he shows that everything eternal is indestructible;

secondly, that everything eternal is ungenerated, at it is also ungenerated (281b25; [259]).

He says therefore first (281b18), as a conclusion from the foregoing (in which it was said that the "possible" is determined for some certain time), that if something is capable of several things during an infinite time, it cannot be said that one of them is possible at one time and another at another time, but whatever it is capable of is possible with respect to this time, because there is no time outside the infinite time. If therefore we should posit something existing in an infinite time to be destructible, from its destructibility it follows that it has the power not to exist at some time; and this must be understood with respect to the same infinite time in which it exists or in respect to some part of that time. Now since it exists in an infinite time and yet is supposed capable of not existing (since it is destructible), then let what is capable of not existing be such, i.e., let it be assumed not to exist, since you say that it is able not to exist. And because it had this capability (of not existing) with respect to infinite time, or some part of it, it follows that it simultaneously actually exists and does not exist—since it is assumed to be existing in infinite time, and later not to exist with respect to the same time. It is plain that this falsity occurs on account of the false assumption that the thing existing in infinite time does not exist at some time. But if this falsehood were not something impossible, an impossibility would not follow. However an impossibility does follow, namely, that the same thing exists and does not exist at the same time. Therefore it was impossible for it not to exist. It had not been able, therefore, not to exist—and thus it was not destructible. Consequently it is plain that whatever is always an existing being cannot be destructible, and thus is absolutely indestructible.

258. But it seems that this reasoning of Aristotle does not conclude with necessity. For although nothing has the power to have two opposite things in existence at the same time, yet nothing prevents a thing from being at the same time capable of two opposites disjunctively, equally and in the same way For example, I have the power to sit or to stand tomorrow at sun-up; not that both might take place at the same time but I am equally capable either of standing without sitting, or of sitting without standing. Hence someone could object to the argument of Aristotle thus: Let us suppose something always existing, yet in such a way that its eternity is contingent and not necessary. It would have the power therefore not to exist with respect to any part of the infinite time in which it is posited as always existing—yet it will not follow because of this that something is existing and not existing at the same time. For the same notion seems to be valid in infinite time and in some finite time. For although we might say that someone is always in his house throughout the whole day, it is not impossible for him not to be in the house at any part of the day—for he is not of necessity in the house throughout the whole day, but contingently.

But it must be answered that the same notion does not apply in both cases. For what exists always, i.e., through infinite time, has the power to exist in infinite time. But the power to exist is not undetermined to either alternative with respect to the time in which someone is able to exist—for all things seek to exist and each thing exists as long as it can. And this is particularly true in things of nature, because nature is determined to one. Consequently whatever exists always, does so not contingently but of necessity.

259. Then, at it is also ungenerated (281b25), he proves the same on the part of the generated or ungenerated. And he says that in like manner what exists always, i.e., in an infinite time, is necessarily ungenerated. If it were generated, it would be possible that at some time it not exist, as was said of the destructible—for just as the destructible is what, although previously existing, does not now exist or is able at some future time not to exist, so the generated is what now exists but previously was not. But there is, neither in finite time nor in infinite time, any time in which what always exists is able not to exist—for what can exist in infinite time, just as what always exists, can exist in any finite time, which is included by infinite time. Accordingly, it will follow, according to the aforesaid deduction, that something simultaneously exists and does not exist, which is impossible. Therefore it does not happen that one and the same thing is able always to exist and always not to exist—since this would be the same as always to exist and always not to exist for an infinite time. Likewise it is not possible to deny the existence of what always exists, for example, to say that what always exists is able not always to exist: for this would imply the possibility of not existing at least for a finite time.

Thus it is plain that it is impossible for something always to exist and to be destructible, or also to be generated. If there are two terms so related that the second cannot exist without the first, as man cannot be without being an animal, then, if the first cannot be, it follows that the second cannot be—just as, if it is impossible for a stone to be animal, it is impossible for a stone to be man. Now not to be at some time follows the destructible and the generated as something more common, as is plain from what was said. Therefore, if what exists always cannot at some time not exist, it follows also that it is impossible for what always exists to be generated, and likewise that it is impossible for it to be destructible. Consequently, it is plain that everything eternal is ungenerated and indestructible.