Aristotle · a new plain-English translation from the original language
1| On the Heavens, Book 1. The science of nature deals, for the most part, with bodies and magnitudes and their attributes and motions, and also with the principles that belong to substance of this kind. For among the things constituted by nature, some are bodies and magnitudes, some possess body and magnitude, and some are principles of the things that possess these. Now the continuous is that which is divisible into parts that are always further divisible, and body is that which is divisible in every direction. Of magnitude, that which extends in one direction is a line, that which extends in two is a surface, and that which extends in three is body. And beyond these there is no other magnitude, because the three are all, and 'three times' is 'in every way.' For as the Pythagoreans also say, the all and all things are bounded by three: end, middle, and beginning give the number of the whole, and these have the number of the triad. That is why, having taken this over from nature as if it were one of nature's own laws, we also use this number for the ceremonial rites of the gods. And we assign our names in the same way: two things we call 'both,' and two people 'both of them,' but we do not say 'all' of two — it is of three that we first use this word. And in this, as has been said, we are simply following nature's own lead. So then, since 'all things' and 'the whole'
2| and 'the complete' do not differ from one another in kind, but only, if at all, in the matter and the things of which they are said, body alone among magnitudes would be complete: for it alone is bounded by the three, and this is 'all.' And being divisible in three ways, it is divisible in every way, whereas of the others one is divisible in one direction, another in two; for as they stand with respect to number, so they also stand with respect to divisibility and continuity: one is continuous in one direction, another in two, and one in every direction. All magnitudes, then, that are divisible are also continuous. Whether all continuous things are also divisible is not yet clear from what has been said; but this much is clear, that there is no passing over into another genus, as from length to surface, or from surface to body — for then the resulting thing would no longer be a complete magnitude, since the transition would have to come about through some deficiency, and it is not possible for the complete to be deficient, since it extends in every direction. Now each of the bodies that exist in the character of a part is, by definition, of this kind, for it has all the dimensions; but it is bounded in relation to what is next to it by contact, and that is why in a sense each of the bodies is many. But the whole of which these are parts must necessarily be complete, and, as the word signifies, complete in every direction, and not in one respect and not in another.
3| 2 Concerning the nature of the whole — whether it is unlimited in magnitude or its total bulk is bounded — we must consider later; but I now speak of its parts taken according to their species, and I make this my starting point. For we say that all natural bodies and magnitudes are, in their own right, capable of motion with respect to place — for we say that nature is a principle of motion for them. Now every motion that is with respect to place, which we call locomotion, is either straight, or circular, or a mixture of these two — for these are the only two simple kinds. The reason is that these magnitudes too are the only simple ones, the straight and the curved. Circular motion is motion about the center, and straight motion is upward and downward. I call 'upward' motion away from the center, and 'downward' motion toward the center. So all simple locomotion must be either away from the center, or toward the center, or about the center. And this seems to follow, and to accord in reason, with what was said at the start: for body was completed in three, and so was its motion. Since, then, among bodies some are simple and some are composed of these (I call simple those that have a principle of motion by nature, such as fire and earth and their species and things akin to them), motions too must be either simple or in some way mixed — simple for the simple bodies, mixed for the composite ones — and a composite body moves according to whichever simple body predominates in it.
4| If, then, there is a simple motion, and circular motion is simple, and the motion of a simple body is simple while a simple motion belongs to a simple body (for if it belonged to a composite body, it would be so according to whichever component predominates), then there must necessarily be some simple body whose nature it is to move with circular motion in accordance with its own nature. By force it may indeed undergo the motion proper to something else, but by nature this is impossible, if indeed each of the simple bodies has one natural motion. Further, if the motion contrary to nature is the opposite of the motion in accordance with nature, and one thing has one opposite, then, since circular motion is simple, if it is not in accordance with the nature of the moving body, it must be contrary to that body's nature. If, then, it is fire or something else of that kind that moves in a circle, its motion in accordance with nature will be the opposite of circular motion. But one thing has one opposite, and up and down are opposite to each other. And if the body moving in a circle is something else, moving so contrary to its own nature, then it will have some other motion that is in accordance with its nature. But this is impossible: for if that motion is upward, the body will be fire or air, and if downward, water or earth. But moreover, this circular motion must necessarily be primary.
5| For the complete is by nature prior to the incomplete, and the circle is among complete things, while no straight line is: not the unlimited straight line, for it would then have a limit and an end, nor any of the limited ones, for there is always something outside any of them, since it is possible to extend any of them further. So then, if the prior motion belongs to a body prior by nature, and circular motion is prior to straight motion, while motion along a straight line belongs to the simple bodies (for fire moves in a straight line upward and the earthy bodies move downward toward the center), then circular motion too must necessarily belong to some one of the simple bodies — for we said that the motion of composite bodies is determined by whichever of the simple bodies predominates in the mixture. From these considerations, then, it is clear that there naturally exists some substance of body other than the compounds formed here, more divine and prior to all of these; and this becomes even clearer if one further grants that every motion is either in accordance with nature or contrary to nature, and that what is contrary to nature for one thing is in accordance with nature for another, as is the case with upward and downward motion — the one being in accordance with nature for fire and the other for earth, while each is contrary to nature for the other. So it is necessary that circular motion too, since it is contrary to nature for these bodies, be in accordance with nature for some other body.
6| Furthermore, if circular locomotion belongs to something in accordance with nature, then clearly there would be some simple and primary body whose nature it is, just as fire moves upward and earth downward, to move in a circle in accordance with its own nature. But if the things that move in a circle move with this circuit contrary to their own nature, it would be astonishing and altogether unreasonable that this alone among motions should be continuous and everlasting, even though it is contrary to nature — for in all other cases, it is plain that what is contrary to nature perishes most quickly. So if, as some say, it is fire that so moves, this motion is no less contrary to its nature than downward motion is; for we observe the motion of fire to be in a straight line away from the center. For all these reasons, then, one might reasonably become convinced, reasoning from all of them together, that there exists, distinct from the bodies around and about us here, some other body, separate from them, and possessing a nature the more excellent the further removed it is from the things here.
7| 3 Since, of the things stated, some are laid down as hypotheses and some have been demonstrated, it is clear that not every body has either lightness or heaviness. But we must lay down what we mean by "heavy" and "light" — sufficiently for present purposes now, and more precisely again when we examine their substance. Let the heavy, then, be what is naturally borne toward the middle, and the light what is borne away from the middle; let the heaviest be what settles beneath everything that moves downward, and the lightest what rises above everything that moves upward. Now everything that moves, whether downward or upward, must have either lightness or heaviness or both — though not relative to the same thing; for things are heavy and light relative to one another, as air is relative to water, and water relative to earth. The body that moves in a circle, then, cannot have either heaviness or lightness; for it is not possible for it to move toward the middle or away from the middle, either in accordance with nature or contrary to nature. It does not move in accordance with nature by straight-line motion, for each of the simple bodies has one natural motion, so that it would be the same as one of the bodies that move in this way. And if it were carried contrary to nature, then if downward motion were contrary to its nature, upward motion would be in accordance with its nature, and if upward motion were contrary to its nature, downward motion would be in accordance with its nature —
8| for we laid it down that, of two contraries, if one motion is contrary to nature, the other is in accordance with nature. But since the whole and the part are borne to the same place in accordance with nature — for instance all earth and a small clod — it follows, first, that this body has neither any lightness nor any heaviness (for otherwise it could, in accordance with its own nature, be borne either toward the middle or away from the middle), and second, that it is impossible for it to be moved in local motion by being drawn either upward or downward; for it is not possible for it to be moved by any other motion, either in accordance with nature or contrary to nature, neither itself nor any of its parts — for the same account holds of the whole and of the part. And it is likewise reasonable to suppose about it that it is ungenerated and indestructible and unincreasable and unalterable, because everything that comes to be comes to be out of a contrary and some underlying subject, and likewise perishes by means of some underlying subject, by a contrary, and into a contrary, as has been said in our first accounts; and the motions of contraries are themselves contrary. If, then, nothing can be contrary to this body, because there cannot be any motion contrary to circular motion, nature seems to have rightly exempted from the contraries the thing that was going to be ungenerated and indestructible —
9| for coming-to-be and perishing occur among contraries. Moreover, everything that grows grows, and everything that diminishes diminishes, by the addition of something akin to it that is resolved into its matter; but for this body there is nothing out of which it has come to be. And if it is both unincreasable and imperishable, it belongs to the same line of thought to suppose that it is also unalterable. For alteration is motion in respect of quality, and of quality, states and dispositions do not come about without changes in respect of affections — for example, health and disease. And we observe that all the natural bodies that change in respect of affection also have growth and diminution — for instance the bodies of animals and their parts, and those of plants, and likewise those of the elements too; so that if the body that moves in a circle can have neither growth nor diminution, it is reasonable that it should also be unalterable.
10| That the first of bodies, then, is eternal, and has neither growth nor diminution, but is unaging and unalterable and unaffected — if one trusts our hypotheses — is clear from what has been said. And it seems that our account bears witness to the appearances, and the appearances to our account. For all human beings have a conception of gods, and all assign the topmost place to the divine, both barbarians and Greeks, all those who believe that gods exist, evidently because they connect the immortal with the immortal; for it cannot be otherwise. If, then, there is something divine, as indeed there is, what has now been said about the first substance of bodies has been well said. And this is also confirmed sufficiently by perception, as far as human conviction goes; for throughout all past time, according to the record handed down from generation to generation, nothing appears to have changed, either in the whole outermost heaven or in any of its proper parts. It appears, too, that the name has been handed down from the ancients even to the present time, since they understood the matter in the same way that we ourselves state it; for we must suppose that the same beliefs have reached us not once, nor twice, but many times over. This is why, on the supposition that the first body is something other than earth, fire, air, and water, they named the topmost place "aether," giving it this name from the fact that it always runs (thein) for eternal time. Anaxagoras, however, misuses this name; for he calls fire "aether."
11| It is also clear from what has been said why the number of the bodies called simple cannot be more than the ones stated; for the motion of a simple body must itself be simple, and we say there are only these simple motions: the circular and the straight-line, and of the latter two divisions — one away from the middle, the other toward the middle. One should grasp the conviction that there is no motion contrary to circular motion, from several considerations. First, because we hold that the straight is above all opposed to the curved. For the concave and the convex seem to be opposed not only to each other but also to the straight, when they are paired together and combined; so that if there is any contrary at all, it is the straight-line motion that is most necessarily contrary to circular motion. And the straight-line motions are opposed to each other because of their places; for the
12| up and down are a difference and an opposition of place. Next, suppose someone assumes that the same account that holds for the straight line holds also for the curved — namely that the motion from A to B is contrary to the motion from B to A — he means the motion on the straight line; for this is finite, whereas circular lines about the same points would be infinite. The same holds likewise for a single semicircle, for instance the motion from C to D and from D to C; for this is the same as the motion on the diameter, since we always take each point as marked off by the straight line joining them. Similarly, even if someone, having made a circle, were to posit that the motion on one semicircle is contrary to that on the other — for instance, in the whole circle, the motion from S to E on the semicircle H contrary to the motion from Z to E on the semicircle Th — even if these are contrary, still the motions on the whole circle are not on that account contrary to one another. But neither, indeed, is the circular motion from A to B contrary to the motion from A to C;
13| for the motion is from the same point to the same point, whereas a contrary locomotion was defined as being from a contrary point to a contrary point. And if the circular motion were contrary to circular motion, one of the two would exist in vain; for they would arrive at the same place, since a body moving in a circle, whatever point it starts from, must necessarily arrive alike at all the contrary places. Now the oppositions of place are up and down, front and back, and right and left. And the oppositions of locomotion correspond to the oppositions of place; so if the two motions were equal, there would be no motion of the bodies at all, and if one motion prevailed, the other would not exist; so that if both existed, one of the two bodies would exist in vain, not moving with its own proper motion — for we call a shoe "in vain" when there is no foot for it to be put on. But god and nature do nothing in vain. But since these matters are clear, as to the remaining ones —
14| We must examine, first, whether there is some infinite body, as most of the ancient philosophers supposed, or whether this is one of the impossibilities. For being one way rather than the other makes no small difference but a total and complete difference for the study of the truth. For this is nearly the source of all the disagreements among those who have declared something about nature as a whole, both in the past and in what may come, since even a small deviation from the truth, as one moves further from it, becomes a myriad times greater — as, for example, if someone were to say that there is some smallest magnitude. For by introducing the smallest magnitude, this person upsets the greatest things in mathematics. The reason for this is that a starting-point is greater in power than in magnitude, so that what is small at the start becomes enormous at the end. And the infinite has both the power of a starting-point and the greatest power of quantity, so that it is neither strange nor unreasonable that the difference should be remarkable that results from taking it that there is some infinite body. That is why we must speak about it, taking it up from the beginning. Every body, then, must be either simple or composite, so that the infinite too must be either simple or composite. But it is also clear that if the simple bodies are finite, the composite must be finite as well;
15| for what is composed of finite things, both in number and in magnitude, is itself finite both in number and in magnitude — for it is only as great as the things of which it is composed amount to. It remains, then, to see whether it is possible for one of the simple bodies to be infinite in magnitude, or whether this is impossible. Let us take up first the first of the bodies, and consider it in this way, and examine the rest in the same way afterward. That the body carried in a circle must be finite is clear from the following. For if the body carried in a circle were infinite, the lines drawn out from the center would be infinite. But of infinite lines the interval between them is infinite — for by interval I mean, of the lines, that outside of which no magnitude can be taken that touches the lines. This, then, must be infinite; for of finite lines the interval will always be finite. And since it is always possible to take something greater than what is given, so that just as we call a number infinite because there is no greatest number, the same argument applies to the interval as well. If, then, it is impossible to traverse the infinite, and if, the line from the center being infinite, the interval must be infinite, then it would not be possible for the body to move in a circle. But we see the heaven turning in a circle, and we have determined by argument that circular motion belongs to something definite. Further, if from a finite time you subtract a finite time, what remains must also be finite and have a starting-point.
16| And if the time of the walking has a starting-point, there is also a starting-point of the motion, and so too of the magnitude that has been walked. And the same holds likewise in the other cases. So let there be an infinite line, on which is ΑΓΕ, extended in one direction, at Ε; and another, on which is ΒΒ, infinite in both directions. Now if the line ΑΓΕ, drawn as a circle from the center Γ, cuts the line ΒΒ, then the line ΑΓΕ, cutting it, will at some point have been carried around in a circle in a finite time — for the whole time in which the heaven was carried around in a circle is finite. And so too the time subtracted, in which the cutting line was carried, is finite. There will therefore be some first starting-point at which Ε cut ΒΒ. But this is impossible. Therefore it is not possible for the infinite to be turned in a circle; and so neither could the universe, if it were infinite. Further, it is also clear from the following that it is impossible for the infinite to be moved. Let Α be carried alongside Β, a finite line alongside a finite line. Then Α must at the same time be released from Β, and Β from Α; for by as much as the one overlaps the other, by that much the other overlaps it in turn. If, then, both were moved in opposite directions, they would be released more quickly; but if one were carried past the other while it remained at rest, more slowly, given that the one carried past moves at the same speed as before.
17| But this at least is clear, that it is impossible to traverse the infinite in a finite time. It must then be traversed in an infinite time — this has already been shown earlier, in the discussion of motion. And it makes no difference whether the finite is carried past the infinite or the infinite past the finite; for when the one moves past the other, the other likewise moves past the first, whether it is 272b moving or at rest — except that if both are moving, they will be released more quickly. Yet nothing sometimes prevents the moving line from passing the resting one more quickly than one moving against it would, if one makes both of the oppositely-moving lines move slowly, while the one passing the resting line moves much faster than they do. So it is no obstacle to the argument that one line is at rest, since it is possible for Α, while moving, to pass the moving Β more slowly. If, then, the time in which the finite line, while moving, is released is infinite, then the time in which the infinite line moved past the finite one must also be infinite. It is therefore altogether impossible for the infinite to move; for even if it moves the smallest amount, the time that results must be infinite. But the heaven does go around and turn completely in a circle in a finite time, so that it goes around the whole of what is within it, such as the finite line ΑΒ. It is therefore impossible for what moves in a circle to be infinite.
18| Further, just as it is impossible for a line that has a limit to be infinite — but only, if at all, in length — likewise a plane surface too cannot be infinite in the respect in which it has a limit; but when it is nowhere bounded, it may be infinite, as, for instance, no square is infinite, nor a circle, nor a sphere, just as no line a foot long is infinite. If, then, neither a sphere nor a square nor a circle is infinite, and if, there being no circle, there could be no circular motion either, and likewise, there being no infinite, there could be no infinite motion, since not even the circle is infinite, then an infinite body could not move in a circle. Further, if Τ is the center, and ΑΒ is an infinite line, and Ε is a line at right angles to it, infinite, and ΓΔ is moving, it will never be released from Ε but will always reach it, as ΓΕ does; for it cuts it at Ζ. Therefore the infinite does not go around in a circle. Further, if the heaven is infinite and moves in a circle, it will have traversed an infinite distance in a finite time. For let the heaven that stays still be infinite, and let the one moving within it be equal to it. Then, since it has gone around in a circle while being infinite, it has traversed, in a finite 273a time, an infinite distance equal to itself. But this was shown to be impossible. It can also be put the other way around: if the time in which it turned around is finite, then the magnitude it has traversed must also be finite; and it has traversed a distance equal to itself; therefore it too is finite. It is clear, then, that what moves in a circle is not without end nor infinite, but has a limit.
19| 6 But neither will what moves toward the center nor what moves away from the center be infinite; for the motions upward and downward are contrary, and contrary motions are toward contrary places. Now if one of a pair of contraries is bounded, the other must also be bounded. And the center is bounded; for wherever a settling body moves downward from, it cannot go farther than the center. The center, then, being bounded, the upward place must also be bounded. And if the places are bounded and finite, the bodies too will be finite. Further, if up and down are bounded, what lies between them must also be bounded. For if it were not bounded, motion would be infinite — and it has been shown earlier that this is impossible. The middle, then, is bounded, so that the body in this place either actually is there or is capable of coming to be there. But indeed the body that moves up or down can come to be in it; for it is the nature of the one kind to move away from the center, and of the other to move toward the center. These points together show that a body cannot be infinite; and further, if weight is not infinite, none of these bodies could be infinite either;
20| For an infinite body must also have infinite weight. And the same account holds for the light as well: for if there is infinite heaviness, there is also infinite lightness, if what floats to the top is infinite. This is clear from the following. Let it be finite, and let the infinite body be taken as AB, and its weight as Γ. Let a finite magnitude, BΔ, then be taken away from the infinite body; and let its weight be E. Now E will be less than Γ, for the weight of the lesser is less. Let the lesser measure the greater some number of times, and let BΔ be to 273b BZ as the lesser weight is to the greater; for it is possible to take away any amount whatever from the infinite. If, then, the magnitudes are proportional to the weights, and the lesser weight belongs to the lesser magnitude, then the greater weight will belong to the greater magnitude. So the weight of the finite body and the weight of the infinite body will turn out equal. Further, if the greater body has the greater weight, the weight of HB will be greater than that of ZB, so that the weight of the finite body will be greater than that of the infinite.
21| And unequal magnitudes will turn out to have the same weight; for the infinite is unequal to the finite. And it makes no difference whether the weights are commensurable or incommensurable, for even if they are incommensurable the same argument will hold — for example, if E, in measuring the weight Γ, overshoots it at the third measure: for if three whole magnitudes equal to BΔ are taken together, their weight will be greater than that of Γ. So the same impossibility will result. Further, it is also possible to take them as commensurable; for it makes no difference whether one starts from the weight or from the magnitude. For example, let E be taken as a weight commensurable with Γ, and let the body having the weight E, namely BΔ, be taken away from the infinite; then, as weight is to weight, let BΔ be to some other magnitude, say BZ — for since the magnitude is infinite, it is possible to take away any amount whatever from it; for once these are taken, both the magnitudes and the weights will be commensurable with one another. Nor again will it make any difference to the demonstration whether the magnitude is uniform in weight throughout or not uniform; for it will always be possible to take bodies equal in weight to BΔ, by taking away or adding any amount whatever from the infinite.
22| So it is clear from what has been said that the weight of the infinite body cannot be finite. It will therefore be infinite. If, then, this is impossible, it is also impossible for there to be any infinite body. But that it is impossible for weight to be infinite is clear from the following. For if a weight of a given amount moves a given distance in a given time, a weight so much greater will move that same distance in still less time, and the times will stand in the inverse of the ratio the weights have — for instance, if the half weight moves it in this time, the double weight will move it in half of this time. Further, a finite weight traverses any finite distance in some finite time. It follows necessarily from this that, if there is an infinite weight, it must both move a given distance the same as the finite weight does, and also not move it — since it must move in proportion to the excess of weight, while conversely the greater weight must move it in less time. But there is no ratio of the infinite to the finite, whereas there is a ratio of the lesser time to the greater finite time; rather, the time keeps getting less, and there is no least time. Nor would it help even if there were a least time; for another finite weight could be taken standing in the same ratio in which the infinite stands to some other, greater, weight, so that the infinite would move the same distance as the finite body in an equal time.
23| But that is impossible. Yet it is necessary, if the infinite moves in any finite time whatever, that some other finite weight should also move some finite distance in this very same time. It is impossible, therefore, for weight to be infinite, and likewise for lightness. So it is also impossible for there to be bodies having infinite weight or infinite lightness. That there is no infinite body, then, is clear both to those who examine the matter point by point in this way, and to those who consider it generally — not only from the arguments stated in our discussion of first principles (for there too we determined earlier, in general, in what sense the infinite exists and in what sense it does not), but also now in another way. After this we must examine whether, even if the body of the whole universe is not infinite, it may nonetheless be so great that there are several heavens; for someone might well raise this puzzle, that, just as the ordered world about us has been constituted, nothing prevents there being others too, more than one, though not infinitely many. But first let us speak generally about the infinite.
24| 7 Every body, then, must be either infinite or finite; and if infinite, it must be either wholly non-uniform in its parts or uniform throughout; and if non-uniform, it must consist either of a finite number of forms or of an infinite number. That it cannot consist of an infinite number is clear, if one will allow our original hypotheses to stand: for since the primary motions are finite in number, the 274b forms of the simple bodies must also be finite. For the motion of a simple body is simple, and the simple motions are finite in number; and every natural body must always have some motion. Yet if the infinite is to consist of a finite number of forms, each of its parts must also be infinite — I mean, for example, the water or the fire. But this is impossible; for it has been shown that neither weight nor lightness can be infinite. Further, their places too would necessarily be infinite in extent, so that the motions of them all would be infinite as well. But this is impossible, if we lay it down that our original hypotheses are true, and that what moves downward cannot travel to infinity, nor, by the same reasoning, what moves upward. For it is impossible for things to come to be that cannot come to be, and this holds alike for quality, for quantity, and for place. I mean, if it is impossible to become white, or a cubit long, or to be in Egypt, then it is also impossible for anything to come to be any of these. It is impossible, therefore, also to travel to a place which nothing that travels can possibly reach. Further, even if it is scattered apart, the fire made up of all its parts together could nonetheless turn out to be infinite. But body was defined as that which has extension in every direction; so how can there be several unlike bodies, each of them infinite? For each would have to be infinite in every direction. But indeed, nor can the infinite be wholly uniform in its parts either. For, in the first place, there is no motion besides these already named. It will therefore have one of these. And if this is so,
25| it will follow that either its weight or its lightness is infinite. But indeed, nor can the body that moves in a circle be infinite. For it is impossible for the infinite to move in a circle: to say this is no different from saying that the heaven is infinite, and this has been shown to be impossible. But indeed, nor can the infinite move at all, taken generally. For it will move either in accordance with its nature or by force; and if by force, then it also has a motion in accordance with its nature, so that there is also another place proper to it, into which it will be carried. But this is impossible. That it is altogether impossible for the infinite to be affected in any way by the finite, or for it to act upon the finite, is clear from the following. Let the infinite be A, 275a the finite be B, and the time in which the one moved the other, or was moved, be Γ. If, then, A was heated by B, or pushed by it, or affected in some other way by it, or moved in any way whatever, in the time Γ, let Δ be less than B, and let the lesser move a lesser amount in an equal time; and let E be the thing altered by Δ. Then whatever ratio Δ has to B, E will have to some finite thing.
26| Let it be granted that an equal (force) alters an equal (amount) in an equal time, that a lesser (force) alters less in the same time, and a greater (force) alters more — by just so much as is proportional to the ratio of the greater to the lesser. It follows that the infinite cannot be moved by anything finite in any time whatsoever; for something else, smaller, will be moved in the same time by a smaller (force), and there will be some finite thing proportional to that finite force; but the infinite bears no ratio at all to the finite. But equally, the infinite will not move the finite in any time either. For let A be the infinite, B the finite, and C the time in which (A moves B). Then in time C, D will move something less than B; let this be Z. Now let E stand to D in the same ratio that the whole BZ stands to Z. Then E will move BZ in time C. So the finite (force) and the infinite (force) will produce their alteration in an equal time. But that is impossible, since it was assumed that the greater (force) produces its effect in less time. And whatever time is taken will produce the same result, so that there will be no time at all in which (the infinite) will move (the finite). And yet, in an infinite time, it is not possible either to move something or to be moved;
27| for infinite time has no limit, while acting and being acted on do have a limit. Nor, then, is it possible for anything infinite to be acted on by anything infinite. For let A be the infinite, and B likewise infinite, and let CD be the time in which B was acted on by A. Now E, a part of the infinite B, since the whole of B was acted on, will not be acted on to the same effect in an equal time; for it has been assumed that the smaller (part) is moved in a smaller time. Let S have been moved by A in time D. Then as D is to (the time for) S, so E is to some finite part of B. That finite part, then, must necessarily be moved by A in time D; for it was assumed that, by the same agent, the greater and the lesser are acted on in the greater and the lesser time respectively, in whatever cases are divided in proportion to time. So it is not possible, in any finite time, for the infinite to be moved by the infinite; therefore it must happen in an infinite time. But infinite time has no end, while what has been moved (i.e. the completed motion) does have one. If, then, every perceptible body has a power of acting, or of being acted on, or both, it is impossible for an infinite body to be perceptible. And indeed all bodies that are in a place are perceptible.
28| There is, then, no infinite body at all outside the heaven. Nor, again, is there one extending up to some point. There is, then, no body whatsoever outside the heaven. For if it were an object of thought only, it would still be in a place; for 'outside' and 'inside' signify place. So it would be perceptible. But nothing that is not in a place is perceptible. One can also argue more dialectically, as follows. The infinite, since it is uniform in its parts, cannot move in a circle; for there is no center of the infinite, and circular motion is around a center. Nor again can the infinite move in a straight line; for there would have to be another place, equally infinite, into which it would move by nature, and yet another, equally infinite, into which it would move contrary to nature. Further, whether it has by nature a motion in a straight line, or is moved by force, in either case the moving
29| power would have to be infinite; for an infinite (body) requires an infinite power, and an infinite power requires an infinite (body), so that what moves it will also be infinite (it is argued in the treatises on motion that nothing finite has an infinite power, and nothing infinite has a finite power). If, then, motion both natural and unnatural is possible for it, there will be two infinites, both the thing that moves it in this way and the thing moved. Again, what is it that moves the infinite? For if it moves itself, it will be ensouled. But how can an infinite thing possibly be a living creature? And if something else is what moves it, there will be two infinites, the mover and the thing moved, differing in form and in power. And if the whole is not continuous, but, as Democritus and Leucippus say, divided by void, the motion of all (its parts) must necessarily be one. For they are distinguished by their shapes, but their nature, they say, is one, as if each were a separate piece of gold. And of these, as we say, the motion must necessarily be the same; for wherever a single clod of earth moves, the whole of earth moves too, and both the whole of fire and a single spark move to the same place. So that none of the bodies will be light without qualification, if all of them have weight;
30| and if they have lightness, none will be heavy. Further, if it has weight or lightness, there will be either some extremity of the whole, or a center. But this is impossible if (the whole) is infinite. And in general, where there is no center and no extremity, and no up and no down, there will be no place at all for the bodies' motion. And if this does not exist, there will be no motion; for motion must be either natural or unnatural, and these are defined by places that are proper or alien (to each body). Further, the place in which something stays or moves unnaturally must necessarily be, for something else, its natural place (and this is confirmed by induction); so not everything can have either weight or lightness, but some things must, and others not. That, then, the body of the universe is not infinite is clear from these considerations.
31| 8 Let us now say why it is also not possible for there to be more heavens than one. For we said this needed examination, in case someone thinks it has not been shown in general, regarding bodies, that it is impossible for any of them to be outside this world, but that the argument has been stated only for bodies whose kind is left unspecified. For all things both stay at rest and are moved, either by force or by nature; and by nature: the place in which a thing stays without force is also the place to which it moves, and in which, once it moves there, it also stays; and by force: the place in which a thing stays by force is also the place to which it moves by force, and in which, once it moves there by force, it also stays by force. Further, if this motion here is by force, the contrary motion is by nature. So if earth from over there is moved by force to the center here, then earth from here will be moved there by nature. And if the earth from over there stays here without force, then (earth from here) will likewise be moved here by nature. And the natural motion is one. Further, all the worlds must necessarily be made of the same bodies, since they are alike in nature. And indeed each of the bodies must necessarily have the same power — I mean fire and earth and the things between them; for if these things there are called by the same names as ours but not in accordance with the same form, then the whole too would be called 'world' only equivocally.
32| It is clear, then, that one element naturally moves away from the center, and another toward the center, if indeed all fire is of the same kind as fire here, and likewise each of the other elements, just as the parts of fire within this world are of the same kind as one another. And that this must necessarily be so is clear from the assumptions laid down about motions; for the motions are limited in number, and each of the elements is defined by reference to each of the motions. So that, if the motions are indeed the same everywhere, the elements too must necessarily be the same everywhere. The parts of earth in another world, then, will naturally move toward this center here, and the fire there will naturally move toward this extremity here; but this is impossible. For if this were so, it would follow necessarily that earth moves upward in its own world, and fire moves toward the center there, and likewise that the earth from here would move away from the center by nature, moving toward the center over there, because the worlds are situated in that way relative to one another. (Textual note: for δή, Bekker prints δέ, following a single manuscript, at 273b5; ὁμοειδές is read with Simplicius, following Torstrik, against Bekker's ὁμοιοειδές.) For either one must not posit that the simple bodies have the same nature in the several heavens, or (the text breaks off here)
33| ...saying so, the middle must be one, and so must the outermost point; and since this is absurd, it is impossible for there to be more worlds than one. To claim that simple bodies have a different nature depending on whether they are a shorter or longer distance from their proper places is unreasonable — for what difference does it make to say a body is such-and-such a distance away, or such-and-such another distance? It will differ only in degree, the more so the greater the distance, but the form remains the same. But surely there must be some motion belonging to them — that they move is evident. Shall we then say that all of them, even the contrary motions, move by force? But what is not by nature such as to move at all cannot possibly be made to move by force. If, then, there is some motion belonging to them by nature, then for things of the same species — even taken individually — the motion must be toward one and the same place in number, for instance toward this particular middle and toward this particular outermost point. But if the motions are toward the same place in form, though more numerous in number — because the individuals too are more numerous, yet each is undifferentiated in form — then it will not be the case that this holds for some of the parts but not for others; rather it will hold alike for all of them. For all things alike are undifferentiated from one another in form, though each differs in number from every other. I mean this: if the parts here stand to one another just as the parts in another world do, then a part taken from here will differ in no way from the parts in some other world, any more than from the parts in this same world — rather it will be just the same.
34| For they do not differ from one another in form at all. So we must either give up these assumptions, or hold that the middle is one and the outermost point is one. And since this is so, it is necessary too that the heaven be one only, and not more than one, on these same grounds and by these same necessities. That there is some place to which earth and fire naturally move is also clear from other considerations. For in general what is in motion changes from one thing to another, and the terms it moves from and moves to differ in form. Every change is finite — for instance, that which is being restored to health changes from disease to health, and that which is growing changes from smallness to magnitude. And so too with what is carried along — for this too becomes something from somewhere. The point it moves from and the point it is by nature carried to must therefore differ in form, just as with what is being restored to health, and not to just any point whatever it happens to be, nor to whatever point the mover wishes. So fire and earth are not carried to infinity, but toward opposite points. And up is opposite to down in place, so that these will be the limits of locomotion, since even circular motion has, in a way, opposite points along the diameter — though to the circle as a whole there is nothing contrary.
35| So in these cases too, motion is in a sense toward opposite and finite points. There must therefore be some end, and motion is not carried on to infinity. A proof that motion is not to infinity is this: earth moves faster the closer it is to the middle, and fire moves faster the closer it is to the upper region. But if the motion were infinite, the speed too would be infinite, and if the speed, then also the weight and the lightness. For just as a thing would be swift in speed the lower it is, because it is heavier, so, if its increase were infinite, the increase in speed would also be infinite. But then again, neither of them is carried, the one up and the other down, by something else, nor by force, as some say, through compression. For then the greater mass of fire would move more slowly upward, and the greater mass of earth downward; but in fact the opposite is true — a greater mass of fire always moves faster, and a greater mass of earth moves faster toward its own place. Nor would either move faster as it approached its end, if it moved by force and compression — for everything that is forced moves more slowly the farther it gets from what forces it, and it is carried, not by force, toward the very place from which it was forced.
36| So from these considerations one can, on examination, gain sufficient conviction about what has been said. It could also be shown by arguments drawn from first philosophy, and from the circular motion, which must be eternal alike here and in the other worlds. It would also become clear if one considers the matter this way: that the heaven must be one. For since the bodily elements are three, there will also be three places belonging to the elements — one belonging to the settling body, which is around the middle; another belonging to the body carried in a circle, which is the outermost; and a third, between these two, belonging to the middle body. For that which floats up must necessarily be in this middle place; for if it is not in this place, it will be outside. But it is impossible for it to be outside — for the one is without weight, the other has weight, and the place of the body having weight is lower, if indeed the place next to the middle belongs to the heavy. But neither can it be contrary to its nature — for then it would be natural to something else, and there was no other such thing. It must, therefore, be in the middle place.
37| What the differentiae of this middle body itself are, we shall say later. As for the bodily elements, then — what they are and how many, and what the place of each is, and further, how many places there are in all — this is clear to us from what has been said. 9 That there is not only one heaven, but that it is impossible for there to be more than one, and further that it is eternal, being both indestructible and ungenerated, let us now state, first raising the difficulties about it. For on examination in the following way it might seem impossible for it to be one and only one. For in all things composed by nature and all things that come to be by craft alike, the form taken just by itself is one thing, and the form mixed together with matter is another — for instance, the form of a sphere is one thing, and the golden sphere and the bronze sphere are another, and again the form of a circle is one thing, and the bronze circle and the wooden circle are another. For in stating what it is to be a sphere or a circle we will not include gold or bronze in the account, on the ground that these do not belong to the substance; but if we are speaking of the bronze or golden circle, we will include them — and this holds even if we are unable to conceive or grasp anything else beyond the particular. For sometimes nothing prevents this from happening, as when only a single circle is taken — for it will be no less true that being-a-circle is one thing and being this particular circle another, the one being form, the other being form in matter and among particulars.
38| Since, then, the heaven is perceptible, it would belong among the particulars — for everything perceptible exists in matter. But if it belongs among the particulars, then being this particular heaven and being heaven without qualification would be different things. This particular heaven, then, is different from heaven without qualification, the one being as form and shape, the other as mixed with matter. Now of things that have some shape and form, the particulars either already are, or admit of becoming, more than one. For if there are Forms, as some say, this must be the case; and even if none of these is separable, it is no less so — for we see this holding in all cases where the substance is in matter, that the things alike in form are more than one, and indeed indefinitely many. So either there are more heavens than one, or it is possible for there to be more than one. From these considerations, then, one might suppose both that there are, and that there can be, more heavens than one. But we must examine again which of these claims is rightly said and which is not. That the account of the form apart from matter is different from the account of the form in matter is rightly said, and let this stand as true. But it is no less true that there is no necessity, on this account, for there to be more worlds, nor is it possible for there to be more, if this world is made of all the matter there is, as in fact it is.
39| Perhaps what is meant will be clearer put this way. If snub-nosedness is a curvature in a nose or in flesh, and flesh is the matter for the snubness, then if a single piece of flesh were formed out of all flesh whatsoever and the snub belonged to it, nothing else either would be snub or could come to be snub. Likewise, if flesh and bones are the matter of man, and if a man were formed out of all flesh and all bones, these being incapable of being dissolved, it would not be possible for there to be another man. And the same holds for the other cases too: in general, of all things whose substance is in some underlying matter, none of them can come to be unless matter is available. Now the heaven is one of the particulars, one of the things made of matter; but if it is composed not out of a portion of that matter but out of all of it, then, while being heaven in general and being this heaven are different things, there could not be another heaven, nor could more come to be, because this heaven has taken in all the matter there is. It remains, then, to show this: that it is composed out of the whole of natural and perceptible body. Let us first say what we mean by "the heaven," and in how many senses, so that what we are looking into becomes clearer to us.
40| In one sense, then, we call "heaven" the substance of the outermost revolution of the whole, or the natural body that is at the outermost revolution of the whole; for we are accustomed to call "heaven" above all the outermost and uppermost region, in which we say the whole divine is seated. In another sense, again, we call "heaven" the body continuous with the outermost revolution of the whole, in which are the moon and the sun and some of the stars; for we say that these too are in the heaven. And in yet another sense we call "heaven" the body enclosed by the outermost revolution; for we are accustomed to call the whole and the all "heaven." Since "heaven" is said in three ways, the whole enclosed by the outermost revolution must necessarily be composed out of the whole of natural and perceptible body, because there is no body outside the heaven, nor can there come to be one. For if there is a natural body outside the outermost revolution, it must necessarily be either one of the simple bodies or one of the compound ones, and it must have its condition either in accordance with nature or contrary to nature. Now it could not be any of the simple bodies. For it has been shown that what moves in a circle cannot change its own place.
41| But neither, on the other hand, can what moves from the center, nor what settles below, be outside. For they would not be there in accordance with their nature (since their proper places are elsewhere), and if they are there contrary to nature, then the place outside will be in accordance with nature for something else; for what is contrary to nature for this body must necessarily be in accordance with nature for another. But there was no body besides these. It is therefore not possible for any of the simple bodies to be outside the heaven. And if not one of the simple bodies, then not one of the mixed bodies either; for the simple bodies must exist as well, given that the mixed body exists. But nor is it possible for one to come to be; for it would come to be either in accordance with nature or contrary to nature, and either simple or mixed, so that the same argument will come round again.
42| For it makes no difference whether we examine whether it exists or whether it is possible for it to come to be. It is plain, then, from what has been said, that no bulk of body exists outside, nor can one come to be; the whole ordered universe, therefore, is made out of the whole of its proper matter, for its matter was the natural and perceptible body. So there are not now several heavens, nor did several come to be, nor can several come to be; but this heaven is one, alone, and complete. And it is at the same time plain that there is neither place, nor void, nor time outside the heaven. For in every place body can possibly be present; and they say void is that in which body is not present but could possibly come to be present; and time is a number of motion, and there is no motion without a natural body. But it has been shown that outside the heaven there neither is nor can come to be a body. It is plain, then, that there is neither place nor void nor time outside. For that reason, the things there are not by nature situated in a place, nor does time make them grow old, nor is there any change at all in anything set beyond the outermost motion; rather, unalterable and unaffected, possessing the best and most self-sufficient life, they continue through the whole of eternity. And indeed this very name was spoken divinely by the ancients.
43| For the end that encompasses the time of each thing's life, outside of which nothing exists in accordance with nature, has been called that thing's "eternity." By the same reasoning, the end that encompasses the whole of time and infinity belonging to the whole heaven is eternity, taking its name from "always being," immortal and divine. From it, too, being and living are suspended for other things as well, for some more exactly, for others dimly. For indeed, just as in the popular philosophical discussions about divine matters it is often shown by argument that whatever is first and highest must necessarily be unchangeable, this fact bears witness to what has been said. For there is nothing else better that could move it (for that would be more divine still), nor does it have any defect, nor is it lacking in any of its own proper goods. And it is reasonable that it moves with unceasing motion; for all things that move come to a stop when they arrive at their proper place, but for the body that moves in a circle the place from which it starts and the place at which it ends are the same.
44| 10 Having settled these points, let us next say whether the heaven is ungenerated or generated, and imperishable or perishable, going through first the opinions held by others; for the proofs of contrary positions are difficulties concerning the contraries. At the same time, too, what is going to be said will be more credible to those who have first heard the claims of the opposing arguments. For to seem to be condemned in default would apply to us less; and indeed those who are going to judge the truth adequately must be arbiters, not litigants. Everyone, then, says the heaven has come to be, but some say that, having come to be, it is everlasting, others that it is perishable like anything else that is composed, and others again that it alternates, existing now in one condition, now in another, perishing, and going on doing this forever, as Empedocles of Acragas and Heraclitus of Ephesus say. Now to say that it came to be but is nevertheless everlasting is among the impossible things. For it is only reasonable to posit those things that we see holding in many cases or in all, and here the opposite is what happens: everything that comes to be is observed also to perish. Further, a thing that has no starting point for being in this condition, but was incapable of being otherwise throughout all prior time, is incapable of changing as well; for there would have to be some cause, which, had it been present earlier, would have made it possible for what is incapable of being otherwise to be otherwise.
45| And if the world was formerly composed out of things that were in a different condition, then, if those things were always in that condition and incapable of being otherwise, it would not have come to be. But if it has come to be, then clearly those things too must be capable of being otherwise and of not always being in the same condition, so that what is now composed will be dissolved, and what is now dissolved was composed before, and this happened, or was possible, infinitely many times. But if this is so, it would not be imperishable, whether it was once in a different condition or whether it is capable of being in a different condition. The defense that some of those who say it is imperishable but has come to be attempt to bring to their own aid is not true. For they say that they have spoken about its coming to be in the same way as those who draw geometrical diagrams, not implying that it ever actually came to be, but for the sake of teaching, as making it more intelligible, just as one grasps a diagram better by watching it being drawn. But this, as we say, is not the same thing. For in the construction of diagrams, once all the elements have been laid down, the same thing results as existing all at once, whereas in demonstrations about these matters it is not the same. Rather it is impossible; for the things taken as earlier and later are mutually incompatible. For they say that ordered things came to be out of unordered ones, and it is impossible for the same thing to be at once unordered and ordered; there must instead be a coming-to-be, and time, that keeps them apart.
46| But in diagrams nothing is separated by time. That it is therefore impossible for the heaven to be at once eternal and to have come to be is clear. And composing and dissolving it alternately does nothing different from establishing it as eternal but changing in shape, as if someone thought that a boy becoming a man, and a man becoming a boy, was at one time perishing and at another existing; for it is clear that when the elements come together into one another, it is not just any chance ordering and combination that comes about, but the same one, especially according to those who have stated this account, since they hold that each disposition is caused by its contrary. So that if the whole body, being continuous, is at one time disposed and arranged this way, and at another that way, while the combination of the whole is the world-order and the heaven, then it would not be the world-order that comes to be and perishes, but its dispositions. But for what has come to be absolutely to perish and not to reverse is impossible, if it is one thing; for before it came to be, the arrangement prior to it always existed, which we say could not have changed unless it had come to be; but if the things are infinite, this is more possible. But whether this too is impossible or possible will become clear from what follows later.
47| For there are some to whom it seems possible for a thing that is ungenerated to perish, and for a thing that has come to be to continue imperishable, as in the Timaeus. For there he says that the heaven came to be, but nevertheless will exist for all time to come. Against these people it has been stated concerning the heaven alone in a manner proper to natural science, but for those who examine the matter universally concerning everything, it will become clear about this case too. 11 First we must distinguish in how many senses we speak of things as ungenerated and generated, and as perishable and imperishable; for since these are said in many ways, even if it makes no difference to the argument, the mind is bound to be in an indefinite state if one treats what is divisible in many ways as though it were undivided; for it is unclear in respect of which nature the statement holds of it. A thing is called ungenerated in one sense if it is now, though it previously did not exist, without coming to be or change, as some say of touching and being moved: for they say that what touches does not come to be touching, nor does what is moved come to be moving. In another sense, if something capable of coming to be, or of having come to be, is not: for this too is likewise ungenerated, in that it is capable of coming to be. In another sense, if something is wholly incapable of coming to be, so that it exists at one time and not at another. And the impossible is spoken of in two ways: either because it is not true to say that it would come to be, or because it would not come to be easily or quickly or well. In the same way too the generated is spoken of: in one sense, if what previously was not later is, whether it has come to be or without coming to be, being at one time not existing and again existing; in another sense, if it is possible, whether the possible is determined by the true or by the easy.
48| In another sense, if its coming-to-be is out of not-being into being, whether it already exists, having come to be through the process of coming-to-be, or does not yet exist, but is merely possible. And perishable and imperishable are spoken of similarly: for whether something previously existing later either does not exist or is capable of not existing, we say it is perishable, whether it is at some point perishing and changing, or not. And there are times when we call perishable also what is capable of not being through the process of perishing, and again in another sense what perishes easily, which one might call easily-perishable. And the same account holds concerning the imperishable: either what without perishing is at one time existing and at another not, such as instances of touching, because without perishing, though existing before, they later do not exist; or what exists but is capable of not existing, or will not exist at some point though it now exists — for you exist, and the touching exists now; but nevertheless it is perishable, because there will be a time when it will not be true to say that you exist, nor that these things are touching. But what is imperishable in the strictest and most proper sense is what exists but is incapable of perishing in such a way that, being now, it later is not, or is capable of not being — or also what has not yet perished but is not capable of not being later.
49| And what does not perish easily is also called imperishable. If this is how these matters stand, we must examine how we speak of the possible and the impossible. For what is called imperishable in the most proper sense is so called because it is incapable of ever perishing, and incapable of at one time existing and at another not; and the ungenerated too is called impossible in the sense of what is incapable of coming to be in such a way that it previously did not exist and later does exist, as, for example, the diagonal being commensurable. If, then, something is capable of moving a hundred stades or of lifting a weight, we always speak with reference to the maximum, for example lifting a hundred talents or walking a hundred stades (and yet it is also capable of the lesser amounts within that, if indeed it is capable of the excess), on the ground that the capacity ought to be defined by its end-point and its maximum. It is necessary, then, that what is capable with respect to such-and-such an excess is also capable of the amounts within it — for example, if it can lift a hundred talents, it can also lift two, and if it can walk a hundred stades, it can also walk two. But the capacity belongs to the excess; and if something is said to be incapable of such-and-such by way of excess, then it is also incapable of the greater amounts, as, for example, one who is not capable of walking a thousand stades is clearly also incapable of walking a thousand and one. But let none of this trouble us.
50| For let it be determined that what is called the end with reference to the excess is what is capable in the proper sense. For perhaps someone might object that what has been said is not necessary: for one who sees a stade does not thereby also see the magnitudes within it, but rather, on the contrary, one who is capable of seeing a point or of hearing a small sound will also have perception of the greater ones. But this makes no difference to the argument; for let the excess be determined either with respect to the capacity or with respect to the thing. For what is meant is clear: sight is superior with respect to the smaller thing, whereas speed is superior with respect to the greater.
51| 12 Now that these points have been determined, we must state what comes next. If, then, there are some things capable both of being and of not being, there must be some maximum time determined both for their being and for their not being — I mean the time within which the thing is capable of existing, and the time within which it is capable of not existing, under whatever category, for example man, or white, or three cubits long, or anything else of that sort. For if it is not to be some determinate quantity, but always greater than whatever is proposed, and there is none smaller, then the same thing will be capable of existing for an infinite time and of not existing for another infinite time. But this is impossible. Let this be the starting point: for the impossible and the false do not signify the same thing. The impossible and the possible, and the false and the true, are in one sense spoken of hypothetically (I mean, for example, that a triangle's having two right angles is impossible, if such-and-such holds, and that the diagonal is commensurable, if such-and-such holds), while in another sense things are possible and impossible, false and true, without qualification. It is not, then, the same thing to be false without qualification and to be impossible without qualification. For to say of you, when you are not standing, that you are standing, is false, but not impossible. Likewise, to say of one who is playing the lyre but not singing that he is singing is false, but not impossible.
52| But standing and sitting at the same time, and the diagonal being commensurable, are not only false but impossible; so supposing something false is not the same as supposing something impossible. And an impossibility follows from an impossibility. Now a thing has the capacity for sitting and for standing at the same time, in the sense that when it has the one capacity it also has the other; but not so as to sit and stand at the same time — rather, at different times. So if a thing possesses a capacity for more than one thing throughout infinite time, that capacity does not belong to it at different times, but all at once. So if something that exists for infinite time is perishable, it would have the capacity for not existing. Now if it exists for infinite time, then what it is capable of will come to belong to it. So it will both be and not be, in actuality, at the same time. A falsehood, then, would result, because a falsehood was assumed. But if what was assumed were not impossible, what results from it would not be impossible either. Everything, then, that exists always is unqualifiedly imperishable. And likewise ungenerated: for if it were generated, it would be capable of not existing at some time. For perishable is what existed before but now does not, or what admits of not existing at some later time; and generated is what admits of not having existed earlier — but there is no time in which what always exists is capable of this.
53| So it cannot be capable of not existing either for infinite or for finite time; for it is capable of existing for finite time too, if indeed for infinite time. It is not possible, then, for one and the same thing both to be capable of always existing and capable of not existing. Nor, again, is it capable of the negation, I mean of not always existing. It is impossible, then, for a thing both to exist always and to be perishable. And likewise impossible for it to be generated. For given two terms, if it is impossible for the later to hold without the earlier, and the earlier is impossible, then the later is impossible too. So if what always exists cannot at any time not exist, it is also impossible for it to be generated. Now since the negation of what is capable of always existing is what is not capable of always existing, while what is capable of always not existing is the contrary of that, and the negation of this contrary is what is not capable of always not existing, the negations of both must belong to the same thing; and there must be a middle term, between what always exists and what always does not exist, namely what is capable both of existing and of not existing — for the negation of each will hold at some time, if the thing is not always. So what does not always fail to exist will at some time exist and at some time not exist, and clearly the same holds of what is not capable of always existing, but it will exist at some time;
54| so it will also not exist. The same thing, then, will be capable both of existing and of not existing, and this is the middle term between the two. The argument stated generally runs as follows. Let A and B be terms incapable of belonging to the same thing, while to everything belongs either A or C, and either B or D. It is necessary, then, that whatever has neither A nor B has both C and D. Let E, then, be the middle term between A and B, since what is neither of two contraries is a middle term. To this both C and D must necessarily belong. For to everything belongs either A or C, so also to E; since then A is impossible for it, C will belong. And the same argument holds for D. So what always exists is neither generated nor perishable, nor is what always does not exist. And it is clear that if a thing is generated or perishable, it is not eternal. For it would then at the same time be capable of always existing and capable of not always existing; and that this is impossible has been shown earlier. Is it the case, then, that if something is ungenerated, and exists, it must necessarily be eternal? And likewise if it is imperishable, and exists? By ungenerated and imperishable I mean these terms in their strict sense: ungenerated is what exists now, and it was not true earlier to say that it did not exist; imperishable is what exists now, and it will not be true later to say that it does not exist.
55| Now if these follow from each other, the ungenerated being imperishable and the imperishable ungenerated, then eternity must follow from each of them as well: whether a thing is ungenerated, it is eternal, or whether it is imperishable, it is eternal. This is also clear from their definitions. For it is necessary that, if a thing is perishable, it is generated. For it is either ungenerated or generated; and if ungenerated, it is by our assumption imperishable. And if it is generated, it must be perishable; for it is either perishable or imperishable, but if imperishable, it was by our assumption ungenerated. But if the imperishable and the ungenerated do not follow from each other, then neither the ungenerated nor the imperishable need be eternal. That they must follow from each other is clear from the following. For the generated and the perishable follow from each other. This too is clear from what was said before: between what always exists and what always does not exist there is a middle term to which neither of these follows, and this is what is generated and perishable. For each of these is capable both of existing and of not existing for a determinate time; I mean that each of them both exists for some amount of time and does not exist for some amount of time. If, then, there is anything generated or perishable, it must be this middle term. Let A, then, be what always exists, B what always does not exist, C what is generated, and D what is perishable.
56| C, then, must necessarily be intermediate between A and B. For in the case of A and B there is no time at either limit in which A did not exist or B did exist; but the generated thing must, if not in actuality, exist potentially, whereas neither of these holds of A and B. So C will exist for some determinate quantity of time, and again will not exist. And likewise for D, the perishable. So each of them is both generated and perishable. The generated and the perishable, therefore, follow from each other. Now let E stand for the ungenerated, Z for the generated, H for the imperishable, and Θ for the perishable. It has been shown that Z and Θ follow from each other. Now whenever terms are arranged as these are — Z and Θ following each other, while E and Z belong to nothing in common, though one or the other belongs to everything, and likewise H and Θ — then E and H must also follow each other. For suppose E does not follow H. Then Z will follow instead, since to everything belongs either E or Z. But whatever has Z also has Θ.
57| So Θ will follow H. But this was assumed to be impossible. And the same argument shows that H follows E. And this is indeed how the ungenerated, E, stands to the generated, Z, and how the imperishable, H, stands to the perishable, Θ. To say, then, that there is nothing to prevent something that comes to be from being imperishable, or something ungenerated from perishing, generation belonging to the one and destruction to the other just once, is to do away with one of the things granted. For everything is capable of acting or being acted on, or of existing or not existing, either for infinite time or for some determinate amount of time; and it is capable of the infinite time for this reason, that the infinite time is in a sense determinate, in that there is none greater than it. But what is infinite only in a certain respect is neither infinite nor determinate. Again, why should a thing that has always existed have perished at this particular point rather than another, or why, not having existed, should it have come to be after an infinite time? For if there is no more reason for one point than another, and the points are infinite, it is clear that something was, for infinite time, both generable and perishable. It is capable, then, of not existing for infinite time; at the same time
58| for it will have the potentiality both of not being and of being — the former, if it is perishable, the latter, if it is generated. So if we posit that what things are capable of holds, the opposites will hold at the same time. And further, this will hold alike at every point of time, so that for infinite time it will have the potentiality both of not being and of being; but it has been shown that this is impossible. Again, if the potentiality is prior to the actuality, it will hold throughout all time — even for what was ungenerated and non-existent, capable of coming to be for infinite time. At the same moment, then, it both did not exist and had the potentiality of existing, and this for infinite time both then and afterward. It is also evident in another way that it is impossible for something perishable never to perish. For it will always be at once both perishable and imperishable in actuality, so that it will at the same time be possible for it both always to be and not always to be. So the perishable does at some time perish, and if it is generated, it has come to be; for it is possible for it to have come to be, and therefore possible for it not always to be. One can also see it this way: it is impossible either for something that has at some time come to be to go on being imperishable forever, or for something ungenerated, always existing before, to perish. For nothing can be, from mere chance, either imperishable or ungenerated.
59| For the spontaneous and the result of chance occur or come to be apart from what is always or for the most part; but what exists for infinite time — whether without qualification, or from some point of time onward — exists either always or for the most part. It is necessary, then, that such things exist by nature at one time and not at another. And for such things the potentiality for the contradictory pair is the same, and matter is the cause both of their being and of their not being. So it is necessary that opposites hold in actuality at the same time as well. But surely it is not true to say now that it is last year, nor last year that it is now. It is therefore impossible for what did not exist at some time to be everlasting afterward; for it will afterward also have the potentiality of not being — not the potentiality of not being at the time when it is (for it exists in actuality then), but of not being last year and in the time past. Now that of which it has the potentiality will hold in actuality; so it will be true to say now that it is not last year. But this is impossible; for there is no potentiality of having come to be, but only of being or of coming to be. Likewise too if what was previously everlasting later ceases to be; for it will have a potentiality for something that does not exist in actuality.