Aristotle · a new plain-English translation from the original language
1| and they say this, drawing evidence also from the elephants, on the ground that this kind of animal exists around both regions, since they lie at the extremities, on the assumption that they have this in common because the extremities join one another. And of the mathematicians, those who try to calculate the size of the circumference say that it comes to four hundred thousand stades; from which, if one draws the inference, it is necessary not only that the mass of the earth be spherical, but also that it not be great in size compared to the size of the other stars.
2| Concerning the primary heaven, then, and its parts, and further concerning the stars carried within it, of what they are composed and what their nature is, and in addition that they are ungenerated and indestructible, we have already given a full account. But since, among the things called natural, some are substances and others are the workings and affections of these — I mean by substances the simple bodies, such as fire and earth and those in the same series with them, and whatever is composed of these, such as the heaven as a whole and its parts, and again animals and plants and their parts; and by affections and workings I mean the motions of each of these and of the others, of whatever these are the causes according to their own power, and further the alterations and the changes of things into one another — it is clear that most of the inquiry concerning nature turns out to be concerned with bodies. For all natural substances either are bodies or come to be together with bodies and magnitudes. This is clear both from the fact that what things are natural has been determined, and from the examination of particular cases. Concerning the first of the elements, then, it has been stated both what its nature is, and that it is indestructible and ungenerated;
3| It remains to speak about the two. And at the same time it will turn out, in discussing these, that we also examine generation and destruction; for either generation does not exist at all, or it exists only in these elements and in the things composed from them. This very question, then, is perhaps the first thing that must be looked at: whether it exists or does not exist. Now those who philosophized earlier about the truth were divided both against the accounts we are now giving and against one another. For some of them did away with generation and destruction altogether; they say that nothing among the things that are either comes to be or is destroyed, but only seems to us to do so — for instance the followers of Melissus and Parmenides, whom, even if what they say on other points is fine, one must still not think spoke as students of nature; for that certain of the things that are should be ungenerated and altogether unmoved belongs to a different and prior inquiry rather than to the inquiry into nature. Those men, because they supposed there to be nothing else besides the substance of perceptible things, and were the first to conceive of such natures, if indeed there is to be any knowledge or practical wisdom at all, in this way transferred the accounts proper to that other inquiry over onto these things. But certain others held, as if on purpose, the opinion contrary to these.
4| For there are some who say that nothing among things is ungenerated, but that all things come to be, and that of the things that have come to be, some remain indestructible while others in turn are destroyed — most of all the followers of Hesiod, and then, among the others, those who first wrote about nature. Others say that all other things come to be and flow, and that nothing stands fixed, but that one single thing alone persists, out of which all these are by nature transformed — which is what many others, and in particular Heraclitus of Ephesus, seem to want to say. And there are some who make every body generated as well, composing and dissolving it into and out of planes. Now about the others let there be a separate discussion; but as for those who speak in this way and construct all bodies out of planes, the various consequences they are found to assert that run contrary to the mathematical sciences can be seen on the surface (though it would have been right either not to disturb these things or to disturb them with arguments more credible than the hypotheses. Next, it is clear that it belongs to the same account both that solids are composed of planes and that planes are composed of lines, and these of points; and if that is so, it is not necessary that the part of a line be a line — but this has been examined earlier, in the discussions concerning motion, that there are no indivisible lengths).
5| But as for the impossibilities that follow, concerning natural bodies, for those who posit indivisible lines, let us now also give them brief consideration; for whatever impossibilities follow for those thinkers will also follow for students of nature, while not everything that follows for the latter follows for the former, because mathematical objects are spoken of by way of abstraction, while natural objects are spoken of by way of addition. Now there are many things that cannot belong to indivisibles but must necessarily belong to natural bodies — for instance, whether something is divisible; for a divisible cannot belong to an indivisible, and affections are all divisible in two ways: either in respect of form or in respect of accident — in respect of form, for instance, of color, white or black; in respect of accident, whenever the thing to which the affection belongs is divisible. So all the simple affections are divisible in this latter way. Hence one must examine what is impossible among such cases. If, then, it is among the impossibilities that when neither of two parts has any weight the two together should have weight, and perceptible bodies either all, or at least some — for instance earth and water — do have weight, as they themselves would say: then if the point has no weight, it is clear that neither do lines, and if not these, neither do planes.
6| So neither, then, does any body. But it is in fact evident that a point cannot possibly have weight. For everything heavy admits of being both heavier and less heavy, and likewise the light, of being lighter and less light. But what is heavier or lighter is perhaps not necessarily heavy or light, just as what is large is larger, but what is larger is not in every case large; for there are many things which, though small without qualification, are nonetheless larger than certain others. If then whatever, being heavy, is heavier, must necessarily be greater in weight, then everything heavy would be divisible.
7| But the point is posited as indivisible. Further, if the heavy is something dense and the light something rarefied, and the dense differs from the rarefied by containing more matter in an equal bulk, then if there is a point that is heavy and light, it will also be dense and rarefied. But the dense is divisible, and the point is indivisible. And if everything heavy must be either soft or hard, it is easy to draw an impossibility from these premises as well. For the soft is what yields into itself, and the hard is what does not yield; and what yields is divisible. But surely weight will not come to be out of things that have no weight either. For as to how many such things, and of what sort, this will happen, how will they define it without simply making it up? And if every weight is greater than a weight by a weight, it will follow that each of the partless units also has weight; for if the four points have weight, then that which is composed of more points, being heavier than a given heavy thing, and that by which one thing is heavier than a heavy thing must itself be heavy — just as that by which one white thing is whiter than another must itself be white — so that the amount by which the larger exceeds by one point will be heavier once the equal part has been subtracted off.
8| So the single point too will have weight. Further, if planes can be combined only along a line, that is absurd; for just as a line can be combined with a line in both ways, both lengthwise and breadthwise, so a plane too ought to combine with a plane in the same way. Now a line can be combined with a line by being laid upon it along a line, but not by being added on lengthwise. But surely if combination breadthwise is also possible, there will be some body, neither an element nor composed out of elements, arising from planes combined in this way. Further, if bodies are heavier in proportion to the number of their planes, as is laid down in the Timaeus, it is clear that the line and the point will have weight too, for they stand in the same proportion to one another as we have said before. But if it is not in this way that they differ, but rather by earth being heavy and fire light, then among the planes too some will be light and some heavy — and likewise among the lines and the points; for the plane of earth will be heavier than that of fire. And in general it follows either that there is never any magnitude at all, or that it could be done away with, if indeed point stands to line as line stands to plane, and this to body.
9| For all things, resolved one into another, will be resolved into the primary elements; so that it could turn out that there are only points, and no body at all. And in addition to this, if time is similarly constituted, it too could either be done away with at some point or could be capable of being done away with; for the now, being indivisible, is like a point of a line. The same consequence befalls also those who construct the heaven out of numbers; for some construct nature out of numbers, as certain of the Pythagoreans do — for natural bodies plainly have weight and lightness, while units, when combined, cannot possibly make a body, nor can they have weight.
10| 2 That motion of some kind must of necessity belong by nature to all the simple bodies is clear from the following. Since they are observed to move, it is necessary that they move by force if they do not have a motion of their own; and being by force and being contrary to nature are the same thing. But surely if there is some motion contrary to nature, there must also be one in accordance with nature, alongside which this other one is contrary; and if there are many motions contrary to nature, the one in accordance with nature is single; for a thing has its motion according to nature in a single way, but has many motions contrary to nature. It is clear too from rest; for a thing must be at rest either by force or by nature, and by force it remains where it is also carried by force, and by nature where it is by nature. Since, then, something is observed remaining at the middle, if it remains there by nature, it is clear that its motion there too is according to nature for it; but if by force, what is it that prevents it from being carried? If it is something at rest, we shall run into the same argument in a circle; for it is necessary either that the first thing at rest be so by nature, or that this go on to infinity, which is impossible. But if...
11| what is in motion by what prevents it from being carried along — as Empedocles says the earth is kept at rest by the whirl — where would it have been carried, since it is impossible to traverse the infinite? For nothing impossible comes to be, and to traverse the infinite is impossible. So what is being carried must come to rest somewhere, and there it remains not by force but in accordance with nature. But if there is a rest that is in accordance with nature, there is also a motion in accordance with nature, namely the carrying to that place. This is why Leucippus and Democritus too, who say that the primary bodies are always in motion in the void and the infinite, must state what kind of motion this is, and what their natural motion is. For if one element is moved by another by force, still there must be some motion that belongs to each in accordance with nature, alongside which the forced motion occurs; and the first mover must move not by force but in accordance with nature. Otherwise it goes on to infinity, unless there is something that moves first in accordance with nature, and instead the prior thing, itself moved by force, will always be what moves the next. And this same consequence necessarily follows even if, as is written in the Timaeus, before the universe came to be the elements were in disordered motion. For their motion must be either forced or in accordance with nature.
12| But if it was moving in accordance with nature, there must be a universe, as anyone will see who applies his attention to the matter. For the first mover must move itself, being moved in accordance with nature, and the things moved — not by force, but coming to rest in their own proper places — must produce the very order they now have: the things with weight moving toward the middle, the things with lightness moving away from the middle. And this is the arrangement the universe has. Further, one might raise this much of a question: whether it was possible or not possible, given disordered motion, for such mixtures also to be formed by mingling as those out of which the bodies that are naturally constituted are put together — I mean bones and flesh, for instance, as Empedocles says come to be under the rule of Love; for he says that 'many heads sprang up without necks.' But for those who make the things in motion infinite in an infinite space — if the mover is one, the motion must be a single carrying, so that the motion will not be disordered; but if the movers are infinite, then the carryings too must be infinite. For if 301 a they were finite, there would be some order; for disorder does not result from things not being carried to the same place — indeed not even now do all things get carried to the same place, but only things of the same kind.
13| Further, disordered is nothing other than contrary to nature; for the proper order of perceptible things is their nature. But this too is absurd and impossible — that the infinite should have disordered motion; for the nature of things is that which most of them have, and for most of the time. So it turns out, on their view, the opposite: that disorder is in accordance with nature, while order and the universe are contrary to nature — and yet nothing that occurs in accordance with nature occurs at random. Anaxagoras seems to have grasped this very point well; for he begins his account of the making of the universe from things at rest. The others too try, after a fashion, to bring things together and set them moving again, and to separate them out. But it is not reasonable to produce coming-to-be out of things already separated and in motion. This is why Empedocles too omits the phase under Love; for he could not have constructed the heaven by building it up out of things already separated, producing combination by means of Love — since the universe is constituted out of the elements in a state of separation. So it must come to be out of what is one and combined. It is clear, then, from these considerations that there is some natural motion belonging to each of the bodies, with which they are moved neither by force nor contrary to nature. And that some bodies must have an inclination of weight and of lightness is clear from what follows.
14| For we say motion is necessary; but if what is in motion does not by nature have an inclination, it is impossible for it to move either toward the middle or away from the middle. For let A be a body without weight, and B a body having weight, and let the weightless body have traversed the line ΓΔ, while B in an equal time traverses ΓΕ (for the body having weight will be carried a greater distance). Now if the body having weight is divided in the ratio of ΓΕ to ΓΔ (for it is possible for it to stand in this ratio to one of its own parts), then, if the whole body is carried the whole distance ΓΕ, the part must in the same time be carried the distance ΓΔ, so that the weightless body and the body having weight will be carried an equal distance — which is impossible. And the same argument applies to lightness as well. Further, if there is to be some body in motion having neither lightness nor weight, this must be moved by force, and being moved by force it will make the motion infinite. For since the mover is some power, and the smaller and lighter thing will be moved further by the same power, let A, the weightless body, have been moved the distance ΓΕ, and let B, the body having weight, in an equal time have been moved the distance ΓΔ.
15| Now with the body having weight divided in the ratio of ΓΕ to ΓΔ, it will follow that the portion removed from the body having weight is carried the distance ΓΕ in the equal time, since the whole was carried the distance ΓΔ. For the speed of the smaller body will stand to that of the larger as the larger body stands to the smaller. The weightless body, then, will be carried an equal distance to the body having weight in the same time. But this is impossible. So, since the weightless body will always be moved a greater distance than whatever is added, it would be carried an infinite distance. It is clear, then, that every body must have weight or lightness, one or the other, definitely. And since nature is the principle of motion present within the thing itself, while power is that principle present in another thing qua other, and motion is in every case either in accordance with nature or by force, then the power will produce more quickly the motion in accordance with nature — for instance, for the stone, the downward motion — while the motion contrary to nature it produces entirely by itself. Toward both it uses the air as an instrument, so to speak; for air is naturally suited to be both light and heavy. So it will produce the upward carrying insofar as it is light, when it has been pushed and has received its starting point from the power, and again the downward carrying insofar as it is heavy;
16| for the power, as it were, kindles the air and hands it over to each motion in turn. This is why what is moved by force continues to be carried along even when the mover is no longer following alongside it; for if the body did not have some such character, there would be no motion by force. And it likewise assists the motion in accordance with nature belonging to each thing, in the same way. That everything, then, is either light or heavy, and how the motions contrary to nature stand, is clear from this. And that there is neither coming-to-be of all things, nor, without qualification, of none of them, is clear from what has been said. For it is impossible for there to be coming-to-be of every body, unless it is also possible for there to be some void existing separately. For in the place in which what is now coming to be would be, if it were coming to be, there must previously have been void with no body in it. For while it is possible for one body to come to be out of another — fire out of air, for instance — it is altogether impossible for it to come to be out of nothing, out of no magnitude previously existing. For a body might most of all come to be in actuality out of something that is a body in potentiality. But if the body that exists in potentiality is not, prior to this, some other body in actuality, there will be a separately existing void.
17| 3 It remains to say what bodies come to be, and why. Since in all cases knowledge proceeds through first things, and among the things present in a thing the elements are first, we must consider whether there are elements of such bodies, and why there are, and then after this how many there are and of what sort. This will become clear once we lay down what the nature of an element is. Let an element of bodies be that into which the other bodies are divided, being present in them potentially or actually (which of the two, is still disputable), and which is itself indivisible into things differing in form; for something of this sort is what everyone means by "element," and in every case. If, then, what has been said is an element, there must be some such things among bodies. For in flesh and wood and each of such things fire and earth are present potentially; for these are plainly separated out from them. But in fire flesh or wood are not present, neither potentially nor actually; for otherwise they would be separated out. Likewise, not even if there were only one such thing would flesh or bone be present in it either; for it is not the case that, because flesh or bone or anything else will come to be, one must already say it is present potentially — rather, one must further consider what the manner of its coming-to-be is.
18| Anaxagoras speaks about the elements in a manner opposite to Empedocles. For the one says that fire and earth and the things ranked with them are elements of bodies and that all things are composed out of these, while Anaxagoras says the opposite: the homoiomerous things are the elements (I mean, for example, flesh and bone and each such thing), while air and fire are mixtures of these and of all the other seeds; for each of these, he says, consists of all the invisible homoiomerous things gathered together. Hence all things come to be out of these; for he calls fire and aether the same thing. Since every natural body has a motion proper to it, and of motions some are simple and some mixed, and the mixed motions belong to mixed bodies while the simple ones belong to simple bodies, it is clear that there will be some simple bodies. For there are also simple motions. So it is clear both that there are elements and why there are.
19| 4 Next it would follow to examine whether they are finite or infinite, and if finite, how many in number. First, then, we must consider that they are not infinite, as some suppose — first, those who make all the homoiomerous things elements, as Anaxagoras does. For none of those who make this claim grasps the element correctly; for we see many even of the mixed bodies divided into homoiomerous parts — I mean, for example, flesh and bone and wood and stone. So that, if the composite is not an element, not everything homoiomerous will be an element, but only what is indivisible into things differing in form, as was said before. Further, not even on this way of taking the element is it necessary to make them infinite; for everything will be accounted for equally well even if they are finite, should one take them so — the same result will follow even if one takes only two or three such things, as indeed Empedocles attempts. For since even on their view it turns out that not everything is made out of homoiomerous parts (they do not make a face out of faces, nor anything else of the things shaped by nature), it is clear that it is far better to make the principles finite, and indeed as few as possible, provided the same things are going to be demonstrated — just as those in mathematics also hold it right to do;
20| for they always take finite principles, either in form or in quantity. Further, if one body is said to differ from another body according to its own proper differentiae, and the differentiae of bodies are finite (for they differ in respect of perceptible qualities, and these are finite — though this must be demonstrated), it is clear that the elements too must necessarily be finite. But surely not even what certain others say, such as Leucippus and Democritus of Abdera, has reasonable consequences; for they say that the primary magnitudes are infinite in multitude but indivisible in magnitude, and that neither does one thing come to be out of many nor many out of one, but that all things are generated by the interweaving and entanglement of these. For in a way these thinkers too make all beings numbers and out of numbers; for even if they do not state it clearly, still this is what they mean to say. And besides this, since bodies differ in shapes, and the shapes are infinite, they say the simple bodies too are infinite. But what the shape of each of the elements is, and of what kind, they have in no way further determined, except that they assigned the sphere to fire alone; air and water and the rest they distinguished by largeness and smallness, on the view that their nature is, as it were, a mixture of the seeds of all the elements.
21| Now, in the first place, these thinkers too make the same error, in not taking the principles as finite, though they could say everything they say equally well with finite ones. And it is clear that if the differentiae of bodies are not infinite, the elements will not be infinite either. Besides this, those who speak of indivisible bodies are bound to conflict with the mathematical sciences, and to do away with many of the reputable views and the things apparent to perception, about which we have spoken earlier in our discussion of time and motion. At the same time they are also bound to contradict themselves; for if the elements are indivisible, it is impossible for air and earth and water to differ by largeness and smallness — for they could not come to be out of one another in that case, since the largest bodies would always be left over as they are separated out, and yet they say that water and air and earth do come to be out of one another in this way. Further, not even on their own supposition would the elements seem to be infinite, since bodies differ in shapes, and all shapes are composed out of pyramids — the rectilinear ones out of rectilinear pyramids, and the sphere out of eight parts. For there must be certain principles of the shapes. So that, whether there is one, or two, or more, the simple bodies too will be that many in number.
22| Further, if each of the elements has some motion proper to it, and the motion of a simple body is simple, and the simple motions are not infinite, because the simple locomotions are not more than two, nor are the places infinite, then not even on this ground would the elements be infinite. 5 Since the elements must be finite, it remains to consider whether they are several or one. For some suppose only one — some water, some air, some fire, and some something thinner than water but denser than air, which they say surrounds all the heavens, being infinite. Now all those who make this one thing water or air, or something thinner than water but denser than air, and then generate the rest out of it by density and rarity, fail to notice that they are themselves making something else prior to the element; for the coming-to-be out of the elements is, as they say, a combination, and the dissolution into the elements is a separating-out, so that what is finer-parted must necessarily be prior in nature. Since, then, they say that fire is the finest of all bodies, fire would be first in nature (it makes no difference — one of the others must be first, not the middle one). Further, generating the rest by density and rarity is no different from generating them by fineness and coarseness; for they mean the fine to be rare, and the coarse to be dense. Again, differing by fineness and coarseness is the same as differing by largeness and smallness;
23| For what has small parts is fine, and what has large parts is coarse; for what is drawn out over a great extent is fine, and what is composed of small parts is of this kind. So it turns out that these thinkers distinguish the substance of the other bodies by size and smallness. But when things are marked off in this way, it will follow that everything is said relative to something, and there will not be, without qualification, this a fire, that a water, and that an air, but the same thing will be fire relative to one thing and air relative to something else — which is exactly what happens to those who say the elements are more than one, and claim they differ by size and smallness. For since each is marked off by quantity, there will be some ratio of the magnitudes to one another, so that things that have this ratio to one another will of necessity be, one air, one fire, one earth, one water, because the ratios of the smaller are present within the larger. But those who posit fire as the element escape this difficulty, but other, irrational consequences are forced on them instead. For some of them attach a shape to fire, as those do who make it a pyramid — and of these, some put it more simply, saying that of shapes the pyramid is the most cutting, and of bodies fire is the most cutting; while others bring it forward more elaborately by an argument: that all bodies are composed of what has the finest parts, and solid shapes are composed of pyramids, so that since among bodies fire is the finest, and among shapes the pyramid has the smallest parts and is the first, and the first shape belongs to the first body, fire would be a pyramid.
24| Others declare nothing about shape, but only make fire the thing with the finest parts, and then say the other things come to be when this is compounded, as if by a fusing-together of filings. But the same difficulties confront both views. For if they make the first body indivisible, the arguments stated earlier will come back to bear against this hypothesis; and further, it is not possible to say this
25| for those who wish to study nature physically. For if every body is commensurable with every body in respect of quantity, and the magnitudes of the homoeomerous bodies are proportional to one another, and likewise those of the elements (for example, that of all the water to all the air, and of element to element, and similarly for the rest), while air is more than water, and in general the finer-parted is more than the coarser-parted, it is clear that the element of water will also be less than that of air. If, then, the lesser magnitude is present within the greater, the element of air would be divisible. And likewise the element of fire, and in general of the finer-parted bodies. But if it is divisible, then for those who give fire a shape it will follow that the part of fire is not fire, because the pyramid is not composed of pyramids; and further, that not every body is either an element or composed of elements (for the part of fire is neither fire nor any other element); while for those who make the distinction by size, it will follow that there is some element prior to the element, and that this goes on without limit, if indeed every body is divisible and the smallest-parted thing is the element. And further, it turns out for these thinkers too that they must say that the same thing is fire relative to one thing and air relative to another, and again water and earth.
26| A mistake common to all who posit a single element is to make there be only one natural motion, and the same for everything. For we observe that every natural body has a principle of motion. If, then, all bodies are some one thing, there would be one motion for all of them; and this motion, of necessity, the more of the body there comes to be, the more it must move — just as fire, the more of it there comes to be, is carried faster upward, its own proper motion. But in fact many things are carried faster downward the more there is of them. So for these reasons, and further, since it has been determined earlier that the natural motions are more than one, it is clear that it is impossible for the element to be one. And since it is neither infinite nor one, it must of necessity be more than one and limited in number.
27| 6 We must first examine whether the elements are eternal or come to be and perish; for once this has been shown, it will also be clear how many there are and of what kind. Now it is impossible for them to be eternal; for we observe fire, water, and each of the simple bodies being dissolved. The dissolution, then, must of necessity either go on without limit or come to a stop. If it is without limit, then the time of the dissolution will also be infinite, and again that of the composition; for each part is dissolved and composed in a different time. So it will follow that outside the infinite time there is another infinite time, when the time of composition is infinite, and further, prior to this, that of dissolution. So an infinite comes to be outside the infinite — which is impossible. But if the dissolution comes to a stop somewhere, either the body in which it stops will be indivisible, or it will be divisible but never in fact going to be divided, as Empedocles seems to want to say. It will not, then, be indivisible, for the reasons stated earlier; but neither can it be divisible yet never going to be dissolved. For the smaller body is more easily destroyed than the larger; if, then, the bulk too perishes by this kind of destruction, so that it is dissolved into smaller parts, it is reasonable that the smaller should undergo this even more.
28| We observe fire perishing in two ways: it perishes by being extinguished through its opposite, and it also wastes away of itself, by itself. And this the lesser undergoes at the hands of the greater, and the faster, the smaller it is. So the elements of bodies must of necessity be perishable and subject to coming-to-be. And since they come to be, their coming-to-be will be either out of what is bodiless or out of body, and if out of body, either out of some other body or out of one another. Now the account that generates them out of what is bodiless makes what comes to be come to be out of a void. For everything that comes to be, comes to be in something, and that in which the coming-to-be occurs will be either bodiless or will contain a body; and if it will contain a body, there will be two bodies at once in the same place, the thing coming to be and the thing already there; but if it is bodiless, there must of necessity be
29| a void, marked off as such. That this is impossible has also been shown before. But neither is it possible for the elements to come to be out of some body; for it will follow that there is another body prior to the elements. And this, if it has weight or lightness, will be one of the elements; while if it has no inclination at all, it will be unmoved and mathematical — and being such, it will not be in place. For that in which a thing is at rest is also that in which it can be moved; and if by force, contrary to nature, while if not by force, in accordance with nature. If, then, it will be in place, then some one of the elements will also be somewhere; but if it is not in place, nothing will come from it; for what comes to be, and that out of which it comes to be, must of necessity exist together. Since, then, it is not possible for them to come to be either out of what is bodiless or out of some other body, it remains that they come to be out of one another.
30| 7 We must, then, examine again what the manner is of their coming-to-be out of one another — whether it is as Empedocles and Democritus say, or as those who resolve bodies into planes say, or whether there is some other manner besides these. Now Empedocles and Democritus and their followers fail to notice that they are not making a coming-to-be out of one another at all, but only an apparent coming-to-be; for they say that each thing, being already present within, is separated out — as though the coming-to-be were out of a vessel, rather than out of some matter, and as though nothing comes to be by changing. But even so, the consequences are no less irrational. For the same magnitude does not seem to become heavier when compressed; yet this is what those who say water is separated out from air, being present within it, must of necessity say; for when water comes to be from air, it is heavier. Further, when mixed bodies are separated, it is not necessary that whichever part is separated off should always occupy more space; but when air comes to be from water, it occupies more space, and what has the finer parts comes to occupy more space. This much is clear too in the actual transition: for when the liquid is turned to vapor and made into breath, the vessels containing the masses burst because of the lack of room. So if there is no void at all, and bodies do not expand, as those who say this claim, the impossibility is evident;
31| But if there is void and extension, it is unreasonable that what separates off should necessarily always occupy a greater place. But it is also necessary that the generation of things from one another should eventually give out, if infinitely many finite magnitudes cannot be present within a finite magnitude. For whenever water comes to be from earth, something has been taken away from the earth, if generation happens by separating-out; and again, when water comes from what is left of the earth, the same thing happens. If, then, this is to go on forever, it will follow that infinitely many things are present within the finite; but since this is impossible, things could not always come to be from one another in this way. That the change of things into one another does not happen by separating-out, then, has been stated. What remains is that they come to be by changing into one another, and this in two ways: either by reshaping, just as a sphere and a cube might come to be from the same wax, or by dissolution into planes, as some say. Now if it happens by reshaping, it follows necessarily that the bodies must be said to be indivisible; for if they were divisible, a part of fire would not be fire, nor a part of earth earth, because a part of a pyramid is not in every case a pyramid, nor a part of a cube a cube. But if it happens by dissolution of the planes, then, in the first place, it is absurd that not everything should be generated from everything else, which they are forced to say, and do say.
32| For it is neither reasonable that one thing alone should have no share in the change, nor is this what appears to perception; rather, all things alike appear to change into one another. And it turns out that, in speaking about the appearances, they say things that do not agree with the appearances. The cause of this is that they have not correctly grasped the first principles, but wish to refer everything to certain fixed opinions; for presumably the principles of perceptible things ought to be perceptible, of eternal things eternal, of perishable things perishable, and in general of the same kind as the things that underlie them. But out of fondness for these principles they seem to do the same thing as those who defend fixed positions in arguments; for they put up with every consequence, on the assumption that they hold true principles, as though some principles ought not to be judged by their outcomes, and above all by their end. Now the end of productive knowledge is the work produced, while the end of natural science is always, properly speaking, what appears according to perception. And it follows for them, above all, that earth is an element, and the only imperishable one, if what cannot be dissolved is both imperishable and an element; for earth alone is not dissolved into another body. But moreover, even among the bodies that are dissolved, the free floating of the triangles is not reasonable. And this too happens in the change of things into one another, because they are composed of unequal numbers of triangles.
33| Further, those who say these things are forced not to derive generation from body; for when a thing comes to be out of planes, what has come to be will not have come to be out of body. Besides this, they are forced not to say that every body is divisible, but to conflict with the most exact sciences; for the mathematical sciences take even the intelligible object to be divisible, while these thinkers do not concede that even everything perceptible is divisible, because they wish to save their hypothesis. For all who assign a shape to each of the elements, and by this shape mark off their substances, are necessarily bound to make them indivisible; for when a pyramid or a sphere is divided in some way, what is left over will not be a sphere or a pyramid. So either a part of fire is not fire, but there will be something prior to the 306b element, since everything is either an element or composed of elements, or else not every body is divisible.
34| 8 In general, the attempt to give the simple bodies shapes is unreasonable, first because it will follow that the whole of space is not filled up; for among plane figures, three shapes seem to fill up a space completely, the triangle, the square, and the hexagon, while among solid figures only two do, the pyramid and the cube; but they are forced to take more shapes than these, because they posit more elements. Next, all the simple bodies evidently take on the shape of the place that contains them, water and air most of all. So it is impossible for the shape of the element to remain fixed; for then it would not be in contact everywhere with the whole of what contains it. But then again, if it is going to be reshaped, it will no longer be water, if indeed it differed from the others by its shape. So it is clear that its shapes are not fixed. But nature itself seems to be signaling this to us, and it is also in accordance with reason; for just as in other cases, what underlies must be without form and without shape, since it is in this way that it could best be given shape, as is written in the Timaeus concerning the all-receiving substrate. In the same way, we must think of the elements as being like matter for the composite bodies; and this is why they are also able to change into one another, once the differentiae belonging to their affections are stripped away.
35| Besides this, how is it possible for flesh or bone or any other continuous body to come to be? For it cannot come to be from the elements themselves, since a continuous body does not result from their composition, nor from planes put together; for it is the elements that are generated by that composition, and not the bodies composed out of the elements. So if anyone wishes to be exact, and not to accept arguments of this kind in passing, he will see that they do away with the generation of things out of what exists. Moreover, the shapes are also out of accord with the bodies' affections, powers, and motions, the very things they had chiefly in view when they distributed the shapes as they did. For instance, since fire is easily moved, heating, and burning, some made it a sphere, others a pyramid; for these shapes are the most easily moved, because they touch the least and are least firmly planted, and they are the most heating and burning because the one is entirely angle, and the other is the most acute-angled of all, and, as they say, it burns and heats by its angles. Now in the first place, both are mistaken about the motion; for even if these are the most easily moved of the shapes, they are not easily moved with the motion proper to fire; for the motion of fire is upward and in a straight line, while these shapes move easily in a circle, in what is called rolling.
36| Next, if earth is a cube because it is firmly planted and stays at rest, but it stays at rest not everywhere, only in its own place, while it moves, unless prevented, from a place not its own, and fire and the other elements likewise, then it is clear that fire too, and each of the elements, will be a sphere or a pyramid in a place not its own, but a cube in its own place. Further, if fire heats and burns because of its angles, then all the elements will be heating, though perhaps one more than another; for all of them have angles, for instance both the octahedron and the dodecahedron. And for Democritus even the sphere, being a kind of angle, cuts, as being easily moved. So the difference will be one of more and less. But that this is false is evident. At the same time it will follow that the mathematical bodies too burn and heat; for these also have angles, and within them there are indivisible spheres and pyramids, especially if there are indivisible magnitudes, as they say. For if some bodies burn and heat and others do not, the difference must be stated, and one must not simply speak without qualification as they do. Further, if what is burned turns to fire, and fire is a sphere or a pyramid, then what is burned must necessarily become spheres or pyramids.
37| So then, let cutting and dividing be understood as happening in proportion to the shape. But that the pyramid should necessarily make pyramids, or the sphere spheres, is entirely unreasonable, and like someone claiming that a knife should be divided into knives, or a saw into saws. Further, it is absurd to assign the shape to fire only with a view to dividing; for fire seems rather to combine and unite than to separate. For it separates things not of the same kind, and combines things of the same kind; and combination belongs to it in its own right (for uniting and bounding together belong to fire), while separation belongs to it accidentally (for fire, in combining what is of the same kind, thereby expels what is foreign). So they ought to have assigned the shape with a view to both, or rather more with a view to combining. Besides this, since hot and cold are opposite in power, it is impossible to assign any shape to the cold; for what is assigned must be opposite to something, and nothing is opposite to a shape. That is why everyone has left this out — and yet it was fitting either to mark off all the elements by shapes or none. Some, in trying to state its power, contradict themselves. For they say that what is cold is what has large parts, on the ground that it compresses and does not pass through the pores.