Lecture 8 — Not everything is generated. Elements and their existence

449 From what has been said earlier it is plain that there cannot be generation either of everything or in an absolute sense of anything.

450 It is impossible that everything should be generated, unless an extra-corporeal void is possible. For, assuming generation, the place which is to be occupied by that which is coming to be, must have been previously occupied by void in which no body was.

451 Now it is quite possible for one body to be generated out of another, air for instance out of fire, but in the absence of any pre-existing mass generation is impossible. That which is potentially a certain kind of body may, it is true, become such in actuality, But if the potential body was not already in actuality some other kind of body, the existence of an extra-corporeal void must be admitted.

452 It remains to say what bodies are subject to generation, and why. Since in every case knowledge depends on what is primary, and the elements are the primary constituents of bodies, we must ask which of such bodies are elements, and why; and after that what is their number and character. The answer will be plain if we first explain what kind of substance an element is.

453 An element, we take it, is a body into which other bodies may be analysed, present in them potentially or in actuality (which of these, is still disputable), and not itself divisible into bodies different in form.

454 That, or something like it, is what all men in every case mean by element.

455 Now if what we have described is an element, clearly there must be such bodies. For flesh and wood and all other similar bodies contain potentially fire and earth, since one sees these elements exuded from them; and, on the other hand, neither in potentiality nor in actuality does fire contain flesh or wood, or it would exude them. Similarly, even if there were only one elementary body, it would not contain them. For though it will be either flesh or bone or something else, that does not at once show that it contained these in potentiality: the further question remains, in what manner it becomes them.

456 Now Anaxagoras opposes Empedocles' view of the elements. Empedocles says that fire and earth and the related bodies are elementary bodies of which all things are composed; but this Anaxagoras denies. His elements are the homoeomerous things, viz. flesh, bone, and the like. Earth and fire are mixtures, composed of them and all the other seeds, each consisting of a collection of all the homoeomerous bodies, separately invisible; and that explains why from these two bodies all others are generated. (To him fire and aither are the same thing.)

457 But since every natural body has it proper movement, and movements are either simple or mixed, mixed in mixed bodies and simple in simple, there must obviously be simple bodies; for there are simple movements.

458 It is plain, then, that there are elements, and why.

595. After inquiring whether generation and motion are present in natural bodies, and supposing from the previous discussion that they are, the Philosopher here begins to inquire how this is. In regard to this he does two things:

first he takes up again, in order to disprove it, something he had previously disproved incompletely;

secondly, he pursues his proposition, at it remains to say (302a10; [599]).

About the first he does three things:

first, he states what was proved above;

secondly, he completes the proof, at it is impossible (301b33; [596]);

thirdly, he excludes an objection, at now it is quite possible (302a3; [597]).

596. He says therefore first (301b31) that it is plain, from what was stated above, that there is neither generation of all things, as those claimed who posited that all things are composed from surfaces, nor no generation at all, as Parmenides and Melissus supposed.

Then at it is impossible (301b33) he completes the refutation of those who posited that there is generation of all things. For he had disproved this previously by showing that bodies are not composed of surfaces. But someone could say that there is generation of all bodies in many other ways. Consequently, the Philosopher presents this more universal proof. And he says that we can get confirmation of the fact that there is not generation of all things from this, namely, because it is impossible for there to be generation of every body, unless a void separated from bodies be posited—which he says because certain philosophers, as Democritus and Leucippus, posited a void inherent in bodies. Now by a separated void is meant a place that is not filled with any body, but which can be filled, as was had in Physics IV. The reason why a separated void follows if every body is generated is that, in the place in which a newly generated body exists, if that place existed prior to that body, there would have to be a void there, because no body existed there. But no body would have existed there previously, if every body is generated. Hence the assumption that every body is generated requires the existence of a separated void.

597. Then, at now it is quite possible (302a3) he excludes an objection, for someone could say that we see each body being generated, even though no void exists. But to this he answers that when a certain particular body comes to be, it is generated from some other body, for example, fire from air—and thus, before the generation of the fire, air was in the same place, and so it is not void. But if every body should be generated, we cannot posit another body that previously filled the place, because there is no other body outside of every body. Hence, the body would have to be made from non-body. But it is impossible that a body be made entirely from no pre-existing bodily magnitude. For there would be produced a body in act, above all from that which is body in potency. And if that which is that body in potency is so in such a way as to be actually another body, nothing impossible follows, for that is the way we explain fire as coming to be from matter that is potentially fire, but actually air. But if it were a body in potency in such a way as not to be in act some other body, as those who posit that every body is generated would be forced to assume, it would follow that, before the generation of every body, there would be a separated void.

598. It should be noted that Aristotle intends to prove here that there is not generation of every body, in the sense of the whole universality of bodies being generated simultaneously. But it is not his intention to prove that some particular body is not generated from non-body. For then there would arise against Aristotle's proof the objection mentioned by Simplicius in his commentary, namely, that a void would not be necessary, either on account of rarefaction and condensation, or because, when this body is generated, another is corrupted. Whence, too, this would not be, as he thought, a sufficient proof that there is not generation of things in common, but of particulars (for there is not generation of man absolutely, but of this man), for the whole universality of body is as one complete body existing in one species, as was had previously. But there is nothing to prevent an individual alone in its species from being generated and corrupted, as they say of the Phoenix. Hence there would not be excluded by this the generation of every body, which the Philosopher intends to reject. Nor is the Philosopher's proof against the doctrine of our faith which teaches that the sum total of bodies at some time began to exist, because we do not posit a pre-existent place, as the Philosopher here supposes; nor do we posit that bodies were generated from what is in potency, but through creation.

599. Then, at it remains to say (302a10), he explains how there is generation and motion of bodies. And about this he does two things:

first he states his intention and the order to be followed;

secondly, he executes his plan, at an element, we take it (302a15; [600]).

He says therefore first (302a10) that, since neither is it true that all bodies can be generated, nor that none can, as was said, we are left with the task of showing which bodies are involved in generation, and because of what this is, i.e., what is the cause of generation. This consideration begins in this book but is completed in the book On Generation. But because all knowledge is through certain first things, from which definitions and demonstrations proceed, and it is plain that the elements of any things are first among what is present in the things (although certain extrinsic principles could be prior, e.g., the agent and end), the consequence is that, if we are to understand the generation of bodies, we must first know what are the elements of bodies that can be generated and destroyed, and why they are elements, and how many elements there are, and how many kinds of bodies there are. Now in order to elucidate all this, it is necessary to take as a supposition and principle what the nature of an element is. And this is revealed by its definition.

600. Then, at an element, we take it (302a15), he carries out his plan according to the aforesaid order.

First, he shows what is the nature of an element, as signified by its definition;

secondly, what are the elements of bodies and their condition, at now if what we have described (302a19; [601]);

third, he inquires how there is generation of bodies;

As to the first he does two things:

first, he sets down the parts of the definition of element;

secondly, he proves this definition of element, at that, or something like it (302a18; [600]).

In regard to the first he presents three parts of the definition of element.

The first of these is that the element is of other bodies, that into which other bodies are divided or resolved. Not every cause can be called an "element," but only one that enters into the composition of the thing. Hence the universal elements are matter and form, as is plain in Physics I. But these are not bodies, whereas the Philosopher is here treating of the elements that are bodies.

The second particle is that an element exists in that of which it is an element, and does so either potentially or actually. (The question of how elements are present in the products of elements, i.e., whether they are present actually or potentially, is for the moment left open). For if the generation and corruption of bodies takes place through assembling and dispersing, as Empedocles and Anaxagoras supposed, then the elements are actually in the compound. But if generation and corruption of bodies are the results of alteration, it is necessary to say that the elements are in potency in the compound.

The third particle is that an element is not divided into other things, namely, things diverse in species. For every body has to be divisible: but some bodies are divided into things that are specifically diverse, as the hand into flesh and bones, out of which it is compacted by a certain composition, or as flesh is resolved into air, fire, water and earth, by a certain alteration. But fire and air, water and earth, are in neither way resolved into things specifically diverse. This particle completes the notion of element; just as letters are called the "elements" of a word, not being divided into things specifically diverse.

Then at that, or something like it (302a18), he proves the aforesaid definition by appealing to the way people generally speak—for words are to be used as they are generally accepted, as is said in Topics II. And this is what he says, namely, that every one intends to mean by "element" something such as has been described, no matter what the field, for example, in corporal speech, and in demonstrations, in which the principles are called "elements" that are not resolved into other principles.

601. Then, at now if what we have described (302a19), he shows which things are elements and how many there are. In regard to this he does three things:

first he shows that it is necessary for there to be elements of bodies;

secondly, he inquires into whether they are finite or infinite (ch. 4);

thirdly, whether there is but one element (ch. 5).

Concerning the first he does two things:

first he concludes from the foregoing definition that it is necessary to posit certain elements of bodies;

secondly, he shows how these were diversely posited by Anaxagoras and Empedocles, at now Anaxagoras (302a28; [602]).

He says therefore first (302a19) that, if the foregoing is the definition of element, it is necessary to say that there are certain elements of bodies, for there exist certain bodies in which the foregoing conditions are verified. For in flesh and wood and all such bodies, i.e., compounds, fire and earth are present in potency, since it is from fire and earth and the like that, by a certain alteration, the above-mentioned bodies are composed. And this is evident by the segregation by which mixed [compound] bodies are resolved into such simple bodies, as is evident when an animal body is resolved, which breaks down into dust and a certain moistness and certain vapors—and similar things happen to other mixed bodies. That such bodies into which other bodies are resolved are themselves not resolved into others, which also belongs to the definition of element, he shows when he adds that in fire neither flesh nor wood is present, either potentially or actually. A sign of this he takes to be the fact that if flesh and wood existed in fire, fire would be resolved into them, and that never is seen to happen. For flesh or wood are generated from fire, not by resolution, but by the addition of other simple bodies altered at the same time for the composite. But because some philosophers posited but one element, as Thales of Miletus water, he adds that whether one element is posited or many, it is still true that in one element there will not exist other bodies. For although other bodies besides the element may be found, for example, flesh or bone or something of this kind, it must not be said that any of them is present either actually or potentially in the body taken as an element. Since it is true that there are certain elements of bodies, one must consider what the manner of generation is, by which either other bodies are generated from elements, namely, by compounding, or elements from other bodies, namely, by resolution. And he will settle this as to truth in the book On Generation.

602. Then, at now Anaxagoras (302a28), he shows how Anaxagoras differed from Empedocles on the question of bodily elements.

First he presents the opinions of each;

secondly, he shows which opinion is to be preferred, at but since every (302b5; [603]).

He says therefore first (302a28) that Anaxagoras and Empedocles held contrary opinions on elements. For Empedocles posited that fire and earth, and other intermediates, which are elements with these, are the elemental bodies of bodies, from which all other bodies are composed. But Anaxagoras says the contrary, namely, that other homoemeric bodies, i.e., of similar parts, for example, flesh and bone and the like, are the elements of bodies, while air and fire and earth and water he said to be compounded out of the foregoing, i.e., out of flesh and bone and all the other seeds of natural bodies. For Anaxagoras posited that infinite and indivisible parts of similar bodies were the seeds of all things that appear in nature, in the sense that, by their extraction from some compound, all natural sensible bodies are generated. Therefore, because all other bodies seem to be generated from fire and earth and the like, he estimated that fire and earth and other intermediate things resulted from all the indivisible similar parts assembled together. And according to this, he posited the consimilar parts to be the elements of these four bodies, from which he nevertheless said all things come to be on account of the seeds existing therein. And since he did not mention fire, therefore, lest any doubt arise concerning this, he adds that he [Anaxagoras] called fire aether.

603. Then, at but since every (302b5), he shows that the opinion of Empedocles is to be preferred. For as is plain from the discussion in book I, every natural body possesses some proper motion, and since some motions are simple and some mixed, it is clear that mixed motions belong to mixed bodies, and simple motions to simple bodies. And from this it is evident that there are certain simple bodies, since (302b9) there are certain simple motions. And since the simple motions, which are from the middle and to the middle, belong more to the elements posited by Empedocles, it is plain that his opinion should be preferred.

However, this could be called a second argument in support of the principal conclusion which he draws as a summary, saying that it is plain that elements exist and for what purpose they exist.

Here ends the exposition of Thomas Aquinas

Continuation of Commentary

Peter of Auvergne

Chapter 4

The next question to consider is whether the elements are finite or infinite in number, and, if finite, what their number is.

Let us first show reason or denying that their number is infinite, as some suppose. We begin with the view of Anaxagoras that all the homoeomerous bodies are elements. Any one who adopts this view misapprehends the meaning of element. Observation shows that even mixed bodies are often divisible into homoeomerous parts; examples are flesh, bone, wood, and stone. Since then the composite cannot be an element, not every homoeomerous body can be an element; only, as we said before, that which is not divisible into bodies different in form.

But even taking 'element' as they do, they need not assert an infinity of elements, since the hypothesis of a finite number will give identical results. Indeed even two or three such bodies serve the purpose as well, as Empedocles' attempt shows. Again, even on their view it turns out that all things are not composed of homocomerous bodies. They do not pretend that a face is composed of faces, or that any other natural conformation is composed of parts like itself. Obviously then it would be better to assume a finite number of principles. They should, in fact, be as few as possible, consistently with proving what has to be proved. This is the common demand of mathematicians, who always assume as principles things finite either in kind or in number.

Again, if body is distinguished from body by the appropriate qualitative difference, and there is a limit to the number of differences (for the difference lies in qualities apprehended by sense, which are in fact finite in number, though this requires proof), then manifestly there is necessarily a limit to the number of elements.

There is, further, another view—that of Leucippus and Democritus of Abdera—the implications of which are also unacceptable. The primary masses, according to them, are infinite in number and indivisible in mass: one cannot turn into many nor many into one; and all things are generated by their combination and involution. Now this view in a sense makes things out to be numbers or composed of numbers. The exposition is not clear, but this is its real meaning.

And further, they say that since the atomic bodies differ in shape, and there is an infinity of shapes, there is an infinity of simple bodies. But they have never explained in detail the shapes of the various elements, except so far to allot the sphere to fire. Air, water, and the rest they distinguished by the relative size of the atom, assuming that the atomic substance was a sort of master-seed for each and every element.

Now, in the first place, they make the mistake already noticed. The principles which they assume are not limited in number, though such limitation would necessitate no other alteration in their theory.

Further, if the differences of bodies are not infinite, plainly the elements will not be an infinity.

Besides, a view which asserts atomic bodies must needs come into conflict with the mathematical sciences, in addition to invalidating many common opinions and apparent data of sense perception. But of these things we have already spoken in our discussion of time and movement.

They are also bound to contradict themselves. For if the elements are atomic, air, earth, and water cannot be differentiated by the relative sizes of their atoms, since then they could not be generated out of one another. The extrusion of the largest atoms is a process that will in time exhaust the supply; and it is by such a process that they account for the generation of water, air, and earth from one another.

Again, even on their own presuppositions it does not seem as if the clements would be infinite in number. The atoms differ in figure, and all figures are composed of pyramids, rectilinear the case of rectilinear figures, while the sphere has eight pyramidal parts. The figures must have their principles, and, whether these are one or two or more, the simple bodies must be the same in number as they.

Again, if every element has its proper movement, and a simple body has a simple movement, and the number of simple movements is not infinite, because the simple motions are only two and the number of places is not infinite, on these grounds also we should have to deny that the number of elements is infinite.

Chapter 5

Since the number of the elements must be limited, it remains to inquire whether there is more than one element. Some assume one only, which is according to some water, to others air, to others fire, to others again something finer than water and denser than air, an infinite body—so they say—bracing all the heavens.

Now those who decide for a single element, which is either water or air or a body finer than water and denser than air, and proceed to generate other things out of it by use of the attributes density and rarity, all alike fail to observe the fact that they are depriving the element of its priority. Generation out of the elements is, as they say, synthesis, and generation into the elements is analysis, so that the body with the finer parts must have priority in the order of nature. But they say that fire is of all bodies the finest. Hence fire will be first in the natural order. And whether the finest body is fire or not makes no difference; anyhow it must be one of the other bodies that is primary and not that which is intermediate.

Again, density and rarity, as instruments of generation, are equivalent to fineness and coarseness, since the fine is rare, and coarse in their use means dense. But fineness and coarseness, again, are equivalent to greatness and smallness, since a thing with small parts is fine and a thing with large parts coarse. For that which spreads itself out widely is fine, and a thing composed of small parts is so spread out. In the end, then, they distinguish the various other substances from the element by the greatness and smallness of their parts. This method of distinction makes all judgement relative. There will be no absolute distinction between fire, water, and air, but one and the same body will be relatively to this fire, relatively to something else air. The same difficulty is involved equally in the view elements and distinguishes them by their greatness and smallness. The principle of distinction between bodies being quantity, the various sizes will be in a definite ratio, and whatever bodies are in this ratio to one another must be air, fire, earth, and water respectively. For the ratios of smaller bodies may be repeated among greater bodies.

Those who start from fire as the single element, while avoiding this difficulty, involve themselves in many others.

Some of them give fire a particular shape, like those who make it a pyramid, and this on one of two grounds. The reason given may be—more crudely—that the pyramid is the most piercing of figures as fire is of bodies, or—more ingeniously—the position may be supported by the following argument. As all bodies are composed of that which has the finest parts, so all solid figures are composed of pryamids: but the finest body is fire, while among figures the pyramid is primary and has the smallest parts; and the primary body must have the primary figure: therefore fire will be a pyramid.

Others, again, express no opinion on the subject of its figure, but simply regard it as the of the finest parts, which in combination will form other bodies, as the fusing of gold-dust produces solid gold.

Both of these views involve the same difficulties. For (1) if, on the one hand, they make the primary body an atom, the view will be open to the objections already advanced against the atomic theory.

And further the theory is inconsistent with a regard for the facts of nature. For if all bodies are quantitatively commensurable, and the relative size of the various homoeomerous masses and of their several elements are in the same ratio, so that the total mass of water, for instance, is related to the total mass of air as the elements of each are to one another, and so on, and if there is more air than water and, generally, more of the finer body than of the coarser, obviously the element of water will be smaller than that of air. But the lesser quantity is contained in the greater. Therefore the air element is divisible. And the same could be shown of fire and of all bodies whose parts are relatively fine.

(2) If, on the other hand, the primary body is divisible, then (a) those who give fire a special shape will have to say that a part of fire is not fire, because a pyramid is not composed of pyramids, and also that not every body is either an element or composed of elements, since a part of fire will be neither fire nor any other element. And (b) those whose ground of distinction is size will have to recognize an element prior to the element, a regress which continues infinitely, since every body is divisible and that which has the smallest parts is the element.

Further, they too will have to say that the same body is relatively to this fire and relatively to that air, to others again water and earth.

The common error of all views which assume a single element is that they allow only one natural movement, which is the same for every body. For it is a matter of observation that a natural body possesses a principle of movement. If then all bodies are one, all will have one movement. With this motion the greater their quantity the more they will move, just as fire, in proportion as its quantity is greater, moves faster with the upward motion which belongs to it. But the fact is that increase of quantity makes many things move the faster downward.

For these reasons, then, as well as from the distinction already established of a plurality of natural movements, it is impossible that there should be only one element. But if the elements are not an infinity and not reducible to one, they must be several and finite in number.

Chapter 6

First we must inquire whether the elements are eternal or subject to generation and destruction; for when this question has been answered their number and character will be manifest. In the first place, they cannot be eternal. It is a matter of observation that fire, water, and every simple body undergo a process of analysis, which must either continue infinitely or stop somewhere. (1) Suppose it infinite. Then the time occupied by the process will be infinite, and also that occupied by the reverse process of synthesis. For the processes of analysis and synthesis succeed one another in the various parts.

It will follow that there are two infinite times which are mutually exclusive, the time occupied by the synthesis, which is infinite, being preceded by the period of analysis. There are thus two mutually exclusive infinites, which is impossible.

(2) Suppose, on the other hand, that the analysis stops somewhere. Then the body at which it stops will be either atomic or, as Empedocles seems to have intended, a divisible body which will yet never be divided.

The foregoing arguments show that it cannot be an atom; but neither can it be a divisible body which analysis will never reach. For a smaller body is more easily destroyed than a larger; and a destructive process which succeeds in destroying, that is, in resolving into smaller bodies, a body of some size, cannot reasonably be expected to fail with the smaller body. Now in fire we observe a destruction of two kinds: it is destroyed by its contrary when it is quenched, and by itself when it dies out. But the effect is produced by a greater quantity upon a lesser, and the more quickly the smaller it is. The elements of bodies must therefore be subject to destruction and generation.

Since they are generated, they must be generated either from something incorporeal or from a body, and if from a body, either from one another or from something else.

The theory which generates them from something incorporeal requires an extra-corporeal void. For everything that comes to be comes to be in something, and that in which the generation takes place must either be incorporeal or possess body; and if it has body, there will be two bodies in the same place at the same time, viz. that which is coming to be and that which was previously there, while if it is incorporeal, there must be an extra-corporeal void. But we have already shown that this is impossible.

But, on the other hand, it is equally impossible that the elements should be generated from some kind of body. That would involve a body distinct from the elements and prior to them. But if this body possesses weight or lightness, it will be one of the elements; and if it has no tendency to movement, it will be an immovable or mathematical entity, and therefore not in a place at all. A place in which a thing is at rest is a place in which it might move, either by constraint, i.e. unnaturally, or in the absence of constraint, i.e. naturally. If, then, it is in a place and somewhere, it will be one of the elements; and if it is not in a place, nothing can come from it, since that which comes into being and that out of which it comes must needs be together.

The elements therefore cannot be generated from something incorporeal nor from a body which is not an element, and the only remaining alternative is that they are generated from one another.

Chapter 7

We must, therefore, turn to the question, what is the manner of their generation from one another? Is it as Empedocles and Democritus say, or as those who resolve bodies into planes say, or is there yet another possibility?

(1) What the followers of Empedocles do, though without observing it themselves, is to reduce the generation of elements out of one another to an illusion. They make it a process of excretion from a body of what was in it all the time—as though generation required a vessel rather than a material—so that it involves no change of anything.

And even if this were accepted, there are other implications equally unsatisfactory. We do not expect a mass of matter to be made heavier by compression. But they will be bound to maintain this, if they say that water is a body present in air and excreted from air, since air becomes heavier when it turns into water.

Again, when the mixed body is divided, they can show no reason why one of the constituents must by itself take up more room than the body did: but when water turns into air, the room occupied is increased. The fact is that the finer body takes up more room, as is obvious in any case of transformation. As the liquid is converted into vapour or air the vessel which contains it is often burst because it does not contain room enough. Now, if there is no void at all, and if, as those who take this view say, there is no expansion of bodies, the impossibility of this is manifest: and if there is void and expansion, there is no accounting for the fact that the body which results from division cfpies of necessity a greater space.

It is inevitable, too, that generation of one out of another should come to a stop, since a finite quantum cannot contain an infinity of finite quanta. When earth produces water something is taken away from the earth, for the process is one of excretion. The same thing happens again when the residue produces water. But this can only go on for ever, if the finite body contains an infinity, which is impossible. Therefore the generation of elements out of one another will not always continue. We have now explained that the mutual transformations of the elements cannot take place by means of excretion.

(2) The remaining alternative is that they should be generated by changing into one another. And this in one of two ways, either by change of shape, as the same wax takes the shape both of a sphere and of a cube, or, as some assert, by resolution into planes.

(a) Generation by change of shape would necessarily involve the assertion of atomic bodies. For if the particles were divisible there would be a part of fire which was not fire and a part of earth which was not earth, for the reason that not every part of a pyramid is a pyramid nor of a cube a cube.

But if (b) the process is resolution into planes, the first difficulty is that the elements cannot all be generated out of one another. This they are obliged to assert, and do assert. It is absurd, because it is unreasonable that one element alone should have no part in the transformations, and also contrary to the observed data of sense, according to which all alike change into one another. In fact their explanation of the observations is not consistent with the observations. And the reason is that their ultimate principles are wrongly assumed: they had certain predetermined views, and were resolved to bring everything into line with them. It seems that perceptible things require perceptible principles, eternal things eternal principles, corruptible things corruptible principles; and, in general, every subject matter principles homogeneous with itself. But they, owing to their love for their principles, fall into the attitude of men who undertake the defence of a position in argument. In the confidence that the principles are true they are ready to accept any consequence of their application. As though some principles did not require to be judged from their results, and particularly from their final issue!

And that issue, which in the case of productive knowledge is the product, in the knowledge of nature is the unimpeachable evidence of the senses as to each fact. The result of their view is that earth has the best right to the name element, and is alone indestructible; for that which is indissoluble is indestructible and elementary, and earth alone cannot be dissolved into any body but itself.

Again, in the case of those elements which do suffer dissolution, the 'suspension' of the triangles is unsatisfactory. But this takes place whenever one is dissolved into another, because of the numerical inequality of the triangles which compose them.

Further, those who hold these views must needs suppose that generation does not start from a body. For what is generated out of planes cannot be said to have been generated from a body.

And they must also assert that not all bodies are divisible, coming thus into conflict with our most accurate sciences, namely the mathematical, which assume that even the intelligible is divisible, while they, in their anxiety to save their hypothesis, cannot even admit this of every perceptible thing. For any one who gives each element a shape of its own, and makes this the ground of distinction between the substances, has to attribute to them indivisibility; since division of a pyramid or a sphere must leave somewhere at least a residue which is not sphere or a pyramid.

Either, then, a part of fire is not fire, so that there is a body prior to the element—for every body is either an element or composed of elements—or not every body is divisible.

Chapter 8

In general, the attempt to give a shape to each of the simple bodies is unsound, for the reason, first, that they will not succeed in filling the whole. It is agreed that there are only three plane figures which can fill a space, the triangle, the square, and the hexagon, and only two solids, the pyramid and the cube. But the theory needs more than these because the elements which it recognizes are more in number.

Secondly, it is manifest that the simple bodies are often given a shape by the place in which they are included, particularly water and air. In such a case the shape of the element cannot persist; for, if it did, the contained mass would not be in continuous contact with the containing body; while, if its shape is changed, it will cease to be water, since the distinctive quality is shape. Clearly, then, their shapes are not fixed.

Indeed, nature itself seems to offer corroboration of this theoretical conclusion. Just as in other cases the substratum must be formless and unshapen—for thus the 'all-receptive', as we read in the Timaeus, will be best for modelling—so the elements should be conceived as a material for composite things; and that is why they can put off their qualitative distinctions and pass into one another.

Further, how can they account for the generation of flesh and bone or any other continuous body? The elements alone cannot produce them because their collocation cannot produce a continuum. Nor can the composition of planes; for this produces the elements themselves, not bodies made up of them. Any one then who insists upon an exact statement of this kind of theory, instead of assenting after a passing glance at it, will see that it removes generation from the world.

Further, the very properties, powers, and motions, to which they paid particular attention in allotting shapes, show the shapes not to be in accord with the bodies. Because fire is mobile and productive of heat and combustion, some made it a sphere, others a pyramid. These shapes, they thought, were the most mobile because they offer the fewest points of contact and are the least stable of any; they were also the most apt to produce warmth and combustion, because the one is angular throughout while the other has the most acute angles, and the angles, they say, produce warmth and combustion.

Now, in the first place, with regard to movement both are in error. These may be the figures best adapted to movement; they are not, however, well adapted to the movement of fire, which is an upward and rectilinear movement, but rather to that form of circular movement which we call rolling. Earth, again, they call a cube because it is stable and at rest. But it rests only in its own place, not anywhere; from any other it moves if nothing hinders, and fire and the other bodies do the same. The obvious inference, therefore, is that fire and each several element is in a foreign place a sphere or a pyramid, but in its own a cube.

Again, if the possession of angles makes a body produce heat and combustion, every element produces heat, though one may do so more than another. For they all possess angles, the octahedron and dodecahedron as well as the pyramid; and Democritus makes even the sphere a kind of angle, which cuts things because of its mobility.

The difference, then, will be one of degree: and this is plainly false. They must also accept the inference that the mathematical produce heat and combustion, since they too possess angles and contain atomic spheres and pyramids, especially if there are, as they allege, atomic figures. Anyhow if these functions belong to some of these things and not to others, they should explain the difference, instead of speaking in quite general terms as they do.

Again, combustion of a body produces fire, and fire is a sphere or a pyramid. The body, then, is turned into spheres or pyramids. Let us grant that these figures may reasonably be supposed to cut and break up bodies as fire does; still it remains quite inexplicable that a pyramid must needs produce pyramids or a sphere spheres. One might as well postulate that a knife or a saw divides things into knives or saws.

It is also ridiculous to think only of division when allotting fire its shape. Fire is generally thought of as combining and connecting rather than as separating. For though it separates bodies different in kind, it combines those which are the same; and the combining is essential to it, the functions of connecting and uniting being a mark of fire, while the separating is incidental. For the expulsion of the foreign body is an incident in the compacting of the homogeneous. In choosing the shape, then, they should have thought either of both functions or preferably of the combining function.

In addition, since hot and cold are contrary powers, it is impossible to allot any shape to the cold. For the shape given must be the contrary of that given to the hot, but there is no contrariety between figures. That is why they have all left the cold out, though properly either all or none should have their distinguishing figures. Some of them, however, do attempt to explain this power, and they contradict themselves. A body of large particles, they say, is cold because instead of penetrating through the passages it crushes.

Clearly, then, that which is hot is that which penetrates these passages, or in other words that which has fine particles. It results that hot and cold are distinguished not by the figure but by the size of the particles. Again, if the pyramids are unequal in size, the large ones will not be fire, and that figure will produce not combustion but its contrary.

From what has been said it is clear that the difference of the elements does not depend upon their shape. Now their most important differences are those of property, function, and power; for every natural body has, we maintain, its own functions, properties, and powers. Our first business, then, will be to speak of these, and that inquiry will enable us to explain the differences of each from each.