CH. 1. — The science of Nature has for its principal object — Bodies, Magnitudes, and the various affections and movements of Bodies and Magnitudes; also the beginnings or principles of this sort of Essence. The Continuous is that which is divisible into parts perpetually divisible: and Body is that which is divisible in every direction. Of magnitudes, some (lines) are divisible only in one direction; others (planes) only in two directions; others again (bodies) in three directions. This is the maximum: there is no other magnitude beyond; for three are all, and to say “in three directions” is the same as to say “in all directions.” As the Pythagoreans say, The Universe and All Things are determined by Three: in End, Middle, and Beginning, lies the number of the Universe, or the Triad. We have received these as laws from nature, and we accordingly employ this number (Three) for solemnities in honour of the Gods. Moreover, we apply our predicates on the same principle; for we call Two, and The Two — Both, but we do not call them all. Three is the first number to which we apply the predicate All. Herein (as was observed before) we follow the lead of Nature herself. Since therefore these three phrases — All Things, The Universe, The Perfect or Complete — do not specifically differ from each other, but are distinguished only in respect of the matter or occasions on which they are applied. Body is the only kind of magnitude which can be declared Perfect or Complete, that is, All; for it is the only magnitude determined or defined by the Three. Being divisible in three directions, it is divisible every way; other magnitudes are divisible either only in one way or only in two. Magnitudes are both divisible and continuous according to the number by which they are designated — continuous in one direction, in two, in three, or all. All divisible magnitudes are also continuous: whether all continuous magnitudes are divisible, is not yet clear. But what is clear is — that there is no upward transition to a higher genus beyond Body, as there is from line to surface, and from surface to Body. If there were, Body would not be perfect or complete as a magnitude; for the transition would be made at the point of deficiency; but the perfect or complete can have no deficiency: it stretches every way. Such is each body included as a part in the universe: it has dimensions in every direction. Yet each is distinguished from its neighbour by contact, and each therefore in a certain sense is many. But the Universe (t? p??) including all these parts is of necessity perfect and complete; extending not merely in one way, and in another way not, but p??t?, as the word literally means (ss. 1-4).

CH. 2. — Respecting the nature of the Universe, we shall enquire presently whether in the aggregate it be infinite or of finite magnitude. But first let us speak about its different constituent species, proceeding on the following basis. I affirm that all natural bodies and magnitudes are per se locally moveable; and that Nature is to them a beginning or principle of motion. Now all Local Motion (known by the name of f???) is either Rectilinear or Circular, or compounded of the two; for these two are the only simple motions, by reason that the only two simple magnitudes are the rectilinear and the circular. The circular is motion round the Centre; the rectilinear is motion either downwards towards the centre or upwards from the centre. These three are the only simple modes of motion or currents: as I said in the last chapter that body was made complete in the number three, so also the motion of body is made complete in the number three. Now, as there are some bodies (such as fire, earth, and their cognates) which are simple (i.e. which have in themselves a natural beginning or principle of motion), and others which are compounds of these, so also there must be simple motions belonging to the former and compound motions belonging to the latter; such compound motions being determined by the preponderant element therein. Since, therefore, circular motion is a simple mode of motion, and since simple modes of motion belong only to simple bodies, there must of necessity be a particular variety of simple body, whose especial nature it is to be carried round in circular motion. By violence, indeed, one body might be moved in a mode belonging to another; but not by nature. Moreover, since motion against nature is opposite to motion conformable to nature, and since each mode has one single opposite, simple circular motion, if it be not conformable to the nature of this body, must be against its nature. If then the body rotating in a circle be fire or any of the other elements, its natural mode of motion must be opposite to circular motion. But each thing has only one opposite; and up and down are each other’s opposites. If then the body which rotates in a circle rotates thus against nature, it must have some other mode of motion conformable to nature. But this is impossible: for, if the motion conformable to its nature be motion upwards, the body must be fire or air; if motion downwards, the body must be earth or water (and there is no other simple mode of motion that it can have). Moreover, its rotatory motion must be a first motion; for the perfect is prior in nature to the imperfect. Now the circle is perfect; but no straight line is perfect: neither an infinite straight line, for in order to be perfect, it must have an end and a boundary; nor any finite straight line, for each has something without it and may be prolonged at pleasure. So that, if motion first by nature belong to a body first by nature, if circular motion (as being perfect) be prior to rectilinear motion, and if rectilinear motion belong to a first or a simple body, as we see both in fire and in earth, — we may be sure À fortiori that circular motion belongs to a simple body, and that there is, besides the four elements here, prior to them and more divine than them, a different body cf special nature and essence. Indeed, since circular motion is against the nature of these four elements, there must be some other different body to whose nature it is conformable. There must thus be some simple and primary body, whose nature it is to be carried round in a circle, as earth is carried downwards and fire upwards. On the assumption that the revolving bodies revolved against their own nature, it would be wonderful and even unreasonable that this one single mode of motion, being thus contrary to nature, should be continuous and eternal; for in all other things we see that what is contrary to nature dies away most speedily. Now, if the revolving body were fire, as some affirm, the revolving motion would be just as much contrary to its nature as motion downwards; for the natural motion of fire is upwards or away from the centre. Reasoning from all these premisses, we may safely conclude that, distinct from all these bodies which are here around us, there exists a body whose nature is more honourable in proportion to its greater distance from us here (ss. 1-13).

CH. 3. — We plainly cannot affirm that every body is either heavy or light: meaning by heavy, that which is carried by its nature downwards or towards the centre; by light, that which is carried by its nature upwards or away from the centre. Heaviest (or earth) is that which underlies all other downward moving bodies, lightest (fire) is that which floats above all upward moving bodies. Air and water are both light and heavy, relatively, but relatively to different terms of comparison; thus, water is heavy as compared to air and fire, light as compared to earth. But that body whose nature it is to revolve in a circle, cannot possibly have either heaviness or levity; for it cannot move in a right line, either upwards or downwards, nor either by nature or against nature. Not by nature, for, in that case, it must be identical with some one of the four elements; not against nature, because, if it moved upwards against nature, this would prove that motion downwards was conformable to its nature, and it would thus be identical with earth: we have already seen that, if a body moves upwards against nature, it must move downwards according to nature, and vice versÂ. Now the same natural motion which belongs to any body as a whole, belongs also to its minute fragments (to the whole earth and to any of its constituent clods). Accordingly the revolving body in its local movement of revolution cannot possibly be dragged in any other direction, either upward or downward, — neither the whole nor any portion thereof. It is alike reasonable to conceive it as ungenerable, indestructible, incapable both of increase and of qualitative change (??a???? ?a? ??a?????t??). It cannot be generated, because every thing generated comes out of a substratum and an opposite, into which it relapses on being destroyed. Now the revolving body has no opposite; for we have already seen that opposite bodies have their currents of motion opposite, and there is no current of motion opposite to that of circular rotation. Nature has rightly excepted this ungenerable and indestructible substance from the action of contraries, in which generation and destruction occur. It is also incapable of increase or diminution, because these processes take place through the accession of new cognate materials; and in this case there are none such. It is farther incapable of qualitative change, because this always implies the being affected favourably or unfavourably (p????); and this last never takes place, in plants or in animals, without some increase or diminution in quantity (ss. 1-5).

This Celestial Substance is thus eternal, ungenerable, indestructible, noway increased nor diminished, neither growing old nor capable of disturbing affections nor changeable in quality. Herein the evidence of reason and that of phenomena concur. For all men, Hellenes and Barbarians, have some belief respecting the Gods, and all who believe Gods to exist assign to the divine nature the uppermost place in the Kosmos; an immortal place going naturally along with immortal persons. Our perceptions confirm this sufficiently, at least when we speak with reference to human belief. For not the smallest change has ever been observed in the celestial substance, throughout all past time. Under these impressions, the ancients gave to it the name which it now bears; for the same opinions suggest themselves to us not once, nor twice, but an infinite number of times. Hence the ancients, regarding the First Body as something distinct from Fire, Earth, Air, or Water, called the uppermost place Æther, from its being always running (?p? t?? ?e?? ?e?), the adverbial designation being derived from eternal duration. Anaxagoras employs this name improperly: he calls Fire by the name of Æther (s. 6).

It is plain, from all we have said, that the simple bodies cannot be more in number than those just indicated; for a simple body must of necessity have a simple mode of motion, and there are only three simple modes of motion — one circular and two rectilinear, one of these being from the centre, the other towards the centre (s. 7).

CH. 4. — That Circular Rotation has no motion opposed to it, may be shown by several different arguments. If there were any, it would certainly be rectilinear motion; for convex and concave, though each respectively opposed to the other, are, when both put together, opposed as a couple to rectilinear motion. But each variety of rectilinear motion has another variety of rectilinear motion opposed to it; and each thing has but one opposite. Moreover the oppositions between one motion (or one current — f???) and another are founded upon oppositions of place, which are three in number: (1) Above and Below; (2) Before and Behind; (3) Right and Left. Now the motion in circular rotation from A to B is not opposite to that from B to A: the opposition of motion is along the straight line which joins the two; for an infinite number of different circles may be drawn, not interfering with each other but all passing through the same two points A and B. In the same circle, the opposition between the current from A to B and that from B to A, is along the line of diameter — not along the line of circumference. If one circular current were really opposed to any other circular current, one or other of the two would have existed to no purpose; for both have the same object. That is to say: what is carried round in a circle, let it begin from any point whatever, must necessarily come round equally to all the opposite places, above, below, before, behind, right, left. If the two (presumed) opposite circular currents were equal, they would neutralize each other, and there would be no motion at all of either of them. If one of the two were the more powerful, it would extinguish the other; so that to suppose the existence of both is to suppose that one or both exists in vain (i.e., can never be realized). We say that a sandal exists in vain (?t??), when it cannot be fastened on. But God and nature do nothing in vain (ss. 1-8).

CH. 5. — Most of the ancient philosophers admitted an infinite body; but this may be shown to be impossible. The question is very important; for the consequences which follow from admitting the Infinite as principium, affect our speculations concerning the whole of Nature (s. 1).

Every body is of necessity either simple or compound. The infinite body therefore, if it exists, must of necessity be either one or the other. But there can be no infinite compound composed of simple bodies finite in magnitude and in number: so that, if an infinite body exist, it must be simple. We shall first enquire whether the First Body, whose nature it is to move in a circle, can be infinite in magnitude. Now, if it were infinite, the radii thrown out from the centre would be infinite, and the distance between them would also be infinite; that is, no finite peripheral line can be found touching all the extremities of the radii without: if any such line be assumed, you may always assume a greater. We call Number infinite, because the greatest number cannot be given; and the like may be said about this distance. Now, as an infinite distance cannot be passed over, no circular motion passing over it is possible, so as to come round to the point of departure. But we see plainly that the First Body or the Heaven does come round in a circle; and it has been shown by reasoning À priori that there is a variety of body whose nature it is to move in a circle. Such a body therefore as the First (revolving) Body cannot be infinite (ss. 2, 3).

Four other arguments are added, proving the same conclusion (s. 4, seq.). One of them is: That an infinite square, circle, or sphere, is an impossibility; each of these figures being defined or determined. As there can be no infinite circle, so neither can an infinite body be moved round in a circle (s. 7).

CH. 6. — As the First Body cannot be infinite, so neither can those bodies be infinite whose nature it is to move to the centre and from the centre — neither the centripetal nor the centrifugal body. For these two currents are opposite in nature; opposite currents being characterized by the opposite places to which they tend. But of two opposites, if the one be fixed and determinate, the other must be fixed and determinate also. Now the centre is determined; for the centripetal body, let it fall from what height it will, can never fall lower than the centre; and, since the centre is determined, the upper region or extremity must also be determined. The places at each extreme being thus determined, the intermediate space must be determined also; otherwise there would exist motion undetermined or infinite, which has been shown in a former treatise to be impossible (Physica, VIII. viii.); and therefore that body which either is therein, or may possibly be therein, must be determined. But it is a fact that the centripetal body and the centrifugal body can be therein; for centripetality and centrifugality are of the nature of each respectively (ss. 1, 2).

Hence we see that there can be no infinite body. There are other reasons also. As the centripetal body is heavy, if it be infinite, its gravity must also be infinite; and, if gravity cannot be infinite, neither can any heavy body be infinite. The like about any light body, such as the centrifugal (s. 3).

He then shows (by a long process of reasoning, not easy to follow) first, that there cannot be an infinite body with finite gravity; next, that there can be no infinite gravity. Accordingly there can be no infinite body at all, having gravity. At the end, he considers that this is established, (1) by the partial arguments (d?? t?? ?at? ????) immediately preceding; (2) by the general reasonings in his other treatises respecting first principles, in which he explained the Infinite — in what sense it existed and did not exist; (3) by an argument about the Infinite, upon which he touches in the next chapter (ss. 4-13).

CH. 7. — Every body is of necessity either infinite or finite. If infinite, it is as a whole either of like constituents or of unlike. If the latter, either of a finite number of species, or of an infinite number. The last is impossible, if our fundamental assumptions are allowed to stand. For since the simple modes of motion are limited in number, the simple bodies must be alike limited; each simple mode of notion belonging to its own special simple body, and each natural body having always its own natural motion. But, if the Infinite be composed of a finite number of species, each of these constituent parts must be infinite; that is, water and fire must be infinite. Yet this too, is impossible; for we have seen that there cannot be either infinite levity or infinite gravity (the attributes of fire and water). Moreover, if these bodies be infinite, the places which they occupy, and the motions which they make, must also be infinite; but this also we have shown to be inadmissible, if our fundamental assumptions are admitted. The centripetal body cannot be carried to an infinite distance downward, nor the centrifugal body to an infinite distance upward. That which cannot come to pass, cannot be in course of coming to pass; thus, if a thing cannot come to be white, or a cubit long, or domiciled in Egypt, it cannot be in course of becoming white, or a cubit long, &c. It cannot be in course of being carried to a terminus which cannot be reached. It might be argued that fire, though discontinuous and dispersed, might still be infinite, in the sum total of its different masses. But body is that which is extended in every direction: how can there be many bodies unlike to each other, yet each of them infinite? Each of them, if infinite at all, ought to be infinite in every direction (ss. 1-5).

We thus see that the Infinite cannot consist of unlike constituents. But neither can it consist of constituents all similar. For, first, there are only three simple motions, and one of the three it must have; but we have shown that it cannot have either centripetal or centrifugal motion (i.e., that it cannot have either infinite gravity or infinite levity); nor can it again have circular motion, for the Infinite cannot be carried in a circle: this would amount to saying that the Heaven is infinite, which we have shown to be impossible. The Infinite indeed cannot be moved in any way at all; for, if moved, it must be moved either according to nature, or contrary to nature (violently), and, if its present motion be violent, it must have some other mode of motion which is natural to it. But, if it have any such, this assumes that there exists some other place belonging to it, into which it may be conveyed — an obvious impossibility (ss. 6, 7).

Farthermore, the Infinite cannot act in any way upon the Finite, nor be acted upon thereby (ss. 8-10). Nor can the Infinite be acted upon in any way by the Infinite (ss. 11-12).

If then every perceptible body possesses powers, as agent or patient or both, there can be no perceptible body which is infinite. But all bodies which are in any place are perceptible; therefore no body which is in any place can be infinite. There is no infinite body, indeed there can be no body at all, outside of the Heaven; for that which is outside of the Heaven is in a place. Even if perceivable only up to a certain point (???? t????), even if merely intelligible, it would still be in a place, and would therefore come under the foregoing argument — that there is no body outside of the Heaven (ss. 13, 14).

The foregoing reasoning may be summed up, in more general language (??????te???), as follows:— The Infinite assumed as homogeneous cannot be moved in a circle, since the Infinite has no centre; nor in a straight line, since this would imply a second infinite place into which it must be moved according to nature, and a third infinite place into which it must be moved against nature, and since in either case the force which causes it to be moved must be infinite. But we have already argued, in treating of Motion (Phys. VIII. x.) that nothing finite can have infinite power, nothing infinite can have finite power; and, if that which is moved according to nature can also be moved contrary to nature, there must of necessity be two Infinites — Movens and Motum. Yet what can that be which causes the Infinite to move? If it cause itself to move, it must be animated (??????): but how can an infinite animated being (????) exist? And, if there be anything else which causes it to move, there must exist two Infinites, each distinguished from the other in form and power (ss. 15-17).

Again, even if we admit the doctrine of Leukippus and Demokritus — That the whole is not continuous, but discontinuous, atoms divided by intervening spaces — still the Infinite is inadmissible. For the nature and essence of these atoms is all the same, though they are different from each other in figure and arrangement; accordingly the motion of all must be the same: if one is heavy or centripetal, all must be so alike; if one is light or centrifugal, all must be so alike. But either of these motions would imply the existence of centre and periphery; which does not consist with an infinite whole. In the Infinite, there is neither centre nor periphery; no terminus prefixed either for upward or downward motion; no own place either for centripetal or centrifugal matter. Therefore in an infinite universe, there can be no motion at all (ss. 18, 19).

CH. 8. — There cannot be more than one Kosmos. All things both rest and are moved, either by violence, or according to nature. In that place to which it is carried by nature, it also rests by nature: in that place to which it is carried by violence, it rests by violence. If the current which we see towards the centre is by violence, the opposite current must be natural; if earth is carried by violence from thence hitherward, its natural current must be from hence thitherward; and, if being here it rests without violence, its current towards here must be a natural one. For there is one only which is natural. Now, if there be many Kosmi, they must be alike in their nature, and must be composed of the same bodies, having the same nature and powers — fire, earth, and the two intermediate elements: for, if the bodies here are not the same as those in other Kosmi — if the same names are given in an equivocal sense and do not connote the same specific attributes — the name Kosmos must be equivocal also, and there cannot be many true or real Kosmi, in the same sense. To the parts or elements of each Kosmos, therefore, the centripetal and centrifugal currents are natural; for the simple currents are limited in number, and each element is so named as to connote one of them specially; and, if the currents are the same, the elements must also be the same everywhere. If there were another Kosmos, the earth in that would tend towards the centre of our Kosmos, and the fire in that would tend towards the periphery of our Kosmos. But this is impossible; since in that case the earth in that Kosmos would run away from the centre of its own Kosmos, and the fire therein would run away from its own periphery. Either we must not admit the same nature in the simple elements of the numerous Kosmi; or, if we do admit it, we must recognize only one centre and one periphery. This difficulty prevents our recognizing more than one Kosmos (ss. 1-6).

It is unphilosophical to affirm that the nature of these simple elements becomes changed according as they are more or less distant from their own places. The difference is at best one of degree, not one of kind. That they are moved, we see plainly; there must therefore be some one current of motion natural to them. Accordingly every portion of the same element (or of elements the same in kind) must tend towards the same numerical place — towards this actual centre (p??? t?de t? ?s??), or that actual periphery; and, if the tendency be towards one centre specie, but towards many centres numero, because particulars differ numero alone, and not specie, still the attribute will be alike in all, and will not be present in some portions, absent in others: I mean that, if the portions of this Kosmos are relative to each other, those in another Kosmos are in the like condition, and what is taken from this Kosmos will not be different from what is taken from the corresponding elements of any other Kosmos. Unless these assumptions can be overthrown, it is indisputably certain that there can be only one centre and one periphery; by consequence therefore, only one Kosmos and not more (ss. 7-10).

There are other reasons to show that there is a given terminus for the natural current both of fire and of earth. A thing moved, speaking generally, changes from something definite into something else definite; but there are different species of such change: the change called getting-well is from sickness to health; that called growth is from the little to great; that called local movement is from a terminus to another terminus, and local movements are specifically different from each other, according as the terminus a quo and the terminus ad quem is defined in each. The terminus is always a known and definite point: it is not accidental, nor dependent upon the arbitrium of the mover. Fire and earth therefore do not move on to infinity, but to definite points in opposite directions; and the local antithesis is between above and below: these are the two termini of the respective currents. Earth is carried with greater velocity, the nearer it approaches to the centre; fire is carried with greater velocity, the nearer it approaches to the periphery. This shows that its current does not stretch to infinity; for its velocity would then increase infinitely. Earth is not carried downward by the force of any thing else, nor fire upwards: not by any violence, nor by squeezing out (??????e?), as some say. If this were so, a larger quantity of earth would move downward, and a larger quantity of fire upward, more slowly than a smaller. But the reverse is what occurs: the larger quantity of earth moves downward more rapidly than the smaller; if its motion had been caused by violence or by squeezing out, such motion would have slackened as it became more widely distant from the moving force (ss. 11-14).

We may deduce the same conclusion from the reasonings of the First Philosophy, also from the fact of circular motion which of necessity is constant both here and everywhere. Further, it is clear that there can be only one Kosmos; for, as there are three bodily elements, so there are three special places of such elements: one the undermost, at the centre; another the uppermost, at the periphery, revolving in a circular orbit; the third, in the intermediate place between the two, being the light or floating element (t? ?p?p??a???); for, if not there, it must be outside of the Kosmos, which is impossible (ss. 15, 16).

CH. 9. — We must however now examine some reasons, which have been alleged to prove the contrary; and which seem to show, not only that there are many Kosmi, but even that there must be many, and that the hypothesis of one single Kosmos is inadmissible. It is urged that in all aggregates, natural as well as artificial, the Form by itself is one thing, and the Form implicated with Matter is another. When we declare the definition of a sphere or a circle, we do not include therein gold or brass, for this makes no part of the essence: if we mention these metals, it is when we cannot conceive or grasp anything beyond the particular case; for example, if we have one particular circle before us. Nevertheless, even here the circle in the abstract is one thing, and this particular circle is another: the first is the Form by itself, the last is the Form along with Matter, one among particular objects. Now, since the Heaven is perceivable by sense, it must be one among particular objects; for every thing perceivable is implicated with Matter. As such, it is this Heaven: to be this Heaven (Form along with Matter) is one thing; to be the Heaven simply and absolutely (Form without Matter) is another. Now, wherever there is Form, there either are or may be many distinct particulars; whether we admit (with Plato) that the Forms exist separately, or not. In all things where the Essence is implicated with Matter, we see that the particular manifestations are many and of indefinite number. Upon this reasoning therefore, there are or at least may be many Heavens: the supposition that there can be no more than one, is inadmissible (ss. 1-2).But we must see how far this reasoning will hold. That the Form without Matter differs from the Form with Matter, is perfectly true. But this does not show that there must be many Kosmi; nor can there be many, if this one Kosmos exhausts all the matter that exists. If the matter of man were flesh and bone, and if a single man were formed, including all flesh and all bone indissolubly united; there could not possibly exist any other man; and the like is true about other objects; for, where the essence is implicated with an underlying matter, no object can come into existence unless some matter be furnished. The Kosmos, or Heaven, is a particular object, composed partly out of appropriate matter: but if it absorbs all the appropriate matter, no second Kosmos can come to pass. We shall now show that it does include all the appropriate matter (ss. 3-5).

The word Heaven has three different senses. 1. It means the essence of the extreme periphery of the universe, or the natural body which is there situated: we call this highest and farthest place Heaven, where we suppose all the divine agency to be situated (?? ? t? ?e??? p?? ?d??s?a? fae?). 2. It means the body continuous (t? s??e??? s?a) with the extreme periphery of the universe, wherein are contained Sun, Moon, and some of the Stars (Planets); for these we affirm to be in the Heaven. 3. In a third sense, it means the body circumscribed (pe??e??e???) by this extreme periphery: for we usually call the Whole and the Universe, Heaven. — These being the three senses of Heaven, the Whole circumscribed by the extreme periphery must by necessity consist of all the natural and perceivable body existing, since there neither is nor can be any such outside of the Heaven. For, if there were any such outside of the Heaven, it must be either one of the elements or a compound thereof — either by nature or contrary to nature. For we have shown that each of the three elements — the circular, the centrifugal, and the centripetal — has its own special place by nature; and that, even if the place in which it now is were not its natural place, that place would be the natural place of another one among the three; for, if a place be contrary to nature in reference to one, it must be conformable to nature in reference to another. Neither of these three elements therefore can be outside of the Heaven, nor, of course, any of their compounds. And there exists no other body besides these; nor can there exist any other (ss. 6, 7).

We see therefore plainly that there neither is nor can be any mass of body (s?at?? ?????) outside of the Heaven; and that the Heaven comprehends all matter — all body natural and perceptible. So that there neither are, nor ever have been, nor ever can be, many Heavens: this one is unique as well as perfect. Nor is there either place, or vacuum, or time, outside of the Heaven. There is no place or vacuum; because, if there were, body might be placed therein; which we have shown to be impossible. There is no time; because time is the number of motion, and there can be no motion without some natural body; but there cannot exist any extra-celestial body. Neither, therefore, are the things outside of the Heaven in place, nor is there time to affect them with old age, nor do they undergo change of any kind. They are without any change of quality and without susceptibility of suffering; they remain, throughout the entire Æon, in possession of the best and most self-sufficing life. The word Æon is a divine expression proposed (?e??? ?f?e??ta?) by the ancient philosophers: they call the Æon of each creature that end which circumscribes the natural duration of the creature’s life. Pursuant to this same explanation, the end of the whole Heaven — the end comprising all time and the infinity of all things — is Æon, so denominated ?p? t?? ?e? e??a?, immortal and divine. From this is suspended existence and life for all other things; for some closely and strictly, for others faintly and feebly. For it is a doctrine often repeated to us in ordinary philosophical discourse (?? t??? ?????????? f???s?f?as?) respecting divine matters — that the Divine, every thing primary and supreme, is by necessity unchangeable; and this confirms what has been just affirmed. For there exists nothing more powerful than itself which can cause it to be moved (if there were, that would be more divine); nor has it any mean attribute; nor is it deficient in any of the perfections belonging to its nature. Its unceasing motion too is easily explained. For all things cease to be moved, when they come into their own place; but with the circular or revolving body the place in which it begins and in which it ends is the same (ss. 8-10).

CH. 10. — We shall next discuss whether the Kosmos be generable or ungenerable, and perishable or imperishable; noticing what others have said on the subject before. All of them consider the Kosmos to be generated: but some think it (although generated) to be eternal; others look upon it as perishable, like other natural compounds; others again — Empedokles and Herakleitus — declare it to be generated and destroyed in perpetual alternation. Now to affirm that it is generated and yet that it is eternal, is an impossibility: we cannot reasonably affirm any thing, except what we see to happen with all things or with most things; and, in the case before us, what happens is the very reverse of the foregoing affirmation, for all things generated are seen to be destroyed. Again that which has no beginning of being as it is now — that which cannot possibly have been otherwise previously throughout the whole Æon — can never by any possibility change; for, if it could ever change, there must exist some cause, which, if it had existed before, would have compelled what is assumed to be incapable of being otherwise, to be otherwise. To those who say that the Kosmos has come together from materials previously existing in another condition, we may reply: If these materials were always in this prior condition and incapable of any other, the Kosmos would never have been generated at all; and, if it has been generated, we may be sure that the antecedent materials must have been capable of coming into another condition, and were not under a necessity to remain always in the same condition; so that aggregations once existing were dissolved, and disgregations brought into combination, many times over before the present Kosmos; at least they possibly may have been so: and this is enough to prove that the Kosmos is not indestructible (ss. 1-3).

Among those who maintain the Kosmos to have been generated yet to be indestructible, there are some who defend themselves in the following manner. They tell us that the generation of which they speak is not meant to be affirmed as a real past fact, but is a mere explanatory or illustrative fiction, like the generation of a geometrical figure, introduced to facilitate the understanding by pupils. But such an analogy cannot be admitted. For in geometry the conclusions are just the same, if we suppose all the figures existing simultaneously; but it is not so with the demonstrations which they tender about the generation of the Cosmos, where the antecedent condition and the consequent condition are the reverse of each other. Out of disorder (they tell us) things came into order: these two conditions cannot be simultaneous; generation must be a real fact, and distinction of time comparing the one condition with the other; whereas in geometrical figures no distinction of time is required (ss. 4-6).

To assume alternate generation and dissolution, over and over again, is in fact to represent the Kosmos as eternal, but as changing its form; as if you should suppose the same person to pass from boyhood to manhood and then back again from manhood to boyhood — calling that by the name of generation and destruction. For, if the elements come together, the aggregation resulting will not be accidental and variable but always the same, especially upon the assumptions of these philosophers. So that, if the whole Kosmos, remaining continuous, is sometimes arranged in one way, sometimes in another, it is these arrangements which are generated and destroyed, not the Kosmos itself (ss. 7, 8).

Total generation, and total destruction without any renovation, of Kosmos might be possible, if there were an infinity of Kosmi, but cannot be possible with only one; for anterior to the moment of generation there existed the antecedent condition, which, never having been generated, could not be destroyed (s. 9).

There are some who think (with Plato in TimÆus) that the non-generable may yet be destroyed, and that the generated may be indestructible. We have combated this opinion on physical grounds, respecting the Heaven specially. We shall now treat the subject upon universal reasonings (i.e., belonging to Logic or Metaphysics — p??? ??? f?s???? ?? pe?? t?? ??????? ???? e???ta?· ?a????? d? pe?? ?pa?t?? s?e?a?????, ?sta? ?a? pe?? t??t?? d???? — s. 10).

CH. 11. — In this reasoning, the first step is to point out that Generable and Non-Generable, Destructible or Indestructible, are words used in many different senses, which must be discriminated (p???a??? ?e??e?a). If a man uses these words in an affirmative proposition without such discrimination, his affirmation is indeterminate; you cannot tell in which of their many different senses he intends to affirm. Non-Generable means: (1) That which now is, having previously not been, even though without either generation or change, as, to touch or to be moved; for, according to some persons, touching or being moved are not cases of generation; you cannot become touching, or become moved; you are moved, or you are not moved; you touch, or you do not touch (?? ??? e??a? ???es?a? fas?? ?pt?e???, ??d? ?????e???. He means, I presume, that to touch, and to be moved, are instantaneous acts, though how they can be said to occur ??e? eta????, I do not see.). It means: (2) That which, though capable of coming to pass or of having come to pass (??de??e??? ???es?a? ? ?e??s?a?), nevertheless is not; for this too is non-generable, since it might have come to be. Again, it means: (3) That which cannot by possibility sometimes exist, sometimes not exist. Impossible has two meanings: (1) That of which you cannot truly say that it might be generated (?t? ?????t’ ??); (2) That which cannot be generated easily, or quickly, or well (?a???). So also the Generable (t? ?e???t??) means: (1) That which, not existing previously, afterwards exists at one time and not at another, whether generated or not (he seems here to point to t? ?ptes?a? or t? ???e?s?a?); (2) The possible, whether it be the strictly possible, or the easily possible; (3) That of which there is generation out of the nonexistent into existence, whether it now does actually exist, or may exist hereafter. The Destructible and Indestructible (f?a?t?? ?a? ?f?a?t??) have similar differences of meaning (ss. 1-6).

If we say that a man can raise a weight of 100 pounds, or march 100 stadia, we speak always with reference to a certain extreme, meaning to imply that he can also raise a weight of 50, 40, 30 pounds, and that he can also walk 50, 40, 30 stadia. If we say that he cannot raise a weight of 100 pounds, we mean to imply, À fortiori, that he cannot raise a weight of 110 pounds. In regard to sight and hearing, the case is opposite; he who can see a small object, can certainly see a large one; he who can hear a faint sound, can certainly hear a loud one. But he who can see a large object, is not necessarily able to see a small one; he who can hear a loud sound, is not necessarily able to hear a faint one. In sight and hearing, superior power is indicated by the less including the greater; in motion, by the greater including the less (ss. 7-8).

CH. 12. — If there are some things capable both of existence and of nonexistence, we must define on which falls the major portion of time; for, if we cannot in either case define the time, and can only say that it is greater than any assumed length of time and never less than any assumed length, — the same thing will be capable both of existence and of non-existence for an infinite time; which is an impossibility. We must take our departure from this principle: Impossibility is one thing, Falsehood another. Both the impossible and the false are, however, either conditional (as when it is said to be impossible that the triangle should have its three angles equal to two right angles, if such and such things are granted, and that the diameter should be commensurate with the periphery, if such and such positions were true), or absolute. But there are matters absolutely false, which are not absolutely impossible. When you are standing, I affirm that you are sitting: this is absolutely false, but not absolutely impossible. On the other hand, if I affirm that you are at the same time sitting and standing, or that the diameter is commensurable with the periphery, the proposition is not merely absolutely false, but absolutely impossible. An assumption simply false is not the same thing as an assumption absolutely impossible: from an impossible assumption there follow other impossibilities. The power of sitting or standing means that you can do either one at any given time — one at one time, the other at another; but not that you can do both at the same time. But, if any thing has throughout an infinite time the power of doing more things than one, it must have the power of doing more things than one at the same time; for this infinite time comprehends its whole existence. Accordingly, if any thing existing for an infinite time is nevertheless destructible, this means that it has the possibility not to exist. This being a possibility, let us imagine it realized: then the thing in question will both exist actually for an infinite time and yet not exist; which is a consequence not only false, but impossible, and thus proves the premiss assumed to be impossible (i.e., that a thing existing for an infinite time is nevertheless destructible). We thus see that what exists always is absolutely indestructible (ss. 1-3). It is also ungenerable; for, if generable, there will be a possibility that at some time or other it did not exist. That is generable, which may possibly have not existed at some anterior time, finite or infinite: so that, if t? ?e? ?? cannot possibly not exist, it cannot be generable. Now that which is always possible to exist, has, for its correlate negative (?p?fas??), that which is not always possible to exist; and that which is always possible not to exist, has, for its contrary, that which is not always possible not to exist. These two negatives must of necessity be true of the same subject: there must be something of which we may truly say — It has no possibility always to exist — It has no possibility always not to exist. This therefore is something intermediate between that which always exists, and that which always exists not, viz., That which may exist and may not exist (?a? e??a? ?s?? t?? ?e? ??t?? ?a? t?? ?e? ? ??t??, t? d???e??? e??a? ?a? ? e??a?); for both the negative predicates will find application, if it do not exist always. The possible to exist, and the possible not to exist, must therefore be the same thing — a mean between the two above-mentioned extremes (ss. 4, 5).After a long metaphysical deduction, occupying from sections 6 to 17, Aristotle proceeds as follows.

We may also discern in the following manner that nothing which has been once generated, can continue indestructible; nothing which is ungenerable and which always existed heretofore, can ever be destroyed. For it is impossible that any thing which arises spontaneously (?p? t?? a?t??t??) can be either indestructible or ungenerable. The Spontaneous, and the Casual (t? ?p? t?? t????), are in antithesis to the always or the most frequently Ens or Fiens (pa?? t? ?e? ?a? t? ?? ?p? t? p??? ? ?? ? ????e??? — s. 18); but that which has existed for an infinite or a very long tine, must belong to this last category. Accordingly, such things must by nature sometimes exist, sometimes not exist. In them, both sides of the contradiction are alike true, owing to the matter of which they are composed: they exist, and they do not exist. But you cannot say with truth now that the thing exists last year; nor could you say last year that it exists now. Having once been non-existent, it cannot be eternal for future time; for it will still possess in future time the possibility of non-existence, yet not the power of non-existing at the moment when it does exist, nor with reference to last year and to past time; there being no power bearing upon past time, but only on present and future time. (Sections 21 and 22 are hardly intelligible to me.)

On physical grounds also it appears impossible that what is eternal in the past should be destroyed afterwards, or that what did not exist at some former time should afterwards be eternal. Those things which are destructible, are all of them generable and changeable (?e???t? ?a? ??????t? p??ta). Those things which exist by nature, are changed by their opposites and by their component materials, and are destroyed by the same agencies (s. 23).