The Politics of Aristotle

by Aristotle

  It is plain, then, from the foregoing arguments that it is impossible for an [25] infinite force to reside in a finite magnitude or for a finite force to reside in an infinite magnitude. But first it will be well to discuss a difficulty that arises in connexion with locomotion. If everything that is in motion with the exception of things that move themselves is moved by something, how is it that some things, e.g. things thrown, continue to be in motion when their mover is no longer in contact [30] with them? If we say that the mover in such cases moves something else at the same time, e.g. the air, and that this in being moved is also a mover, then it will similarly be impossible for this to be in motion when the original mover is not in contact with it or moving it: all the things moved would have to be in motion simultaneously and also to have ceased simultaneously to be in motion when the original mover ceases to [267a1] move them, even if, like the magnet, it makes that which it has moved capable of being a mover. Therefore, we must say that the original mover gives the power of being a mover either to air or to water or to something else of the kind, naturally adapted for imparting and undergoing motion; but this thing does not cease simultaneously to impart motion and to undergo motion: it ceases to be in motion at [5] the moment when its mover ceases to move it, but it still remains a mover, and so it causes something else consecutive with it to be in motion, and of this again the same may be said. The motion ceases when the motive force produced in one member of the consecutive series is at each stage less, and it finally ceases when one member no longer causes the next member to be a mover but only causes it to be in motion. The [10] motion of these last two—of the one as mover and of the other as moved—must cease simultaneously, and with this the whole motion ceases. Now the things in which this motion is produced are things that admit of being sometimes in motion and sometimes at rest, and the motion is not continuous but only appears so; for it is motion of things that are either successive or in contact, there being not one mover [15] but a number consecutive with one another. That is why motion of this kind takes place in air and water. Some say that it is mutual replacement; but the difficulty raised cannot be solved otherwise than in the way we have described. Mutual replacement makes all the members of the series move and impart motion simultaneously, so that their motions also cease simultaneously; but there appears to be continuous motion in a single thing, and therefore, since it cannot be moved by [20] the same mover, the question is, what moves it?

  Since there must be continuous motion in the world of things, and this is a single motion, and a single motion must be a motion of a magnitude (for that which is without magnitude cannot be in motion), and of a single magnitude moved by a single mover (for otherwise there will not be continuous motion but a consecutive [25] series of separate motions), then if the mover is a single thing, it is either in motion or unmoved: if, then, it is in motion, it will have to keep pace with that which it moves and itself be in process of change, and it will also have to be moved by [267b1] something: so we have a series that must come to an end, and a point will be reached at which motion is imparted by something that is unmoved. Thus we have a mover that has no need to change along with that which it moves but will be able to cause motion always (for the causing of motion under these conditions involves no effort); and this motion alone is regular, or at least it is so in a higher degree than any other, [5] since the mover is never subject to any change. So, too, in order that the motion may continue to be of the same character, the moved must not be subject to change in relation to it. So it must occupy either the centre or the circumference, since these are the principles. But the things nearest the mover are those whose motion is quickest, and in this case it is the motion of the circumference that is the quickest: therefore the mover occupies the circumference.

  There is a difficulty in supposing it to be possible for anything that is in motion [10] to cause motion continuously and not merely in the way in which it is caused by something repeatedly pushing (in which case the continuity amounts to no more than successiveness). Such a mover must either itself continue to push or pull or perform both these actions, or else the action must be taken up by something else and be passed on from one mover to another (the process that we described before as occurring in the case of things thrown, since the air, being divisible, is a mover in virtue of the fact that different parts of the air are moved one after another); and in [15] either case the motion cannot be a single motion, but only a consecutive series of motions. The only continuous motion, then, is that which is caused by the unmoved mover; for it remains always invariable, so that its relation to that which it moves remains also invariable and continuous.

  Now that these points are settled, it is clear that the first unmoved mover cannot have any magnitude. For if it has magnitude, this must be either a finite or [20] an infinite magnitude. Now we have already proved in our course on Physics that there cannot be an infinite magnitude; and we have now proved that it is impossible for a finite magnitude to have an infinite force, and also that it is impossible for a thing to be moved by a finite magnitude during an infinite time. But the first mover [25] causes a motion that is eternal and causes it during an infinite time. It is clear, therefore, that is indivisible and is without parts and without magnitude.

  **TEXT: W. D. Ross, OCT, Oxford, 1950

  1The bracketed words are probably wrongly inserted from 185a9–12.

  2I.e. water, air, fire.

  3Retaining the MS text; Ross reads: κεχωρισμένα μέντoι ἀπ’ άλλἡλων ἡoὔά (‘not, however, separated from one another’).

  4Ross excises ‘time’.

  5Ross omits ‘the matter and’.

  6Reading μὶα τὀ εἶδoς ἤ ὀ λόγoς (Bonitz).

  7See Metaphysics Δ 7, and Θ.

  8I.e. Plato.

  9Reading τέχνη, with the MSS, for Ross’ φύσις.

  10Reading τoῦτo ἔσχατoν.

  11Omitting ἡ ἀρχιτεκτoνικἡ.

  12Reading μέχρι τoυ. τἱνoς γἁρ (Jaeger).

  13Frag. 53 Diels-Kranz.

  14Reading κoμιζόμενoς, with one MS, for Ross’s κoμιζoμένoυ.

  15Omitting τoῦ κoμὶσασθαι ἕνεκα (Bonitz).

  16Reading τῷ ἕνεκα ἄλλoυ ὲκεῖνo oὗ (Prantl).

  17‘The spontaneous’: τò αὐτόματoν; ‘the thing itself happens in vain’: αὐτò μάτην γένηται.

  18Frag. 61 Diels-Kranz.

  19Empedocles, frag. 62 Diels-Kranz.

  20See VIII 1–6.

  21Compare the Pythagorean columns at Metaphysics A 5, 986a25.

  22Ross excises the bracketed sentence as an alternative version of 206a18–29.

  23Rings are ἄπειρoι in the sense of having no ends (πέρατα).

  24Frag. 8, line 44, Diels-Kranz.

  25Theogony 116.

  26Aristotle’s remarks rest on the use of the Greek preposition ‘ἐν’, to which (evidently) the English ‘in’ does not precisely correspond.

  27Ross excises the bracketed lines as an alternative version of 211a29–36.

  28See On Generation and Corruption I 3.

  29These lines are bracketed by editors as a later addition.

  30The words in brackets are excised as an alternative version of 217b2-11.

  31Change = μεταβoλά, in which Aristotle construes ‘μετἁ’ in the sense of ‘after’.

  32Ross excises the clause in brackets.

  33Ross brackets καά τῷ πoτέ.

  34Transposed by Ross.

  35‘φoρά’ (‘locomotion’) means, taken strictly, ‘being carried’.

  36Ross transposes 227a7–9 and 226b26–7 to follow 226b22.

  37Ross excises this sentence as a doublet of 227b11.

  38The final paragraph, which several MSS omit, is regarded as an alternative version of 230b10–28 by Ross and others.

  39Retaining oὐ (MSS) for Ross’s oὔπω.

&nb
sp; 40Retaining the MSS reading εά δ’ for Ross’s ἐάτ’.

  41See 233a21ff.

  42Reading τoῦ μέσoυ τῶν A (τoῦ μέσoυ, Ross).

  43Reading πάντα τὰ A (πάντα, Ross).

  44Ross excises the clause marked *…* .

  45See 227b3ff.

  46Reading αἱ γενέσεις αὗται (αἱ γενέσεις, Ross).

  47Both water and speech can be called λευκός or limpid.

  48Reading πᾶσιν, with the MSS (πᾶσαν, Ross).

  49Frag. 17, lines 9–13, Diels-Kranz.

  50Retaining τῶν κινoύντων, excised by Ross.

  51Retaining τoῦ ὀργάνoυ, which Ross excises.

  52Omitting τῷ ABΓ in line 31.

  53Omitting λευκόν at line 23; the received text reads: ‘. . . call the thing white or not white’.

  ON THE HEAVENS**

  J. L. Stocks

  BOOK I

  1 · The science which has to do with nature clearly concerns itself for the [268a1] most part with bodies and magnitudes and their properties and movements, but also with the principles of this sort of substance, as many as they may be. For of things constituted by nature some are bodies and magnitudes, some possess body and [5] magnitude, and some are principles of things which possess these. Now a continuum is that which is divisible into parts always capable of subdivision, and a body is that which is every way divisible. A magnitude if divisible one way is a line, if two ways a surface, and if three a body. Beyond these there is no other magnitude, because the three dimensions are all that there are, and that which is divisible in three directions is divisible in all. For, as the Pythagoreans say, the universe and all that is in it is [10] determined by the number three, since beginning and middle and end give the number of the universe, and the number they give is the triad. And so, having taken these three from nature as (so to speak) laws of it, we make further use of the number three in the worship of the Gods. Further, we use the terms in practice in [15] this way. Of two things, or men, we say ‘both’, but not ‘all’: three is the first number to which the term ‘all’ is applied. And in this, as we have said, we do but follow the lead which nature herself gives. Therefore, since ‘every’ and ‘all’ and ‘complete’ do [20] not differ from one another in respect of form, but only, if at all, in their matter and in that to which they are applied, body alone among magnitudes can be complete. For it alone is determined by the three dimensions, that is, is an ‘all’. But if it is divisible in three dimensions it is every way divisible, while the other magnitudes are divisible in one dimension or in two; for the divisibility and continuity of [25] magnitudes depend upon the number of the dimensions, one sort being continuous in one direction, another in two, another in all. All magnitudes, then, which are divisible are also continuous. Whether we can also say that whatever is continuous is divisible does not yet, on our present grounds, appear. One thing, however, is clear. We cannot pass beyond body to a further kind, as we passed from length to [268b1] surface, and from surface to body. For if we could, it would cease to be true that body is complete magnitude. We could pass beyond it only in virtue of a defect in it and that which is complete cannot be defective, since it extends in every direction. [5] Now bodies which are classed as parts of the whole are each complete according to our formula, since each possesses every dimension. But each is determined relatively to that part which is next to it by contact, for which reason each of them is in a sense many bodies. But the whole of which they are parts must necessarily be complete, and must, as the term indicates, extend in every direction and not just in [10] some.

  2 · The question as to the nature of the whole, whether it is infinite in size or limited in its total mass, is a matter for subsequent inquiry. We will now speak of those parts of the whole which are specifically distinct. Let us take this as our [15] starting-point. All natural bodies and magnitudes we hold to be, as such, capable of locomotion; for nature, we say, is their principle of movement. But all movement that is in place, all locomotion, as we term it, is either straight or circular or a combination of these two which are the only simple movements. And the reason is [20] that these two, the straight and the circular line, are the only simple magnitudes. Now revolution about the centre is circular motion, while the upward and downward movements are in a straight line, ‘upward’ meaning motion away from the centre, and ‘downward’ motion towards it. All simple motion, then, must be motion either away from or towards or about the centre. This seems to be in exact [25] accord with what we said above: as body found its completion in three dimensions, so its movement completes itself in three forms.

  Bodies are either simple or compounded of such; and by simple bodies I mean those which possess a principle of movement in their own nature, such as fire and earth with their kinds, and whatever is akin to them. Necessarily, then, movements [269a1] also will be either simple or in some sort compound—simple in the case of the simple bodies, compound in that of the composite—and the motion is according to the prevailing element. Supposing, then, that there is such a thing as simple movement, and that circular movement is simple, and that both movement of a simple body is simple and simple movement is of a simple body (for if it is movement [5] of a compound it will be in virtue of a prevailing element), then there must necessarily be some simple body which moves naturally and in virtue of its own nature with a circular movement. By constraint, of course, it may be brought to move with the motion of something else different from itself, but it cannot so move naturally, since there is one sort of movement natural to each of the simple bodies. Again, if the unnatural movement is the contrary of the natural and a thing can [10] have no more than one contrary, it will follow that circular movement, being a simple motion, must be unnatural, if it is not natural, to the body moved. If then the body whose movement is circular is fire or some other element, its natural motion must be the contrary of the circular motion. But a single thing has a single contrary; and upward and downward motion are the contraries of one another. If, on the other hand, the body moving with this circular motion which is unnatural to it is [15] something different from the elements, there will be some other motion which is natural to it. But this cannot be. For if the natural motion is upward, it will be fire or air, and if downward, water or earth. Further, this circular motion is necessarily primary. For the complete is naturally prior to the incomplete, and the circle is a complete thing. This cannot be said of any straight line:—not of an infinite line; for [20] then it would have a limit and an end: nor of any finite line; for in every case there is something beyond it, since any finite line can be extended. And so, since the prior movement belongs to the body which is naturally prior, and circular movement is prior to straight, and movement in a straight line belongs to simple bodies—fire [25] moving straight upward and earthy bodies straight downward towards the centre—since this is so, it follows that circular movement also must be the movement of some simple body. For the movement of composite bodies is, as we said, determined by that simple body which prevails in the composition. From this it is clear that there is in nature some bodily substance other than the formations we [30] know, prior to them all and more divine than they. Or again, we may take it that all movement is either natural or unnatural, and that the movement which is unnatural to one body is natural to another—as for instance, is the case with the upward and downward movements, which are natural and unnatural to fire and earth respectively. It necessarily follows that circular movement, being unnatural to these [269b1] bodies, is the natural movement of some other. Further, if, on the one hand, circular movement is natural to something, it must surely be some simple and primary body which naturally moves with a natural circular motion, as fire moves up and earth [5] down. If, on the other hand, the movement of the rotating bodies about the centre is unnatural, it would be remarkable and indeed quite inconceivable that this movement alone should be continuous and eternal, given that it is unnatural. At any
rate the evidence of all other cases goes to show that it is the unnatural which quickest passes away. And so, if, as some say, the body so moved is fire, this [10] movement is just as unnatural to it as downward movement; for any one can see that fire moves in a straight line away from the centre. On all these grounds, therefore, we may infer with confidence that there is something beyond the bodies that are about us on this earth, different and separate from them; and that the superior glory [15] of its nature is proportionate to its distance from this world of ours.