2 [ἐπεὶ...ἐχόμενον Met. 1068 Ὁ 4 ΑΡ, The unfamiliarity of ὥστε in apodosi (for which cf. 232 a 2 and 13) would lead to the two obvious attempts to supply a main clause which appear in the alternative readings: (1) ἐπὶ (for ga in Simplicius 846. 24 (with omission of τι, as in E here), and (2) ἐπεὶ δὲ τῶν ἀπ. οὐκ ἔστι τι πρῶτον, οὐκ ἔσται τὸ πρῶτον, Gor κτλ., the reading of most ss. here and at Met. 1068 Ὁ 4 (though F here omits οὐκ ἔστι τι πρῶτον). The superfluity of words is out of Senne with the style of our passage.—C.]
> [γένηται ἘΠῚ Met. 1068 Ὁ 8: γίγνηται cett. Simplic.
* [The Greek is obscure. If a process-of-ceming-into- being (genesis 4) could itself be in a process-of-coming-into- being (genesis B), it must be possible that it should be in a process-of-perishing. But when? For a thing to perish it must be ‘in being’ (εἶναι δεῖ τὸ φθειρόμενον). Hence our genesis A cannot perish either (1) εὐθὺς γιγνόμενον (1.6. ἐν ἀρχῇ τοῦ γίγνεσθαι, Simplic.), at the moment when it enters on the supposed genesis B, for then it was not yet in being, or (2) ὕστερον, which seems to mean the moment when genesis B is complete, so that genesis 4 has come-to-be, and 26 PHYSICS, V. 1.
26 PHYSICS, V. 1.
the generand was. And again, taking the ultimate genesis as itself a generand, zfs genesis was once in process of generation, so that it was not itself yet generated, and so forth. And since there is no first link of our infinitely receding chain, neither is there the next or any following link; so it would be impossible that anything should ever come into existence, or move, or change.
(3) Again, the subject of any specific movement is identically the subject of the contrary movement (and of its cessation in rest) and what is capable of being generated is also capable of being destroyed. If, then, genesis is capable of being generated, it is capable of being destroyed. But when? As it begins? <As it ends? No; for to be destroyed a thing must be there to destroy. Genesis, then, would have to be being destroyed while it was being generated; which is impossible.* (4) Again, in a case of genesis, as in all cases of change, there must be a subject which passes from the starting-point to the goal. Thus, in all modifica- tions there must be a body that undergoes the modi- fication, if it be physical, or a mind, if it be mental; but what is the corresponding thing that becomes a movement or a genesis? Besides, what goal can we assign to the genesis of a pea or the movement of a movement? The goal can only be the moveall later times. For genesis A cannot perish at that moment, since it is the moment when it comes-to-be, or later, because a genesis is not the sort of thing that persists ‘in being’ after it has come to be, but is over from that moment. So the only time left for perishing is ὅταν γένηται γιγνόμενον, ‘when it has begun to be a ee is coming-into-being ἢ and is in the process of genesis B. But during that process it is coming-into-being and cannot also be in process of perishing.—C. | 27 ARISTOTLE 226a εἶναι τὴν τοῦδε ἐκ τοῦδε εἰς τόδε κίνησιν ἢ γένεσιν. 16 ἅμα δὲ πῶς καὶ ἔσται; οὐ γὰρ ἔσται μάθησις ἡ 20 25 τῆς μαθήσεως γένεσις, WOT οὐδὲ γενέσεως γένεσις, οὐδέ τίς τινος. Ere εἰ τρία εἴδη κινήσεως ἔστι, τούτων τινὰ ἀνάγκη εἶναι καὶ τὴν ὑποκειμένην φύσιν καὶ εἰς ἃ κινοῦνται" οἷον τὴν φορὰν ἀλλοιοῦσθαι ἢ φέρεσθαι. Ὅλως δ᾽, ἐπεὶ κινεῖται τὸ κινούμενον πᾶν τριχῶς, ἢ τῷ κατὰ συμβεβηκὸς ἢ τῷ μέρος τι ἢ τῷ Kal? αὑτό, κατὰ συμβεβηκὸς μόνον ἂν ἐνδέχουτο μεταβάλλειν τὴν μεταβολήν, οἷον εἰ ὁ ὑγιαζόμενος τρέχοι ἢ μανθάνοι: τὴν δὲ κατὰ συμβεβηκὸς ἀφεῖμεν πάλαι. Επεὶ δὲ οὔτε οὐσίας οὔτε τοῦ πρὸς TL οὔτε τοῦ ποιεῖν καὶ πάσχειν, λείπεται KATA TO ποιὸν καὶ TO ποσὸν Kal TO ποὺ κίνησιν εἶναι μόνον" ἐν ἑκάστῳ 9 ον A yap ἐστι τούτων ἐναντίωσις. ἡ μὲν οὖν κατὰ TO ποιὸν κίνησις ἀλλοίωσις ἔστω" τοῦτο yap ἐπέζευκ- 1. (det...γένεσιν Simplic. 853. 1 (lemma). The mss. exhibit various mixtures of this reading with the alternative reading given in note a.—C.]
Seal α [The alternative reading δεῖ γὰρ εἶναί τι τὴν τοῦδε ἐκ τοῦδε εἰς τόδε κίνησιν, καὶ μὴ κίνησιν ἢ γένεσιν would refer to the first question: what is the subject which undergoes the becoming or change? The movement itself? No, for then ‘the movement of something from this to that must be something that is in being (and so can undergo the change and persist through it) and not a movement or becoming.’—C. | δ (Or " And how can the goal just described ever exist at all? For the becoming of a process of learning will never actually be the process of learning; so neither will the becoming of “ὁ becoming” (ever actually be ‘* becoming ”’) 28 PHYSICS, V. 11.
ment or genesis of something from something to something else.* ὃ And how could the motion be at the same time the station in which it ceases? Ifthe generating process were coming to know, the goal would be knowledge, not coming to it. So with all else, and so with genesis: the goal cannot be genesis, but the something generated.
(5) Again, if there are only three kinds of “move- ment’ in the wide sense, both the movement which is supposed to undergo the change and the move- ment into which it changes can only be a movement of one of these three kinds; thus a local movement must undergo a process of qualitive modification or be itself locally moved.
In conclusion, then, since any subject of move- ment moves in one of three ways—either inciden- tally, or in virtue of a part, or primarily, it is only in the incidental sense that a change can be changing, as, for instance, when a man who is recovering his health carries his ‘recovering’ with him as he changes his place in a race or passes from ignorance to knowledge of something. And we have already agreed to dismiss the ‘ incidental’ sense of change from our consideration.¢ Since, then, movement can pertain neither to substantive being nor to relation nor to acting and being acted on, it remains that it pertain exclusively to quality, quantity, and locality, each of which embraces contrasts. Movement in quality is what we call ‘ modification,’ which is a common term applicable to change in either direction between the nor will the particular becoming of any particular “ be- coming ”’ (ever be that particular “* becoming ”’).’-—C.
29 ARISTOTLE 226a Tat Κοινὸν ὄνομα. λέγω δὲ TO ποιὸν οὐ TO ἐν TH οὐσίᾳ (καὶ γὰρ ἡ διαφορὰ ποιότης) ἀλλὰ τὸ παθη- τικόν, καθ᾽ ὃ λέγεται πάσχειν ἣ ἀπαθὲς εἶναι. ἡ 80. δὲ κατὰ τὸ ποσὸν τὸ μὲν κοινὸν ἀνώνυμος, καθ᾽ ἑκάτερον δ᾽ αὔξησις Kat φθίσις--- μὲν εἰς TO τέλειον μέγεθος αὔξησις, ἡ δ᾽ ἐκ τούτου φθίσις. ἡ δὲ κατὰ τόπον καὶ τὸ κοινὸν καὶ τὸ ἴδιον ἀνώ- νυμος, ἔστω δὲ φορὰ καλουμένη τὸ κοινόν: καΐτοι λέγεταί ye ταῦτα φέρεσθαι μόνα κυρίως, ὅταν μὴ 86 ἐπ᾿ αὐτοῖς ἦ TO στῆναι τοῖς μεταβάλλουσι τὸν 226b τόπον, καὶ ὅσα μὴ αὐτὰ ἑαυτὰ κινεῖ κατὰ τόπον. Ἢ δὲ ἐν τῷ αὐτῷ εἴδει μεταβολὴ ἐπὶ τὸ μᾶλλον Kal ἧττον ἀλλοίωσίς ἐστιν. ἡ γὰρ ἐξ ἐναντίου εἰς ἐναντίον κίνησίς ἐστιν ἢ ἁπλῶς ἢ πῆ ἐπὶ μὲν γὰρ τὸ ἧττον ἰοῦσα εἰς τοὐναντίον λεχθήσεται μεταβάλλειν, ἐπὶ δὲ τὸ μᾶλλον ὡς ἐκ τοὐναντίου εἰς αὐτό. διαφέρει γὰρ οὐδὲν πῇ μεταβάλλειν 7 ἁπλῶς, πλὴν πῇ δεήσει τἀναντία ὑπάρχειν" τὸ δὲ κι} 1 [ἀνώνυμος KE: ἀνώνυμον cett., but ἀνώνυμος (ἀνώνυμοι I) in ¢ [Unlike ‘growth’ (in quantity), which means only transition in one direction, from small to large.—C.]
> [τὸ ἐν τῇ οὐσίᾳ πάθος, a quality which constitutes the differentia of an essence, 6.9. ‘having no angles,’ when ‘circle’ is defined as ‘a figure having no angles’ (Met. 1020 a 33). A thing cannot part with such a quality without ceasing to be the thing it is heing destroyed ).—C.]
¢ [The Greek φέρεσθαι, though it often means ‘to move (voluntarily) from τ to place,’ is passive in form, and strictly means ‘to be borne (along).’ Aristotle eliminates 30 PHYSICS, V. 11.
contraries concerned.* By quality I do not mean any quality that is of the essence of the thing that undergoes the change ὃ (though its differentia is of course a quality in the general sense of the word), but that passive quality with regard to which it is said to be ‘ affected’ or to be incapable of being affected. As to quantity, there is no general term that applies equally to changes in either direction between greater and less; but ‘increase’ is used for the movement towards the full size, ‘decrease’ for movement in the contrary direction. As to motion from place to place, we have neither common nor particular terms, but let ‘locomotion’ pass as the common term, though the Greek word ὁ in its strict sense applies only to things which, in changing their place, have not the power to stop, and to things that do not move themselves from place to place.
The change towards a greater or a less degree of the same quality is a ‘ modification’ ὦ; for the movement from contrary to contrary may be either complete or partial. If a thing moves towards the lesser degree of one contrary it is said to be changing towards the other, and if towards the greater degree, to be changing from the other. Nor is there any difference between complete and partial change save in the partial persistence of both contraries in this suggestion from gopd—his regular name for ‘ locomo- tion ’ generally.—C.]
@ [The term ‘ modification’ includes (besides changes from white to black and from black to white) the changes from ‘ white’ (2.6. prevailingly white, cf. p. 191) to ‘ whiter’ or to ‘ less white.’ The change from ‘ white’ to ‘less white’ can be described as a change towards the contrary ‘black ’; that from ‘white’ to ‘whiter’ as a change from the contrary black towards white itself (εἰς atré).—C.
31 ARISTOTLE 31 ARISTOTLE 2285 μᾶλλον καὶ ἧττόν ἐστι τῷ πλέον ἢ ἔλαττον ἐν- υπάρχειν τοὐναντίου καὶ μή. Ὅτι μὲν οὖν αὗται τρεῖς μόναι κινήσεις εἰσίν, 10 ἐκ τούτων δῆλον. Ακίνητον δ᾽ ἐστὶ τό τε ὅλως ἀδύνατον κινηθῆναι (ὥσπερ 6 ψόφος ἀόρατος), Kal τὸ ἐν πολλῷ χρόνῳ “A μόλις κινούμενον ἢ τὸ βραδέως ἀρχόμενον (ὃ λέγεται δυσκίνητον), καὶ τὸ πεφυκὸς μὲν κινεῖσθαι καὶ δυνάμενον μὴ κινούμενον δὲ τότε ὅτε πέφυκε 15 καὶ οὗ καὶ ὥς, ὅπερ ἠρεμεῖν καλῶ τῶν ἀκινήτων la μόνον" ἐναντίον yap ἠρεμία κινήσει, ὥστε στέρησις ἂν εἴη τοῦ δεκτικοῦ. Τί μὲν οὖν ἐστι κίνησις καὶ τί ἠρεμία, καὶ πόσαι μεταβολαὶ καὶ ποῖαι κινήσεις, φανερὸν ἐκ τῶν εἰρημένων. α [Οὐ 229 ἃ 2,‘ a lesser degree of something always means an admixture of the contrary.’—C.] > (Cf. Simplic. 865. 11, who instances the fixed stars, whose risings shift only a degree in a hundred years. But Aristotle may mean the popular use of ‘immovable’ for ‘ that which can only be moved by a great effort taking a long time.” This can be described alternatively (4) as ‘ slow to begin ’ or ‘ hard to move.’—C.]
CHAPTER III ARGUMENT [Certain terms which will occur in the analysis of motion, must be defined (226 b 18-21).
Things are together in place when they are in the same proper place. Things touch when their extremes are in this sense “ together’ (Ὁ 21-23). Between is applicable only to change (of quality, quantity, or place) where the opposite eatremes are contraries, not to ‘ becoming, where they are contradictories (227 a 7-10). A term is between two other 32 the latter; and the difference of degree means the presence or absence in it of more or less of the other contrary ὦ The conclusion is now established that the three movements examined are the only ones that there are.
We say a thing is ‘ moveless ’ either because by its nature it is insusceptible of motion (as a sound is in- visible); or because its movement is so slow as to be hardly perceptible,® or because it is ‘ slow to begin, ὁ which is equivalent to ‘inapt to move,’ or lastly because, though it could move under given conditions of time, place, and manner, it is not actually moving. And it is only to this last class of ‘ moveless ’ things that I apply the term ἡ rest.’ For rest is the contrary of motion and must therefore be the shortage of that which might by nature be present to the subject in question.
We have now elucidated the questions, what motion is, and what station or rest, and how many kinds of change there are, and how many of motion.
¢ As a man may be‘ slow to wrath ᾽ (Themistius).
CHAPTER III ARGUMENT (continued) terms, if something that changes continuously reaches tt before reaching the extreme or contrary. Meanings of ‘con- tinuously changing,’ and of ἡ contrary’ as applied to local A thing is next-in-succession to another, if it comes after the starting-point and has nothing of the same kind between it and that which it succeeds (Ὁ 34-227 a 6).
VOL. II D 33 ARISTOTLE ARGUMENT (continued) If it is next-in-succession and also touches the other, it is contiguous (a 6~7).
The continuous 15 a species of the contiguous, found where the extremities of the two things coalesce into one or are bound to be together (a 10-17).
Of these last three terms, “ next-in-succession ’ is implied e26bis Mera δὲ ταῦτα λέγωμεν τί ἐστι TO ἅμα Kal χωρίς, καὶ τί τὸ ἅπτεσθαι, καὶ τί τὸ μεταξύ, καὶ 20 τί τὸ ἐφεξῆς, καὶ τί τὸ ἐχόμενον καὶ συνεχές, καὶ τοῖς ποίοις ἕκαστον τούτων ὑπάρχειν πέφυκεν. "Aya μὲν οὖν λέγεται ταῦτ᾽ εἶναι κατὰ τόπον, ὅσα ἐν ἑνὲ τόπῳ ἐστὶ πρώτῳ, χωρὶς δὲ ὅσα ἐν ἑτέρῳ" ¢ The term ‘together’ is somewhat misleading, for it sug- gests close proximity rather than absolute identity of posi- tion. We speak of things being together when we mean that their common place includes little besides their several proper places, as sheep in a fold or a concourse of people in a hall or market-place, and in that sense of the term any number of bodies can be together in one common place. Whereas it is impossible for two bodies to be ‘together ’ in the sense in which the term is used by Aristotle: for two bodies can- not occupy the same space, and as the proper place of a thing includes no space except what is in the occupation of that thing, two bodies cannot exist in the same proper place. On the other hand the several qualities (6.9. colour, weight, temperature, etc.) of a thing are bound all to exist ‘together’ in the sense of each permeating the whole of the space filled by the thing they qualify. Consequently the proper place of each is identical with that of each of the others. (See Vol. 1. Introd. pp. liv sqg., and Bk. IV. Introd., for the connexion and distinction between space and place.)
Again, points which occupy no space at all nevertheless have proper places, defined unequivocally by position, and there is no difficulty about any number of points being 34 PHYSICS, V. ut.
ARGUMENT (continued) in ‘contiguous, contiguous is imphed in ‘ continuous,’ which therefore comes last in order of genesis (a 17-27). Polemic against the Pythagorean doctrine of separately existing monads which are both units of number and points, 1.6. units of magnitude having position in space Summary (a 82-b 2).—C,] Ler us proceed to consider the meaning of the terms ‘together,’ “ apart,’ ‘ touching,’ ‘ between,’ ‘ next in succession (but not touching),’ ‘ contiguous,’ and ‘continuous,’ and the question to what each of the qualifications so described naturally belongs.
Things are said to be ‘ together’ in place when the immediate and proper place of each is identical with that of the other,® and ‘ apart’ (or ‘severed ’) when this is not so.
‘together’ in the same proper place, for the presence of one presents no obstacle to the presence of another. For instance, the mid-points of the several diameters of a single sphere are bound to be ‘together’ at the centre.
Things which are not bound to be together may happen, under certain conditions, to be so: e.g. the mid-points of the diameters of different spheres will be together if the spheres happen to be concentric, but they are no more bound to be so than the spheres are bound to be con- centric.
Things ‘touch’ each other if any point on the boundary of the one is in the same proper place as any point on the boundary of the other. If these points only happen to be together, the things are said to be ‘ contiguous,’ if they are ‘held together’ or in other words are bound to be so, they are said to be ‘continuous.’ [The notion of ‘contact’ is more carefully analysed in De gen. et corr. 322 b 30 ff., and it is there explained in what sense contact is possible between mathematical entities, as conceived by Aristotle, 35 ARISTOTLE 35 ARISTOTLE 226} ἅπτεσθαι δὲ ὧν τὰ ἄκρα ἅμα. 2211] (Ἐπεὶ δὲ πᾶσα μεταβολὴ ἐν τοῖς ἀντικειμένοις, A τὰ δὲ ἀντικείμενα τά τε ἐναντία Kal τὰ κατὰ ἀντίφασιν, ἀντιφάσεως δ᾽ οὐδὲν ava μέσον, φανερὸν ὅτι ἐν τοῖς ἐναντίοις ἔσται TO μεταξύ.) ὅρου μεταξὺ δέ, εἰς ὃ πέφυκε πρότερον" ἀφικνεῖσθαι 2 τὸ μεταβάλλον ἢ εἰς ὃ ἔσχατον μεταβάλλει κατὰ φύσιν συνεχῶς μεταβάλλον. ἐν ἐλαχίστοις δ᾽ ἐστὶν τὸ μεταξὺ τρισίν: ἔσχατον μὲν γάρ ἐστι τῆς μεταβολῆς τὸ ἐναντίον, συνεχῶς δὲ κινεῖται τὸ μηθὲν ἢ ὅτι ὀλίγιστον διαλεῖπον τοῦ πράγματος --μὴ τοῦ χρόνου (οὐδὲν γὰρ κωλύει διαλείποντα, \ so καὶ εὐθὺς δὲ μετὰ τὴν ὑπάτην φθέγξασθαι τὴν νεάτην) ἀλλὰ τοῦ πράγματος--ν ᾧ κινεῖται. τοῦτο δὲ ἔν τε ταῖς κατὰ τόπον καὶ ἐν ταῖς ἄλλαις μεταβολαῖς φανερόν. ἐναντίον δὲ κατὰ τόπον τὸ 1 [This sentence stands here in Themistius. It is clearly out of place in the mss. (here and at Met. 1069 a 2) after ἅπτηται in 227 aT. Prantl proposed to place it after φανερόν 226 b 32. The logic would be improved by also transposing the next sentences thus: ἐν ἐλαχίστοις δ᾽ ἐστὶν τὸ μεταξὺ τρισίν" ἔσχατον μὲν γάρ ἐστι τῆς μεταβολῆς τὸ ἐναντίον, μεταξὺ δέ, εἰς ὃ.. συνεχῶς μεταβάλλον. συνεχῶς δὲ κινεῖται, κτλ. But Themistius does not support this.—C.] 3 a Them. 172. 24, Met. 1068 Ὁ 28: πρῶτον codd.
« α [ἔσχατον μὲν γάρ xrr.. Literally, ‘for extreme (as used in the above definition) means the contrary, in a process of change.’—C. ] > Colour, for instance, or pitch, not necessarily ‘ dis- tance.’ The meaning of the qualification ‘only the mini- mum’ has perplexed the commentators, but it is shown at 239 a 20 that there is no minimum of anything continuous, and therefore no break (however small) would be the minimum in a continuous thing. So the definition resolves itself into ‘no break.’
¢ (Literally, ‘For there is nothing to prevent one from 86 PHYSICS, V. m1.
They ‘touch’ each other when their extremes are in this sense ‘ together.’
Since all change is between opposites, and opposites are either contraries or contradictories, and there is nothing between contradictories, it is clear that the intermediate or ἡ between ’ can only exist when there are two contraries. B is ‘ between’ A and C if any- thing passing (locally or otherwise) by a continuous change in accordance with its nature must necessarily come to B before it reaches the extreme C on its way thereto from A. ‘Between’ implies at least three terms: the ‘ whence’ of the passing, the opposite of the whence, namely the ‘ whither,’ and something on the line of passage, nearer to the whence than the whither is *; and the passage is ‘continuous’ if there is no break or leap in the course—or, if any, only the minimum. I am speaking of a break not in time, but in that with respect to which the changing thing is changing ὃ; for in time the bottom note of the dia- pason may be followed by the top note (which consti- tutes the maximum possible break or leap in the scale) just as immediately as any two notes severed by the smallest conceivable interval.¢ All which applies not only to changes of place but the other kinds of change as well. In the local application of the word, one thing is the ‘ contrary ἡ of another, if it is farther from it, in a straight line, than any other individual thing leaving a gap (in time, and yet covering the whole course “ὁ continuously,” 6.0. a man walking from London to Cambridge may stop a night at Hitchin and yet cover every yard of the road), and, on the other hand, the highest note can be sounded by a player immediately after the lowest’ (but then, though there is no gap in time, he will not have covered the musical interval ‘continuously.’ So continuity of time does not involve continuity in the change. Cf.
ARISTOTLE 226 "κατ᾽ εὐθεῖαν ἀπέχον πλεῖστον: ἡ γὰρ ἐλαχίστη / πεπέρανται, μέτρον δὲ TO πεπερασμένον. ἧς e a 7 a\ 35 ᾿Εφεξῆς δὲ οὗ μετὰ τὴν ἀρχὴν ὄντος ἢ θέσει 7 227 εἴδει ἢ ἄλλῳ τινὶ οὕτως ἀφορισθέντος μηδὲν μεταξύ ἐστι τῶν ἐν ταὐτῷ γένει καὶ οὗ ἐφεξῆς ἐστιν (λέγω δ᾽ οἷον γραμμὴ γραμμῆς ἢ γραμμαί, ἢ μονάδος s a\ / an δου >, ᾿ χλλ ὃ᾽ δὲ μονὰς ἢ μονάδες, ἢ οἰκίας οἰκία: ἄλλο οὐδὲν κωλύει μεταξὺ εἶναι). τὸ yap ἐφεξῆς τινὶ ἐφεξῆς, ὅ καὶ ὕστερόν τι" οὐ γὰρ τὸ ἕν ἐφεξῆς τῶν δύο, οὐ ἡ νουμηνία τῆς δευτέρας ἐφεξῆς, ἀλλὰ ταῦτ ἐκείνων. ᾿Εχόμενον δὲ ὃ ἂν ἐφεξῆς ὃν ἅπτηται. 10 Τὸ δὲ συνεχὲς ἔστι μὲν ὅπερ ἐχόμενόν τι" λέγω \ δ᾽ εἶναι συνεχὲς ὅταν ταὐτὸ γένηται καὶ ἕν τὸ ἑκατέρου πέρας οἷς ἅπτονται Kal (ὥσπερ σημαίνει τοὔνομα) συνέχηται: τοῦτο δὲ οὐχ οἷόν τε δυοῖν ὄντοιν εἶναι τοῖν ἐσχάτοιν. τούτου δὲ διωρισμένου on φανερὸν ὅτι ἐν τούτοις ἐστὶ τὸ συνεχὲς ἐξ ὧν ἕν τι πέφυκε͵ γίγνεσθαι κατὰ τὴν σύναψιν. καὶ ὥς + [τινὶ all mss. here. At Jet. 1068 Ὁ 835 A>-has τινὶ, the rest τινὸς —C.]
“ “ [The rendering ‘contiguous ’ is justified because ‘ in no passage other than the present is there any attempt to dis- tinguish ἐχόμενον from ἁπτόμενον, Ross on Met. 1068 Ὁ 26- > Cf. continent =continuous land unparted by sea, a ‘continent ’ person, one who can ‘hold himself together.’ In Greek and Latin the etymological implication of the phrase is more general and obvious than in English.
PHYSICS, V. uu.
of the same order in the field under consideration. The straight line is chosen because, as the shortest, it is the only definite one between any two positions, and a measure or standard must be definite.
One thing is ‘ next in succession’ to another if it comes after the point you start from in an order deter- mined by position, or ᾿ form,’ or whatsoever it may be, and if there is nothing of its own kind between it and that to which it is said to be next in succession. (By ‘nothing of its own kind ’ I mean, for instance, that there must be no other line or lines between one line and the line to which it is next in succession; or no monad or monads, or no house or houses, between the one next in succession and the one it is next in succession to, But there is nothing against a thing being said to be next in succession to another because things of a different kind to themselves intervene between them.) For what is next in succession must succeed something and be a thing that comes later; for no one would say that “ one’ comes next in suc- cession to ‘two,’ or the first of the month to the second, but the other way round.
‘ Contiguous’* means next in succession and touching.
Lastly, the ‘ contsnwous’ is a subdivision of the contiguous; for I mean by one thing being continuous with another that those limiting extremes of the two things in virtue of which they touch each other be- come one and the same thing, and (as the very name indicates) are ‘ held together,’ ὃ which can only be if the two limits do not remain two but become one and the same. From this definition it is evident that continuity is possible in the case of such things as can, in virtue of their natural constitution, 39 ARISTOTLE 221 ἃ ΤΟΤΕ γίγνεται TO συνέχον EV, OUTW καὶ TO ὅλον ha at / N ε a ON 7 ἔσται ἕν, οἷον ἢ γόμφῳ ἢ κόλλῃ ἢ ἀφῇ ἢ προσφύσει. Φανερὸν δὲ καὶ ὅτι πρῶτον τὸ ἐφεξῆς ἐστιν. τὸ μὲν γὰρ ἁπτόμενον ἐφεξῆς ἀνάγκη εἶναι, τὸ δ᾽ 20 ἐφεξῆς od πᾶν ἅπτεσθαι (διὸ καὶ ἐν προτέροις τῷ λόγῳ τὸ ἐφεξῆς ἔστι, οἷον ἐν ἀριθμοῖς, ἁφὴ ὃ οὐκ ἔστιν). Kal εἰ μὲν συνεχές, ἀνάγκη ἅπτεσθαι, εἰ δὲ ἅπτεται, οὔπω συνεχές" od yap ἀνάγκη ἕν iA εἶναι αὐτῶν τὰ ἄκρα, εἰ ἅμα elev, ἀλλ᾽ εἰ ἕν, ἀνάγκη καὶ ἅμα. ὥστε ἡ σύμφυσις ὑστάτη κατὰ 3 as τὴν γένεσιν: ἀνάγκη γὰρ ἅψασθαι, εἰ συμφύσεται 3 co) / τὰ ἄκρα: Ta δὲ ἁπτόμενα οὐ πάντα συμπέφυκεν, ἐν οἷς δὲ μὴ ἔστιν ἁφή, δῆλον ὅτι οὐκ ἔστιν οὐδὲ σύμφυσις ἐν τούτοις. Qor’ εἰ ἔστι στιγμὴ καὶ μονὰς οἵας λέγουσι κεχω- ρισμένας, ody οἷόν τε εἶναι μονάδα καὶ στιγμὴν τὸ αὐτό: ταῖς μὲν γὰρ ὑπάρχει τὸ ἅπτεσθαι, ταῖς δὲ δι A ~ μονάσι τὸ ἐφεξῆς. καὶ τῶν μὲν ἐνδέχεται εἶναί τι « Cf. Vol. I. Introd. p. 1. The more general and abstract has the rational priority, but the more concrete and particular the experiential priority. Abstract numbers are ‘nexts’ to each other (for in the abstract there is not a monad between the monad and the dyad, or between the two monads of the dyad), but abstract numbers must be spaced and cannot touch one another.
> [Aristotle here draws a controversial conclusion against those Pythagoreans who identified the monads of which numbers are composed with points, existing in space, of which bodies are composed, and interpreted ‘ All things (bodies) are numbers’ in this literal sense. (See Met. 1080 b 16 and Ross ad loc.)—C.]
¢ [According to Aristotle, two pomts cannot touch each other without coinciding; but he may be thinking of the’ Pythagorean ° points,’ which had (indivisible) magnitude and 40 PHYSICS, V. 11.
become one by touching; and the whole will have the same sort of union as that which holds it together, e.g. by rivet or glue or contact or organic union.
It is further evident that of these terms—‘ next-in- succession, ‘contiguous,’ ‘ continuous —‘ next in succession ’ is the first in logical order. For things that touch each other must be nexts-in-succession, but nexts-in-succession need not be touching; and accordingly ‘next-in-succession’ is a property of things of a higher order of abstraction, such as num- bers, where there is no question of contact. And again, if things make a continuous whole, there must be touching; but if they touch, it does not follow that they become continuous; for it does not follow that their extremities become identical if they come to- gether, but they must have come together if they have become identical. Thus, genetically, natural coalescence comes last of all; for if the extremities are to coalesce, they must come into contact; but not all extremities that come into mutual contact therefore become identified, while obviously things incapable of touching each other are also incapable of natural coalescence.
It follows that if, as they say, there were such things as sejunct points and monads,® then the point and the monad. could not be identical; for two points could touch each other,° but two monads can only be next- in-succession to each other. And between any two points there can be found intermediate points, for position in space. So far, this argument and the next are ad homines; but that numbers (and hence the units com- posing them) cannot touch is common ground. See the next note.—C. ] 4] ARISTOTLE 227 a μεταξύ (πᾶσα γὰρ γραμμὴ μεταξὺ στιγμῶν), τῶν ὃ οὐκ ἀνάγκη" οὐδὲν γὰρ μεταξὺ δυάδος καὶ μονάδος.
Τί μὲν οὖν ἐστι τὸ ἅμα καὶ χωρίς, καὶ τί τὸ 227b ἅπτεσθαι, Kal Ti TO μεταξὺ καὶ TO ἐφεξῆς, καὶ τί TO ἐχόμενον Kal TO συνεχές, καὶ τοῖς ποίοις ἕκαστον τούτων ὑπάρχει, εἴρηται.
α What is actually in the text is ‘every line lies between two points.” So too ‘there need not be anything between, etc.” The commentators are agreed as to the meaning, but the expression as it stands is strange, not to say perverse.
Aristotle’s logic can be saved by translating: Also there can be something between two points, for every line is between points; but 1t does not follow (that there can be anything) between the monads (units) composing numbers, for between 2 and 1 there is nothing at all.’ Two Pyth- CHAPTER IV ARGUMENT [There are various senses in which a movement or change may be said to have unity (227 Ὁ 3-4).
(1) All changes are generically one, which fall within the same category, or summum genus, of entities (Ὁ 4-6).
(2) All changes are specifically one, which fall within one indivisible species of entity. There are also the intermediate cases of the divisible species which le between the highest genus and the lowest species (Ὁ 6-14).
It might be suggested that specific unity could be claimed Jor any change that returns to its starting-point. But, since a point may do this either by vibrating to and_fro along a straight line or by going round a circle, we should then have to say that vibration and circulation are specifically identical, which they are not. Also it would mean that different modes of covering the same track (such as walking and rolling) would be specifically identical, which they are not. So our requirement that ‘ that in which the change 42 between every two points there is a line,? and in every line there are points; but there can be nothing between two successive numbers, the monad and the dyad for instance.
So now the meaning of ‘ together’ and ‘ apart,’ ‘touching,’ ‘between’ and ‘next-in-succession,’ “con- tiguous ᾿ and ‘ continuous’ has been set forth, and also of what things these several terms can be predicated.
agorean points can indeed (as Aristotle has just said) be in contact, but they can be at the two ends of a line with a row of contiguous points (constituting the Pythagorean line) between them. But the numbers of the series 1, 2, 3, etc. and the units composing these numbers are (according to the Pythagoreans) separated from one another by ‘ nothing’ —a ‘void’ (213 b 28), which cannot be filled by a row of units connecting the numbers or the units.—C.]
CHAPTER IV ARGUMENT (continued) takes place’ must be an indivisible species is to be under- stood as applying both to the track followed and the mode of progression (Ὁ 14-20).
(3) A change has absolute or unqualified unity, when it is one in essence and numerically. The conditions to be satisfied are: (a) that ‘in which’ the change takes place must be an indivisible species, (b) the time occupied must be essentially one and unintermittent, and (c) the thing moved must be essentially one thing (not merely accidentally one, like a man and his colour) and numerically one (not merely specifically one, like two particular instances of the same sort of change) (b 20-228 a 3).
With respect to this last condition difficulties might be raised. Suppose one and the same individual repeatedly under- goes a change that is specifically the same. Is the change then one and the same? Only if we admit that one and the same thing can exist, cease to exist, and then exist again (a 3-6).
43 ARISTOTLE ARGUMENT (continued) Another problem: According to the doctrine of Flua, my body (the subject of changes of state and affections) is itself becoming different at every moment. Can its state of health, then, be one and the same from dawn till now? If so, why not say that my state of health which I had and lost is one and the same as my state of health which I now have? Here we must distinguish. (a) If we accept the Flux doctrine, all the states of the changing body must be numerically different at different moments; but (Ὁ) if a state (and a fortiori its subject) can remain one and the same for a stretch of time (e.g. from dawn till now), then there can be two numerically different actualities of the same potentiality in the same subject (two actual states of health) separated by an interval, and we need not say that these are one and the same. Or we might say they are one and the same, if it is possible to hold that one and the same thing can exist, cease to exist, 227bs Mia δὲ κίνησις λέγεται πολλαχῶς" τὸ yap ἕν πολλαχῶς λέγομεν. Γένει μὲν οὖν μία κατὰ τὰ σχήματα τῆς κατη- δ γορίας ἐστίν: φορὰ μὲν γὰρ πάσῃ φορᾷ τῷ γένει ία, ἀλλοίωσις δὲ φορᾶς ἑτέρα τῷ γένει. Hider δὲ μία, ὅταν τῷ γένει μία οὖσα καὶ ἐν ἀτόμῳ εἴδει ἧ. ᾿'οῖον χρώματος μέν εἰσι διαφοραί: a aa clumsiness and repetitions of the following sentences could be remedied by transposing λευκότητος δ᾽ οὐκέτι and reading ἁπλῶς for τῷ (πῶς H: πως Simplic. 882. 22) in 1. 11 as follows: οἷον χρώματος μέν εἰσι διαφοραί---τοιγαροῦν ἄλλη τῷ εἴδει μέλανσις καὶ λεύκανσις---(λευκότητος δ᾽ οὐκέτὼ. πᾶσα οὖν λεύκανσις πάσῃ λευκάνσει ἡ αὐτὴ κατ' εἶδος ἔσται, καὶ πᾶσα μέλανσις μελάνσει. διὸ ἁπλῶς εἴδει μία λεύκανσις λευκάνσει πάσῃ, εἰ δ᾽ ἔστιν ἄτθ᾽ κτλ, * For instance, “colour ᾽ has specific differences (¢.g. black and white)—accordingly, the processes of blackening and whitening are specifically different—but ‘whiteness’ has not; so every case of whitening or of blackening is specifically the same as every other. Hence absolute specific unity will subsist between every whitening 44 PHYSICS, V. τν.
ARGUMENT (continued) and exist again. These difficulties are, however, outside our scope (a 6-20).
In order to be ‘ one’ absolutely, a change must have con- tinuity. This means that there must be no shift from a change of one specific kind to a change of another kind and no intervals of rest in the time occupied (a 20-b 11).
(4) By the unity of a motion we sometimes mean that it is complete (b 11-15).
(5) Another meaning of unity is uniformity. Uniformity or its opposite is found in changes of every kind, in respect of their path, time, goal, and manner (quick and slow). Any movement that is one and continuous can be either uniform or not. But amovement composed of two specifically different movements cannot be uniform. Therefore such movements cannot be one and continuous (b 15-229 a 6). ‘ One single movement,’ or “ change ’ is an ambiguous term, because ἡ oneness’ itself has a variety of mean- ings.
(1) Changes are of one kind generically when they fall within the same category of existence; thus, every kind of local movement, or change as to place, is generically one with every other; but a change of quality would differ from it generically.
(2) Changes are of one and the same kind specifi- cally when they are identical both in the genus and in the species speciahssima* to which they belong. Thus, all changes of colour constitute a species α [Or ‘ indivisible species.’ In a Table of Division of a genus into species and subspecies, we arrive finally at a lowest species, which cannot be further subdivided by a ‘snecific difference,’ but is directly predicable of existin individuals, whose ‘ form’ or ‘ essence’ it constitutes.—C. and every other; but, since certain terms are both genera and species, clearly the changes in such cases will specifically identical in a sense, but not absolutely.—C.]
AS 10 15 20 ARISTOTLE τοιγαροῦν ἄλλη τῷ εἴδει μέλανσις καὶ λεύκανσις" πᾶσα δ᾽ οὖν' λεύκανσις πάσῃ λευκάνσει ἡ αὐτὴ κατ᾽ εἶδος ἔσται, καὶ πᾶσα μέλανσις μελάνσει. λευκότητος δ᾽ οὐκέτι" διὸ τῷ εἴδει pia λεύκανσις λευκάνσει πάσῃ. εἰ δ᾽ ἔστιν ἄτθ᾽ ἃ καὶ γένη ἅμα καὶ εἴδη ἐστίν, δῆλον ὡς ἔστιν ὡς εἴδει μία ἔσται, ἁπλῶς δὲ μία εἴδει οὔ: οἷον ἡ μάθησις, εἰ ἡ ἐπιστήμη εἶδος μὲν ὑπολήψεως γένος δὲ τῶν ἐπιστημῶν.
Απορήσειε δ᾽ ἄν τις εἶ εἴδει μία κίνησις, ὅταν ἐκ τοῦ αὐτοῦ τὸ αὐτὸ εἰς τὸ αὐτὸ μεταβάλλῃ (οἷον ἡ μία στιγμὴ ἐκ τοῦδε τοῦ τόπου εἰς τόνδε τὸν τόπον πάλιν καὶ πάλι): εἰ δὲ τοῦτ᾽, ἔσται ἡ κυκλοφορία τῇ εὐθυφορίᾳ ἡ αὐτή, καὶ ἡ κύλισις ὃ τῇ βαδίσει. ἣ διώρισται, TO ἐν @ ἂν ἕτερον ἢ τῷ εἴδει, OTL ἑτέρα κίνησις" TO δὲ περιφερὲς TOD εὐθέος ἕτερον τῷ εἴδει. Γένει μὲν οὖν καὶ εἴδει κίνησις μία οὕτως"