κατὰ τὴν ἀναλογίαν τοῦ ἐμποδίζοντος σώματος. ἔστω γὰρ τὸ μὲν B ὕδωρ, τὸ δὲ ἃ ἀήρ' ὅσῳ δὴ λεπτότερον ἀὴρ ὕδατος καὶ ἀσωματώτερον, τοσούτῳ θᾶττον τὸ A διὰ τοῦ A οἰσθήσεται ἢ διὰ τοῦ Β. ἐχέτω δὴ τὸν αὐτὸν λόγον ὅνπερ διέστηκεν ἀὴρ πρὸς ὕδωρ, τὸ τάχος πρὸς τὸ τάχος. ὥστ᾽ εἰ διπλασίως λεπτόν, ἐν διπλασίῳ χρόνῳ τὴν τὸ Β δέεισιν ἢ τὴν τὸ A, καὶ ἔσται 6 ef ᾧ Τ' χρόνος δυπλάσιος τοῦ ἐφ᾽ ᾧ E. καὶ ἀεὶ δὴ ὅσῳ ἂν ἢ ἀσωματώτερον καὶ ἧττον ἐμποδιστικὸν καὶ εὐ- διαιρετώτερον δι᾽ οὗ φέρεται, θᾶττον οἰσθήσεται. Τὸ δὲ κενὸν οὐδένα ἔχει λόγον ᾧ ὑπερέχεται ὑπὸ τοῦ σώματος, ὥσπερ οὐδὲ τὸ μηδὲν πρὸς ἀριθμόν. εἰ γὰρ τὰ τέτταρα τῶν τριῶν ὑπερέχει ἑνί, πλείονι δὲ τοῖν δυοῖν, καὶ ἔτι πλείονι τοῦ ἑνὸς ἢ τοῖν δυοῖν, τοῦ δὲ; μηδενὸς οὐκέτι ἔχει λόγον ᾧ ὑπερέχει" ἀνάγκη γὰρ τὸ ὑπερέχον διαιρεῖσθαι εἴς τε τὴν ὑπεροχὴν καὶ τὸ ὑπερεχόμενον, ὥστε ἔσται τὰ τέτταρα ὅσῳ τε ὑπερέχει καὶ οὐδέν (διὸ οὐδὲ γραμμὴ στιγμῆς ὑπερέχει, εἰ μὴ σύγκειται ἐκ στιγμῶν). ὁμοίως δὲ καὶ τὸ κενὸν πρὸς τὸ πλῆρες Σ [δὲ σπι. 1. It is doubtful where the apodosis begins; possbly at 19 ὁμοίως δὲ (δὴ 8), 16 ἀνάγκη...19 ἐκ στιγμῶν eing a parenthesis.—C.]} Es * Tlere and elsewhere J follow the usual custom of simplify- ing the cumbrous mathematical methods often employed by Greek writers, The paraphrase, I trust, accurately repre- sents the reasoning of the original, > And however often you ‘ don’t take any,’ you will never have taken all, whereas if you take some (However little) often enough, you will eventually have taken all, [17 dere ἔσται, κτλ, literally, ‘ conscquently four will have to consist of the amount by which it exceeds (zero, namely 4) and nothing * (but it 1s absurd to speak of ‘nothing’ as a constituent of four).—C.]
PHYSICS, IV. vir.
travelling a given distance through it will be pro- portionately less? ρος, if the media are water and air, the ratio of air’s cleavableness and unsub- stantiality to that of water will give the ratio of the velocity of the passage through air lo that through water.
Velocity in air: velocity in water = Cleavability of air: cleavability of water.
So, if sir is twice as easy to cleave as water, the passage through ar will be twice as swift, and the time taken in covering a given distance half as long in air as in water. According to this universal prineiple, then, the veloety will in every case be greater in proportion to the unsubstantiality and duninished power of impeding and easier cleayability of the medium.
Bul the nonexistent substantiality of vacnity cannot bear any ratio whatever to the substantality of any material substance, any more than zero can bear a ratio to a number. For if we divide a constant quantity ¢ (that which exceeds) into two variable parts, a (the excess) and ὁ (the exceeded), then, as a increases, 6 will decrease and the ratio a: 6 will increase; but when the whole of ¢ is in section ἃ there will be none of ¢ for section 6; and it is absurd to speak of ‘none of σ᾽ as ‘a part of ο᾽ So the ratio a:b will cease to exist, because b has ceased to exist and only a 1s left, and there is no proportion between something and nothing.» (And in the same way there js no such thing as the proportion between a line and a poiut, because, since a point is no part of a line, taking a point is not taking any of the line.) And in like manner there is not any ratio that can ᾿ ARISTOTLE ᾿ ARISTOTLE 216} οὐδένα οἷόν τε ἔχειν λόγον’ ὥστ᾽ οὐδὲ THY κίνησιν, ἀλλ᾽ εἰ διὰ τοῦ λεπτοτάτου ἐν τοσῳδὲ τὴν τοσήνδε φέρεται, διὰ τοῦ κενοῦ παντὸς ὑπερβάλλει λόγου. "Ἔστω γὰρ τὸ Z κενόν, ἴσον δὲ τῷ μεγέθει τοῖς Β καὶ A. τὸ δὴ A εἰ δίεισι καὶ κινηθήσεται ἐν 48 τινὶ μὲν χρόνῳ, τῷ ἐφ᾽ οὗ Ἡ, ἐν ἐλάττονι δὲ ἢ τῷ ἐφ᾽ οὗ ἸΏ, τοῦτον ἕξει τὸν λόγον τὸ κενὸν πρὸς τὸ πλῆρες. ἀλλ᾽ ἐν τοσούτῳ χρόνῳ ὅσος ἐφ᾽ οὗ τὸ H, τοῦ ἃ τὸ A δίεισι τὴν τὸ ©, δίεισι δέ γε κἂν ἦ τι fot: a λεπτότητι διαφέρον τοῦ ἀέρος ἐφ᾽ ᾧ τὸ Z, ταύτην τὴν ἀναλογίαν ἣν ἔχει 6 χρόνος ἐφ᾽ ᾧ E πρὸς τὸν wep ᾧ H, ἂν γὰρ ἢ τοσούτῳ λεπτότερον τὸ ἐφ᾽ ᾧ 2 σῶμα τοῦ A, ὅσῳ ὑπερέχει τὸ Ἐὶ τοῦ H, ἀντεστραμ.- a > a 26a μένως δίεισι TH τάχει ἐν TH τοσούτῳ, ὅσον τὸ H, τὴν τὰ L τὸ ἐφ᾽ οὗ A, ἐὰν φέρηται, ἐὰν τοίνυν μηδὲν ἦ σῶμα ἐν τῷ Z, ἔτι θᾶττον. ἀλλ᾽ ἦν ἐν τῷ Ἡ, ΜῊ + aoe 4 », δί λῇ Fd bal Y ͵ ὥστ᾽ ἐν ἴσῳ χρόνῳ δίεισι πλῆρές τε ὃν καὶ κενόν. ἀλλ᾽ ἀδύνατον. φανερὸν τοίνυν ὅτι, εἰ ἔστι τις χρόνος ἐν ᾧ τοῦ κενοῦ ὁτιοῦν οἰσθήσεται, συμ- βήσεται τοῦτο τὸ ἀδύνατον" ἐν low yap ληφθήσεται MM 4 Wo4 i. " / Ug i πλῆρές τε Ov! διεξιέναι τι καὶ κενόν' ἔσται γάρ τι ἀνάλογον σῶμα ἕτερον πρὸς ἕτερον ws χρόνος πρὸς χρόνον.
PHYSICS, IV. vit.
express the excess of the resistance of a plenum over that of a vacuum, or of the consequential velocity in the vacuum over that in the plenum; but if movement through the finest medium covers a given distance in a given time, movement through the void is out of all proportion.
Vor if we take D, and D, to represent the densities of any two media, and Τὶ and T, to repiesent the length of time occupied by a body under otherwise similar conditions in passing through equal spaces in the respective media, then if there be any proportion that expresses the ratio of the velocity through vacancy, let it be that which covers the constant distance in 'T,, less than T, but standing 10 it in a certain ratio. Now take a medium with a density D, that stands to D, in the inverse proportion of T, to T, Dy: Dy T,: Ts Dy: Dy T,: Ts T, will represent the time taken to traverse the constant distance through the medium of D,. But the time occupied if there were no medium at all should be less than T,, whereas T, was taken as that time itself. Thus a body would pass through a plenum and a vacuum with equal velocity. Which ig impossible. Iividently, then, if any period of time be assigned for the passage of any selected distance you may choose through vacancy, we shal] be landed in this impossible consequence; for the assumption will involve the passage of a body through a material medium ard through vacancy at the same velocity, since one may always take a medium whose density bears such a proportion to that of a sLandard medium as will correspond to the proportion of the supposed transit through vacancy to that of the standard transit.
ARISTOTLE ea Ὡς δ᾽ ἐν κεφαλαίῳ εἰπεῖν, δῆλον τὸ τοῦ συμ- βαίνοντος αἴτιον, ὅτι κινήσεως μὲν πρὸς κίγησιν WW πάσης ἔστι λόγος (ἐν χρόνῳ γάρ ἐστι, χρόνου δὲ παντὸς ἔστι πρὸς χρόνον, πεπερασμένων ἀμφοῖν), κενοῦ δὲ πρὸς πλῆρες οὐκ ἔστιν.
Ἢ μὲν οὖν διαφέρουσι δι’ ὧν φέρονται, ταῦτα συμβαίνει, κατὰ δὲ τὴν τῶν φερομένων ὑπεροχὴν τάδε' ὁρῶμεν γὰρ τὰ μείζω ῥοπὴν ἔχοντα ἢ βάρους ἢ κουφότητος (ἐὰν τἄλλα ὁμοίως ἔχῃ τοῖς σχήμασι) θᾶττον φερόμενα τὸ ἴσον χωρίον καὶ κατὰ λόγον ὃν ἔχουσι τὰ μεγέθη πρὸς ἄλληλα. ὥστε καὶ διὰ τοῦ κενοῦ. ἀλλ᾽ ἀδύνατον: διὰ τίνα γὰρ αἰτίαν οἰσθήσεται θᾶττον; ἐν μὲν γὰρ τοῖς πλήρεσιν ἐξ ἀνάγκης" θᾶττον yap διαιρεῖ τῇ ἰσχύι τὸ μεῖζον: 7) γὰρ σχήματι διαιρεῖ, ἢ ῥοπῇ ἣν ἔχει τὸ φερόμενον ἢ τὸ ἀφεθέν. ἰσοταχῆ ἄρα πάντ᾽ ἔσται. ἀλλ᾽ ἀδύνατον.
“Ort μὲν οὖν εἰ ἔστι κενόν, συμβαίνει τοὐναντίον ἢ δι’ ὃ κατασκευάζουσιν οἱ φάσκοντες εἶναι κενόν, φανερὸν ἐκ τῶν εἰρημένων.
4“ The word ῥοπή is diffienlt to translate without giving Aristotle credit for a closer approach to the conceptions of modern science than would be justified; for‘ vrtual velocity ἡ is the term we should use to express the thrust or pressure by which the falling stone makes its way downwards through the water or a rising bubble upwards through it, and Aris- totle had no such precise conception of the phenomenon as would be imphed in these words. He uses ῥοπή pretty much as ἃ term applicable alike to the downward trend of a body heavicr than its medium and to the upward trend of one lighter. Aquinas scems to me entirely correct in explaining that this greater ῥοπή may be due either to the greater size of the one body if they are of the same texture or to its greater ravity or levity if they arc of the same size. On the radical allacies of this whole section consult page Ixiv.
ὁ [tis tantalizing to find Aristotle actually arrivipg at the fact, familiar in modern laboratories, that a feather and a ἜΝ δι 2 5» PHYSICS, IV. vin.
To sum up. The principle that leads to our con- clusion is that there must always be a ratio between any two velocities (for they are both measured by time, and between two determinate periods of time there inast be ratio): but there is no such ratio of densities between vacancy and any kind of fullness.
This is haw velocities are affected by the media through which the movement takes place. But (2) as to differences that depend on the moving bodies themselves, we see that of two bodies of similar fonnation the one that has the stronger trend @ downward by weight or upward by buoyancy, as the case may be, will be carried more quickly than the other through a given space in proportion ta the greater strength of this trend. And this should hold in vacancy as elsewhere. But it cannot; for what reason can be assizned for this greater velocity? If the passage is through a medium, there must be such a difference; for when there is anything there to cleave, the body superior in force of its thrust will necessarily cleave the medium faster, since either its more suitable shape or the natural thrust it exercises, whether following its natural movement or being thrown, makes it cleave the better. Where there is nothing to cleave, therefore, all bodies will move at the same velocity; which is impossible” It is obvious, then, that the hypothesis of ‘ the void ’ leads to conclusions the precise opposite of those in support of which it was invented by its advocates. guinea, to take the classical example, will fall at the same pace through a vacuum, but treating it as a reductio ad absurdum, — |'Vhis truth was divined, without experiment, hy Epicurus, Ly. 1. 61 ἰσοταχεῖς ἀναγκαῖον ras ἀτόμους εἶναι, ὅταν διὰ rot κενοῦ εἰσφέρωνται μηθενὸς ἀντικόπτοντος, Cf. Luer. ii.
ARISTOTLE ARISTOTLE 26a Οἱ μὲν οὖν οἴονται τὸ κενὸν εἶναι, εἴπερ ἔσται ἡ κατὰ τόπον κίνησις, ἀποκεκριμένον καθ᾽ αὑτό" 46 τοῦτο δὲ ταὐτόν ἐστι τῷ τὸν τόπον φάναι εἷναΐ τι κεχωρισμένον: τοῦτο δ᾽ ὅτι ἀδύνατον, εἴρηται πρότερον. καὶ καθ᾽ αὐτὸ δὲ σκοποῦσι φανείη ἂν A λ, ‘ e ir θῶς / Lia 4 τὸ λεγόμενον κενὸν ὡς ἀληθῶς κενόν. ὥσπερ yap ἐὰν ἐν ὕδατι τιθῇ τις κύβον, ἐκστήσεται τοσοῦτον ὕδωρ ὅσος 6 κύβος, οὕτω καὶ ἐν ἀέρι" ἀλλὰ τῇ 80 αἰσθήσει ὄδηλον. καὶ ἀεὶ δὴ ἐν παντὲ σώματι ἔχοντι μετάστασιν, ἐφ᾽ ὃ πέφυκε μεθίστασθαι ἀνάγκη (ἂν μὴ συμπιλῆτα!) μεθίστασθαι, ἢ κάτω ee > / ς x ν ~ bal Mu » a ay det, εἰ κάτω ἡ φορὰ ὥσπερ γῆς, ἢ ἄνω, εἰ πῦρ, ἢ én’ ἄμφω, ἢ" ὁποῖον ἄν τι ἦ τὸ ἐντιθέμενον. ἐν δὲ ἡ τῷ κενῷ τοῦτο μὲν ἀδύνατον---οὐδὲ yap σῶμα--- a διὰ δὲ τοῦ κύβου τὸ ἴσον διάστημα διεληλυθέναι 316} δόξειεν <ay>* ὅπερ ἦν καὶ πρότερον ἐν τῷ κενῷ, ὥσπερ ἂν εἰ τὸ ὕδωρ μὴ μεθίστατο τῷ ξυλίνῳ κύβῳ μηδ᾽ ὁ ἀὴρ ἀλλὰ πάντῃ διήεσαν δι’ αὐτοῦ. ἀλλὰ μὴν Kat ὁ κύβος ἔχει τοσοῦτον μέγεθος ὅσον KQTEXEL TO KEVOV' O εἰ Και θερμὸν ἢ ψυχρόν ἐστιν 5% βαρὺ ἢ κοῦφον, οὐδὲν ἦττον ἕτερον τῷ εἶναι 1 [ἢ om. Prantl Philop. 665. 1 records the reading ἢ ὁποῖον ἂν τι ἢ, but questions it, adding εἰ δὲ ἔστιν (4 γραφὴ) εὅποι ἂν ἢ, τουτέστιν κτλ.---Ο, PHYSICS, IV. vin.
PHYSICS, IV. vin.
The hypothesis of the void, then, was introduced under the belief that the phenonienon of local mnove- ment involved the reality of self-existing vacancy, which is equivalent to the reality of ‘ space’ sejunct from material content or continent; and this we have already shown to be impossible. But a con- sideration of the question on its own merits will also demonstrate the inanity, in very truth, of this doctrine of the ‘inane,’ For just as a cube displaces its own bulk of water if immersed χη it, so does it also if the medium be air, only that the displacement is not perceptible to the senses. So, whatever the yielding medium may be, it must (unless τῦ condenses) yield in whatever direction is determined by the natural movement of the intrusive body, always making way underneath it if it be earth, above it if it be fire, or below it or above it according as the medium may be lighter or heavier than the moving body.* Now this yielding is impossible in vacuity, which is not a material entity at all, and one must suppose that the dimensionality already there in the place before it was occupied must interpenetrate the equal dimensionality of the in- trusive cube when it enters; just as if the water or air should not make way for the wooden cube but should permeate it ali through. But then the cube itself has its own bulk equal to that of the vacancy that now permeates it, which bulk, whether it be hot or cold or heavy or buoyant, is nevertheless different Lal α Tf the medium be air, for example, it will make way for water on the water’s under side (and well up over it), but to fire on the fire’s upper side, ete.—one way or the other, therefore, as determined by the natural movement of the intrusive body.
ARISTOTLE 216 b πάντων τῶν παθημάτων. eS, Ke Leb μὴ χωριστόν" λέγω δὲ τὸν ὄγκον τοῦ ξυχιους κύβου. ὥστ᾽ εἰ καὶ χωρισθείη τῶν ἄλλων πάντων eset μήτε βαρὺ μήτε κοῦφον εἴη, καθέξει τὸ ἶσον κενὸν καὶ ἐν τῷ αὐτῷ ἔσται τῷ τοῦ τόπου καὶ τῷ τοῦ κενοῦ μέρει 1) ἴσῳ αὐτῷ. τί οὖν διοίσει τὸ τοῦ κύβου, σῶμα τοῦ ἴσου κενοῦ καὶ τόπου; καὶ εἰ δύο τοιαῦτα, διὰ τί οὐ καὶ ὁποσαοῦν ἐν τῷ αὐτῷ ἔσται; ἕν μὲν δὴ τοῦτο ἄτοπον καὶ ἀδύνατον.
Ἔτι δὲ φανερὸν ὅτι τοῦτο ὁ κύβος ἕξει καὶ μεθιστάμενος, ὃ καὶ τὰ ἄλλα σώματα πάντ᾽ ἔχει. ὥστ᾽ εἰ τοῦ τόπου μηδὲν διαφέρει, τί δεῖ ποιεῖν ᾿ὸ τόπον τοῖς σώμασι παρὰ τὸν ἑκάστου ὄγκον, εἰ ἀπαθὲς ὁ ὄγκος; οὐδὲν γὰρ συμβάλλεται, εἰ ἕτερον περὶ αὐτὸν ἴσον διάστημα τοιοῦτον εἴη.
[Ἔτι δεῖ δῆλον εἶναι οἷον κενὸν ἐν τοῖς κινου- μένοις. νῦν δ᾽ οὐδαμοῦ ἐντὸς τοῦ κόσμου' ὄ γὰρ ἀὴρ ἔστι τι, οὐ δοκεῖ δέ γε. οὐδὲ τὸ ὕδωρ, εἰ ἦσαν 80 οὗ ἰχθύες σιδηροῖ: τῇ ἀφῇ “γὰρ ἡ κρίσις τοῦ ἁπτοῦ] Ὅτι μὲν τοίνυν οὐκ ἔστι κεχωρισμένον κενόν, ex τούτων ἐστὶ δῆλον.
* [On this ‘bulk’ as the ‘ matter of growth and diminu~ tion, logically (though not actually) distinguishable from the ‘matter of qualitative chanjre,’ see De gen. et corr, 320 b 16 ff, and Joachim ad loe.—C.]
δ The old commentators add the corollary that, if the dimensions of a body qua dimensions require a place to be in or to go into, so must the dimensions of a vacuum, and so on ad infinituim, “ The bracketed passage (which was unknown to the Greek commentators ns evidently and adinittedly spurious, What it means is that, if fishes were made of iron, they would not be able to feel the water and would be as apt to- equate PHYSICS, IV. vin.
in its nature from all these qualities, even though it may not be separable from them—I mean the bulk, as such, of the wooden cube itself.¢ So that, even if this bulk could be isolated fiom all these other qualities and be neither heavy nor buoyant, τἱ would still embrace an equal measure of vacancy, and would comeide with a portion of ‘space ’ and ‘vacuity’ equal to itself. How, then, would the material bulk of the cube differ from an equal portion of vacancy or space * And if there could be two sueh coincident entities, why not any number you ehoase to name * So this is one paradoxical and absurd implication of the doctrine of the void.
But further the cube in question, if it should shift, will still have its own bulk, just as every other body has, as such. And if this differs in no respect from ‘place,’ why image a place for a body Lo go into in addition to its own bulk. if that bulk as such has no physical properties? For if another equal dimen- sionality were to permeate it, it would make no difference.
[Vurther, vacancy (if it exist) should mamfest its distinctive character amongst the transmutable substances that constitute the realm of nature. But in fact 1t is nowhere to be discovered in the cosmos, For air is substantial, though it does not appcar so, any more than water would to fishes if they were made of iron; for touch is the test of existence for the tangible.]° From albthis it is clear that there is no such thing as a sclf-existing void. water with nothing: as we are to equate air with it. Prantl appositely refers us to the myth in Plato’s Phaedo, 109 ον, 25 ARISTOTLE CHAPTER IX ARGUMENT [Having disposed of the argument that motion requires a void ‘ separate from bodies,’ in and through which bodies may move, Aristotle turns to the supposed necessity of empty interstices inside bodies, unto which they may contract. This internal void had been invoked to account for differences of specific density, of lightness or heaviness, and of hardness or softness, Tt was argued that without it no campression wus possible, and hence either (1) there could be no movement at all, ar (2) movement must cause the whole material universe to bulge, since nothing can contract to make room for tt, or (3) whenever a given amount af air passes into water (with ὦ reduction of volume), @ corresponding amount of water must simultaneously expand, somewhere else, into air The alleged internal void, accounting for tenuity and con- traction, might be conceived in two ways: (a) As sporadic cavities into which particles of the con- tracting body can draw together. But our arguments against self-determined ‘ places’ exclude the ewistence of such‘ voids’ Ψ ἢ rg a A - ~ \ fol Εἰσὶ δέ τινες of διὰ τοῦ μανοῦ καὶ πυκνοῦ οἴονται φανερὸν εἶναι ὅτι ἔστι κενόν. εἰ μὲν yap μὴ ἔστι μανὸν καὶ πυκνόν, οὐδὲ συνιέναι καὶ πιλεῖσθαι οἷόν te εἰ δὲ τοῦτο μὴ εἴη, ἢ ὅλως i? uw ss - A ¢ a μὴ κίνησις οὐκ ἔσται, ἢ κυμανεῖ τὸ ὅλον (ὥσπερ ἔφη “a Lil 2 Ww \ Ξοῦθος), ἢ εἰς ἴσον det’ μεταβάλλειν ἀέρα καὶ 1 [ἀεὶ {δεῖ Bonita, Prantl.—cC.]
4 [A Pythagorean, Diels, Vors. 23.—C.]
PHYSICS, IV. rx.
CHAPTER IX ARGUMENT (continued) (b) As somehow diffused throughout the lenuous substance, In this case its function is changed: it is no longer a vacancy in which movement takes place, but could only account for the rising upward of buoyant things, Rut this is open to the abjection that void cannot move or have a place Since, however, not all movement is re-entrant, contraction and expansion nuust be possible, or one of the three alters natives above stated cannot be eseaped (a 10-20).
The true enplunation is that, gust as the same matter passes from hot to cold without any accession or loss, so the same matter serves fur ὦ large and far @ small body unthout accession or loss, without any need of empty interstices The internal void has been invoked to explain both light~ ness and soft texture. But, if both qualities were due to more void in the body, they ought always to go together, whereas in fact iron is lighter than lead but harder (Ὁ 11-20), Conclusion: the void does not exist, cither as separate from bodies or as involved in tenuous substances (Ὁ 20-28).—C.]
Bur other thinkers hold that it is tenuity and density that prove the existence of the void. Yor they can only be caused by things drawing together and being compressed, which involves the existence of vacant spaces through which their particles can approach or recede from each other. And if there were no such drawing of things together to make room, then either (1)"there would be no movement at all, or (2) the universe would (to use Xuthus’s * expression) be thrust up into a wave, or (3) a balance must always. be preserved, for instance, between the transformation of water into air and air into water.
80 BS ata ARISTOTLE ὕδωρ. λέγω δ᾽ οἷον εἰ ἐξ ὕδατος κυάθου γέγονεν ἀήρ, ἅμα ἐξ ἴσου ἀέρος ὕδωρ τοσοῦτον γεγενῆσθαι, ἢ κενὸν εἶναι ἐξ ἀνάγκης" συμπιλεῖσθαι γὰρ καὶ συνεπεκτείνεσθαι οὐκ ἐνδέχεται ἄλλως.
Εἰ μὲν οὖν τὸ μανὸν λέγουσι τὸ πολλὰ κενὰ κεχωρισμένα ἔχον, φανερὸν ὡς, εἰ μηδὲ κενὸν ἐνδέχεται εἶναι χωριστὸν ὥσπερ μηδὲ τόπον ἔχοντα διάστημα αὑτοῦ, οὐδὲ μανὸν οὕτως Εἰ δὲ μὴ χωριστόν, ἀλλ᾽ ὅμως ἐνεῖναί τι κενόν, ἧττον μὲν ἀδύνατον, συμβαίνει δὲ πρῶτον μὲν οὐ πάσης κινήσεως αἴτιον τὸ κενὸν ἀλλὰ τῆς ἄνω (τὸ γὰρ μανὸν κοῦφον, διὸ καὶ τὸ πῦρ μανὸν εἶναί φασιν)" ἔπειτα κινήσεως αἴτιον οὐχ οὕτω τὸ κενὸν ὡς ἐν ᾧ, ἀλλ᾽ ὥσπερ of ἀσκοὶ τῷ φέρεσθαι αὐτοὶ ἄνω φέρουσι τὸ συνεχές, οὕτω τὸ κενὸν ἀνωφερές. καίτοι πῶς οἷόν τε φορὰν εἶναι κενοῦ ἢ τόπον κενοῦ; κενοῦ γὰρ γίγνεται κενόν, εἰς ὃ φέρεται. ἔτι δὲ πῶς ἐπὶ τοῦ βαρέος ἀποδώσουσι τὸ φέρεσθαι κάτω; καὶ δῆλον ὅτι εἰ ὅσῳ ἂν μανότερον καὶ κενώτερον ἢ ἄνω οἰσθήσεται, εἰ ὅλως εἴη κενόν, τάχιστ᾽ ἂν φέροιτο. ἴσως δὲ καὶ τοῦτ᾽ ἀδύνατον κινηθῆναι: λόγος δ᾽ ὁ αὐτός, ὥσπερ ὅτι ἐν τῷ « [By ‘self-determined (or ‘ separate,’ ef. ἀποκεκριμένον, 217b 20) voids’ Philoponus understands empty interstices occurring here and there in bodies (like pores in a sponge), and large enough for other bodies to move into them; whereas the alternative (4) in the next paragraph he takes to mean: interstices so small and diffused that nothing can intrude (as in a body coniposed of spherical &toms all in contact wilh one another). Alternative (u) professes to explain compression by particles drawing together into the empty pores (still regarding void as that ‘ in which’ move- ment can take place, 21741). Alternative (ὁ), Aristotle says, could profess to explain only movement of buoyancy PELYSICS, IV. rx.
I mean, for example, that if a ecupful of water becomes an, at the same thine a corresponding amount of air must become water, unless there is such a thing as void: for without void nothing can be pressed together or stretched out.
Well, but if (a) they mean by ‘tenuous’ that which has.a great number of self-determined ‘ voids’ # in it, we have only to pomt out that there can be no such things, any more than there can be a‘ place’ with self-determined dimensions. So neither can the tenuous so conceived exist.
But, if (6) they mean that the vacuum is not self- determined, but nevertheless 1s there in the tenuous body, then they are talking more reasonably, But. in the first place, this means that we are no longer speaking of the youl as the condition of all movement, but only of the movement of ascending (for the tenuous is light, which is why tenuity is asenbed to fire); and, in the second place, that we are no lonver supposing it to be the necessary condition of movement as being ‘ that in which the movement takes place,’ but as being the efficient cause of a movement in the eapacity of an ‘ elevator,’ just as bladders elevate whatever is attached to them, But how can a void move or have a place? The void would require another void to move into. Again, how do they account for the downward trend of the weighty? Moreover, if things tend upwards in proportion to their rarity and emptiness, that which is,pure emptiness should move upwards quickest of all. Or perhaps we should say that even this will not do; for the same reasoning which (for nothing can get into these diffused mterstices), and cannot really explain that—C.]
ARISTOTLE 217410 κενῷ ἀκίνητα πάντα, οὕτω καὶ TO κενὸν OTL ἀκίνητον: ἀσύμβλητα γὰρ τὰ τάχη. "Emel δὲ κενὸν μὲν οὔ φαμεν εἶναι, τἄλλα δ᾽ ἠπόρηται ἀληθῶς---ὅτι ἢ κίνησις οὐκ ἔσται, εἰ μὴ ἔσται πύκνωσις καὶ μάνωσις, ἢ κυμανεῖ 6 +, noo. M “ὃ Ω 27 " Yoon οὐρανός, ἢ det ἴσον ὕδωρ ἐξ ἀέρος ἔσται καὶ ἀὴρ na? ἐξ ὕδατος (δῆλον yap ὅτι πλείων ἀὴρ ἐξ ὕδατος 16 γίνεται)---ἀνάγκη τοίνυν, εἰ μὴ ἔστι πίλησις, ἣ ἐξωθούμενον τὸ ἐχόμενον τὸ ἔσχατον κυμαΐίνειν ποιεῖν, ἢ ἄλλοθί που ἴσον μεταβάλλειν ἐξ ἀέρος ὑδ ἵν᾿ ὁ πᾶς ὄγκος τοῦ ὅλου ἴσος ἢ, ἢ ὕδωρ, ἵ πᾶς ὄγκος ἴσος Hs ἢ a x μηδὲν κινεῖσθαι. ἀεὶ yap μεθισταμένου τοῦτο συμ- βήσεται, ἂν μὴ κύκλῳ περιίστηται' οὐκ ἀεὶ ὃ 20 εἰς τὸ κύκλῳ ἡ φορά, ἀλλὰ καὶ εἰς εὐθύ. A A, a Of μὲν δὴ διὰ ταῦτα κενόν τι φαῖεν ἂν εἶναι" ἢ al δὲ λέ 2 ~ e ΓΑ Ψ“ 3 \ ἡμεῖς δὲ λέγομεν ee τῶν ὑποκειμένων ὅτι ἐστὶν ὕλη μία τῶν ἐναντίων (θερμοῦ καὶ ψυχροῦ καὶ τῶν ἄλλων τῶν φυσικῶν ἐναντιώσεων), καὶ ἐκ lj 3 f Ni δυνάμει ὄντος ἐνεργείᾳ ὃν γίνεται, Kal od χωριστὴ a μὲν ἡ ὕλη τῷ δ᾽ εἶναι ἕτερον, Kal μία τῷ ἀριθμῷ (εἰ ἔτυχε) χροιᾶς καὶ θερμοῦ καὶ ψυχροῦ. ἔστι δὲ καὶ σώματος ὕλη καὶ μεγάλου Kale μικροῦ ἡ ® The moving body must thrust out some other body, and the thrust must be passed on till something is thrust up beyond the previous limits of the universe.
PHYSICS, IV. rx.
showed that nothing can move in vacuo would also show that vacuum itself cannot move either, for its velocity would be out of all proportion to that of anything else.
Since, then, we deny the existence of the void and the other alternatives are really exhaustive—namely that, on the supposition of there being no possibility of densification and tenuification, either there can be no movement at all, or else the universe must fluctu- ate, or when water turns into air a corresponding amount of air must change into water (since the bulk of the air is obviously greater than that of the water)— it does follow necessarily that, if no condensation has taken place, either the continuously transmitted thrust must cause the boundary of the universe to bulge ἢ or somewhere else an equivalent amount of air must be changed into water so that the whole bulk of the universe shall remain the same, or nothing must move at all. For a choice between these alterna- tives is all that is left when anything occupies a new place otherwise than in a re-entrant cycle; and such movements straight on, and not re-entrant, do actually occur.
Now, whereas our opponents would find in this dilemma a ground for asserting the existence of a void, our own explanation is based on the estab- lished principle that it is the same matter which experiences the contrasted affections of heat and cold and the other physical opposites, passing either way from a potential to an actual affection, never existing in separation from all attributes, but maintaining its identity through the changing modes of its existence —-for instance its colour or its temperature. Similarly the matter of a body may also remain identical when 80 Ὧν 10 ARISTOTLE αὐτή. δῆλον δέ: ὅταν yap ἐξ ὕδατος ἀὴρ γένηται, ἡ αὐτὴ ὕλη οὐ προσλαβοῦσά τι ἄλλο ἐγένετο, ἀλλ᾽ ὃ ἦν δυνάμει, ἐνεργείᾳ ἐγένετο" καὶ πάλιν ὕδωρ ἐξ ἀέρος ὡσαύτως---ὁτὲ μὲν εἰς μέγεθος ee μικρό- τῆτος, ὁτὲ δ᾽ εἰς μικρότητα ἐκ μεγέθους. ‘Onolus τοίνυν κἂν ἀὴρ πολὺς ὧν ἐν ἐλάττονι γίγνηται ὄγκῳ καὶ ἐξ ἐλάττονος μείζων, ἡ δυνάμει οὖσα γίνεται ὕλη ἄμφω. ὥσπερ γὰρ καὶ ἐκ ψυχροῦ θερμὸν καὶ ἐκ θερμοῦ ψυχρὸν ἡ αὐτή, ὅτι ἦν δυνάμει, οὕτω καὶ ἐκ θερμοῦ μᾶλλον θερμόν, οὐδενὸς γενομένου ἐν τῇ ὕλῃ θερμοῦ ὃ οὐκ ἦν θερμὸν ὅτε ἧττον ἣν θερμόν. ὥσπερ γε οὐδ᾽ ἡ τοῦ μείζονος κύκλου περιφέρεια καὶ κυρτότης ἐὰν γίνηται ἐλάττονος κύκλου (ἡ αὐτὴ οὖσα ἢ ἄλλη), ἐν οὐθενὶ ἐγγέγονε τὸ κυρτὸν ὃ Hv οὐ κυρτὸν ἀλλ᾽ εὐθύ--οὐ γὰρ τῷ διαλείπειν τὸ ἧττον ἣ τὸ μᾶλλόν ἐστιν--οὐδ᾽ ἔστι τῆς φλογὸς λαβεῖν τι μέγεθος ἐν ᾧ οὐ καὶ θερμότης καὶ λευκότης ἔνεστιν, οὕτω τοίνυν καὶ ἡ πρότερον θερμότης τῇ ὕστερον. ὥστε καὶ τὸ μέγεθος καὶ ἡ μικρότης τοῦ αἰσθη- τοῦ ὄγκου οὐ προσλαβούσης τι τῆς ὕλης ἐπεκ- τείνεται, GAN’ ὅτι δυνάμει ἐστὶν ἡ ὕλη ἀμφοῖν' 4“ [Or ‘without any part of the matter becoming hot, which (part) was not hot when the whole was less hot.’ Both the original and the increased heat can be equably diffused throughout the whole. We need not suppose that some could part has got warmer.--C,] ε » [τῷ διαλείπειν. The lesser heat iy not to be explained by the failura or omission of heat in some part of the hody, nor the subsequent greater heat by the making up of the omission, No more need change of bulk be explained by addition or subtraction of matter.—C.]
PHYSICS, IV. ix.
it becomes greater or smaller in bulk. This is mani- festly the case; for when water is transformed into air ihe same matter, without taking on anything additional, is transformed from what it was, by passing into the actuahty of that which hefore was only a potentiality to it. And it is just the same when air is transformed into water, the one transition being from smaller to greater bulk, and the other from greater to smaller, And, again on just the same principle, when a greater mass of air contracts into a smaller bulk, or the reverse, it is the same matter which, having the potentiality of cither bulk, realizes one or the other alternatively. Tor just as it is the same matter that passes from cold to hot and from hot to cold, because in either case it was already in potentiality what it now becomes in actuahty, so also the same matter can pass from hot to hotter, without any other hot thing coming into it that was not in it when less hot.¢ Just as, when the circumference and curvature of the greater circle becomes that of a lesser one (whether you regard it as retaining its identity or not), in no part of it does something acquire curvature that was not curved but straight before—for the more or less of things does not come about by discontinuity and interpolation ’—so neither can you find in a flame any tract which is not both hot and bright. It is in this way, then, and not by interpolations, that a former heat becomes subse- quently greater. So, too, the smallness of a physical bulk is not stretched into largeness by the matter of it annexing anything to itself, but is possible because that matter had itself the potentiality of 12 16 25 ARISTOTLE ὥστ᾽ ἐστὶ τὸ αὐτὸ πυκνὸν καὶ μανόν, καὶ μία ὕλη αὐτῶν.
\ Ἔστε δὲ τὸ μὲν πυκνὸν βαρύ, τὸ δὲ μανὸν κοῦφον. δύο yap ἔστιν ἐφ᾽ ἑκατέρου, τοῦ τε πυκνοῦ καὶ τοῦ μανοῦ: τό τε γὰρ βαρὺ καὶ τὸ σκληρὸν πυκνὰ δοκεῖ εἶναι, καὶ τἀναντία μανά, τό τε κοῦφον καὶ τὸ μαλακόν. διαφωνεῖ δὲ τὸ βαρὺ καὶ τὸ σκληρὸν ἐπὶ μολίβδου καὶ σιδήρου. Ἐκ δὴ τῶν εἰρημένων φανερὸν ὡς οὔτ᾽ ἀπο- ᾿ \ uv eal ‘ - ἘΝῚ > lal κεκριμένον κενὸν ἔστιν (οὔθ᾽ ἁπλῶς οὔτ᾽ ἐν τῷ μανῷ) οὔτε δυνάμει, εἰ μή tis βούλεται πάντως καλεῖν κενὸν τὸ αἴτιον τοῦ φέρεσθαι. οὕτω δ᾽ ἡ a 4 a τοῦ βαρέος καὶ κούφου ὕλη, ἧ τοιαύτη, εἴη ἂν τὸ Kevov' TO γὰρ πυκνὸν Kal TO μανὸν κατὰ ταύτην \ τὴν ἐναντίωσιν φορᾶς ποιητικά, κατὰ δὲ τὸ σκληρὸν καὶ μαλακὸν πάθους καὶ ἀπαθείας, καὶ a t a οὐ φορᾶς ἀλλ᾽ ἑτεροιώσεως μᾶλλον. Καὶ περὶ μὲν κενοῦ, πῶς ἔστι καὶ πῶς οὐκ ἔστι, διωρίσθω τὸν τρόπον τοῦτον.
1 [After κοῦφον our mss. read: ἔτι ὥσπερ ἡ τοῦ κύκλου περι- φέρεια συναγομένη εἰς ἔλαττον οὐκ ἄλλο τι λαμβάνει τὸ κοῖλον, GAN ὃ ἣν συνήχθη, καὶ τοῦ πυρὸς ὅ τι ἄν τις λάβῃ πᾶν ἔσται θερμόν, οὕτω καὶ τὸ πᾶν συναγωγῇ καὶ διαστολῇ τῆς αὐτῆς ὕλης. This interpolation, omitted by Themistius, 139, 28, ‘ not in certain copies’ (Simpl. 691. 2), ‘regarded as spurious’ (Philop. 701. 4), is a doublet of the illustrations in the pre- ceding paragraph.—C.]
α (Gf. Joachim on De gen. et corr. p. 124: * We must not think of a dense body as one in which there are few or small ‘“‘ pores,” and of a “ rare” body as one with large or many PHYSICS, IV. ix.
either bulk, So it is the very same thing that is now dense and now tenuous, and the matter of both is identically the same.4 And note that the dense is heavy, and the tennous light. For density and tenuity are accompanied by two characteristics cach, inasmuch as heavy and hard things are held to be dense, and light and soft ones tenuous. But in the case of iron and lead, the superior heaviness does not go with superior hard- ness, Our conclusion is that the void does not exist either in separation (whether considered by itself or as implicated in tenuous substances) or even potentially;¥ unless anyone should choose to call that which causes local movement ‘ vacancy.’ For in that case the material components of the heavy and buoyant would, as such, be vacancy, for the dense and rare under that aspect are the causes of movement, whereas under their aspect of hard and soft they are the cause of readiness or unreadiness to yield, and so of qualitive modification rather than of local movement.
Let this stand then as our conclusion about how the void does or does not exist.
gaps interspacing its corporeal particles. We must rather conceive of ὕλη as a material capable of filling space with all possible degrees of intensity, or capable of expanding and contracting without a break in its continuity.’—C.]} > On the hypothesis that the void receives that which moves into itgind is vacated by that which moves out of it, it will be void in actuality when it is unoceupied, and in potentiality when it is occupied by what may move oul of it. Hence the potentiality of the occupied vacancy is conirasted with the two supposed forms of actual vacancy, namely the vast inane outside the material universe and the interspersed inane amongst its particles, ARISTOTLE CHAPTER X ARGUMENT Difficulties presented by the conception of time. No light on the subject to be found in the speculations of earlier (At thas point Aristotle makes a fresh start, and the remaining portion properly belongs to Chapter XT, the subject being an examination of our general impression that there ig a close connexion betweun time and meoventent or change.)
27h ᾿Εχόμενον δὲ τῶν εἰρημένων ἐστὶν ἐπελθεῖν περὶ χρόνου. πρῶτον δὲ καλῶς ἔχει διαπορῆσαι περὶ αὐτοῦ καὶ διὰ τῶν ἐξωτερικῶν λόγων, πότερον τῶν ὄντων ἐστὶν ἢ τῶν μὴ ὄντων, εἶτα τίς ἡ φύσις αὐτοῦ.
Ὅτι μὲν οὖν ἢ ὅλως οὐκ ἔστιν ἢ μόλις καὶ ἀμυδρῶς, ἐκ τῶνδέ τις ἂν ὑποπτεύσειεν.
Τὸ μὲν γὰρ αὐτοῦ γέγονε καὶ οὐκ ἔστι, τὸ δὲ 518 α μέλλει Kal οὔπω ἔστιν' ἐκ δὲ τούτων Kal ὁ ἄπειρος καὶ ὁ ἀεὶ λαμβανόμενος χρόνος σύγκειται, τὸ δ᾽ ἐκ μὴ ὄντων συγκείμενον ἀδύνατον ἂν εἶναι δόξειε μετέχειν οὐσίας.
Πρὸς δὲ τούτοις παντὸς μεριστοῦ, ἐάνπερ ἢ, υ ἀνάγκη, ὅτε ἔστιν, ἤτοι πάντα τὰ μέρη εἶναι ἢ ἔνια. τοῦ δὲ χρόνου τὰ μὲν γέγονε τὰ δὲ μέλλει, w > Ry hs » ~ ‘ Ν A a: ie ἔστι δ᾽ οὐδέν, ὄντος μεριστοῦ. τὸ δὲ νῦν οὐ μέρος" μετρεῖ τε γὰρ τὸ μέρος, καὶ συγκεῖσθαι δεῖ τὸ PHYSICS, IV. x.
CHAPTER X ARGUMENT (continued) Time is evidently connected with change and movement, but not ulentical with them. It determines ‘ fast’ and ‘ slow’ because it determines in how much of itself a move- ment covers a given distance (which distance is a spatial magnitude), or @ change effects a given qualitive modifica- tion. But it cannot measure utself, for it presents no spatial magnitude and no change of quality for itself to measure Tue subject of inquiry next in succession is ‘ time.’ It will be well to begin with the questions which general reflections suggest as to its existence or non-existence and its nature.
The following considerations might make one suspect either that there is really no such thing as time, or at least that it has only an equivocal and obscure existence.