¢ [Se yap κτλ, is obscure in construction and interpretation. (1) Carteron translates: ‘en effet il faut que le vide soit un lew ot il y ait extension Gun carps tangible.’ (2) Perhaps, ‘for that in which (as in the void) there is extension of tangible body (ae. room, whether empty or full, for an extended body) niust be a place (and a point 19 not a place),’ or (3) ‘ for it (the pomt, if it were a void) must be a place in which there is extension of tangible body (but a point is not that).’—C.]
PHYSICS, IV. vu.
PHYSICS, IV. vu.
To determine whether the void exists or not, we must know what. they who use the word really mean by it.¢ The current answer is, ‘a place in which there is nothing.’ But that is in the mouths of people who consider that. nothing ‘ exists’ except matcrial substances;® so they mean that a body must be in a place, but a place in which there is not a body must be absolutely empty; so that wherever there is not ‘ body’ there is vacancy. Again they regard all corporeal substances as ‘tangible’; and this they regard as identical with ‘ possessed of gravity or levity.” Thus we may logically expand their definition of the void as ‘ that in which there is nothing that is either heavy or buoyant.’ For this, as we have just said, is implicit in their actual words; but no one could suppose them to mean that a point is a void, though it complies with the definition just given, We must add that in defining a void as a place they assign to it dimensionality as of a tangible body.¢ However, this seems to be one conception of the void; ‘ that which is empty of all tangibly perceptible body ᾿---΄ tangibly perceptible’ being equated with ‘ possessed of gravity or levity.’ So. on this line of inquiry, if we go on to ask whether dimensional extension would be empty if it were coloured or sonant, presumably the answer would be, ‘ If it were still capable of receiving corporeal bulk, yes; if otherwise, no.’ ὦ 4 Tf lightand sound can be propagaled over void spaces, are those spaces still empty while they are passing through them? A curious anticipation of the question raised im connexion with the hypothesis of the ὁ wmimferous aether.’ Is the space that only contains the ethereal vibrations that constitute light full or empty? Can it mterpenetrate bodies? Does it pervade infinite space (whatever that means!)? ete, VOL. I Z 337 2tha "Adov δὲ τρόπον, ἐν ᾧ μὴ τόδε τι μηδ᾽ οὐσία τις σωματική. διό φασί τίνες εἶναι τὸ κενὸν τὴν τοῦ σώματος ὕλην, οἵπερ καὶ τὸν “τόπον, τὸ αὐτὸ τοῦτο λέγοντες οὐ καλῶς" ἡ μὲν γὰρ ὕλη οὐ χωριστὴ τῶν πραγμάτων, τὸ δὲ κενὸν ζητοῦσιν ὡς χωριστόν.
᾿Επεὶ δὲ περὶ τόπου διώρισται, καὶ τὸ κενὸν ἀνάγκη τόπον εἶναι (εἰ ἔστιν) € ἐστερημένον σώματος, τόπος δὲ καὶ πῶς ἔστι καὶ πῶς οὐκ ἔστιν εἴρηται, φανερὸν ὅτι οὕτω μὲν κενὸν οὐκ ἔστιν, οὔτε ἀχώριστον οὔτε κεχωρισμένον! τὸ γὰρ κενὸν οὐ σῶμα ἀλλὰ σώματος διάστημα “βούλεται εἶναι, διὸ καὶ τὸ κενὸν δοκεῖ τι εἶναι, ὅτι καὶ 6 τόπος, καὶ διὰ ταὐτά. ἥκει γὰρ δὴ ἡ κίνησις ἡ κατὰ τόπον καὶ τοῖς τὸν τόπον φάσκουσιν εἶναί τι παρὰ τὰ σώματα τὰ ἐμπίπτοντα καὶ τοῖς τὸ κενόν’ αὔτιον δὲ κινήσεως οἴονται εἶναι τὸ κενὸν οὕτως ὡς ἐν ᾧ κινεῖται" τοῦτο δ᾽ ἂν εἴη οἷον τὸν τόπον φασί τινες εἶναι.
* [The identification of matter and space is attributed to Plato, 209 b Lt.—C.]
ὁ It is difficult to be sure what ‘ inseparable ἡ and ‘ separable’ here refer to; and the commentators are not convineing. I take it to mean: ' If we mean hy δ place ” the inner surface of the containing body which is inseparably inherent in that body itself, it is clear that the void cannot be that kind of place. If, on the other hand, we mean the intramural space apart from any body contained, we have seen that neither has that any independent and detachable existence.’ [Aristotle argues: against the existence of (1) a void ‘ separate from hodies,’ in the sense of a spatial frame containing bodies (¢.g. atoms) moving about in it, with empty intervals between them, chap. viil. to 216 ὁ 26; (2) a void occupied by hodies, 216 a 26—b 213 (3) void interstices inside bodies, ehap. ix.—C.| ® Because, as we saw, the dimensions of the retreating PHYSICS, IV. vi.
According to another representation, however, the void is ‘ that in which there is no concrete compositum uniting form and matter, or corporcal entity.’ It is from this point of view that some thinkers regard the void as the ‘ matter’ of corporcal entities, regarding it as identical with ‘ place,’ to which they assign the same role.t But this will not do, for things cannot detach themselves from their matezial, and what the believers in the vord are in quest of is something from which things can separate themselves and come uM ay.
Now since we have already determined the nature of ‘place’ and the way in which it does or does not exist, and since the void (if there is such a thing) must be conceived as place in which there might be body but is not, 1t is clear that, so conceived, the void cannot exist at all, either as inseparable or separable 3% for what is meant by at is not body but the bodiless dimensions of body. So we see that vacuity was supposed to have an independent existence of its own because ‘ place’ was so conceived, and for the same reasons. For those who have given ‘place’ an existence of its own, apart from the corporeally extended bodies that successively occupy it, have done so in view of the phenomenon of local movement,? and so too with vacuity, the essential function assigned to vacuity in this connexion being that of the medium ‘in which’ the inotion takes place, which is just what certain other thinkers would say af space.
body that are inherent in it ure not left behind itas a‘ place ἧς whereas, 1f we suppose il to have dimensions that ean he left behind, we are led into many self-contradietions. Cf p. 309. ἃ Tine’ local movement ὁ resudts” ‘ is obtained.” Bonits (Index, 316 b £4) compares the phrase ὁ αὐτὸς ἥξει A6yos.—C.]
Οὐδεμία δ᾽ ἀνάγκη, εἰ κίνησις ἔστι, εἶναι κενόν, ὅλως μὲν οὖν πάσης κινήσεως οὐδαμῶς, διὸ καὶ Μέλισσον ἔλαθεν: ἀλλοιοῦσθαι γὰρ τὸ πλῆρες ἐνδέχεται. ἀλλὰ δὴ οὐδὲ τὴν κατὰ τόπον κίνησιν’ ἅμα γὰρ ἐνδέχεται ὑπεξιέναι ἀλλήλοις, οὐδενὸς ὄντος διαστήματος χωριστοῦ παρὰ τὰ σώματα τὰ κινούμενα: καὶ τοῦτο δῆλον καὶ ἐν ταῖς τῶν συνεχῶν Sivas, ὥσπερ καὶ ἐν ταῖς τῶν ὑγρῶν.
᾿ἘἘνδέχεται δὲ καὶ πυκνοῦσθαι μὴ εἰς τὸ κενὸν ἀλλὰ διὰ τὸ τὰ ἐνόντα ἐκπυρηνίζειν (οἷον ὕδατος συνθλιβομένου τὸν ἐνόντα ἀέρα), καὶ αὐξάνεσθαι \ οὐ μόνον εἰσιόντος τινὸς ἀλλὰ καὶ ἀλλοιώσει, οἷον εἰ ἐξ ὕδατος γίνοιτο ἀήρ.
6) δὲ ce ol? 2 λό " λως δὲ ὅ τε περὶ τῆς αὐξήσεως λόγος καὶ n 3 εἰ τοῦ εἰς τὴν τέφραν ἐγχεομένου ὕδατος αὐτὸς αὑτὸν ἐμποδίζει. ἢ γὰρ οὐκ αὐξάνεται ὁτιοῦν, ἢ οὐ σώματι, ἢ ἐνδέχεται δύο σώματα ἐν ταὐτῷ * δίνῃ may mean either the revolution of a ring or of a wheel round its centre or the swirl of a vortex within a medium only differentiated from it by not sharing the movement, > One explanation of contraction is given and one of expansion, but both are evidently meaut to apply to both expansions and contractions. The expulsion and intrusion hypothesis is probably introduced with reference to the supposed case of the wine and wine-skins (213 b 16), though we are not told how to apply it. Jn any case it 1s of minor importance. On the other hand, the theory that matter is intiinsically ‘ contractile’ (i.e. capable of, dimensional expansion and contraction while preserving its continuity} is of fundamental importance to <Aristotle’s physical philosophy.
4 In this passage Aristotle shows neither how the dilemma PHYSICS, IV. viz.
But the truth is that the selfexistence of vacuity is not involved in any way whatever in the fact of motion. This needs no proof, if ‘ motion’ be taken as the typical and inclusive expression for every kind of ‘ passing from this to that,’ for a plenum might undergo qualitive modification without the aid of any vacuum—though this obvious fact escaped Melissus. But. further, even for motion in the restricted sense of veetion and rotation vacuity is not necessary; for things can simultaneously give place to each other without there being any intervenient dimensionality sejunct from the moving bodies, as is evident in the case of the rotation of continuously cohcrent bodies aud also in the vortices of liquids through liquids.¢ Nor docs condensation necessarily imply the entrance of particles into vacant dimensional interstices; for we may suppose the condensing body to be squeezing out some foreign substance that it contained, as water for instance when pressed together extrudes the air that is in it. Or we may suppose a body to expand under the imfluence of qualitive modification without anything else entering into it, as in the case of water becoming air.° To put the case more generally, the argumenis derived from the phenomenon of growth or expansion and from the case of the water poured into the ashes, refute themselves by proving too much. For the problem of growth lands us in the dilemma: ὦ Either the,growth does not occur in any and every part of the growing body, or things grow without the access of any corporeal substance, or two bodies rises nor haw it can be solved. But the question is treated at length in De gen. et cor. A δ.
5140 εἶναι (ἀπορίαν οὖν κοινὴν ἀξιοῦσι λύειν, ἀλλ᾽ οὐ κενὸν δεικνύουσιν ὡς ἔστιν), ἢ πᾶν εἶναι ἀναγκαῖον τὸ σῶμα κενόν, εἰ πάντῃ αὐξάνεται καὶ αὐξάνεται 10 διὰ κενοῦ. ὁ δ᾽ αὐτὸς λόγος καὶ ἐπὶ τῆς τέφρας. Ὅτι μὲν οὖν ἐξ ὧν δεικνύουσιν εἷναι τὸ κενὸν λύειν ῥᾷάδιον, φανερόν.
Let us now rehearse our reasons for denying the reality of a self-exsstent and self-constituted ‘ void’ (in the sense of abstract or absolute ‘ space’) such us some thinkers have assumed.
Mere limitless vacancy cannot be, as is alleged, the cause of motion either in the proper sense of vection and rotation or as the type ofall‘ change’ or‘ passing.’ Indeed it 1 only in the narrower sense that anyone makes the claim for it. And in this sense we see that the elementary bodies have each their specific direction (fire‘ up’ from the centre and earth ‘down’ towards the centre, for example) and obviously mere ‘ vacancy’ cannot aiffrrentiate its causal action so as to produce these different effects (214 Ὁ 12-17).
Again, if the void be conceived as the potential recipient of body that lachs the actuality of having received it, then, if we start with it as an undifferentiated emptiness outside all body and with a body that has no differentiated trend, how could there be anywhere in the vacancy to which the body should go rather than anywhere else or rather than remain motionless? For it cannot go into the void every way at The same argument applies to those who allege an unoccupied void not as the cause but the condition of movement, on the ground that a body cannet move into a place except if PHYSICS, IV. vit-—vur.
can occupy the same spacc—our friends, then, are attempting to solve a problem common to us and to them, but they throw no light on the nature of the ‘ vacuity’ they wish to establish—or the whole growing body is vacuity and nothing else, if the body is growing or expanding at every point and can only do so where there is vacuity to grow or expand into. The same argument applics to the ‘ ashes * case. Obviously, then, there is no difficulty in refuting the arguments urged to prove the existence of vacuity.
ARGUMENT (continued) that place be a something which is detached from hody and unoccupied (b 19-22 It is quite natural that the same reasoning should be re~ peated in dealing with the void and with ‘ place’; for it applies to the void, and whenever the champions of the‘ void’ try to define rt, they can only do so by making τὲ (with whatever qualification) a kind of place (b 22-24).
And then how ran any determined or defined place or void be‘ in’ place or void at large? For it is one thing for a given undifferentiated mass to be ‘ in’ a body differentiated from ἐξ that abides unaffected by its departure, and another thing for a given ‘ space’ to be in abstract or undifferentiated “ space.’ This latter could but be‘ in’ aa the part is‘ in’ the whole, not as the content locally‘ in’ « continent differentiated [Void, so far from being necessary to motion, makes motion unpossible (b 28-216 a 1).
The natural motion of the simple bodies is prior to all other motions, but could not uceur in vord (a 1-14), al projectile could not move wn vord (a 14-22).
ARGUMENT (continued) The speed of a mowng body varies erther (1) with the resistance of the medium traversed or (2) with its own weight or lightness. (1) If water offers (say) twice the resistance of air, the times taken to traverse equal distances in water und uir will be as 2 tol. But void offers a zero resistance, Ὅτι δ᾽ οὐκ ἔστι κενὸν οὕτω κεχωρισμένον ὡς ἔνιοί φασι, λέγωμεν πάλιν.
Εἰ yap ἐστιν ἑκάστου φορά τις τῶν ἁπλῶν σωμάτων. φύσει (οἷον τῷ πυρὶ μὲν ἄνω, τῇ δὲ γῇ κάτω καὶ πρὸς τὸ μέσον), δῆλον ὅτι οὐκ ἂν τὸ κενὸν αἴτιον εἴη τῆς φορᾶς. τίνος οὖν αἴτιον ἔσται τὸ κενόν; δοκεῖ γὰρ αἴτιον εἶναι κινήσεως τῆς κατὰ τόπον, ταύτης δ᾽ οὐκ ἔστιν.
"Ἔτι εἰ ἔστι τι οἷον τόπος ἐστερημένος σώματος, ὅταν ἢ κενόν, ποῦ οἰσθήσεται τὸ εἰστεθὲν εἰς αὐτὸ σῶμα; οὐ γὰρ δὴ εἰς ἅπαν. ὁ δ᾽ αὐτὸς λόγος καὶ πρὸς τοὺς τὸν τόπον οἰομένους εἷναί τι κε- χωρισμένον, εἰς ὃν φέρεται: πῶς γὰρ οἰσθήσεται τὸ ἐντεθὲν ἢ μενεῖ; καὶ περὶ τοῦ ἄνω καὶ κάτω καὶ περὶ τοῦ κενοῦ 6 αὐτὸς ἁρμόσει λόγος εἰκότως" α * Return,’ because the treatment of topos has already covered from one point of view what will now he re-investigated from another, namely in relation to motion.
> When you suppose the kenon to be emptiness within a topos, or the fopos itself to be abstract dimensionality, this is to say abstract space; in either case it can exercise no influence on the entrant body to determine its motion or rest. We must remember that our present hypothesis is tat bodies have no inherent trend of their own; but if they had, the direction in which their trend would manifest itself would depend at any moment on the relative gravity or levity of the immediately adjacent material surrounding—a function which yacancy could not perform.
Bd PHYSICS, IV. vit.
ARGUMENT (continued) and shoud be traversed in no time at all (a 24-) 22), Tf it took any time, τέ can be shawn that τὲ would travel through a plenum and a void in the same time; which is absurd (h 22-216 a 11). (2) Ina void all bodies, however hight or heany, would move at the same rate; whieh 18. impossible A void ocenpied by bodies ts superfluous, if we concewe the bulk: of a body us distinct from its qualities (a 28-- 21). --Οἡ Ler us return® to the demonstration that vacuum with the independent existence that some assign to it does not really exist.
For if each of the elementary bodies has a natural trend of its own—fire upwards, and earth downwards and towards the centre—it is clear that vacancy cannot be the cause of these trends. Of what kind of motion-change, then, can it be the cause? For it is just of this local movement that it is supposed to be the cause and that it is not.
Again, if, when there is vacancy, there is something that might be called a place bereft of any niaterial content, whither shall the body placed in it move? Clearly not anywhere-or-everywhere. And the same argument applies to those who hold that ‘ place’ is itself something that exists apart from matter, into which the travelling body is carried. For how can the body placed in it either move or stay still?® And it is nothing astonishing *that the same argument should occur positively with respect to the up-and-downness of place as we conceive it (which makes vacancy superfluous as the condition of movement of the elements) and with reference to the supposed nature of vacancy τὸ yap κενὸν τόπον ποιοῦσιν οἱ εἶναι φάσκοντες. καὶ πῶς δὴ ἐνέσται ἢ ἐν τῷ τόπῳ ἢ ἐν τῷ κενῷ; οὐ γὰρ συμβαίνει, ὅταν ὅλον τεθῇ ὡς ἐν κεχωρι- σμένῳ τόπῳ καὶ ὑπομένοντι σῶμά tu: τὸ γὰρ μέρος ἂν μὴ χωρὶς τιθῆται, οὐκ ἔσται ἐν τόπῳ ἀλλ᾽ ἐν τῷ ὅλῳ. ἔτι εἰ μὴ τόπος, οὐδὲ κενὸν ἔσται.
Συμβαίνει δὲ τοῖς λέγουσιν εἶναι κενὸν ὡς ἀναγ- καῖον, εἴπερ ἔσται κίνησις, τοὐναντίον μᾶλλον, ἄν 1 [σώματι codd. contradicts the assumption above, οἱ ἔστι τι οἷον τόπος ἐστερημένος σώματος, σῶμά τι (as read in the Tauchnitz ed. 1881) can be supported by Simplic. 665, 39 οὐ yap συμβαίνει, τουτέστιν οὐ κατὰ λόγον ἀπαντᾷ, ἂν ἢ ὁ τύπος ὑπομένοισά τις φύσις τριχῇ διαστατὴ καὶ ἐν αὐτῷ ὑποτεθῇ σῶμα, mt...35 ὅταν ὅλον τι σῶμα τεθῇ ἐν τόπῳ, Plulop, 636. 11 οὐ συμβαίνει τοῦτο, ὅταν σῶμά τι ἐν κεχωρισμένῳ καὶ διαστηματικῷ τόπῳ ἐντεθῇ.---Ο] ὶ « We have shown that the vacuum cannot be the cause of the up-and-down motion natural to the several clements, because that is already determined by their relation to the supreme cosmic place and by the nature of the several media in which they may find themselves, causing them to rise through media less buoyant than themselves and to sink through media less dense than themselves but to rest in those of the same gravity as themselves. We are now to prove further that, even if the motion of the natural bodies were not already accounted for without recourse to the idea of vacuity, 1t would still be vain to introduce vacuity as the cause of these movements, For the movements are differentiated from each other and vacancy as such 18 undifferentiated, and if this is nothing hut the same argument taken from the negative side, this is nothing surprising. For those we are arguing against, by defining the kenon as a kind of topos and ie itself as bare dimensionality, reduce topos and kenon to identity.
> For in a vacuum, supposing the body in question to be ‘in’ it as determined or Jocated by it, any portion of that PHYSICS, IV. vir.
itself (which precludes all possibility of its being such a cause in any case); for our adversaries reduce both place and void to mere abstract dimenstonality.¢ And indeed how can anything be i either ‘ place ’ so conceived or void, in the proper local sense of ‘in’? But when (as with us) the place of a body is external to itself and has material existence of its own as its contents come and go, this is not what happens but the parts of it exist in it as pacts exist in the whole, not as the content in the continent.’ Finally, in whatever sense the void is identified with ‘ place,’ when ‘ place’ in that sense is shown not to exist the void vamshes with 1,4 But indeed on reflection we see that the assertion ‘motion is impossible except into vacancy ‘ is not only untrue but the contradiction of the truth, for body would equally be determined by the special space assigned to il and oceupied by it.
¢ This passage is hyhtly passed over by Themistius as identical in purpurt with 21 Ὁ 19 ft. which has already heen dealt with. Phtloponus further remarks on the relative lucidity of this former passage, contrasted with its obscure and truncated form here. [Simplicius, 665. 26, says that οὐ γὰρ συμβαίνει...ἐν τῷ ὅλῳ 15 added in certain cupies after καὶ πῶς δὴ ἐνέσται ἐν τόπῳ (sic) ἣ ἐν τῷ κενῷ τ which would be plain enough without the addition.--C.] I take it to be an interpolation. In any case it is difficult to get any sense out of it and it has no independent value. [Simplicius explains: When a whole body 1s put in a paces it is held that the whole oceupies the place, whereas the parts, 1f continuous, are in that whole which is in a place, but not in a place on their own account unless they are separated from the whole and their continuity with respect to it 1s dissolved, The resulting absurdities are set forth at 211 b 19,—C.]| 4 The boldness of the explanation and general snterpretation of this seclion 1s supporled by all the old commentators, Greek, “Arabic, and mediaeval Latin. Averroes 18 more than usually helpful here.
το τις ἐπισκοπῇ, μὴ ἐνδέχεσθαι μηδὲ ἕν κινεῖσθαι, ἐὰν ἣ κενόν. ὥσπερ γὰρ of διὰ τὸ ὅμοιον φάμενοι τὴν γῆν ἠρεμεῖν, οὕτως καὶ ἐν τῷ κενῷ ἀνάγκη ἠρεμεῖν" οὐ γὰρ ἔστιν οὗ μᾶλλον ἢ ἧττον κινηθήσεται" ἦ γὰρ κενόν, οὐκ ἔχει διαφοράν. Πρῶτον μὲν οὖν ὅτι πᾶσα κίνησις ἢ βίᾳ ἣ κατὰ φύσιν: ἀνάγκη δ᾽, ἄνπερ ἢ βίαιος, εἶναι καὶ τὴν κατὰ φύσιν (ἡ μὲν yap βίαιος παρὰ φύσιν ἐστίν, ἡ δὲ παρὰ φύσιν ὑστέρα τῆς κατὰ φύσω)-: wor εἰ μὴ κατὰ φύσιν ἐστὶν ἑκάστῳ τῶν φυσικῶν σωμάτων κίνησις, οὐδὲ τῶν ἄλλων ἔσται κινήσεων οὐδεμία. ἀλλὰ μὴν φύσει γε πῶς ἔσται μηδεμιᾶς a A \ οὔσης διαφορᾶς κατὰ TO κενὸν Kal τὸ ἄπειρον; μὲν γὰρ ἄπειρον, οὐδὲν ἔσται ἄνω οὐδὲ κάτω οὐδὲ μέσον, 7 δὲ κενόν, οὐδὲν διαφέρει τὸ ἄνω τοῦ a ͵ lq κάτω (ὥσπερ γὰρ τοῦ μηδενὸς οὐδεμία ἔστι διαφορά, οὕτως καὶ τοῦ μὴ ὄντος" τὸ δὲ κενὸν μὴ ὄν τι καὶ στέρησις δοκεῖ elvar): ἡ δὲ φύσει φορὰ Bil διάφορος, ὥστ᾽ ἔσται τὰ φύσει διάφορα. ἢ οὖν οὐκ ἔστι φύσει οὐδαμοῦ οὐδενὶ φορά, ἢ εἰ τοῦτ ἔστιν, οὐκ ἔστι κενόν. "Ere νῦν μὲν κινεῖται τὰ ῥιπτούμενα τοῦ ὥσαντος αἱ 3 οὐχ ἁπτομένου, ἢ δι’ ἀντιπερίστασιν (ὥσπερ ἔνιοί 4 {Anaximander first declared that the earth was freely suspended and was not held in place by anything? but stayed where it was διὰ τὴν ὁμοίαν πάντων ἀπόστασιν, Hippol. Ref. i. 6.3, Aristot. De caegle 295 Ὁ 11 διὰ τὴν ὁμοιότητα μένειν, Plato, Phaedo 109 a.—C,] > Plato's “" matter ’’ is not conceived by him as equivalent to “ nothing,”’ but at the same time it is “ποῦ anything ” it is impossible for there to be any motion at all if there be a circumambient void. Just as it has been asserted that the earth is at rest by the law of symmetry,4 so must it be in vacancy, since no preference can be given to one line of motion more than to another, inasmuch as the void, as such, is ineapable of differentiation.
To begin with, every motion must be cither natural or forced, and there can be no such thing as forced movement if there is no natural movement (for forced movement is movement counter to that which is natural, and the unnatural presupposes the natural); so that, unless every natural body has a natural movement, there cannot be any other mosement at all. But how can there be any natural movement in the undifferentiated limitless void? Vor gua limitless it can have no top or bottom or middle, and qua vacancy it can have no differentiated directions of up and down (since the non-existent can no more be differentiated than ‘ nothing ἡ can, and the void is conceived as not being a thing, but as mere shortage >) τ, whereas natural trends are differentiated and differentiate the substances that manifest them. So it follows either that nothing has any natural trend in any direction or (since this 15 not so) that the supposed vacancy-as-conditioningmovement 1s a fiction.
In the second place, projectiles move when the body that impelled them is no longer in contact with them, whether this be due (as some suppose) till itis differentiated by “form.” (Or, ‘ the void is regarded us a sort of “ nothing ”—a no- thing in the privative sense.’ The Atomists called the void ‘ nothing,’ meaning not that it was snun-ewiste πὲ (μὴ ὃν ἀπλῶς), but that it was noé any thing (μὴ ὃν 7.)—the only ‘ things’ being sohd atoms.—C.} 215 a paw) ἢ διὰ τὸ ὠθεῖν τὸν ὠσθέντα ἀέρα θάττω κίνησιν τῆς τοῦ ὠσθέντος φορᾶς ἣ ἣν φέρεται εἰς τὸν οἰκεῖον τόπον. ἐν δὲ τῷ κενῷ οὐδὲν τούτων ἐν- δέχεται ὑπάρχειν, οὐδ᾽ ἔσται φέρεσθαι ἀλλ᾽ ἢ ὡς τὸ ὀχούμενον. ἔτι οὐδεὶς ὁ ἂν ἔχοι εἰπεῖν διὰ τί κινηθὲν 90 στήσεταί που' τί γὰρ μᾶλλον ἐνταῦθα ἢ ἐνταῦθα; ὥστ' 7 ἠρεμήσει ἢ εἰς ἄπειρον ἀνάγκη φέρεσθαι, ἐὰν μή τι ἐμποδίσῃ κρεῖττον.
"Ἔτι viv μὲν εἰς τὸ κενὸν διὰ τὸ ὑπείκειν φέ- ρεσθαι δοκεῖ" ἐν δὲ τῷ κενῷ πάντῃ ὁμοίως τὸ τοιοῦτον, ὥστε πάντῃ οἰσθήσεται.
2% "Ἔτι δὲ καὶ ἐκ τῶνδε φανερὸν τὸ λεγόμενον. ὁρῶμεν γὰρ τὸ αὐτὸ βάρος καὶ σῶμα θᾶττον φε- ρόμενον διὰ δύο αἰτίας, ἣ τῷ διαφέρειν τὸ δι᾽ οὗ (οἷον δι᾿ ὕδατος ἢ ἢ γῆς ἢ ἀέρος) ὴ τῷ διαφέρειν τὸ φερόμενον, ἐὰν Tae ταὐτὰ ὑπάρχῃ, διὰ τὴν ὑπεροχὴν τοῦ βάρους ἢ τῆς κουφότητος.
Τὸ μὲν οὖν δι’ οὗ φέρεται αἴτιον ὅτι ἐμποδίζει, 80 μέλ μὲν ἀντιφερόμενον, ἔπειτα καὶ μένον" μᾶλλον δὲ τὸ μὴ εὐδιαίρετον; τοιοῦτο δὲ τὸ παχύ- 21bb TEpov. τὸ δὴ ἐφ᾽ οὗ A οἰσδήσεται διὰ τοῦ Β τὸν ἐφ᾽ a7 ee διὰ δὲ τοῦ Δ λεπτομεροῦς ὄ ὄντος τὸν ἐφ᾽ ᾧ Ἐ, εἰ ἴσον τὸ μῆκος τὸ τοῦ Β τῷ Δ, 4 [ἀντιπερίστασις is defined by Simplicius (on 267 a 19 ff.) as the interchange of places, when a body A thrusts a body B out of its place and occupies that place, and B similarly displaces C, and go on until the last displaced body occupies the nlace of A,.—-C.]
b Here we should suppose Aristotle to have in his mind, not the ‘‘ vast inane” eneral, but either a vacant space deross which, or ΕΝ space into which, the projectile is launched. For the impact itself must have a direction relatively to the movement of the impelling body and the PHYSICS, IV. vit.
to a circulating thrust,* or to the air being set by the original impact in more rapid motion than that of the natural movement of the missile towards the place proper to it. But in vacancy neither of these agencies would be in operation, so that nothing could go on moving unless it were carried. Nor (if it did move) could a reason be assigned why the projectile should ever stop—for why here more than there? It must therefore cither not move at all, or continue its movement without limit, unless some stronger force impedes it.
Yet ayain, we are told that things go into vacant spaces because they offer no resistance; but in vacancy there is no resistance m any direction, 50 that, as to direction of movement, 1t would be a case of onc-as-good-as-another,é A further proof of our thesis is this: We see that the velocity of a moving weight or mass depends on two conditions: (1) the distinctive nature of the medium—water, carth, or air—through which the molion takes place, and (2) the comparative gravity or levity of the moving body itself, other conditions being equal.
(1) Now the medium reduces velocity all the more if it is itself moving in the opposite direction, but it also reduces it, though in a lesser degree, if it is quiescent; and this impedium of motion is proportional to the resistance the medium offers to cleavage, which is to say its density. Thus, if one medium is easier to cleave than another, the time taken in centre of gravity of the body impinged upon. <A frame of reference of some sort, therefore, }s a ae in the hypothesis of any impact and projechon at all, But it does not look as if Aristotle had thought this out.
τὸ 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 simplifying the cumbrous mathematical methods often employed by Greek writers, The paraphrase, I trust, accurately represents 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 proportionately less? ρος, if the media are water and air, the ratio of air’s cleavableness and unsubstantiality 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 ᾿ ᾿ 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.
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