894. Deinde cum dicit: sed si id quod movetur etc., ostendit quomodo praedicta ratio efficaciam habere possit: 894. Then, at but if (242b24), he shows how to make the argument efficacious: et primo quomodo habeat efficaciam ex suppositione facta; first, how it can be made efficacious by making another assumption; secundo quomodo habeat efficaciam simpliciter, ibi: nihil autem differat etc. second, how it is efficacious all by itself, at for the fact that (242b34). Dicit ergo primo, quod id quod localiter et corporaliter movetur primo et immediate ab aliquo mobili movente, necesse est quod tangatur ab eo, sicut baculus tangitur a manu; vel quod continuetur ei, sicut continuatur una pars aeris alteri, et sicut pars continuatur animali. Et hoc videtur contingere in omnibus, quod movens semper coniungitur mobili altero istorum modorum. He thus says first that what is locally and corporeally being moved first and immediately by a mobile mover must be touched by it, as a stick is touched by the hand, or must be continuous with it, as one part of the air is continuous with the next part or as one part of an animal is continuous with another. And this seems to occur in everything, namely, that the mover is always in contact with the mobile in one of these ways. Accipiatur ergo alter istorum modorum, scilicet quod ex omnibus infinitis mobilibus et moventibus efficiatur unum, scilicet ipsum totum universum, per continuationem quandam. Hoc ergo, quia contingens est, supponatur: et istud totum, quod est quaedam magnitudo et continuum, vocetur abcd, et motus eius vocetur ezit. Et quia posset aliquis dicere quod ezit erat motus finitorum mobilium, et ita non potest esse motus totius infiniti; subiungit quod nihil differt quantum ad propositum pertinet, utrum accipiatur finita magnitudo quae movetur, aut infinita. Sicut enim simul quando movebatur a, in tempore scilicet finito, quod est k, movetur quodlibet finitorum mobilium, quae sunt numero infinita; ita etiam simul in eodem tempore movetur tota magnitudo infinita. Sequitur ergo impossibile, quodcumque horum detur, sive quod sit magnitudo finita constans ex magnitudinibus numero infinitis, sive quod sit magnitudo infinita, et motus eius in tempore finito; cum sit ostensum supra quod mobile infinitum non potest moveri tempore finito. Ergo impossibile est hoc ex quo sequebatur, scilicet quod procedatur in infinitum in moventibus et motis. Manifestum est ergo quod hoc quod unum moveatur ab altero, non procedit in infinitum: sed stabit alicubi, et erit aliquod primum mobile, quod scilicet moveatur ab altero immobili. Let us therefore take one of these ways, namely, that from all the infinite mobiles and movers there is formed one thing—namely, the whole universe—through some kind of continuity. Since this is something contingent, let us take it for granted and let that whole unit—which is a continuous magnitude—be called ABCD and its motion EZIT. And, because someone could say that EZIT was the motion of finite mobiles, and so not the motion of an infinite whole, he adds that, so far as our proposition is concerned, it makes no difference whether the magnitude is finite or infinite. For just as, when A was being moved in a finite time K, each of the finite mobiles that are infinite in number were being moved at the same time, so also, in the same time, the entire infinite magnitude will be moved all at once. Therefore, an impossibility follows whichever one is taken: either a finite magnitude composed of magnitudes infinite in number, or an infinite magnitude whose motion occurs in finite time. For it has been proved above that an infinite mobile cannot be moved in finite time. Therefore, the premise from which this impossibility followed is itself impossible, that is, that we go to infinity in the series of movers and things moved. It is clear, therefore, that the process of one thing being moved by another does not go on to infinity, but a halt must be made and there will exist a first mobile that is being moved by a mover that is immovable. 895. Et quia praedicta probatio procedit supposito quodam, scilicet quod omnia infinita moventia et mota continuentur ad invicem et constituant unam magnitudinem, et sic posset alicui videri quod non simpliciter concludatur; ideo subiungit quod non differt hanc demonstrationem processisse quodam supposito; quia ex contingenti supposito, etiam si sit falsum, non potest sequi aliquod impossibile. 895. Since our proof depended on an assumption—namely, that all the infinite movers and moved form a continuum and constitute one magnitude—it might seem to someone that the conclusion is not absolute. Consequently, he adds that it makes no difference to the validity of this conclusion that it should have proceeded from this assumption. For an impossibility cannot follow from an assumption that is contingent, even if the assumption be false. Cum ergo praedicta ratio ducat ad impossibile, illud impossibile non sequitur ex isto contingenti supposito, sed ex alio, quod oportet esse impossibile, cum ex eo impossibile sequatur. Therefore, since the proof led to an impossibility, that impossibility did not follow from our contingent premise, but from some other cause that must be impossible, since an impossibility followed from it. Et sic patet quod in demonstrationibus ad impossibile ducentibus, nihil refert utrum accipiatur falsum contingens adiunctum impossibili, vel verum. So it is clear that, in demonstrations that lead to an impossibility, it makes no difference whether a false contingent assumption or something true be joined to what is impossible. Ostenditur enim impossibile esse illud, ex quo, cum adiunctione contingentis falsi, sequitur impossibile, sicut si ex eo impossibile sequeretur, adiuncto quodam vero: quia sicut ex vero non potest sequi impossibile, ita nec ex contingenti. For that is shown to be impossible that, by the addition of some false contingent statement, gives rise to an impossibility, just as if something impossible should follow from it by the addition of a true proposition. For just as an impossibility cannot follow from a true premise, so neither can it from a contingent one. 896. Sed potest aliquis dicere, quod non est contingens omnia mobilia continuari; sed impossibile est continuari elementa ad invicem, et cum caelestibus corporibus. 896. But someone could say that for all mobiles to form one continuum is not contingent, but impossible, for the elements cannot form a continuum with one another and with the heavenly bodies. Sed dicendum est quod alio modo accipitur contingens et impossibile, cum demonstratur aliquid de genere, et cum demonstratur aliquid de specie. Quia cum agitur de specie, oportet accipi ut impossibile esse illud, cui repugnat vel genus vel differentia speciei, ex quibus ratio speciei constituitur. But it must be answered that “contingent” and “impossible” are taken in one sense when something is demonstrated about a genus and in another sense when something is demonstrated about a species. When a discussion is about the species, whatever is repugnant either to the genus or the specific difference, which forms the account of the species, must be regarded as impossible. Cum vero agitur de genere, accipitur ut contingens omne illud cui non repugnat ratio generis, licet ei repugnet differentia constituens speciem: sicut si loquerer de animali, possem accipere ut contingens, quod omne animal esset alatum; sed si descenderem ad considerationem hominis, impossibile esset hoc animal esse alatum. But when the discussion is about the genus, we can take as contingent anything to which the genus is not repugnant, even though the difference that constitutes a species of that genus is repugnant to it. For example, if I am speaking of animal, I can suppose as a contingent proposition that all animals are winged; but if I go a step further and consider man, it is impossible for this animal to have wings. Quia igitur Aristoteles hic loquitur de mobilibus et moventibus in communi, nondum applicando ad determinata mobilia; esse autem contiguum vel continuum indifferenter se habet ad rationem moventis et mobilis; ideo accepit ut contingens, quod omnia mobilia sint continua ad invicem: quod tamen est impossibile, si mobilia considerentur secundum suas naturas determinatas. Now, since Aristotle is here speaking about mobiles and movers in a general way without making applications to particular mobiles, and to be in contact or to be continuous is a matter of indifference if you consider the general account of mover and mobile, he therefore takes it as contingent that all mobiles mutually form a continuum, even though this is impossible if you consider the mobiles in their specific natures. Lectio 3 Lecture 3 Probatur in motu locali quod movens et motum oportet esse simul In local motion, the mover and the moved must be together Primum autem movens, non sicut cuius causa, sed unde est principium motus, est simul cum eo quod movetur. Simul autem dico, quia nihil ipsorum medium est: hoc enim commune est in omni quod movetur et quod movet. The first mover, not as the cause for the sake of which, but as the principle of motion, is together with that which is moved. I say “together” because there is no intermediate between them. And this is found universally in everything that moves and is moved. Quoniam autem tres sunt motus, qui secundum locum, et qui secundum qualitatem, et secundum quantitatem; necesse est et ea quae moventur tria esse. Qui quidem igitur secundum locum, loci mutatio; qui vero secundum quantitatem, alteratio; qui vero secundum quantitatem, augmentum vel decrementum. Primum quidem igitur de loci mutatione dicamus: haec enim primus motuum est. Since there are three motions, i.e., in respect to place, in respect to quality, and in respect to quantity, there must be three things that are moved. Motion in respect to place is local motion; motion in respect to quality is alteration; motion in respect to quantity is increase or decrease. We should speak first of local motion. For this is the first of motions. Omne igitur quod fertur, aut ipsum a seipso movetur aut ab altero. Si igitur a seipso, manifestum est quod cum in ipso movens sit, simul movens et quod movetur erit, et nullum illius medium. Whatever is moved is moved either by itself or by another. If by itself, then since the mover is in it, it is clear that the mover and that which is moved will be together, and there will be no intermediary between them. Quod autem ab alio movetur, quadrifariam movetur. Qui enim sunt ab altero motus, quatuor sunt: pulsio, tractio, vectio, vertigo. Et namque omnes alios in hos reduci accidit. That which is moved by another is moved in one of four ways. The motions which are from another are four: pushing, pulling, carrying, and twirling. For all the others are reduced to these. Pulsionis igitur alia impulsio, alia expulsio. Impulsio quidem est cum movens ei quod movetur non deficit: expulsio cum expellens deficit. Pushing is either pushing on or pushing off. Pushing on occurs when the mover does not leave that which is moved. Pushing off occurs when the pusher leaves. Vectio autem in tribus erit motibus. Quod quidem enim vehitur, non secundum se movetur, sed secundum accidens. In eo enim quod est in eo quod movetur, aut super id quod movetur, movetur ipsum. Vehens autem movetur aut pulsum aut tractum aut vertigine ductum. Manifestum igitur quoniam vectio in tribus motibus erit. Carrying will be in the three other motions. For that which is carried is not moved in itself but accidentally. For in this that which is moved is either in that which is moved or is on that which is moved. The carrier is moved either by a pushing or a pulling or else it is led on by a twirling. Therefore it is clear that carrying will be in these three motions. Tractio autem est, cum etiam ad ipsum vel ad alterum velocior sit motus trahentis, non separatus ab eo quod trahitur: et namque ad ipsum est tractio, et ad alterum. Et reliqui tractus idem specie in hos reducuntur; ut inspiratio et expiratio, et spuitio, et quicumque corporum emissivi aut receptivi sunt, et spathesis et kerkisis. Aliud est quidem ipsorum congregatio, aliud disgregatio. Et omnis igitur motus qui est secundum locum, aggregatio et disgregatio est. Pulling occurs when there is a faster motion of the puller either to itself or to another, not separated from that which is pulled. For pulling occurs both to itself and to another. Other pullings that are the same in species are reduced to these, for example, inhaling and exhaling, and spitting, and whatever bodies are emitted or received, and spathesis, and kerkisis. Gathering of things is one thing and separating is another. Therefore all motion in respect to place is a gathering or a separating. Vertigo autem componitur quidem ex tractu et pulsione: hoc quidem pellit movens, illud autem trabiit. Twirling is composed of pushing and pulling. For the mover pushes this and pulls that. Manifestum igitur est quod si simul pellens et trahens est cum eo quod pellitur et trahitur, nullum medium eius quod movetur et moventis est. Therefore it is clear that if the pusher and the puller are together with that which is pushed and pulled, there is no intermediate between that which is moved and the mover. Hoc autem manifestum ex dictis. Pulsio quidem aut a seipso aut ab alio ad aliud motus est: tractus autem ab alio ad ipsum aut ad aliud est. Adhuc autem synosis et diosis. This is clear from what was said. Pushing is motion either from itself or from another to another. But pulling is from another to itself or to another. Thus far there is coming together and going apart. Proiectio autem, quando velocior motus fiat quam qui secundum naturam lati, fortiori facta pulsione: et hoc facto, tamdiu accidit ferri, quousque fortior sit motus eius quod fertur. Manifestum igitur quoniam quod movetur et movens simul sunt, et nullum medium est ipsorum. There is throwing when there occurs a faster motion than that which is borne according to nature, a stronger pushing having been made. This being done, it is borne as long as the motion of that which is borne is stronger. Therefore it is clear that the mover and that which is moved are together, and there is no intermediary between them. 897. Quia Philosophus in demonstratione praecedenti supposuerat quod movens est contiguum vel continuum mobili, hoc intendit nunc probare. 897. In the previous demonstration, the Philosopher had assumed that a mover is continuous, or at least contiguous, with the mobile. This he now intends to prove. Et primo ostendit propositum; First, he proves his proposition; secundo probat quoddam, quod in hac probatione supponit, ibi: quoniam autem quae alterantur etc. second, he proves something he had assumed in his proof, at all things that are altered (245b19; [913]). Circa primum duo facit: About the first, he does two things: primo proponit intentum; first, he states his intention; secundo probat propositum, ibi: quoniam autem tres sunt motus etc. second, he proves his proposition, at since there are three (243a35; [898]). Dicit ergo primo, quod movens et motum sunt simul. He says first (243a3) that mover and moved are together. Sed aliquid dicitur movere dupliciter. But something is said to be moved in two senses. Uno modo sicut finis movet agentem; et tale movens aliquando distans est ab agente quem movet: One sense is as the end moves the agent, and such a mover is sometimes distant from the agent it moves; alio modo sicut movet id quod est principium motus; The other sense is as that moves that is the actual beginner of the motion.