Authors/Thomas Aquinas/physics/L7/lect2

Lecture 2 No process to infinity in movers and moved. One must arrive at a first mover unmoved

Latin	English
	Lecture 2 No process to infinity in movers and moved. One must arrive at a first mover unmoved.
lib. 7 l. 2 n. 1 Postquam ostendit philosophus quod omne quod movetur, movetur ab alio, hic accedit ad principale propositum ostendendum, scilicet quod sit primus motus et primus motor. Et circa hoc duo facit: primo proponit quod intendit; secundo probat propositum, ibi: si enim non est, sed in infinitum procedet et cetera. Dicit ergo primo, quod cum ostensum sit universaliter, quod omne quod movetur ab aliquo alio movetur, necesse est hoc etiam verum esse in motu locali, scilicet ut omne quod movetur in loco, ab altero moveatur. Applicat autem specialiter ad motum localem quod supra universaliter demonstratum est, quia motus localis est primus motuum, ut in octavo ostendetur; et ideo secundum hunc motum procedit hic ad demonstrandum primum motorem. Accipiatur igitur aliquid quod movetur secundum locum; hoc movetur ab altero; aut ergo illud alterum movetur, aut non. Si non movetur, habetur propositum, scilicet quod aliquid sit movens immobile; quod est proprietas primi moventis. Si autem et ipsum movens movetur, oportet quod moveatur ab altero movente; et hoc iterum movens, si et ipsum movetur, movetur ab altero. Sed hoc non potest procedere in infinitum, sed oportet in aliquo stare. Erit ergo aliquid primum movens, quod erit prima causa motus: ita scilicet quod ipsum non movetur, sed movet alia.	891. After showing that whatever is moved is moved by some other, the Philosopher now turns to the proof of his main proposition, namely, that there exists a first motion and a first mover. About this he does two things: First he proposes what he intends; Secondly, he proves his proposition, at 892. He says therefore first (678 242 a16) that since it has been proved for all cases that whatever is moved is moved by some other, it must be true even in regard to local motion that whatever is being moved with respect to place is being moved by something else. Now he applies to local motion in particular the very proposition which he proved universally true, because local motion is the first of the motions, as will be proved in Book VIII. Therefore, it is according to this motion that he now proceeds to demonstrate a first mover. Therefore, let us take something that is being moved in regard to place. This thing is being moved by something else. Now that something else is in turn being moved by something else or it is riot. If it, is not, we have the proposition clinched; namely, that there exists a mover that is immovable, which is a property of the first mover. But if that something else is also being moved by something other, this other is being moved by still another which is itself being moved by yet another mover. This, however, cannot go on ad infinitum, but a halt must be made at some mover. Therefore, there will be a first mover which will be the first cause of the motion, and of such a nature that it is itself not being moved but moves the others.
lib. 7 l. 2 n. 2 Deinde cum dicit: si enim non etc., probat quod supposuerat. Et circa hoc tria facit: primo inducit probationem; secundo ostendit probationem esse insufficientem, ibi: sic igitur videtur etc.; tertio supplet quoddam per quod ratio fortificatur, ibi: sed si id quod movetur et cetera. Dicit ergo primo, quod si hoc non concedatur, quod sit aliqua prima causa motus, cum omne quod movetur ab alio moveatur, sequitur quod procedatur in infinitum in moventibus et motis. Et hoc ostendit esse impossibile. Sit enim a quoddam quod movetur secundum locum, et moveatur ab ipso b; b vero a c, c vero a d; et sic procedatur in infinitum ascendendo. Manifestum est autem, quod cum aliquid movet ex eo quod movetur, simul movetur movens et ipsum mobile; sicut si manus suo motu movet baculum, simul movetur manus et baculus. Sic ergo simul movetur b quando movetur a; et eadem ratione quando movetur b simul movetur c, et cum movetur c simul movetur d. Sic ergo simul et in eodem tempore est motus ipsius a et omnium aliorum; et poterit seorsum accipi motus uniuscuiusque horum infinitorum. Et quamvis unumquodque horum mobilium moveatur ab unoquoque moventium, non ita quod unum ab omnibus, sed singula a singulis; nihilominus tamen, licet sint infinita moventia et mobilia, tamen uniuscuiusque mobilium motus est unus numero. Et licet omnes motus sint infiniti numero, non tamen sunt infiniti in ultimis, idest per privationem ultimorum, sed uniuscuiusque motus est finitus, habens determinata ultima. Et quod uniuscuiusque infinitorum mobilium motus sit unus numero et finitus, probat quia, cum omne quod movetur moveatur inter duos terminos, ex quodam scilicet in quiddam, necesse est quod secundum diversum modum identitatis terminorum, etiam ipse motus sit diversimode unus, scilicet aut numero aut specie aut genere. Numero quidem est idem motus, qui est ex eodem termino a quo in idem numero sicut in terminum ad quem; ita tamen quod sit etiam in eodem numero tempore; et cum hoc oportet quod sit eiusdem mobilis numero. Et ad exponendum quod dixerat, subiungit quod motus numero unus est ex eodem in idem, sicut ex hoc albo, quod significat unum numero, in hoc nigrum, quod etiam nominat aliquid idem numero, et secundum hoc tempus determinatum, quod etiam est unum numero: quia si esset motus secundum aliud tempus, licet aequale, non esset numero unus, sed specie tantum. Sed motus est unus genere, qui est in eodem praedicamento, vel substantiae vel cuiuscumque alterius generis; sicut omnis generatio substantiae est eadem genere, et omnis alteratio similiter. Sed motus est specie unus, qui est ex eodem secundum speciem in idem secundum speciem; sicut omnis denigratio, quae est ex albo in nigrum, est eadem specie, et omnis depravatio, quae est ex bono in malum. Et haec etiam in quinto dicta sunt. His igitur duobus suppositis, scilicet quod simul movetur et movens et motum, et quod potest accipi motus uniuscuiusque mobilium tanquam finitus et unus; accipiatur motus huius mobilis quod est a, et sit e; et motus ipsius b sit z, et motus cd et omnium consequentium sit it. Tempus autem in quo movetur a, sit k. Sed quia motus ipsius a est determinatus, idest finitus, etiam tempus in quo est iste motus, scilicet k, est determinatum et non infinitum: quia sicut in sexto ostensum est, finitum et infinitum simul invenitur in tempore et motu. Ex dictis autem patet, quod in eodem tempore in quo movetur a, movetur et b, et omnia alia: ergo motus omnium, qui est ezit, est in tempore finito. Sed iste motus est infinitus, cum sit infinitorum. Ergo sequetur quod motus infinitus sit in tempore finito; quod est impossibile. Hoc autem ideo sequitur, quia in quo tempore movetur a, moventur omnia alia, quae sunt infinita numero. Nec differt quantum ad propositum pertinet, utrum motus omnium mobilium sit aequalis velocitatis, aut inferiora mobilia tardius moveantur et in maiori tempore; quia omnino sequetur quod motus infinitus sit in tempore finito, quia unumquodque mobilium necesse est quod habeat velocitatem et tarditatem finitam. Hoc autem est impossibile, scilicet motum infinitum esse in tempore finito. Ergo et primum est impossibile, scilicet quod procedatur in mobilibus et moventibus in infinitum.	892. Then at (679 242 a20) he proves a statement not yet proved. About this he does three things: First he gives the proof; Secondly, he shows that the proof he gives is insufficient, at 893; Thirdly, he supplies what was lacking in the insufficient proof, at 894. He says therefore first (680 242 b19) that if it is not granted that there is a first cause of the motion, then, since whatever is being moved is moved by some other, it follows that an infinite series of movers and moved is involved. And he shows that such a situation is impossible. Let A, then, be something that is being moved in respect of place and let it be moved by B; let B be moved by C, and C by D, and so on ad infinitum in ascending order. Now it is evident that, when something moves by virtue of the fact that it is itself being moved by another, then both the mover and the mobile are being moved simultaneously, just as, when the hand by its motion moves a stick, the hand and the stick are moved at one and the same time. Therefore, B is being moved simultaneously with A, and C with B, and D with C. Therefore, the motion of A and that of all the others exist together and at the same time. And we could have considered one by one each of these infinite motions. Likewise, although each one of these mobiles is being moved by some mover—not in the sense that one is being moved by all, but one by another—nevertheless, even though there be an infinitude of movers and mobiles, yet the motion of each of the mobiles is numerically one motion. And although all the motions are infinite in number, they are not infinite in a privative sense, i.e., as though lacking a boundary, but the motion of each mobile is finite and has its own definite boundaries. That the motion of each one of the infinite mobiles is numerically one and finite, he proves by the fact that since whatever is moved is moved between two termini, i.e., from something to something, then necessarily according to the diverse ways in which the termini are identical, the motion itself will be one in diverse ways, i.e., numerically, or specifically, or generically. Motions are numerically the same when they are from the same terminus a quo into the same numerical terminus ad quem, provided that it takes place in the same numerical time and that the numerically same mobile is involved. To explain what he means, he adds that a motion that is numerically one is “from the same into the same”, for example, from this white, i.e., from the same numerical white, into this black, i.e., the same numerical black, and in this same numerical time— because if all the conditions but time were numerically the same, the motion would be not numerically, but specifically one. But a motion is generically one, when it is in the same predicament, i.e., of substance or some other genus; for example, all generations of substance are generically the same, and all alterations likewise. But a motion is specifically one, when it is from the same specific terminus to the same specific terminus; for example, every case of blackening, which is from white to black, is specifically the same, and every case of becoming depraved, i.e., from good to bad, is specifically the same. All this was explained in Book V. Keeping in mind, therefore, these two facts, namely, that the mover and the moved are being moved together, and that the motion of each of the mobiles can be taken as one and finite, let us take the motion of mobile A and call it motion E, and the motion of B and call it Z, and let the motion of C, D and of all the others following be called IT. Also let the time in which A is being moved be K. Now, since the motion of A is finite, then the time K of that motion is definite and not infinite, because we showed in Book VI that the finite in time corresponds to a finite in motion and an infinite in time corresponds to an infinite in motion. From what we have said, however, it is clear that in the very same time that A is being moved, B is being moved, and so for all the others; hence the motion of all, i.e., the motion EZIT, occurs in finite time. But this motion is infinite, since it is the motion of an infinite number. Therefore it will follow that an infinite motion occurs in finite time, which is impossible. Now why does our conclusion follow? Because in the very same time that A is being moved all the others are being moved and they are infinite in number. It makes no difference, so far as our proposition is concerned, whether the motion of all the mobiles had equal velocity or not, or whether the lower mobiles move more slowly and in a greater time, because in any case it will follow that an infinite motion occurs in finite time—since each of the mobiles must have a finite rapidity and a finite slowness. However, it is impossible for an infinite motion to occur in finite time. Therefore, it is also impossible that we go to infinity in the series of mobiles and movers.
lib. 7 l. 2 n. 3 Deinde cum dicit: sic igitur etc., ostendit quod praecedens ratio non efficaciter concludit. Et dicit quod praedicto modo videtur demonstrari principale propositum, scilicet quod non in infinitum procedatur in moventibus et motis; non tamen efficaciter demonstratur, quia nullum inconveniens accidit ex praemissis. Contingens est enim et possibile, quod in tempore finito sit motus infinitus; ita tamen quod non sit unus et idem, sed alius et alius; inquantum scilicet infinita sunt quae moventur. Nihil enim prohibet infinita in tempore finito moveri simul. Et hoc concludebat ratio praedicta. Erant enim mobilia infinita diversa, et sic motus eorum erant diversi: quia ad unitatem motus non solum requiritur unitas temporis et termini, sed etiam unitas mobilis, ut in quinto dictum est.	893. Then at (680 242 b19) he shows that the foregoing argument is not conclusive. And he says that in the above way we seemed to have demonstrated the main proposition, namely, that one does not go to infinity in the series of movers and mobiles. Yet it is not an efficacious proof, because no impossibility flows from these premises. For it is possible that there be an infinite motion in finite time, so long as the motion is not one and the same but other and other, insofar, namely, as an infinite number of things are being moved. For there is nothing to prevent an infinite number of things from being moved at once in finite time. And it was this that our argument concluded. For the infinite mobiles were diverse and so their motions were diverse, because for a motion to be one it is required not only that the time be one and that the termini be identical but also that the mobile be one, as was proved in Book V.
lib. 7 l. 2 n. 4 Deinde cum dicit: sed si id quod movetur etc., ostendit quomodo praedicta ratio efficaciam habere possit: et primo quomodo habeat efficaciam ex suppositione facta; secundo quomodo habeat efficaciam simpliciter, ibi: nihil autem differat et cetera. 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. 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.	894. Then at (681 242 b23) he shows how to make the argument efficacious. First, how it can be made efficacious by making another assumption; Secondly, how it is efficacious all by itself, at 895. He says therefore 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 all, i.e., that the mover is always in contact with the mobile in one of these ways. 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 which 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, i.e., 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, i.e., 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 ad infinitum, but a halt must be made and there will exist a first mobile which is being moved by a mover that is immovable.
lib. 7 l. 2 n. 5 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. 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. Et sic patet quod in demonstrationibus ad impossibile ducentibus, nihil refert utrum accipiatur falsum contingens adiunctum impossibili, vel verum. 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.	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. Therefore, since the proof led to an impossibility, that impossibility did not follow from our contingent premis but from some other cause which must be impossible, since an impossibility followed from it. 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. For that is shown to be impossible which, 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 premis, so neither can it from a contingent one.
lib. 7 l. 2 n. 6 Sed potest aliquis dicere, quod non est contingens omnia mobilia continuari; sed impossibile est continuari elementa ad invicem, et cum caelestibus corporibus. 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. 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. 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.	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. 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 nature of the species, must be regarded as impossible. 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 which 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. 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 nature of mover and mobile, therefore he 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.