Authors/Thomas Aquinas/physics/L6/lect5

Lecture 5 The “now” as the indivisible of time. Everything that moves is divisible. Difficulties solved

Latin	English
	Lecture 5 The “now” as the indivisible of time. Everything that moves is divisible. Difficulties solved
lib. 6 l. 5 n. 1 Postquam ostendit philosophus quod nullum continuum ex indivisibilibus componitur, neque indivisibile esse, ex quibus apparet motum esse divisibilem; hic determinat de divisione motus. Et primo praemittit quaedam necessaria ad motus divisionem; secundo de ipsa motus divisione determinat, ibi: motus autem est divisibilis dupliciter et cetera. Circa primum duo facit: primo ostendit quod in indivisibili temporis non contingit esse motum neque quietem; secundo ostendit quod indivisibile non potest moveri, ibi: quod mutatur autem omne et cetera. Circa primum duo facit: primo ostendit quod indivisibile temporis est ipsum nunc; secundo quod in nunc nihil movetur aut quiescit, ibi: quod autem nihil in ipso nunc movetur et cetera. Circa primum tria facit: primo ponit quod intendit; secundo ponit ea ex quibus probari potest propositum, ibi: est enim aliquid ultimum eius etc.; tertio ostendit id quod ad haec consequitur, ibi: necesse est igitur et cetera.	787. After showing that no continuum is composed of indivisibles and that no continuum is indivisible, thus making it seem that motion is divisible, the Philosopher now determines about the division of motion. First he states certain facts necessary for the division of motion; Secondly, he treats of the division of motion, L. 6. About the first he does two things: First he shows that in an indivisible of time, there is neither motion nor rest; Secondly, that an indivisible cannot be moved, at 796. About the first he does two things: First he shows that the indivisible of time is the “now”; Secondly that in the “now” nothing is being moved or is at rest, at 794. About the first he does three things: First he states his intention; Secondly, he states facts from which his proposition can be reached, at 789. Thirdly, he shows what follows from his proposition, ?90.
lib. 6 l. 5 n. 2 Circa primum considerandum est, quod aliquid dicitur nunc secundum alterum, et non secundum seipsum: sicut dicimus nunc agi quod in toto praesenti die agitur; tamen totus dies praesens non dicitur praesens secundum seipsum, sed secundum aliquid sui. Manifestum est enim quod totius diei aliqua pars praeteriit, et aliqua futura est: quod autem praeteriit vel futurum est, non est nunc. Sic ergo patet quod totus dies praesens non est nunc primo et per se, sed per aliquid sui: et similiter nec hora, nec quodcumque aliud tempus. Dicit ergo quod id quod dicitur nunc primo et per se, et non secundum alterum, ex necessitate est indivisibile, et iterum ex necessitate est in omni tempore.	788. About the first (599 233 b33) we must take into account that something is called “now” in relation to something else and not in relation to itself; for example, we say that what is being done in the course of a whole day is being done “now”, yet the whole day is not said to be present according to its entirety but according to some part of itself. For it is evident that part of a whole day has passed and part is still to come, and neither of them is “now”. Thus it is evident that the entire present day is not a “now” primarily and per se but only according to something of itself—and what is true of the day is true of an hour or any period of time. He says therefore that what is “now” primarily and per se and not according to something else is necessarily indivisible and present in every time.
lib. 6 l. 5 n. 3 Deinde cum dicit: est enim aliquid etc., probat propositum. Manifestum est enim quod cuiuslibet continui finiti est accipere aliquod ultimum, extra quod nihil est eius cuius est ultimum; sicut nihil lineae est extra punctum, quod terminat lineam. Tempus autem praeteritum est quoddam continuum finitum ad praesens. Est ergo accipere aliquod ultimum eius quod factum est, idest praeteriti, extra quod nihil est praeteriti, et infra quod nihil est futuri. Et similiter erit accipere aliquod ultimum futuri, infra quod nihil est praeteriti. Et illud ultimum est terminus utriusque, scilicet praeteriti et futuri; quia cum totum tempus sit continuum, oportet quod praeteritum et futurum ad unum terminum copulentur. Si igitur de aliquo demonstretur quod ipsum sit tale per seipsum, quod est esse nunc per seipsum et non per aliquid sui, simul cum hoc manifestum erit quod sit indivisibile.	789. Then at (600 233 b35) he proves his proposition, For it is evident that it is possible in regard to any finite continuum to take an extremity outside of which there is existing nothing of that of which it is the extremity, just as nothing of a line is outside the point which terminates the line. But past time is a continuum which is terminated at the present. Therefore it is possible to take something as the extremity of the past, so that beyond it there is nothing of the past, and previous to it nothing of the future. In like manner, it is possible to take an extremity of the future, beyond which there is nothing of the past. Now that extremity will be the limit of both, i.e., of the past and of the future; for since the totality of time is a continuum, the past and the future must be joined at one term. And if the “now” fits the description just given, it is clear that it is indivisible.
lib. 6 l. 5 n. 4 Deinde cum dicit: necesse est igitur etc., ostendit quoddam consequens ad praemissa. Et circa hoc duo facit: primo ostendit, supposito quod nunc sit indivisibile, quod oporteat idem nunc esse quod est terminus praeteriti et terminus futuri; secundo ostendit quod e converso, si est idem utrumque nunc, oportet quod nunc sit indivisibile, ibi: at vero si idem est et cetera. Circa primum duo facit: primo concludit ex dictis, quod necesse est esse idem nunc, quod est ultimum utriusque temporis, scilicet praeteriti et futuri.	790. Then he shows what follows from these premises. About this he does two things: First he shows that on the supposition that the “now” is indivisible, the limit of the past and the limit of the future must be one and the same “now”. Secondly, that on the other hand, if each is the “now”, then the “now” must be indivisible, at 79-3. About the first he does two things: First at (601 234 a5) he concludes from the foregoing that it must be the same “now” which is the limit of the past and of the future.
lib. 6 l. 5 n. 5 Secundo ibi: si enim alterum est etc., probat tali ratione. Si est alterum nunc quod est principium futuri, et alterum quod est finis praeteriti, oportet quod haec duo nunc vel sint consequenter ad invicem, ita quod immediate sibi succedant; vel oportet quod unum sit seorsum ab altero, distans ab eo. Sed non potest dici quod unum consequenter se habeat ad alterum; quia sic sequeretur tempus componi ex nunc aggregatis; quod non potest esse propter id quod nullum continuum componitur ex impartibilibus, ut supra ostensum est. Nec etiam dici potest quod unum nunc sit seorsum ab altero, distans ab eo, quia tunc oporteret quod inter illa duo nunc esset tempus medium. Haec est enim natura omnis continui, quod inter quaelibet duo indivisibilia sit continuum medium, sicut inter quaelibet duo puncta, linea. Quod autem hoc sit impossibile ostendit dupliciter. Primo quia si aliquod esset tempus medium inter praedicta duo nunc, sequeretur quod aliquod univocum, idest eiusdem generis, esset medium inter duos terminos; quod est impossibile. Non enim est possibile quod inter extrema duarum linearum se tangentium vel consequenter se habentium, sit aliqua linea media. Hoc enim esset contra rationem eius quod est consequenter: quia consequenter sunt, ut supra dictum est, quorum nihil est medium proximi generis. Et sic, cum tempus futurum consequenter se habeat ad praeteritum, impossibile est quod inter terminum futuri et terminum praeteriti cadat aliquod tempus medium. Alio modo ostendit idem sic. Quidquid est medium inter praeteritum et futurum, dicitur nunc: si igitur tempus aliquod sit medium inter extrema temporis praeteriti et futuri, sequetur quod totum illud dicatur nunc. Sed omne tempus est divisibile, ut ostensum est. Ergo sequetur quod ipsum nunc sit divisibile.	791. Secondly, at (602 234 a6) he proves this statement with the following argument: If the “now” which is the beginning of the future is other than the “now” which is the end of the past, then either these two “now’s” are consecutive and immediately follow one upon the other or one is apart from and distinct from the other. But it cannot be that they are immediately consecutive, because then it will follow that time is composed of an aggregate of “now’s”—which cannot be, because no continuum is composed of indivisible parts, as was said above. Neither can it be that one “now” is apart from the other and distant from it, because then there would have to be a time between those two “now’s”. For it is the very nature of a continuum that there is something continuous between any two given indivisibles, just as there is line between any two given points of a line. But that this is impossible, he proves in two ways. First of all, because if there were a period of time between the two “now’s” in question, it would follow that something of the same kind would exist between the two, which is impossible, for it is not possible that between the extremities of two lines that touch or are consecutive, there be a line between. For that is against the nature of consecutive things, which were defined as things between which nothing like them occurs. And so, since future time is consecutive to past time, it is impossible that between the end of the past and the beginning of the future there be an intervening time. He proves the same point in another way: Whatever is intermediate between the past and the future is called “now”. If, therefore, there is any time between the limits of the past and future, it will follow that that will also be called a “now.” But all time is divisible, as has been proved. Consequently, it would follow, that the “now” is divisible.
lib. 6 l. 5 n. 6 Et quamvis supra posuerit principia ex quibus probari potest quod nunc sit indivisibile; quia tamen conclusionem non deduxerat ex principiis, hic consequenter ostendit quod nunc sit indivisibile, ibi: si autem divisibile est et cetera. Et hoc triplici ratione. Quarum prima est, quia si nunc sit divisibile, sequetur quod aliquid de praeterito sit in futuro, et aliquid futuri sit in praeterito. Cum enim nunc sit extremum praeteriti et extremum futuri; omne autem extremum est in eo cuius est extremum, sicut punctum in linea; necesse est quod totum nunc et sit in tempore praeterito ut finis, et in tempore futuro ut principium. Sed si nunc dividatur, oportet quod illa divisio determinet praeteritum et futurum. Omnis enim divisio in tempore facta, distinguit praeteritum et futurum; cum omnium partium temporis una comparetur ad aliam ut praeteritum ad futurum. Sequetur ergo quod ipsius nunc aliquid sit praeteritum, et aliquid futurum. Et ita cum nunc sit in praeterito et in futuro, sequetur quod aliquid futuri sit in praeterito, et aliquid praeteriti sit in futuro. Secundam rationem ponit ibi: simul autem etc.: quia si nunc sit divisibile, non erit nunc secundum seipsum, sed secundum alterum. Nullum enim divisibile est sua divisio qua dividitur: ipsa autem divisio temporis est nunc. Nihil enim est aliud divisio continui quam terminus communis duabus partibus: hoc autem intelligimus per nunc, quod est terminus communis praeteriti et futuri. Sic ergo manifestum est quod id quod est divisibile, non potest esse nunc secundum seipsum. Tertiam rationem ponit ibi: adhuc autem ipsius nunc etc.: quae talis est. Semper, facta divisione temporis, una pars est praeterita, et alia futura. Si igitur et nunc dividatur, oportet quod aliquid eius sit praeteritum, et aliquid futurum. Sed non idem est praeteritum et futurum: sequetur ergo quod ipsum nunc non sit idem sibi ipsi, quasi totum simul existens (quod est contra rationem eius quod dicitur nunc: cum enim dicimus nunc, intelligimus simul in praesenti esse); sed oportebit multam diversitatem esse in nunc et successionem, sicut et in tempore, quod multipliciter est divisibile.	792. Although in the immediately foregoing he had laid down the principles from which it could be proved that the Now is indivisible, yet because he had not derived the conclusion from these principles, he now shows that the Now is indivisible at (603 234 a11). And he does this with three arguments. The first of these is that if Now be divisible, it will follow that something of the past is in the future and something of the future in the past. For since the Now is the extremity of the past and the extremity of the future, and every extremity is in that of which it is the extremity, as a point in a line, then necessarily the entire Now is both in the past as its end and in the future as its beginning. But if the Now be divided, that division must determine the past and the future. For any division made in time distinguishes past and future, since among any parts of time taken at random, one is related to the other as past to future. It will follow, therefore, that part of the Now is past and part future. And so, since the Now is in the past and in the future, it will follow that something of the future is in the past and something of the past in the future. The second argument he gives at (604 234 a14): If the Now be divisible, it will be such, not according to itself, but according to something else. For no divisible is the very division by which it is divided. But the division of time is the Now. For that by which a continuum is divided is nothing but a term common to two parts. But that is what we understand by the Now, that it is a term common to the past and future. Thus, therefore, it is clear that what is divisible cannot be the Now according to itself. The third argument is given at (605 234 a16): Whenever time is divided, one part is always past and the other future. If, therefore, the Now is divided, necessarily part of it will be past and part future. But past and future are not the same. It will follow, therefore, that the Now is not the same as itself, i.e., something existing as a whole all at once (which is against the definition of the Now: for when we speak of the Now, we consider it as existing completely in the present); rather there will be much diversity and even succession in the Now, just as there is in time, which can be divided any number of times.
lib. 6 l. 5 n. 7 Sic ergo ostenso quod nunc sit divisibile, quod erat consequens ad hoc quod dicebatur non esse idem nunc quod est extremum praeteriti et futuri, et destructo consequente, concludit destructionem antecedentis. Et hoc est quod dicit, quod si hoc est impossibile inesse ipsi nunc, scilicet quod sit divisibile, necesse est dicere quod idem sit nunc quod est extremum utriusque temporis. Deinde cum dicit: at vero si idem etc., ostendit quod e contrario, si idem est nunc praeteriti et futuri, necesse est quod nunc sit indivisibile: quia si esset divisibile, sequerentur omnia praedicta inconvenientia. Et sic ex quo non potest dici quod nunc sit divisibile, quasi existente altero nunc praeteriti et altero nunc futuri: nec etiam est divisibile si ponatur idem; concludit manifestum esse ex dictis, quod necesse est in tempore esse aliquid indivisibile, quod dicitur nunc.	793. Therefore, having thus shown that the Now is divisible (as a consequence of supposing that the Now which is the extremity of the past and of the future is not identical), and having rejected this consequent, he concludes to the rejection of the antecedent. And that is what he says: If it is impossible for the Now to be divisible, then it must be admitted that the Now which is the extremity of the past and of the future is one and the same. Then at (606 234 a20) he shows that conversely, if the Now of the past and of the future is the same, then it must be indivisible; because if it were divisible, all the aforementioned inconsistencies would follow, And so, from the fact that the Now cannot be admitted to be divisible (as though the Now of the past were something distinct from the Now of the future) and is indeed not divisible, if the Now of the present is the same as the Now of the future, he concludes from the foregoing that it is clear that in time there must be something indivisible which is called the Now.
lib. 6 l. 5 n. 8 Deinde cum dicit: quod autem nihil in ipso nunc etc., ostendit quod in nunc non potest esse nec motus nec quies. Et primo ostendit de motu; secundo de quiete, ibi: at vero neque quiescere et cetera. Dicit ergo primo, manifestum esse ex iis quae sequuntur, quod in nunc nihil possit moveri: quia si aliquid potest moveri in nunc, continget in nunc moveri duo mobilia, quorum unum sit velocius, et aliud tardius. Sit ergo ipsum nunc n, et aliquod corpus velocius moveatur in n per ab magnitudinem. Sed tardius in aequali minus movetur: ergo tardius in hoc instanti movetur per minorem magnitudinem quae est ag. Sed velocius idem spatium pertransit in minori quam tardius. Quia ergo corpus tardius movebatur per ag magnitudinem in toto ipso nunc, sequitur quod velocius moveatur per eandem magnitudinem in minori quam nunc: ergo nunc dividitur. Sed ostensum est quod nunc est indivisibile: ergo non potest aliquid moveri in nunc.	794. Then at (607 234 a24) he shows that in the Now there can be neither motion nor rest. First he shows it for motion; Secondly, for rest, at 795. He says therefore first (607 234 a24) that it is clear from what follows that in the Now nothing can be in motion, for if anything were in motion in the Now, two things could be in motion then, one of which is faster than the other. So let N be the Now, and let there be a faster body being moved in N through the magnitude AB. In an equal time, a slower body is moved a smaller distance. Therefore, in this instant, it traverses the smaller magnitude AG. But the faster will. cover the same distance in less time than the slower. Therefore, because the slower body traversed the magnitude AG in the very Now, the faster traversed the same magnitude in less than the Now. Hence the Now is divided. But it was already proved that the Now cannot be divided. Therefore, nothing can be moved in a Now.
lib. 6 l. 5 n. 9 Deinde cum dicit: at vero neque quiescere etc., ostendit idem de quiete tribus rationibus. Quarum prima talis est. Dictum est enim in quinto, quod illud quiescit quod est aptum natum moveri et non movetur quando aptum natum est moveri, et secundum illam partem qua natum est moveri, et eo modo quo natum est moveri. Si enim aliquid caret eo quod non est natum habere, ut lapis visu; aut eo tempore quando non natum est habere, ut canis ante nonum diem; aut in ea parte qua non natum est habere, sicut in pede vel in manu; aut eo modo quo non natum est habere, ut si homo non videat ita acute ut aquila: non propter hoc dicitur esse privatum visu. Quies autem est privatio motus: unde nihil quiescit nisi quod est aptum natum moveri, et quando et sicut natum est moveri. Sed ostensum est quod nihil aptum natum est moveri in ipso nunc. Ergo manifestum est quod nihil quiescit in nunc. Secundam rationem ponit ibi: amplius si idem etc.: quae talis est. Illud quod movetur in toto aliquo tempore, movetur in quolibet illius temporis in quo natum est moveri: et similiter quod quiescit in aliquo toto tempore, quiescit in quolibet illius temporis in quo natum est quiescere. Sed idem nunc est in duobus temporibus, in quorum uno toto quiescit, et in altero toto movetur; sicut apparet in eo quod post quietem movetur, et post motum quiescit. Si ergo in nunc aliquid natum est quiescere et moveri, sequeretur quod aliquid simul quiesceret et moveretur; quod est impossibile. Tertiam rationem ponit ibi: amplius autem quiescere etc.: quae talis est. Illud dicimus quiescere, quod se habet similiter et nunc et prius, et secundum se totum et secundum partes suas. Ex hoc enim aliquid dicitur moveri, quod nunc et prius dissimiliter se habet, vel secundum locum vel secundum quantitatem vel secundum qualitatem. Sed in ipso nunc non est aliquid prius; quia sic nunc esset divisibile quia ly prius pertinet ad praeteritum: ergo non contingit in nunc quiescere. Ex hoc autem ulterius concludit, quod necesse est omne quod movetur, et omne quod quiescit, moveri et quiescere in tempore.	795. Then at (608 234 a31) he proves the same thing for rest, giving three arguments. The first of which is this: It was said in Book V that an object at rest is one that is naturally capable of being in motion, but is not in motion when it is capable of being in motion and in respect to the part by which it is capable of being in motion and in the manner in which it is apt to be in motion. For if a thing lacks what it is not naturally capable of having (as a stone lacks sight) or lacks it when it is not naturally due to have it (as a dog lacks sight before the ninth day) or in the part in which it is not naturally capable of having it (as sight in the foot or in the hand) or in the way in which it is not apt to have it (as for a man to have sight as keen as an eaglets), none of these reasons is sufficient for saying that a thing is deprived of sight. Now rest is privation of motion. Hence nothing is at rest except what is apt to be moved and when and as it is apt. But it has been shown that nothing is naturally capable of being moved in the very Now. Therefore, it is clear that nothing is at rest in the Now. The second argument is given at (609 234 a34): That which is being moved in an entire period of time is being moved in each part of that time, in which it is apt to be moved; likewise, what is at rest in a given period of time is at rest in each period of that time in which it is apt to be at rest. But the same Now is in two periods of time, in one of which the mobile is totally at rest and in the other of which it is totally in motion (as appears in that which is in motion after rest or at rest after motion). Therefore, if in the Now something is apt to rest and be in motion, it will follow that something is at once in motion and at rest which is impossible. The third argument is given at (610 234 b5): Rest is said of things which maintain themselves now just as they were previously, but in their entirety and in respect of all their parts. For it is on this account that a thing is said to be in motion, that now it is different from what it was previously, either in respect to place or quantity or quality. But in the Now itself, there is nothing previous; otherwise, the Now would be divisible, because the word “previous” refers to the past. Therefore, it is impossible to rest in the Now. From this he further concludes that necessarily anything that is being moved and anything that is at rest, is being moved and is at rest in time.
lib. 6 l. 5 n. 10 Deinde cum dicit: quod mutatur autem omne etc., ostendit quod omne quod movetur est divisibile, tali ratione. Omnis mutatio est ex quodam in quiddam: sed quando aliquid est in termino ad quem mutatur, ulterius non mutatur, sed iam mutatum est; non enim simul aliquid movetur et mutatum est, ut supra dictum est. Quando vero est aliquid in termino ex quo mutatur, secundum se totum et secundum omnes partes suas, tunc non mutatur: dictum est enim quod illud quod similiter se habet et ipsum et omnes partes eius, non mutatur, sed magis quiescit. Addit autem et omnes partes eius; quia cum aliquid incipit mutari, non simul totum egreditur de loco quem prius occupabat, sed pars post partem. Neque iterum potest dici quod sit in utroque termino secundum se totum et secundum partes suas, dum movetur: sic enim aliquid esset simul in duobus locis. Neque iterum potest dici quod in neutro terminorum sit: loquimur enim nunc de proximo termino in quem mutatur, et non de ultimo extremo; sicut si ex albo aliquid mutetur in nigrum, nigrum est ultimum extremum, fuscum vero est proximum. Et similiter si sit una linea divisa in tres partes aequales, scilicet linea abcd, manifestum est quod mobile, quod in principio motus est in parte ab sicut in loco sibi aequali, contingit in aliqua parte sui motus non esse neque in ab neque in cd: quandoque enim est totum in bc. Cum ergo dicitur quod illud quod mutatur, quando mutatur, non potest in neutro esse, accipitur non extremus terminus, sed proximus. Relinquitur ergo quod omne quod mutatur, dum mutatur, secundum aliquid sui est in uno, et secundum aliquid sui est in altero; sicut cum aliquid mutatur de ab in bc, in ipso moveri pars egrediens de loco ab, ingreditur locum bc; et quod movetur de albo in nigrum, pars quae desinit esse alba, fit fusca vel pallida. Sic igitur manifestum est quod omne quod mutatur, cum sit partim in uno et partim in altero, est divisibile.	796. Then at (611 234 b10) he shows that whatever is in motion is divisible: For every change is from this to that. But when something is at the goal, it is no longer being changed but has been changed, for nothing can be at the same time in the state of being changed and having been changed, as was said above. But when something is at the starting-point of change both in its entirety and in regard to all its parts, then it is not being changed; for it was said above that whatever maintains itself constant in its entirety and in regard to all its parts is not being changed but is at rest. He adds “In regard to all its parts”, because when a thing is beginning to be changed, it does not emerge in its entirety from the place it previously occupied, but part emerges after part. Moreover, it cannot be said that it is in both terms in its entirety and in regard to its parts, while it is being moved; for then something would be in two places at one time. Nor, again, can it be said that it is in neither of the terms: for we are now speaking of the nearest goal into which a thing is being changed and not of the remotest; for example, if something is being changed from white to black, black is the remote goal, but grey is the nearer one. In like manner, if a line ABCD is divided into three equal parts, it is clear that a mobile, which in the beginning of the motion was in AB as in a place equal to itself, can during the motion be neither in AB nor in CD; for at some time it is in its entirety in BC. Therefore, when it is said that what is being moved cannot happen to be in neither extremity while it is being moved, must be understood as referring not to the remotest extremity but to a nearer one. What is left, therefore, is that whatever is being changed is, while it is being changed, partly in one and partly in the other; for example, when something is being changed from AB to BC, then during the motion, the part leaving the place AB is entering the place BC; likewise, when something is being moved from white to black, the part which ceases to be white becomes grey or light grey. Consequently, it is clear that anything that is being moved, since it is partly in one and party in the other, is divisible.
lib. 6 l. 5 n. 11 Sciendum est autem quod Commentator in hoc loco movet dubitationem de hoc, quod si Aristoteles non intendit hic demonstrare quod mobile sit divisibile, nisi de mobili quod movetur motu quem dixit esse in solis tribus generibus, scilicet quantitate, qualitate et ubi, demonstratio sua non erit universalis, sed particularis: quia illud etiam quod mutatur secundum substantiam, divisibile invenitur. Unde videtur quod intelligat de eo quod transmutatur secundum quamcumque transmutationem, ut includatur generatio et corruptio in substantia. Et hoc etiam ex ipsis verbis eius apparet: non enim dicit quod movetur sed quod mutatur. Sed tunc videtur sua demonstratio non valere: quia aliquae transmutationes sunt indivisibiles, sicut ipsa generatio substantialis et corruptio, quae non sunt in tempore; et in huiusmodi transmutationibus non est verum, quod illud quod mutatur, sit partim in uno et partim in alio; non enim cum ignis generatur, partim est ignis et partim non ignis.	797. But it should be mentioned that the Commentator here raises the problem that if Aristotle does not intend in this place to demonstrate that every mobile is divisible but only what is mobile in regard to motion (which he said is present in only three genera; namely, quantity, quality and where), then his demonstration will not be universal but particular; because even the subject of substantial change is found to be divisible. Hence, he seems to be speaking of what is subject to any and every type of change, including even generation and ceasing-to-be in the genus of substance. And this is evident from his very words: for he does not say “what is being moved”, but “what is being changed”. But in that case his demonstration has no value, because some changes are indivisible, such as generation and ceasing-to-be of substance, which do not consume time. In such changes it is not true that what is being changed is partly in one extremity and partly in the other, for when fire is generated, it is not partly fire and partly non-fire.
lib. 6 l. 5 n. 12 Et inducit ad hoc plures solutiones: quarum una est Alexandri, dicentis quod nulla transmutatio est indivisibilis, aut in non tempore. Sed hoc reprobatur; quia per hoc destruitur quoddam probabile et famosum apud Aristotelem et omnes Peripateticos, scilicet quod aliquae transmutationes sint in non tempore, ut illuminatio et alia huiusmodi. Inducit etiam solutionem Themistii, dicentis quod etsi sit aliqua transmutatio in non tempore, tamen hoc latet; et Aristoteles utitur eo quod est manifestum, scilicet quod transmutatio sit in tempore. Sed hoc reprobat; quia eodem modo se habet de divisione mutationis et mutabilis; et adhuc videtur latentius divisibilitas mobilis quam mutationis. Unde demonstratio Aristotelis non esset efficax: quia posset aliquis dicere, quod licet ea quae mutantur mutationibus manifeste divisibilibus, sint divisibilia, sunt tamen aliqua mutabilia latentia, quae sunt indivisibilia. Ponit etiam solutionem Avempacis, dicentis quod hic non agitur de divisione mutabilis secundum quantitatem, sed de divisione mutabilis secundum quod subiectum dividitur per accidentia contraria, de quorum uno mutatur in alterum.	798. In the face of this problem he proposes a number of solutions, one of which is Alexander’s, who says that no change is indivisible or in non-time, But this must be rejected, because it conflicts with an opinion that is held as probable and famous with Aristotle and all Peripatetics, namely, that certain changes are in non-time, such as illumination and the like. He mentions also the solution of Themistius, who says that even if there be changes in non-time, they are hidden, whereas Aristotle appeals to what is evident, namely, that change occurs in time. But this he also rejects, because change and the changeable are divided in the same way, and the divisibility of a mobile is more hidden than the divisibility of change. Hence Aristotle’s demonstration would not be valid, because someone could say that although things which changed by changes evidently divisible are themselves divisible, yet there are some hidden changeable beings which are indivisible. He mentions, too, the solution of Avempace [Ibn-Bajja], who says that the problem here is not about the quantitative division of the things capable of change but of that division whereby the subject is divided by contrary accidents, one of which is changed into the other.
lib. 6 l. 5 n. 13 Et addit postea suam solutionem, quod illae mutationes quae dicuntur fieri in non tempore, sunt termini quorundam motuum divisibilium. Accidit ergo aliquid transmutari in non tempore, inquantum scilicet quilibet motus terminatur in instanti. Et quia illud quod est per accidens praetermittitur in demonstrationibus, ideo illo Aristoteles in hac demonstratione utitur, ac si omnis mutatio sit divisibilis et in tempore.	799. Then the Commentator adds his own solution: namely, that those changes which are said to occur in non-time are the extremities of certain divisible motions, It happens, therefore, that something should be changed in non-time, insofar as every motion is terminated in an instant. And because what is accidental is ignored when it comes to demonstrating, for that reason Aristotle proceeds in this demonstration as though every change were divisible and in time.
lib. 6 l. 5 n. 14 Sed si quis recte consideret, haec obiectio non est ad propositum. Non enim Aristoteles in sua demonstratione utitur quasi principio, quod omnis mutatio sit divisibilis; cum magis e converso ex divisione mobilis procedat ad divisionem mutationis, ut infra patebit. Et sicut ipse post dicit, divisibilitas per prius est in mobili quam in motu vel mutatione. Sed utitur principiis per se notis, quae necesse est concedere in quacumque mutatione: scilicet quod illud quod mutatur, quando est secundum totum et partes in termino a quo mutatur, nondum mutatur secundum illam mutationem; et quod quando est in termino ad quem, non mutatur sed mutatum est; et quod non potest esse nec in utroque totum, nec in neutro, sicut expositum est. Unde ex necessitate sequitur quod in qualibet mutatione, illud quod mutatur, dum mutatur, sit partim in uno termino et partim in alio. Sed hoc diversimode invenitur in diversis mutationibus. Nam in illis mutationibus, inter quarum extrema est aliquod medium, contingit quod id quod mutatur, dum mutatur, partim sit in uno extremo et partim in alio, secundum ipsa extrema. In illis vero inter quarum terminos non est aliquod medium, id quod mutatur non est secundum diversas partes suas in diversis extremis secundum ipsa extrema, sed secundum aliquid eis adiunctum. Sicut cum materia mutatur de privatione ad formam ignis, dum est in ipso mutari, est quidem sub privatione secundum seipsam; sed partim est sub forma ignis non secundum seipsam, sed secundum aliquid ei adiunctum, scilicet secundum dispositionem propriam ignis, quam partim recipit antequam formam ignis habeat. Unde infra probabit Aristoteles quod etiam generatio et corruptio sunt divisibiles: quia quod generatur, prius generabatur; et quod corrumpitur, prius corrumpebatur. Et forte hoc modo intellexit Alexander quod omnis transmutatio est divisibilis, scilicet vel secundum seipsam vel secundum motum ei adiunctum. Sic etiam intellexit Themistius quod Aristoteles assumpsit id quod erat manifestum, et praetermisit id quod erat latens: quia nondum erat locus tractandi de divisibilitate vel indivisibilitate mutationum; sed hoc reservatur in posterum. In omnibus tamen vel divisibilibus vel indivisibilibus salvatur quod Aristoteles hic dicit: quia etiam quae dicuntur indivisibiles mutationes, sunt quodammodo divisibiles, non secundum propria sua extrema, sed per ea quae eis adiunguntur. Et hoc est quod Averroes dicere voluit, quod hoc est per accidens, aliquas mutationes esse in non tempore.	800. But if you consider the matter correctly, you will see that this objection is not to the point. For in his demonstration Aristotle does not use as his principle the statement that every change is divisible (since he proceeds rather from the divisibility of the mobile to the division of change, as will be clear later, for as he says later, divisibility is first in the mobile, before it is in motion or change). Rather he uses principles that are evident and which must be conceded in any and every case of change; namely, (1) that what is being changed in regard to a certain matter is not being changed in regard to that matter as long as it is totally and according to all its parts still in the starting point, and (2) when it is in the goal, it is not being changed but has been changed, and (3) that it cannot be entirely in both terms or entirely in either of them, as was explained. Hence, it necessarily follows that in any change whatsoever, what is being changed is, during the change, partly in one extremity and partly in the other. But this occurs in various ways in various changes. For in changes between whose extremities there is something intermediate, it can happen that the mobile is, during the change, partly in one extreme and partly in the other extreme, precisely as extremes. But in those between whose extremes there is nothing intermediate, that which is being changed does not have different parts in different extremities precisely as extremities, but by reason of something connected with the extremities. For example, when matter is being changed from privation of fire to the form of fire, then while it is in the state of being changed, it is indeed under privation as to itself, but yet it is partly under the form of fire, not inasmuch as it is fire, but according to something connected with it, i.e., according to the particular disposition for fire, which disposition it partly receives before it has the form of fire. That is why Aristotle will later prove that even generation and ceasing-to-be are divisible, because what is generated was previously being generated, and what ceases-to-be was previously ceasing-to-be. Perhaps this was the sense in which Alexander understood the statement that every change is divisible; namely, either according to itself or according to a motion connected with it. So also Themistius understood by the statement that Aristotle took what was evident and abstracted from what was hidden, that the proper place for treating of the divisibility or indivisibility of changes would not be reached until later. Nevertheless, in all divisibles and indivisibles, what Aristotle says here is true: because even changes that are called indivisible are in a sense divisible, not by reason of their extremities but by reason of something connected to them. And this is what Averroes wanted to say when he said that it is per accidens that some changes occur in non-time.
lib. 6 l. 5 n. 15 Est etiam hic alia dubitatio. Non enim videtur hoc verum in motu alterationis, quod id quod alteratur, partim sit in uno termino et partim in altero, dum alteratur. Non enim sic procedit motus alterationis, quod prius una pars alteretur et postea altera: sed totum prius est minus calidum, et postea magis calidum. Unde etiam Aristoteles in libro de sensu et sensato dicit, quod non similiter se habet in alteratione sicut in latione. Lationes namque rationabiliter in medio prius attingunt: quaecumque vero alterantur, non adhuc similiter. Contingit enim simul alterari, et non dimidium prius; velut aquam simul omnem coagulari.	801. However, there is here another difficulty. For when it comes to alteration, it does not seem to be true that what is being altered is partly in one term and partly in the other, during the alteration. For the motion of alteration does not take place in such a way that first one part and then another is altered; rather the entire thing that was less hot becomes hotter. For which reason Aristotle even says in the book On Sense and the Thing Sensed that alterations are not like local motions. For in the latter, the subject reaches the intermediate before the goal, but such is not the case with things that are altered; for some things are altered all at once and not part by part, for it is the entire water that all at once freezes.
lib. 6 l. 5 n. 16 Est autem ad hoc dicendum quod Aristoteles in hoc sexto libro agit de motu secundum quod est continuus. Continuitas autem primo et per se et proprie invenitur in motu locali tantum, qui solum potest esse continuus et regularis, ut ostendetur in octavo. Et ideo demonstrationes in hoc libro positae, pertinent quidem ad motum localem perfecte, ad alios autem motus non totaliter, sed secundum quod aliquid continuitatis et regularitatis participant. Sic ergo dicendum est quod mobile secundum locum semper prius subintrat locum in quem tendit secundum partem quam secundum totum: in alteratione autem est quidem ut sic, est autem ut non. Manifestum est enim quod omnis alteratio fit per virtutem agentis quod alterat, cuius virtus quanto fuerit maior, tanto maius corpus alterare potest. Quia ergo alterans est finitae virtutis, usque ad determinatam quantitatem corpus alterabile subditur eius virtuti, et simul recipit impressionem agentis; unde simul alteratur totum, non pars post partem. Sed illud alteratum iterum alterat aliquid aliud sibi coniunctum: est tamen minoris efficaciae in agendo. Et sic inde quousque deficiat virtus alterativa; sicut ignis calefacit unam partem aeris statim, et illa calefacta calefacit aliam: et sic pars post partem alteratur. Unde et Aristoteles in libro de sensu et sensato, post verba praemissa subiungit: attamen si multum fuerit quod calefit aut coagulatur, habitum ab habito patitur. Primum autem ab ipso faciente transmutari necesse est, et simul alterari et subito. Verumtamen et in hoc ipso quod simul alteratur, est quandam successionem considerare; quia cum alteratio fiat per contactum alterantis, partes alterati quanto magis appropinquant ad corpus alterans, perfectius a principio recipiunt impressionem alterantis: et sic successive secundum ordinem partium ad perfectam alterationem pervenitur; et maxime quando in corpore alterabili est aliquid contra resistens alteranti. Sic ergo id quod concludit, quod videlicet id quod mutatur, dum mutatur partim est in termino a quo et partim in termino ad quem, quasi una pars prius perveniat ad terminum ad quem quam alia, simpliciter et absolute verum est in motu locali: in motu autem alterationis aliqualiter, ut dictum est.	802. But to this it must be replied that in this Sixth Book Aristotle is treating of motion as continuous. And continuity is primarily and per se and strictly found only in local motion, which alone can be continuous and regular, as will be shown in Book VIII. Therefore, the demonstrations given in Book VI pertain perfectly to local motion but imperfectly to other motions, i.e., only to the extent that they are continuous and regular. Consequently, it must be said that what is mobile in respect of place always enters a new place part by part before it is there in its entirety; but in alteration, that is only partially true. For it is clear that every alteration depends on the power of the agent that causes the alteration—as its power is stronger it is able to alter a greater body. Therefore, since the cause of the alteration has finite power, a body capable of being altered is subject to its power up to a certain limit of quantity, which receives the impression of the agent all at once; hence the whole is altered all at once, and not part after part. Yet that which is altered can in turn alter something else conjoined to it, although its power in acting will be less forceful, and so on, until the power involved in the series of alterations is depleted. An example of this is fire which all at once heats one section of air, which in turn heats another, and thus part after part is altered. Hence in the book On Sense and the Thing Sensed, after the above-quoted passage, Aristotle goes on to say: “Yet if the object heated or frozen is large, part after part will be affected. But the first part had to be altered all at once and suddenly by the agent”. Yet even in things that are altered all at once, it is possible to discover some kind of succession, because since alteration depends on contact with the cause which alters, the parts closer to the body that causes the alteration will more perfectly receive at the very beginning an impression from the agent: and thus the state of perfect alteration is reached successively according to an order of parts. This is especially true when the body to be altered has something which resists the power of the altering cause. Consequently, the conclusion (that what is being changed, is, while it is being changed, partly in the terminus a quo and partly in the terminus ad quem, in the sense that one part reaches the terminus ad quem before another does) is unqualifiedly and absolutely true in local motion. But in alteration it is qualifiedly true, as we have said.
lib. 6 l. 5 n. 17 Quidam vero e converso dixerunt quod hoc quod hic dicitur, magis habet veritatem in motu alterationis quam in motu locali. Dicunt enim quod hoc quod dicitur, quod id quod mutatur partim est in termino a quo et partim in termino ad quem, non sic est intelligendum, quod una pars eius quod movetur sit in uno termino et alia in alio, sed est referendum ad partes terminorum: quia scilicet id quod movetur partem habet de termino a quo et partem de termino ad quem; sicut illud quod movetur de albedine in nigredinem, primo non habet perfecte albedinem nec perfecte nigredinem, sed aliquid participat imperfecte de utroque. In motu autem locali hoc non videtur verum nisi secundum quod id quod movetur, dum est in medio duorum terminorum, quodammodo aliquid participat de utroque extremo. Sicut si terra moveatur ad locum ignis, dum est in loco aeris in suo moveri, partem habet utriusque termini; inquantum scilicet locus aeris et est sursum respectu loci terrae, et deorsum respectu loci ignis.	803. Some on the other hand have held that the present doctrine is truer when applied to alteration than when applied to local motion, For they hold that the statement “what is being changed is partly in the terminus a quo and partly in the terminus ad quem is not to be interpreted as meaning that one part of the thing in motion is in one term and another in the other, but that reference is being made to the parts of the termini, i.e., that what is being moved has part of the terminus a quo and part of the terminus ad quem, as something in motion from white to black, is at the very beginning neither perfectly white nor perfectly black, but imperfectly partakes of both; whereas in local motion this does not seem to be true, except in the sense that the thing in motion, while it is between the two extremities, somehow partakes of both extremities. For example, if earth were to be moved to the place normal to fire, then while it was in the region proper to air, it would have a part of each extremity, (i.e., earth and fire), in the sense that the place of air is above that of earth, and below that of fire,
lib. 6 l. 5 n. 18 Haec autem expositio extorta est, et contra opinionem Aristotelis. Et primo quidem apparet hoc ex ipsis verbis Aristotelis. Concludit enim: necesse igitur hoc quidem aliquid in hoc esse, aliud vero in altero mutantis, idest eius quod mutatur. Loquitur ergo de partibus mobilis, non de partibus terminorum. Secundo ex eius intentione. Inducit enim ad probandum id quod mutatur esse divisibile: quod non posset concludi ex praemissis. Unde et Avempace dixit, quod non intendit hic probare quod mobile sit divisibile in partes quantitativas, sed secundum formas: inquantum scilicet id quod mutatur de contrario in contrarium, dum est in ipso mutari, habet aliquid de utroque contrario. Sed intentio Aristotelis est expresse, ostendere quod mobile est divisibile in suas partes quantitativas, sicut et alia continua. Et sic utitur in sequentibus demonstrationibus. Nec hoc videtur esse conveniens quod dicunt quidam, quod per hoc probatur etiam divisibilitas mobilis secundum continuitatem. Quia per hoc quod mobile, dum movetur, participat utrumque terminum, et non statim habet perfecte terminum ad quem, manifestum apparet mutationem esse divisibilem secundum continuitatem: et ita, cum divisibile non possit esse in indivisibili, sequitur quod etiam mobile sit divisibile ut continuum. Manifeste enim Aristoteles in subsequentibus ostendit divisionem motus ex divisione mobilis. Unde si intenderet concludere divisionem mobilis per divisionem motus, esset demonstratio circularis. Tertio apparet hanc expositionem esse inconvenientem ex ipsa expositione Aristotelis, cum dicit: dico autem in quod mutatur primum secundum mutationem. Ex quo apparet quod non intendit dicere quod partim sit in termino a quo et partim in termino ad quem, propter hoc quod sit in medio, quasi participans utrumque extremum; sed quia secundum unam partem sui est in uno extremo, et secundum aliam in medio.	804. But this is a forced explanation and against Aristotle’s opinion. For in the first place we need only look at the very words of Aristotle. For he says as a conclusion: “it follows therefore that part of that which is being changed must be at the starting-point and part at the goal”. He is speaking therefore about the parts of the mobile and not about the parts of the termini. In the second place it is against Aristotle’s intention, For Aristotle brings to light facts that will prove that what is being changed is divisible—a statement that could not be proved, if you held to the interpretation given. Hence Avempace said that Aristotle does not intend here to prove that a mobile can be divided into quantitative parts but according to forms, in the sense that what is being moved from contrary to contrary has, while it in being changed, something from each contrary. But the intention of Aristotle is expressly to show that a mobile can be divided into its quantitative parts, just as any continuum, for he makes use of that fact in the demonstrations that will follow. Nor can we heed the opinion that such an interpretation will help to prove that a mobile can be divided on the basis of continuity. Because the very fact that a mobile, while it is being moved, partakes of each terminus and does not perfectly possess the terminus ad quem all at once, reveals that change is divisible on the basis of continuity. And thus, since a divisible cannot exist in an indivisible, it follows that the mobile also can be divided as a continuum. For in the matters to follow, Aristotle will clearly prove that motion is divisible, because the mobile is divisible. Hence, if he intended to conclude that a mobile is divisible because motion is divisible, he would be arguing in a circle. Thirdly, such an interpretation appears to conflict with Aristotle’s own interpretation at (611 bis 234 b17) where he says “here by ‘goal’ of change I mean that into which it is first changed during the process of change”. This shows that he does not intend to say that it is partly in the terminus a quo and partly in the terminus add quem just because it is midway and, as it were, sharing in both extremities, but because in regard to one part of itself it is in one extreme, and according to another part in what is midway.
lib. 6 l. 5 n. 19 Sed circa hanc expositionem Aristotelis dubium esse videtur quod dicit in quod primum mutatur. Non enim videtur posse accipi in quod primum mutatur, propter divisibilitatem magnitudinis in infinitum. Et ideo dicendum est, quod id in quod primum mutatur in motu locali, dicitur locus qui contingit locum a quo mutatur, ita quod nihil est eius. Si enim acciperetur secundus locus qui haberet aliquid primi, non esset accipere primum locum in quem mutatur. Quod sic patet. Sit locus unde mutatur aliquod mobile ab, et locus ei contactus aequalis sit bc. Quia enim ab divisibile est, dividatur in puncto d, et sumatur de loco bc versus c, quod sit aequale ei quod est bd; et sit illud gc. Manifestum est igitur quod mobile prius mutatur ad locum dg quam ad locum bc. Et iterum, cum ad sit divisibile, erit accipere alium locum priorem; et sic infinitum. Et similiter in motu alterationis accipiendum est primum in quod mutatur, medium alterius speciei; sicut cum mutatur de albo in nigrum, accipi debet fuscum, non autem minus album.	805. But with respect to this explanation of Aristotle, one might wonder why he says “that into which it is first changed” for it seems impossible to discover that into which it is first changed, since a magnitude can be divided ad infinitum. Therefore, it must be said that “That into which it is first changed” in local motion is the place next to but not part of the place from which the local motion starts. For if we took it to mean a place that included part of the original place, we would not be assigning the first place into which it is being moved. The following example will illustrate this: Let AB be the place whence a mobile is being moved, and let BC be the adjacent place equal to AB. Now, since AB can be divided, let it be divided at D and take a point G near C so that the place GC is equal to BD. It is clear that the mobile will arrive at DG before it reaches BC. Moreover, since AD can be divided, a place prior to DG can be take n, and so on ad infinitum. Similarly, in regard to alteration, “the first into which something is changed” must be considered to be an intermediate; for example, when something is changed from white to black, the first into which the subject is changed is into grey, not into less white.