Authors/Thomas Aquinas/physics/L5

Translated by Richard J. Blackwell, Richard J. Spath & W. Edmund Thirlkel Yale U.P., 1963

Lecture 1 Per se motion is distinguished from per accidens

Latin	English
	Lecture 1 Per se notion is distinguished from per accidens
lib. 5 l. 1 n. 1 Postquam philosophus determinavit de motu et de his quae consequuntur motum in communi, hic iam accedit ad dividendum motum. Et dividitur in partes duas. In prima agit de divisione motus secundum quod dividitur in species; in secunda de divisione motus in partes quantitativas, et hoc in sexto libro, ibi: si autem est continuum et cetera. Prima autem pars dividitur in duas. In prima agit de divisione motus in suas species; in secunda agit de unitate et oppositione motus, ibi: post haec autem dicamus quid est simul et cetera. Prima dividitur in duas. In prima distinguit motum per se a motu per accidens; in secunda dividit motum per se in suas species, ibi: quoniam autem omnis mutatio et cetera. Prima dividitur in duas. In prima distinguit motum per se a motu per accidens; in secunda praetermittendum docet motum per accidens, et determinandum esse de motu per se, ibi: secundum quidem igitur accidens et cetera. Circa primum duo facit: primo distinguit motum per se a motu per accidens; secundo epilogat praedicta, ibi: quomodo quidem et cetera. Distinguit autem in prima parte motum per se a motu per accidens, tripliciter: primo quidem ex parte mobilis; secundo ex parte moventis, ibi: est autem et in movente etc.; tertio ex parte termini, ibi: quoniam autem est aliquid et cetera.	638. After discussing motion and the things that accompany motion in general, the Philosopher now undertakes to give various divisions of motion. And his treatment falls into two parts: In the first he divides motion into its species; In the second he divides motion into quantitative parts in Book VI. In the first he makes two parts: First he divides motion into its species; Secondly, he discusses unity and opposition of motion, at L. 5. The first is divided into two sections: In the first he distinguishes motion per se from per accidens; In the second he divides motion into its species, at L. 2. The first is divided into two parts: In the first he distinguishes per se motion from per accidens; In the second he shows that per accidens need not be discussed but that per se motion must, at 647. In regard to the first he does two things: First he distinguishes per se from per accidens motion; Secondly, he makes a summary at 646. In the first part he distinguishes per se motion from per accidens motion in three ways: First, on the side of the mobile; Secondly, on the side of the mover, at 640; Thirdly, on the side of the termini of motion, at 641.
lib. 5 l. 1 n. 2 Dicit ergo primo quod omne transmutans, idest transmutatum, tribus modis dicitur transmutari. Uno enim modo dicitur aliquid transmutari per accidens, sicut cum dicimus musicum ambulare, quoniam hic homo, cui accidit esse musicum, ambulat. Alio modo dicitur aliquid transmutari simpliciter, quia aliqua pars eius mutatur, sicut omnia quae dicuntur mutari secundum partes. Et ponit exemplum in motu alterationis: dicitur enim sanari corpus animalis, quia sanatur oculus aut thorax, idest pectus, quae sunt partes totius corporis. Tertio modo dicitur aliquid moveri, quod neque secundum accidens movetur, neque secundum partem, sed ex eo quod ipsum movetur primo et per se; ut per hoc quod dicit primo, excludatur motus secundum partem; per id quod dicit secundum se, excludatur motus per accidens. Hoc autem per se mobile variatur secundum diversas species motus; sicut alterabile est mobile secundum alterationem, et augmentabile secundum augmentum. Et iterum in specie alterationis differt sanabile, quod movetur secundum sanationem, et calefactibile, quod movetur secundum calefactionem.	639. He says therefore first (465 224 a1) that whatever changes, i.e., whatever is being changed, is described as doing so in three ways. First, per accidens, as when we say that a musician is walking, because the person who is walking happens to be a musician. Secondly, a thing is described as being changed without qualification even though only some part of it is changing, i.e., in statements which refer to part of the thing in question: thus the body is said to be restored to health, because the eye or the chest, which are parts of the body, are restored to health. Thirdly, there is the case of a thing that is in motion neither accidentally nor in respect of something that belongs to it as a part but in virtue of its being directly and per se in motion. And he says “directly” to exclude motion of a part, and per se to exclude motion that is per accidens. Now this per se mobile is a different thing according to the various kinds of motion: for example, it may be a thing capable of alteration—in which case it is called alterable—or it may be capable of growing—in which case it is called augmentable. Again, in the sphere of alteration it is called heal-able, if it is moved in respect of health, and heat-able, if it is moved in respect of heat.
lib. 5 l. 1 n. 3 Deinde cum dicit: est autem et in movente etc., distinguit motum per se a motu per accidens ex parte moventis. Et dicit quod similiter praedicta distinctio, quae posita est ex parte mobilis, potest attendi in movente. Tripliciter enim dicitur aliquid movere. Uno modo per accidens, sicut musicus aedificat. Alio modo secundum partem, inquantum aliqua pars eius movet, sicut homo dicitur percutere quia manus eius percutit. Tertio modo dicitur aliquid movere primo et per se, sicut medicus sanat.	640. Then at (466 224 a30) from the side of the mover he distinguishes per se from per accidens motion, And he says that the preceding distinctions which were posed from the side of the mobile can be found in the mover. For a thing is described in three ways as causing motion. First, per accidens, as “the musician is building”. Secondly, by reason of a part (when some part of the mover causes motion), e.g., the man is said to strike, because his hand strikes. In a third way, something is described as acting or moving directly and per se, as “the healer heals”.
lib. 5 l. 1 n. 4 Deinde cum dicit: quoniam autem est aliquid etc., procedit ad dividendum motum eodem modo ex parte termini. Et primo praemittit quaedam praeambula; secundo ponit divisionem, ibi: est autem et in illis et cetera. Circa primum tria facit: primo ponit quot requirantur ad motum; secundo comparat ea ad invicem, ibi: alterum enim est quod etc., tertio solvit quandam dubitationem, ibi: quid quidem igitur et cetera. Dicit ergo primo quod ad motum requiruntur quinque. Primo requiritur primum movens, a quo scilicet est principium motus. Secundo requiritur mobile quod movetur. Tertio, tempus in quo est motus. Et praeter ista tria requiruntur duo termini; unus scilicet ex quo incipit motus; et alius in quem motus procedit: omnis enim motus est a quodam in quiddam.	641. Then at (467 224 a34) looking at the terminus of motion, he divides motion once more in the same manner. First he lays down some presuppositions; Secondly, he gives his division, at 645. About the first he does three things: First he declares how many things are required for motion; Secondly, he mutually compares them, at 642; Thirdly, he settles a question, at 644. He says therefore (467 224 a34) that five things are needed for motion, First, there must be a first mover, i.e., a source from which the motion originates; secondly, a mobile that is being moved; thirdly, a time in which the motion occurs. In addition to these three are required the two termini; one from which the motion starts and another into which the motion tends; for every motion is from something into something.
lib. 5 l. 1 n. 5 Deinde cum dicit: alterum enim etc., comparat praemissa ad invicem. Et primo mobile ad duos terminos motus; secundo duos terminos motus ad invicem, ibi: magis autem in quod et cetera. Dicit ergo primo quod id quod primo et per se movetur, alterum est a termino in quem tendit motus, et a termino a quo motus incipit; sicut patet in istis tribus, lignum, calidum et frigidum. In motu enim calefactionis, lignum quidem est subiectum mobile, aliud vero, scilicet calidum, est terminus ad quem, aliud autem, scilicet frigidum, est terminus a quo. Dicit autem id quod movetur primum esse alterum ab utroque termino, quia nihil prohibet id quod movetur per accidens, esse alterum terminorum: subiectum enim, ut lignum, est id quod calefit per se; privatio vero et contrarium, ut frigidum, est quod calefit per accidens, ut in primo dictum est. Quod autem mobile sit alterum ab utroque termino, consequenter probat per hoc quod motus est in subiecto, sicut in ligno; non autem est in altero terminorum, neque in specie albi neque in specie nigri. Et hoc patet per hoc, quod illud in quo est motus, movetur: terminus autem motus neque movet neque movetur: sive terminus motus sit species, idest qualitas, ut in alteratione: sive sit locus, ut in motu locali; sive sit quantum, ut in motu augmenti et decrementi. Sed movens movet subiectum quod movetur, in quod movetur, idest in terminum ad quem. Quia ergo motus est in subiecto quod movetur, non autem in termino, manifestum est quod subiectum mobile est aliud a termino motus.	642. Then at (468 224 b1) he compares these five things: First he compares the mobile to the two termini; Secondly, he compares one terminus with the other, at 643, He says therefore (468 224 b1) that whatever is being moved directly and per se is distinct from the terminus into which the motion tends and from the terminus from which the motion begins, as is evident in these three things: wood, hot and cold. For in the motion called heating, the wood is the mobile subject, whereas the hot which is the terminus into which, is something else, as is the cold, which is the terminus from which. Now he says that what is moved directly is distinct from both termini, because there is nothing to prevent what is being moved per accidens from being either of the termini: for a subject, such as wood, is what becomes hot per se; but the privation, which is a contrary, namely, cold, is what becomes hot per accidens, as was explained in Book I. That the mobile is distinct from each terminus he proves on the ground that motion is in its subject, for example, in the wood, and not in either of the termini, i.e., not in the species “white” or in the species “black”. This is clear from the fact that that in which the motion exists is what is being moved. But the terminus of motion neither moves nor is moved: whether the terminus be a quality, as in alteration, or a place, as in local motion, or quantity, as in the motion called growing and decreasing. However, the mover moves the subject, which is being moved, into the terminus ad quem, Therefore, since motion exists in the subject being moved but not in the termini, it is clear that the mobile subject is distinct from the termini of the motion,
lib. 5 l. 1 n. 6 Deinde cum dicit: magis autem in quod etc., comparat utrumque terminorum ad invicem. Et dicit quod mutatio magis denominatur a termino ad quem, quam a termino a quo: sicut corruptio dicitur mutatio in non esse, quamvis illud quod corrumpitur mutetur ex esse; e contrario generatio est mutatio in esse, quamvis incipiat a non esse. Nomen autem generationis ad esse pertinet, corruptionis vero ad non esse. Huius autem ratio est, quia per mutationem aufertur terminus a quo, et acquiritur terminus ad quem: unde motus videtur repugnare termino a quo, et convenientiam habere cum termino ad quem; et propter hoc ab eo denominatur.	643. Then at (469 224 b7) he compares one terminus with the other. And he says that a change gets its name from the terminus ad quem rather than from the terminus a quo; for example, a change into non-being has the special name “corruption’, while, on the other hand, “generation” is the change into being, even though it starts from non-being. Consequently, the name “generation” pertains to being and “corruption” to non-being. The reason for this is that through change the terminus a quo is taken away, but a terminus ad quem is acquired: for which reason, motion seems to have a repugnance for the terminus a quo and a kinship to the terminus ad quem—that is why it gets its name from the latter.
lib. 5 l. 1 n. 7 Deinde cum dicit: quid quidem igitur motus sit etc., solvit quandam dubitationem. Et circa hoc tria facit. Primo praemittit duo quae ex praemissis sunt manifesta: quorum primum est quod in tertio dictum est quid sit motus; secundum est quod in praecedentibus immediate dictum est, quod species, idest qualitas, et locus et quaecumque passiones, idest passibiles qualitates, quae sunt termini motus, non moventur, cum in eis non sit motus, ut dictum est; ut patet in scientia, quae est quaedam species, et calore, qui est quaedam passio vel passibilis qualitas. Secundo ibi: et dubitabit aliquis etc., ponit tertium, de quo est dubitatio. Et dicit quod aliquis dubitare potest, utrum passiones, idest passibiles qualitates, ut calor et frigus et albedo et nigredo, ex quo non moventur, sint quidam motus. Tertio ibi: erit enim ad motum etc., ducit ad inconveniens, si hoc ponatur. Cum enim albedo sit terminus in quem est motus, si albedo sit motus, sequitur quod motus sit terminus motus, quod non potest esse, ut infra probabitur. Et ex hoc determinat veritatem, et dicit quod albedo non est motus, sed albatio. Addit autem fortassis, quia nondum probavit quod motus non terminetur in motum.	644. Then at (470 224 b10) he settles a doubt, About which he does three things: First, he mentions two things that are clear from the foregoing: first, that we have already pointed out in Book III what motion is; secondly, that in the immediately foregoing we have said that qualities and place and passible qualities that are the termini of motion are not themselves being changed, since there is no motion existing in them, as we have already said and as is clear from heat, which is a passible quality, and from science, which is a quality. Secondly, at (471 224 b13) he mentions a matter about which there is doubt, saying that someone may wonder whether passible qualities, such as heat and coldness and whiteness and blackness might not be types of motion, since none of them is a subject of motion. Thirdly, at (472 224 b14) he mentions a discrepancy that would arise if such a view were posited. For since whiteness is a terminus into which a motion tends, then if whiteness itself were a motion, it would follow that there is motion in the terminus of a motion, which cannot be, as will be proved later. And from this he arrives at the truth that it is not whiteness but whitening that is motion, But he adds “perhaps” because he has not yet proved that a motion cannot end up in a motion.
lib. 5 l. 1 n. 8 Deinde cum dicit: est autem et in illis etc., ex quo termini motus sunt aliud a mobili et a movente, ut ostensum est, ostendit quod praeter divisionem motus, quae accipitur ex parte moventis et mobilis, dividitur tertio motus ex parte termini. Et quia terminus ad quem magis denominat motum quam terminus a quo, ut dictum est, accipit divisionem motus non ex parte termini a quo, sed ex parte termini ad quem. Et dicit quod etiam ex parte illorum, scilicet terminorum, potest accipi in motu aliquid quod est per accidens, et aliquid quod est secundum partem et secundum aliud, et aliquid quod est primo et non secundum aliud. Per accidens quidem, sicut si dicatur de eo quod fit album, quod mutatur in id quod intelligitur vel cognoscitur ab aliquo, erit hoc per accidens: accidit enim colori albo quod intelligatur. Si autem dicatur de eo quod fit album, quod mutetur in colorem, hoc erit secundum partem: dicitur enim mutari in colorem, quia mutatur in albedinem, quae est pars coloris. Et simile est si dicam de aliquo qui vadit Athenas, quod vadit in Europam; quia Athenae sunt pars Europae. Si autem dicatur de eo quod fit album, quod mutatur in album colorem, hoc erit primo et per se. Non autem dividit motum ex parte temporis, quod videbatur residuum: quia tempus comparatur ad motum ut mensura extrinseca.	645. Then at (473 224 b16) from the fact that termini of motion are distinct from the mover and from the mobile, he shows that in addition to the divisions of motion taken on the side of the mover and of the mobile, there is a third, i.e., one taken on the side of the terminus. And since it is from the terminus ad quem rather than from the terminus a quo that motions are named, he develops his division not on the side of the latter but of the former. And he says that even on the side of the termini it is possible to find in motion (1) a goal that is so per accidens or (2) partially, i.e., with reference to a part or to something other than itself or (3) directly and not with reference to something else. And first of all, per accidens: when it is said of what is becoming white that it is being changed into something that can be understood or recognized by someone—that will be per accidens for it is accidental to the color white that it is recognized. But if it is said of what is becoming white that it is being changed into a color—this will be according to a part: for it is said to be changing into a color because it is becoming white, which is a part of the genus color. Likewise, if I should say of someone who is going to Athens that he is going to Europe, for Athens is a part of Europe. However, if it is said of what is becoming white that it is being changed into the color white, this will be directly and per se. The Philosopher does not divide motion from the viewpoint of time (which was one of the five things required for motion) because time is related to motion as an extrinsic measure.
lib. 5 l. 1 n. 9 Deinde cum dicit: quomodo quidem igitur per se etc., epilogat quod dixerat: et dicit quod manifestum est, quomodo aliquid per se movetur, et quomodo secundum accidens, et quomodo secundum aliquid aliud, idest secundum partem; et iterum, quomodo hoc quod dico primo et per se, invenitur tam in movente quam in mobili. Dictum est enim quid est movens primo et per se, et quid est quod movetur primo et per se. Et iterum dictum est quod motus non est in specie, idest in qualitate, quae est terminus motus; sed est in eo quod movetur, sive in mobili secundum actum, quod idem est.	646. Then at (474 224 b22) he summarizes what he has said. And he says that it is clear how something is in motion per se and how per accidens and how in respect of something not its entire self, i.e., in respect of a part, and again how what is referred to as directly and per se is found both in the mover and in the mobile, For it has been said what a direct and per se mover is and also what is being moved directly and per se. Finally, we have said that there is no motion in the quality which is the terminus of motion; rather motion is in what is being moved, i.e., in the actually mobile, which is the same thing.
lib. 5 l. 1 n. 10 Deinde cum dicit: secundum quidem igitur accidens etc., ostendit de quo motu sit agendum. Et primo ostendit propositum; secundo manifestat quoddam quod dixerat, ibi: ex medio autem et cetera. Dicit ergo primo quod mutatio quae est per accidens, dimittenda est: sive per accidens accipiatur ex parte moventis, sive ex parte mobilis, sive ex parte termini. Et hoc ideo quia motus per accidens est indeterminatus: est enim in omnibus sicut in terminis, et in omni tempore, et omnium subiectorum vel moventium; quia uni infinita possunt accidere. Sed mutatio quae non est secundum accidens, non est in omnibus; sed est tantum in contrariis et mediis, quantum ad motum qui est in quantitate, qualitate et ubi; et in contradictione, quantum ad generationem et corruptionem, quorum termini sunt esse et non esse: et hoc patet per inductionem. Sub arte autem non cadunt nisi ea quae sunt determinata; nam infinitorum non est ars.	647. Then at (475 224 b26) he shows which kind of motion needs to be discussed. First he states his proposition; Secondly, he explains something he said, at 648. He says therefore first that per accidens change will not be the subject of our discussion, whether it be per accidens on the side of the mover or of the mobile or of the terminus. The reason for this is that per accidens motion is indeterminate: for it is present in all things, in all termini, in all times, in all subjects and in all movers, and an infinity of things can be per accidens in something. But a change that is not per accidens is not found in all things; it is found only in situations (1) that involve contraries or the intermediate between contraries in respect to motions that affect quantity, quality and place, or (2) that involve contradictories, for example, generation and corruption, whose termini are being and non-being—and all this is evident by induction. Now art concerns itself only with things that are determinate, and there is no art to deal with the infinite.
lib. 5 l. 1 n. 11 Deinde cum dicit: ex medio autem mutatur etc., manifestat quoddam quod dixerat, scilicet quod motus sit in mediis. Et dicit quod contingit mutari ex medio ad utrumque extremorum et e converso, inquantum scilicet possumus uti medio ut contrario respectu utriusque extremi. Medium enim inquantum habet convenientiam cum utroque extremorum, est quodammodo utrumque eorum; et ideo potest dici hoc ad illud, et illud ad hoc: sicut si dicam quod media vox inter gravem et acutam est gravis ad ultimam, idest per comparationem ad acutam, et subtilis, idest acuta, per comparationem ad extremam, idest ad gravem; et fuscum est album per comparationem ad nigrum, et e converso.	648. Then at (476 224 b30) he explains his statement that motion can be in the intermediates. And he says that an intermediate may be a starting point of change and go to either of two contraries, inasmuch as we can take the intermediate as being contrary to both extremes. For the intermediate, inasmuch as it is akin to both extremes is in a sense either of them. Hence, we speak of the intermediate as in a sense contrary relatively to the extremes and of either extreme as a contrary relatively to the intermediate; for instance, the central note is low relatively to the highest and high relatively to the lowest, and grey is light relatively to black and dark relatively to white.

Lecture 2 The species of change; which one is motion

Latin	English
	Lecture 2 The species of change; which one is motion
lib. 5 l. 2 n. 1 Postquam philosophus distinxit motum per se a motu per accidens, hic dividit mutationem et motum per se in suas species. Ubi considerandum est quod Aristoteles supra in tertio ubi motum definivit, accepit nomen motus secundum quod est commune omnibus speciebus mutationis. Et hoc modo accipit hic nomen mutationis: motum autem accipit magis stricte, pro quadam mutationis specie. Dividitur ergo pars ista in partes duas: in prima dividit mutationem in suas species, quarum una est motus; in secunda subdividit motum in suas species, ibi: si igitur praedicamenta et cetera. Circa primum duo facit: primo ponit divisionem mutationis; secundo manifestat partes divisionis, ibi: ex non subiecto quidem et cetera. Circa primum tria facit: primo praemittit quaedam necessaria ad divisionem mutationis; secundo concludit ex praemissis mutationis divisionem, ibi: quare necesse est etc.; tertio excludit quandam obiectionem, ibi: quae enim est ex non subiecto et cetera.	649. After distinguishing per se from per accidens motion, the Philosopher now divides per se change and motion into its species. Here it should be noted that in Book III when Aristotle defined motion, he took it as being common to all species of change. It is in this sense that he now uses the word “change”. And he is beginning to use the word “motion” in a stricter sense, i.e., for a certain species of change. Therefore, this section is divided into two parts: In the first he divides change into its various species, of which one is motion; In the second he subdivides motion into its species, at L. 3. About the first he does two things: First he gives his division of change; Secondly, he explains the parts of the division, at 654. About the first he does three things: First he states certain things that must be mentioned before dividing change; Secondly, from these he concludes to the division of change, 651; Thirdly, he answers an objection at 652,
lib. 5 l. 2 n. 2 Dicit ergo primo quod cum omnis mutatio sit a quodam in quiddam, ut manifestatur ex ipso mutationis nomine, quod denotat aliquid esse post aliud, et aliud esse prius et aliud posterius; necesse est his suppositis, quod omne quod mutatur, quatuor modis mutetur. Aut enim uterque terminus est affirmatus; et sic dicitur aliquid mutari ex subiecto in subiectum. Aut terminus a quo est affirmatus, et terminus ad quem est negatus; et sic dicitur aliquid moveri ex subiecto in non subiectum. Aut e converso terminus a quo est negatus, et terminus ad quem est affirmatus; et sic dicitur aliquid moveri ex non subiecto in subiectum. Aut uterque terminus est negatus; et sic dicitur aliquid mutari ex non subiecto in non subiectum. Non enim accipitur hic subiectum eo modo quo sustinet formam; sed omne illud quod affirmative significatur, dicitur hic subiectum.	650. He says therefore first (477 224 b35) that since every change is from something to something—as is clear from the very word “change” which denotes something after something else, i.e., something earlier and something later—it follows from all this that what changes must change in one of four ways. (1) For both termini might be affirmed, in which case something is said to be changed from subject to subject; or (2) the terminus a quo is affirmed and the terminus ad quem negated, in which case something is changed from subject to non-subject; or (3) on the other hand, the terminus a quo is negated and the terminus ad quem affirmed, in which case something is moved from non-subject to subject. Finally (4), both termini might be negated, in which case something is said to be changed from non-subject to non-subject. (Here the word “subject” is not taken in the sense of that which sustains a form; rather, anything that is affirmatively expressed is here called a “subject”.
lib. 5 l. 2 n. 3 Deinde cum dicit: quare necesse est etc., concludit ex praemissis divisionem mutationis. Et dicit quod necessario ex praemissis sequitur, quod tres sint mutationis species: quarum una est ex subiecto in subiectum, sicut cum aliquid mutatur de albo in nigrum; alia autem est ex subiecto in non subiectum, sicut cum aliquid mutatur de esse in non esse; tertia est e converso ex non subiecto in subiectum, sicut cum aliquid mutatur de non esse in esse.	651. Then at (478 225 a7) he derives from these premises his division of change. And he says that it necessarily follows from these premises that there are three kinds of change: one is from subject to subject, as when something is changed from white to black; another is from subject to non-subject, as when something is changed from being to non-being; the third is from non-subject to subject, as when something is changed from non-being to being,
lib. 5 l. 2 n. 4 Deinde cum dicit: quae enim est ex non subiecto etc., excludit quandam obiectionem. Posset enim aliquis obiicere, quod cum praemiserit quatuor modis aliquid mutari, debuisset concludere quatuor esse species mutationis, et non tres tantum. Sed hanc obiectionem excludit dicens, quod non potest esse aliqua mutationis species de non subiecto in non subiectum; quia omnis mutatio est inter opposita; duae autem negationes non sunt oppositae. Neque enim dici potest quod sint contraria, neque quod sint contradictoria. Et huius etiam signum est, quia quascumque negationes contingit simul esse veras de aliquo uno et eodem, sicut lapis nec est sanus nec aeger. Unde cum mutatio per se sit solum in contrariis et in contradictione, ut supra dictum est, sequitur quod ex negatione in negationem non sit mutatio per se, sed solum sic mutatur aliquid per accidens. Cum enim aliquid fit de albo nigrum, fit etiam per accidens de non nigro non album. Et per hunc modum dixit aliquid mutari ex non subiecto in non subiectum. Quod autem est per accidens in aliquo genere, non potest esse species illius generis. Et ideo ex non subiecto in non subiectum non potest esse aliqua mutationis species.	652. Then at (479 225 a10) he precludes a possible objection. For someone might object that since he mentioned four ways in which change can take place, he should have derived four kinds of change and not merely three. But he dismisses this objection by saying that there cannot be any kind of change from non-subject to non-subject, because every change takes place between opposites and two negations are not opposites. For they are neither contrary nor contradictory. A further proof of this is that any pair of negatives may chance to be true of one and the same thing at the same time; for example, a stone is neither healthy nor sick. Hence, since per se change occurs only between contraries and contradictories, as was pointed out above, it follows that there is no per se change from one negation to another. Such changes would always be per accidens, for when something changes from white to black, it changes at the same time, but per accidens, from non-black to non-white. This is the way that something is changed from non-subject to non-subject. However, what is per accidens in any genus cannot be a species of that genus. Therefore, there can be no species of change from non-subject to non-subject.
lib. 5 l. 2 n. 5 Deinde cum dicit: ex non subiecto quidem etc., manifestat partes positae divisionis. Et circa hoc tria facit: primo manifestat duas partes divisionis; secundo ostendit quod neutra earum est motus, ibi: si igitur quod non est etc.; tertio concludit quod residua pars divisionis est motus, ibi: quoniam autem motus et cetera. Circa primum duo facit: primo manifestat unam partem divisionis; secundo aliam, ibi: quae vero ex subiecto in non et cetera.	653. Then at (480 225 a12) he explains the parts used in his division. About this he does three things: First he explains the first two parts; Secondly, he shows that neither of them is motion, at 656; Thirdly, he concludes that the remaining part is motion, at 659. About the first he does two things,, First he explains one part of the division; Secondly, he explains a second part, at 655.
lib. 5 l. 2 n. 6 Dicit ergo primo quod illa mutatio quae est ex non subiecto in subiectum, est inter opposita secundum contradictionem, et vocatur generatio, quae est mutatio de non esse in esse. Sed haec est duplex: quaedam enim est simplex generatio, qua aliquid simpliciter generatur; alia vero est generatio quaedam, qua aliquid secundum quid generatur. Et ponit exemplum de utraque generatione. Et primo de secunda, dicens quod cum aliquid mutatur de non albo in album, est generatio huius et non simpliciter. Et secundo de prima; et dicit quod illa generatio, quae est ex non esse simpliciter in ens quod est substantia, est generatio simpliciter, secundum quam simpliciter dicimus aliquid fieri et non fieri. Cum enim generatio sit mutatio de non esse in esse, secundum illum modum dicitur aliquid generari, quo ex non esse in esse mutatur. Cum autem ex non albo fit album, non mutatur aliquid ex non esse simpliciter in esse simpliciter. Quod enim mutatur proprie, subiectum est; subiectum autem albi est aliquod ens actu. Unde cum subiectum maneat in tota mutatione, etiam in principio mutationis erat ens actu, simpliciter loquendo; non tamen erat ens actu hoc, scilicet album: et ideo non dicitur fieri simpliciter sed fieri hoc, scilicet album. Subiectum vero formae substantialis non est aliquod ens actu, sed ens in potentia tantum, scilicet materia prima, quae in principio generationis est sub privatione, in fine autem sub forma: et ideo secundum generationem substantiae fit aliquid simpliciter. Et ex hoc haberi potest, quod secundum nullam formam quae praesupponit aliam formam in materia, attenditur generatio simpliciter, sed solum secundum quid; quia quaelibet forma facit ens actu.	654. He says therefore first (480 225 a12) that the change from non-subject to subject takes place between contradictories and is called generation, which is the change from non-being to being. Now this can take place in two ways: one is unqualified generation, by which something comes to be in the strict sense of the word; the other is a particular kind of coming to be, i.e., in a qualified way, And he gives an example of both kinds. First of all, of the second kind, saying that when some thing is changed from non-white to white, it is not an unqualified coming to be of the whole thing, but a mere coming to be of its whiteness. Then he gives an example of the first: and he says that generation from non-being to being in the order of substance is generation in an unqualified way, in regard to which we say that a thing comes to be without qualification. And since generation is a change from non-being to being, a thing is said to be generated when it is changed from non-being to being. However, when something passes from non-white to white, it is not being changed from absolute non-being to absolute being. For, speaking strictly, what is being changed is the subject, and the subject of white is an actually existing being. Hence, since the subject remains throughout the whole change, there already was an actually existing being at the beginning of the change, although it was not a being actually existing as white. Consequently, it was not a case of unqualified coming to be but a coming to be white. But the subject of substantial form is not an actual being but a merely potential one, namely, prime matter, which at the beginning of generation is under privation and at the end under forms And so, in the case of a substance being generated, it is said that something comes to be in an unqualified sense. From this it can be concluded that when it is a case of the coming to be of a form that presupposes another form remaining in the matter, it is not unqualified generation but generation in a particular way; because each form makes a being actual.
lib. 5 l. 2 n. 7 Deinde cum dicit: quae vero ex subiecto etc., manifestat aliam partem divisionis. Et dicit quod illa mutatio quae est ex subiecto in non subiectum, vocatur corruptio. Sed quaedam est corruptio simpliciter, quae scilicet est ex esse substantiali in non esse: quaedam vero est in oppositam negationem cuiuscumque affirmationis, sicut de albo in non album, quae est corruptio huius, sicut etiam de generatione dictum est.	655. Then at (481 225 a17) he makes clear the other part of the division and states that that change which is from subject to non-subject is called “corruption”. Rut there is a corruption which is so absolutely speaking and which, namely, is from substantial being to non-being; while there is a certain corruption which is into the opposite negation of any affirmation, as from white to non-white, which is the corruption “of this”, as has already been said of generation.
lib. 5 l. 2 n. 8 Deinde cum dicit: si igitur quod non est etc., ostendit quod neutra praedictarum partium est motus. Et primo quod generatio non sit motus; secundo quod neque corruptio, ibi: neque iam corruptio et cetera. Primum probat duabus rationibus. Quarum prima talis est. Quod simpliciter non est hoc aliquid, non potest moveri; quia quod non est, non movetur: sed quod generatur simpliciter, non est hoc aliquid; est enim non ens simpliciter: ergo quod generatur simpliciter, non movetur: ergo generatio simplex non est motus. Ad manifestationem autem primae propositionis, dicit quod non ens dicitur tripliciter; et duobus modis dictum, non ens non movetur; tertio modo dictum, movetur per accidens. Uno modo dicitur ens et non ens secundum compositionem et divisionem propositionis, prout sunt idem cum vero et falso: et sic ens et non ens sunt in mente tantum, ut dicitur in VI Metaphys.; unde non competit eis motus. Alio modo dicitur non ens quod est in potentia, secundum quod esse in potentia opponitur ei quod est esse in actu simpliciter: et hoc etiam non movetur. Tertio modo dicitur non ens quod est in potentia, quae non excludit esse in actu simpliciter, sed esse actu hoc, sicut non album dicitur non ens, et non bonum: et huiusmodi non ens contingit moveri, sed per accidens, secundum quod huiusmodi non ens accidit alicui existenti in actu, cui competit moveri, sicut cum homo est non albus. Quod autem id quod simpliciter non est hoc aliquid, nullo modo moveatur, nec per se nec per accidens, patet ex hoc, quod impossibile est quod non est moveri. Unde impossibile est generationem esse motum: illud enim quod non est, fit sive generatur. Et quamvis, ut in primo huius dictum est, ex non ente fiat aliquid per accidens, ex ente autem in potentia per se; nihilominus tamen verum est dicere de eo quod fit simpliciter, quod simpliciter non est: unde moveri non potest; et eadem ratione nec quiescere. Unde generatio nec motus est, nec quies. Haec igitur inconvenientia sequuntur, si quis ponat generationem esse motum, scilicet quod non ens moveatur et quiescat.	656. Then at (482 225 a20) he shows that neither of these cases is motion. First that generation is not motion; Secondly, that corruption is not motion, at 658. He proves the first by two arguments. In the first of which he says: What is not unqualifiedly a “this something” cannot be moved, because what does not exist is not moved; but what is unqualifiedly generated is not a “this something” for it is strictly speaking a non-being. Therefore, what is unqualifiedly generated is not being moved. Hence, unqualified generation is not motion. In explanation of the first premise he says that non-being is spoken of in three senses: in the first two senses, non-being is not subject to motion, but in the third it is subject to per accidens motion. In one sense, being and non-being refer to the affirmation and negation of a predicate in a proposition, where they refer to truth and falsity; in which sense being and non-being exist only in the mind, as is said in VI Metaphysics. Hence, they are not subject to motion. In another sense, what is in potency is called non-being insofar as being in potency is the opposite of unqualified being in act. Taken in this sense no motion is possible, In a third sense, that is called “non-being” which is in potency, in such a way as to exclude not unqualified actual existence, but actually being such-and-such; for example, when non-white is called nonbeing and non-good. Such non-being is subject to motion per accidens, inasmuch as such non-being is attached to an actually existing thing subject to motion; as when a man is said to be non-white. Now, why is it that what is not unqualifiedly a “this something” is not subject to motion at all, i,e., neither per se nor per accidens? It is because it is impossible for the non-existent to be moved, Consequently, it is impossible for generation to be a motion; for generation concerns itself with what is not. And although it was said in Book I that something comes to be per accidens from non-being and per se from a being in potency, yet it is true to say of what is absolutely coming to be that, strictly speaking, it is non-being; hence, such a thing cannot be moved and, for the same reasons cannot be at rest. Hence, generation is neither motion nor rest, But if anyone insists that generation is motion, he will be forced to admit the strange proposition that non-being can be moved and can be at rest.
lib. 5 l. 2 n. 9 Secundam rationem ponit ibi: et si omne etc.: quae talis est. Omne quod movetur est in loco: sed quod non est, non est in loco, quia posset de eo dici quod alicubi esset: ergo quod non est, non movetur, et sic idem quod supra. Veritas autem primae propositionis apparet ex hoc, quod cum motus localis sit primus motuum, oportet quod omne quod movetur, moveatur secundum locum, et ita sit in loco. Remoto enim priori, removentur ea quae consequenter sunt.	657. At (483 225 a31) he gives a second reason: Whatever is moved is in a place; but what does not exist is not in a place, otherwise its place could be pointed out, Therefore, what does not exist is not moved. The truth of the first statement is evident from the fact that since local motion is the first of all motions, whatever is moved has to be moved in respect of place and, consequently, must be in a place. But if you remove the previous, you remove whatever depends upon it.
lib. 5 l. 2 n. 10 Deinde cum dicit: neque iam corruptio etc., probat quod corruptio non sit motus, quia motui nihil contrariatur nisi motus vel quies: sed corruptioni contrariatur generatio, quae neque est motus neque quies, ut ostensum est: ergo corruptio non est motus.	658. Then at (484 225 a32) he proves that ceasing-to-be is not a motion, because nothing is contrary to a motion but motion and rest, whereas the contrary of ceasing-to-be is generation, which is neither motion nor rest, as we have shown. Therefore, ceasing-to-be is not a motion.
lib. 5 l. 2 n. 11 Deinde cum dicit: quoniam autem etc., concludit ex praemissis, quod residua pars supra positae divisionis sit motus. Cum enim motus sit quaedam mutationis species, quia in eo est aliquid post aliud, quod supra dixit ad rationem mutationis pertinere; motus autem neque est generatio neque corruptio, quae sunt mutationes secundum contradictionem; relinquitur ex necessitate, cum non sint nisi tres species mutationis, quod motus sit mutatio de subiecto in subiectum. Ita tamen quod per duo subiecta, idest per duo affirmata, intelligamus contraria aut media: quia etiam privatio quodammodo est contrarium, et quandoque significatur affirmative; ut nudum, quod est privatio, et album et nigrum, quae sunt contraria.	659. Then at (485 225 a34) he concludes that the remaining member of the above-given division is motion: for since motion is a definite kind of change, because there is in it something following something (which pertains to the very idea of motion), whereas motion is neither generation nor ceasing-to-be (which are changes between contradictories), it follows of necessity, since there are only three species of change, that motion is from subject to subject. By two subjects is understood two that are affirmative, whether they be contraries or intermediates; because even privation is a kind of contrary that is expressed affirmatively, as nude, which is a privation, and as white and black, which are contraries.

Lecture 3 Per se motion is not in other predicaments than quantity, quality, and place

Latin	English
	Lecture 3 Per se motion is not in other predicaments than quantity, quality, and place
lib. 5 l. 3 n. 1 Postquam philosophus divisit mutationem in generationem et corruptionem et motum, hic subdividit motum in suas partes. Et quia oppositorum est eadem scientia, primo assignat species motus; secundo ostendit quot modis immobile dicatur, ibi: immobile autem et cetera. Circa primum duo facit: primo ponit quandam conditionalem, per quam accipitur divisio motus in suas partes; secundo manifestat conditionalem praemissam, ibi: secundum substantiam autem et cetera.	660. After dividing change into generation, ceasing-to-be and motion, the Philosopher now subdivides motion into its parts. And because it is the same science that deals with a thing and with its opposite, He first derives the species of motion; Secondly, he explains the various senses of immobile, at 683, About the first he does two things: First he posits a conditional proposition in the light of which he deduces the parts of motion; Secondly, he explains this conditional proposition, at 662.
lib. 5 l. 3 n. 2 Concludit ergo ex praemissis, quod cum motus sit de subiecto in subiectum, subiecta autem sint in aliquo genere praedicamentorum; necesse est quod species motus distinguantur secundum genera praedicamentorum, cum motus denominationem et speciem a termino trahat, ut supra dictum est. Si ergo praedicamenta sunt divisa in decem rerum genera, scilicet substantiam et qualitatem etc., ut dictum est in libro praedicamentorum et in V Metaphys.; et in tribus illorum inveniatur motus; necesse est esse tres species motus, scilicet motus qui est in genere quantitatis, et motus qui est in genere qualitatis, et motus qui est in genere ubi, qui dicitur secundum locum. Qualiter autem motus sit in istis generibus, et qualiter pertineat motus ad praedicamentum actionis et passionis, in tertio dictum est. Unde nunc breviter dicere sufficiat, quod quilibet motus est in eodem genere cum suo termino, non quidem ita quod motus qui est ad qualitatem sit species qualitatis, sed per reductionem. Sicut enim potentia reducitur ad genus actus, propter hoc quod omne genus dividitur per potentiam et actum: ita oportet quod motus, qui est actus imperfectus, reducatur ad genus actus perfecti. Secundum autem quod motus consideratur ut est in hoc ab alio, vel ab hoc in aliud, sic pertinet ad praedicamentum actionis et passionis.	661. He concludes therefore (487 225 b10) from the previous lecture that, since motion goes from subject to subject, and subjects are involved in certain genera of the predicaments, the species of motion must be distinguished according to the genera of predicaments, especially since motions derive their nature and name from the terminus, as was said above. Therefore, if the predicaments are divided into ten genera of things; namely, substance, quality, etc. (as is explained in the book of Predicaments and in V Metaphysics) and motion is found in three of these genera, there must be three species of motion, i.e., in the genus of quantity and in the genus of quality and in the genus of where, which is motion in respect of place. The way in which motion is present in these three genera as well as how it is related to the predicaments of action and passion has been explained in Book III. Hence it is enough to mention briefly that a motion is in the same genus as its terminus, not that the motion itself would be in the genus, for example of quality, but it is placed there by reduction. For just as potency is reduced to the same genus as its act, inasmuch as every genus is divided by potency and act; so it is necessary for motion, which is an imperfect act, to be reduced to the genus of its perfect act. But when motion is regarded as being in something, though originating from something else, or as originating from one thing and being in something else, then it belongs to the predicaments of action and passion.
lib. 5 l. 3 n. 3 Deinde cum dicit: secundum substantiam autem etc., manifestat conditionalem praemissam. Et primo ostendit quod in aliis generibus a tribus praedictis, non potest esse motus; secundo ostendit quomodo in istis tribus generibus motus sit, ibi: quoniam autem neque substantiae et cetera. Circa primum tria facit: primo ostendit quod in genere substantiae non est motus; secundo quod nec in genere ad aliquid, ibi: neque est in ad aliquid etc.; tertio quod nec in genere actionis et passionis, ibi: neque agentis neque patientis et cetera. Praetermittit autem tria praedicamenta, scilicet quando et situm et habere. Quando enim significat in tempore esse; tempus autem mensura motus est: unde per quam rationem non est motus in actione et passione, quae pertinent ad motum, eadem ratione nec in quando. Situs autem ordinem quendam partium demonstrat; ordo vero relatio est: et similiter habere dicitur secundum quandam habitudinem corporis ad id quod ei adiacet: unde in his non potest esse motus, sicut nec in relatione. Quod ergo motus non sit in genere substantiae, sic probat. Omnis motus est inter contraria, sicut supra dictum est: sed substantiae nihil est contrarium: ergo secundum substantiam non est motus.	662. Then at (487 225 b10) he explains the conditional proposition. First, that there is no motion in any but the three genera mentioned; Secondly, how motion is present in those three genera, at 678. About the first he does three things., First he shows that motion is not in the genus of substance, Secondly, that it is not in the genus of relation, at 666; Thirdly, that it is not in the genera of action and passion, 668. He passes over the three predicaments of when, situs and habitus. For when expresses existence in time, which is the measure of motion, Hence for the same reason that there is no motion in action and passion which pertain to motion, there is no motion in when. Situs denotes order of parts, and order is a relation; in like manner, habitus bespeaks a relationship existing between a body and what is adjacent to it. Hence there can be no motion in situs and habitus any more than in relation. That motion (487 225 b10) is not found in the genus of substance he proves by saying that every motion is between contraries, as we have said; but nothing is contrary to substance. Therefore, there is no motion in respect of substance.
lib. 5 l. 3 n. 4 Habet autem dubitationem quod hic dicitur, propter hoc quod idem philosophus dicit in libro de generatione, quod ignis est contrarius aquae. Et in libro de caelo dicitur, quod caelum non est generabile nec corruptibile, quia non habet contrarium: unde videtur relinquere, quod ea quae corrumpuntur, vel sint contraria vel ex contrariis composita. Dicunt autem quidam ad hoc, quod una substantia potest esse alteri contraria, ut ignis aquae, secundum suam formam, non secundum suum subiectum. Sed secundum hoc probatio Aristotelis non valeret: sufficeret enim ad hoc quod motus sit in substantia, quod formae substantiales sint contrariae. Est enim motus de forma in formam, quia et in alteratione subiectum non est contrarium subiecto, sed forma formae. Et ideo aliter dicendum, quod ignis est contrarius aquae secundum qualitates activas et passivas, quae sunt calidum et frigidum, humidum et siccum; non autem secundum formas substantiales. Non enim potest dici quod calor sit forma substantialis ignis, cum in aliis corporibus sit accidens de genere qualitatis. Quod enim est de genere substantiae, non potest esse alicui accidens. Sed haec etiam responsio difficultatem patitur. Manifestum est enim quod propriae passiones causantur ex principiis subiecti, quae sunt materia et forma. Si igitur propriae passiones ignis et aquae sunt contrariae, cum contrariorum sint contrariae causae, videtur quod formae substantiales sint contrariae. Item in X Metaphys. probatur quod omne genus dividitur per contrarias differentias: differentiae autem sumuntur a formis, ut in VIII eiusdem libri habetur: videtur ergo quod sit contrarietas in formis substantialibus.	663. Now, there seems to be a disagreement between this doctrine of the Philosopher and what he says in the book On Generation, that fire is contrary to water. And again in the book On the Heavens he says that the heaven is capable neither of coming to be nor ceasing to be, because it does not have a contrary—which seems to imply that things which cease to be are either contrary or composed of contraries. To reconcile this, some assert that one substance can be contrary to another, as fire to water, in respect to form but not in respect to their subject. But if that were so, Aristotle’s proof at the end of 662 would be worthless; for then there would be motion in substance as long as the substantial forms were contrary. For motion is from form to form, because even in alteration subject is not contrary to subject, but form to form. Consequently, another explanation must be given; namely, that fire is contrary to water in respect of their active and passive qualities, which are hot and cold, wet and dry, but not in respect of their substantial forms. For it cannot be said that heat is the substantial form of fire, since in other bodies it is an accident in the genus of quality. And substance cannot be an accident of something. But even this answer presents a difficulty. For it is clear that properties originate from the principles of the subject, i.e., from matter and form. Now, if the properties of fire and water are contrary, then since the causes of contraries are themselves contrary, it seems that the substantial forms are contrary. Moreover, it is proved in X Metaphysics that every genus is divided by differences that are contrary, and differences are traced to the forms, as VIII Metaphysics explains. Therefore, it seems that there is contrariety between substantial forms.
lib. 5 l. 3 n. 5 Dicendum est igitur quod contrarietas differentiarum, quae est in omnibus generibus, attenditur secundum communem radicem contrarietatis, quae quidem est excellentia et defectus, ad quam oppositionem omnia contraria reducuntur, ut in primo huius habitum est. Omnes enim differentiae dividentes aliquod genus, hoc modo se habent, quod una earum est ut abundans, et alia ut deficiens respectu alterius. Propter quod Aristoteles dicit in VIII Metaphys., quod definitiones rerum sunt sicut numeri, quorum species variantur per additionem et subtractionem unitatis. Non tamen oportet quod in quolibet genere sit contrarietas secundum propriam rationem huius et illius speciei; sed solum secundum communem rationem excellentiae et defectus. Quia enim contraria sunt quae maxime distant, oportet quod in quocumque genere invenitur contrarietas, quod inveniantur duo termini maxime distantes, inter quos cadunt omnia quae sunt illius generis. Nec hoc sufficeret ad hoc quod in illo genere esset motus, nisi de uno extremo in aliud contingeret continue pervenire. In quibusdam ergo generibus hae duae conditiones desunt, ut patet in numeris. Quamvis enim omnes species numerorum differant secundum excellentiam et defectum; tamen non est accipere duo extrema maxime distantia in illo genere: est enim accipere minimum numerum, scilicet dualitatem, non tamen maximum. Similiter inter species numerorum non est continuitas; quia quaelibet species numerorum formaliter perficitur per unitatem, quae indivisibilis est, et alteri unitati non continua. Et similiter etiam est in genere substantiae. Sunt enim formae diversarum specierum ab invicem differentes secundum excellentiam et defectum, inquantum una forma est nobilior alia; et propter hoc ex diversis formis possunt causari diversae passiones, ut obiectum est: tamen una forma speciei secundum propriam suam rationem non habet contrarietatem ad aliam. Primo quidem quia in formis substantialibus non attenditur maxima distantia inter aliquas duas formas, ita quod ab una earum non veniatur ordinatim nisi per media: sed materia dum exuitur una forma, potest indifferenter recipere diversas formas absque ordine. Unde Aristoteles dicit in II de generatione, quod cum ex terra fit ignis, non oportet quod fiat transitus per media elementa. Secundo quia, cum esse substantiale cuiuslibet rei sit in aliquo indivisibili, non potest aliqua continuitas attendi in formis substantialibus, ut motus continuus possit esse de una forma in aliam secundum remissionem unius formae et intensionem alterius. Unde probatio Aristotelis, qua probat in substantia non esse motum quia non est ibi contrarietas, est demonstrativa, et non probabilis tantum, ut Commentator innuere videtur. Licet possit et alia ratione probari quod motus non est in substantia, quam supra posuit: quia scilicet subiectum formae substantialis est ens in potentia tantum.	664. Consequently, it must be asserted that contrariety of differences are all the genera is based on the common root of contrariety, which is excellence and defect, to which set of contraries all others are reduced, as was explained in Book I. For all differences that divide a genus are so related that one is like abundance and the other is like defect in relation to the first. For which reason Aristotle says in VIII Metaphysics that the definitions of things are like numbers in which the addition or subtraction of unity makes a different number. However, it is not necessary that there be in every genus the same detailed contrariety between species as exists in some genera; for a contrariety of excellence and deficiency is enough. For since contraries are things most distant, then in order to have contrariety in a genus there must be found two extremes that are most distant, so that between them fall all the things in that genus. Yet that is not enough for positing motion in a genus, unless it is possible to pass without a break from one extreme to the other. Now these two conditions are lacking in some genera; for example, in numbers. For although all numbers differ according to excellence or defect, yet there cannot be found in that genus two extremes that are most distant; for it is possible to find a lowest number, i.e., 2, but not a greatest. In like manner, there are breaks between the species of number, for each number is formally constituted by unity, which is indivisible and not continuous with another unity. Likewise, in the genus of substance. For the forms of diverse species differ in respect to excellence and defect, inasmuch as one form is more noble than another, for which reason diverse qualities can be caused by diverse forms, as the objection mentions. Yet one form of a species is not contrary to another, if you consider it in regard to its own specific nature. First of all, because when you are speaking of substantial forms, there is no maximum distance between any two forms, such that you must pass through an orderly array of intermediate forms to go from the one extreme to the other. Rather, matter when it doffs one form can indiscriminately receive any other form in just any order. For which reason Aristotle says in II On Generation that when fire comes to be from earth, it is not necessary that the intermediate elements be involved at all. Secondly, because, since the substantial essence of anything consists in an indivisible, no continuity can be found in substantial forms so as to make a continuous motion from one form to another by one form growing weak and the other growing strong. Hence the proof by which Aristotle shows that there is no motion in substance because contrariety is absent is a demonstration and not merely a probability, as the Commentator seems to suggest, However, besides the reason given above, there is another which proves that in substance there is no motion, and it is this: that the subject of substantial form is merely a being in potency.
lib. 5 l. 3 n. 6 In qualitatibus autem tertiae speciei manifeste apparet contrarietas secundum utramque rationem: et quia qualitates possunt intendi et remitti, ut sic possit esse continuus motus de qualitate in qualitatem; et quia invenitur maxima distantia in uno genere inter duo determinata extrema, sicut in coloribus inter album et nigrum, in saporibus inter dulce et amarum. In quantitate autem et loco, alterum istorum manifeste invenitur, scilicet continuitas: sed aliud, scilicet maxima distantia determinatorum extremorum, non invenitur in eis, si secundum communem rationem quantitatis et loci accipiantur; sed solum secundum quod accipiuntur in aliqua re determinata; sicut in aliqua specie animalis vel plantae est aliqua minima quantitas, a qua incipit motus augmenti, et aliqua maxima, ad quam terminatur. Similiter etiam in loco inveniuntur duo termini maxime distantes per comparationem ad motum aliquem, a quorum uno incipit motus, et in aliud terminatur, sive sit motus naturalis sive violentus.	665. In qualities of the third species, the two above-mentioned characteristics of contraries (namely, continuity and maximum distance between the extremes) are clearly manifest: first, because qualities can be weakened and strengthened so as to make for a continuous motion from quality to quality, and, secondly, because there exists a maximum distance between two definite extremes of one genus, as black and white in the genus of color, and sweet and bitter in the genus of taste. However, in quantity and place one of these two characteristics is evident; namely, continuity, but the other, which is max mum distance between definite extremes is not found in them, if you seize upon the general notion of quantity and place. But it is found, if you look for it in a definite thing. For example, in a definite species of animal or plant there is a minimum quantity at which the motion of growing begins and a maximum at which it is terminated. Likewise, in place there are involved two termini that are most distant in respect to some particular motion: from one of them motion begins and at the other it is terminated, and this happens whether the motion be natural or compulsory.
lib. 5 l. 3 n. 7 Deinde cum dicit: neque est in ad aliquid etc., ostendit quod non est motus in genere ad aliquid. In quocumque enim genere est per se motus, nihil illius generis de novo invenitur in aliquo, absque eius mutatione; sicut novus color non invenitur in aliquo colorato absque eius alteratione. Sed contingit de novo verum esse aliquid relative dici ad alterum altero mutato, ipso tamen non mutato. Ergo motus non est per se in ad aliquid, sed solum per accidens, inquantum scilicet ad aliquam mutationem consequitur nova relatio; sicut ad mutationem secundum quantitatem sequitur aequalitas vel inaequalitas, et ex mutatione secundum qualitatem similitudo vel dissimilitudo.	666. Then at (488 225 b11) he shows that there is no motion in the genus to something, i.e., relation. For in any genus in which per se motion exists, nothing can newly arise in that genus without its being changed, just as new color is never found in a colored object without that object’s being changed. But it does happen that something can be newly said truly of one thing relative to another, where the latter is changed but the former not. Therefore, in relation motion is not found per se but only per accidens, inasmuch as a new relation follows upon some change; for example, equality or inequality accompany a quantitative change and resemblance or dissimilarity qualitative change.
lib. 5 l. 3 n. 8 Hoc autem quod hic dicitur, in quibusdam non videtur habere difficultatem, in quibusdam autem sic. Sunt enim quaedam relationes quae non sunt aliquid realiter in eo de quo praedicantur. Quod quidem quandoque contingit ex parte utriusque extremi, sicut cum dicitur idem eidem idem: haec enim identitatis relatio in infinitum multiplicaretur, si quaelibet res esset sibi eadem per relationem additam: manifestum est enim quod quodlibet sibi ipsi est idem. Est ergo haec relatio secundum rationem tantum, inquantum scilicet unam et eandem rem ratio accipit ut duo extrema relationis. Et similiter est in multis aliis. Quaedam vero relationes sunt, quarum una realiter est in uno extremo, et alia secundum rationem tantum in altero, sicut scientia et scibile: scibile enim relative dicitur, non quia ipsum refertur per aliquam relationem in ipso existentem, sed quia aliud refertur ad ipsum, ut patet per philosophum in V Metaphys. Et similiter est cum columna dicitur dextra animali: dextrum enim et sinistrum sunt relationes reales in animali, quia in eis inveniuntur determinatae virtutes, in quibus huiusmodi relationes fundantur: in columna autem non sunt secundum rem, sed secundum rationem tantum, quia non habet praedictas virtutes, quae sunt fundamenta harum relationum. Quaedam vero relativa sunt, in quibus ex parte utriusque extremi invenitur relatio realiter existens, sicut in aequalitate et similitudine: in utraque enim invenitur quantitas vel qualitas, quae est huius relationis radix. Et simile etiam apparet in multis aliis relationibus. In illis igitur relationibus quae non ponunt rem aliquam nisi in uno extremorum, non videtur difficile quod mutato illo extremo, in quo relatio realiter existit, de novo dicatur aliquid relative de altero, absque sui mutatione, cum nihil ei realiter adveniat. Sed in illis in quibus relatio invenitur realiter in utroque extremorum, videtur difficile quod aliquid relative dicatur de uno per mutationem alterius absque mutatione sui: cum nihil de novo adveniat alicui absque mutatione eius cui advenit. Unde dicendum est quod si aliquis per suam mutationem efficiatur mihi aequalis, me non mutato, ista aequalitas primo erat in me quodammodo, sicut in sua radice, ex qua habet esse reale: ex hoc enim quod habeo talem quantitatem, competit mihi quod sim aequalis omnibus illis, qui eandem quantitatem habent. Cum ergo aliquis de novo accipit illam quantitatem, ista communis radix aequalitatis determinatur ad istum: et ideo nihil advenit mihi de novo per hoc quod incipio esse alteri aequalis per eius mutationem.	667. What has just been said seems to offer difficulty in respect of some types of relation and not of others. For there are some relations that do posit no reality at all in the thing of which they are predicated. This happens sometimes on the side of both extremes, as when it is said that the same thing is the same to the same: for this relation of identity would be multiplied ad infinitum, if each thing were the same as itself through an added relation, since it is evident that each thing is the same as itself. Consequently, this relation exists only in the reasoning power, inasmuch as the reason takes one and the same thing as the two extremes of the relation. The same thing is true in many other relations. But there are some relations in which one relation is really in one of the extremes but only according to reason in the other; for example, knowledge and the knowable. For “knowable” is a relative term, which is applied to an object not because it is related to something else by reason of a relationship existing in the object but because that something else is related to it, as is clear in V Metaphysics. In like manner, when a pillar is said to be on the right of an animal: for right and left are real relations in the animal (because animals possess definite energies on which these relations are based), but in the pillar they are not present in reality but only according to reason, for the pillar lacks the energies which are the basis of these relations. Again, there are relationships in which both extremes possess a real relation; for example, in equality and resemblance, for both extremes possess the quantity or the quality, which serve as the root of the relationship. The same is apparent in many other relationships. Now in those relations which put something real in only one of the extremes it is not hard to see that if the extreme in which the relation really exists undergoes a change, something new will be said correlatively of the other extreme, even though it remains unchanged, since nothing really happened to it. However, in those cases in which the relation is really found in both extremes, it is hard to see how something relative can be said of A if B changes but A does not, for nothing can be newly acquired by A without A being changed. Hence it must be said that if some change in X makes him equal to me (even though I do not change at all), that equality was in a sense in me in advance as in its root, from which that equality has real existence: for since I have such and such a quantity, it belongs to me to be equal to anything having the same quantity. Hence, when X newly acquires that quantity, that common basis of equality reaches to him: that is why nothing new happens to me, when I begin to be equal to X, as he changes.
lib. 5 l. 3 n. 9 Deinde cum dicit: neque agentis etc., probat quod non sit motus in genere actionis et passionis. Actio enim et passio non differunt subiecto a motu, sed addunt aliquam rationem, ut in tertio dictum est. Unde idem est dicere quod motus sit in agere et pati, et quod motus sit in motu. Circa hoc ergo tria facit: primo proponit quod intendit; secundo probat propositum, ibi: primum quidem enim contingit etc.; tertio ponit quandam distinctionem ad propositi manifestationem, ibi: omnino autem quoniam movetur et cetera. Dicit ergo primo quod sicut motus non est eius quod est ad aliquid, ita etiam non est agentis et patientis, neque etiam, ut absolute loquamur, est moventis aut moti: quia non potest esse quod aliquis motus sit alicuius motus, neque quod generatio sit generationis, quae sunt species mutationis; neque etiam quod mutationis sit mutatio, quae est genus eorum et etiam corruptionis.	668. Then at (489 225 b13) he proves that motion is not in the genera of action and passion. For action and passion do not differ really from motion, but they add to it something of reason, as we said in Book III. Hence, it is the same thing to say that motion is present in acting and being acted upon as to say that motion is present in motion, Therefore in regard to this he does 3 things: First he proposes what he intends; Secondly, he proves his proposition, at 669; Thirdly, he posits a distinction that will explain the proposition, at 677. Accordingly, he says at (489 225 b13) that just as motion is not found in something relative, so also there is no motion of an agent or a patient and, strictly speaking, not even of the mover and moved: for there cannot be motion of motion or a coming-to-be of coming-to-be, which are types of change, nor even a change of change (which is the genus) or a ceasing-to-be of a ceasing-to-be.
lib. 5 l. 3 n. 10 Deinde cum dicit: primum quidem enim contingit etc., probat quod mutationis non possit esse mutatio; et hoc per sex rationes. Quarum prima est, quia si mutationis sit mutatio, hoc potest intelligi dupliciter. Uno modo ut mutatio sit mutationis sicut subiecti quod movetur: sicut aliqua mutatio est hominis, quia homo movetur, puta de albedine in nigredinem. Sic ergo potest intelligi quod motus aut mutatio sit mutationis aut motus ut subiecti, ita scilicet quod motus aut mutatio moveatur; puta quod calescat aut infrigidetur vel moveatur secundum locum aut secundum augmentum et diminutionem. Sed hoc est impossibile, quia mutatio non est de numero subiectorum, cum non sit substantia per se subsistens. Non ergo potest esse mutatio mutationis ut subiecti.	669. Then at (490 225 b16) he proves that there cannot be change of changes. And he does this with six arguments. The first of which is that there are two ways of interpreting change of change. In one sense it means that there is a change of a change, i.e., of the subject which is being changed, as there is change of a man, because the man is being changed, for example, from white to black. In this interpretation there would be a motion or change of a change or motion as of a subject, in such a way that the motion or charge are changed; for example, that the change gets hot or cold or changes place or grows or decreases. This, however, is impossible, because change is not listed among the subjects of change, for it is not a substance existing by itself. So there cannot be change of change in this sense.
lib. 5 l. 3 n. 11 Alio modo potest intelligi ut sit mutatio mutationis ut termini, ita scilicet quod aliquod subiectum moveatur ex una specie mutationis in alteram, sicut ex calefactione in infrigidationem aut sanationem ut duae mutationes intelligantur duo termini unius mutationis, sicut aegritudo et sanitas intelliguntur duo termini mutationis, cum homo mutatur a sanitate in aegritudinem. Sed non est possibile quod aliquod subiectum moveatur per se de mutatione in mutationem, sed solum per accidens. Et quod hoc non sit possibile per se, probat dupliciter. Primo quidem sic. Omnis enim motus est mutatio ab una specie determinata in aliam speciem determinatam. Et similiter generatio et corruptio, quae condividuntur motui, habent determinatos terminos: sed est differentia intantum quod generatio et corruptio sunt in terminum oppositum sic, idest secundum contradictionem; sed motus est in terminum oppositum non similiter, sed secundum contrarietatem. Si igitur aliquod subiectum mutetur de mutatione in mutationem, puta de aegrotatione in dealbationem, simul dum mutatur subiectum de sanitate in aegritudinem, mutabitur etiam ex hac mutatione in aliam. Dum enim subiectum adhuc est partim in termino a quo, movetur in terminum ad quem, sicut dum aliquis aliquid habet de sanitate, movetur ad aegritudinem. Si igitur motus de sanitate in aegritudinem sit terminus a quo alicuius motus, dum adhuc durat ista mutatio, qua scilicet aliquis mutatur de sanitate in aegritudinem, simul mutabitur subiectum de hac mutatione in aliam, quae succedit in subiecto huic mutationi. Manifestum est autem quod quando prima mutatio fuerit terminata, scilicet cum iam quis ex sanitate mutatus est in aegritudinem, poterit deinceps succedere sibi quaecumque alia mutatio. Nec hoc est mirum; quia contingit terminata prima mutatione, subiectum quiescere et nulla mutatione mutari; et eadem ratione contingit quod mutetur alia quacumque mutatione. Si igitur est aliquis motus de prima mutatione in secundam mutationem, quae succedit in subiecto, sequetur quod motus sit de prima mutatione in quamcumque aliam indeterminate. Et hoc est contra rationem motus per se: quia omnis motus est de determinato ad determinatum terminum: non enim corpus movetur per se de albo in quodcumque, sed in nigrum aut medium. Patet ergo quod duae mutationes non sunt per se termini mutationis alicuius.	670. In another way it can be interpreted that there be change of change as of a terminus, so that subject A is moved from one type of change to another; for example, from getting hot to getting cold or healthy, so that two changes are understood to be the termini of one change, as sickness and health are taken as the two termini of a change when a man is changed from health to sickness. But it is not possible for a subject to be moved per se from one change to another but only per accidens. And that it is impossible per se, he proves in two ways: for every motion is a change from one definite form to another definite form. Even generation and ceasing-to-be, which are co-divided with motion, have their definite termini; but there is this difference, namely, that generation and ceasing-to-be are to opposite termini “thus”, i.e., according to contradiction, whereas motion tends to an opposite terminus “not in a like way” but according to contrariety. Therefore, if a subject should be passing from one change to another, for example, from getting sick to getting white, while it is at the same time changing from health to sickness, it will be passing from one change into another change. For while the subject is still partially in the terminus a quo it is being moved to the terminus ad quem, just as while it still health it is being moved to sickness. Now, if the very motion from health to sickness is the terminus a quo of some motion, then while that change (from health to sickness)is still going on, the subject is at the same time passing from this change into another change, which succeeds in the subject to the first change. But it is evident that when the first change shall have ended, i.e., when someone has now already changed from health to sickness, subsequently some other change could succeed it, And this is not strange: for after the first change is over, the subject might remain at rest or it might be affected by another change, Therefore, if there is a passing from the first to the second change, it will follow that the motion goes from the first change to an indeterminate goal. And this is against the true nature of per se motion, because every motion is from a definite terminus to a determinate goal, for a body does not change per se from white to just anything but to black or to something intermediate. It is evident, therefore, that two changes cannot be the per se termini of a change.
lib. 5 l. 3 n. 12 Secundo autem probat idem per aliam rationem. Quia si mutatio quaedam per se est de mutatione praecedente in mutationem subsequentem, non oportet quod semper sit mutatio in mutationem contingentem, idest quam contingat simul esse cum mutatione praecedente: sicut dealbatio simul potest esse cum aegrotatione, sed sanatio non potest simul esse cum aegrotatione, quia sunt contrariae mutationes. Contingit tamen quod aegrotationi succedat in eodem subiecto sicut dealbatio, ita et sanatio. Et hoc est quod dicit, quod mutatio quae ponitur esse de una mutatione in aliam, non semper erit in mutationem contingentem, cum quandoque succedat non contingens. Et illa etiam mutatio non contingens est ex quodam in quoddam alterum, idest inter duos alios terminos. Quare ista mutatio non contingens, in quam aliquis mutatur de aegrotatione, erit sanatio opposita aegrotationi. Quod autem hoc sit inconveniens, patet ex propositione supra inducta, scilicet quod simul dum est prima mutatio, mutabitur in secundam: simul ergo dum aliquis movetur ad aegritudinem, mutabitur ad sanationem. Sanationis autem terminus est sanitas: est enim de quodam in quoddam aliud, ut dictum est. Unde relinquitur quod simul dum aliquid movetur ad aegritudinem, moveatur etiam ad sanitatem: quod est moveri ad duo contraria simul, et intendere ea simul; quod est impossibile. Sic igitur manifestum est quod nulla mutatio est per se de una mutatione in aliam. Sed quod hoc contingat esse per accidens, ut praemisit, manifestat subdens quod per accidens hoc contingit, sicut quando subiectum nunc mutatur una mutatione et postmodum alia: puta si dicatur aliquid mutari per accidens de recordatione in oblivionem, vel in quamcumque aliam mutationem: quia subiectum mutationis quandoque mutatur in scientiam, quandoque in aliquid aliud, puta in sanitatem.	671. He proves this same point again with another argument: If the passing from a previous changing to a subsequent change were motion per se, it would not be necessary that the passing be always to a “contingent” change, i.e., one which could co-exist with the previous change: as becoming white can co-exist with becoming sick, but getting well cannot co-exist with getting sick, because these are contrary changes. But it is possible that just as becoming white can follow becoming sick in the same subject, so also could becoming well. And this is what he says: that the passing from one change to another will not always be to a contingent change, since it is sometimes to a non-contingent, and that non-contingent change proceeds from something to something else, that is, it is between two other termini, Hence that non-contingent change into which something passes from the change called “getting sick” will be “getting well”, which is the opposite of “getting sick”. Now that this is strange is evident from what we have said above, that while the first change is still going on, it is being changed to the second change: therefore, while something is being moved to sickness, it will be changing to another change called “getting well”. Hat the goal of getting well is health (for it is from something to something, as was said). Hence it remains that while something is being moved to sickness it is at the same time being moved to health, which means it is being moved toward two contraries at the same time and intends them at the same time—which is impossible. Consequently, it is clear that no change from one change to another is per se. However, that such a thing can take place per accidens, as he had said before, he makes clear, when he says that this can happen per accidens, as when a subject is now affected by one change and later by another; for example, if someone is changed per accidens from remembering to forgetting or to any other change: because the subject of the change is sometimes changed to knowledge and sometimes to something else, for example, to health.
lib. 5 l. 3 n. 13 Secundam rationem ponit ibi: amplius autem in infinitum etc., et praemittit duas conditionales. Quarum prima est, quod si mutatio est mutationis vel generatio generationis, quocumque modo necesse est procedere in infinitum: quia eadem ratione generatio secunda habebit aliam generationem, et sic in infinitum. Secunda conditionalis est, quod si ordinentur hoc modo generationes et mutationes, quod mutatio sit mutationis et generatio generationis, si ultima mutatio vel generatio erit, necesse est quod prima sit. Hanc autem secundam conditionalem sic probat. Sit enim aliquid quod generetur simpliciter, puta ignis: si generationis est generatio, oportet dicere quod etiam ista simpliciter generatio aliquando generabatur, et hoc ipsum fieri fiebat. Cum autem fiebat ipsa generatio, nondum erat illud quod generatur simpliciter, scilicet ignis; quia aliquid non est dum fit, sed quando iam factum est, tunc primo est. Quamdiu ergo fiebat generatio ignis, ignis nondum erat factus: nondum ergo erat. Et iterum ipsa generatio suae generationis eadem ratione aliquando fiebat: et sicut quando fiebat generatio ignis, nondum erat ignis, ita sequitur quod quamdiu fiebat generatio generationis ignis, nondum esset generatio ignis. Ex quo manifestum est quod generatio ignis esse non potest, nisi completa sua generatione: et eadem ratione nec illa, nisi fuerit praecedens; et sic usque ad primam. Si igitur non fuerit prima generatio, non erit ultima, quae est generatio ignis. Sed si procedatur in generationibus in infinitum, non est accipere primam mutationem vel generationem, quia in infinitis non est primum. Unde sequitur quod neque sit habitum, idest consequenter se habens, in generationibus et mutationibus. Si autem non sit aliqua generatio nec mutatio, nihil fit neque movetur. Si igitur generationis sit generatio, et mutationis sit mutatio, nihil fit neque movetur. Est autem attendendum, quod haec ratio non excludit quin mutatio possit sequi mutationem per accidens in infinitum: quod oportet dicere secundum opinionem Aristotelis, qui posuit motum aeternum. Sed intendit ostendere, sicut prius dictum est, quod mutatio non sit mutationis per se in infinitum. Sic enim postrema dependeret ex infinitis praecedentibus, et nunquam finiretur.	672. Before giving the second of the six reasons he promised, he presents (491 225 b33) two conditional propositions: the first of which is that if there is change of change and generation of generation, in either case it would be necessary to go on ad infinitum; because, for the same reason the second generation will have another generation, and so on ad infinitum. The second conditional is that if generations and changes are so arranged that there is change of change and generation of generation, then, if there is a last change or generation, there necessarily had to be a first. This second conditional he now proves: Let fire be the thing that is unqualifiedly generated; if, then, there is a generation of generation, it is necessary to say that that unqualified generation was itself generated and that its coming-to-be came to be. When, however, that coming-to-be was being generated, the fire was not existing (for it is being assumed that the fire is being unqualifiedly generated): because a thing does not exist while it is coming to be, but it exists for the first time after it has come to be. Therefore, as long as the coming-to-be of fire was in the state of coming to be, the fire had not yet come to be; therefore, it was not yet existing. And again the very coming-to-be of its coming-to-be was itself (for the same reason) coming to be. Consequently, just as when the coming-to-be of the fire was coming to be, the fire did not exist, so also as long as the coming-to-be of the coming-to-be was taking place, the coming-to-be of the fire was not existing. From this it is clear that coming-to-be of fire cannot exist till that coming-to-be is completed and, for the same reason, the previous coming-to-be of the coming-to-be of the fire and so on to the first. Consequently, if there was no first coming-to-be, there will be no last, i.e., no coming-to-be of the fire. But if an infinite process be posited in cases of coming-to-be, there will be no first change and no first coming-to-be, because in the realm of the infinite there is no first. Hence, it follows that there is no sequence at all among generations and among changes. But if there is no generation or change, nothing comes to be and nothing changes. Consequently, if there were coming-to-be of coming-to-be or change of change, nothing ever comes to be or changes. Note, however, that this argument does not exclude the possibility of one change following another ad infinitum. per accidens: which has to be admitted according to the opinion of Aristotle, who posited eternal motion. But the argument intends to show that there is no per se change ad infinitum, for in that case a present change would depend on an infinitude of preceding changes and would never end.
lib. 5 l. 3 n. 14 Tertiam rationem ponit ibi: amplius eiusdem motus etc.: quae talis est. Eidem motui contrariatur et motus et quies, sicut ascensioni contrariatur descensus et quies in loco inferiori; et similiter generatio et corruptio contrariantur: contraria autem nata sunt fieri circa idem. Ergo quidquid generatur, potest corrumpi. Sed si generationis est generatio, oportet quod generatio generetur: ergo generatio corrumpitur. Sed quod corrumpitur oportet esse: sicut enim generatur quod non est, ita corrumpitur quod est. Ergo oportet quod cum fiat quod fit, idest cum generatur aliquid, generatione existente, tunc ipsa generatio corrumpatur: non quidem statim cum generatio desierit, neque iterum in posteriori tempore, sed simul; quod videtur inconveniens. Est autem considerandum quod generatio est ut terminus eius quod generatur sicut substantia, quia generatio est transmutatio ad substantiam: quod autem est generationis subiectum, non est id quod generatur, sed materia eius. Unde Aristoteles non recedit a suo proposito, quo intendebat ostendere quod mutatio non est mutationis ut termini.	673. He gives the third reason at (492 226 a6) and it is this. One and the same motion has as its contraries both motion and rest; for example, both descending and rest in the lower place are contrary to ascending. In the same way are generation and ceasing-to-be contrary. But contraries are apt to affect the same thing. Therefore, whatever comes to be can cease to be. But if there is coming-to-be of coming-to-be, then coming-to-be must come to be. Therefore coming-to-be ceases to be. But what ceases to be must be: for just as it is what is not that comes to be, so it is what is that ceases to be. Therefore, it is necessary that when what comes to be comes to be, i.e., when something-comes to be and the coming-to-be exists, then the very coming-to-be ceases to be, not indeed as soon as the coming-to-be is finished or some time after it is finished, but during the coming to be-which seems absurd. But it should be observed that coming-to-be is as a terminus of what comes to be as a substance does, because coming-to-be is a change tending to substance. But the subject of coming-to-be is not what comes to be but its matter. Hence Aristotle is not departing from his proposition that there is no change of change, as of a terminus.
lib. 5 l. 3 n. 15 Quartam rationem ponit ibi: amplius oportet materiam etc.: quae talis est. In omni generatione oportet esse aliquam materiam, ex qua fiat illud quod generatur, sicut et in omni mutatione oportet esse aliquam materiam vel subiectum; ut in alteratione subiectum est corpus quantum ad corporales alterationes, et anima quantum ad animales. Si igitur generatio generetur, oportet quod sit aliqua materia ipsius generationis, quae scilicet in speciem generationis transeat, sicut materia ignis generati transit in speciem ignis: et talem materiam non est assignare. Ponit etiam sub eadem ratione aliud medium: quia scilicet in qualibet generatione vel mutatione oportet esse aliquem terminum, in quem aliquid movetur. Et huiusmodi terminum oportet esse hoc aliquid demonstratum vel determinatum: huiusmodi autem non est neque motus neque generatio. Non est ergo possibile quod generationis aut motus sit aliqua generatio.	674. At (493 226 a10) he gives the fourth reason, In every coming to be there must be matter from which that which comes to be is generated, just as every change requires some matter or subject: for example, in alteration the subject is the body, if you are dealing with bodily qualities, or the soul, if you are dealing with soul qualities. If, therefore, coming-to-be comes to be, there must be some matter involved which passes into the form coming to be as the matter of generated fire passed into the form fire. However, such matter is not discoverable. In the same vein he makes use of another medium: namely, that in every coming-to-be or change there must be involved a goal toward which something is moved. And this goal must be something definite and capable of being pointed out. But neither change nor coming-to-be is such a goal. Therefore, it is not possible that there be either change of change or coming to be of coming-to-be.
lib. 5 l. 3 n. 16 Quintam rationem ponit ibi: similiter autem etc.: quae talis est. Sicut se habet genus ad genus, sic et species ad speciem: si igitur generationis sit generatio, oportebit quod etiam doctrinae generatio sit doctrina. Sed hoc apparet manifeste falsum: doctrina enim est generatio scientiae, et non generatio doctrinae. Ergo neque generationis potest esse generatio.	675. At (494 226 a14) he gives the fifth reason: Genus is to genus as species is to species. If, therefore, there is coming to be of coming-to-be, then the coming to be of teaching is itself teaching. But this is evidently false: for teaching is the generation of science and not of teaching. Therefore, neither can there be a coming to be of coming-to-be.
lib. 5 l. 3 n. 17 Sextam rationem ponit ibi: amplius, si tres species etc.: quae talis est. Si mutationis sit mutatio vel sicut subiecti vel sicut termini, cum tres sint species motus, ut dictum est, scilicet motus in ubi, in quantitate et qualitate; sequetur quod una harum specierum possit esse subiectum alterius et terminus, et etiam sui ipsius. Sequetur ergo quod loci mutatio alteretur vel etiam feratur secundum locum. Quae quidem evidentius apparent inconvenientia in speciali quam in communi. Non ergo dicendum est quod mutationis sit mutatio, aut generationis generatio.	676. The sixth reason is given at (495 226 a16) and it is this: If there is change of change, whether as of a subject or as of a terminus, then, since there are three species of motion, as was said above (motion to where and quantity and quality), it will follow that one of these species could be the subject and terminus of some other species or even of its own species. Therefore, it will follow that local motion can be altered or even be moved locally. Such a thing is more plainly absurd when you get down to cases than when you speak in general. Therefore, it cannot be admitted that there is change of change or coming to be of coming-to-be.
lib. 5 l. 3 n. 18 Deinde cum dicit: omnino autem etc., ostendit quomodo possit esse mutationis mutatio. Et dicit quod cum tripliciter aliquid moveatur, ut supra est dictum, vel secundum accidens vel secundum partem vel per se, solummodo per accidens contingit mutari mutationem; inquantum scilicet subiectum mutationis mutatur: puta si aliquis dum fit sanus, currat aut discat; tunc enim sanatio curret aut discet per accidens, sicut musicus aedificat. Sed de eo quod movetur per accidens, non intendimus nunc tractare: hoc enim iam supra praetermisimus.	677. Then at (496 226 a19) he shows in what sense there can be change of change. And he says that since there are three ways in which something can be moved, (namely, in respect to an accident or in respect to a part or per se, it is only per accidens that there could be change of change, i.e., only inasmuch as the subject of the change changes: for example, if someone, while he is becoming healthy, would run or learn; for then the healing process would be running or learning per accidens, just as a musician builds per accidens. But it is not our intention to treat of per accidens motion, for we have already decided to pass it by.

Lecture 4 Motion is solely in quantity, quality, and place

Latin	English
	Lecture 4 Motion is solely in quantity, quality, and place
lib. 5 l. 4 n. 1 Ostenso quod non est motus in substantia, neque in ad aliquid, neque in actione et passione, concludit in quibus generibus sit motus. Et circa hoc tria facit: primo inducit conclusionem intentam; secundo ostendit qualiter sit motus in unoquoque trium generum, ibi: motus quidem igitur etc.; tertio removet quandam dubitationem, ibi: quae autem est in eadem specie et cetera. Dicit ergo primo quod cum motus non sit neque in substantia, neque in ad aliquid, neque in facere et pati, ut ostensum est; relinquitur quod motus sit solum in istis tribus generibus, scilicet quantitate, qualitate et ubi: quia in unoquoque horum generum contingit esse contrarietatem, quam requirit motus. Quare autem praetermittat tria genera, scilicet quando, situm et habere; et quomodo in istis tribus generibus in quibus est motus, sit contrarietas, supra ostensum est.	678. Having shown that there is no motion in substance or in relation or in action and passion, the Philosopher now tells in which genera motion does exist. And about this he does three things: First he arrives at the intended conclusion; Secondly, he shows how motion is found in each of three genera, 679; Thirdly, he answers a difficulty, at 682. He says therefore first at (497 226 a23) that since motion is neither in substance nor in relation nor in acting and being-acted-upon, as has been explained, there remain but three genera in which there is motion: quantity, quality and where, for in each of these genera there is apt to be the contrariety which motion requires. He has already explained both why he omits the three genera of when, situs and habitus and how there is contrariety in the three genera in which motion is found.
lib. 5 l. 4 n. 2 Deinde cum dicit: motus quidem igitur etc., ostendit qualiter sit motus in praedictis generibus. Et primo qualiter sit in qualitate; secundo qualiter in quantitate, ibi: qui vero secundum etc.; tertio qualiter in ubi, ibi: qui autem est secundum locum et cetera. Dicit ergo primo quod motus qui est in qualitate, vocatur alteratio. Huic enim generi alludit hoc commune nomen, quod est alteratio: nam alterum solet dici quod differt secundum qualitatem. Loquimur autem nunc de qualitate, non secundum quod quale invenitur in genere substantiae, secundum quod differentia substantialis dicitur praedicari in eo quod quale: sed de quali passivo, quod continetur in tertia specie qualitatis, secundum quod quale dicitur aliquid pati aut non pati, ut calidum et frigidum, album et nigrum, et huiusmodi. In his enim contingit esse alterationem, ut in septimo huius probabitur.	679. Then at (498 226 a26) he explains how motion is found in the three genera: First in quality; Secondly, in quantity, at 680; Thirdly, in where, at 681. He says therefore first that motion in the genus of quality is called “alteration”. And he refers to this genus a common name—alteration; for in Latin the word alterum (other) is customarily applied to things that differ in respect of quality. And we are speaking of quality not in the sense in which it is found in the genus of substance, where the substantial difference is said to be predicated in regard to that which qualifies, but in the sense of a passive characteristic (contained in the third species of quality) in virtue of which something is said to receive or not receive a quality such as hot and cold, black and white, and so on. It is in respect to these that things are said to be “altered”, as will be shown in Book VII.
lib. 5 l. 4 n. 3 Deinde cum dicit: qui vero secundum quantum etc., ostendit quomodo sit motus in quantitate. Et dicit quod motus qui est in quantitate, non est nominatus secundum suum genus, sicut alteratio; sed nominatur secundum suas species, quae sunt augmentum et decrementum. Motus enim qui est ab imperfecta magnitudine ad perfectam, vocatur augmentum; qui vero est a perfecta magnitudine in imperfectam, vocatur decrementum.	680. Then at (499 226 a29) he shows how there is motion in quantity, And he says that motion in respect to quantity does not have a name for its genus, as quality has the generic name “alteration”. Rather it is named according to its species, which are “growth” and “decrease”. For the movement from imperfect size to perfect is called “growth”; the one from perfect size to imperfect is called “decrease”.
lib. 5 l. 4 n. 4 Deinde cum dicit: qui autem est secundum locum etc., ostendit qualiter sit motus in ubi. Et dicit quod motus secundum locum non habet nomen commune generis, neque nomina propria specierum; sed imponit ei nomen commune, ut vocetur latio: quamvis hoc nomen non sit proprium omnino motus localis in communi. Illa enim sola dicuntur proprie ferri, quae sic moventur secundum locum, quod non est in potestate eorum quod stent; et huiusmodi sunt illa, quae non moventur a seipsis secundum locum, sed ab aliis. Ideo autem imponi potuit nomen commune motui in qualitate, quia qualitates sunt contrariae secundum propriam rationem suarum specierum, secundum quas continentur sub genere qualitatis. Contrarietas autem in quantitate non est secundum rationem suarum specierum, sed secundum perfectum et diminutum, ut supra dictum est; et secundum hoc denominantur species. Sed in loco est contrarietas solum per comparationem ad motum, respectu cuius duo termini maxime distant: et ideo, quia ista contrarietas est secundum id quod omnino extraneum est ab hoc genere, non potuit motus qui in hoc genere est, habere nomen, neque in generali neque secundum partes.	681. Then at (500 226 a32) he explains how there is motion in where. And he says that motion in respect of place has neither a common name for its genus nor a particular name for its species, yet he gives it the general name latio—although this is not the generic name of every type of local motion. For it is properly used of things which are so moved in respect of place that it is not due to their own power that their local motion stops; in other words, things that are moved not by themselves but by others. The reason why the common name could be applied to motion in quality is that qualities are contrary in the very notion of their species according to which they are contained under the genus of quality. But quantities are contrary, not according to the very characteristics of their species, but according to “perfect” and “diminished”; and it is according to these that the species of quantity derive their name. However, in place the only contrariety that exists is founded on motion in respect to which two termini are most distant, Consequently, because such contrariety is based on something entirely foreign to place, no motion in this genus could possess a name based either on the genus, or the species under the genus.
lib. 5 l. 4 n. 5 Deinde cum dicit: quae autem est in eadem specie etc., manifestat quoddam quod poterat esse dubium, ostendens ad quam speciem motus reducatur mutatio quae est secundum magis et minus; puta cum aliquid de magis albo fit minus album, et e converso. Posset enim alicui videri quod reduceretur ad motum augmenti et decrementi. Sed ipse ostendit quod reducitur ad motum alterationis: et dicit quod mutatio quae est in eadem specie qualitatis, puta in albedine, vel in magis vel in minus, est alteratio. Et hoc probat per hoc, quod alteratio est mutatio de contrario in contrarium secundum qualitatem, quod contingit dupliciter: aut simpliciter, sicut cum aliquis mutatur de albo in nigrum, vel e converso; aut sic, scilicet cum aliquid mutatur de magis albo in minus album, et e converso. Et quod sic mutari sit mutari de contrario in contrarium, probat per hoc, quod cum aliquid mutatur de magis albo in minus album, potest dici mutari de contrario in contrarium, quia appropinquat ad contrarium, scilicet ad nigrum. Cum autem mutatur aliquid de minus albo in magis album, idem est ac si mutaretur de contrario in contrarium, scilicet de nigro in ipsum album: ex hoc enim fit magis album, quod magis recedit a nigro, et perfectius participat albedinem. Et nihil differt quantum ad hoc quod sit alteratio, quod mutetur aliquid de contrario in contrarium vel simpliciter vel sic, scilicet secundum magis et minus; nisi quod quando mutatur aliquid simpliciter de contrario in contrarium, necesse est quod sint duo contraria in actu termini alterationis, ut album et nigrum; sed mutatio secundum magis et minus est inquantum est plus et minus de altero contrariorum, vel non est. Ulterius ibi: quod quidem igitur hi tres etc., concludit manifestum esse ex dictis, tres solum praedictas species motus esse.	682. Then at (501 226 b1) he clears up a point about which there could be doubt and shows to which species of motion should be reduced a change from lesser to greater or greater to lesser; for example, when something white becomes less white or more white. For at first sight it might seem that it should be reduced to the motions called “increase” and “decrease”. But he shows that it should be reduced to alteration, saying that any change within the same species of quality, for example, change to whiteness or to more or less whiteness, is alteration. He proves this by the fact that alteration, which is change from one contrary to the other in respect of quality, can occur in two ways: first, unqualifiedly, as when something changes from white to black or vice versa; or secondly, qualifiedly, when something changes from more white to less white, and vice versa. And that such a change is a change from contrary to contrary he now proves: for when something is changed from more white to less white, such a thing is said to be changed from one contrary to its opposite, because it is approaching the true contrary, which is black. And when it is changed from less white to more white, it is as though it were changed from one contrary to its opposite, namely, from black to white. For it becomes more white by becoming further removed from black and acquiring more perfect possession of whiteness. In order for there to be alteration, it makes no difference whether the change is unqualifiedly from contrary to contrary, or from more to less or less to more, except that in the former case the termini of the alteration must be two actual contraries; whereas the change in regard to more and less involves the subject’s having or not having in a greater or lesser degree one or another of the contraries. At the end of (502 226 b8) he concludes that it is now clear that there are only these three kinds of motion.
lib. 5 l. 4 n. 6 Deinde cum dicit: immobile autem est etc., ostendit quot modis dicitur immobile: et ponit tres modos. Primo enim dicitur immobile illud quod nullo modo est aptum natum moveri, ut Deus; sicut dicitur invisibile quod non est natum videri, ut sonus. Secundo modo dicitur immobile, quod difficile est moveri. Et hoc dupliciter: vel quia postquam incepit moveri, tarde et cum magna difficultate movetur, sicut si quis dicat claudum immobilem; vel quia difficile est quod incipiat moveri, et per multum tempus oportet ad hoc laborare, sicut si dicamus quod aliquis mons vel aliquod magnum saxum est immobile. Tertio modo dicitur aliquid immobile, quod natum est moveri et potest de facili moveri, non tamen movetur quando natum est moveri, et ubi natum est moveri, et eo modo quo natum est moveri. Et hoc solum proprie dicitur quiescere: quia quies est contraria motui. Et accipit hic contrarietatem large, secundum quod includit etiam privationem. Unde concludit quod oportet quod quies sit privatio in susceptivo motus. Contrarium enim et privatio non est nisi in susceptivo sui oppositi. Ultimo ibi: quid quidem igitur est motus etc., epilogat quae dicta sunt, dicens manifestum esse ex dictis, quid sit motus et quid quies, et quot sint mutationes, et quales mutationes possint dici motus.	683. Then at (503 226 b10) he explains the various senses of “immobile”, giving three. The term “immobile” is applied in the first place to what is absolutely incapable of being moved, as God; just as we correspondingly apply the word “invisible” to sound’, In a second sense, it is applied to what is moved with difficulty (in two ways) either because, after it has begun to be moved, it continues slowly and with great difficulty (as when we call a lame person “immobile”) or because it is difficult to get it started both on account of the labor and time involved, as when we say that a mountain or a large rook is immobile, In a third sense something is called “immobile”, when it is capable of being easily moved, but it is not in motion when and where and in the manner in which it is capable. This alone is called “rest”, because rest is the contrary of motion. Here “contrary” is used in a wide sense, i.e., in the sense that includes even privation. Hence he concludes that rest is privation of motion in that which is capable of motion. For “contrary” and “privation” are applied only to things that are susceptible of opposites. Finally, at (504 226 b16) he summarizes and says that it is now clear what motion is and what rest is and what are the varieties of change and which of them can be called motion.

Lecture 5 The definitions of “in contact,” “consecutive,” “continuous”

Latin	English
	Lecture 5 The definitions of “in contact,” “consecutive,” “continuous”
lib. 5 l. 5 n. 1 Postquam philosophus divisit mutationem et motum in suas species, hic procedit ad determinandum de unitate et contrarietate motus in suas species. Et circa hoc duo facit: primo praemittit quaedam necessaria ad sequentia; secundo prosequitur principale propositum, ibi: unus autem motus et cetera. Circa primum tria facit: primo dicit de quo est intentio; secundo exequitur propositum, ibi: simul igitur etc., tertio recapitulat, ibi: quid quidem igitur et cetera. Dicit ergo primo, quod dicendum est post praedicta, quid est simul, et quid est extraneum vel separatum, et quid est tangere, et quid est medium, et quid consequenter, et quid habitum, et quid continuum, et in quibus haec nata sunt esse. Praemittit autem haec, quia horum definitionibus utitur in demonstrationibus consequentibus per totum librum; sicut et in principio Euclidis ponuntur definitiones, quae sunt sequentium demonstrationum principia.	684. After dividing change and motion into its species, the Philosopher now begins to discuss the senses in which motion is said to be one, and the senses in which motions are said to be contrary. About this he does two things: First he establishes a background of preliminary notions that will be of use; Secondly, he pursues his main objective, at L. 6. About the first he does three things: First he states his intention; Secondly, he pursues it, here at 684; Thirdly, he makes a summary, at 694. He says therefore first that we must now define the terms together, extraneous or separate, touching [in contact], intermediate [or between], consecutive to. The reason for positing these definitions now is that they will be used in later demonstrations, just as in the beginning of Euclid are posited definitions that serve as principles of later demonstrations.
lib. 5 l. 5 n. 2 Deinde cum dicit: simul igitur dicuntur haec etc., exequitur propositum. Ea primo definit quae praemissa sunt; secundo comparat ea ad invicem, ibi: manifestum autem et quod primum et cetera. Circa primum tria facit: primo definit ea quae pertinent ad tangere; secundo ea quae pertinent ad hoc quod est consequenter, ibi: medium vero etc.; tertio ea quae pertinent ad continuum, ibi: continuum autem et cetera. Et quia in definitione eius quod est tangere, ponitur simul, ideo primo definit ipsum: et dicit quod illa dicuntur esse simul secundum locum, quae sunt in uno loco primo; et dicitur primus locus uniuscuiusque, qui est proprius locus eius. Ex hoc enim aliqua dicuntur esse simul, quod sunt in uno loco proprio: non autem ex hoc quod sunt in uno loco communi; quia secundum hoc posset dici quod omnia corpora essent simul, quia omnia continentur sub caelo. Dicit autem quod simul dicuntur haec esse secundum locum, ad differentiam eorum quae dicuntur esse simul tempore: hoc enim non est nunc ad propositum. Per oppositum autem dicuntur esse separatim vel seorsum, quaecumque sunt in alio et alio loco. Tangere autem se dicuntur, quorum sunt ultima simul. Ultima autem corporum sunt superficies, et ultima superficierum sunt lineae, et ultima linearum sunt puncta. Si ergo ponatur quod duae lineae se tangant in suis ultimis, duo puncta duarum linearum se tangentium continebuntur sub uno puncto loci continentis. Nec propter hoc sequitur quod locatum sit maius loco: quia punctum additum puncto nihil maius efficit. Et eadem ratione se habet in aliis.	685. Then at (506 226 b22) he carries out his plan. First he defines the terms he mentioned; Secondly, he compares one to the other, at 692. About the first he does three things: First he defines those that pertain to contact, i.e., touching; Secondly, those which pertain to consecutiveness, at 686; Thirdly, those that pertain to continuum, at 691. Since “together” occurs in the definition of in contact, the Philosopher defines it first (506 226 b22) and says that those things are said to be together in respect of place which are in one first place, where first place refers to proper rather than common place. For things are said to be together not because they are in one common place but in one proper place; otherwise, we should be able to say that all bodies are together, since they are all contained under the heavens. He speaks of such things that are together in respect of place, in distinction to those that are said to be together in time—a point we are not now discussing, Conversely, whatever things are one in one place, and another in another place, are said to exist separate or apart. But in contact is said of things whose termini are together. The termini of bodies are surfaces and of surfaces, lines, and of lines, points. Therefore, if two lines are in contact as to their termini, the two points of the two lines in contact will be contained under one point of the place containing them. From this, however, it does not follow that the thing in place is greater than the place, for point added to point does not make anything larger. And the same holds for the others.
lib. 5 l. 5 n. 3 Deinde cum dicit: medium vero in quod aptum etc., definit ea quae pertinent ad hoc quod consequenter se habet. Et circa hoc tria facit: primo definit medium, quod ponitur in definitione eius quod est consequenter; secundo definit hoc quod est consequenter, ibi: consequenter autem est etc.; tertio infert quoddam corollarium ex dictis, ibi: quoniam autem omnis mutatio et cetera. Dicit ergo primo, quod medium est, in quod primo aptum natum est pervenire id quod continue mutatur secundum naturam, quam in ultimum terminum motus, in quem mutatur: sicut si aliquid mutatur de a in c per b, dummodo sit continuus motus, primo pervenit ad b, quam ad c. Medium autem potest quidem esse in pluribus; quia inter duo extrema possunt esse multa media, sicut inter album et nigrum sunt multi colores medii: sed ad minus oportet quod sit in tribus, quorum duo sunt extrema, et unum medium. Sic igitur medium est per quod in mutatione pervenitur ad ultimum; sed ultimum mutationis est contrarium. Dictum est enim supra quod motus est de contrario in contrarium.	686. Then at (507 226 b24) he defines the things that pertain to consecutiveness, About this he does three things: First he defines between, which is placed in the definition of consecutive to; Secondly, he defines consecutive to, at 689; Thirdly, he draws a corollary, at 690. He says therefore first (507 226 b24) that the between is what a naturally and uninterruptedly changing thing is apt to arrive at before it reaches the ultimate terminus of the motion, into which terminus it is being changed; for example, if something is changing from A to C through B, then, provided it is a continuous motion, it reaches B before C. In some cases there are a number of “betweens” to be traversed as you pass from one extreme to the other, as from black to white there are many colors between; but there must be at least three things involved, two of which are extremes and one the between. Consequently, the between is what must be passed through before arriving at the terminus of a change: but the terminus of a change is a contrary; for it has already been stated that motion goes from contrary to contrary.
lib. 5 l. 5 n. 4 Et quia in definitione medii posuerat continuationem motus, consequenter ostendit quid dicatur continue moveri. Potest autem continuatio motus ex duobus attendi: et ex tempore in quo movetur, et ex re per quam transit, sicut est magnitudo in motu locali. Ad hoc igitur quod sit motus continuus, requiritur quod nulla interpolatio sit in tempore: quia quantumcumque modicum interpolaretur motus secundum tempus, non esset continuus. Sed ex parte magnitudinis per quam transit motus, potest esse aliqua modica interpolatio sine praeiudicio continuationis motus; sicut patet in transitibus viarum, in quibus ponuntur lapides modicum ab invicem distantes, per quos homo transit de una parte viae ad aliam, motu continuo. Hoc est ergo quod dicit, quod continue movetur illud quod nihil aut paucissimum deficit rei, idest quod non habet interpolationem ex parte rei per quam transit; aut si deficit, paucissimum deficit. Sed temporis non potest nec paucissimum deficere, si sit motus continuus. Quomodo autem res possit deficere in motu continuo, manifestat, subdens quod nihil prohibet aliquod moveri continue cum defectu rei, sed non temporis; sicut si aliquis citharizans, statim post hypaten, idest primam chordam gravem, sonet ultimam acutam, intermissis quibusdam chordis in medio. Sed iste defectus est rei in qua est motus, non autem temporis. Hoc autem quod dictum est de continuitate motus, intelligendum est tam in motu locali, quam in aliis motibus.	687. Because the definition of between made mention of continuity of motion, he now shows what continuous movement means. Now continuity of motion may be viewed from two aspects: first, from the time during which the movement occurs and, secondly, from the thing through which the motion takes place for example, the magnitude, in local motion. For a motion to be continuous it is required that there be no interruptions in time, because even the slightest interruption of the motion as to time prevents the motion from being continuous. But on the side of the magnitude through which the motion passes there can be slight variations without prejudice to the continuity of the motion. This is clear in crossings over streets, at which stones are placed slightly distant from each other, and over which a person passes from one side of the street to another without interrupting his motion. This, therefore, is what he says: that continuity of motion is present when there is no gap or only the slightest in the thing, i.e., when there is no interruption in the thing over which the motion passes or, if there is, it is very slight. But there cannot be the slightest interruption of time, if the motion is to be continuous. How there can be a gap in continuous motion he explains by adding that a motion will be continuous even if there is a gap in the material, as long as there is no time-gap; for example, if in playing the harp one strikes the highest note immediately after having sounded the lowest and none of the intermediate ones. But this is not a gap in time, but in the material in which the motion takes place. What has been said about the continuity of motion applies not only to local motion but to all the others as well.
lib. 5 l. 5 n. 5 Sed quia non est manifestum quomodo ultimum in motu locali sit contrarium, quia locus non videtur esse contrarius loco, ideo hoc manifestat. Et dicit quod contrarium secundum locum est, quod plurimum distat secundum lineam rectam. Et intelligendum est plurimam distantiam esse secundum comparationem ad motum et mobilia et moventia: sicut maxime distant secundum locum per comparationem ad motum gravium et levium, centrum et extremitas caeli quoad nos; secundum autem motum meum vel tuum, maxime distat id quo intendimus ire, ab eo a quo incepimus moveri. Quid autem sibi velit quod dixit secundum rectitudinem, exponit subdens, minima enim finita et cetera. Ad cuius intellectum considerandum est, quod minima distantia quae est inter quaecumque duo puncta signata, est linea recta, quam contingit esse unam tantum inter duo puncta. Sed lineas curvas contingit in infinitum multiplicari inter duo puncta, secundum quod duae lineae curvae accipiuntur ut arcus maiorum vel minorum circulorum. Et quia omnis mensura debet esse finita (alias non posset certificare quantitatem, quod est proprium mensurae), ideo distantia maxima quae est inter duo, non potest mensurari secundum lineam curvam, sed solum secundum lineam rectam, quae est finita et determinata.	688. But because it is not evident how the terminus of a local motion is a contrary, since one place does not seem to be contrary to another, he now gives an explanation. And he says that the contrary in respect of place is the greatest rectilinear distance, where greatest distance is taken in relation to the motion and the mobiles and the movers, for example, for the motion of heavy and light things the distance from the center of the earth to the extremity of the sky is the greatest distance, while in regard to my motion and your motion, the greatest distance is the interval between where we start and where we intend to arrive. What he means by the phrase “in a straight line” he explains by adding “that the shortest line is definitely limited”. To understand this, consider that the shortest distance between two points is a straight line, for between any two points there is only one straight line. But there are any number of curved lines between two points, where by curved lines we mean the arcs of major or minor circles, Now since every measure should be finite (otherwise there would be no way of knowing the quantity of a thing—for that is the purpose of measuring), the greatest distance between two objects is not measured by a curved line but by a straight line which is finite and determinate.
lib. 5 l. 5 n. 6 Deinde cum dicit: consequenter autem est etc., definit hoc quod est consequenter, et quandam speciem eius, scilicet habitum. Et dicit quod ad hoc quod aliquid dicatur esse consequenter ad alterum, duo requiruntur. Quorum unum est, quod sit post aliquod principium quodam ordine; vel secundum positionem, sicut in iis quae habent ordinem in loco; vel secundum speciem, sicut dualitas est post unitatem; vel quocumque alio modo aliqua determinate ordinentur, sicut secundum virtutem, secundum dignitatem, secundum cognitionem, et huiusmodi. Aliud quod requiritur est, quod inter id quod est consequenter, et id cui est consequenter, non sit aliquod medium de numero eorum quae sunt in eodem genere: sicut linea consequenter se habet ad lineam, si nulla linea sit in medio; et similiter est de unitate ad unitatem, et de domo ad domum. Sed nihil prohibet, ad hoc quod aliquid sit alteri consequenter, quin aliquid sit medium inter ea alterius generis; sicut si aliquod animal sit medium inter duas domus. Quare autem dixerit et cuius est consequenter, et quod est post principium, manifestat subdens, quod omne quod dicitur consequenter, est consequenter respectu alicuius, et non tanquam prius, sed tanquam posterius. Non enim dicitur quod unum sit consequenter duobus, neque nova luna secundae, sed e converso. Deinde definit quandam speciem eius quod est consequenter, quae dicitur habitum. Et dicit quod non omne quod est consequenter, est habitum; sed quando sic est consequenter, quod tangit; ita quod nihil sit medium, non solum eiusdem generis, sed nec alterius.	689. Then at (508 226 b34) he defines what is meant by consecutive to and a species of it, namely, contiguous. And he says that two things are required in order that something be called consecutive to another. One is that it be after the first and in a certain order: either according to position, as things that are in order in place; or according to species, as 2 comes after 11 or in any way in which things can be in order, as according to virtue, according to dignity, according to knowledge, and so on. The other requirement is that between that which is consecutive and that to which it is consecutive there not be anything of the same kind intervening; for example, one line is consecutive to another, if there is no line between—likewise from one unit to another and one house to another. However, this does not forbid something else intervening. For example, an animal could be found between two houses. Why he said “to which it is consecutive” and “that it is after the first” he explains by adding that whatever is said to be consecutive is so in respect to something else, not as being prior to it but as following it. For 1 is not said to be consecutive to 2, or a new moon to a second new moon; rather, it is just the opposite. Then he defines a certain species of consecutive called contiguous. And he says that not everything consecutive is also contiguous, but only when it is consecutive and in contact, so that there is nothing at all between, i.e., nothing of the same genus or of any other genus.
lib. 5 l. 5 n. 7 Deinde cum dicit: quoniam autem omnis mutatio etc., concludit ex praemissis quod, cum medium sit per quod aliquid mutatur in ultimum, et omnis mutatio sit inter opposita, quae vel sunt contraria vel contradictoria, in contradictoriis autem nihil est medium; relinquitur quod omne medium sit inter contraria aliquo modo.	690. Then at (509 226 b31) he concludes from the foregoing that since the between is that through which something is changed into what is final, and since every change is between opposites which are either contrary or contradictory, although there is no between in contradictories, it follows that it is between contraries that the between is found.
lib. 5 l. 5 n. 8 Deinde cum dicit: continuum autem est quidem etc., manifestat quid sit continuum: et dicit quod continuum est aliqua species habiti. Cum enim unus et idem fiat terminus duorum quae se tangunt, dicitur esse continuum. Et hoc etiam significat nomen. Nam continuum a continendo dicitur: quando igitur multae partes continentur in uno, et quasi simul se tenent, tunc est continuum. Sed hoc non potest esse cum sint duo ultima, sed solum cum est unum. Ex hoc autem ulterius concludit, quod continuatio esse non potest, nisi in illis ex quibus natum est unum fieri secundum contactum. Ex eadem enim ratione aliquod totum est secundum se unum et continuum, ex qua ex multis fit unum continuum, vel per aliquam conclavationem, vel per aliquam incollationem, vel per quemcumque modum contingendi, ita quod fiat unus terminus utriusque; vel etiam per hoc quod aliquid naturaliter nascitur iuxta aliud, sicut fructus adnascitur arbori et continuatur quodammodo ei.	Then at (510 227 a10) he shows what a continuum is and he says that it is a species of the contiguous. For when the terminus of two things in contact is one and the same, then something is continuous. And the very word “continuum” denotes this. For “continuum” is derived from “continere” (to hold together): when, therefore, many parts are held together in a unit and, as it were, keep themselves together, then there is a continuum. But this cannot be while the endings are two but only when they are one. From this he further concludes that continuity can occur only in things from which a unity through contact is naturally apt to come about. For in whatever way a whole is naturally one and continuous in the same way is a continuous unity formed from many things, whether by riveting, by gluing or by any form of contact that makes one terminus for two parts, or even by being born of another, as fruit is born of a tree and forms a sort of continuum with it.
lib. 5 l. 5 n. 9 Deinde cum dicit: manifestum autem et quod primum etc., comparat tria praemissorum ad invicem, de quibus principaliter intendit, scilicet consequenter se habens, contactum et continuum. Et circa hoc tria facit: primo comparat consequenter se habens ad contactum; secundo contactum ad continuum, ibi: et si continuum etc.; tertio infert quoddam corollarium ex dictis, ibi: quare si est unitas et cetera. Dicit ergo primo manifestum esse, quod consequenter se habens est primum inter tria praemissa ordine naturae, secundum quod dicitur esse prius, a quo non convertitur consequentia essendi; quia omne contactum necesse est esse consequenter: oportet enim inter ea quae se contingunt, esse aliquem ordinem, ad minus positione. Sed non oportet omne quod consequenter se habet, esse tangens: quia ordo potest esse in quibus non est tactus, sicut in separatis a materia. Unde hoc quod est consequenter, invenitur in iis quae sunt priora secundum rationem: invenitur enim in numeris, in quibus non invenitur tactus, qui invenitur solum in continuis. Numeri autem secundum rationem sunt priores continuis quantitatibus, sicut magis simplices et magis abstracti.	692. Then at (511 227 a17) he compares three of the foregoing with one another; namely, the consecutive to the continuous, and the continuum. About this he does three things: First he compares consecutiveness to contact; Secondly, contact with continuum, at 693; Thirdly, he draws a corollary, at 694. He says therefore first (511 227 a17) that it is clear why among these three, consecutiveness is naturally first in the order of nature, for in the cases of contact there is always consecutiveness, since there must be an order, at least of position, among things that are in contact. Bat not all cases of consecutiveness involve contact, for an order can exist among things in which there is no contact, as in substances separated from matter. Hence, consecutiveness is present in things that are prior in definition, for it is found in numbers, in which there is no contact, which is present only among continua. Numbers, however, are prior to continuous quantities in definition, for they are more simple and more abstract.
lib. 5 l. 5 n. 10 Deinde cum dicit: et si continuum est etc., comparat contactum ad continuum. Et dicit quod eadem ratione contactum est prius quam continuum: quia si aliquid est continuum, necesse est quod sit tangens; sed non est necessarium, si tangit quod sit continuum. Et hoc probat per rationem utriusque. Non enim necessarium est quod ultima aliquorum sint unum, quod est de ratione continui, si sunt simul, quod est de ratione contacti: sed necesse est e converso, si ultima sunt unum, quod sint simul, ea ratione qua potest dici, quod unum sit simul sibi ipsi. Si autem hoc quod dico simul, importat habitudinem distinctorum, non possunt esse unum quae sunt simul: et secundum hoc nec contacta esse possunt quae sunt continua, sed communiter accipiendo. Unde concludit quod insertus, idest continuatio secundum quam una pars inseritur alteri in uno termino, est ultimus in ordine generationis, prout specialia sunt posteriora communibus, sicut prius generatur animal quam homo. Et ideo dico esse ultimum insertum, quia necesse est aliqua se tangere ad invicem, si ultima eorum sunt adnata, idest naturaliter unita; sed non est necessarium quod omnia quae se tangunt, quod sint naturaliter adnata ad invicem. Sed in quibus non potest esse contactus, manifestum est quod in his non potest esse consertus, idest continuatio.	693. Then at (512 227 a21) he compares in contact with continuous and says that for the same reason in contact is prior to continuous, because if a thing is continuous it must be in contact, but it does not necessarily follow that if it is in contact it is continuous, And he proves this from the definitions of the two. For it is not necessary that the endings of things be one (which is implied in the notion of continuum), if they are together (which is implied in the notion of contact). But, on the other hand, if the endings are one, they must be together, for what is one is together unto itself. However, if “together” implies a relationship between distinct things, then things that are together are not one: and according to this, continua are not in contact. But they are, if we do not speak so precisely. Hence he concludes that natural junction, i.e., continuity, in which one part is joined to another at one terminus, is last in coming to be, in the sense that what is specific comes to be after what is general, as animal comes to be before man. And, therefore, I say that natural junction is last, because things must mutually touch if their extremities are naturally united; however, it is not necessary that all things that touch be naturally joined to one another. But in regard to things which cannot touch, it is clear that continuity is impossible.
lib. 5 l. 5 n. 11 Deinde cum dicit: quare si est unitas etc., concludit quoddam corollarium ex dictis; scilicet quod si unitas et punctum sunt separata, sicut quidam dicunt, ponentes mathematica separari secundum esse, sequitur quod unitas et punctum non sunt idem. Et hoc manifestum fit duabus rationibus. Primo quidem, quia puncta sunt in his quae nata sunt se tangere, et secundum puncta aliqua se tangunt ad invicem: in unitatibus autem non invenitur contactus, sed solum hoc quod est consequenter. Secundo vero, quia inter duo puncta contingit esse aliquid medium; omnis enim linea est media inter duo puncta: sed inter duas unitates non necesse est esse aliquod medium. Patet enim quod inter duas unitates, quae constituunt dualitatem, et ipsam primam unitatem, nihil est medium. Ultimo ibi: quid quidem igitur est simul etc., epilogat quae dicta sunt: et est planum in littera.	694. Then at (513 227 a27) he draws a corollary from the preceding: i.e., if point and unit have an independent existence of their own, as some say who suppose a separated existence for mathematical objects), it follows that unity and point are not the same. And this is clear for two reasons: first, because points are present in things that are capable of mutual contact and certain things touch at points; but in units contact is never found, but only consecutiveness. Secondly, because there must be something existing between two points, but between two unities there is not necessarily anything between. For it is evident that between the two unities that form 2 and the very first unity, which is 1, there is nothing intermediate. Finally, at (514 227 a32) he makes a summary and says that we have defined what is meant by together and apart, contact, between, consecutiveness, contiguous and continuous. Also we have shown in which circumstances each of these terms is applicable,

Lecture 6 Generic, specific, and numerical unity of motion

Latin	English
	Lecture 6 Generic, specific, and numerical unity of motion
lib. 5 l. 6 n. 1 Postquam philosophus posuit quasdam definitiones necessarias ad sequentia, procedit ad tractandum de unitate et diversitate motus. Et primo determinat de unitate et diversitate motus; secundo de contrarietate, quae est quaedam diversitatis species, ibi: amplius autem determinandum et cetera. Circa primum duo facit: primo distinguit unitatem motus secundum tres communes modos; secundo alterum eorum subdividit, ibi: quoniam autem continuus est et cetera. Circa primum tria facit: primo ostendit quomodo motus dicatur unus genere; secundo quomodo dicatur unus specie, ibi: specie autem unus est etc.; tertio quomodo dicatur unus numero, ibi: simpliciter autem unus et cetera.	695. After positing some definitions to be used later, the Philosopher now proceeds to discuss unity of motion and contrariety of motions. First he treats of the unity and diversity of motion; Secondly, of its contrariety, which is a kind of diversity, L.8, About the first he does three things: First he shows how motion is said to be generically one; Secondly, how it is specifically one, at 697; Thirdly, how it is numerically one, at 699.
lib. 5 l. 6 n. 2 Dicit ergo primo quod motus dicitur unus multipliciter, secundum quod et ipsum unum in communi acceptum multipliciter dicitur, scilicet genere et specie et numero. Dicitur autem motus unus genere, secundum figuras praedicamenti. Omnes enim qui sunt in una coordinatione praedicamenti, possunt dici unus motus genere: sicut omnis loci mutatio est unus motus genere, quia est in uno praedicamento ubi; differt autem genere ab alteratione, quae est in praedicamento qualitatis, ut supra dictum est.	696. He says therefore (515 227 b3) that there are a number of ways in which a motion is one, just as one itself has many senses: i.e., generically, specifically and numerically. A motion is said to be generically one according to the different predicaments. For all motions that are assigned to one and the same predicament can be called generically one; thus every local motion is one generic motion, because each is in the predicament where, and differs generically from alteration, which is in the predicament quality, as has been said above.
lib. 5 l. 6 n. 3 Deinde cum dicit: specie autem unus est etc., ostendit quomodo motus sit unus specie. Et primo ostendit propositum; secundo movet quandam dubitationem, ibi: dubitabit autem aliquis et cetera. Dicit ergo primo quod motus dicitur unus specie, cum non solum est unus secundum genus, sed etiam secundum speciem individuam, idest specialissimam, quae non dividitur in alias species. Sunt enim quaedam species quae dividuntur in alias species; sicut color species est qualitatis, sed tamen habet differentias, quibus in diversas species dividitur. Unde motus qui sunt secundum colores, possunt esse diversi specie, sicut dealbatio et denigratio: sed omnis dealbatio est eadem secundum speciem, et similiter omnis denigratio; quia albedini non sunt amplius species, in quas dividatur. Sed tamen si sunt quaedam quae sunt simul genera et species, manifestum est quod motus qui conveniunt in specie subalterna, sunt ut unum specie, idest secundum quid unus; sed simpliciter non sunt unus specie. Sicut scientia est quaedam species existimationis, et genus diversarum scientiarum: unde omnis doctrinatio, quae est motus ad scientiam, est quodammodo una specie, non tamen simpliciter; quia doctrinatio qua docetur grammatica, est simpliciter alia specie ab ea qua docetur geometria. Attendendum est autem, quod in praemissis unitatem et diversitatem motus determinavit secundum genera et species in quibus contingit motum esse, quia motus quodammodo reducitur ad genus rerum in quibus est motus.	697. Then at (516 227 b6) he shows how motions are specifically one. First he shows this; Secondly, he raises a question, at 698. He says therefore first (516 227 b6) that a motion is called specifically one when, besides being a generic one, it also takes place in a species incapable of subdivision. For some species can be subdivided into other species, as color, which is a species of quality, is capable of differences that make for sub-species. Hence motions in regard to color can be diverse in species, as whitening and blackening; but all cases of whitening are specifically the same (just as all cases of blackening are), for there are no sub-species of whitening. But when it happens that the species is at the same time a genus, then the motions found in a subalternate species are qualifiedly one, although, strictly speaking, they are not of the same species. Thus science is a species of knowledge, as well as a genus of the various types of science. Hence all indoctrination, which is a movement toward science, is in some sense specifically the same, although, strictly speaking, it is not, for the indoctrination by which grammar is taught is absolutely different in species from that by which geometry is taught. Now it should be observed that in the foregoing the Philosopher has based the unity and diversity of motion on the genera and species in which motion can occur, because motion is in a certain way reduced to the genus in which the motion is.
lib. 5 l. 6 n. 4 Deinde cum dicit: dubitabit autem aliquis etc., movet quandam dubitationem circa praemissa: utrum scilicet ex necessitate sit unus specie motus, cum aliquid idem mutatur multoties de eodem in idem; sicut si unum punctum secundum geometras, qui imaginantur punctum moveri, moveatur ex hoc loco in hunc locum multoties. Et hoc quidem videtur secundum praemissa. Si enim motus qui in eandem speciem sunt, ut in albedinem, sunt idem specie, multo magis duo motus qui sunt in eundem locum numero. Si autem hoc concedatur, sequitur inconveniens, scilicet quod motus rectus sit unus specie motui circulari. Contingit enim ab hoc loco in hunc locum primo quidem moveri circulariter, quasi per arcum quendam; postmodum vero motu recto, quasi per lineam rectam. Et similiter sequitur in motibus animalium, quod ambulatio, quae est per lineam rectam, sit eadem secundum speciem volutationi, qua animal per lineam circularem volvendo se movetur. Hanc autem dubitationem solvit secundum praemissa. Determinatum est enim quod, si id in quo est motus, est alterum specie, et motus est alter specie; ut sic ad hoc quod motus sit idem specie, non solum requiratur identitas termini secundum speciem, sed etiam identitas eius per quod transit motus. Manifestum est autem quod linea recta et circularis sunt diversae secundum speciem: unde motus circularis et rectus, et volutatio et ambulatio, non sunt idem secundum speciem, quamvis sint inter eosdem terminos; quia via non est eadem secundum speciem. Sed si sint idem termini, et eadem via secundum speciem, sunt idem motus secundum speciem. Et multo magis si termini et via sunt eadem numero, motus iterati erunt idem secundum speciem.	698. Then at (517 227 b14) he raises a question about the foregoing: Whether a motion is specifically one and the same when the same thing changes frequently from the same to the same, e.g., when a point (according to the geometers who imagine that a point can be moved) changes again and again from this place to that. Now according to the foregoing it seems that the answer should be Yes. For if all motions that tend to the same species, e.g., whiteness, are specifically the same, a fortiori two motions from the same origin to the same terminus should be specifically one. But if that were so, then it would follow that a rectilinear motion is specifically the same as a circular motion. For it is possible to pass from this place to that by means of a circular motion, i.e., by describing an arc, and after by going in a straight line. Likewise, it would follow that in the motions of animals, walking (which is in a straight line) would be specifically the same as whirling, which consists in turning oneself in circles. However, he answers this difficulty in the light of the foregoing. For it has been decided that if that in which the motion takes place is specifically different (as in the present instance the circular path is specifically different from the straight), the motion itself is also different. Consequently, in order that two motions be specifically the same, not only must the goal be specifically the same but also that through which the motion passes. Now it is clear that a straight line is specifically different from the curved. Consequently, a circular and a rectilinear motion, as well as walking and whirling, are not specifically the same, even though they tend to the same goal, because the paths are not specifically the same. But if the goals are identical and the paths specifically the same, then the motions are specifically the same; and much more so, if the goals and the path are numerically the same, the same repeated motions will be specifically the same.
lib. 5 l. 6 n. 5 Deinde cum dicit: simpliciter autem unus motus est etc., ponit tertium modum, quo motus dicitur unus numero. Et circa hoc duo facit: primo manifestat quis motus sit unus numero; secundo circa hoc movet quasdam dubitationes, ibi: Socratem autem et cetera. Dicit ergo primo quod secundum praedictos modos non dicitur motus unus simpliciter, sed secundum quid, scilicet genere et specie. Tertio autem modo dicitur motus simpliciter unus, qui est unus numero secundum suam essentiam. Quis autem motus sit hoc modo unus, manifestum erit distinguendo ea quae requiruntur ad motum. Sunt enim numero tria circa quae consistit unitas motus: scilicet subiectum quod movetur; et genus vel species, in qua est motus; et tempus quando movetur. Et manifestat singula. Quod movetur quidem dictum est, quia necesse est aliquid esse in quocumque motu quod movetur, sicut hominem aut aurum vel quodcumque corpus. Et similiter necesse est hoc, vel quaecumque alia mobilia, moveri in aliquo genere vel specie, puta in loco aut in passione, idest in passibili qualitate. Et similiter necesse est considerare quando movetur: quia omne quod movetur, movetur in tempore. Contingit autem de numero horum trium inveniri unum genere aut specie in re in qua est motus, sicut in loco vel in qualitate. Sed in tempore non est attendenda quantum ad unitatem motus unitas generis vel speciei, cum non sit nisi unum tempus secundum speciem; sed quod sit habitum, idest continuo consequens absque interpolatione. Unitas autem motus secundum quam dicitur simpliciter unus, consistit in unitate omnium horum. Oportet enim id in quo est motus, esse unum et indivisibile, eo modo quo species specialissima indivisibilis dicitur. Et iterum oportet ipsum tempus, quando fit motus, esse unum continuum et non deficiens, idest absque interpolatione. Et tertio oportet id quod movetur esse unum. Sed excludit duos modos unitatis subiecti, qui non sufficiunt ad hoc, quod motus sit unus simpliciter. Primus modus est secundum accidens; sicut Coriscus et albus sunt unum secundum accidens, nec tamen motus proprius Corisci, et motus proprius albi est unus. Motus enim proprius albi est nigrum fieri, et motus proprius Corisci est ambulare; qui quidem motus differunt. Secundus modus est unitas generis vel speciei: non enim ad hoc quod sit unus motus numero, sufficit quod subiectum sit unum sicut aliquid commune, vel genus vel species. Contingit enim duos homines in eodem tempore sanari, et secundum eandem speciem sanationis, puta quia sanantur de ophthalmia, quae est infirmitas oculorum: et sic concurrit unitas ipsius quando, et eius in quo, et unitas subiecti secundum speciem. Non tamen hae duae sanationes sunt unus motus numero, sed unus specie.	699. Then at (518 227 b21) he posits the third way in which a motion is said to be one; namely, numerically. About this he does two things: First he explains when a motion is numerically one; Secondly, he raises some question on this point, at 700. He says therefore first at (516 227 b6) that in the first two senses motions are not unqualifiedly one, but they are one only in a sense, i.e., in genus and species. But in the third sense a motion is unqualifiedly one, i.e., when it is numerically one in its essence. Which motion is one in this way will be clear, if we distinguish the things required for motion: for numerically there are three things on which the unity of a motion depends: first, the subject which is being moved; secondly, the genus or species of the motion; thirdly, the time in which the motion takes place. And he explains each of these individually. A subject of motion is required, because in every case of motion there must be something that is being moved, as a man or gold or some body. Likewise the subject must be affected by some genus or species of motion, such as place or a passible quality. Again, the time must be considered, because whatever is moved is moved in time. Now among these three things, the generic or specific unity of the motion can depend on the thing in which there is motion; for example, on the place or quality. But the time does not account for the generic or specific unity of the motion, for there is only one specific time; rather it accounts for the continuity of the motion, i.e., that it flows on without interruption. But unity of motion, in the sense of unqualified unity, depends on all three. For that in which the motion exists must be one and indivisible in the way that a species incapable of further subdivision is said to be one. Further, the time during which the motion occurs must be continuous without any breaks. Thirdly, the subject in motion must be one. However, there are two types of unity of subject which are not sufficient to guarantee that the motion is unqualifiedly one. The first type is accidental: for example, Coriscus and white are accidentally one, but the motion proper to Coriscus in not the same as the motion proper to white. For the proper motion of white is to become black and the motion proper to Corisicus is to walk; and these are different. The second type is generic and specific unity. For in order that a motion be numerically one, it is not enough that the subject be one as something common either generically or specifically. For it is possible that two men are being healed during the same period of time in regard to the same thing; for example, from inflammation of the eye, so that the time is one and the species of motion is one, and the subject is one in species. Yet these two healings are not one numerically but only specifically.
lib. 5 l. 6 n. 6 Deinde cum dicit: Socratem autem etc., introducit quandam dubitationem. Et circa hoc tria facit: primo ponit id quod videtur in primo aspectu de unitate motus secundum numerum; secundo movet dubitationem circa hoc, ibi: habet autem dubitationem etc.; tertio determinat veritatem, ibi: eadem enim ratio est et cetera. Dicit ergo primo quod contingit aliquod unum mobile, ut Socratem, secundum alterationem eandem specie, alterari in uno tempore, et iterum in alio; sicut si sanetur bis de ophthalmia. Haec autem iterata alteratio erit unus motus numero, ut videtur in primo aspectu, si sanitas quae acquiritur sit eadem numero. Et hoc erit si contingat id quod est corruptum, iterum fieri unum numero, quod videtur impossibile. Sanitas enim quae in prima alteratione fuit acquisita, postmodum fuit corrupta; et non potest recuperari eadem numero. Sed videtur quod si recuperetur eadem numero, quod alteratio sequens esset unus numero motus cum prima: si vero non recuperetur eadem sanitas numero, erit quidem motus idem specie, sed non unus numero.	700. Then at (519 228 a3) he raises a question. And about this he does three things: First he mentions what at first glance seems to be a motion numerically one; Secondly, he raises a question about this, at 701; Thirdly, he gives the true solution, at 702. He says therefore first (519 228 a3) that it is possible for one mobile, e.g., Socrates, to be altered at two different times with respect to the same specific disease, for example, if he is twice healed of eye-inflammation. This repeated healing will at first sight be numerically one motion, if the health acquired is numerically the same in both cases. And this will be so, if it is possible for that which ceased to be to come again into being as the same numerical thing—which seems impossible. For the health acquired after the first alteration was later lost and the same numerical health cannot be regained. But it seems that if the same numerical health were regained, the second alteration would be numerically the same motion as the first; whereas if the same numerical health is not regained, the motion will not be numerically the same but specifically.
lib. 5 l. 6 n. 7 Deinde cum dicit: habet autem dubitationem etc., movet quandam aliam dubitationem circa hoc. Et dubitatio talis est: si aliquis continue perseveret in sanitate, vel in quocumque alio accidente, utrum una sanitas, vel quicumque alius habitus aut passio, possit esse in corporibus? Et videtur quod non; quia quibusdam philosophis visum fuit, quod omnia subiecta quae habent aliquas qualitates aut habitus, sint in continuo motu et fluxu. Si ergo in aliquo qui sanus perseverat, una et eadem sanitas est, quae fuit in mane et quae est nunc in meridie vel sero; non videtur posse reddi ratio quare, etiam si aliquis deficit a sanitate et iterum accipiat sanitatem, secunda sanitas recuperata non sit una numero cum sanitate prius habita. Hanc autem dubitationem Aristoteles non solvit, quia non est ad propositum; sed magis ad considerationem metaphysici pertinet, ad quem pertinet considerare communiter de uno et multo, et eodem et diverso. Et iterum quia illa dubitatio super falso fundatur, scilicet quod omnia sint in continuo motu et fluxu, quod Heraclitus opinatus est, et Aristoteles improbat in IV Metaphys. Nec tamen est similis ratio: quia quamdiu sanitas manet, licet varietur homo secundum sanitatem, ut puta si fiat homo magis vel minus sanus, non intercipitur esse sanitatis, sicut intercipitur quando totaliter corrumpitur sanitas.	701. Then at (520 228 a6) he raises another difficulty on this point. It is this: if someone continually perseveres in health or any other accident, could the health, or any other habit or passion in bodies, be one? It seems not, because certain philosophers believe that all subjects that possess certain qualities or habits are in continuous motion and flux. If, therefore, in the case of a person who remains healthy, there is one and the same health at dawn and at noon and in the evening, there seems to be no reason why in the case of a person who gets sick and then recovers, the health recovered is not numerically the same as the one previously possessed. Aristotle does not settle this question: first, because it is not ad rem, since it pertains to metaphysics, whose province is to consider the one and the many, the same and the diverse; and, secondly, because this difficulty is based on the false assumption that all things are in a state of continuous change and flux, as Heraclitus believed—an opinion which Aristotle refutes in IV Metaphysics. Moreover, the two cases are not the same: for as long as health remains in spite of fluctuations in degree, the original health is not interrupted, as it is in the case of one who completely loses his health.
lib. 5 l. 6 n. 8 Deinde cum dicit: eadem enim ratio etc., determinat veritatem circa id quod praedixerat. Dixerat enim supra, quod si sit eadem qualitas quae recuperatur, erit idem motus numero secunda alteratio cum prima; si vero non redit eadem numero qualitas, sequitur quod non sit unus actus numero. Et interposita quadam dubitatione, quasi assignans rationem praemissorum, subdit quod ideo praemissa dicta sunt, quia eadem ratio videtur in primo aspectu de unitate qualitatis et motus. Sed intantum differunt, quia bene sequitur, si duo motus sint idem eo modo sicut aliquis motus dicitur unus numero, necesse est quod habitus, id est qualitas acquisita per motum, sit una: quia unus numero actus est unius numero qualitatis acquisitae per actum illum. Sed si qualitas sit una quae redit, potest alicui videri quod non propter hoc sit unus actus: non enim, si terminus motus est unus numero, oportet quod motus sit unus numero. Quod patet in motu locali. Cum enim ambulans pausat, cessat illa ambulatio: sed quando iterum ambulare incipit, iterum ambulatio erit. Si ergo dicatur quod sit una et eadem ambulatio, contingit quod unum et idem sit et corrumpatur multoties; quod est impossibile. Sic igitur et si contingeret quod eadem numero sanitas reparetur, non sequeretur quod secunda sanatio esset idem numero motus cum prima; sicut nec secunda ambulatio cum prima, quamvis utraque sit ad eundem locum numero. Ulterius concludit quod istae dubitationes sunt extra principalem intentionem, et ideo sunt praetermittendae.	702. Then at (521 228 a12) he determines the truth in regard to the case mentioned in 700. For he mentioned there that if it is the same quality that is recovered, the second alteration will be numerically the same motion as the first; if the same numerical quality is not recovered, then it is not numerically the same act. Having presented a certain difficulty as though giving a reason for what was set down above, he adds that the reason for raising the difficulty was that at first sight it seemed that the same argument would hold good for the unity of quality and of motion. But there is a difference: for it does follow that if two motions are the same in the manner in which a motion is said to be numerically one, then the habit, i.e., the quality, acquired by the motion is one; because numerically the same quality is produced by an act numerically one. However, if the quality that returns is one, not everyone would agree that the act is one; for if the terminus of two motions is numerically one, it does not mean that the motions were numerically one. This is evident in local motion. For when a person interrupts his walk, the act of walking ceases; but when he resumes, the act resumes. Now, if you were to say that the whole journey is one act of walking that ceases to be and is then revived, then it would follow that one and the same thing can exist and cease to exist any number of times—which is impossible. In like manner if the same numerical health is again and again recovered, it does not follow that the second healing was the same motion as the first, any more than a second walk is the same as a first, even though both go toward the same numerical goal. Finally, he concludes that these difficulties lie outside the present enquiry and are for that reason to be passed over.

Lecture 7 Numerical unity of motion (continued)

Latin	English
	Lecture 7 Numerical unity of motion (continued)
lib. 5 l. 7 n. 1 Postquam philosophus posuit quod tria requiruntur ad hoc quod sit unus motus simpliciter, scilicet unitas temporis, et rei in qua est motus, et subiecti; hic hoc probare intendit. Cum enim multipliciter dicatur unum simpliciter, uno modo sicut aliquod indivisibile est unum, alio modo sicut continuum est unum; motus non potest dici simpliciter unus sicut indivisibilis, quia nullus motus indivisibilis est. Unde relinquitur quod hoc modo dicatur unus sicut continuus; et quod hoc sit motui esse unum simpliciter, quod est ei esse continuum; et ipsa continuitas motus sufficiat ad eius unitatem. Sequitur enim quod si est continuus, quod sit unus. Quaecumque igitur requiruntur ad continuitatem motus, requiruntur ad eius unitatem.	703. After positing that three things are required in order that a motion be unqualifiedly one, namely, unity of time, unity of that in which the motion takes place and unity of subject, the Philosopher now intends to prove this. Now while there are a number of ways in which things are unqualifiedly one, one being the way in which an indivisible is one and another the way in which a continuum is one, no motion can be unqualifiedly one in the way that an indivisible is one, because no motion is indivisible. Consequently, it remains that a motion is one to the extent that it is continuous and that, insofar an a motion is concerned, to be continuous is to be unqualifiedly one, so that the very continuity of motion suffices for its unity. For if it is continuous, it is one. Accordingly, whatever is required to make a motion be continuous is also required to make it one.
lib. 5 l. 7 n. 2 Ad continuationem autem motus requiruntur tria. Quorum primum est unitas speciei. Non enim omnis motus potest continuari omni motui; sicut etiam in aliis continuis non indifferenter qualecumque contingat esse aliquid, continuari potest cuicumque, qualecumque illud esse contingat: sed illa continuari possunt, quorum ultima contingit esse unum, quod est de ratione continui, ut supra dictum est. Sed quaedam sunt quae nulla ultima habent, ut formae et indivisibilia omnia: et ideo eorum non potest esse continuatio. Quorundam vero sunt aliqua ultima, quae sunt divisibilia et quantitatem habentia, quae sunt aequivoca, idest non convenientia in nomine et ratione: et ista etiam non possunt continuari. Nec etiam potest esse contactus in quibusdam eorum. Non enim potest dici quod linea et ambulatio se contingant, vel quod unum sit eorum ultimum, quod est ea continuari ad invicem. Ex quo patet quod ea quae sunt diversorum generum vel specierum, non possunt continuari ad invicem. Ergo motus qui differunt genere vel specie, possunt esse habiti, idest consequenter ad invicem se habere, sicut aliquis post cursum potest statim febricitare; cursus autem et febricitatio sunt in diversis generibus. Et in eodem genere, scilicet loci mutationis, una loci mutatio est consequenter se habens ad aliam, cum tamen non sit continua; sicut patet in diffusione lampadis, ut puta cum candela de manu in manum transfertur: sunt enim ibi diversi motus non continui. Vel potest intelligi quod motum localem liquoris quo flamma sustentatur, quem appellat diffusionem, consequitur motus localis flammae, quae nomine lampadis significatur. Praedictae igitur mutationes, quia differunt genere vel specie, non sunt continuae, cum non possint habere unum ultimum, quod ponitur esse de ratione continui. Unde possunt quidem motus specie vel genere differentes, esse consequenter se habentes et habiti, idest quodammodo se tangentes, absque aliqua interpolatione temporis, inquantum tempus est continuum. Quod quidem eadem ratione habet continuitatem, qua et motus, scilicet inquantum est ei unum ultimum. Nihil autem prohibet in uno instanti temporis, ad quod continuantur partes eius, terminari unum motum, et incipere alium alterius generis vel speciei; et sic motus illi erunt habiti, sed non continui. Et ideo secundum praemissa sequitur quod ad hoc quod motus sit continuus, requiritur quod sit unus secundum speciem: quae quidem unitas speciei est in motu ex re in qua est motus, inquantum est indivisibilis secundum speciem.	704. Now, in order that a motion be continuous, three things are required. The first of these is oneness in species. For there will not be continuity between one motion and another indiscriminately any more than there is continuity between just any two continuous things chosen at random in any other sphere. There can be continuity only when the extremities of the two things are one—this is implied in the very notion of continuity, as was explained above. Now, some things have no extremities at all; for example, forms and all indivisibles. Therefore, in regard to such things there can be no continuity. Other things have extremities which are divisible and have quantity. Some such things are equivocal, i.e., not agreeing in name and notion. Such things afford no means of forming continuity; indeed, in many cases no contact is possible. For how could a line and walking be in contact, or how could they possess a common extremity, so as to make continuity possible? This shows that continuity is impossible with things that belong to genera or species that are diverse. However, motions that differ generically or specifically can follow one upon the other, as a person immediately after running can start to get a fever—running and getting a fever being in diverse genera. And even in the same genus, e.g., in local motion, one change of place could follow upon another without the motion being continuous, as is evident in the spreading of the lamp (the torch-race), when the torch is passed from hand to hand. In this case we have diverse non-continuous motions. Or the phrase “spreading of the lamp” could refer to the local motion of the flame—which is signified by the word “lamp”—which is moved according to the local motion of the fuel that feeds the flame—such local motion being called spreading. Therefore the changes mentioned in the preceding paragraph, since they differ either generically or specifically, are not continuous, since they cannot have one extremity, which is required for a continuum. Consequently, motions that differ generically or specifically may be consecutive and “had”, i.e., in contact somehow without any time interruption, inasmuch as time is continuous and has its continuity in the same way that motion has, namely, because there is one extremity (joining two parts). Now there is nothing to prevent one motion from being ended and another of an entirely different kind from beginning at the same instant that two parts of time are being joined. In that case the two motions will be contiguous but not continuous. Therefore, according to our premises, it follows that in order that a motion be continuous, it is necessary that it be one in species: this unity of species being in the motion from the thing in which the motion is, insofar as it is incapable of division according to species.
lib. 5 l. 7 n. 3 Secundo requiritur ad continuitatem motus, quod sit unius subiecti: quia diversorum subiectorum motus possunt esse habiti, sed non continui; sicut dictum est de mutatione candelae per motum diversarum manuum.	705. In the second place, continuity of motion requires unity of subject, for the motions of diverse subjects cannot be continuous, though they can be contiguous, as was said about transferring a lamp from hand to hand.
lib. 5 l. 7 n. 4 Tertio requiritur ad continuitatem motus et unitatem, quod sit unus tempore, ad hoc quod non interveniat aliqua immobilitas vel quies. Quia si deficeret aliquod tempus motui, in quo scilicet non moveretur, sequeretur quod in illo quiesceret: si autem quies interponitur, erunt multi motus et non unus; multi enim motus et non unus sunt, quorum quies in medio est. Unde si aliquis motus sit qui intercipiatur quiete, non erit neque unus neque continuus. Intercipitur autem quiete, si tempus sit in medio, ut ostensum est: unde requiritur ad continuitatem motus, quod sit unum tempus continuum. Sed tamen hoc non sufficit; quia motus qui non est unus specie, non est continuus, etiam si tempus non deficiat: quia etsi sit unum secundum tempus, erit alius secundum speciem. Quia necesse est ad hoc quod sit motus unus continuus, quod sit unus secundum speciem, sed non sequitur quod motus qui est unus secundum speciem, sit unus simpliciter. Sic ergo patet quod tria praedicta requiruntur ad hoc quod sit unus motus simpliciter. Et hoc est quod concludit, quod dictum est quis motus sit simpliciter unus.	706. Thirdly, in order that a motion be continuous and one, it must be one as regards the time, so that no period of immobility or rest intervene. For if there is a time in which it was not moving, then it was at rest during that time, and if a state of rest intervenes, the motion is not one but many; for motions that are interrupted by rest are not one but many. Consequently, if a motion is interrupted by rest, it will be neither one nor continuous. But it is interrupted by rest, if there is a time in the middle of it, as was shown. Hence for continuity of motion, there must be one continuous time. But mere continuity of time is not enough, because a motion that is not specifically one is not continuous, even though time is not interrupted: for although it be one in regard to time, it will be other in regard to species. In other words, in order that a motion be one and continuous, it must be specifically one; but it does not follow that a motion specifically one is unqualifiedly one, Thus, it is clear that the three aforementioned things are required in order that a motion be unqualifiedly one. And so he concludes that we have now explained which motion is unqualifiedly one.
lib. 5 l. 7 n. 5 Deinde cum dicit: amplius autem dicitur unus et perfectus etc., positis tribus modis principalibus unitatis motus, hic ponit duos alios modos secundarios, qui magis pertinent ad quandam formam unitatis, quam ad ipsam unitatem. Secundum ponit ibi: amplius autem aliter et cetera. Dicit ergo primo, quod sive motus dicatur unus secundum genus sive secundum speciem sive secundum substantiam, sicut qui est numero unus, dicitur unus motus ex hoc quod est perfectus, sicut et in aliis rebus perfectum et totum ad unitatis rationem pertinent. Non enim dicimus unum hominem vel unum calceum, nisi de toto. Quandoque autem dicitur unum etiam de imperfecto, dummodo sit continuum. Et ratio huius est, quia unum potest attendi vel secundum quantitatem, et sic sola continuitas sufficit ad unitatem rei; vel secundum formam substantialem, quae est perfectio totius; et sic perfectum et totum dicitur unum.	707. Then at (523 228 b11) having posited the three principal ways in which a motion is one, he mentions two secondary ways, although these pertain more to a certain form of unity than to unity itself. The second of these is given at 708. He says therefore first (523 228 b11) that whether a motion be one in genus or in species or in substance, i.e., numerically one, it is also called one if it is perfect, just as in other things, “perfect” and “whole” pertain to the notion of unity. For we do not speak of one man or one shoe, unless they are whole. However, there are times when we speak of something imperfect as being one, provided it is continuous. And the reason for this is that unity can be regarded from the viewpoint of quantity, in which sense mere continuity suffices for the unity of a thing, or from the viewpoint of the substantial form, which is the perfection of the whole. Thus, what is perfect and whole is said to be one.
lib. 5 l. 7 n. 6 Deinde cum dicit: amplius autem aliter praeter praedictos etc., ponit alium modum secundarium, prout dicitur motus unus qui est regularis, idest uniformis; sicut etiam in aliis rebus dicitur unum, quod est simile in partibus. Et circa hoc tria facit: primo ponit hunc modum unitatis, secundum quod regularis motus dicitur unus; secundo ostendit in quibus inveniatur regularitas et irregularitas, ibi: est autem et in omni motu etc.; tertio ostendit modos irregularitatis, ibi: irregularitatis autem et cetera. Dicit ergo primo, quod praeter praedictos modos unitatis, dicitur motus unus qui est regularis, idest uniformis. Irregularis enim motus, idest difformis, non videtur esse unus, sed magis motus regularis, idest uniformis; sicut motus qui est totus in directum, est uniformis. Ideo autem motus irregularis non videtur unus, quia est divisibilis in partes dissimiles; indivisibilitas autem pertinet ad rationem unius, quia unum est ens indivisum. Sed tamen motus irregularis est quodammodo unus. Sed unitas motus irregularis et regularis videtur differre secundum magis et minus: quia motus regularis est magis unus quam motus irregularis; sicut et corpus similium partium est magis unum quam corpus dissimilium.	708. Then at (524 228 b15) he gives the other secondary way; that a motion is called one when it is regular, i.e., uniform, just as in other things an object is said to be one, if its parts are alike. About this he does three things: First he posits this mode of unity in the sense that a regular motion is one; Secondly, he shows in which motions regularity and irregularity are found, at 709; Thirdly, he explains the modes of irregularity, at 710. He says therefore that in addition to the above-mentioned rays of being one, a motion is called one, if it, is regular, i.e., uniform. For an irregular or non-uniform motion does not seem to be one, whereas a regular, i.e., uniform motion does (as a motion which is entirely straight is uniform). The reason why an irregular motion does not seem to be one is that it can be divided into parts which are not alike, whereas indivisibility pertains to the notion of unity, because that which is one is undivided. However, an irregular motion is one in a sense. But the unity of irregular and regular motions seem to differ according to more and less: because a regular motion is more perfectly one than an irregular one; just as a body whose part’s are alike is more perfectly one than a body of parts that are not alike.
lib. 5 l. 7 n. 7 Deinde cum dicit: est autem et in omni motu etc., ostendit in quibus motibus inveniatur regularitas et irregularitas. Et dicit quod in omni genere vel specie motus, invenitur regulare et non regulare: quia potest aliquid alterari regulariter, sicut quando tota alteratio est uniformis; et potest aliquid ferri, idest secundum locum moveri, in magnitudine regulari, idest uniformi, sicut si feratur aliquid per circulum aut per lineam rectam; et similiter est in augmento et decremento.	709. Then at (525 228 b19) he shows in which motions irregularity and regularity are found. And he says that they are found in every genus and species of motion: for some things can be altered in a regular manner, as when the entire alteration is uniform, and some things can be moved along a magnitude that is regular and uniform, as things that are in circular motion or in rectilinear motion. The same is true of growing and decreasing.
lib. 5 l. 7 n. 8 Deinde cum dicit: irregularitatis autem differentia etc., accedit ad determinandum de motu irregulari. Et primo assignat modos irregularitatis; secundo ostendit quomodo motus irregularis sit unus, quod supra dixerat, ibi: unus igitur et cetera. Circa primum duo facit: primo assignat duos modos irregularitatis in motu; secundo infert quasdam conclusiones ex dictis, ibi: unde neque species et cetera. Dicit ergo primo quod differentia quae facit irregularitatem motus, aliquando est ex parte rei in qua movetur, ut patet praecipue in motu locali: quia impossibile est quod motus sit regularis vel uniformis, qui non transit per magnitudinem regularem, idest uniformem. Dicitur autem magnitudo regularis vel uniformis, cuius quaelibet pars uniformiter sequitur ad aliam partem, et sic quaelibet pars potest supponi alteri parti, ut patet in linea circulari, et etiam in linea recta. Magnitudo autem irregularis est, cuius non quaelibet pars sequitur uniformiter ad aliam partem; sicut patet in duabus lineis facientibus angulum, quarum una applicatur alteri non in directum, sicut partes unius lineae sibi invicem in directum applicantur. Et ideo motus circularis est regularis, et similiter motus rectus: sed motus reflexi aut obliqui, quia faciunt angulum, non sunt regulares nec in magnitudine regulari; vel quicumque alius motus sit per quamcumque magnitudinem, cuius quaecumque pars non conveniat cuicumque parti per uniformitatem applicationis, vel cuius una pars non convenienter possit contingere aliam partem. Si enim illa pars quae continet angulum, supponatur illi parti quae angulum non continet, non erit conveniens contactus.	710. Then at (526 228 b21) he approaches the task of deciding about irregular motion. First he mentions ways of being irregular; Secondly, he shows how an irregular motion is one, at 713. About the first he does two things: First he assigns two ways in which irregularity is present in motions; Secondly, he draws certain conclusions from all this, at 712. He says therefore first (526 228 b21) that the variations that make for irregularity in motion are caused sometimes from the thing in respect to which there is motion, as is evident especially in local motions for it is impossible for a motion to be regular and uniform unless it passes over a magnitude that is regular, i.e., uniform. Now a magnitude is said to be regular or uniform when each part of it follows its neighbor in a uniform manner, so that any part could be superimposed upon any other, as is clear in the case of arcs or straight lines. But a magnitude is irregular, if one part does not uniformly follow another, as is evident in two lines that form an angle, of which one part does not fit perfectly over the other in the way that one part of a line fits perfectly over another, Therefore, a circular motion is regular and so is a rectilinear one: but reflexed or oblique motions, whose path forms an angle, are not regular and do not take place on a uniform magnitude; likewise any motion on a magnitude that is not such that any part of it taken at random fits on any other taken at random, For if the part (of the motion) that contains the angle is superimposed on a part that does not form an angle, they will not match,
lib. 5 l. 7 n. 9 Secunda differentia irregularitatem faciens est, non ex parte loci, neque ex parte temporis, neque in quod quo, idest neque ex parte eius quod dicit quo, idest ex parte cuiuscumque rei in qua fit motus (non enim est solum motus in ubi, sed in qualitate et quantitate): vel potest hoc referri ad subiectum in quo est motus. Sed iste secundus modus irregularitatis accipitur in eo quod ut, idest ex diversitate modi motus. Determinatur enim iste secundus modus irregularitatis velocitate et tarditate: quia ille motus dicitur regularis, cuius est eadem velocitas per totum; irregularis autem, cuius una pars est velocior altera.	711. The second difference that makes for irregularity is found neither in the place nor in the time nor in the goal (for the goal of a motion is not merely a place but also quality or quantity) but in the manner of the motion, For in some cases the motion is differentiated by swiftness and slowness; because a motion that has the same velocity throughout is said to be uniform, while one in which one part is swifter than another is said to be irregular.
lib. 5 l. 7 n. 10 Deinde cum dicit: unde neque species motus etc., concludit duo corollaria ex praemissis. Quorum primum est, quod velocitas et tarditas non sunt species motus, neque differentiae specificae, quia consequuntur omnes species motus; quia velocitate et tarditate determinatur regularitas et irregularitas, quae consequuntur quamlibet speciem motus, ut supra dictum est. Nulla autem species vel differentia consequitur omnem speciem sui generis. Secundum corollarium est, quod velocitas et tarditas non sunt idem quod gravitas et levitas: quia utrumque istorum habet motum semper ad idem; sicut motus terrae, quae est gravis, semper est ad ipsam, idest ad locum ipsius, qui est deorsum, et motus ignis semper est ad ipsum, idest ad locum proprium, qui est sursum. Velocitas autem et tarditas se habent ad diversos motus, ut dictum est.	712. Then at (527 228 b28) he draws two conclusions from the foregoing. The first of which is that swiftness and slowness are neither species of motion nor specific differences, because they can be found in all types of motion, since they determine regularity and irregularity, which follow upon each species of motion, as was said above. And no species or difference is common to every species of a genus. The second corollary is that swiftness and slowness are not the same as heaviness and lightness, because each of the latter has its own motion, for the motion of earth, which is heavy, is always toward a downward place and the motion of fire is always toward an upward. On the other hand, swiftness and slowness are common to diverse motions, as was said.
lib. 5 l. 7 n. 11 Deinde cum dicit: unus igitur irregularis est etc., ostendit quomodo motus irregularis sit unus; secundo infert quoddam corollarium ex dictis, ibi: si autem omnem unum et cetera. Dicit ergo primo, quod motus irregularis potest dici unus, inquantum est continuus; sed minus dicitur unus quam regularis; sicut et linea habens angulum, minus dicitur una quam linea recta. Et hoc maxime apparet in motu reflexivo: quia quasi videntur duo motus. Ex hoc autem quod est minus unus, apparet quod aliquid habet de multitudine: quia ex hoc aliquid est minus, quod habet admixtionem contrarii, sicut minus album habet aliquid admixtum de nigro, ad minus secundum quandam appropinquationem. Et sic patet quod motus irregularis et est unus, inquantum est continuus, et est quodammodo multiplex, inquantum est minus unus.	713. Then at (528 229 a1) he shows how an irregular motion is one; Secondly, he draws a corollary at 714. He says therefore first that an irregular motion can be said to be one insofar as it is continuous, but it is less perfectly one than a regular motion, just as a line having an angle is less perfectly one than a straight line. This is especially clear in a reflected motion, which seems to be, as it were, two motions. Now, since an irregular motion is less perfectly one, it appears to share in the notion of multitude, for a thing is said to be less, because it has an admixture of the contrary, as what is less perfectly white has an admixture of black, at least in being closer to black than a perfectly white object is.
lib. 5 l. 7 n. 12 Deinde cum dicit: si autem omnem etc., concludit ex immediate dictis quod supra proposuerat; scilicet quod motus qui sunt diversi secundum speciem, non possunt continuari. Omnem enim motum unum contingit esse regularem, et iterum non regularem. Sed motus qui est compositus ex diversis motibus secundum speciem, non potest esse regularis. Quomodo enim esset regularis motus compositus ex alteratione et loci mutatione? Necesse est enim ad hoc quod motus sit regularis, quod partes conveniant ad invicem. Ergo relinquitur quod motus diversi, qui non consequuntur se invicem eiusdem speciei existentes, non sunt unus motus et continuus; quod supra positum est et per exempla manifestatum.	714. Then at (529 229 a3) he concludes from the immediately foregoing the conclusion which he had previously proposed; namely, that motions which are specifically diverse cannot form a continuity. For every motion that is one can be either irregular or regular. But a motion that is composed of specifically distinct motions cannot be regular. For how could a regular motion be composed of alteration and local motion? For in order that a motion be regular its parts must agree. Consequently, the conclusion is that diverse motions that are consecutive but not all of the same species do not form a motion that Is one and continuous, as was stated above and explained by examples.

Lecture 8 Contrariety of motions

Latin	English
	Lecture 8 Contrariety of motions
lib. 5 l. 8 n. 1 Postquam philosophus determinavit de unitate et diversitate motus, hic determinat de contrarietate motuum, quae est quaedam diversitatis species, ut patet in X Metaphys. Et dividitur in partes duas: primo ostendit qualiter accipienda est contrarietas in motu, et etiam in quiete; in secunda movet quasdam quaestiones circa contrarietatem praedictam, ibi: dubitabit autem aliquis et cetera. Circa primum duo facit: primo determinat de contrarietate motus; secundo de contrarietate quietis, ibi: quoniam autem motui et cetera. Circa primum tria facit: primo distinguit diversos modos, secundum quos videri posset quod acciperetur contrarietas in motu; secundo removet quosdam illorum, ibi: est autem qui est etc.; tertio assignat verum modum contrarietatis in motu et mutatione, ibi: quoniam autem differt et cetera.	715. After discussing unity and diversity of motions, the Philosopher now discusses contrariety of motions, which is a kind of diversity, as is evident from Book I of Metaphysics. His treatment is divided into two parts: In the first he shows how to understand contrariety in motion and in rest; In the second he raises some questions about such contrariety, at 742. About the first he does two things: First he settles the problem of contrariety of motion; Secondly, about contrariety of states of rest, at 727. About the first he does three things: First he distinguishes diverse ways according to which contrariety of motion might be taken; Secondly, he rejects some of these ways, at 717; Thirdly, he assigns the true way in which motions and changes are contrary, at 722.
lib. 5 l. 8 n. 2 Dicit ergo primo, quod post praedicta determinandum est qualis sit motus contrarius alicui motui; et eodem modo determinandum est de mansione, idest de contrarietate quietis ad motum, et quietis ad quietem. Sed in hoc tractatu hoc primo faciendum est, quod debemus distinguere modos, secundum quos universaliter accipi potest ratio contrarietatis in motibus. Et distinguit quinque modos. Quorum primus est, ut ratio contrarietatis in motibus accipiatur secundum accessum ad aliquem terminum, et recessum ab eodem. Et hoc est quod dicit: utrum contrarius motus sit qui est ex eodem, ei qui est in idem, ut qui est ex sanitate, ei qui est in sanitatem: secundum quam rationem generatio et corruptio videntur esse contraria, quia generatio est motus ad esse, corruptio autem est motus ab esse. Secundus modus est, ut ratio contrarietatis motuum accipiatur secundum contrarietatem terminorum, a quibus incipit motus. Et hoc est quod dicit: aut qui est ex contrariis, ut qui est ex sanitate, ei qui est ex aegritudine. Tertius modus est, ut contrarietas motuum accipiatur secundum contrarietatem terminorum, ad quos terminatur motus. Et hoc est quod dicit: aut qui est in contraria, ut qui est in sanitatem, ei qui est in aegritudinem. Quartus modus est, ut accipiatur motuum contrarietas secundum contrarietatem termini a quo, ad terminum ad quem. Et hoc est quod dicit: aut qui est ex contrario, ei qui est in contrarium, ut qui est ex sanitate, ei qui est in aegritudinem. Quintus modus est secundum contrarietatem ex parte utrorumque terminorum. Et hoc est quod dicit: aut qui est ex contrario in contrarium, ei qui est ex contrario in contrarium, ut qui est ex sanitate in aegritudinem, ei qui est ex aegritudine in sanitatem. Necesse est enim quod contrarietas motuum accipiatur aut secundum unum horum modorum, aut secundum plures: quia non contingit secundum aliquam aliam rationem contraponere motum motui.	716. He says therefore first (530 229 a7) that it is now time to decide how one motion is contrary to another, as well as how rest is contrary to motion and rest to rest. But in this treatment we must first distinguish the ways according to which the idea of contrariety in motions can be taken universally. And he distinguishes five ways. The first of which is that one idea of contrariety in motions is based on one motion approaching a definite terminus and another departing from the name terminus. And this is what he says: “...whether contrary motions are motions respectively from and to the same thing, e.g., a motion from health and a motion to health”. According to this, generation and ceasing-to-be seem to be contrary, because generation is a motion to being, and ceasing-to-be from being. The second way is that the idea of contrariety of motions is based on contrariety of the termini from which the motions begin. And this is what he says: “...or motions respectively from contraries, e.g., a motion from health and one from sickness”. The third way is that contrariety of motions is based on the contrariety of the goals at which they are terminated. And this is what he says: “...or motions respectively to contraries, e.g., a motion to health and a motion to sickness”. The fourth way is to take contrariety of motions according to the contrariety existing between the start of one and the goal of the other. This is what he says: “...or motions respectively one from a contrary and the other to a contrary, e.g., a motion from health and one to sickness”. The fifth way is based upon contrariety on the part of both termini of each motion. This is what he says: “...or motions respectively from a contrary to its opposite and from the latter to the former, e.g., a motion from health to sickness and a motion from sickness to health”. Now contrariety among motions is necessarily based either on one of these five ways or on more than one, for there is no other possible way of one motion being contrary to another.
lib. 5 l. 8 n. 3 Deinde cum dicit: est autem qui est ex contrario etc., excludit duos praedictorum modorum. Et primo quartum, qui accipiebatur secundum contrarietatem termini a quo, ad terminum ad quem; secundo secundum modum, qui est secundum contrarietatem terminorum, ex quibus incipit motus, ibi: neque qui est ex contrario etc.; tertio concludit quomodo se habeant duo modi reliqui ad invicem, ibi: relinquitur igitur et cetera. Dicit ergo primo, quod motus qui est ex uno contrario, non potest dici contrarius ei qui est in aliud contrarium, ut si diceretur quod motus qui est ex sanitate, sit contrarius motui qui est in aegritudinem. Idem enim non est sibi ipsi contrarium: sed motus qui est ex sanitate, motui qui est in aegritudinem, est unus et idem subiecto, sed non est idem esse ipsis, idest differunt ratione, eo modo quo non est idem secundum rationem moveri a sanitate, et moveri in aegritudinem; quia unus importat habitudinem motus ad terminum a quo, alius autem habitudinem eiusdem motus ad terminum ad quem. Non est igitur accipienda contrarietas motus secundum contrarietatem unius termini ad alium.	717. Then at (531 229 a16) he rejects two of these five: First of all the fourth, which based contrariety on the opposition between the start of one and the goal of the other; Secondly, the second, which based contrariety on the opposition between the start of one and the start of the other, at 716. Thirdly, he concludes how two of the remaining ways are related, at 721. He says therefore first (531 229 a16) that a motion which begins at one contrary cannot be called contrary to a motion that tends to the opposite contrary, so as to say that a change from health is contrary to a change to sickness. For nothing is contrary to itself; but a motion from health is one and the same as a motion to sickness, although they differ in thought inasmuch as a change from health is not the same idea as a change to sickness—for one stresses the starting point and the other the goal of the same notion. Consequently, contrariety of motion must not be taken from the viewpoint of the contrariety existing between the start of one and the end of the other.
lib. 5 l. 8 n. 4 Deinde cum dicit: neque qui est ex contrario etc., ostendit quod contrarietas motuum non est accipienda secundum contrarietatem terminorum ex quibus incipit motus. Et hoc tribus rationibus, quarum prima talis est. Duo motus qui in idem tendunt, non sunt contrarii: sed duo motus ex contrariis recedentes, possunt in unum et idem tendere; simul enim accidit mutari, idest aequaliter, ex contrario in contrarium aut in medium, ut postea dicetur; et sic ex utroque contrario contingit in unum medium mutari. Non ergo motus propter hoc sunt contrarii, quia a contrariis incipiunt moveri.	718. Then at (532 229 a20) he shows that contrariety must not be taken from the contrariety existing between the two starting points of two motions: and this for three reasons, of which the first is the following. Two motions that tend to the same goal are not contrary; but two motions that start from contraries can tend to one and the same goal, for a motion can go either to a contrary or to what is intermediate between the contraries, as will be said later. Thus two motions that start from contraries could terminate at the same intermediate. Consequently, motions are not contrary just because they start at terms that are contrary.
lib. 5 l. 8 n. 5 Secundam rationem ponit ibi: sed magis in contrarium mutari etc.; quae talis est. Ex illo accipienda est ratio contrarietatis in motu, quod magis facit motum esse contrarium: sed contrarietas terminorum ad quos motus terminatur, magis videtur esse causa contrarietatis motuum, quam contrarietas terminorum a quibus incipit motus; quia cum dico motus incipere a contrariis terminis, dico remotionem contrarietatis; cum vero dico motus accedere ad contraria, dico acceptionem contrarietatis: ergo non accipitur contrarietas motuum secundum terminum a quo tantum.	719. He gives the second reason at (533 229 a22), which is this. The idea of contrariety in motion must be based on that which more evidently makes the motion contrary, but contrariety between goals at which motions end seems to be a greater cause of contrariety in motions than is contrariety between termini at which motions start. For when I say that motions begin at contrary terms, I am stressing the removal of contrariety, but when I say that motions are approaching contrary goals, I am stressing the receiving of contrariety. Therefore, contrariety of motions is not based solely on the termini at which they start.
lib. 5 l. 8 n. 6 Tertiam rationem ponit ibi: et dicitur autem unusquisque etc.; quae talis est. Ab eo a quo aliquid recipit nomen et speciem, recipit etiam contrarietatem, cum contrarietas sit differentia secundum formam, ut patet in X Metaphys. Sed unusquisque motus magis dicitur, idest denominatur, et speciem recipit a termino in quem, quam a termino ex quo, sicut sanatio dicitur motus in sanitatem, et aegritudo motus in aegritudinem; et hoc etiam supra dictum est. Magis ergo accipienda est contrarietas motuum secundum terminum in quem, quam secundum terminum a quo. Et sic idem quod prius.	720. He gives the third reason at (534 229 a25) and it is this. Things receive contrariety from that from which they take their name and species, for contrariety is a difference based on form, as in clear in Book X of Metaphysics. But every motion gets its name and species from the goal more than from the starting point, as healing is a motion to health and getting sick is a motion to sickness. This point was mentioned before. Therefore, contrariety of motions is taken rather from the goal than from the terminus at which they start. Thus our conclusion is the same as before.
lib. 5 l. 8 n. 7 Deinde cum dicit: relinquitur igitur etc., concludit quod, remotis duobus modis secundum contrarietatem terminorum acceptis, relinquuntur duo alii, scilicet tertius et quintus: quorum unus est secundum solam contrarietatem terminorum ad quos, quem tangit cum dicit qui est in contraria; alius qui est secundum contrarietatem utrorumque terminorum, quem tangit cum dicit et qui est in contraria ex contrariis. Primus autem modus non accipiebatur secundum contrarietatem aliquam terminorum, sed secundum accessum et recessum ab eodem termino. Concludit autem ulterius, quod forte hi duo modi residui sunt idem subiecto, quia illi motus qui sunt in contraria, sunt etiam ex contrariis: sed forte secundum rationem non sunt idem, propter diversas habitudines motus ad terminos, ut supra dictum est. Et exemplificat quod motus qui est in sanitatem, ei qui est ex aegritudine est idem subiecto, sed non ratione. Et similiter qui est ex sanitate, ei qui est in aegritudinem.	721. Then at (535 229 a27) he concludes that having rejected the two ways that were based on the contrariety of termini, there remain two other ways, namely, the third and the fifth. Of these, one is based solely on the contrariety of goals and the other on the contrariety of both sets of termini. Way #1 was not based on any contrariety of termini but on approach and departure from the same terminus. He further concludes that perhaps these two remaining ways are really the same, because motions that tend to contrary goals also start at contraries; but perhaps they are not the same in conception, on account of the various relationships that exist between motions and their termini, as was said above. For example, a motion to health is really the same as a motion from sickness, but they differ in conception. The same is true for a motion from health and a motion to sickness.
lib. 5 l. 8 n. 8 Deinde cum dicit: quoniam autem differt etc., ostendit quomodo accipiatur contrarietas in motu. Et primo secundum quod motus est ad contrarium; secundo prout motus est ad medium, ibi: qui autem ad medium et cetera. Circa primum duo facit: primo ostendit quid facit contrarietatem in motibus; secundo quid in mutationibus, ibi: qui autem est in contrarium et cetera. Circa primum duo facit: primo ostendit propositum syllogismo; secundo inductione, ibi: manifestum est autem et cetera. Ponit autem primo talem rationem. Contrarietas aliquorum accipitur secundum propriam speciem et rationem ipsorum: sed propria ratio specifica motus est, quod sit quaedam mutatio a quodam subiecto affirmato in quoddam subiectum affirmatum, habens duos terminos (in quo differt a mutatione, quae non semper habet duos terminos affirmatos): ergo relinquitur quod ad contrarietatem motus requiritur contrarietas ex parte utrorumque terminorum; ut scilicet proprie dicatur motus contrarius, qui est ex contrario in contrarium, ei qui est ex contrario in contrarium, sicut qui est ex sanitate in aegritudinem, ei qui est ex aegritudine in sanitatem.	722. Then at (536 229 a30) he explains how to take contrariety in motion. First, when the motion tends toward a contrary; Secondly, when it tends toward the intermediate, at 726. About the first he does two things: First he explains what makes for contrariety in motions; Secondly, in changes, at 724. About the first he does two things: First he explains his proposition with a syllogism; Secondly, by induction, at 723. As to the first, he gives this reason at (536 229 a30): The contrariety of things is based on their specific nature and definition. But the specific definition of motion is that it is a change which takes place from a definite affirmed subject to a definite affirmed subject and that two termini are involved—on this point, motion differs from change, which does not always require two affirmed termini. Therefore, we are left with the fact that for contrariety of motion there must be contrariety on the side of both termini. In other words, a motion which goes from contrary to contrary is, strictly speaking, contrary to one that is from contrary to contrary; for example, one that is from health to sickness is contrary to one from sickness to health.
lib. 5 l. 8 n. 9 Deinde cum dicit: manifestum est autem etc., manifestat idem per inductionem. Et primo in alteratione corporali: quia aegrotare est contrarium ei quod est sanari, quorum primus est motus a sanitate in aegritudinem, alius vero ab aegritudine in sanitatem. Hoc etiam patet in alterationibus animae: quia ei quod est addiscere, contrarium est decipi, non ab ipso, sed ab alio. Hi enim motus sunt in contraria ex contrariis; quia addiscere est motus ab ignorantia ad scientiam, decipi autem a scientia ad ignorantiam. Quare autem addit non per ipsum, ostendit subdens, quia sicut in scientia contingit quod aliquis per seipsum acquirat eam, et hoc vocatur invenire; quandoque vero non per seipsum sed ab alio, et hoc vocatur addiscere; ita contingit quod aliquando aliquis decipitur a seipso, aliquando ab alio; et hoc proprie opponitur ei quod est addiscere. Et hoc etiam apparet in motu locali: quia motus sursum est contrarius ei qui est deorsum, quae sunt contraria secundum longitudinem; et motus qui est ad dextrum, est contrarius ei qui est ad sinistrum, quae sunt contraria secundum latitudinem; et motus qui est ante, est contrarius ei qui est retro, quae sunt contraria secundum altitudinem. Sed considerandum est quod hic loquitur de istis differentiis positionum, scilicet de longitudine, latitudine et altitudine, secundum quod sunt in homine: quia sursum et deorsum considerantur secundum longitudinem hominis: dextrum autem et sinistrum secundum latitudinem eius; ante et retro secundum grossitiem eius, quae dicitur altitudo vel profunditas. Item considerandum est quod secundum sursum et deorsum invenitur contrarietas etiam in motibus naturalibus: sed secundum dextrum et sinistrum, ante et retro, invenitur contrarietas in motibus, non secundum naturam, sed secundum motum qui est ab anima, quae movet in has contrarias partes.	723. Then at (537 229 b2) he proves the same by induction. And first of all in bodily alterations: for to fall ill is contrary to getting well. In these two examples the first is from health to sickness and the other from sickness to health. This is also evident in changes that occur in the soul: for to learn is contrary to being led into error (not by oneself but by another). These two motions are also from contraries to contraries, because learning is a motion from ignorance to knowledge, and being deceived is from knowledge to ignorance. He says “not by oneself”, because just as, in the case of knowledge, it is possible for a person to acquire it by himself (and this is called “discovery) or with someone’s help (and this is called “learning”), so also it can happen that a person is led into error sometimes by himself and sometimes by another. It is the latter that is properly opposed to learning. Continuing, we take an example from local motion: for an upward motion is contrary to a downward (and these are contraries in respect of length); a motion to the right is contrary to one to the left (and these are contrary in respect of breadth); and a motion to the fore is contrary to one to the rear (and these are contrary in respect of depth). But notice that Aristotle is here speaking of differences of position as they apply to man: for up and down are measured in respect to man’s length; left and right in respect to his breadth; fore and after in respect to his thickness, which is called height or depth. Moreover, it should be noted that even in natural motions, there is a contrariety based on up and down; but in regard to right and left, or fore and aft, the contrariety is not according to nature but according to motions that originate from the soul, which has motions toward these contrary directions.
lib. 5 l. 8 n. 10 Deinde cum dicit: qui autem est in contrarium etc., ostendit qualiter sit contrarietas in mutationibus. Et primo ostendit quomodo accipiatur contrarietas mutationum in rebus, in quibus invenitur contrarietas; secundo quomodo accipiatur in rebus, in quibus non est contrarietas, ibi: quibus autem non est contrarium et cetera. Dicit ergo primo, quod si accipiatur contrarietas solum ex parte termini ad quem, ut dicatur contrarius qui est in contrarium, hoc non facit contrarietatem motus sed mutationis, quae est generatio et corruptio; sicut fieri album et fieri nigrum contraria sunt. Nec oportet quod contrarietas harum generationum attendatur secundum contrarietatem termini a quo; quia in generatione terminus a quo non est aliquid affirmatum, sed aliquid negatum; fit enim album ex non albo, non autem ex aliquo affirmato. Non enim mutatio de subiecto in subiectum est mutatio, sed motus.	724. Then at (538 229 b10) he shows how there is contrariety in changes. First he explains how to take contrariety of change in things in which contrariety is found; Secondly, how to take it in things in which there is no contrariety, at 725. He says therefore first (538 229 b10) that if contrariety is taken merely from the goal so that what tends to a contrary is said to be contrary, such a process does not make for contrariety of motion, but of change, which is generation and ceasing-to-be, as becoming white and becoming black are contrary. Now the contrariety of these instances of generation is not based on the contrariety of starting point; because in generation the starting point is not something affirmed but something negated, for the white comes to be from the non-white and not from something affirmed. For a change from subject to subject is not change but motion.
lib. 5 l. 8 n. 11 Deinde cum dicit: quibus autem non est contrarium etc., ostendit quod in illis, in quibus non est contrarietas, sicut in substantiis et aliis huiusmodi, accipitur contrarietas mutationum secundum accessum et recessum ab eodem termino. Et hoc est quod dicit, quod in illis in quibus non est contrarium, accipitur contrarietas mutationis ex eo quod est recessus ab ipso, et quod est accessus in ipsum idem; sicut accessus ad formam ignis, quod pertinet ad generationem ignis, et recessus ab eadem forma, quod pertinet ad eius corruptionem, sunt contraria. Unde generatio contraria est corruptioni, et quaecumque remotio cuicumque acceptioni. Sed huiusmodi non sunt motus, sed mutationes. Patet ergo quod ex quinque modis supra positis, duo, scilicet secundus et quartus, ad nihil utiles sunt; unus autem convenit ad contrarietatem motuum; duo autem congruunt ad contrarietatem mutationum.	725. Then at (539 229 b11) he shows that in things in which there is no contrariety, for example, in substances and the like, contrariety of change is based on approach and departure from the same terminus, as accession to the form of fire, which pertains to the generation of fire, and receding from the same form, which pertains to its ceasing-to-be, are contraries. Hence generation is contrary to ceasing-to-be and any loss is contrary to any gain, But these are changes, not motions. It is evident, therefore, that of the five ways listed above, the second and fourth are of no use; one of the remaining is suitable for knowing contrariety of motions, and the other two are suitable for contrariety of changes.
lib. 5 l. 8 n. 12 Deinde cum dicit: qui autem ad medium etc., determinat de contrarietate motus ex parte medii. Et dicit quod in quibuscumque contrariis invenitur medium, motus qui terminantur ad medium, hoc modo ponendi sunt esse contrarii, sicut illi qui terminantur ad contraria: quia motus utitur medio sicut contrario, ita quod ex medio contingit mutari in utrumque contrariorum. Sicut ex fusco, quod est medium inter album et nigrum, hoc modo mutatur in album, ac si mutaretur ex nigro in album; et e converso ex albo sic mutatur aliquid in fuscum, ac si mutaretur in nigrum; et ex nigro sic mutatur in fuscum, ac si mutaretur in album: quia fuscum, cum sit medium ad utrumque extremorum, dicitur utrumque; quia in comparatione albi est nigrum, et in comparatione nigri est album, ut supra dictum est. Ultimo autem concludit quod principaliter intendit, scilicet quod motus sit contrarius motui secundum contrarietatem utrorumque extremorum.	726. Then at (540 229 b14) he decides about contrariety of motion from the viewpoint of the intermediate between contraries. And he says that wherever a pair of contraries admit of an intermediate, motions to that intermediate must be held to be somehow motions to one or other of the contraries, for the intermediate serves as a contrary for the purposes of motion, no matter in which direction the change may be. For example, grey in a motion from grey to white takes the place of black as starting point, but in a motion from white to grey, it takes the place of black as goal. For the middle is, in a sense, opposed to either of the extremes, as has been said above. Finally, he concludes what he mainly intended; namely, that motions are contrary to one another, only when one is a motion from a contrary to the opposite contrary and the other is a motion from the latter to the former.

Lecture 9 Contrariety of rest to motion, and of rest to rest

Latin	English
	Lecture 9 Contrariety of rest to motion, and of rest to rest
lib. 5 l. 9 n. 1 Postquam determinavit philosophus de contrarietate motuum, hic determinat de contrarietate quietum. Et primo in motibus; secundo in mutationibus, ibi: quibus autem non sunt contraria et cetera. Circa primum duo facit: primo ostendit quod quies sit contraria motui; secundo quae cui, ibi: qualis autem et cetera. Dicit ergo primo, quod quia motui non solum videtur contrariari motus, sed etiam quies, determinandum est hoc, qualiter scilicet quies contrarietur motui: quia simpliciter quidem et proprie et perfecte contrariatur motus motui; sed etiam quies motui opponitur, cum sit privatio motus, et privatio quodammodo sit contrarium. Est enim privatio et habitus prima contrarietas, ut dicitur in X Metaphys.: quia scilicet in omnibus contrariis salvatur privationis ratio et habitus, cum semper alterum contrariorum sit quasi privatio respectu alterius, ut album respectu nigri, et amarum respectu dulcis.	727. After discussing contrariety of motions, the Philosopher now determines about contrariety of states of rest. First, in motions; Secondly, in changes, at 732. About the first he does two things: First he shows how rest is contrary to motion; Secondly, which is contrary to which, at 728. He says first (541 229 b23) that since not only motion but also rest seem to be contrary to motion, we have to decide how rest is contrary to motion, for, strictly speaking, it is motion that is perfectly contrary to motion. However, even rest is opposed to motion, since it is the privation of motion, and privation is somehow a contrary. For privation and possession form the fundamental contraries, as is said in Book X of Metaphysics, since the idea of privation and possession are involved in every type of contrary, inasmuch as in any set of contraries, one of them is as privation in respect of the other; for example, black in relation to white and sweet in relation to bitter.
lib. 5 l. 9 n. 2 Deinde cum dicit: qualis autem quali etc., ostendit quae quies cui motui contrarietur. Et circa hoc tria facit: primo movet quaestionem; secundo determinat veritatem, ibi: manifestum igitur est etc.; tertio probat, ibi: motui autem ei et cetera. In quaestione autem quam ponit, unum supponitur, scilicet quod non omnis quies omni motui opponatur, sed aliqualis quies aliquali motui; sicut motui qui est secundum locum, quies secundum locum. Sed quia hoc simpliciter, idest universaliter, dicitur, restat secundum ulterius quaerendum, utrum mansioni, idest quieti, quae est in aliquo termino, puta in albo, opponatur motus, aut ille qui est in album, scilicet dealbatio, aut ille qui est ex albo, scilicet denigratio.	728. Then at (542 229 b26) he shows which rest is contrary to which motion. About this he does three things: First he phrases the question; Secondly, he determines the truth, at 729; Thirdly, he proves it, at 731. In the question which he proposes (542 229 b26) he assumes that not any state of rest is indiscriminately opposed to just any state of motion, but a definite type of rest to a definite type of motion; for example, rest in place is opposed to motion in regard to place. But because the question here is a general one, there still remains another problem: whether the opposite of that rest which consists in possessing its goal, for example, whiteness, is the motion to whiteness, i.e., whitening, or the one from whiteness, namely, blackening.
lib. 5 l. 9 n. 3 Deinde cum dicit: manifestum igitur est etc., determinat veritatem: et primo quantum ad contrarietatem motus ad quietem; secundo quantum ad contrarietatem quietum ad invicem, ibi: simul autem et cetera. Dicit ergo primo, quod cum motus sit inter duo subiecta, idest inter duos terminos affirmatos, motui qui est ex hoc termino in suum contrarium, contrariatur quies quae est in hoc termino; sicut motui qui est ex albo in nigrum, contrariatur quies quae est in albo: et motui qui est ex contrario in hoc, contrariatur quies quae est in contrario; sicut motui qui est ex nigro in album, contrariatur quies quae est in nigro.	729. Then at (543 229 b29) he determines the truth. First as to the contrariety of motion to rest; Secondly, as to the contrariety of rest to rest, at 730. He says therefore first (543 229 b29) that since motion is between two affirmed termini, the contrary of a motion from A to its contrary B is rest in A; for example, the contrary of a motion from whiteness to blackness is rest in whiteness, while the contrary of a motion from the contrary B to A is rest in B. For example, the contrary of a motion from black to white is rest in black.
lib. 5 l. 9 n. 4 Deinde cum dicit: simul autem etc., agit de contrarietate quietum ad invicem. Et dicit quod hae quietes sunt contrariae ad invicem, quae sunt in contrariis terminis. Inconveniens enim est, si motus sint contrarii ad invicem, et quietes ad invicem non opponantur. Et quomodo quietes sunt oppositae, quae sunt in oppositis, exemplificat subdens, quod quies quae est in sanitate, opponitur quieti quae est in aegritudine.	730. Then at (544 229 b31) he treats of the contrariety of one state of rest to another. And he says that those states of rest which are in contrary termini are mutually contrary. For it is not suitable to have motions contrary to one another and states of rest not contrary. And how states of rest in opposites are opposite, he explains with the example that rest in health is the opposite of rest in sickness.
lib. 5 l. 9 n. 5 Deinde cum dicit: motui autem ei qui est etc., probat quod dixerat de contrarietate quietis ad motum. Et dicit quod motui qui est ex sanitate in aegritudinem, opponitur quies quae est in sanitate; quia irrationabile esset quod quies quae est in sanitate, opponeretur motui qui est ex aegritudine in sanitatem. Et hoc sic probat: quia eius motus qui est in ipso, idest ad aliquem terminum, status in eodem termino est magis quietatio, idest eius consummatio vel perfectio, quam quod ei opponatur. Et quod quies in termino ad quem sit motus perfectio, patet per hoc quod simul fit illa quies cum motu: quia ipsum moveri ad terminum est fieri quietem. Unde cum motus sit causa illius quietis, non potest ei opponi, quia oppositum non est causa sui oppositi. Sed necesse est quod motui contrarietur aut haec quies quae est in termino ad quem, aut quies quae est in termino a quo. Non enim potest dici quod quies quae est in aliqua alia specie, contrarietur motui aut quieti: sicut quod quies quae est in albedine, contrarietur quieti quae est in sanitate, aut motui qui est in sanitate. Cum ergo quies quae est in termino ad quem, non contrarietur motui, relinquitur quod contrarietur ei quies quae est in termino a quo.	731. Then at (545 230 a2) he proves what he had said about the contrariety of rest to motion. And he says that the opposition of a motion from health to sick is rest in health; for it is not reasonable that rest in health be the opposite of a motion from sickness to health. This he now proves: Rest in the very goal toward which something else is in motion is the consummation and perfection rather than the opposite of that motion. And that rest in the goal toward which there is motion is its perfection is evident from the fact that the state of rest is coming to be during the motion, because the very movement toward the goal means that rest is coming to be. Hence, since motion is the cause of that rest, it cannot be its opposite, because a thing is not the cause of its opposite. Now the contrary of a motion must be either rest in its goal or rest in the starting point. For it is not reasonable to say that rest in some other species is contrary to a given motion or rest, any more than rest in whiteness is contrary to rest in health or motion to health. Consequently, since rest in the goal is not contrary to motion toward that goal, the only thing that remains is that it is contrary to rest in the starting point.
lib. 5 l. 9 n. 6 Deinde cum dicit: quibus autem non sunt contraria etc., determinat de contrarietate quietis in mutationibus. Et circa hoc tria facit: primo resumit quod dictum est de contrarietate mutationum; secundo ostendit quod mutationi non opponitur quies, sed non mutatio, ibi: quies quidem horum etc., tertio ostendit quomodo non mutatio contrarietur mutationi, ibi: simile autem aliquid est et cetera. Resumit ergo primo quod supra dictum est, scilicet quod in mutationibus in quibus non est contrarietas in terminis, sicut in generatione et corruptione substantiae, oppositio accipitur secundum accessum et recessum ex eodem termino. Est enim mutatio quae est ex ipso aliquo termino, opposita mutationi quae est in ipsum. Sicut mutatio quae est ex esse, scilicet corruptio, opponitur mutationi quae est in esse, scilicet generationi; cum tamen neutra earum sit motus.	732. Then at (546 230 a7) he determines about contrariety of rest in changes. About this he does three things: First he repeats what has already been said about contrariety of changes; Secondly, he shows that the opposite of change is not rest but non-change, at 733; Thirdly, how non-change is contrary to change, at 736. He repeats therefore first (546 230 a7) that in changes that do not involve termini that are contrary, for example, in the generation and ceasing-to-be of substance, opposition is based on approach and departure from the same terminus. For a change from A is opposed to a change to A, as a change from existence, i.e., corruption, is opposed to a change to existence, i.e., generation. However, neither of these is called motion.
lib. 5 l. 9 n. 7 Deinde cum dicit: quies quidem horum etc., ostendit quod his mutationibus non opponitur quies. Et circa hoc tria facit: primo proponit quod intendit; secundo interserit quandam dubitationem, ibi: et si quidem aliquid erit etc.: tertio probat propositum, ibi: si autem hoc et cetera. Dicit ergo primo, quod in his mutationibus quae non sunt inter contraria, non invenitur quies opposita: sed illud quod opponitur eis, sicut quies motui, potest vocari immutatio, idest non mutatio.	733. Then at (547 230 a9) he shows that these changes do not have an opposing state of rest. About this he does three things: First he proposes what he intends; Secondly, he interposes a question, at 734; Thirdly, he proves his proposition, at 133-5. He says therefore first (547 230 a9) that changes which do not pass from contrary to contrary have no states of rest opposed to them; rather what is opposed to them in the way that rest is opposed to motion can be called non-change.
lib. 5 l. 9 n. 8 Deinde cum dicit: et si quidem aliquid erit etc., interserit quandam dubitationem circa praemissa. Dictum est enim quod mutatio quae est ad esse, contrariatur mutationi quae est ex esse; quae quidem est in non esse. Hoc autem quod dico non esse, potest dupliciter accipi. Uno modo quod habeat aliquod subiectum, vel ens actu, sicut non album in corpore, vel in potentia tantum ens, sicut privatio formae substantialis est in materia prima. Aut intelligitur tale non esse, quod non habet aliquod subiectum, sed est omnino non ens. Si primo modo accipiatur non esse, quod habeat aliquod subiectum, tunc inveniri poterit quomodo una non mutatio sit contraria alii non mutationi: quia poterit dici quod non mutatio quae est in esse, opponitur non mutationi quae est in non esse. Ex quo enim non esse habet subiectum, nihil prohibebit dicere, quod illud subiectum permaneat in illo non esse, quod est ipsum non mutari. Si vero non est aliquid quod non est, idest si ipsi non esse non est aliquod subiectum, tunc dubitatio remanet, cui non mutationi sit contraria illa non mutatio vel quies, quae est in esse. Quod enim omnino non est, non potest dici quiescere aut immutabiliter permanere. Et quia necesse est quod non mutationi vel quieti quae est in esse, sit aliqua non mutatio contraria, manifestum ex hoc fit quod illud non esse, a quo est generatio et in quod tendit corruptio, est non esse habens subiectum.	734. Then at (548 230 a10) he interposes a question on this matter. For it has been said that a change to being is contrary to a change from being, which is really a change to non-being. Now the expression “non-being” has two senses: In one sense, it implies a subject, which is either an actual being, as when non-white is in a body, or a potential being, as when privation of substantial form is in first matter. In a second sense, non-being can imply that no subject is involved, i.e., that we are dealing with absolute non-being. If non-being is taken in the first sense, i.e., that a subject. is implied, then it would be possible to find out how one non-change is contrary to another non-change: for it could be said that a non-change in being is opposed to a non-change in non-being. For, since non-being has a subject, there is nothing to prevent that subject from persevering in non-being, which is the same as not changing. Rut if there is nothing which is not, i.e., if non-being has no subjects then the question remains: to which non-change is the non-change or rest in being contrary? For what does not exist at all cannot be said to be at rest or to be unchangeably permanent. And since some kind of non-change must be contrary to non-change or rest in existence, it follows that that non-existence from which generation begins and toward which ceasing-to-be tends is a nonbeing that has a subject.
lib. 5 l. 9 n. 9 Deinde cum dicit: si autem hoc est, aut non omnis etc., ostendit quod supposuerat, scilicet quod id quod opponitur generationi et corruptioni non sit quies. Si enim hoc daretur, scilicet quod esset quies, sequeretur alterum duorum; scilicet quod aut non omnis quies esset contraria motui, aut quod generatio et corruptio sit motus. Unde manifestum est quod id quod opponitur generationi et corruptioni, non dicitur quies, nisi generatio et corruptio esset motus, quod supra improbatum est.	735. Then at (549 230 a12) he explains something he had supposed, namely, that the opposite of generation and of ceasing-to-be is not rest. For if it were, then either of two things would follow: first, that not every rest is contrary to motion, or, secondly, that generation and ceasing-to-be are motions. So it is clear that whatever it is that is opposed to generation and ceasing-to-be, it is not rest, unless generation and ceasing-to-be are motion—which they are not, as we have proved above.
lib. 5 l. 9 n. 10 Deinde cum dicit: simile autem aliquid est etc., ostendit quomodo non mutatio sit contraria mutationi. Et dicit quod simile est de contrarietate immutationis ad mutationem, sicut de contrarietate quietis ad motum: quia immutatio quae est in esse, contraria est vel nulli immutationi (quod esset si non esse non haberet subiectum): aut ei non mutationi quae est in non esse, si non esse habet subiectum. Et haec contrarietas est per modum quo quies opponitur quieti. Aut etiam non mutatio quae est in esse, opponitur corruptioni, ut quies motui. Non autem opponitur generationi, quia corruptio recedit ab immutatione vel quiete quae est in esse, generatio vero tendit in illam; motui autem et mutationi non opponitur quies in termino ad quem, sed quies in termino a quo.	736. Then at (550 230 a16) he shows how non-change is contrary to change. And he says that there is a parallel between the contrariety of non-change to change and that of rest to motion: for a non-change An being is contrary, either to no non-change (which would be, if non-being has no subject) or to that non-change which is in nonbeing (if non-being has a subject). And this contrariety is like the opposition between one rest and another. Or we can say that a non-change in being is the opposite of corruption, as rest is of motion. However, it is not the opposite of generation, because corruption departs from non-change and rest in being, whereas generation tends to it. And we already know that the opposite of motion and change is not rest in the goal but rest in the starting point.

Lecture 10 Certain difficulties are resolved

Latin	English
	Lecture 10 Certain difficulties are resolved
lib. 5 l. 10 n. 1 Postquam philosophus determinavit de contrarietate motuum et quietum, hic movet quasdam dubitationes circa praemissa. Et circa hoc duo facit: primo ponit dubitationes et solvit eas; secundo manifestat quaedam, quae in illis dubitationibus possent esse dubia, ibi: dubitabit autem quis et cetera. Prima pars dividitur in tres, secundum tres dubitationes quas movet; et patent partes in littera. Circa primum duo facit: primo movet dubitationem; secundo solvit, ibi: at si est quod violentia fit et cetera.	737. After discussing the contrariety of motions and of rests, the Philosopher now raises some questions concerning these matters, About this he does two things: First he raises questions and solves them; Secondly, he explains certain matters that may still be doubtful in regard to these questions, at 747. The first part is divided into three sections, one for each question he raises. About the first point he does two things; First he raises a question; Secondly, he solves it, at 740.
lib. 5 l. 10 n. 2 Movet ergo primo dubitationem, quare in genere motus localis inveniuntur quidam motus et quaedam quietes secundum naturam, et quaedam extra naturam, et in aliis generibus hoc non invenitur: puta quod una alteratio sit secundum naturam, et alia extra naturam; quia non videtur magis esse sanatio secundum naturam vel extra naturam, quam aegrotatio, cum utrumque procedat a principio naturali intrinseco. Et similiter est in dealbatione et denigratione, et in augmento et decremento: quia neque isti duo motus sic contrariantur ad invicem, ut unus sit secundum naturam et alter extra naturam, cum utrumque naturaliter proveniat. Neque augmentum sic contrariatur augmento, ut quoddam sit secundum naturam et quoddam extra naturam. Et eadem ratio est de generatione et corruptione: non enim potest dici quod generatio sit secundum naturam et corruptio extra naturam; quia senescere, quod est via in corruptionem, accidit secundum naturam. Neque etiam videmus quod una generatio sit secundum naturam et alia extra naturam.	738. Therefore he first (551 230 a18) raises the question why it is that in the genus of local motion, but not in the other general there are found some motions and rests that are according to nature and some not according to nature. For example, why in it that there are alterations according to nature but none not according to nature? For getting well does not seem to be according to nature or not according to nature any more than getting sick, since each originates from a natural intrinsic principle. The same is true in regard to getting white and getting black or in growing and decreasing, for the former motions are not so contrary to one another that one is according to nature and the other not, since each is a natural process. Nor is growing contrary to growing in such a way that one is according to nature and the other not. The same is true of generation and ceasing-to-be: for generation cannot be said to be according to nature and ceasing-to-be not according to nature, for growing old--which is the road to ceasing-to-be-is according to nature. Nor does it appear that one generation is according to nature and another not.
lib. 5 l. 10 n. 3 Videtur autem quod hic dicitur esse contrarium ei, quod dicitur in II de caelo, quod senium, et omnis defectus et corruptio est contra naturam. Sed dicendum est, quod senium et corruptio et decrementum est quodammodo contra naturam, et quodammodo secundum naturam. Si enim consideretur propria natura alicuius rei, quae dicitur natura particularis, manifestum est quod omnis corruptio et defectus et decrementum est contra naturam: quia uniuscuiusque natura intendit conservationem proprii subiecti; contrarium autem accidit ex defectu seu debilitate naturae. Si autem consideretur natura in universali, tunc omnia huiusmodi proveniunt ex aliquo principio naturali intrinseco, sicut corruptio animalis ex contrarietate calidi et frigidi; et eadem ratio est in aliis.	739. Now it seems that what he says here is opposed to a declaration in On the Heavens, that old age and every defect and ceasing-to-be are against nature. But it must be said that old age and ceasing-to-be and decreasing are against nature in one sense and according to nature in another. For if we consider the specific nature of anything, i.e., its particular nature, it is clear that all ceasing-to-be and all defects and decrease are against nature: because each thing’s nature tends to preserve the subject in which it exists, whereas the contrary of this happens when the nature is weak or defective. But if we consider nature in general, all these things are the result of a natural intrinsic principle, as the destruction of an animal results from the contrariety of hot and cold; and the same is true for all the others.
lib. 5 l. 10 n. 4 Deinde cum dicit: at si est quod violentia etc., solvit propositam quaestionem per interemptionem. Et circa hoc duo facit: primo ostendit quod in quolibet genere motus invenitur secundum naturam et extra naturam; secundo ostendit quomodo haec duo in motibus et quietibus contrarientur, ibi: omnino quidem et cetera. Circa primum duo facit: primo determinat veritatem; secundo removet obiectionem, ibi: erunt igitur corruptiones et cetera. Dicit ergo primo, quod cum illud quod fit ex violentia, sit extra naturam (quia violentum est cuius principium est extra, nihil conferente vim passo; naturale autem est, cuius principium est intra), sequitur quod corruptio violenta sit corruptioni naturali contraria, sicut corruptio extra naturam ei quae est secundum naturam. Et per eandem rationem concludit quod quaedam generationes sunt violentae, et non fatatae, idest non procedentes secundum ordinem naturalium causarum (quia ipse ordo causarum naturalium fatum dici potest), sicut patet cum aliquis facit nasci rosas aut aliquos fructus per aliqua artificia, temporibus non suis; et similiter etiam aliquo artificio procuratur generatio ranarum, aut aliquorum huiusmodi naturalium. Unde cum hae generationes sint violentae, per consequens sunt extra naturam, quibus contrariantur generationes quae sunt secundum naturam. Idem etiam ostendit consequenter in augmento et decremento. Sunt enim quaedam augmenta violenta et extra naturam; sicut patet in illis qui velocius debito ad pubertatem perveniunt, propter teneritudinem vel propter alimentum, idest propter hoc, quod delitiose et abundanti alimento nutriuntur. Idem etiam apparet in augmento tritici: quandoque enim frumenta augentur innaturaliter propter abundantiam humorum, et non constringuntur, ut sint spissa et solida, per debitam digestionem. Et similiter apparet in alterationibus. Sunt enim quaedam alterationes violentae, et quaedam naturales, ut patet maxime in sanatione. Quidam enim dimittuntur a febribus, non in criticis diebus; et isti alterantur extra naturam: alii vero in criticis diebus; et isti alterantur secundum naturam.	740. Then at (552 230 a29) he answers this question by invalidating it. About this he does two things: First he shows that things according to nature and not according to nature are found in every genus; Secondly, how these two things are contrary when they occur in motions and it states of rest, at 742. About the first he does two things: First he determines the truth; Secondly, he removes an objection, at 741. He says therefore first (552 230 a29) that since what takes place through compulsion is contrary to nature (because compulsion arises from a principle outside a thing in such a way that the thing suffering compulsion does not cooperate, whereas what is natural comes from an intrinsic principle) it follows that compulsive ceasing-to-be is contrary to natural ceasing-to-be, just as a ceasing-to-be that is outside of nature is opposed to one according to nature. According to the same argument, he concludes that some generations are compulsory and not according to fate, i.e., not according to the order of natural causes (because the order of natural causes. can be called “fate”), as when a person grows roses or fruits by artificial means out of season or when the generation of frogs or other natural things is procured artificially. Consequently, since these generations are compulsory, they are outside of nature and are contrary to generations according to nature. He shows the same for growing and decreasing. For some cases of growth are compulsory and unnatural, as is evident in persons who reach the state of puberty in an abnormally short time, on account of soft living or on account of the food, i.e., they are fed abundantly and delicately. The same is also apparent in the growing of wheat, for sometimes the grains grow unnaturally through abundance of moisture and are not compact, i.e., made thick and solid by normal digestion. Likewise in alterations. Some are compulsory and some natural, as is especially evident in the process of getting well. For some recover from fever on the critical days and some not on the critical days. The former are cured according to nature and the latter not according to nature.
lib. 5 l. 10 n. 5 Deinde cum dicit: erunt igitur corruptiones etc., obiicit contra praedicta. Cum enim id quod est extra naturam, contrarietur ei quod est secundum naturam, si inveniatur quaedam generatio secundum naturam et quaedam contra naturam, et corruptio similiter, sequetur quod corruptiones sint contrariae ad invicem, et non generationi: quia unum non potest esse duobus contrarium. Et hoc solvit, dicens quod nihil prohibet generationem generationi esse contrariam, et corruptionem corruptioni. Sic enim verum est hoc, etiam remota contrarietate eius quod est secundum naturam et eius quod est extra naturam: quia si est quaedam generatio et corruptio dulcis, et alia tristis, oportet generationem generationi esse contrariam, et corruptionem corruptioni. Dicitur autem generatio et corruptio dulcis, quando ex minus nobili corrupto, generatur magis nobile, sicut si ex aere corrupto generetur ignis; generatio autem et corruptio tristis, quando ex magis nobili corrupto, generatur minus nobile, ut si ex igne generetur aer. Non tamen sequitur, si corruptio opponitur corruptioni, quod non opponatur generationi: quia corruptio opponitur generationi secundum rationem sui generis; corruptio autem corruptioni, secundum rationem propriae speciei: sicut avaritia contrariatur largitati secundum contrarietatem vitii ad virtutem, prodigalitati vero secundum propriae speciei rationem. Et hoc est quod concludit, quod corruptio non est contraria corruptioni simpliciter, idest in universali: sed corruptionum haec quidem est talis, illa vero talis, idest violenta et extra naturam, vel dulcis et tristis.	741. Then at (553 230 b6) he raises an objection against the foregoing. For since what is outside the nature is contrary to what is according to nature, then if there are generations that are according to nature and some not, and the same for ceasing-to-be, it follows that instances of ceasing-to-be are contrary not to generation but to one another, because one thing cannot be contrary to two. But he solves this by saying that there is nothing to prevent generation from being contrary to generation, and ceasing-to-be to ceasing-to-be. This is true, even if you were to abstract from the contrariety between what is according to nature and what is against nature. For if you take the case of something sweet coming to be and then ceasing to be, and the case of something sad coming to be and ceasing to be, the two cases of coming-to-be would be contrary and the two of ceasing-to-be would be contrary. (When he speaks of the coming to be and the ceasing to be of the “sweet”, he means when “something more noble comes to be from the less noble that has ceased to be, as when fire is generated from air; on the other hand, the coming to be and ceasing to be of the “sad” refers to the less noble coming to be from the ceasing-to-be of the more noble, as when air is generated from fire). Now even though ceasing-to-be is contrary to ceasing-to-be, it does not follow that it is not opposed to coming-to-be, for ceasing-to-be is opposed to coming-to-be when both are taken generically, while ceasing-to-be is opposed to ceasing-to-be in a specific sense. For example, avarice is contrary to liberality in the way that a vice is contrary to a virtue, but it is opposed to prodigality as one species to another. So that what he concludes is this: ceasing-to-be is contrary to ceasing-to-be, not in a generic sense, but one ceasing-to-be is this and another that, i.e., compulsory and beyond nature, or sweet and sad.
lib. 5 l. 10 n. 6 Deinde cum dicit: omnino quidem igitur contrarii etc., ostendit quomodo sit contrarietas in motu et quiete per id quod est extra naturam et secundum naturam. Et dicit quod non solum generatio est contraria generationi et corruptioni per id quod est secundum naturam et extra naturam, sed etiam universaliter motus et quietes sunt hoc modo contrarii. Sicut motus qui est sursum, est contrarius motui qui est deorsum (quia sursum et deorsum sunt contrarietates loci), et uterque istorum motuum est naturalis alicui corporum; ignis enim naturaliter fertur sursum, terra vero deorsum. Et iterum utriusque horum motuum est accipere contrarias differentias has, scilicet quod est secundum naturam et extra naturam. Et hoc est quod dicit, et contrariae ipsorum, scilicet motuum differentiae sunt. Vel potest intelligi quod ipsorum corporum quae moventur, sunt contrariae differentiae motuum, scilicet secundum naturam et extra naturam: motus enim sursum est quidem naturalis igni, sed moveri deorsum est ei extra naturam. Et sic patet quod motus qui est secundum naturam, est contrarius ei qui est extra naturam. Et similiter est de quietibus. Quia quies quae est sursum, est contraria motui qui est de sursum in deorsum. Sed illa quies est terrae innaturalis: sed motus qui est deorsum est ei secundum naturam. Unde patet secundum praemissa, quod quies quae est extra naturam, est contraria motui naturali eiusdem corporis: quia etiam in eodem corpore motus sic contrariantur ad invicem, quod scilicet motus naturalis unius corporis est contrarius motui non naturali eiusdem corporis. Et sic est etiam de quiete: quia alia quietum contrariarum erit secundum naturam, ut sursum igni et deorsum terrae; alia vero extra naturam, ut deorsum igni, sursum terrae.	742. Then at (554 230 b10) he explains contrariety in motion and rest on the basis of their being outside nature and according to nature. And he says that not only coming-to-be is contrary to coming-to-be and to ceasing-to-be from the viewpoint of being outside nature and according to nature, but in general all motions and rests are contrary in this way. For example, an upward motion is contrary to a downward one (because up and down are contrarieties of place) and each of these motions is natural to certain bodies: for fire is naturally carried upward and earth downward. And again in regard to each of these motions, one can take as contrary differences that which is according to nature and that which is outside the nature. And this is what he means when he says that “these contrarieties in motion are differences”, or he might mean that in respect to the very bodies that are moved there are contrary differences in their motions, namely, according to nature and outside their nature. For an upward motion is natural to fire but a downward not. So it is clear that a motion which is according to nature is contrary to one that is outside nature. Likewise for states of rest. For rest which is above is contrary to a downward movement. But rest above is not natural to earth, whereas a downward motion is. According to the foregoing then, it is clear that rest which is outside the nature is contrary to the natural motion of the body involved, for even in the same body, motions ate mutually contrary, in the sense that the natural motion of one body is contrary to an unnatural motion of the same body. The same is true of rest; for some contrary rests will be according to nature, as rest above for fire and rest down for earth; others are outside the nature? as down for fire and up for earth.
lib. 5 l. 10 n. 7 Deinde cum dicit: habet autem dubitationem etc., movet secundam dubitationem: utrum scilicet omnis quietis, quae non semper fuit, sit aliqua generatio, et generatio quietis vocatur stare; ut per stare non intelligamus idem quod quiescere, sed stare sit idem quod pervenire ad quietem; quod forte in Graeco magis proprie sonat. Et videtur determinare in partem negativam per duas rationes. Quarum prima est, quod si omnis quietis quae non semper fuit, est generatio, sequetur quod quietis quae est extra naturam (sicut quando terra quiescit sursum), sit aliqua generatio. Quies autem generari non potest nisi per motum praecedentem: motus autem praecedens quietem innaturalem est violentus. Sic ergo sequitur quod cum terra per violentiam ferebatur sursum, quod tunc stetit, idest quod tunc generabatur eius quies. Sed hoc non potest esse, quia semper quod stat videtur ferri velocius, idest dum generatur quies per motum, semper quanto magis appropinquat ad quietem, tanto est motus velocior. Cum enim res generata sit perfectio generationis; unumquodque autem quanto est propinquius suae perfectioni, tanto est virtuosius et intensius; sequitur quod motus per quem generatur quies, tanto sit velocior, quanto magis appropinquat ad quietem, ut apparet manifeste in motibus naturalibus. Sed in his quae moventur per violentiam, accidit contrarium: quia semper invenitur remissior, quanto magis appropinquat ad quietem. Non ergo quies violenta habet generationem. Et hoc est quod dicit, quod erit aliquid quiescens violente, sed non factum quiescens, idest absque hoc quod sua quies generetur.	743. Then at (555 230 b21) he raises the second question; Has every state of rest that is not eternal a becoming, which becoming is called a coming to a standstill? The answer seems to be “no” for two reasons. First of all, if there is coming-to-be of every state of rest that is not eternal, it will follow that there is coming-to-be for states of rest which are outside nature (as when earth is at rest above). Now rest can be produced only by a previous motion, and the motion preceding an unnatural state of rest is compulsory. Consequently, it follows that when earth is violently projected upwards, it is then that rest comes to be. But this cannot be, because “the velocity of that which comes to a standstill seems always to increase”, i.e., when rest is being generated through motion, it is true that as the state of rest gets closer, the motion gets swifter. For since the perfection of coming-to-be is the thing produced, and since each thing gets stronger and more intense as it gets closer to its perfection, it follows that the motion through which rest is produced is swifter the more it approaches rest, as is abundantly clear in natural motions. But in things that are moved by compulsion the contrary happens: for the motion grows less intense the closer it gets to the state of rest. Consequently, compulsory rest is not generated. This is what he means when he says that some things come to rest by compulsion “without having become so”, i.e., in such a way that their rest is not generated.
lib. 5 l. 10 n. 8 Secundam rationem ponit ibi: amplius videtur ipsum stare etc., quae talis est: quia stare, idest generari quietem, aut omnino est idem cum motu naturali quo aliquid fertur in proprium locum, aut simul cum eo accidit. Et manifestum est quod sunt idem subiecto, sed differunt ratione. Terminus enim motus naturalis est esse in loco naturali: esse autem in loco naturali et quiescere in eo, sunt idem subiecto: unde et motus naturalis et generatio quietis sunt idem subiecto, sed differunt ratione tantum. Manifestum est autem quod quies violenta non generatur per motum naturalem: ergo quies violenta non habet stationem, seu generationem.	744. He gives the second reason at (556 230 b26) and it is this: Coming to a standstill, i.e., the coming-to-be of rest, is either entirely the same as the natural motion by which something is carried to its natural place or it is something that happens to accompany it. Now it is clear that both are the same reality though differing in conception. For the goal of a natural motion is to be in a natural place, but to be in a natural place and to be at rest in it are really the same thing. Consequently, a natural motion and the coming-to-be of rest are the same thing in reality and differ only in conception. However, it is evident that compulsory rest is not brought about by a natural motion. Therefore, coming to a standstill is not present in compulsory states of rest, i.e., such states are not generated.
lib. 5 l. 10 n. 9 Deinde cum dicit: habet autem dubitationem si contraria etc., movet tertiam quaestionem de hoc quod supra dictum est, quod quies quae est in aliquo termino, contrariatur motui quo receditur ab illo termino. Sed hoc videtur esse falsum: quia cum aliquis moveatur ex hoc termino sicut ex loco, aut abiiciatur ille terminus, sicut qualitas vel quantitas, adhuc dum movetur, videtur habere illud quod abiectum est vel derelictum. Non enim subito deserit aliquid totum locum, sed successive; et similiter successive amittit albedinem. Ergo dum movetur, adhuc remanet in termino a quo. Si igitur quies qua aliquid manet in termino a quo, contrariatur motui quo inde recedit, sequitur quod duo contraria sint simul; quod est impossibile.	745. Then at (557 230 b28) he raises a third question about a point mentioned in Lecture 3, that rest in A is contrary to motion from A. Now this seems to be false, because when something is moved from A as from a place, or A is being abandoned, as in the case of a quality or quantity, while it is being moved it still seems to have that which is cast off or left behind. For a thing does not leave its entire place all of a sudden but successively; likewise, it is only gradually that it loses whiteness. Therefore, while it is being moved it still retains something of the starting point. If, therefore, the state of rest whereby something remains in a starting point is contrary to the motion by which departure is made therefrom, it follows that two contraries are together—which is impossible.
lib. 5 l. 10 n. 10 Solvit autem hanc dubitationem cum dicit: aut aliquo modo quiescit et cetera. Et dicit quod illud quod movetur recedendo a termino, quiescit in termino a quo recedit, non simpliciter sed secundum quid, scilicet secundum quod adhuc manet in illo non totaliter, sed partim: quia hoc est universaliter verum, quod semper eius quod movetur, una pars est ibi, scilicet in termino a quo, et alia in termino ad quem. Nec est inconveniens quod unum contrariorum secundum quid permisceatur alteri; sed quanto est magis impermixtum, tanto est magis contrarium. Et ideo motus est magis contrarius motui, cum nunquam ei permisceatur, quam quies, quae quodammodo permiscetur. Et ultimo epilogat quod dictum est de motu et quiete, quomodo in eis sit unitas et contrarietas.	746. So at (558 230 b32) he solves this difficulty. And he says that what is being moved by departing from its starting point is at rest therein not absolutely but in a certain sense only, i.e., in the sense that it is there not in its entirety but partly, because it is universally true that in all cases of motion, part of the mobile is in the terminus a quo and part in the terminus ad quem. Nor is it unacceptable that one contrary be mixed with another in a certain respect; but the less it is mixed, the more perfectly is it contrary. Therefore, a motion is more contrary to another motion (since they are never intermingled) than a rest is, which somehow intermingles. Finally, in summary, he says that we have spoken about motion and rest and how unity and contrariety are found therein.
lib. 5 l. 10 n. 11 Deinde cum dicit: dubitabit autem quis etc., ponit quaedam ad manifestationem praemissorum, quae tamen in exemplaribus Graecis dicuntur non haberi; et Commentator etiam dicit quod in quibusdam exemplaribus Arabicis non habentur: unde magis videntur esse assumpta de dictis Theophrasti vel alicuius alterius expositoris Aristotelis. Tria tamen ponuntur hic ad manifestationem praecedentium. Quorum primum pertinet ad quaestionem quam supra movit de generatione quietis non naturalis. Unde dicit quod dubitabit aliquis de ipso stare, quod est generari quietem: quia si omnes motus qui sunt praeter naturam, habent quietem oppositam, scilicet non naturalem, utrum et illa quies habeat stare, idest generari? Quia si dicatur quod non sit aliqua statio quietis violentae, sequetur inconveniens. Manifestum est enim quod id quod per violentiam movetur, quandoque manebit, idest quiescet, et hoc per violentiam. Quare sequetur quod aliquid erit quiescens non semper, sine hoc quod fiat quiescens: quod videtur impossibile. Sed palam est quod erit quandoque quies violenta. Sicut enim movetur aliquid praeter naturam, ita et quiescit aliquid praeter naturam. Est autem hic attendendum, quod hoc quod hic dicitur, videtur esse contrarium ei quod supra dictum est. Unde Averroes dicit quod dubitatio superius mota, hic solvitur. Sed melius est ut dicatur quod id quod supra positum est, est magis verum: licet et quod hic dicitur quodammodo sit verum. Quies enim violenta non habet generationem proprie, sicut procedentem ab aliqua causa per se factiva quietis, sicut quies naturalis generatur: sed habet generationem per accidens, per defectum virtutis factivae: quia quando cessat violentia moventis vel impeditur, tunc fit quies violenta. Et propter hoc motus violentus in fine remittitur; naturalis autem in fine intenditur. Sciendum tamen est quod alia littera invenitur in hoc loco, quam oportet ad aliam intentionem referre. Dicit enim sic: quod quaeret aliquis utrum motui extra naturam contrarietur aliqua quies non secundum naturam. Non quod quies quae est contra naturam, opponatur motui qui est contra naturam proprie, ut supra Aristoteles docuit: sed hic dicitur large et improprie, secundum communem oppositionem quietis ad motum. Et dicit quod irrationabile videtur, si non inveniatur quaedam quies non naturalis. Manifestum est enim quod violentia moventis remanebit, idest cessabit quandoque: et nisi quies aliqua fiat consequenter, motus non perveniet ad statum. Unde manifestum est quod motibus violentis opponitur quies violenta: quia quod extra naturam movetur, habet etiam extra naturam quiescere.	747. Then at (559 231 a5) he states some things that will clarify the foregoing. (These passages are said not to be found in the Greek MSS. and, according to the Commentator, not even in the Arabic MSS.; consequently, these statements seem to have been lifted from the sayings of Theophrastus or some other expositor of Aristotle). Three things are here posited in an attempt to clarify the foregoing. The first pertains to the question previously raised about the generation of unnatural rest. And he says that someone may wonder about “Coming to a standstill”, i.e., about the coming-to-be of rest, for if all motions that are outside nature have an opposing state of rest, i.e., an unnatural one, does that state of rest come to be? If it is held that there is no “coming to a standstill” in cases of compulsory rest, something unacceptable follows. For it is clear that a thing in compulsory motion will sometimes remain, i.e., come to rest, by compulsion. Consequently, it will follow that something will be at rest not eternally without having come to rest—which seems impossible. But it is plain that sometimes there is compulsory rest. For just as things are moved outside their nature, so also they rest outside their nature. Rut it should be observed that what is said here appears contrary to what was said above (at 743). Hence Averroes says that a solution is now being given to a question previously raised. However, it is better to say that the previous doctrine contains more truth, although what is being said here is somehow true also. For compulsory rest is not, strictly speaking, generated in the sense that it proceeds from a cause that is essentially productive of rest, as happens when natural rests are generated. But compulsory rest is generated per accidens through lack of a productive force, because when the compulsion of the mover either ceases or meets an obstacle, the state of compulsory rest comes to be. This is why compulsory motions peter out at the end, whereas natural ones become more intense. It should be noted also that there is found another text for this place, to which we should give our attention. For it reads., Someone may ask whether to a motion outside nature there is any contrary rest not according to nature? This does not inquire whether, properly speaking, a state of rest that is contrary to nature is opposed to a motion that is contrary to nature, as Aristotle taught above; rather, here one is now speaking in wide and loose terms in the sense of the general opposition between rest and motion. And he says that it seems unreasonable not to find unnatural states of rest. For it is clear that the violence of the mover will cease at some time and unless rest eventuates, the motion will not come to a standstill. Hence it is clear that. to compulsory motions are opposed compulsory states of rest, because to what is moved outside its nature there belongs to rest outside its nature.
lib. 5 l. 10 n. 12 Deinde cum dicit: quoniam autem est quibusdam etc., ponit secundum, ad explanationem eius quod dictum est de contrarietate motus naturalis et violenti. Et dicit quod, cum in quibusdam sit motus secundum naturam et praeter naturam, sicut ignis, qui movetur sursum secundum naturam et deorsum praeter naturam: quaeritur utrum motui naturali ignis sursum, sit contrarius motus violentus ignis deorsum, vel motus terrae, quae naturaliter movetur deorsum. Et solvit quod ambo ei contrariantur, sed non eodem modo: sed motus terrae deorsum contrariatur motui ignis sursum, sicut naturalis naturali; motus autem ignis deorsum contrariatur motui ignis sursum, sicut violentus naturali. Et eadem ratio est de contrarietate quietum.	748. Then at (560 231 a9) he mentions a second fact to explain his doctrine on the contrariety of natural and compulsory motion. And he says that since certain things are subject to motions that are according to nature and outside their nature, as fire is moved upward according to nature and downward outside its nature, the question arises whether the natural upward motion of fire has for its contrary the compulsory downward motion of fire or the natural downward motion of earth. He answers that both are contrary to the natural upward motion of fire but not in the same way. For the downward motion of earth is contrary to the upward motion of fire as something natural contrary to something natural, whereas a downward motion of fire is contrary to the upward motion of fire as something natural contrary to something compulsory. The same is true for the contrariety of states of rest.
lib. 5 l. 10 n. 13 Deinde cum dicit: forte autem quieti etc., ponit tertium, ad manifestandum id quod dictum est de contrarietate quietis ad motum. Et dicit quod forte quieti motus aliquatenus opponitur, et non simpliciter. Cum enim aliquis movetur ex hoc in quo quieverat, et abiiciat illud, videtur adhuc habere illud quod abiicitur. Unde si quies quae est hic, sit contraria motui qui est hinc in contrarium, sequitur quod simul sint contraria. Sed adhuc aliquatenus quiescit dum manet in termino a quo; et universaliter eius quod movetur, aliquid est in termino a quo, et aliquid in termino ad quem: unde quies minus opponitur motui quam motus contrarius, sicut supra expositum est. Et ultimo recapitulat, ut per se manifestum est. Ex hoc autem ipso quod eadem verba repetuntur, quae supra dicta sunt, manifestum esse potest, quod non sunt verba Aristotelis, sed alicuius expositoris.	749. Then at (561 231 a17) he mentions a third point to explain what he previously said about contrariety of rest to motion. And he says that perhaps motion is not strictly opposed to rest, but only in some sense. For when someone is being moved from A, in which he was at rest, and is doffing it, it seems to retain something of A. Hence if rest in this place is contrary to a motion from this place to a contrary place, it follows that contraries are together. But yet a thing is somehow still at rest while it perseveres in A; indeed, speaking generally of a thing in motion, part of it is in the terminus a quo and part in the terminus ad quem. Consequently, rest is less contrary to motion than a contrary motion is, as was explained above. Finally, he sums up, as is clear of itself. Now the fact that the same words that appeared in an earlier passage (see end of 246 above) are repeated, lends support to the possibility that they are not the words of Aristotle, but of some expositor.