Authors/Thomas Aquinas/physics/L4/lect23

Lecture 23 The Problems are Solved as to the Existence and Unity of Time

Latin	English
	Lecture 23 The Problems are Solved as to the Existence and Unity of Time.
lib. 4 l. 23 n. 1 Postquam philosophus determinavit de tempore, hic removet quasdam dubitationes circa tempus. Et primo circa existentiam temporis; secundo circa temporis unitatem, ibi: dubitabit autem aliquis et cetera. Circa primum duo facit: primo movet duas dubitationes; secundo solvit eas, ibi: aut quia motus et cetera. Dicit ergo primo quod hae dubitationes indigent diligenti consideratione: scilicet quomodo tempus se habeat ad animam; et iterum quare tempus videatur esse ubique, scilicet in terra, in mari et in caelo.	625. After determining the truth about time, the Philosopher now settles certain doubts about time: First in regard to the existence of time; Secondly, in regard to the unity of time, at no. 630. As to the first he does two things: First he raises the doubts; Secondly, he solves them, at no. 626. He says therefore first [451 223 a16] that certain problems require diligent consideration: namely, that of how time is related to the soul; and that of how time seems to be everywhere, i.e., an earth, on the sea, and in the air.
lib. 4 l. 23 n. 2 Deinde cum dicit: aut quia motus etc., solvit praemissas quaestiones. Et primo secundam, quae facilior est; secundo primam, ibi: utrum autem cum non sit et cetera. Dicit ergo quod tempus est quoddam accidens motus, quia est numerus eius (accidens autem consuevit nomine habitus et passionis nominari): unde ubicumque est motus oportet quod sit tempus. Omnia autem corpora sunt mobilia, etsi non aliis motibus, saltem motu locali; quia omnia sunt in loco. Et quia posset aliquis dicere quod licet sint mobilia, non tamen omnia moventur, sed quaedam quiescunt, et sic tempus non videtur in omnibus esse: ad hoc excludendum subiungit quod tempus est simul cum motu, sive motus accipiatur secundum actum sive secundum potentiam. Quaecumque enim sunt possibilia moveri et non moventur actu, quiescunt. Tempus autem non solum mensurat motum, sed etiam quietem, ut supra dictum est. Unde relinquitur quod ubicumque est motus, vel actu vel potentia, quod ibi sit tempus.	626. Then [452 223 a18] he answers these questions: First he answers the second question, because it is easier; Secondly, he answers the first one, at no. 627. He says therefore [452 223 a18] that time is a certain accident of motion, because it is its number (an accident is wont to be called a “possession” [habitus] and “property” [passio]: hence, wherever there is motion, time must be. Now all bodies are mobile, if not with other motions, at least with respect to local motion, because all things are in place. And because someone could say that although they are mobile, they are not all being moved, but some are at rest, and thus time does not seem to be in all, to counter this he adds that time accompanies motion, whether motion be actual or potential. For things that are capable of motion, and are not actually being moved, are at rest. But time measures not only motion but rest as well, as was said above. Hence, wherever there is motion either actually or potentially, there time is.
lib. 4 l. 23 n. 3 Deinde cum dicit: utrum autem cum non sit anima etc., solvit primam quaestionem. Et circa hoc tria facit: primo movet dubitationem; secundo obiicit ad quaestionem, ibi: impossibile enim etc.; tertio solvit, ibi: sed aut hoc et cetera. Est ergo dubitatio, utrum non existente anima esset tempus, aut non.	627. Then [453 223 a21] he answers the first question, and as to this he does three things: First he raises the question; Secondly, he gives an objection to the question, at no. 628; Thirdly, he resolves the question, at no. 629. The question, therefore, is this: Would time exist if no mind existed?
lib. 4 l. 23 n. 4 Secundo ibi: impossibile enim cum sit etc., obiicit ad ostendendum quod non. Quia si impossibile esset esse aliquod potens numerare, impossibile esset esse aliquod numerabile, potens scilicet numerari. Sed si non est numerabile, non est numerus; quia numerus non est nisi in eo quod numeratur actu, vel quod est numerabile in potentia. Relinquitur ergo quod si non est aliquod potens numerare, quod non sit numerus. Sed nihil aliud natum est numerare quam anima, et inter partes animae non alia quam intellectus; quia numeratio fit per collationem numeratorum ad unam primam mensuram, conferre autem rationis est. Si igitur non est anima intellectiva, non est numerus. Tempus autem est numerus, ut dictum est. Si ergo non est anima intellectiva, non est tempus.	628. Secondly, [454 223 a22] he objects, to say it would not. For if it were impossible for something able to count to exist, it would be impossible for some thing countable to exist, i.e., able to be counted. But if there is nothing countable, then there is no number, because number does not exist except in that which is being actually counted or which is potentially countable. Consequently, if there is no one able to count, there is no number. But only the soul is disposed by nature for counting, and among the parts of the soul only the intellect; for counting consists in comparing the things counted with one primary measure, and comparing is a function of reason. Consequently, if there is no intellective soul, there is no number. But time is a number, an was said. If therefore, there is no intellective soul, there is no time.
lib. 4 l. 23 n. 5 Deinde cum dicit: sed aut hoc etc., solvit dubitationem. Et dicit quod aut oportet dicere quod tempus non sit, si non est anima; aut oportet hoc dicere verius, quod tempus est utcumque ens sine anima, ut puta si contingit motum esse sine anima. Sicut enim ponitur motus, ita necesse est poni tempus: quia prius et posterius in motu sunt; et haec, scilicet prius et posterius motus, inquantum sunt numerabilia, sunt ipsum tempus. Ad evidentiam autem huius solutionis considerandum est, quod positis rebus numeratis, necesse est poni numerum. Unde sicut res numeratae dependent a numerante, ita et numerus earum. Esse autem rerum numeratarum non dependet ab intellectu, nisi sit aliquis intellectus qui sit causa rerum, sicut est intellectus divinus: non autem dependet ab intellectu animae. Unde nec numerus rerum ab intellectu animae dependet: sed solum ipsa numeratio, quae est actus animae, ab intellectu animae dependet. Sicuti ergo possunt esse sensibilia sensu non existente, et intelligibilia intellectu non existente, ita possunt esse numerabilia et numerus, non existente numerante. Sed forte conditionalis quam primo posuit, est vera, scilicet quod si est impossibile esse aliquem numerantem, impossibile est esse aliquod numerabile: sicut haec est vera, si impossibile est esse aliquem sentientem, impossibile est esse aliquid sensibile. Si enim est sensibile, potest sentiri, et si potest sentiri, potest esse aliquod sentiens; licet non sequatur quod si est sensibile, quod sit sentiens. Et similiter sequitur quod si est aliquid numerabile, quod possit esse aliquid numerans. Unde si impossibile est esse aliquod numerans, impossibile est esse aliquid numerabile: non tamen sequitur quod si non est numerans, quod non sit numerabile, ut obiectio philosophi procedebat. Si ergo motus haberet esse fixum in rebus, sicut lapis vel equus, posset absolute dici quod sicut etiam anima non existente est numerus lapidum, ita etiam anima non existente esset numerus motus, qui est tempus. Sed motus non habet esse fixum in rebus, nec aliquid actu invenitur in rebus de motu, nisi quoddam indivisibile motus, quod est motus divisio: sed totalitas motus accipitur per considerationem animae, comparantis priorem dispositionem mobilis ad posteriorem. Sic igitur et tempus non habet esse extra animam, nisi secundum suum indivisibile: ipsa autem totalitas temporis accipitur per ordinationem animae numerantis prius et posterius in motu, ut supra dictum est. Et ideo signanter dicit philosophus quod tempus, non existente anima, est utcumque ens, idest imperfecte; sicut et si dicatur quod motum contingit esse sine anima imperfecte. Et per hoc solvuntur rationes supra positae ad ostendendum quod tempus non sit, quia componitur ex partibus non existentibus. Patet enim ex praedictis, quod non habet esse perfectum extra animam, sicut nec motus.	629. Then [455 223 a25] he answers the question. And he says that it is necessary to say either that time is not, if the soul is not; or to say what is truer, that time is still some sort of being even without the soul’s existing, similar to motion’s existing without the soul’s existing. For as motion is posited, so is it also necessary to posit time, because “before” and “after” exist in motion, and it is these things, namely, the “before” and “after” in motion, insofar as they are numberable, that are time. To make this solution more evident it must be considered that once a series of numbered things is posited, it is necessary to posit number. Hence just as counted things depend on someone’s counting, so also their count [or number]. However, the existence of counted things does not depend on an intellect, unless it be an intellect which is the cause of things, as is the divine intellect, It does not depend on the intellect of the same. Hence neither does the number of things depend on the intellect in the human soul; only the counting of them, which counting is an act of the soul, depends on the intellect in the soul. Consequently, just as there can be things perceptible to sense even though no sense exists, and intelligible even though no intelligence exists, so there can exist both numberable [countable] things, and number even though no counter exist. But perhaps the conditional he first mentioned is true, namely, that if no counter could exist, nothing countable could exist, just as the proposition is true that if there could be no one to sense, there could be nothing sensible. For if there is something sensible, it can be sensed, and if it can be sensed, there can be something to sense it—although it does not follow that if there is something sensible, there is something sensing. In like manner, it follows that if there is something countable, there can be someone to count. Consequently, if no one to count could exist, nothing countable could exist. However, it does not follow that if there is no one counting, there is nothing countable, which is the objection raised by the Philosopher. Therefore, if motion had a fixed existence in reality, as a stone or a horse has, one could say unqualifiedly that, just as with no soul existing there exists a number of stones, so also with no soul existing, there would exist a number of motion, which is time. However, motion does not have a fixed existence in reality, nor is anything actual of motion found in things but a certain indivisible of motion which divides motion; indeed, the totality of motion comes to be on account of the mind considering and comparing a previous state of the mobile to a subsequent state. According to this, then, time also has no existence outside the soul except according to its indivisible; while the totality of time is had by an ordering process of the mind enumerating the prior and subsequent in motion [i.e., “before” and “after”], as was said above. And therefore the Philosopher said significantly that with no soul existing time is a being “of a sort,” i.e., imperfectly; this is similar to the statement that motion exists imperfectly without a soul existing. So this answers the arguments mentioned earlier, to show that time does not exist on the ground that it is composed of parts that do not exist. For it is clear from the foregoing that like motion it does not have perfect existence outside the soul.
lib. 4 l. 23 n. 6 Deinde cum dicit: dubitabit autem aliquis etc., movet quaestionem de unitate temporis, sive de comparatione temporis ad motum. Et circa hoc tria facit: primo movet dubitationem; secundo solvit, ibi: aut cuiuslibet etc., tertio manifestat quoddam quod supposuerat, ibi: dicitur autem recte et cetera. Dicit ergo primo quod dubitatio est, cum tempus sit numerus motus, cuius vel qualis motus sit numerus. Deinde cum dicit: aut cuiuslibet etc., solvit dubitationem. Et primo excludit falsam solutionem; secundo ponit veram, ibi: quoniam autem est loci mutatio et cetera. Circa primum tria facit: primo ponit solutionem falsam; secundo improbat eam ducendo ad inconveniens, ibi: sed est nunc moveri etc.; tertio ostendit illud inconveniens esse impossibile, ibi: aut non: omne namque et cetera.	630. Then [456 223 a29] he raises a question about the oneness of time, or about the relation of time to motion. As to this he does three things: First he raises the question; Secondly, he answers it, at no. 631; Thirdly, he explains something he took as a presupposition, at no. 637. So he says first [456 223 a29] that there is question, since time is the number of motion, of whose, or of what sort of, motion it is the number. Then [457 223 a30] he answers the question. First he rejects a false solution; Secondly, he gives the true one, at no. 634; In regard to the first he does three things: First he gives the false answer; Secondly he disproves it by leading to a discrepancy, at no. 632; Thirdly, he shows that this discrepancy is really an Impossibility, at no. 633.
lib. 4 l. 23 n. 7 Est ergo prima solutio, quod tempus sit numerus cuiuslibet motus. Et ad hoc probandum inducit quod omnis motus est in tempore; scilicet et generatio et augmentum et alteratio et loci mutatio. Quod autem convenit omni motui, convenit motui secundum quod ipsum: esse autem in tempore est numerari tempore. Sic igitur videtur quod quilibet motus, inquantum huiusmodi, habet numerum: unde cum tempus sit numerus motus, videtur sequi quod tempus sit numerus motus continui universaliter, et non alicuius determinati motus.	631. The first solution, therefore, is that time is the number of any motion whatsoever. To prove this he brings up that every motion exists in time; namely, generation, and increase, and alteration, and local motion. Now what is found in every motion belongs to motion as such. But to exist in time is to be numbered by time. Consequently, it seems that every motion as such has a number; hence, since time is the number of motion, it seems to follow that time is the number of each and every continuous motion and not of some definite motion.
lib. 4 l. 23 n. 8 Deinde cum dicit: sed est nunc moveri etc., improbat praedictam solutionem. Contingit enim aliqua duo simul moveri: si ergo cuiuslibet motus tempus sit numerus, sequetur quod duorum motuum simul existentium sit alterum et alterum tempus: et sic ulterius sequetur quod duo tempora aequalia sint simul, utpote duo dies vel duae horae. Duo autem tempora inaequalia simul esse, non est admirabile, ut diem et horam.	632. Then [458 223 b1] he disproves this solution. For let us assume two things that are moving together: if, therefore, time to the number of any motion at all, it will follow that of two simultaneous motions each will have its own time, and so it will further follow that two equal times exist at once—e.g., two days or two hours. Now it is not strange for two unequal times to exist at once, e.g., a day and an hour.
lib. 4 l. 23 n. 9 Deinde cum dicit: aut non: omne namque tempus etc., ostendit hoc esse impossibile, scilicet duo tempora aequalia simul esse: quia omne tempus quod est simul et similiter, idest aequaliter, est unum tantum: sed tempus quod non est simul, non est unum numero; sed species eius est una, sicut dies cum die, et annus cum anno. Et hoc manifestat per simile in aliis numeratis. Si enim sunt septem equi et septem canes, non differunt secundum numerum, sed differunt secundum speciem rerum numeratarum. Et similiter omnium motuum qui simul terminantur et secundum principium et secundum finem, est idem tempus: sed motus differunt secundum proprias rationes, inquantum forte unus est velox et alius tardus, et unus est loci mutatio et alius alteratio. Sed tempus est idem, si alterationis et loci mutationis sit aequalis numerus, supposito quod sint simul. Et propter hoc oportet quod motus sint alteri et divisi ab invicem, sed tempus in omnibus est idem: quia unus et idem numerus est eorum quae sunt aequalia et simul, ubicumque sint.	633. Then [459 223 b3] he shows that it is impossible for two equal times to exist at once. For every time that is simultaneous and similar , i.e., equal, is one; but time that is not simultaneous is not numerically one, although it is one in species, as day with day and year with year. And he explains this by a similarity in other things that are numbered. For if there are seven horses and seven dogs, there is no difference so far as the number is concerned, but the difference is due to the species of the things counted. In like manner, for all motions which have simultaneous terms both as to their beginning and as to their end, there is the same time; yet the motions differ according to their proper notions, in that, perchance, one is fast and the other slow, one is local motion and the other alteration. But the time is the same if the number of the alteration and of the local motion is the same, supposing, of course, that they are simultaneous. Consequently, motions must be distinct from one another, but the time in all of them is the same— because there is one and the same number for all those that are equal and simultaneous, no matter where they occur.
lib. 4 l. 23 n. 10 Deinde cum dicit: quoniam autem est loci mutatio etc., ponit veram solutionem. Et circa hoc tria facit: primo praemittit, quaedam quae sunt necessaria ad solutionem; secundo ex praemissis solutionem concludit, ibi: si igitur quod primum etc.; tertio manifestat solutionem per dicta aliorum, ibi: unde et videtur et cetera. Circa primum praemittit tria. Quorum primum est, quod inter alios motus, primus et magis simplex et regularis est motus localis; et inter alios motus locales, motus circularis, ut in octavo probabitur. Secundum est quod unumquodque numeratur uno quodam proximo, idest sui generis, sicut unitates unitate, et equi equo, ut patet in X Metaphys.: unde oportet quod tempus quodam determinato tempore mensuretur, sicut videmus quod omnia tempora mensurantur per diem. Tertium quod praemittit est, quod tempus mensuratur motu et motus tempore, ut supra dictum est: et hoc ideo est, quia aliquo determinato motu, et aliquo determinato tempore, mensuratur quantitas cuiuslibet motus et temporis.	634. Then [460 223 b12] he gives the true solution. Concerning this he does three things: First he prefaces certain facts required for the solution; Secondly, from these he arrives at the solution, at no. 635; Thirdly, he makes the solution clear by appealing to the statements of others, at no. 636. In regard to the first he mentions three preliminary facts. The first of these is that among motions, the first and more simple and regular is local motion, and among these, circular motion, as will be proved in Book VIII. The second is that each thing is numbered by something near it, i.e., by something homogeneous with it, as units by a unit and horses by a horse, as is clear in Metaphysics X; hence time must be measured by some definite time, as we see that all times are measured by the day. The third presupposition is that time is measured by motion, and motion by time, as was said above. This is so because it is in terms of some definite motion and some definite time that the quantity of any motion and time is measured.
lib. 4 l. 23 n. 11 Deinde cum dicit: si igitur quod primum mensura est etc., concludit ex praemissis, quod si aliquid quod est primum, est mensura omnium proximorum, idest omnium quae sunt sui generis, necesse est quod circulatio, quae est maxime regularis, sit mensura omnium motuum. Dicitur autem motus regularis, qui est unus et uniformis. Haec autem regularitas non potest inveniri in alteratione et augmento, quia non sunt usquequaque continui nec aequalis velocitatis. Sed in loci mutatione inveniri potest regularitas, quia potest esse aliquis motus localis continuus et uniformis; et talis est solus motus circularis, ut in octavo probabitur. Et inter alios motus circulares, maxime uniformis et regularis est primus motus, qui revolvit totum firmamentum motu diurno: unde illa circulatio, tanquam prima et simplicior et regularior, est mensura omnium motuum. Oportet autem motum regularem esse mensuram seu numerum aliorum, quia omnis mensura debet esse certissima; et talia sunt quae uniformiter se habent. Ex hoc igitur colligere possumus, quod si prima circulatio mensurat omnem motum, et motus mensurantur a tempore, inquantum mensurantur quodam motu; necesse est dicere quod tempus sit numerus primae circulationis, secundum quam mensuratur tempus, et ad quem mensurantur omnes alii motus temporis mensuratione.	635. Then [461 223 b18] he concludes from the foregoing that if something that is first is the measure of all things that are near it, i.e., of all the things in its genus, it is necessary that circular motion, which is regular above all, be the measure of all motions. Now a motion is called “regular,” if it is one and uniform. But such regularity cannot be found in alteration and growth, because they are not incessantly continuous or of equal [constant] speed. But regularity can be found in change of place, because there can be a local motion that is continuous and uniform, and the only such motion is circular motion, as will be proved in Book VIII. Now among circular motions the most uniform and regular is the first motion which turns the whole firmament in a daily cycle; hence that revolution, as being the first and simplest and most regular, is the measure of all motions. But a regular motion must be the measure and number of the others, because every measure ought to be most certain—and those that are uniform are such. Consequently, from this we can gather that if the first circular motion measures every motion, and motions are measured by time insofar as they are measured by some motion, it has to be said that time is the number of the first circular motion, according to which time is measured, and in relation to which are measured all other motions that are timed.
lib. 4 l. 23 n. 12 Deinde cum dicit: unde et videtur tempus etc., approbat praedictam solutionem per opiniones aliorum. Et primo per opinionem errantium, qui moti fuerunt ad dicendum quod motus sphaerae caelestis sit tempus, propter hoc quod hoc motu mensurantur omnes alii motus, et tempus mensuratur hoc motu: manifestum est enim quod dicimus diem vel annum completum, attendentes ad motum caeli. Secundo ex usu communiter loquentium, ibi: propter hoc autem et cetera. Et dicit quod propter hoc, scilicet quod tempus est numerus circulationis primae, accidit quod consuevit dici, scilicet quod quidam circulus sit in rebus humanis, et in aliis quae moventur naturaliter et generantur et corrumpuntur. Quod ideo est, quia omnia huiusmodi mensurantur tempore, et accipiunt principium et finem in tempore, ac si tempus secundum quandam circulationem sit: quia et ipsum tempus videtur esse quidam circulus. Et hoc iterum videtur propter hoc, quod est mensura circulationis, et etiam a tali circulatione mensuratur. Et ideo dicere quod eorum quae fiunt in tempore, est quidam circulus, nihil est aliud quam dicere temporis esse quendam circulum; quod accidit propter hoc quod tempus mensuratur circulatione. Illud enim quod mensuratur, non videtur esse aliud quam mensura: sed multae mensurae videntur facere unum totum, sicut multae unitates unum numerum, et multae mensurae panni unam quantitatem panni. Et hoc verum est, quando accipitur mensura unius generis. Sic igitur patet quod tempus primo mensurat et numerat primum motum circularem, et per eum mensurat omnes alios motus. Unde est unum tempus tantum propter unitatem primi motus; et tamen quicumque sentit quemcumque motum, sentit tempus, eo quod ex primo motu causatur mutabilitas in omnibus mobilibus, ut supra dictum est.	636. Then [462 223 b21] he corroborates his solution by appealing to the opinions of others, and first of all by the opinion of those who were led to assert that the movement of the heavenly sphere is time, on the ground that all other motions, and time itself, are measured by that movement; for it is evident that we speak of a complete day or year by reckoning from the motion of the heavens. Secondly [463 223 b23] from a common saying. And he says that because of this, namely, that time is the number of the first circular movement, it comes about that people are want to say that there is a cycle in human affairs, and in other things that move naturally and come into being and pass away. This is so because all such things are measured by time, and have a beginning and an end in time, as if time moved in a circle, because time itself seems to be a certain circle. And this again seems to be so because time is a measure of circular movement and is also measured by such a circular movement. And therefore, to say that of things which take place in time there is a certain circle, is nothing other than to say that time is a certain circle—which occurs because time is measured by a circular movement. For that which is measured is not seen to be different from its measure: but rather many measures are seen to make one whole, as many units make one number, and many measures of cloth one quantity of cloth. And this is true when a homogeneous measure is taken. From all this it is clear that time first measures and numbers the first circular motion and through it measures all other motions. Consequently, there is but one time, due to the oneness of the first motion; and yet whoever perceives any motion whatever, perceives time, because from the first motion there is caused, mutability in all mobile- things, as was said above.
lib. 4 l. 23 n. 13 Deinde cum dicit: dicitur autem recte etc., manifestat quoddam, quod supra dixerat, qualiter sit intelligendum. Dixerat enim quod idem est numerus septem canum et septem equorum. Quomodo ergo hoc sit verum ostendit: et dicit quod recte potest dici, si aequalis est numerus aliquarum rerum diversarum, puta ovium et canum, quod idem sit numerus utrorumque, ut puta si tam oves quam canes sint decem. Sed non potest dici quod hoc ipsum quod est esse decem, sit idem canum et ovium: non enim eadem decem sunt decem canes et decem oves. Et hoc ideo, quia genus potest cum additione unitatis vel identitatis praedicari de pluribus individuis existentibus in una specie, et similiter genus remotum de pluribus speciebus existentibus sub uno genere propinquo; neque tamen species de individuis, neque genus propinquum de speciebus diversis potest praedicari cum additione unitatis vel identitatis. Et huius consequenter ponit exemplum. Sunt enim duae species trianguli, scilicet aequilaterus, idest habens tria latera aequalia, et gradatus, idest habens tria latera inaequalia; figura autem est genus trianguli. Non ergo possumus dicere quod aequilaterus et gradatus sit idem triangulus; sed possumus dicere quod sunt eadem figura, quia utrumque continetur sub triangulo, qui est una species figurae. Et huius assignat rationem: quia cum idem et diversum seu differens opponantur, ibi possumus identitatem dicere, ubi differentia non invenitur; sed non possumus dicere identitatem, ubi invenitur differentia. Manifestum est autem quod aequilaterus et gradatus differunt ad invicem differentia trianguli, idest quae est proprie trianguli divisiva; et hoc ideo quia sunt diversae species trianguli. Sed aequilaterus et gradatus non differunt secundum differentiam figurae, sed sub una et eadem differentia divisiva figurae continentur. Et hoc sic patet. Si enim dividamus figuram in suas species, quae per differentias constituuntur, invenietur quod alia erit circulus, et alia triangulus, et sic de aliis speciebus figurae; sed si dividamus triangulum, inveniemus quod alia species eius est aequilaterus, et alia gradatus. Manifestum est igitur quod aequilaterus et gradatus sunt una figura, quia continentur sub una specie figurae, quae est triangulus: sed non sunt unus triangulus, quia sunt diversae trianguli species. Et similiter est in proposito. Numerus enim dividitur in diversas species, quarum una est decem. Omnia ergo quae sunt decem, dicuntur habere unum numerum; quia non differunt ad invicem secundum speciem numeri, cum contineantur sub una numeri specie. Sed non potest dici quod sint eadem decem; quia ea quibus applicatur numerus denarius, differunt, cum quaedam horum sint canes et quaedam equi. Videtur autem hoc introduxisse Aristoteles, ne aliquis ad sustinendam unitatem temporis sit contentus eo quod dicitur unum numerum esse aequalium numero, licet diversorum: quia licet sit idem denarius vel ternarius propter unitatem speciei, non tamen est idem denarius vel ternarius propter diversitatem quae est secundum numerum ex parte materiae. Unde secundum istam rationem sequeretur quod tempus esset unum specie, sed non numero. Et ideo ad accipiendam veram temporis unitatem, oportet recurrere ad unitatem primi motus, qui primo mensuratur tempore, et quo etiam mensuratur tempus. Ultimo autem epilogando concludit, dictum esse de tempore, et de iis quae sunt propria ad considerationem temporis.	637. Then [464 224 a2] he explains how something he mentioned above is to be understood. For he said that the number of seven dogs and seven horses is the same number. How this is true he now explains. And he says that it is correct to say, if the number of certain different things is equal, for example, of sheep and dogs, that the number is the same—for example, if the sheep and the dogs are both 10. But it cannot be said that to be 10 is the same for the dogs and sheep, for 10 dogs are not the same 10 as 10 sheep. The reason for this is that a genus can be predicated, with the addition of unity or identity [i.e., as “one genus” or “the same genus”], of several individuals of the same species; and in like manner, the remote genus can be predicated of several species existing under one proximate genus; but neither can the species be predicated of individuals, nor the proximate genus of diverse species, with the addition of unity or identity. And he then gives an example of what he means. For there are two species of triangle, equilateral, i.e., having three equal sides, and scalene, i.e., having three unequal sides. Now “figure” is the genus for “triangle.” We therefore can not say that equilateral and scalene are the same “triangle,” but we can say that they are the same “figure,” because both are contained under “triangle” which is one species of “figure.” He gives the reason for this, which is that since “identical,” and “diverse” or “different,” are opposed, we can speak of identity whenever no difference is found, but we cannot speak of identity where there is a difference. But it is clear that equilateral and scalene differ mutually by reason of a difference that divides “triangle,” because they are diverse species of triangle. But “equilateral” and “scalene” do not differ in respect of the difference “figure”; rather, they are contained under one and the same difference that divides “figure.” And this is clear thus. If we divide “figure” into its species which are brought about by differences, it will be found that one species is a circle, another a triangle, and so on for the other species of figure. But if we divide “triangle,” we will find that one species is “equilateral,” another “scalene.” It is clear, therefore, that equilateral and scalene are one “figure,” because they are contained under the one species of “figure,” the species “triangle,” but they are not one “triangle,” because they are diverse species of “triangle.” The same thing applies to our proposition. For number is divided into diverse species, one of which is 10. Therefore all things that are 10 are said to have one number, because they do not differ from the other in regard to the species of their number, since they are contained under one and the same species of number. But we cannot say that they are the same 10, because the things being called “10” are different, since some are dogs and some horses. Aristotle seems to have brought up this point so that no one, in trying to uphold the unity of time, would be content with saying that there is one number for things that are equal in number, even though the things be diverse; for although one might have a same 10 or 3 on account of a unity of species, yet it is not the same 10 or 3 on account of the diversity in number as based on matter. Hence, according to this reasoning, it would follow that time would be specifically, but not numerically, one. Therefore to get at the true unity of time, we must have recourse to the unity of the first motion, which is the first thing measured by time, and by which time itself is measured. Finally, in summary, he concludes that we have finished with our consideration of time, and of the things that are proper to a consideration of time.