Volume 1 · pp. 200–201
End of Chapter III and Chapter IV. How time is continuous quantity
per nomen quod est notio prædicabilis: et ideo dicit Aristoteles sic, Abstrahentium non est mendacium 1. Quinimo est certissime verum, quamvis secundum esse ista non inveniantur distincta in natura: insunt enim hoc modo quo determinata sunt in ipsa substantia quantorum.
Attendendum etiam quod non potest esse quarta species quantitatis continuæ habentis in partibus positionem et ex seipsa continuitatem et substantiam circa quam ponit formam communitatis et continuitatis: quia non est motum intelligere alicujus aliquo modo indivisibilis, nisi vel in longum, vel in latum, vel in profundum: altum enim est a profundo terminis tantum differens: et ideo non sunt nisi tres species hujus quantitatis, a quibus prædicabilia sumi possint.
Sciendum est etiam, quod linea est quantitas unius divisibilitatis, superficies autem est quantitas duarum divisionum, et corpus quantitas est trium divisionum propter causas quæ in ante habitis sunt determinatæ.
CAPUT IV.
Qualiter tempus est quantitas continua.
Est autem de numero talium quantitatum continuarum et tempus et locus: præsens enim tempus copulatur et ad præteritum et ad futurum per instans medium quod est terminus talis copulationis. Accipimus autem hic præsens, tempus divisibile quod adjacet motui et actioni præsenti. Præteritum autem dicimus, quod terminatur ad præsens per instans quod est præteriti finis et principium præsentis: et præsens etiam copulatur ad futurum per instans quod est finis præsentis et principium futuri: et sic totum tempus continuum est. Sicut enim in aliis continuis fluxus continui est ab uno aliquo secundum aliquem modum indivisibili, ita est etiam in tempore.
Intelligendum igitur est, quod si non esset motus, non esset tempus, et motus extensio est causa extensionis temporis, sicut motus etiam est causa temporis. Motus autem est in eo quod movetur sicut in subjecto. Est autem id quod fertur sive movetur, idem secundum substantiam in toto motu: secundum esse autem ipsius secundum quod motus est in ipso, protensum et procedens est de ante in spatio in post, sive de anteriori parte spatii in posteriorem non interrumpendo. Protensio autem, ut sæpe diximus, causa est quantitatis. Protensum est partim hic et partim ibi, continua et non interrupta protensione. Quod autem sic divisibile est, continuum est. Motus igitur (qui secundum esse protensum inest ei quod movetur) est continuus, non ex seipso, sed ex spatio distantiæ quæ est inter duo motus extrema. Cum autem sit continuum et quantum aliquo modo, sequitur quod sit ejus aliquid mensura: et quia omne quantum habet mensurans proprium secundum propriam divisionem, sicut secundum spatium continuum ad modum lineæ vel superficiei vel corporis, habet ulnam vel palmam vel pedem, vel decempedam et aliquid talium: propter quod in omnem diametrum certa
through the name which is the notion of the predicable; and therefore Aristotle says thus, There is no falsehood among those who abstract 1. Rather it is most certainly true, although according to being those things are not found distinct in nature; for they are present in this mode in which they have been determined in the very substance of quantified things.
It must also be noted that there cannot be a fourth species of continuous quantity having position in its parts and from itself continuity and substance around which it places the form of commonness and continuity; because one cannot understand the motion of something in some way indivisible except either in length, or in breadth, or in depth. For height differs from depth only by its terms; and therefore there are only three species of this quantity, from which predicables can be taken.
It must also be known that line is quantity of one divisibility, but surface is quantity of two divisions, and body is quantity of three divisions, on account of the causes that have been determined in the things held before.
CHAPTER IV.
How time is continuous quantity.
But of the number of such continuous quantities there are also time and place: for present time is joined both to past and to future through the middle instant which is the term of such joining. But here we take the present as divisible time which lies adjacent to motion and to present action. But we call past that which is terminated at the present through an instant which is the end of the past and the principle of the present; and the present also is joined to the future through an instant which is the end of the present and the principle of the future; and thus the whole of time is continuous. For just as in other continuous things the flux of the continuous is from some one thing indivisible according to some mode, so also it is in time.
Therefore it must be understood that if there were no motion, there would be no time, and the extension of motion is the cause of the extension of time, just as motion also is the cause of time. But motion is in that which is moved as in a subject. But that which is carried or moved is the same according to substance in the whole motion; but according to its being, according as motion is in it, it is stretched out and proceeding from before in space into after, or from the prior part of space into the posterior, without interruption. But stretching-out, as we have often said, is the cause of quantity. What is stretched out is partly here and partly there, by a continuous and uninterrupted stretching-out. But what is thus divisible is continuous. Therefore motion, which according to stretched-out being inheres in that which is moved, is continuous, not from itself, but from the space of the distance which is between the two extremes of motion. But since it is continuous and quantified in some mode, it follows that there is some measure of it; and because every quantified thing has its proper measurer according to its proper division, as according to continuous space in the mode of line or of surface or of body it has an ell or a palm or a foot, or a ten-foot measure and something of such things, on account of which in every diameter a certain
redditur quantitas ipsius, nec certificari potest nisi secundum hoc quod dividitur. Oportet igitur, quod per hunc modum mensurans motum, secundum esse quod habet in eo quod movetur, sit certificans quantitatem ipsius.
In eo autem quod movetur secundum quod motus est actus ejus sunt tria, scilicet indivisibilis substantia ipsius quod movetur, quæ eadem manet in toto motu: et esse protensum in spatio continuo: et divisio prioris quod accipit in spatio quod derelinquit continue, a posteriori quod jam accepit in illo protendendo. Si ergo sic debeat mensurari, tria sunt in mensura reddente quantitatem ipsius: quia aliter mensura rei mensuratæ non esset adæquata: mensurans autem ipsum sic non potest sibi esse intrinsecum, eo quod intrinsecum est alterius generis: est enim in motu locali intrinsecum motui ubi fluens, et hoc non est secundum sui naturam in genere quantitatis, sed in genere ubi: et ideo motus in ubi non est in genere quantitatis, sed est in genere ubi. In alteratione autem est quale fluens quod per fluxum non amittit proprii generis naturam: et ideo sicut quale est in qualitate, sic et motus in qualitate. Similiter et motus augmenti quamvis sit in quantitate, non tamen sic est in quantitate, quod motus faciat ipsum in quantitate esse tanquam in genere, sed potius per hoc est in genere quia est quantum continuum positionem habens in partibus fluens, sicut corpus quod per fluxum non amittit naturam corporis. Et ideo motus non per partem motus vel per substantiam est in genere vel specie quantitatis, sed per hoc quod est quantum fluens quod fluxu non amittit naturam fluentis. Similiter est in generatione et corruptione, quæ sunt mutationes in substantia: propter quod dicit Aristoteles 2, quod via in naturam dicitur natura, cum motus et mutatio non possit habere mensurans circa quod sit substantia motus, et circa quod ponat motus suam continuitatem. Relinquitur igitur quod habeat mensurans extrinsecum adjacens, et hoc vocatur tempus, et tempus in sua substantia et suo esse diversum et linea et superficie et corpore.
Quod ergo per intellectum adjacet ei quod defertur et in toto motu est idem per substantiam, cum hoc semper objiciatur præsentiæ accipientis ipsum, est præsens quod vocatur instans quasi non stans, sicut et id quod movetur, non stat quamdiu motus est ejus actus. Quod autem adjacet protensioni ejus, quod secundum quod movetur, est continue protensum a retro in ante, illud est et vocatur tempus. Et id quod adjacet ei quod est in spatio accepto in retro, vocatur in tempore prius vel præteritum. Et quod adjacet ei quod in motu est in spatio accepto in ante, est et vocatur futurum. Et quod adjacet ei quod objicitur præsentiæ accipientis in protensione motus et spatii, vocatur præsens tempus. Cum tamen tria ista, præteritum, præsens et futurum non sunt diversa et separata, non sunt discreta sed sunt simul copulata. Copulatorum autem semper est communis terminus, qui est finis unius et principium alterius, et est aliquid utriusque et neutrius per se, id copulans particulas temporis vocatur indivisibile instans, quod quidem secundum se est substantia temporis, sicut punctum est substantia lineæ, qui fluxu suo causa est continuitatis quæ est forma successionis continuæ quæ ponitur circa substantiam instantis, sicut dictum est in aliis continuis. Sicut autem ulna iterata est numerus reddens quantitatem continui, ita instans distinguens prius et posterius in motu protensum super partes motus, iteratur et certificat quantitatem motus. Et ideo dicit Aristoteles 3 quod tempus est numerus motus propter prius et posterius.
Et ideo non est inconveniens quod tempus sit continuum, et tamen sit numerus: quia est numerus sicut ulna panni, vel alterius mensurati per ulnam. Et quando dicitur quod tempus est continuum, et
the quantity of it is rendered, nor can it be certified except according to this, that it is divided. Therefore it is necessary that what measures motion in this mode, according to the being which it has in that which is moved, should certify the quantity of it.
But in that which is moved, according as motion is its act, there are three things, namely the indivisible substance of that which is moved, which remains the same in the whole motion; and stretched-out being in continuous space; and the division of the prior thing which it receives in the space which it leaves behind continuously, from the posterior thing which it has already received in that stretching-out. Therefore if it must be measured in this way, there are three things in the measure rendering the quantity of it, because otherwise the measure of the measured thing would not be adequate. But what measures it in this way cannot be intrinsic to it, because the intrinsic thing is of another genus. For in local motion, where flowing is intrinsic to motion, this is not according to its nature in the genus of quantity, but in the genus where; and therefore motion in where is not in the genus of quantity, but is in the genus where. But in alteration there is a flowing quality which through flux does not lose the nature of its proper genus; and therefore just as the quality is in quality, so also the motion is in quality. Similarly also the motion of increase, although it is in quantity, nevertheless is not in quantity in such a way that motion makes it be in quantity as in a genus, but rather it is in the genus through this, that it is a flowing continuous quantity having position in its parts, like a body which through flux does not lose the nature of body. And therefore motion is not in the genus or species of quantity through a part of motion or through substance, but through this, that it is a flowing quantity which by flux does not lose the nature of what is flowing. It is similar in generation and corruption, which are changes in substance; on account of which Aristotle says 2 that the way into nature is called nature, since motion and change cannot have something measuring around which the substance of motion would be, and around which motion would place its continuity. Therefore it remains that it has an extrinsic adjacent measurer, and this is called time, and time in its substance and its being is diverse and line and surface and body.
Therefore what through understanding lies adjacent to that which is carried and is the same through substance in the whole motion, since this is always objected to the presence of the one receiving it, is the present which is called an instant as though not standing, just as also that which is moved does not stand as long as motion is its act. But what lies adjacent to its stretching-out, which, according as it is moved, is continuously stretched from behind into before, that is and is called time. And that which lies adjacent to that which is in space taken behind is called prior in time, or past. And that which lies adjacent to that which in motion is in space taken ahead is and is called future. And that which lies adjacent to that which is objected to the presence of the one receiving in the stretching-out of motion and space is called present time. Yet since those three, past, present, and future, are not diverse and separated, they are not discrete but are joined together. But of joined things there is always a common term, which is the end of one and the principle of the other, and is something of each and of neither through itself; that which joins the particles of time is called the indivisible instant, which indeed according to itself is the substance of time, just as point is the substance of line, which by its flux is the cause of the continuity which is the form of continuous succession that is placed around the substance of the instant, as was said in the other continuous things. But just as an ell repeated is a number rendering the quantity of the continuous, so the instant, distinguishing prior and posterior in motion stretched out over the parts of motion, is repeated and certifies the quantity of motion. And therefore Aristotle says 3 that time is the number of motion on account of prior and posterior.
And therefore it is not unfitting that time is continuous and nevertheless is a number, because it is a number as an ell is of cloth, or of another thing measured by an ell. And when it is said that time is continuous, and
Notes
- Aristotle, book 2 of the Physics, text, commentary 18. There is no falsehood among those who abstract. That is, the intellect, by abstracting one thing from another and considering that apart, commits no falsity; for in order that our cognition and account of conceiving may proceed without falsity, it need not always apprehend that which objectively belongs to some thing, or to the essence of some thing, provided that we do not attribute to the thing what does not belong to it, or apprehend the thing altogether under some false and repugnant account which does not belong to the thing, as Tannerus well pursues at greater length (t. 1, d. 2, q. 2, doubt 5, n. 12), and this is called precisive abstraction. Another is negative, by which one thing is denied of another, where there can be falsity and falsehood. Hence one considering animal in man without rationality does not lie; but one saying, man is not animal, lies. And hence: “Truth and falsity properly are only in the second operation.” Compare Reeb. (Aristoteles, 2 Physic. tex. com. 18. Abstrahentium non est mendacium. Hoc est, intellectus abstrahendo unum ab alio, et illud seorsum considerando, nullam falsitatem committit, nam ut sine falsitate procedat nostra cognitio et concipiendi ratio, non debet semper id quod objective alicui rei, sive essentiæ alicujus rei convenit, apprehendere, dummodo non tribuamus rei quod ei non convenit, aut omnino sub falsa quapiam et repugnante ratione, quæ rei non convenit, rem apprehendamus, ut pluribus bene Tannerus (t. 1, d. 2, q. 2, dub. 5, n. 12) prosequitur, et hæc vocatur abstractio præcisiva. Alia est negativa, quæ unum de alio negatur, ubi potest esse falsitas et mendacium. Hinc considerans animal in homine sine rationalitate, non mentitur: dicens autem, homo non est animal, mentitur. Et hinc: « Veritas et falsitas proprie tantum est in secunda operatione. » Cf. Reeb.) ↩
- Aristotle, in book 2 of the Physics, text, commentary 14. (Aristoteles, In 2 Physic. tex. com. 14.) ↩
- The same, in book 4 of the Physics, text, commentary 101. (Id. In 4 Physic. tex. com. 101.) ↩
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