Volume 1 · pp. 209–210
End of Chapter VIII and Chapter IX. On doubts which concern this, that time is said to be continuous quantity
quarum quælibet directe protrahitur in continuum ad diversa positum, una scilicet secundum longitudinem, et una secundum latitudinem, et tertia secundum altitudinem et profunditatem. Non enim potest intelligi quarta positio continui in quod protrahatur diameter mensurans substantiam: et ideo dicit Aristoteles 1, quod perfectio est in istis secundum tres cæli motus, ab Austro scilicet in Aquilonem, qui est motus profunditatis, quia ante est nobis in Aquilone et Auster est retro: et iste est motus de tropico in tropicum per æquinoctialem. Et motus a dextro in sinistrum, qui est motus latitudinis cæli et planetarum. Sed planetæ dextrum suum habent in Occidente et sinistrum in Oriente primi cæli. Et motus sursum et deorsum qui est motus totius sphæræ secundum totum luminis et virtutis cœlestis ad centrum: propter quod perfectio est in tribus dimensionibus. Et quia perfectum est, ut dicit Aristoteles 2, cui nihil addi potest, ideo quarta addi non potest dimensio.
Ad hoc autem quod quærebatur, quare latitudo non est sine longitudine, sicut e contra, Dicendum quod hoc est idem quærere, quare secundum non est sine primo, sicut primum est sine secundo? quia latum et secundum generatur ex longo et primo: et id ex quo generatur, manet in generato, et non e contra: latum enim ad quod oportet latus moveatur, semper in superficie motum facit latum, et nunquam perficiet longitudinem sine latitudine: sed motum extra superficiem, ad aliam positionem movebitur, aut sursum extra superficiem, aut in profundum subtus superficiem, et tunc quia movetur ad aliam positionem, faciet aliam quantitatis speciem: et sic linea non ad positionem longitudinis mota, sed ad aliam positionem faciet superficiem.
Ad hoc autem quod quæritur, in quo differat substantia corpus, et corpus quantitas, superius jam dictum est: quia materia prout est subjectum generationis, est habens potentia et non actu tres dimensiones: corpus autem quantitatis est ipsa trina dimensio.
Ad hoc autem quod quæritur, utrum ex parte materiæ, vel formæ, vel compositi adveniat quantitas substantiæ, Dicendum sicut in ante habitis, quod potentia suscipiendi est a materia, quæ potentia divisibilis est: actus autem disponendi quamlibet partium in situ et dimensione propria ne effluant partes a terminatione totius, est a forma terminante partes materiæ ad situm proprium ordinatæ: ipsa autem dispositio partium in situ et ordine, est totius et utriusque, tam formæ scilicet quam materiæ secundum quod totum sunt. Et sic patet omnium solutio.
CAPUT IX.
De dubitationibus quæ sunt circa hoc quod dicitur, quod tempus est continua quantitas.
Contra hoc etiam quod tempus dicitur esse quantitas, opponunt quidam dicentes quod cujus partes non sunt, ipsum non est: partes autem temporis non sunt: præteritum namque non est, quia præteriit et abiit in non esse: futurum autem nondum est, sed expectatur: præsens autem est indivisibile nunc, quod non potest esse pars continui si quælibet pars continui divisibilis est sicut ipsum continuum: ergo nulla pars temporis est: et sic ipsum tempus non est: et sic ulterius non continua quantitas est.
Si forte aliquis dicat, quod præsens est pars temporis, in quo tempus habet esse aliquo modo. Contra hoc esse videtur, quod in aliis continuis id in quo copulantur partes continui, est indivisibile et non pars continui, sicut punctum in linea: præsens autem est in quo copulantur partes temporis, præteritum et futurum: ergo præsens est indivisibile tempus et non pars ipsius.
of which each is drawn out directly into the continuum positioned toward diverse things: one, namely, according to length, and one according to breadth, and the third according to height and depth. For a fourth position of the continuous cannot be understood into which a diameter measuring substance would be drawn out; and therefore Aristotle says 1 that perfection is in those things according to the three motions of the heaven, namely from the South to the North, which is the motion of depth, because what is before is for us in the North and the South is behind; and that is the motion from tropic to tropic through the equinoctial. And there is the motion from right to left, which is the motion of the breadth of the heaven and of the planets. But the planets have their right in the West and their left in the East of the first heaven. And there is the motion upward and downward, which is the motion of the whole sphere according to the whole of heavenly light and power toward the center; on account of which perfection is in three dimensions. And because the perfect is, as Aristotle says 2, that to which nothing can be added, therefore a fourth dimension cannot be added.
But to this which was asked, why breadth is not without length, as conversely, one must say that this is the same as asking why the second is not without the first, as the first is without the second. For the broad and second thing is generated from the long and first thing; and that from which something is generated remains in what has been generated, and not conversely. For the broad thing toward which the side must be moved, being moved in surface, always makes a broad thing, and it will never perfect length without breadth; but moved outside surface, it will be moved toward another position, either upward outside surface or into depth beneath surface, and then because it is moved toward another position, it will make another species of quantity; and thus line, moved not toward the position of length but toward another position, will make surface.
But to this which is asked, in what body as substance differs from body as quantity, it has already been said above: because matter, insofar as it is the subject of generation, is having three dimensions in potency and not in act; but the body of quantity is the very threefold dimension.
But to this which is asked, whether quantity comes to substance from the part of matter, or of form, or of the composite, one must say, as in the things held before, that the potency of receiving is from matter, which potency is divisible; but the act of arranging each of the parts in its proper situation and dimension, lest the parts flow away from the termination of the whole, is from the form terminating the parts of matter ordered to their proper situation; but the very disposition of the parts in situation and order belongs to the whole and to both, namely both form and matter, according as they are a whole. And thus the solution of all the things is clear.
CHAPTER IX.
On doubts which concern this, that time is said to be continuous quantity.
Against this also, that time is said to be quantity, certain people object, saying that what does not have parts, itself does not exist; but the parts of time do not exist: for the past is not, because it has passed by and has gone away into non-being; but the future is not yet, but is expected; but the present is the indivisible now, which cannot be a part of the continuous if any part whatever of a continuum is divisible just as the continuum itself is. Therefore no part of time exists, and thus time itself does not exist; and thus further it is not continuous quantity.
If perhaps someone should say that the present is a part of time in which time has being in some mode, against this there seems to be that in other continuous things that in which the parts of the continuum are joined is indivisible and not a part of the continuum, as a point in a line; but the present is that in which the parts of time, past and future, are joined; therefore the present is indivisible time and not a part of it.
Adhuc autem compositum ex aliquibus ut partibus, est divisibile in his ex quibus ut partibus compositum est: tempus autem non est divisibile in nunc: ergo non est compositum ex nunc sicut ex partibus vel parte.
Adhuc quælibet pars continui est alia ab ejusdem continui parte cui continuatur: nunc autem, ut probat Aristoteles 3, non continuatur cum nunc: ergo nunc præsens non est pars continui.
Adhuc autem nunc non potest esse continuum ad nunc, vel cum nunc: continua enim sunt, quorum ultima sunt unum: nunc autem cum sit indivisibile non habet ultimum: igitur cum alio non habebit ultimum idem, et sic nunc non potest esse pars temporis.
Adhuc etiam concesso quod nunc est pars temporis, et quod sit id quod de tempore est accipere, adhuc non sequitur, quod tempus sit actu: quia, ut dicit Aristoteles 4, nunc in tempore non est in actu, sed potentia.
Si propter hoc dicatur quod tempus non est, et ideo non est species continuæ quantitatis, in oppositum objicitur quia constat quod motus est continuus divisibilis, sicut constat ex sexto Physicorum 5. Aut ergo est mensura, aut mensuratum aliquod. Si est mensura, non potest esse mensura nisi aut ejus quod movetur, aut magnitudinis super quam est motus. Et constat quod neutro modo potest esse mensura: mensura enim et mensuratum sunt ejusdem generis: id autem quod movetur est permanens. Similiter autem et magnitudo de permanentibus est. Motus autem est de numero successivorum. Si modo dicatur motus mensuratum quoddam esse, tunc erit aliqua mensura mensurans ipsum: sed constat quod nec id quod movetur, nec magnitudo super quam est motus propter causas quæ dictæ sunt: cum ergo non sit invenire mensuram ejusdem generis cum motu nisi tempus, erit tempus mensura ejus successiva sicut motus. Ex quo sequitur quod tempus est, quia esse mensuram non est determinatio diminuens ad esse, sed in esse constituens.
Dicimus igitur his consentientes quod tempus est, sed est secundum esse successivi, sicut et motus cujus ipsum est mensura.
Ad id autem quod objicitur de partibus temporis quæ non sunt, dicendum quod totum secundum quod in genere totum accipitur, non dependet ab esse partium actu: hoc enim non habet nisi totum in partibus permanens. Et hoc non habet totum successivum, quod non dependet a constitutione partium nisi secundum quod sunt in ordine. Et tales partes habet tempus. Successivum enim totum est dum fit, et habet esse permixtum potentia, et ideo non oportet quod partes simul actu habeant.
Ad hoc autem quod quæritur, utrum nunc sit pars temporis, Dicendum quod præsens accipitur ut divisibile tempus, de quo dicit Priscianus, quod præsens est cujus pars præteriit, et pars in instanti est, et pars in futuro: et hæc copulantur præterito et futuro. Est etiam præsens nunc indivisibile, et hoc non copulatur sed copulat: et hoc quidem est aliquid temporis, sed non est aliqua pars temporis: et secundum hoc facile est solvere objecta.
Si autem quis objiciat dicens quod tempus est numerus motus, et ita discreta et non continua quantitas: est satis responsum per antedicta. Est enim tempus numerus continui primo numeratus, et postea numerans: numeratus quidem a priori et posteriori in magnitudine et motu: numerans autem et certificans quantitatem motus. Taliter autem numeratus numerus non est discreta quantitas sed continua. Sic ergo tempus est continua quantitas, et non discreta. Multa autem de tempore quæ dicenda videntur, ad naturalem pertinent Philosophum.
Further, what is composed from some things as from parts is divisible into those things from which it is composed as from parts; but time is not divisible into a now; therefore it is not composed from a now as from parts or from a part.
Further, any part whatever of a continuum is other than the part of the same continuum to which it is continued; but the now, as Aristotle proves 3, is not continued with the now; therefore the present now is not a part of the continuum.
Further, the now cannot be continuous toward a now, or with a now, for continuous things are those whose outermost parts are one; but since the now is indivisible, it does not have an outermost part; therefore with another it will not have the same outermost part, and thus the now cannot be a part of time.
Further also, granting that the now is a part of time, and that it is that which can be taken from time, still it does not follow that time is in act, because, as Aristotle says 4, the now in time is not in act, but in potency.
If on account of this it is said that time does not exist, and therefore is not a species of continuous quantity, to the contrary it is objected that it is agreed that motion is continuous and divisible, as is agreed from the sixth book of the Physics 5. Therefore either it is a measure, or some measured thing. If it is a measure, it cannot be a measure except either of that which is moved, or of the magnitude upon which the motion is. And it is agreed that it cannot be a measure in either mode; for measure and measured thing are of the same genus, but that which is moved is permanent. Similarly also magnitude is from the permanent things. But motion is of the number of successive things. But if motion is said to be a certain measured thing, then there will be some measure measuring it; but it is agreed that neither that which is moved, nor the magnitude upon which the motion is, is this, on account of the causes which have been stated. Therefore since no measure of the same genus as motion can be found except time, time will be its successive measure, as motion is successive. From this it follows that time exists, because to be a measure is not a determination diminishing toward being, but one constituting in being.
Therefore we say, agreeing with these things, that time exists, but exists according to the being of the successive, just as also motion does, of which it itself is the measure.
But to that which is objected about the parts of time which do not exist, one must say that a whole, according as a whole is taken in the genus, does not depend on the being of the parts in act; for only a whole permanent in parts has this. And a successive whole does not have this, because it does not depend on the constitution of the parts except according as they are in order. And time has such parts. For a successive whole exists while it is coming to be, and has being mixed with potency, and therefore it is not necessary that the parts have being together in act.
But to this which is asked, whether the now is a part of time, one must say that the present is taken as divisible time, concerning which Priscian says that the present is that of which part has passed, and part is in the instant, and part is in the future; and these are joined to the past and to the future. There is also the present indivisible now, and this is not joined but joins; and this indeed is something of time, but is not some part of time; and according to this it is easy to solve the objections.
But if someone objects, saying that time is the number of motion, and thus discrete and not continuous quantity, sufficient response has been given through the things said before. For time is the number of the continuous, first numbered and afterward numbering: numbered indeed by the prior and posterior in magnitude and motion, but numbering and certifying the quantity of motion. But a number numbered in such a way is not discrete quantity but continuous. Therefore in this way time is continuous quantity, and not discrete. But many things about time which seem to have to be said pertain to the natural Philosopher.
Notes
- Aristotle, in book 2 On Heaven and the World, from text, commentary 4. (Aristoteles, In 2 de Cœlo et Mundo, a tex. com. 4.) ↩
- Aristotle, in book 3 of the Metaphysics, text, commentary 21. (Aristoteles, In 3 metaphys. tex. com. 21.) ↩
- Aristotle, in book 6 of the Physics, from text, commentary 24 up to 32. (Aristoteles, In 6 Physic., a tex. com. 24 usque ad 32.) ↩
- The same, in book 4 of the Physics, text, commentary 104. (Id., In 4 Physic., tex. com. 104.) ↩
- The same, in book 6 of the Physics, from text, commentary 33. (Id. In 6 Physic., a tex. com. 33.) ↩
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