Plotino - Tratado 45,8 (III, 7, 8) — Exame e rejeição das definições de tempo

8. Pero, ni reunidos todos los movimientos en uno solo, ni considerado aparte el movimiento ordenado, resulta posible que el tiempo sea el movimiento. En ambos casos, lo que llamamos el movimiento se encuentra siempre en el lu’mpo. Si hubiese un movimiento que no se diese en el liempo, estaría por esto mismo mucho más lejos de ser el liempo. De modo que una cosa es aquello en lo que se da el movimiento y otra, en cambio, el movimiento mismo. Ap;¡rie lo que se dice o se ha estimado sobre esto, basta considerar que el movimiento podría cesar o manifestarse a intervalos, pero no así el tiempo. Sí arguyésemos que el movimiento del universo no se interrumpe, cabría preguntarse entonces si se trata del movimiento circular, porque este movimiento se cumple y vuelve al mismo punto en un cierto tiempo que no es aquel en el que se cumple la mitad de la revolución. Este tiempo es la mitad del otro y el primero doble del segundo, con lo cual la revolución completa y su mitad son, una y otra, movimientos del universo. Dícese, además, que la esfera exterior cuenta con un movimiento más vivo y más rápido, cosa que atestigua contra la tesis; en consecuencia, una cosa es el movimiento de la esfera y otra el tiempo que dura este movimiento. Está claro que la esfera de las estrellas fijas es la más rápida porque recorre una mayor distancia, y aun la mayor posible, en un tiempo menor. Las otras, en cambio, son más lentas porque emplean más tiempo en recorrer una parte de aquella distancia. He aquí, pues, que si el tiempo no es el movimiento de la esfera, con mucha más razón no podrá ser la esfera misma. De resultas del movimiento de ésta se había supuesto precisamente que era el tiempo.

¿Pero es algo propio del movimiento? Si se estima que es su intervalo, deberíamos decir que no todos los movimientos tienen el mismo intervalo, ni siquiera aquellos que son idénticos. Así, los movimientos locales pueden ser más rápidos o más lentos, pero sus distancias se miden por una unidad, diferente de ellos. Sería lo más justo llamar el tiempo u esta misma, unidad. Y si el tiempo es el intervalo de eslos movimientos, hemos de decir de cuál, puesto que existen movimientos infinitos. Si lo suponemos como intervalo del movimiento ordenado, añadamos que no puede serlo de lodo movimiento de esta clase; porque hay realmente muchos, lo cual quiere decir que existirían también muchos tiempos. Supuesto, en cambio, como intervalo del movimiento del universo, si es el intervalo que hay en dicho movimiento, ¿qué otra cosa sería que este movimiento mismo? Se le califica, sin embargo, como un intervalo de magnitud determinada, magnitud que podría medirse por el espacio que el movimiento ha recorrido, aunque entonces ya no se trataría del tiempo, sino del espacio. También podría suponerse que el movimiento tiene este intervalo por su misma continuidad, que no cesa un instante, como no sea para reanudarse siempre. Esto equivaldría a decir que el movimiento se multiplica; y si, al observarlo, lo encontramos múltiple, con ello no se demuestra ni se alcanza el tiempo, como tampoco si se dijese que el calor se multiplica. Tendríamos, de una parte, un movimiento, luego otro, y así sucesivamente -lo mismo que el agua de un río corre y corre sin limitación-, y de otra el intervalo que hay entre ellos. Esa sucesión de movimientos se expresaría por un número, como el dos o el tres, pero el intervalo sería una magnitud espacial. El tiempo, entonces, tendría que ser también una cantidad múltiple de movimiento, como diez, o el intervalo de movimiento que se aparece en el espacio recorrido; aunque este intervalo no implica idea alguna de tiempo, sino tan sólo una cierta magnitud recorrida en el tiempo. Si el tiempo, en fin, no es en modo alguno un intervalo, se dará en el movimiento como en un sujeto, volviendo así a la afirmación de que el tiempo es un movimiento, porque es claro que el intervalo no está fuera del movimiento, a no ser que el movimiento fuese instantáneo.- Pero si lo instantáneo difiere de lo no instantáneo en el hecho de que no se da en el tiempo, ¿en qué diferirá lo no instantáneo de lo instantáneo, sino en el hecho de darse en el tiempo? De manera que el movimiento manifestado en un intervalo y el intervalo mismo no son el tiempo, sino que se dan en el tiempo. Diríase que el tiempo es el intervalo del movimiento, pero no del movimiento mismo, sino el intervalo a lo largo del cual se prolonga el movimiento, avanzando juntamente con él. Con ello no se declara lo que es este intervalo, pero es evidente que se trata del tiempo, puesto que en él se da el movimiento. Ahora bien, esto es justamente lo que nos proponíamos al principio: ¿qué es verdaderamente el tiempo? Pues a ello equivale el decir, si se os pregunta por la naturaleza de] tiempo, que se trata de un intervalo del movimiento en el tiempo. ¿En qué consiste, sin embargo, este intervalo, al que damos el nombre de tiempo, si lo diferenciamos del intervalo del movimiento propiamente dicho?

Una dificultad subsiste para los que ponían el intervalo en el movimiento mismo: ¿dónde tendrían que poner la duración del reposo? Porque tanto tiempo como un objeto se mueve, tanto tiempo que otro puede permanecer inmóvil; el tiempo de uno y otro, diríase, es, sin embargo, el mismo, aunque a la vez diferente, claro está, del movimiento y del reposo. ¿Qué naturaleza tiene, pues, ese intervalo (llamado tiempo)? No es posible que sea un intervalo de lugar, ya que el lugar es extraño al movimiento y al reposo.

VIII. Examinons maintenant en quel sens l’on peut dire que le temps est le nombre et la mesure du mouvement (42) ce qui semble plus raisonnable à cause de sa continuité.

D’abord ici, comme au sujet de la définition qui fait consister le temps dans l’intervalle du mouvement, on peut demander si le temps est la mesure et le nombre de toute espèce de mouvement. Comment, en effet, évaluer numériquement le mouvement inégal et irrégulier ? Quel est le nombre, quelle est la mesure qui sert à évaluer ce mouvement ? Si l’on évalue par la même mesure le mouvement lent et le mouvement rapide, la mesure elle nombre seront pour eux ce qu’est le nombre dix appliqué également à des chevaux et à des bœufs, ce que serait une mesure qui servirait également à mesurer les substances sèches et les liquides. Si le temps est une mesure de cette sorte, on voit bien qu’il est la mesure des mouvements, mais on ne voit pas encore ce qu’il est par lui-même. Si le nombre dix peut être conçu comme nombre, abstraction faite des chevaux qu’il sert à nombrer, si une mesure a par elle-même sa nature propre, même quand elle ne mesure rien, il doit en être de même du temps, puisqu’il est une mesure. Si le temps est un nombre en lui-même, en quoi diffère-t-il du nombre dix ou de tout autre nombre composé d’unités ? S’il est une mesure continue, étant une quantité, il constituera une mesure comme une coudée, par exemple. Il sera donc une grandeur, une ligne, par exemple, qui suit le mouvement ; mais comment cette ligne pourra-t-elle mesurer ce qu’elle suit? Pourquoi mesurera-t-elle une chose plutôt qu’une autre ? Il semble plus raisonnable de regarder cette mesure, non comme la mesure de toute espèce de mouvement, mais seulement comme la mesure du mouvement qu’elle suit (43). Alors cette mesure est continue, en tant que le mouvement qu’elle suit continue lui-même d’exister. Dans ce cas, il ne faut pas regarder la mesure comme une chose extérieure et séparée du mouvement, mais comme unie au mouvement mesuré. Qu’est-ce qui mesurera donc? Est-ce le mouvement qui sera mesuré et l’étendue qui le mesurera ? Laquelle de ces deux choses sera le temps ? Sera-t-il le mouvement mesuré ou l’étendue mesurante ? Le temps sera ou le mouvement mesuré par l’étendue, ou l’étendue mesurante, ou une troisième chose qui se sert de l’étendue, comme on se sert d’une coudée, pour mesurer la quantité du mouvement. Mais, dans tous ces cas, il faut, comme nous l’avons déjà remarqué, supposer que le mouvement est uniforme : car, si le mouvement n’est pas uniforme, un et universel, on trouve la plus grande obscurité dans l’opinion qui suppose que le mouvement est une mesure d’une nature quelconque. Si le temps est le mouvement mesuré, c’est-à-dire mesuré par la quantité, en admettant qu’il ait besoin d’être mesuré, le mouvement ne doit cependant pas être mesuré par lui-même, mais par une chose différente de lui ; d’un autre côté, si le mouvement a une mesure différente de lui, et si, par suite, nous avons besoin d’une mesure continue pour le mesurer, il en résultera que l’étendue elle-même aura besoin d’une mesure, afin que le mouvement, étant mesuré, ait une quantité qui soit déterminée par celle de la chose selon laquelle il est mesuré. Par conséquent, dans cette hypothèse, le temps sera le nombre de l’étendue qui suit le mouvement, et non l’étendue même qui suit le mouvement.

Quel est ce nombre ? Est-il composé d’unités ? Comment mesure-t-il ? Voilà ce qui reste à déterminer. Supposons qu’on trouve comment il mesure, on n’aura pas encore trouvé le temps qui mesure, mais un temps qui est tel ou tel quantum. Or cela n’est pas la même chose que le temps : autre chose est le temps, autre chose telle quantité de temps. Avant d’affirmer que le temps a telle ou telle quantité, il faut déterminer ce qu’est la chose qui a cette quantité. Sans doute le temps est le nombre qui mesure le mouvement en lui restant extérieur, comme dix est dans dix chevaux sans être conçu avec eux (44). Mais, dans ce cas, on n’a pas encore défini ce qu’est ce nombre qui, avant de nombrer, est ce qu’il est, comme serait dix considéré en lui-même (45). C’est le nombre, dira-t-on, qui, en suivant le mouvement, mesure selon l’antériorité et la postériorité de ce mouvement (46). On ne voit pas encore en quoi consiste ce nombre qui mesure selon l’antériorité et la postériorité. En tout cas, ce qui mesure selon l’antériorité et la postériorité, soit par un point (47), soit par toute autre chose, mesure certainement selon le temps. Ainsi, ce nombre (48) qui mesure le mouvement selon l’antériorité et la postériorité doit toucher au temps et y être lié pour mesurer le mouvement. Antérieur et postérieur désignent nécessairement soit des parties diverses de l’espace, comme le commencement du stade, soit des parties du temps. Ce qu’on nomme l’antérieur, c’est le temps qui finit au présent; et ce qu’on appelle le postérieur, c’est le temps qui commence au présent. Le temps est donc autre chose que le nombre qui mesure le mouvement selon l’antériorité et la postériorité, je né dis pas seulement un mouvement quelconque, mais encore le mouvement régulier. D’ailleurs, pourquoi aura-t-on le temps en appliquant le nombre soit à ce qui mesure, soit à ce qui est mesuré (car ici ce qui mesure et ce qui est mesuré peuvent n’être qu’une seule chose) ? Pourquoi sans le nombre n’aura-t-on pas le temps, si le mouvement existe avec l’antérieur et le postérieur qui s’y rapportent? C’est comme si l’on disait que l’étendue n’a telle quantité que s’il y a quelqu’un pour reconnaître qu’elle possède cette quantité. Puisqu’on dit que Je temps est infini (49), et qu’il l’est en effet, comment le nombre peut-il être en lui à moins qu’on ne prenne une portion de temps pour le mesurer? De là résulte que le temps existe avant d’être mesuré. Mais pourquoi le temps n’existerait-il pas avant qu’il existât une âme pour le mesurer? On dira peut-être qu’il est engendré par l’âme. Il n’est pas nécessaire qu’il soit engendré par l’âme par cela seul qu’elle le mesure : il existerait, avec la quantité qui lui est propre, lors même que personne ne le mesurerait. Si l’on dit enfin que c’est l’âme qui se sert de l’étendue pour mesurer le temps, nous répondrons que ce point n’est d’aucune importance pour déterminer la notion du temps.

POLEMIC AGAINST ARISTOTLE  : TIME IS NOT THE NUMBER AND MEASURE OF MOVEMENT.

8. (9). Let us now examine in what sense it may be said (by Aristotle452) that time is the number and measure of movement, which definition seems more reasonable, because of the continuity of movement. To begin with, following the method adopted with the definition of time as "the interval of movement," we might ask whether time be the measure and number of any kind of movement.453 For how indeed could we give a numerical valuation of unequal or irregular movement. What system of numbering or measurement shall we use for this? If the same measure be applied to slow or to swift movement, in their case measure and number will be the same as the number ten applied equally to horses and oxen; and further, such measure might also be applied to dry and wet substances. If time be a measure of this kind, we clearly see that it is the measure of movements, but we do not discover what it may be in itself. If the number ten can be conceived as a number, after making abstraction of the horses it served to measure, if therefore a measure possess its own individuality, even while no longer measuring anything, the case must be similar with time, inasmuch as it is a measure. If then time be a number in itself, in what does it differ from the number ten, or from any other number composed of unities? As it is a continuous measure, and as it is a quantity, it might, for instance, turn out to be something like a foot-rule. It would then be a magnitude, as, for instance, a line, which follows the movement; but how will this line be able to measure what it follows? Why would it measure one thing rather than another? It seems more reasonable to consider this measure, not as the measure of every kind of movement, but only as the measure of the movement it follows.452 Then that measure is continuous, so far as the movement it follows itself continue to exist. In this case, we should not consider measure as something exterior, and separated from movement, but as united to the measured movement. What then will measure? Is it the movement that will be measured, and the extension that will measure it? Which of these two things will time be? Will it be the measuring movement, or the measuring extension? Time will be either the movement measured by extension, or the measuring extension; or some third thing which makes use of extension, as one makes use of a foot-rule, to measure the quantity of movement. But in all these cases, we must, as has already been noticed, suppose that movement is uniform; for unless the movement be uniform, one and universal, the theory that movement is a measure of any kind whatever will become almost impossible. If time be "measured movement," that is, measured by quantity-besides granting that it at all needs to be measured-movement must not be measured by itself, but by something different. On the other hand, if movement have a measure different from itself, and if, consequently, we need a continuous measure to measure it, the result would be that extension itself would need measure, so that movement, being measured, may have a quantity which is determined by that of the thing according to which it is measured. Consequently, under this hypothesis, time would be the number of the extension which follows movement, and not extension itself which follows movement.

NOR CAN TIME BE A NUMBERED NUMBER (AS ARISTOTLE CLAIMED452).

What is this number? Is it composed of unities? How does it measure? That would still have to be explained. Now let us suppose that we had discovered how it measures; we would still not have discovered the time that measures, but a time that was such or such an amount. Now that is not the same thing as time; there is a difference between time and some particular quantity of time. Before asserting that time has such or such a quantity, we have to discover the nature of that which has that quantity. We may grant that time is the number which measures movement, while remaining exterior thereto, as "ten" is in "ten horses" without being conceived with them (as Aristotle claimed, that it was not a numbering, but a numbered number). But in this case, we still have to discover the nature of this number that, before numbering, is what it is, as would be "ten" considered in itself.454 It may be said that it is that number which, by following number, measures according to the priority and posteriority of that movement.452 Nor do we yet perceive the nature of that number which measures by priority and posteriority. In any case, whatever measures by priority or posteriority, or by a present moment,455 or by anything else, certainly does measure according to time. Thus this number (?) which measures movement according to priority or posteriority, must touch time, and, to measure movement, be related thereto. Prior and posterior necessarily designate either different parts of space, as for instance the beginning of a stadium, or parts of time. What is called priority is time that ends with the present; what is called posteriority, is the time that begins at the present. Time therefore is something different from the number that measures movement according to priority or posteriority,-I do not say, any kind of movement, but still regular movement. Besides, why should we have time by applying number either to what measures, or to what is measured? For in this case these two may be identical. If movement exist along with the priority and posteriority which relate thereto, why will we not have time without number? This would amount to saying that extension has such a quantity only in case of the existence of somebody who recognizes that it possesses that quantity. Since (Aristotle456) says that time is infinite, and that it is such effectually, how can it contain number without our taking a portion of time to measure it? From that would result that time existed before it was measured. But why could time not exist before the existence of a soul to measure it? (Aristotle) might have answered that it was begotten by the soul. The mere fact that the soul measures time need not necessarily imply that the soul produced the time; time, along with its suitable quantity, would exist even if nobody measured it. If however it be said that it is the soul that makes use of extension to measure time, we will answer that this is of no importance to determine the notion of time.

VIII. In the next place, it must be considered how time is the number or measure of motion; for it is better to assert this of it, on account of its continuity. In the first place, therefore, here also it may be doubted, whether it is similarly the number or measure of every motion, in the same manner as it was dubious respecting the interval of motion. For how can any one numerate inordinate and anomalous motion, or what number or measure will there be of it, or according to what will the measure subsist ? But if he numerates and measures with the same thing, both irregular and regular motion, whether swift or slow, the number and the measure will be a thing of such a kind, as if it were the decad, measuring both horses and oxen, or as if the same thing were the measure both of moist and dry substances. If, therefore, time is a measure of this kind, it has indeed been shown what the things are of which time is the measure, viz. that it is the measure of motions, but it has not yet been shown what time is. If, however, in the same manner as the decad when assumed without horses, may be understood as number, and a measure is a measure possessing a certain proper nature, though it should not yet measure any thing, thus also it is necessary time should subsist, being a measure; — if therefore time is such a thing in itself as number, in what will it differ from this number which subsists according to the decad, or from any other monadic number ? But if it is a continued measure, being a certain quantity, it will be such a measure as a certain cubital magnitude. It will, therefore, be magnitude, such as a line accompanied with motion. But how, since it also runs, can it measure that with which it runs in conjunction? For why should one measure rather than the other ? And it is better and more probable to admit this not in every motion, but in that with which it concurs. This, however, ought to be continuous, so far as the concurrent motion is successive. But that which measures ought not to be considered as subsisting externally, nor as separate, but as at once measured motion. And what will that be which measures ? Will the motion indeed be measured, but the magnitude be that which measures ? And which of these will time be ? Will it be the measured motion, or the magnitude which measures ? For time will either be the motion which is measured by magnitude, or magnitude which measures, or that which uses magnitude, as a cubit for the purpose of measuring the quantity of the motion. In all these, however, it is more probable as we have said to suppose that the motion is equable. For without equability, and besides this, without one motion of the universe, the doubt will be greater than that which results from admitting that time is in some way or other the measure of motion. But if time is measured motion, and is measured by quantity, then just as if it Avere necessary that motion should be measured, it would not be requisite that it should be measured by itself, but by something else, thus also it is necessary, if motion has another measure besides itself, and on this account we are in want of a continuous measure, for the purpose of measuring it, that magnitude itself should have a measure, in order that the motion may be as much in quantity as its measure. And thus time will be the number of the magnitude attending the motion, and not the magnitude which runs in conjunction with the motion.

It is necessary, however, to doubt what this number is, whether it is monadic, and how it measures ? For though some one should discover how it measures, yet he would not find time measuring, hut a certain quantity of time. This, however, is not the same with time [simply considered]. For it is one thing to speak of time, and another, of so much time. For prior to the so much, it is necessary to say what that is which is so much. Is time, therefore, the number which measures motion externally ? Such as the decad in horses, and not that which is assumed together with horses. What this number, therefore, is, has not been shown, which prior to measuring, is what it is, in the same manner as the decad. Shall we say it is that number which measures by running according to the prior and posterior of motion ? [1] But it is not yet manifest what this number is which measures according to prior and posterior. That, however, which measures according to prior and posterior, whether by a point, or by any thing else, entirely measures according to time. This number, therefore, which measures motion by prior and posterior, will be successive to, and in contact with time, in order that it may measure it. For prior and posterior, must either be assumed locally, as the beginning [and end] of a stadium, or temporally. For in short, with respect to prior and posterior, the former indeed is time ending in the now; but the latter is time beginning from the now. Time, therefore, is different from the number which measures motion according to prior and posterior, not only motion of any kind, but also that which is orderly. In the next place, why when number is adjoined, whether according to the measured, or the measuring, (for the same number may be both that which measures, and is measured) — why therefore when number is added, will there be time; but motion existing, and prior and posterior entirely subsisting about it, there will not be time ? Just as if some one should say that magnitude is not as great as it is, unless some one apprehends what the quantity of it is. Since time, however, is, and is said to be infinite, how will there be number about it, unless a part of it being selected is measured, in which case it will happen that it exists prior to its being measured. But why will not time be prior to the existence of soul that measures it ? Unless it should be said that the generation of it is effected by soul; since it is by no means necessary that time should exist because it is measured by soul. For it would exist as much as it is its quantity, though no one should measure it. – And if some one should say that it is soul which uses magnitude for the purpose of measuring time, what will this have to do with the conception of time ?

8. Movement Time cannot be - whether a definite act of moving is meant or a united total made up of all such acts - since movement, in either sense, takes place in Time. And, of course, if there is any movement not in Time, the identification with Time becomes all the less tenable.

In a word, Movement must be distinct from the medium in which it takes place.

And, with all that has been said or is still said, one consideration is decisive: Movement can come to rest, can be intermittent; Time is continuous.

We will be told that the Movement of the All is continuous [and so may be identical with Time].

But, if the reference is to the Circuit of the heavenly system [it is not strictly continuous, or equable, since] the time taken in the return path is not that of the outgoing movement; the one is twice as long as the other: this Movement of the All proceeds, therefore, by two different degrees; the rate of the entire journey is not that of the first half.

Further, the fact that we hear of the Movement of the outermost sphere being the swiftest confirms our theory. Obviously, it is the swiftest of movements by taking the lesser time to traverse the greater space the very greatest - all other moving things are slower by taking a longer time to traverse a mere segment of the same extension: in other words, Time is not this movement.

And, if Time is not even the movement of the Kosmic Sphere much less is it the sphere itself though that has been identified with Time on the ground of its being in motion.

Is it, then, some phenomenon or connection of Movement?

Let us, tentatively, suppose it to be extent, or duration, of Movement.

Now, to begin with, Movement, even continuous, has no unchanging extent [as Time the equable has], since, even in space, it may be faster or slower; there must, therefore, be some unit of standard outside it, by which these differences are measurable, and this outside standard would more properly be called Time. And failing such a measure, which extent would be Time, that of the fast or of the slow - or rather which of them all, since these speed-differences are limitless?

Is it the extent of the subordinate Movement [= movement of things of earth]?

Again, this gives us no unit since the movement is infinitely variable; we would have, thus, not Time but Times.

The extent of the Movement of the All, then?

The Celestial Circuit may, no doubt, be thought of in terms of quantity. It answers to measure - in two ways. First there is space; the movement is commensurate with the area it passes through, and this area is its extent. But this gives us, still, space only, not Time. Secondly, the circuit, considered apart from distance traversed, has the extent of its continuity, of its tendency not to stop but to proceed indefinitely: but this is merely amplitude of Movement; search it, tell its vastness, and, still, Time has no more appeared, no more enters into the matter, than when one certifies a high pitch of heat; all we have discovered is Motion in ceaseless succession, like water flowing ceaselessly, motion and extent of motion.

Succession or repetition gives us Number - dyad, triad, etc. - and the extent traversed is a matter of Magnitude; thus we have Quantity of Movement - in the form of number, dyad, triad, decade, or in the form of extent apprehended in what we may call the amount of the Movement: but, the idea of Time we have not. That definite Quantity is merely something occurring within Time, for, otherwise Time is not everywhere but is something belonging to Movement which thus would be its substratum or basic-stuff: once more, then, we would be making Time identical with Movement; for the extent of Movement is not something outside it but is simply its continuousness, and we need not halt upon the difference between the momentary and the continuous, which is simply one of manner and degree. The extended movement and its extent are not Time; they are in Time. Those that explain Time as extent of Movement must mean not the extent of the movement itself but something which determines its extension, something with which the movement keeps pace in its course. But what this something is, we are not told; yet it is, clearly, Time, that in which all Movement proceeds. This is what our discussion has aimed at from the first: "What, essentially, is Time?" It comes to this: we ask "What is Time?" and we are answered, "Time is the extension of Movement in Time!"

On the one hand Time is said to be an extension apart from and outside that of Movement; and we are left to guess what this extension may be: on the other hand, it is represented as the extension of Movement; and this leaves the difficulty what to make of the extension of Rest - though one thing may continue as long in repose as another in motion, so that we are obliged to think of one thing Time that covers both Rest and Movements, and, therefore, stands distinct from either.

What then is this thing of extension? To what order of beings does it belong?

It obviously is not spatial, for place, too, is something outside it.