Plotino - Tratado 37,1 (II, 7, 1) — Exame preliminar das aporias da mistura

1. Consideremos ahora lo que se llama la mezcla total de los cuerpos. Si se mezcla un líquido a otro líquido, ¿es posible que cada uno de ellos penetre totalmente a través del otro o que el primero lo haga a través del segundo? Ninguna de las dos soluciones ofrece diferencia apreciable.

Dejemos aparte a quienes estiman la mezcla como una simple vecindad de partículas, lo cual sería, más que una mezcla, una verdadera reunión, dado que, en la mezcla, todo debe resultar homogéneo, y cada una de las partes, aun la más pequeña, habrá de salir de lo mezclado. Otros al afirman, en cambio, que sólo se mezclan las cualidades, con lo que la materia de un cuerpo se presenta en vecindad con la de otro, en tanto las cualidades de cada uno de ellos se introducen en el otro. Y quizá parezcan convincentes en su crítica de la mezcla total, pues según ellos las grandes magnitudes vendrían a parar en partículas, si no subsistiese ningún intervalo para ninguno de los cuerpos y la división se prosiguiese de manera continua hasta que cada uno de ellos atravesase al otro en su totalidad. Es claro además que, cuando los cuerpos están mezclados, ocupan un lugar mayor que cada uno de los cuerpos aisladamente, o tanto, al me nos, como si estuviesen en vecindad. Si los cuerpos se penetrasen totalmente, convendría, dicen, que el volumen del cuerpo en el que otro ha sido arrojado permaneciese el mismo; ya que cuando el lugar de lo mezclado no resulta mayor que el de uno de los cuerpos, establecen como causa de ello que una cantidad de aire ha salido de aquel cuerpo, cuyo lugar fue ocupado por el otro cuerpo. ¿Cómo, además, un cuerpo pequeño podría penetrar en otro mayor y contener a éste en totalidad? Aducen otras muchas razones por el estilo.

En cuanto a quienes admiten la mezcla total tal vez pudiesen decir que los cuerpos se dividen, pero que no llegan a desmenuzarse en partículas, aun en el caso de verificarse la mezcla total. Así, dicen, los sudores del cuerpo no producen en él hendiduras ni brechas de ninguna clase. ¿Cabría afirmar en este caso que la naturaleza ha hecho el cuerpo de tal manera que nada impide que los sudores le atraviesen? Ocurre cos algunas cosas producidas artificialmente, cuando son finas y continuas, que se las ve penetradas enteramente por un líquido e incluso atravesadas por el de parte a parte. Siendo estas cosas cuerpos, ¿cómo es ello posible? Ciertamente no, es fácil de imaginar cómo un cuerpo atraviesa a otro sin necesidad le dividirlo; aunque parece claro que, si se dividiesen, ambos cuerpos se destruirían totalmente. Cuando se habla de que no se produce aumento en la mezcla, se da como causa la salida del aire de uno de los cuerpos; ahora bien si realmente se produce ese aumento, ¿qué impide decir, no obstante su dificultad, que cada uno de los cuerpos ha aportado su masa al conjunto y, con su magnitud, todas las cualidades que posee? Porque la magnitud no se destruye, lo mismo que las demás cualidades; y así como el cuerpo que resulta tiene una cualidad nueva proveniente de las cualidades de ambos cuerpos, del mismo modo hay que contar con otra magnitud, producida por la mezcla de las magnitudes de esos cuerpos. Pero entonces los que sostenían la tesis anterior podrían responder a estos últimos: si la materia de un cuerpo se sitúa en la vecindad de la materia de otro cuerpo, y lo mismo la masa del primer cuerpo, en la que cuenta la magnitud, en relación con la del segundo, la tesis sustentada viene a ser la nuestra; pero si, en cambio, la materia de uno de los cuerpos, junto con su primitiva magnitud, penetra enteramente en la del otro, lo que ocurra no puede guardar relación con la postura de dos líneas que se sitúan una a continuación de otra, y tocándose en sus partes extremas, en cuyo caso se produciría aumento de magnitud, sino con el hecho de que esas mismas líneas se adapten entre sí, con lo cual el aumento de magnitud no tendría lugar.

Veamos ahora el caso del cuerpo más pequeño, que penetra a través de todo el cuerpo más grande, y cuya mezcla parece evidente. Si esa mezcla no es manifiesta, puede afirmarse que el cuerpo pequeño no alcanza a la totalidad del grande, pero cuando se presenta claramente, no podría decirse otro tanto. Diríase mejor que se trata aquí de una extensión pequeña, y no parece fácilmente admisible que un cuerpo tan pequeño se extienda de tal manera; porque, en este caso, aun sin ofrecer ningún cambio esencial, la magnitud del cuerpo se haría mucho mayor, como cuando del agua se produce aire.

1. Nous avons à examiner ici la mixtion où il y a ce que l’on appelle pénétration totale des corps (ἡ δι’ ὅλων λεγομένη τῶν σωμάτων κρᾶσις) .

Est-il possible que deux liquides soient mêlés ensemble de telle sorte qu’ils se pénètrent l’un l’autre totalement, ou que l’un des deux seulement pénètre l’autre? Car il importe peu que le fait ait lieu d’une façon ou de l’autre.

Écartons d’abord l’opinion de ceux qui font consister la mixtion dans la juxtaposition (παράθεσις) [1], parce que c’est là un mélange plutôt qu’une mixtion. En effet, la mixtion doit rendre le tout homogène (ὁμοιομερὲς τὸ πᾶν), de telle sorte que les molécules même les plus petites soient composées chacune des éléments qui composent le mixte.

Quant aux philosophes [Péripatéticiens] qui prétendent que, dans un mixte, les qualités seules se mêlent (τὰς ποιότητας μόνας κιρνάντες) , et que les étendues matérielles des deux corps ne sont que juxtaposées, pendant que les qualités propres à chacun d’eux sont répandues dans toute la masse, ils semblent établir la justesse de leur opinion en attaquant la doctrine qui admet que dans la mixtion deux corps se pénètrent totalement [2]. — Les molécules des deux corps [ objectent-ils ] finiront par perdre toute grandeur dans cette division continue qui ne laisse nul intervalle entre les parties d’aucun des deux corps : car la division est continue puisque les deux corps se pénètrent l’un l’autre mutuellement dans toutes leurs parties. En outre, souvent le mixte occupe une étendue plus grande que chaque corps pris séparément, aussi grande que s’il y avait une simple juxtaposition ; or, si deux corps se pénétraient totalement, le mixte qu’ils constituent n’occuperait pas plus de place que l’un d’eux pris séparément. Quant au cas où deux corps n’occupent pas plus de place qu’un seul, il s’explique, selon les mêmes philosophes, par la sortie de l’air, sortie qui permet à un corps de pénétrer dans les pores de l’autre. Enfin, si l’on mêle deux corps dont les étendues sont inégales , comment le corps le plus petit peut-il s’étendre assez pour se répandre dans toutes les parties du plus grand , Il y a encore cent autres raisons du même genre.

Passons aux philosophes [Stoïciens] qui prétendent que deux corps qui constituent un mixte se pénètrent totalement. Voici ce qu’ils ont à dire à l’appui de leur opinion : Lorsque deux corps se pénètrent totalement, ils sont divisés sans qu’il y ait cependant une division continue [qui fasse perdre toute grandeur à leurs molécules]. En effet, la sueur sort de tout le corps humain sans qu’elle le divise ni, que celui–ci soit percé de trous. Si l’on objecte que la nature peut avoir donné à notre corps une disposition qui permet à la sueur de sortir facilement, [les Stoïciens] répondront que certaines substances, lorsqu’elles sont travaillées par les artisans qui les réduisent en lames minces, se laissent pénétrer et imbiber dans toutes leurs parties d’une liqueur qui passe d’une surface à l’autre [3].

Comme ces substances sont des corps, il n’est pas facile de comprendre comment un élément peut pénétrer l’autre sans en séparer les molécules ; d’un autre côté, s’il y a division totale, les deux corps se détruiront mutuellement [parce que, par suite de cette division, leurs molécules perdront toute grandeur]. --- Lorsque deux corps mêlés ensemble ne tiennent pas plus de place que chacun d’eux pris séparément, [les Stoïciens] semblent obligés d’accorder à leurs adversaires que la sortie de l’air est la cause de ce phénomène. - Dans le cas où le composé tient plus de place que chaque élément seul, on peut soutenir, quoique avec peu de vraisemblance, que, quand un corps en pénètre un autre, l’étendue doit augmenter avec les autres qualités, qu’elle ne saurait être anéantie pas plue que les autres qualités, et que, si deux qualités mêlées ensemble en produisent une autre, deux étendues mêlées ensemble doivent aussi en produire une troisième. Ici [les Péripatéticiens] peuvent répondre [aux Stoïciens] Si vous juxtaposez les substances ainsi que les masses qui possèdent l’étendue , vous adoptez notre opinion. SI l’une des deux masses, avec l’étendue qu’elle avait d’abord, pénètre l’autre masse tout entière, l’étendue, au lieu d’augmenter comme dans le cas où l’on place une ligne à côté d’une autre ligne en joignant leurs extrémités, ne s’accroîtra pas plus que quand on fait coïncider deux droites en les superposant. — Reste le cas où l’on mêle une petite quantité à une grade, un gros corps à un très petit : [les Péripatéticiens] croient impossible que le gros corps se répande dans toutes les parties du petit. Quand la mixtion n’est pas évidente, [les Péripatéticiens] peuvent prétendre que le plus petit corps ne s’unit pas avec toutes les parties du plus grand. Quand la mixtion est évidente, ils peuvent l’expliquer par l’extension (ἐκτάσις) des masses, quoiqu’il soit peu probable qu’une petite masse prenne une telle extension, surtout quand on attribue au corps composé une étendue plus grande, sans admettre cependant qu’il se transforme, comme l’eau se transforme en air.

REFUTATION OF ANAXÁGORAS AND DEMOCRITUS  .

1. The subject of the present consideration is mixture to the point of total penetration of the different bodies. This has been explained in two ways: that the two liquids are mingled so as mutually to interpenetrate each other totally, or that only one of them penetrates the other. The difference between these two theories is of small importance. First we must set aside the opinion of (Anaxágoras   and Democritus), who explain mixture as a juxtaposition, because this is a crude combination, rather than a mixture. Mixture should render the whole homogeneous, so that even the smallest molecules might each be composed of the various elements of the mixture.

REFUTATION OF ARISTOTLE   AND ALEXANDER OF APHRODISIAS  .

As to the (Peripatetic) philosophers who assert that in a mixture only the qualities mingle, while the material extension of both bodies are only in juxtaposition, so long as the qualities proper to each of them are spread throughout the whole mass, they seem to establish the Tightness of their opinion by attacking the doctrine which asserts that the two bodies mutually interpenetrate in mixture. (They object) that the molecules of both bodies will finally lose all magnitude by this continuous division which will leave no interval between the parts of either of the two bodies; for if the two bodies mutually interpenetrate each other in every part, their division must become continuous. Besides, the mixture often occupies an extent greater than each body taken separately, and as great as if mere juxtaposition had occurred. Now if two bodies mutually interpenetrate totally, the resulting mixture would occupy no more place than any one of them taken separately. The case where two bodies occupy no more space than a single one of them is by these philosophers explained by the air’s expuls;on, which permits one of the bodies to penetrate into the pores of the other. Besides, in the case of the mixture of two bodies of unequal extent, how could the body of the smaller extend itself sufficiently to spread into all the parts of the greater? There are many other such reasons.

REFUTATION OF THE STOICS.

We now pass to the opinions of (Zeno   and the other Stoic) philosophers, who assert that two bodies which make up a mixture mutually interpenetrate each other totally. They suppport this view by observing that when the bodies interpenetrate totally, they are divided without the occurrence of a continuous division (which would make their molecules lose their magnitude). Indeed, perspiration issues from the human body without its being divided or riddled with holes. To this it may be objected that nature may have endowed our body with a disposition to permit perspiration to issue easily. To this (the Stoics) answer that certain substances (like ivory), which when worked into thin sheets, admit, in all their parts, a liquid (oat-gruel) which passes from one surface to the other. As these substances are bodies, it is not easy to understand how one element can penetrate into another without separating its molecules. On the other hand, total division must imply mutual destruction (because their molecules would lose all magnitude whatever). When, however, two mingled bodies do not together occupy more space than either of them separately (the Stoics) seem forced to admit to their adversaries that this phenomenon is caused by the displacement of air.

EXPLANATION OF MIXTURE THAT OCCUPIES MORE SPACE THAN ITS ELEMENTS.

In the case where the compound occupies more space than each element separately, it might (though with little probability), be asserted, that, since every body, along with its other qualities, implies size, a local extension must take place. No more than the other qualities could this increase perish. Since, out of both qualities, arises a new form, as a compound of the mixture of both qualities; so also must another size arise, the mixture combining the size out of both. Here (the Peripatetics) might answer (the Stoics): "If you assert a juxtaposition of substances, as well as of the masses which possess extension, you are actually adopting our opinions. If however one of the masses, with its former extension, penetrate the entire mass of the other, the extension, instead of increasing, as in the case where one line is added to another by joining their extremities, will not increase any more than when two straight lines are made to coincide by superimposing one on the other."

CASE OF MIXTURE OF UNEQUAL QUANTITIES.

The case of the mixture of a smaller quantity with a greater one, such as of a large body with a very small one, leads (the Peripatetics) to consider it impossible that the great body should spread in all the parts of the small one. Where thé mixture is not evident, the (Peripatetics) might claim that the smaller body does not unite with all the parts of the greater. When however the mixture is evident, they can explain it by the extension of the masses, although it be very doubtful that a small mass would assume so great an extension, especially when we attribute to the composite body a greater extent, without nevertheless admitting its transformation, as when water transforms itself into air.

1. Some enquiry must be made into what is known as the complete transfusion of material substances.

Is it possible that fluid be blended with fluid in such a way that each penetrate the other through and through? or - a difference of no importance if any such penetration occurs - that one of them pass completely through the other?

Those that admit only contact need not detain us. They are dealing with mixture, not with the coalescence which makes the total a thing of like parts, each minutest particle being composed of all the combined elements.

But there are those who, admitting coalescence, confine it to the qualities: to them the material substances of two bodies are in contact merely, but in this contact of the matter they find footing for the qualities of each.

Their view is plausible because it rejects the notion of total admixture and because it recognizes that the masses of the mixing bodies must be whittled away if there is to be mixture without any gap, if, that is to say, each substance must be divided within itself through and through for complete interpenetration with the other. Their theory is confirmed by the cases in which two mixed substances occupy a greater space than either singly, especially a space equal to the conjoined extent of each: for, as they point out, in an absolute interpenetration the infusion of the one into the other would leave the occupied space exactly what it was before and, where the space occupied is not increased by the juxtaposition, they explain that some expulsion of air has made room for the incoming substance. They ask further, how a minor quantity of one substance can be spread out so as to interpenetrate a major quantity of another. In fact they have a multitude of arguments.

Those, on the other hand, that accept "complete transfusion," might object that it does not require the reduction of the mixed things to fragments, a certain cleavage being sufficient: thus, for instance, sweat does not split up the body or even pierce holes in it. And if it is answered that this may well be a special decree of Nature to allow of the sweat exuding, there is the case of those manufactured articles, slender but without puncture, in which we can see a liquid wetting them through and through so that it runs down from the upper to the under surface. How can this fact be explained, since both the liquid and the solid are bodily substances? Interpenetration without disintegration is difficult to conceive, and if there is such mutual disintegration the two must obviously destroy each other.

When they urge that often there is a mixing without augmentation their adversaries can counter at once with the exit of air.

When there is an increase in the space occupied, nothing refutes the explanation - however unsatisfying - that this is a necessary consequence of two bodies bringing to a common stock their magnitude equally with their other attributes: size is as permanent as any other property; and, exactly as from the blending of qualities there results a new form of thing, the combination of the two, so we find a new magnitude; the blending gives us a magnitude representing each of the two. But at this point the others will answer, "If you mean that substance lies side by side with substance and mass with mass, each carrying its quantum of magnitude, you are at one with us: if there were complete transfusion, one substance sinking its original magnitude in the other, we would have no longer the case of two lines joined end to end by their terminal points and thus producing an increased extension; we would have line superimposed upon line with, therefore, no increase."

But a lesser quantity permeates the entire extent of a larger; the smallest is sunk in the greatest; transfusion is exhibited unmistakably. In certain cases it is possible to pretend that there is no total penetration but there are manifest examples leaving no room for the pretence. In what they say of the spreading out of masses they cannot be thought very plausible; the extension would have to be considerable indeed in the case of a very small quantity [to be in true mixture with a very large mass]; for they do not suggest any such extension by change as that of water into air.