- Igal
- Bouillet
- Guthrie
- MacKenna
Igal
12 —Pero ¿cómo es posible que el bien de los números consista en que cada uno sea uno, si son inanimados?
—Este problema es común a todos los seres inanimados. Y si alguien dice que los números no existen en absoluto, respondemos que nosotros hablábamos de Seres reales en cuanto cada uno era uno. Y si nos preguntan cómo puede el punto participar en el Bien, respondemos que si suponen que el punto existe en sí mismo, entonces, si es inanimado, la pregunta es la misma que sobre los demás seres inanimados, mientras que si suponen que el punto existe en otro, por ejemplo en el círculo, entonces el bien del punto es el círculo; su tendencia es al círculo, y aspira al Bien, como puede, a través del círculo.
—Y los géneros ¿cómo son géneros? ¿Fragmentándose cada uno de ellos?.
—No, cada uno existe entero en la especie de la que es género.
—¿Y cómo puede seguir siendo uno?
—Lo que es uno genéricamente es un todo en cuanto existente en muchos.
—Entonces, ¿existe sólo en sus participantes?
—No, existe en sí mismo y en sus participantes. Pero tal vez esto se aclarará más adelante.
Bouillet
XII. Nous admettons qu’en tendant vers l’Un tout tend vers le Bien. Mais comment se peut-il que, pour le nombre, qui est inanimé, le bien consiste aussi à être un (32)? Et cette question peut se faire également au sujet de tous les autres êtres inanimés. Si l’on nous disait que de tels êtres ne possèdent pas l’existence, nous répondrions que nous traitons ici des êtres en tant que chacun d’eux est un. Si l’on nous demandait comment le point peut participer du bien, nous demanderions à notre tour s’il s’agit du point en soi, et alors nous répondrions que c’est la même question que pour les autres choses de la même espèce ; mais s’il s’agit du point considéré comme existant dans quelque objet, dans le cercle par exemple, nous dirons qu’alors pour lui le bien est le bien du cercle même ; que c’est là le but auquel il aspire, et qu’il y tend autant qu’il le peut par l’intermédiaire du cercle.
Mais comment se représenter de tels genres? Ces genres sont-ils tous susceptibles d’être divisés, ou bien sont-ils tout entiers dans chacun des objets qu’ils comprennent, et alors comment l’un s’y trouve-t-il? L’un s’y trouve comme genre, de même que le tout se trouve dans une pluralité. — L’un ne se trouve-t-il donc que dans les objets qui participent de lui? Il se trouve non-seulement dans ces objets, mais encore en soi. Ce point sera d’ailleurs éclairci plus tard.
Guthrie
BY TENDING TOWARDS THE ONE, EVERYTHING TENDS TOWARDS THE GOOD.
12. We therefore assert (that by moving towards unity everything moves towards the Good). How can it be, however, that Goodness should consist in coming closer to unity, even for number, which is inanimate? This question might as well be asked about any inanimate object whatever. If we were told that such (beings) do not enjoy (existence), we might answer that we are here treating of beings according to their proximity to unity only. If, for instance, we were asked how a point can participate in the Good, we might answer by a retort, asking whether we are dealing with the Point in itself. Then we would answer by the observation that the state of affairs was the same for all things of the same kind. If however we were pressed about the point considered as existing in some object, as, for instance, in the circle, we would answer that for such a point, the Good is the good of the circle (of which it forms part); that such is the Good towards which it aspires, and that it seeks that as far as possible through the intermediation of the circle.
THESE GENERA EXIST IN BOTH THE SUBORDINATE OBJECTS, AND THEMSELVES.
But how could we realize such genera? Are all these genera susceptible of division, or do they lie entire within each of the objects they comprehend? If so, how does this unity find itself? Unity exists therein as a genus, just as the whole exists within the plurality.
Does unity exist only in the objects that participate therein? Not only in these objects, but also in itself. This point will be studied later.
MacKenna
12. Enough upon that side of the question. But how does the perfection [goodness] of numbers, lifeless things, depend upon their particular unity? Just as all other inanimates find their perfection in their unity.
If it should be objected that numbers are simply non-existent, we should point out that our discussion is concerned [not with units as such, but] with beings considered from the aspect of their unity.
We may again be asked how the point – supposing its independent existence granted – participates in perfection. If the point is chosen as an inanimate object, the question applies to all such objects: but perfection does exist in such things, for example in a circle: the perfection of the circle will be perfection for the point; it will aspire to this perfection and strive to attain it, as far as it can, through the circle.
But how are the five genera to be regarded? Do they form particulars by being broken up into parts? No; the genus exists as a whole in each of the things whose genus it is.
But how, at that, can it remain a unity? The unity of a genus must be considered as a whole-in-many.
Does it exist then only in the things participating in it? No; it has an independent existence of its own as well. But this will, no doubt, become clearer as we proceed.