The Lives and Opinions of Eminent Philosophers by Diogenes Laërtius (best free ebook reader txt) 📕

dissolution of combined bodies, there must be something which continues solid and indestructible, of such a kind that it will not change either into what does not exist, or out of what does not exist; but that it results either from a simple displacement of parts, which is the most usual case, or from the addition or subtraction of certain particles. It follows from that, that that which does not admit of any change in itself, is imperishable, participates in no respect in the nature of changeable things, and in a word, has its dimensions and forms immutably determined. And this is proved plainly enough, because even in the transformations which take place under our eyes, in consequence of the retrenchment of certain parts, we can still recognise the form of these constituent parts; while those qualities which are not constituent parts do not remain like the form, but perish in the dissolution of the combination. The attributes which we have indicated suffice to explain all the differences of combined bodies; for we must inevitably leave something indestructible, lest everything should resolve itself into nonexistence.

However, one must not believe that every kind of magnitude exists in atoms, lest we find ourselves contradicted by phenomena. But we must admit that there are atoms of different magnitude because, as that is the case, it is then more easy to explain the impressions and sensations; at all events, I repeat, it is not necessary for the purpose of explaining the differences of the qualities, to attribute to atoms every kind of magnitude.

We must not suppose either, that an atom can become visible to us; for, first of all, one does not see that that is the case, and besides, one cannot even conceive how an atom is to become visible; besides, we must not believe that in a finite body there are particles of every sort, infinite in number; consequently, one must not only reject the doctrine of infinite divisibility in parcels smaller and smaller, lest we should be reducing everything to nothing, and find ourselves forced to admit that in a mass composed of a crowd of elements, existence can reduce itself to nonexistence. But one cannot even suppose that a finite object can be susceptible of transformations ad infinitum, or even of transformation into smaller objects than itself; for when once one has said that there are in an object particles of every kind, infinite in number, there is absolutely no means whatever of imagining that this object can have only a finite magnitude; in fact it is evident that these particles, infinite in number, have some kind of dimension or other, and whatever this dimension may be in other respects, the objects which are composed of it will have an infinite magnitude; in presenting forms which are determined, and limits which are perceived by the senses, one conceives easily, without its being necessary to study this last question directly, that this would be the consequence of the contrary supposition, and that consequently one must come to look at every object as infinite.

One must also admit that the most minute particle perceptible to the sense is neither absolutely like the objects which are susceptible of transformation, nor absolutely different from them. It has some characteristics in common with the object which admit of transformation, but it also differs from them, inasmuch as it does not allow any distinct parts to be discerned in it. When then, in virtue of these common characteristics and of this resemblance, we wish to form an idea of the smallest particle perceptible by the senses, in taking the objects which change for our terms of comparison, it is necessary that we should seize on some characteristic common to these different objects. In this way, we examine them successively, from the first to the last, not by themselves, nor as composed of parts in juxtaposition, but only in their extent; in other words, we consider the magnitudes by themselves, and in an abstract manner, inasmuch as they measure the greater a greater extent and the smaller a smaller extent. This analogy applies to the atom, as far as we consider it as having the smallest dimensions possible. Evidently by its minuteness, it differs from all sensible objects, still this analogy is applicable to it; in a word, we establish by this comparison, that the atom really has some extent, but we exclude all considerable dimensions, for the sake of only investing it with the smallest proportions.141

We must also admit, in taking for our guide the reasoning which discourses to us things which are invisible to the senses, that the most minute magnitudes, those which are not compound magnitudes, and which form the limit of sensible extent, are the first measure of the other magnitudes which are only called greater or less in their relation to the others. For these relations which they maintain with these particles, which are not subject to transformation, suffice to give them this characteristic of first measure. But they cannot, like atoms, combine themselves and form compound bodies in virtue of any motion belonging to themselves.

Moreover, we must not say (while speaking of the infinite) that such or such a point is the highest point of it, or the lowest. For height and lowness must not be predicated of the infinite. We know in reality that if, wishing to determine the infinite, we conceive a point above our head, this point, whatever it may be, will never appear to us to have the character in question: otherwise, that which would be situated above the point so conceived as the limit of the infinite, would be at the same moment, and by virtue of its relation to the same point, both high and low; and this is impossible to imagine.

It follows that thought can only conceive that one single movement of transference,