Metaphysics

​In all these, then, the measure and starting-point is some one and indivisible thing, since even in the case of lines they use the foot-length as indivisible. For everywhere they seek as measure some one and indivisible thing; and this is that which is simple either in quality or in quantity. Where, then, it seems not to be possible to subtract or to add, this measure is exact (wherefore that of number is most exact; for they assume the unit to be indivisible in every way); but in other cases they imitate such a thing. For from a stade and a talent and always from a greater thing, anything added or subtracted would escape notice more easily than from a smaller thing; so that the first point at which, according to perception, it is not possible [to do so], this all men make their measure of liquids and solids, of weight and of magnitude; and they think they know the quantity then, when they know it by means of this measure. And indeed they measure motion too by the simple motion and the fastest (for this takes the least time); wherefore in astronomy such a “one” is the starting-point and measure (for they assume the motion of the heaven to be uniform and the fastest, and by comparison with this they judge the others), and in music the quarter-tone, because it is the least, and in speech the element. And all these are a “one” in this way, not because the “one” is some common universal, but in the way we have said.—But the measure is not always one in number, but sometimes more; for example, the quarter-tones are two, those which are not determined by hearing but in the ratios, and the voices by which we measure are more than one, and the diagonal and the side are measured by two [different measures], and so are all magnitudes. Thus, indeed, the “one” is the measure of all things, because we know that of which the substance consists by dividing it either in respect of quantity or of form. And for this reason the “one” is indivisible, because the first of each class of things is indivisible. But not every indivisible is so in the same way, as for example the foot and the unit; but the latter is indivisible in every way, while the former must be assumed to be indivisible in respect of perception, as has been said already; for perhaps every continuous thing is divisible. And the measure is always homogeneous; for the measure of magnitudes is a magnitude, and in particular that of length is a length, of breadth a breadth, of sound a sound, of weight a weight, of units a unit. For we must understand it in this way, and not that the measure of numbers is a number; and yet it should be so, if the analogy held. But the analogy does not hold in the same way, but it is as if one should claim that the measure of units is units and not a unit; but number is a plurality of units. And we speak of science and perception as a measure of things for the same reason, because we know something by them, although they are measured rather than measure. But it happens to us as if, when another was measuring us, we knew how big we are by his applying the cubit-measure to us so far. And Protagoras says that man is the measure of all things, as if he had said the knower or the perceiver; and these because they possess, the one perception and the other science, which we say are the measures of the subjects. Thus, while saying nothing extraordinary, they appear to be saying something. It is clear, then, that to be one, if we define it according to the name, is most of all to be a measure, and most properly of quantity, and next of quality; and it will be of this character if it is indivisible in quantity in the one case, and in quality in the other; wherefore the “one” is indivisible, either absolutely or as being one.