Chapter 6

Of quantities, some are discrete, others continuous; and some are composed of parts which have position in relation to one another, others of parts which do not have position. Discrete are, for example, number and language (logos); continuous are the line, the surface, the body, and, besides these, time and place.

For the parts of a number have no common boundary at which those parts join together. For instance, if five is a part of ten, the two fives do not join at any common boundary, but are separate; and three and seven likewise join at no common boundary. Nor, in general, could you find in the case of number any common boundary of the parts; they are always separate. Hence number is one of the discrete quantities.

Similarly, language too is one of the discrete quantities. That language is a quantity is evident, for it is measured by the short and the long syllable; and I mean here language that comes to be with the voice, spoken aloud. For its parts join at no common boundary: there is no common boundary at which the syllables join, but each of them is separate in its own right.

A line, on the other hand, is continuous; for it is possible to find a common boundary at which its parts join, namely a point, and for a surface a line, since the parts of a plane join at some common boundary. Similarly, in the case of a body you could find a common boundary, a line or a surface, at which the parts of the body join.

Time and place also belong to this kind. For present time joins on to both past time and future time. Again, place is one of the continuous quantities; for the parts of a body occupy a certain place, and these parts join at some common boundary. Hence the parts of the place, which the several parts of the body occupy, join at the same boundary at which the parts of the body themselves join. And so place too would be continuous, since its parts join at one common boundary.

Again, some quantities are composed of parts which have position in relation to one another, others of parts which do not have position. The parts of a line, for example, have position in relation to one another: each of them lies somewhere, and you could mark them off and state where each lies in the plane and which of the remaining parts it joins on to. Similarly the parts of a plane have a certain position, for in the same way one could state where each of them lies and which of them join one another; and it is the same with the parts of a solid and with those of a place.

But in the case of number one could not show that its parts have any position in relation to one another, or that they lie somewhere, or which of the parts join one another. Nor can one do so for the parts of time, since none of the parts of time endures; and how could what does not endure have any position? Rather, you would say that they have a certain order, in that one part of time is earlier and another later. And it is the same with number, in that one is counted before two, and two before three; in this way it would have a certain order, but position you would hardly find in it. And language likewise: none of its parts endures, but once a part has been uttered it can no longer be grasped, so that there could be no position of its parts, given that none of them endures. Some quantities, then, are composed of parts which have position, others of parts which do not have position.

Only the things we have mentioned are called quantities in the strict sense; all the rest are so called incidentally. For it is with an eye to these that we call the others quantities as well: white is called a large amount, for example, because the surface is large; an action is called long because the time is long; and a change is called great in the same way. For none of these is called a quantity in its own right. If, for instance, one is to state how long an action is, he will define it by the time, saying that it lasts a year or something of that sort; and in stating how much white there is, he will define it by the surface, for however large the surface is, that is how much white he will say there is. Hence only the things mentioned are called quantities strictly and in their own right, and nothing else is so in its own right, but, if at all, only incidentally.

Again, a quantity has no contrary. In the case of definite quantities it is evident that there is no contrary, as with what is two cubits long, or three cubits long, or a surface, or anything of that sort; for nothing is contrary to them, unless someone were to say that much is contrary to little, or great to small. But none of these is a quantity; they belong rather to the relatives.

For nothing is called great or small in its own right, but through being referred to something else. A mountain, for example, is called small and a grain of millet large, because the one is larger than others of its own kind and the other smaller than others of its own kind. So the reference is to something else; for if a thing were called small or great in its own right, the mountain would never be called small and the grain of millet large. Again, we say that there are many people in the village but few in Athens, although the latter are many times more numerous, and many in the house but few in the theatre, although there are far more of them there. Again, 'two cubits long' and 'three cubits long' and each such expression signifies a quantity, but 'great' and 'small' signify not a quantity but rather a relative; for the great and the small are viewed in relation to something else. Hence it is clear that these belong to the relatives.

Again, whether one holds them to be quantities or not, they have no contrary. For how could anyone say that there is a contrary to what cannot be grasped in its own right, but is referred to something else? Further, if the great and the small are to be contraries, it will follow that the same thing admits contraries at the same time, and that they are contrary to themselves. For it happens that the same thing is at the same time both great and small: it is small in relation to this, but this very same thing is great in relation to something else. So it turns out that the same thing is both great and small at the same time, and hence that it admits contraries at the same time.

But nothing seems to admit contraries at the same time. In the case of substance, for example, it does seem to be receptive of contraries, yet nothing is at the same time sick and healthy; nor is anything at the same time white and black; nor is there anything else at all which admits contraries at the same time. It would also follow that they are contrary to themselves; for if the great is contrary to the small, and the same thing is at the same time great and small, then it would be contrary to itself. But it is impossible for anything to be contrary to itself. Therefore the great is not contrary to the small, nor much to little. So even if one says that these belong not to the relatives but to quantity, they will still have no contrary.

Contrariety in respect of quantity seems to belong most of all to place. For people hold the above to be contrary to the below, calling the region towards the centre 'below' because the centre is at the greatest distance from the limits of the world. And they seem to derive the definition of the other contraries from these; for they define as contraries those things within the same genus which are most distant from one another.

A quantity does not seem to admit of the more and the less. Take what is two cubits long: one thing is not more two cubits long than another. Nor is it so with number: three is no more three than five is, nor is five any more five than three is. Nor is one time said to be more a time than another. Nor, in general, is the more and the less spoken of in the case of any of the things mentioned. Hence quantity too does not admit of the more and the less.

What is most distinctive of quantity is its being called equal and unequal. For each of the quantities mentioned is called both equal and unequal: a body, for example, is called equal and unequal, and a time is called equal and unequal; and similarly each of the others we have spoken of is called equal and unequal. But of the remaining things, those which are not quantities would hardly be said to be equal and unequal. A disposition, for instance, is hardly called equal and unequal, but rather similar; and white is hardly called equal and unequal, but similar. Hence it would be most distinctive of quantity to be called equal and unequal.