Глава XLIX. О количественном и количестве

Quantity is a collection of units, but the unit itself is not called quantity. When one unit is connected to another unit, the number two is formed. Thus quantity is not a division, but an aggregate, a combination of units, for division occurs when we resolve two into their constituent units; when we say that one and one make two, then it will rather be a combination. It should be noted that quantity is the very measure and number, i.e. that by which measurement and calculation are carried out; quantitative is that which is subject to number and measure, i.e. measurable and quantifiable. As for the quantitative, it can be separate and continuous (connected). Continuous quantitative occurs when there is one thing being measured; for example, one tree is two cubits, three cubits long, or a stone, or something similar. Separate quantitative consists of objects separate from each other; for example, ten stones or ten dates: both stones and dates are separate objects from each other. Such a quantitative is said to be countable, unless, due to its insignificant size and the multitude of its constituent objects, it is measured by a modium 1 or a similar measure, like grain bread and something similar. Continuous quantities are defined as those quantities whose parts are interconnected within some common boundary. If, for example, there is a tree of two cubits, i.e. having two cubits, then in it the end of one cubit and the beginning of the other coincide, for they are connected and bound together and cannot be separated from each other. Separate quantities are defined as those whose parts are not combined in any general limit, such as ten stones. In fact, if you count five and five stones, they will not have a common limit that would connect them. If you insert something between five and five, then it will be eleven, not ten. This is indicated by the very name of the quantities: continuous and separate. Separate quantity includes number and speech. In this case, we call the countable by number, because the countable, as shown above, is certainly a separate quantity. Speech is also a separate quantity, for it is counted in words and does not have a common limit connecting its parts. Thus, if a speech consists of ten words and if it is divided into five and five words, then they will not have a common limit connecting them. If you insert something between these parts, then there will be eleven of them, not ten. In the same way, a word counted with the help of syllables does not have a common, connecting limit. For example, the word Socrates: between the syllable So- and the syllable -krat there is no common limit connecting them. There are five types of continuous quantities: body, surface, line, place, time. It should be noted that a point has no magnitude, because it is not measured or counted, since it does not have a single dimension. A line has one dimension, for it is a length that has no width. A line belongs to continuous quantities, because, being united, it is measured and its parts have a common limit by which they are connected to each other, namely the point located between them. The surface is the outer part of the body; [in Greek it is called επιφανεια from φαινεσθαι. A surface has two dimensions: length and width. Being unified, the surface is measured, and its parts have a common limit by which they are connected to each other, namely the line passing between them. It should be noted that a smooth and even surface is called a plane, while a non-smooth and curved surface is simply a surface. The body has three dimensions: length, width and depth, or thickness. Being unified, it is measured, and its parts have a common limit by which they are connected - namely the surface. Space is the surface of the air. For example, your place is the surface and limit of the air around you. As a surface, place is related to continuous quantities. Time is also measured by dividing into the past and the future, and these parts of time have a common limit - the present. The present itself has no magnitude. Thus, unit, point and present have no magnitude. All seven of the following objects are called quantities in the proper sense: 1) number, 2) speech, 3) time, 4) place, 5) line, 6) surface, 7) body. In the improper sense, we call quantities what is considered in them - action, movement, color, etc. Thus, if action and motion occur in a large number of objects, then we say that there is a lot of action and a lot of motion; if it’s small, then it’s not enough. In the same way, when we meet whiteness in many parts of the body, we say there is a lot of whiteness; meeting in a few, it is not enough. In addition, one quantity has a limit, while the other is infinite. A quantity that has a limit can be measured and calculated. Infinite magnitude surpasses every measure and every number. It is indifferently called both many and great: for example, we talk about the many mercy of God, about the great mystery of the economy of God the Word. It should be noted that Aristotle great and small, many and few, greater and less, less numerous and more numerous, double and half, etc. counts as a relationship. Thus we say that it is possible that the same thing, viewed from different angles, will belong to different categories. In fact, the names previously listed, since they express number and measure, refer to quantities; and since they have a certain relation to each other and since they are used in relation to each other, since they belong to relations, for the great is called large in relation to the small, double in relation to the half; the same applies to other things. But the body, considered as a physical body, belongs to the category of substance. And since it is a mathematical body, i.e. subject to measurement - to the category of quantity. In addition, the quantitative is divided into magnitude and set: the magnitude is measured, the set is calculated. Magnitude answers the question: how big? many to the question: how much? Quantity has three properties, which are called concomitant properties (παρακολουθματα). The first property is that in itself it has nothing opposite to itself. So the body in itself has nothing contrary to itself; since it happens to be white, it has its opposite, namely a black body. It should be noted that the number two has no other opposite number. In fact, if this were the case, then there would be many such numbers, namely, all numbers would be opposite to the number two. And then nature would turn out to be unfair, opposing many opposites to the same thing, for many opposites for the same thing is something unacceptable. The second property of quantity is that it does not accept definitions - more or less. So two dates are no more two than two people. What does not have an opposite to itself does not accept definitions - more or less. The third property, which belongs both to individual types of quantity and to all quantity, is that it can be equal and unequal. So, one line is equal and unequal to another line. Bread measure - half a measure, half a bucket. You might be interested in: