LESSON 15

The Meaning of Quantity. Its Kinds. The Essentially and Accidentally Quantitative

Chapter 13: 1020a 7-1020a 32

             482. Quantity [or the quantitative] means what is divisible into constituent parts, both or one of which is by nature a one and a particular thing.

             483. Therefore plurality [or multitude] is a kind of quantity if it is numerable; and so also is magnitude [or continuous quantity] if it is measurable. Plurality means what is potentially divisible into non-continuous parts; and magnitude means what is divisible into continuous parts. Again, of the kinds of magnitude, what is continuous in one dimension is length; in two, breadth; and in three, depth. And of these, limited plurality is number; limited length, a line; limited breadth, a surface; and limited depth, a body [or solid].

             484. Again, some things are said to be quantitative essentially and others accidentally; for example, a line is quantitative essentially, but the musical accidentally.

             485. And of those things which are quantitative essentially, some are such by reason of their substance, as a line is quantitative quidditatively. For in the definition expressing its quiddity some kind of quantity is found. Others are properties and states of this kind of substance, as much and little, long and short, broad and narrow, deep and shallow, heavy and light, and the like. And large and small, and larger and smaller, whether they are spoken of essentially or in relation to each other, are properties of quantity. And these terms are also transferred to other things.

             486. But of things which are quantitative accidentally, some are said to be such in the sense in which the musical and the white are quantitative, i.e., because the subject to which they belong is quantitative. Others are said to be quantitative in the sense in which motion and time are, for these too are said to be in a sense quantitative and continuous because the things of which they are the properties are divisible. And I mean not the thing which is moved, but the space through which it is moved. For since space is quantitative, motion is also quantitative; and through it, i.e., motion, time is also quantitative.

COMMENTARY

             977. Since being is divided not only into potency and actuality but also into the ten categories, having given the different senses of the term potency (467-70:C 954-60), the Philosopher begins here to give the different senses of the terms which designate the categories. First (482:C 977), he considers the term quantity; and second (487:C 987), the term quality ("Quality means"). Third (492:C 1001), he gives the different meanings of the term relative ("Some things"). He omits the other categories because they are limited to one class of natural beings, as is especially evident of action and passion, and of place and time.

             In regard to the first he does three things. First, he gives the meaning of quantity. He says that quantity means what is divisible into constituent parts. Now this is said to distinguish this kind of division from that of compounds. For a compound is dissolved into the elements, and these are not present in it actually but only virtually. Hence, in the latter case there is not just division of quantity, but there must also be some alteration by means of which a compound is dissolved into its elements. He adds that both or one of these constituents is by nature "a one," that is, something which is pointed out. He says this in order to exclude the division of a thing into its essential parts, which are matter and form; for neither one of these is fitted by nature to be a particular thing of itself.

             978. Therefore plurality (483).

             Second, he gives the kinds of quantity; and of these there are two primary kinds: plurality or multitude, and magnitude or measure. And each of these has the character of something quantitative inasmuch as plurality is numerable and magnitude is measurable. For mensuration pertains properly to quantity. However, plurality is defined as what is divisible potentially into parts which are not continuous; and magnitude as what is divisible into parts which are continuous. Now this occurs in three ways, and therefore there are three kinds of magnitude. For if magnitude is divisible into continuous parts in one dimension only, it will be length; if into two, width; and if into three, depth. Again, when plurality or multitude is limited, it is called number. And a limited length is called a line; a limited width, surface; and a limited depth, body. For if multitude were unlimited, number would not exist, because what is unlimited cannot be numbered. Similarly, if length were unlimited, a line would not exist, because a line is a measurable length (and this is why it is stated in the definition of a line that its extremities are two points). The same things holds true of surface and of body.

             979. Again, some things (484).

             Third, he gives the different ways in which things are quantitative; and in regard to this he does three things. First, he draws a distinction between what is essentially quantitative, as a line, and what is accidentally quantitative, as the musical.

             980. And of those (485).

             Second, he gives the different senses in which things are essentially quantitative, and there are two of these. For some things are said to be such after the manner of a substance or subject, as line, surface or number; for each of these is essentially quantitative because quantity is given in the definition of each. For a line is a limited quantity divisible in length. The same is true of the other dimensions.

             981. And other things belong essentially to the genus of quantity and are signified after the manner of a state or property of such substance, i.e., of a line, which is essentially quantitative, or of other similar kinds of quantity. For example, much and little are signified as properties of number; long and short, as properties of a line; broad and narrow, as properties of surface; and high and low or deep, as properties of body. And the same is true of heavy and light according to the opinion of those who said that having many surfaces, or atoms, causes bodies to be heavy, and having few causes them to be light. But the truth of the matter is that heavy and light do not pertain to quantity but to quality, as he states below (489:C 993). The same thing is true of other such attributes as these.

             982. There are also certain attributes which are common properties of any continuous quantity, as large and small, and larger and smaller, whether these are taken "essentially," i.e., absolutely, or "in relation to each other," as something is said to be large and small relatively, as is stated in the Categories. But these terms which signify the properties of quantity pure and simple are also transferred to other things besides quantities. For whiteness is said to be large and small, and so also are other accidents of this kind.

             983. But it must be borne in mind that of all the accidents quantity is closest to substance. Hence some men think that quantities, such as line, number, surface and body are substances. For next to substance only quantity can be divided into distinctive parts. For whiteness cannot be divided, and therefore it cannot be understood to be individuated except by its subject. And it is for this reason that only in the genus of quantity are some things designated as subjects and others as properties.

             984. But of things (486).

             Then he gives the different senses in which things are said to be accidentally quantitative. These senses are two. In one sense, things are said to be accidentally quantitative only because they are accidents of some quantity; for example, white and musical are said to be quantitative because they are accidents of a subject which is quantitative.

             985. In another sense, some things are said to be accidentally quantitative, not because of the subject in which they exist, but because they are divided quantitatively as a result of the division of some quantity; for example, motion and time (which are said to be quantitative and continuous because of the subjects to which they belong) are divisible and are themselves divided as a result of the division of the subjects to which they belong. For time is divisible and continuous because of motion, and motion is divisible because of magnitude--not because of the magnitude of the thing which is moved, but because of the magnitude of the space through which it is moved. For since that magnitude is quantitative, motion is also quantitative; and since motion is quantitative, it follows that time is quantitative. Hence these can be said to be quantitative not merely accidentally but rather subsequently, inasmuch as they receive quantitative division from something prior.

             986. However, it must be noted that in the Categories the Philosopher held that time is essentially quantitative, while here he holds that it is accidentally quantitative. There he distinguished between the species of quantity from the viewpoint of the different kinds of measure. For time, which is an external measure, has the character of one kind of measure, and continuous quantity, which is an internal measure, has a different one. Hence in the Categories time is given as another species of quantity, whereas here he considers the species of quantity from the viewpoint of the being of quantity. Therefore those things which only receive their quantitative being from something else he does not give here as species of quantity, but as things which are accidentally quantitative, as motion and time. But motion has no other manner of measure than time and magnitude. Hence neither in this work nor in the Categories does he give it as a species of quantity. Place, however, is given there as a species of quantity. But it is not given as such here because it has a different manner of measure, although not a different quantitative being.