46 On the Items in the Category of Quantity
46: On the Items in the Category of Quantity Now that we have examined the different views on the question of whether quantity is to be identified with substance and quality, we should see which items are subsumed on each view under the genus of quantity.
First I shall deal with the account that seems to me to be Aristotle's. For Aristotle every term by means of which one can answer the question 'How much?' is to be placed in the genus of quantity; and here I am using the expression 'how much' in the broad sense, in the sense in which it is neutral as between 'how much' (in the narrow sense) and 'how many'.
Employing this interrogative one can ask how many things there are, so that the interrogative expresses plurality. Thus, I can ask, "How many are inside?" or "How many men are there?" The terms by which I can answer such questions are to be reckoned discrete quantities since they express plurality. In this way number is a discrete quantity; for if it be asked, "How many men are they?" and I respond by saying "Three," the term by which I respond expresses many things. In the same way speech is a discrete quantity; for when some one asks of speech, "How much?" his questicn should be understood to bear on the plurality of syllables and their quantity. It is otherwise of course when we ask about a letter or a syllable, for these can be only long or short. Thus, that by which we answer the question must be expressive of many; therefore, it is to be reckoned among discrete quantities.
But when the interrogative of quantity does not express many, it expresses one thing having parts which are spatially separated. But in that case it expresses distance according to length—and then we have the line; or distance according to breadth—and then we have the surface; or distance according to depth—and then we have the solid. Or the interrogative raises a question about place or time; thus, the two expressions 'place' and 'time' are to be placed in the genus of quantity.
But in the interests of clarity it should be noted that the expressions 'place' and 'time' do not belong in the genus of quantity per se as the other expressions do. In the case of 'place' and 'time' a special rationale is required.
Thus* time' is not to be subsumed under the genus of quantity per se as the other expressions are, for unlike the other expressions 'time' does not signify a thing existing in nature. Thus, 'line', 'surface', and 'solid' signify objects that really exist; they neither signify nor connote anything but the existing thing. But 'time' as well as 'motion' connotes something which exists neither actually nor potentially. Thus in the view we are examining, time is not something really distinct from motion, nor is motion really distinct
On the Items in the Category of Quantity from enduring objects. Indeed, 'motion' only designates that a thing has one part after another, that a thing is joined to one thing after another, or that were some body at rest to move towards it, a thing would have something else joined to it. Thus, motion is not something really different from enduring objects. The same point holds in the case of time. Thus 'time' is not placed in the genus of quantity except per accidens or because it is a passion of the permanent things which are in that category. And as Aristotle indicates in the fifth book of the Metaphysics, motion is subsumed under the genus of quantity in the same way.
In the case of 'place', a different rationale is required. 'Place' is not said to be in the genus of quantity per se, since place is not something distinct from surface. Furthermore, where a proposition expressing the place of some subject is true, 'place' cannot, in different modes and with different quantityconnoting expressions, be successively affirmed of that subject unless a similar alteration occurs in the predication of that subject of 'surface', 'line', or 'solid'. Thus, suppose the following is now true: 'A is a place'. Given the proposition 'A is a place', the propositions 'A is a greater place', 'A is a smaller place', 'A is longer', and 'A is shorter' cannot successively hold true unless propositions like the following also successively hold true: 'A is a greater surface', 'A is a smaller surface', 'A is a longer line', 'A is a shorter line', 'A is a longer solid', and 'A is a shorter solid'. Speaking generally, no such mutually incompatible qualifications can, by being added to 'place', be successfully affirmed of a place unless they can simultaneously be added to one of the following: 'line', 'surface', and 'solid'.
Thus, although the line, the solid, and the surface are not distinct things (just as place is not distinguished from them), they are more properly construed as per se constituents of the genus of quantity than place. Although the three signify the same thing, the propositions 'A is longer' and 'A is shorter', for example, can be successively true while none of the following are true: 'A is wider', 'A is more narrow', 'A has a greater depth', and 'A has a lesser depth'.
It is clear then that 'place' is not a predicable distinct from 'line', 'surface', and 'body', while these last three are predicables different from each other.
It is also clear that the first and really crucial division and distinction among the things found in the genus of quantity is based on the fact that a term which can be used to answer the question 'How much?' (in the broad sense) expresses either many things (and this gives us number) or one thing composed of many things (and this gives us magnitude which is divided into line, surface, and solid). Thus, neither speech, nor place, nor time finds a place in this division. They are, rather, passions or accidents of these things.
The Philosopher uses this technique for dividing the category in the fifth book of the Metaphysics; while enumerating the things that are quanta per
On the Items in the Category of Quantity se, he mentions only number, line, surface, and solid. Thus, when he first describes quantum he says, "But that is called a quantum which is divisible into constituents which are each of them things capable of being a onesomething and a this-something."! By the first clause ("divisible into constituents"), 'time', 'speech', and 'motion' are excluded. Each of these terms signifies something that is not; or it signifies, either simply or in relation to something else, something which is negative. (In the Fall of the Devil, Anselm employs this form of expression; it is necessary in handling a number of difficulties.) Thus, these things are not called quanta first and foremost. By the second clause all accidents, all forms, and matter as well can be excluded since none can be a this-something. The term 'quantum' then is being used strictly for that which is a per se existent not inhering in another and neither a part nor an accident of something else.
When we take the term 'quantum' strictly, only substances composed of matter and form and, in Aristotle's view, heavenly bodies are quanta. Therefore, after enumerating the things which are quanta the Philosopher says,
"A quantum is a plurality if it is enumerable and a magnitude if it is measurable. A plurality is something potentially divisible into non-continuous elements; whereas, a magnitude is divisible into what is continuous. Of magnitude, that which is continuous in one dimension is length; that which is continuous in two dimensions, breadth; and that which is continuous in three dimensions, depth. Of these things, determinate plurality is number; length is the line; breadth is the surface; and depth is the solid."? It is clear, then, that Aristotle wants to enumerate these four things—the line, the surface, the solid, and number. Neither time, nor speech, nor place, for the reasons provided above, are enumerated.
But in addition to these remarks it should be noted that some things in the category of quantity are terms by which one can answer the question
'how much?'. Thus, 'two cubits', 'three cubits', 'two', 'three', and similar terms fall under the genus of quantity. But other terms fall under the category of quantity because they are common terms predicable in the first mode of perscity of such expressions. Thus, terms like 'line', 'surface', 'solid', and 'number' are in the genus of quantity.