2. QUANTITY.
4. The Aristotelians call quantity first “number,” then “continuous size,” “space,” and “time.” To these concepts they apply the other kinds of quantity; as for instance, they say that movement is a quantity measured by time. It might also be said reciprocally, that time receives its continuity from movement.
CONTINUOUS AND DEFINITE QUANTITY HAVE NOTHING IN COMMON.
If continuous quantity be quantity as far as it is continuous, then definite quantity will no longer be quantity. If, on the contrary, continuous quantity be quantity only accidentally, then there is nothing in common between continuous and definite quantity. We will grant that numbers are quantities, although if their nature of being quantities were plain, one would not see why they should be given that name. As to the line, the surface, and the body, they are called sizes and not quantities; and the latter name is given them only when they are estimated numerically; as when, for instance, they are measured by two or three feet. A body is a quantity only in so far as it is measured, just as space is a quantity only by accident, and not by its spatiality. We must here not consider what is quantity by accident, but by its quantitative-ness, quantity itself. Three oxen are not a quantity; in this case, the quantity is the number found in them. Indeed, three oxen belong already to two categories. The case is similar with the line, and the surface, both of which possess such quantity. But if the quantity of surface be quantity itself, why would surface itself be a quantity? It is no doubt only when determined by three or four lines that the surface is called a quantity.
NUMBERS ARE NOT QUANTITY IN ITSELF.
Shall we then say that numbers alone are quantity? Shall we attribute this privilege to Numbers in themselves, which are beings, because they exist in themselves? Shall we grant the same privilege to numbers existing in things which participate in them, and which serve to number, not unities, but ten oxen, for example, or ten horses? First, it would seem absurd that these numbers should not be beings, if the former ones be such. Then, it will seem equally absurd that they should exist within the things they measure, without existting outside them, as the rules and instruments which serve to measure exist outside of the objects they measure. On the other hand, if these numbers that exist in themselves serve to measure, and nevertheless do not exist within the objects that they measure, the result will be that these objects will not be quantities since they will not participate in quantity itself.
NUMBER IS NOT IN QUANTITY; BUT QUANTITY IS IN NUMBER.
Why should these numbers be considered quantities? Doubtless because they are measures. But are these measures quantities, or quantity itself? As they are in the order of beings, even if they should not apply to any of the other things, the numbers will nevertheless remain what they are, and they will be found in quantity. Indeed, their unity designates an object, since it applies to another; then the number expresses how many objects there are, and the soul makes use of number to measure plurality. Now, when measuring thus, the soul does not measure the “whatness” (or, quality) of the object, since she says “one,” “two,” whatever be their objects, even if of opposite nature; she does not determine the character of each thing, for instance, if it be warm or beautiful; she limits herself to estimating its quantity. Consequently, whether we take Number in itself, or in the objects which participate therein, quantity exists not in these objects, but in the number; quantity finds itself not in the object three feet long, but in the number three.
MAGNITUDE AND NUMBERS WOULD BE OF A DIFFERENT TYPE OF QUANTITY.
Why then should sizes also be quantities ? Probably because they approximate quantities, and because we call quantities all objects that contain quantities, even though we do not measure them with quantity in itself. We call large what numerically participates in much; and small what participates in little. Greatness and smallness are quantities, not absolute, but relative; nevertheless the Aristotelians say that they are relative quantities so far as they seem to be quantities. That is a question to be studied; for, in this doctrine, number is a kind apart, while sizes would hold second rank; it is not exactly a kind, but a category which gathers things which are near each other, and which may hold first or second rank. As to us, we shall have to examine if the Numbers which exist in themselves be only substances, or if they be also quantities. In either case, there is nothing in common between the Numbers of which we speak, and those which exist in things which participate therein.
SPEECH AS A QUANTITY.
5. What relation to quantity exists in speech, time, and movement?
First, let us consider speech. It can be measured. In this respect, speech is a quantity, but not in so far as it is speech, whose nature is to be significant, as the noun, or the verb. The vocal air is the matter of the word, as it also is of the noun and the verb, all which constitute the language. The word is principally an impulse launched on the air, but it is not a simple impulse; because it is articulated it somehow fashions the air; consequently it is a deed, but a significant one. It might be reasonably said that this movement and impulse constitute a deed, and that the movement which follows is a modification, or rather that the first movement is the deed, and the second movement is the modification of another, or rather that the deed refers to the subject, and the modification is in the subject. If the word consisted not in the impulse, but in the air, there would result from the significant characteristic of the expressive impulse two distinct entities, and no longer a single category.
Let us pass to time. If it exist in what measures, that which measures must be examined; it is doubtless the soul, or the present instant. If it exist in what is measured, it is a quantity so far as it has a quantity; as, for instance, it may be a year. But, so far as it is time, it has another nature; for what has such a quantity, without (essentially) being a quantity, is not any the less such a quantity.
QUANTITY AS EQUAL AND UNEQUAL DOES NOT REFER TO THE OBJECTS.
As to (Aristotle’s) assertion that the property of quantity is to be both equal and unequal, this property belongs to quantity itself, and not to the objects which participate in quantity, unless it be by accident, so far as one does not consider these objects in themselves. A three foot object, for instance, is a quantity so far as it is taken in its totality; but it does not form a kind with quantity itself; only, along with it, it is traced back to a kind of unity, a common category.