Enneads VI.1: Of the Ten Aristotelian and Four Stoic Categories
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.