Matter and form, the primary principles of corporeal substances, are not sense perceptible. What we do perceive by sense are size and a variety of qualities. In fact, quantity and quality appear so inseparably one with their subject that some philosophers have denied the real distinction between substance and these accidents. So it is that Descartes thought extension was substance and substance extension. The same mechanistic bias led him to repudiate the objectivity of sensible qualities. In this, moreover, he was a true disciple of the ancient Atomists, even as others were to be of him. Since philosophers have so often divided on the status of quantity and quality in corporeal substance, we must give at least a brief account of the Aristotelian and Scholastic stand on the question. First, however, we shall speak of the nature and the kinds of quantity, a preliminary step to the just resolution of the point at issue.
a) Its nature. - Quantity, at first thought, suggests a multitude of some kind, or the extension of an object. Implicit in this offhand notion are a number of other items, such as divisibility, measurability, and localization, to mention the more obvious. "Which of these aspects denotes, most formally, the essence of quantity?
Aristotle leaves no doubt about his mind. Quantity, essentially, is what causes a thing (a whole) to be divisible into distinct, intrinsic parts, of which each itself can be a thing. In the medieval Latin of St. Thomas the definition reads this way:
quantum dicitur quod est divisibile in ea quae insunt.2
Like Aristotle St. Thomas adds that the parts of quantity can, upon separation, be things by themselves; they are, in the idiom of the logician, integral parts. In this they differ both from the elements in a mixture and from matter and form: from the former, because in a mixture the elements are only "virtually" present; from the latter, because matter and form, essential parts, cannot exist separately.
Some commentators of St. Thomas - John of St. Thomas is one - take a slightly different view, stressing the fact that quantity gives order and arrangement to the parts in relation to the whole. Thus quantity is what causes a substance to have parts that are exterior to each other according to a definite order. This conception makes explicit what is implicit in the other, namely, the position of the parts in respect to the whole of which they are divisible parts. Basically, then, the two definitions are the same. For, if quantity is the order of parts, one of its immediate and essential properties is divisibility, the idea in the foreground of Aristotle's definition. And since, again by definition, the parts are homogeneous, another property of quantity is measurability.
A further property or effect of quantity is impenetrability, which rules out compenetration, the simultaneous occupation of one place by two bodies. The commonly held opinion has it that nature alone cannot bring two bodies to occupy the same place at the same time.3
One of the special problems of quantity has to do with the mystery of the Eucharist. Under the appearances of bread and wine the body of Christ is truly present together with its proper quantity; yet this quantity does not appear to have actual extension. For this reason theologians have found two different orders in quantity: the internal order of parts and their order relative to surrounding bodies, which is their external or spatial extension. The former is internal quantity, the latter external. In the mystery of the Eucharist external quantity (or external extension) is miraculously suspended, but internal quantity remains. Thus, the Eucharistic body of Christ has distinct, integral parts, but they want the externalization that would bring them into spatial relation with other bodies.4
b) The kinds of quantity. - Quantity is of two general kinds: the quantity of extension or dimensional magnitude, and the quantity of number. This distinction is familiar enough. It is also the ground on which the science of mathematics, almost from its inception, branched into its two basic disciplines, geometry and arithmetic. Aristotle, of course, recognized the duality in quantity and saw, besides, that the difference in point reverts to the difference between a continuum and noncontinuum. Dimensive quantity is continuous or concrete, the quantity of multitude discontinuous or discrete. This is the accepted locution; quantity is either concrete or discrete.
Concrete quantity. - A continuum, as defined by Aristotle, is a whole whose parts not only touch (this is mere contiguity) but are so merged as to be indistinguishable. In concrete quantity the parts are therefore not actually separate though separable, which is to divisible into segments whose parts again overlap and are indistinguishable. In concrete quantity the parts are therefore not actually separate though separable, which is to say they are continuous. As St. Thomas remarks, magnitude or concrete quantity is that which can be divided into continuous parts: quod est divisibile in partes continuo. Thus, a line is divisible into segments whose parts again overlap and are indistinguishable.
Moreover, the continuum that characterizes concrete quantity is either simultaneous or successive. Line, surface, and volume are instances of the simultaneous continuum; they belong to the predicament of quantity per se or essentially. The successive continuum, on the other hand, is seen in motion and time, which are quantified by something extrinsic to them, their subject. Since this subject is an extended body, quantity necessarily attaches to its motion, and hence to time, the measure of motion.5 But more of time and motion later.
Discrete quantity. - This is number, the quantity that can be divided into noncontinuous parts: quod est divisibile secundum potentiam in partes non continuas. If, moreover, number is taken absolutely, without reference to things numbered, it is called "numbering" number: numerus numerans. Thus, I may think of "ten" in this abstract sense, but I may also mean by it a group of ten objects, say ten men, and then it is "numbered" number: numerus numeratus. Either way the ultimate and irreducible parts of number are its units, and the unit is also its measure.