Aristotle, in his 'Categories' places quantity (with which he deals at length from the logical standpoint in the sixth chapter) first in his enumeration of the nine accidents.
Quantity (Gr. poson; Lat. quantitas, quantum, correlate to tantum). Aristotle, in his "Categories" places quantity (with which he deals at length from the logical standpoint in the sixth chapter) first in his enumeration of the nine accidents. His list of the possible heads of classification of predicates has reference to a concrete, material subject, and, as shown by the last two predicaments (jacere and habere), principally to man. Quantity does not, therefore, as philosophy is at present divided, fall properly under the treatment of ontology but of cosmology. It presupposes the material. In l'Metaphysics", IV, the concrete quantum is described as "that which is divisible into the parts included in it, of which any and each is potentially one and hoc quid". By this description the inexistent parts of the quantum are discriminated from the elements in the compound, the matter and the form, which are not each potentially "one and hoc quid". Quantity is distinguished into (I) continuous, and (2) discrete. Continuous (geometrical) quantity is that which consists of parts having position in reference to each other, so that the limit of the one is the limit of the next. These parts, each potentially "one and hoc quid", do not form a multitude, an aggregate of units, but one divisible quantum, or measurable size. They are not actual entities. (This doctrine is not unanimously held in the School.) Continuous quantity is further subdivided into (I) successive, and (2) permanent. Time and movement are examples of successive, the line, surface or tridimensional body of permanent continuous quantity. It is to be noted that time and movement have no reality apart from quantified things which move, and of which the movement is measurable; and that the line and superficies are no more than abstractions practiced upon the real quantum—tridimensional body. Discrete (arithmetical) quantity is made up of discontinuous parts. The resultant whole is a unity per accidens, in which the elements coexist as a plurality. Number and speech are given as examples. Quantity has no contrary, nor does it admit degrees. There is no contrary to a given length or superficies; nor is any one quantity, as such, more a quantity than another is. Large, small, etc., as used in reference to extended things, fall more properly under the category of relation. Equal and unequal are affirmed of objects in virtue of their quantity alone. Not only is material substance affected by the accidental form of quantity, but all the other accidents are measurable, at least per accidens, as when we say "much and little white". St. Thomas ("Summa", III, Q. Ixxvii, a. 2) makes all the accidents "related to their subject by the medium of dimensive quantity, as the first subject of color is said to be the superficies".
An important question is raised as to the nature of the distinction to be drawn between substance and quantity. The School generally, following Aristotle, holds that, as quantity is that reality which makes the indivisible substance potentially divisible (Physics, 1. 2), the distinction to be admitted is a real one. There is considerable diversity of opinion as to whether this can be demonstrated by arguments of natural reason. Aristotle's own argument lies in the consideration that length, breadth, and depth are quantities, but are not substances. But against this it has been urged that these things do not exist as such at all. They are abstractions formed by the dissociation produced by varying concomitants. Suarez, Pesch, De San, Nys, and others hold that the distinction is demonstrable; but most of the arguments advanced are negative ones. For Descartes and his school, quantity, or extension, is the essence of corporeal substance. The distinction to which allusion has just been made has no place in the system (cf. Rene Descartes). The definition of the Council of Trent, however, teaches that quantity is really distinct from substance. It is of faith that the substances of bread and wine in the Eucharist are changed at the consecration (Sess. XIII, cap. iv); but the quantity remains sensibly unaltered. To escape this difficulty, the Cartesians had recourse to several explanations, none of which seems to be in any way satisfactory. Continuous quantity is seen to be, in the philosophy of the School, an attribute and accident of body. Corporeal substance, as such, is not quantitatively divisible. When actuated by quantity it becomes so; but is not yet spatially displayed. The accident is thus distinguished by Scholastics from the further accident of formal extension which is complementary to it, and by which the parts, already rendered distinct by quantity, are localized in space. Through the aptitude to being determined by this accidental form, matter is held to be individuated; the principle of individuation of corporeal beings is materia quantitate signata.