QUANTITY. – Q. (ποσότητα) is the property by which a body is “how much” or extended, capable of occupying space. It is among the fundamental concepts of thought, not definable by simpler and better-known notions. Aristotle, indicating its primary property, offers the following description of q.: “Quantity is what is divisible into parts, which are contained and of which each is by nature one and something” (Met., V, 13, 1020 a 7). Quantity forms the object of mathematics (v.) and is divided into continuous and discontinuous; the former is the object of geometry and to it also pertain to philosophical problems of the continuous (v.), the latter gives rise to number (v.) and is the object of arithmetic.
Quantity has received particular consideration in ancient philosophical thought, from Pythagoras (doctrine of numbers) and the atomists (theories on the full and the void). Plato highlighted its full intelligibility, indicating in quantitative elements—figures and numbers—the model of the ideas (Resp., VI, 510 c). For Aristotle, quantity is the second of the categories of real being (Met., V, 7, 1017 a 25-30). According to the Aristotelian-Scholastic doctrine, quantity is not an innate representation, nor an a priori form of the subject, but an objective property of material reality. The notion or concept of quantity derives from an abstract process that disregards not only individuality but also all qualities and “sensible matter,” retaining only the “common intelligible matter” (Sum. Theol., 1, 3, 9, 85, a. 1, ad 2). While notions relating to qualities (v.) and specific natures, the object of physics, involve an immediate relation to external sensation and physical experiment, quantity, the object of mathematics, although also deriving from external sensation, is immediately related to the imagination (v.), by means of which the representation of pure quantitative elements is possible: “In mathematicis enim oportet cognitionem secundum iudicium terminari ad imaginationem” (In Boet. De Triu., q. 6, a. 2).
In modern philosophy, Descartes’ mechanism (v.) identified the essence of bodies with quantity or extension (Princ. philos., II, n. 8, ed. Ch. Adam-P. Tannery, VIII, p. 44), thus endorsing the dominant idea in modern physics that the study of natural phenomena must be reduced to the search for quantitative relations alone, the object of experimental measurement. LOCKE, JOHN (v.), too, reduces objective reality to quantity alone and its determinations, which he calls “primary qualities” in opposition to the “secondary qualities,” purely subjective (An essay concerning human understanding, II, ch. 8, 9-10). BERGER, ELIE (v.), for the very exigencies of his immaterialism, denies the objective reality of quantity. Leibniz (v.) considers extension and space (v.) as an ordering analogous to the relations existing among monads. Kant understands quantity as a mode of judgment or the class of categories to which belong unity, plurality, and totality (Critique of Pure Reason, Italian trans. G. Gentile and G. Lombardo-Radice, I, Bari 1919, pp. 109 ff.). For Hegel, quantity is the second moment in the dialectical development of the idea, “the determination that has become indifferent to being,” “the being-for-self that is absolutely identical with being-for-another” (The Science of Logic, Italian trans. A. Moni, I, Bari 1924, p. 208). Modern mathematicians (Frege, Peano, Russell, Couturat) do not usually consider quantity as the simple and central idea of mathematics, but rather adopt the idea of number, magnitude, order, and the like.
Relation between corporeal substance and quantity. – The identity between corporeal substance and quantity, defended by Cartesianism and also by some Neoscholastics (Tongiorgi and Palmieri), is rejected by Aristotle (Met., VII, 3, 1029 a 15) and, in general, by Scholasticism. The reasons for distinguishing between quantity and corporeal substance are derived first from the distinction and irreducibility of the concepts. Moreover, quantity is specifically the same in all bodies, while substance is specifically different; quantity is a passive principle of divisibility, while substance or nature is a principle of activity; quantity is directly and per se the object of the senses, while substance is intelligible; quantity can actually vary while the substance remains unchanged both specifically and individually, as in living beings, assuming their substantial unity (Aristotle, De gen. et corrupt., I, 5, 321 a 34; St. Thomas, in hunc loc., lect. 11). The argument drawn from the condensation and rarefaction of bodies (Aristotle, Phys., IV, 9, 216 ff.; St. Thomas, in hunc loc., lect. 14) would not retain validity in modern chemistry, since the condensation and rarefaction of macroscopic bodies is explained not by intrinsic variation of quantity but by the greater or lesser approximation of molecules; yet wave mechanics on this point seems to approach the ancient conception, at least in the interpretation that attributes real physical meaning to the wave associated with elementary corpuscles.
The real distinction between corporeal substance and quantity is commonly accepted by theologians in explaining the Eucharistic Transubstantiation (v. EUCHARIST); however, the Eucharistic dogma should not be used as proof, not only out of due distinction between the two orders of knowledge, but also because an interpretation of real presence that does not presuppose a distinction between quantity and corporeal substance does not seem excluded.
The Eucharistic mystery has contributed, in Scholastic thought, to a deeper investigation into the essence of quantity, on account of the dogmatic fact that the Body of Jesus Christ, present in the Eucharist with its quantity, does not, however, occupy the space corresponding to II. Not a few Scholastics therefore hold that the essence of quantity must be traced back to divisibility (Scotus, Capreolus) or impenetrability (Arriaga, Oviedo) or measurability (Simplicius, St. Albert the Great), while extension and actual dimensions are considered effectively secondary, of which the Body of Christ in the Eucharist is miraculously devoid.
This explanation, however, which admits a compenetration and condensation of parts so as to reduce quantity to a point, does not seem satisfactory either from a philosophical or theological standpoint; hence many return to the opinion of St. Thomas (Sum. Theol., 3a, q. 76, aa. 4 and 5), according to which the Body of Jesus Christ in the Eucharist has its full extension, the essence of quantity, but does not occupy the corresponding space because the reason for its presence in the Host (Transubstantiation) differs from the reason for presence by which bodies are naturally in a place and occupy space.