QUANTITY. – Q. (ποσάτης) is the property by which a body is “quantitative” or extended, capable of occupying a space. It is among the fundamental concepts of thought, not definable by means of simpler and better-known notions. Aristotle, indicating its primary property, gives the following description of q.: “Quantity is that which is divisible into parts, each of which is contained in it and is by nature one and something” (Met., V, 13, 1020 a 7). Q. mathematics (v.) and is divided into continuous and discontinuous; the former is the object of geometry, and continuous (v.) are also related to it, while the latter gives rise to number (v.) and is the object of arithmetic.
Q. received particular consideration in ancient philosophical thought, beginning with Pythagoras (the doctrine of numbers) and the atomists (theories concerning the full and the void). Plato brought out its full intelligibility, indicating in quantitative elements, figures and numbers, the model of the ideas (Resp., VI, 510 c). For Aristotle, q. is the second of the categories of real being (Met., V, 7, 1017 a 25-30). According to Aristotelian-scholastic doctrine, q. is neither an innate representation nor an a priori form of the subject, but an objective property of material reality. The notion or concept of q. derives from an abstractive process that disregards not only individuality, but also all qualities and “sensible matter,” retaining only “common intelligible matter” (Sum. Theol., 1°, q. 85, a. 1, ad 2). Whereas notions referring to qualities (v.) and specific natures, the object of physics, entail an immediate relation to external sensation and physical experiment, q., the object of mathematics, although it too derives from external sensation, imagination (v.), through which the representation of pure quantitative elements is possible: “In mathematica enim opportet cognitinem secundum iudicium terminari ad imaginationem” (In Boet. De Trin., q. 6, a. 2). In modern philosophy, the mechanism (v.) Descartes (v.) identified the essence of bodies with q. or extension (Princ. philos., II, n. 8, ed. Ch. Adam-P. Tannery, VIII, p. 44), thus reinforcing the dominant idea in modern physics that the study of natural phenomena should be reduced to the investigation of quantitative relations alone, the object of experimental measurement. LOCKE, JOHN (v.) likewise reduces objective reality to q. alone and to its determinations, which he calls “primary qualities” in opposition to the purely subjective “secondary qualities” (An essay concerning human understanding, II, chap. 8, 9-10). BERGER, ELIE (v.), in accordance with the requirements of his immaterialism itself, denies the objective reality of q. Leibniz (v.) space (v.) as an ordering analogous to the relations prevailing among monads. Nanti understands q. as a mode of judgment or the class of categories to which unity, plurality and totality belong (Critica della ragion pura, Italian trans. G. Gentile and G. Lombardo-Radice, I, Bari 1919, p. 109 ff.). For Hegel, q. is the second moment in the dialectical development of the idea, “the determination that has become indifferent to being,” “being-for-itself that is absolutely identical with being-for-another” (La scienza della logica, Italian trans. A. Moni, I, Bari 1924, p. 208). Modern mathematicians (Frege, Peano, Russell, Couturat) do not usually consider q. the simple and central idea of mathematics, but rather adopt the ideas of number, magnitude, order and the like.
Relation between corporeal substance and q. – The identity between corporeal substance and q., defended by Cartesianism and also by certain neo-scholastics (Tongiorgi and Palmieri), is excluded by Aristotle (Met., VII, 3, 1029 a 15) and, in general, by scholasticism along with him. The reasons for distinguishing between q. and corporeal substance are derived first of all from the distinction and irreducibility of the concepts. Moreover, q. is specifically the same in all bodies, whereas substance is specifically different; q. is the passive principle of divisibility, while substance or nature is the principle of activity; q. is directly and in itself the object of the senses, whereas substance is intelligible; q. can really vary while substance, both specific and individual, remains unchanged, as in living beings, provided their substantial unity is admitted (Aristotle, De gen. et corrupt., I, 5, 321 a 34; s. Tommaso, in hunc loc., lect. 11). The argument drawn from the condensation and rarefaction of bodies (Aristotle, Phys., IV, 9, 216 ff.; s. Tommaso, in hunc loc., lect. 14) would not retain its validity in modern chemistry, since the condensation and rarefaction of macroscopic bodies are explained not by an intrinsic variation of q., but by the greater or lesser proximity of the molecules; yet wave mechanics on this point seems to draw closer again to the ancient conception, at least in the interpretation that attributes a real physical significance to the wave associated with elementary corpuscles.
The real distinction between corporeal substance and q. is commonly accepted by theologians in explaining the Eucharistic Transubstantiation (v. EUCARISTIA); nevertheless, the Eucharistic dogma should not be taken as a proof, not only because of the necessary distinction between the two orders of knowledge, but also because an interpretation of the real presence that dispenses with the distinction between q. and corporeal substance does not seem to be excluded.
The Eucharistic mystery contributed, in scholastic thought, to more profound investigation into the essence of q., because of the dogmatic fact that the Body of Jesus Christ, present in the Eucharist with its q., nevertheless does not occupy the space corresponding to II. Consequently, not a few scholastics hold that the essence of q. must be placed in divisibility (Scotus, Capreolus), or in impenetrability (Arriaga, Oviedo), or in measurability (Simplicio, s. Alberto Magno), whereas extension and actual dimensions are regarded as a “secondary effect,” of which the Body of Christ in the Eucharist would be miraculously deprived.
This explanation, however, which admits an interpenetration and condensation of the parts, so as to reduce q. to a point, does not seem satisfactory either from the philosophical or from the theological point of view; hence many return to the position of s. Tommaso (Sum. Theol., 3°, q. 76, aa. 4 and 5), according to which the Body of Jesus Christ in the Eucharist possesses its entire extension, the essence of q., but does not occupy the corresponding space because the mode of presence in the Host (Transubstantiation) differs from the mode of presence by which bodies are naturally in a place and occupy space.