Quantity

QUANTITY. - Q. (ποσότης) is the property by which a body is "how much" or extended, capable of occupying a space. It is among the fundamental concepts of thought, not definable by simpler and better-known notions. Aristotle, indicating its first property, gives the following description of q.: "Quantity is what is divisible into parts, which are contained in it and of which each is by nature one and something" (Met., V, 13, 1020 a 7). Q. forms the object of mathematics (v.) and is divided into continuous and discontinuous; the former is the object of geometry, and the philosophical problems of the continuum (v.) also refer to it; the latter gives rise to number (v.) and is the object of arithmetic.

Q. received particular consideration in ancient philosophical thought, from Pythagoras (doctrine of numbers) and the atomists (theories on 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 not an innate representation, nor an a priori form of the subject, but is an objective property of material reality. The notion or concept of q. derives from an abstractive process that prescinds not only from individuality, but also from all qualities and from "sensible matter," in order to retain only "common intelligible matter" (Sum. Theol., 1ª, q. 85, a. 1, ad 2). While notions referring to qualities (v.) and to specific natures, the object of physics, entail an immediate relation to external sensation and to physical experiment, q., the object of mathematics, although it too derives from external sensation, is related immediately to the imagination (v.), through which the representation of pure quantitative elements is possible: "In mathematica enim opportet cognitionem secundum iudicium terminari ad imaginationem" (In Boet. De Trin., q. 6, a. 2). In modern philosophy, the mechanism (v.) of Descartes (v.) identified the essence of bodies with q. or extension (Princ. philos., II, n. 8, ed. Ch. Adam-P. Tannery, VIII, p. 44), thereby strengthening the idea dominant 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 (v.) too reduces objective reality to q. alone and to its determinations, which he called "primary qualities" as opposed to the purely subjective "secondary qualities" (An essay concerning human understanding, II, ch. 8, 9-10). Berkeley (v.), for the very requirements of his immaterialism, denies the objective reality of q. Leibniz (v.) considers extension and space (v.) as an ordering analogous to the relations obtaining among monads. Kant understands q. as a mode of judgment or the class of categories to which unity, plurality and totality belong (Critique of Pure Reason, Ital. trans. G. Gentile and G. Lombardo-Radice, I, Bari 1919, p. 109 ff.). For Hegel, q. is the second moment of the dialectical development of the idea, "the determination that has become indifferent to being," "being-for-self that is absolutely identical with being-for-other" (The Science of Logic, Ital. trans. A. Moni, I, Bari 1924, p. 208). Modern mathematicians (Frege, Peano, Russell, Couturat) are not accustomed to consider q. as the simple and central idea of mathematics, but rather assume the idea 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 some Neo-Scholastics (Tongiorgi and Palmieri), is excluded by Aristotle (Met., VII, 3, 1029 a 15) and, with him, generally by Scholasticism. The reasons for the distinction 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 a passive principle of divisibility, substance or nature is a principle of activity; q. is directly and per se the object of the senses, substance is intelligible; q. can really vary while substance, both specific and individual, remains unchanged, as in living beings, granted 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 its validity in modern chemistry, since the condensation and rarefaction of macroscopic bodies is explained not by an intrinsic variation of q., but by the greater or lesser approach of the molecules; but wave mechanics on this point seems to draw closer again to the ancient conception, at least in the interpretation that attributes a real physical meaning to the wave connected with elementary corpuscles.

The real distinction between corporeal substance and q. is commonly accepted by theologians in the explanation of eucharistic Transubstantiation (v. EUCARISTIA); nevertheless the eucharistic dogma must not be taken as an argument of proof, not only because of a due distinction between the two orders of knowledge, but also because an interpretation of the real presence that prescinds from the distinction between q. and corporeal substance does not seem to be excluded.

The eucharistic mystery contributed, in Scholastic thought, to a deeper investigation of the essence of q., because of the dogmatic fact that the Body of Jesus Christ, present in the Eucharist with its q., does not however occupy the space corresponding to it. Not a few Scholastics therefore hold that the essence of q. must be placed in divisibility (Scotus, Capreolus) or in impenetrability (Arriaga, Oviedo) or in measurability (Simplicius, St. Albert the Great), while extension and dimensions in act are held to be a "secondary effect," of which the Body of Christ in the Eucharist would be miraculously deprived.

This explanation, however, which admits a compenetration and condensation of parts, such as to reduce q. to a point, does not seem satisfactory either from the philosophical or from the theological point of view; for which reason many return to the position 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 entire extension, the essence of q., but does not occupy the corresponding space because the reason for presence in the Host (Transubstantiation) differs from the reason for presence by which bodies are naturally in a place and occupy space.

Filippo Selvaggi