82. Analysis of the Concept of Quantity.—A detailed study of Quantity, including Space and Time, and the Aristotelian categories Ubi, Quando and Situs, belongs to Cosmology. Here we shall confine ourselves mainly to the exposition of certain elementary notions preparatory to such detailed study; and we shall assume the validity of the Scholastic Theory of Knowledge: that a real, material world exists independently of our minds; that it consists of material substances or bodies, animate and inanimate, endowed with the fundamental accident of quantity or extension; that these bodies possess, moreover, many other real accidents such as qualities and energies, chemical, physical and mechanical; that they are subject to real change, local, quantitative, qualitative and substantial; that our concepts of space and time, derived from those of extension and change, are not purely subjective or mental forms of cognition, but are objectively valid notions grounded in the reality of the corporeal universe and giving us a genuine, if inadequate, insight into the nature of this reality.
Among the characteristics recognized by physicists in all perceptible matter—divisibility, commensurability, impenetrability, passivity or inertia, subjection to external forces or energies, external extension or volume, internal quantity or mass—there are none more fundamental than those of volume and mass, or extension and quantity.[354] Nowhere, however, do we find a better illustration of the fact that it is impossible to give a definition proper of any supreme category, or even a description of it by the aid of any more elementary notions, than in the attempts of philosophers to describe Quantity. When, for instance, [pg 310] we describe external, actual, local, or spatial extension as that accident of a corporeal substance or body in virtue of which the latter so exists that it has parts outside parts in space, we have to admit at once that the notions expressed by the terms “parts,” “outside” and “space” are no simpler than the notion of extension itself: in fact our notions of “place” (locus) and “space” (spatium) are derived from, and presuppose, that of extension. This, however, is no serious disadvantage; for the description, such as it is, indicates what we mean by the terms “local, spatial, external, actual extension,” and declares this latter to be an accident of corporeal substances.
Extension, as it is actually in the concrete body, affected by a variety of sensible qualities, is called physical extension; regarded in the abstract, apart from these qualities, it is called geometrical or mathematical extension: trina dimensio, or extension in three dimensions, length, breadth and depth. If we abstract from one of these we have extension in two dimensions, superficial extension; if we abstract from two, we have extension in one dimension, linear extension; and if we abstract from all three we have the extreme limiting concept of the mathematical point. Of these four abstract mathematical concepts, “point,” “line,” “surface,” and “volume,” each expresses the mathematical limitation of the succeeding one.
We cannot conceive a body existing by having parts outside parts in space, each part occupying exclusively a place appropriated to itself, unless we conceive the body, the corporeal substance, as having already a plurality of really distinct or distinguishable parts in itself, and abstracting from all relation to space. The substance must be conceived as having a plurality of really distinct or distinguishable integral parts of itself, before these parts can be conceived as existing outside one another, each in its own place. And the property in virtue of which the corporeal substance has in itself this plurality of distinct integral parts, whereby it is capable of occupying space, and of being impenetrable, divisible, measurable, etc., is called internal, radical, potential quantity or extension.[355]
The corporeal substance itself is, of course, essentially composite, essentially divisible into two essential constitutive principles, [pg 311] the passive, determinable, or material principle (materia prima), and the specifying, determining, formative principle (forma substantialis). Then we conceive this essentially composite substance as necessarily endowed with the property of internal quantity whereby it is composite in another order: composed of, and divisible into, really distinct integral parts, each of which is, of course, essentially composite like the whole itself.[356] Finally we conceive that the corporeal substance, endowed with this property, has also, as a connatural but really distinct and absolutely separable effect of the latter, the accidental mode of being, called external or local extension, in virtue of which it actually occupies space, and thus becomes the subject of all those qualities whereby it is perceptible to our senses.
We have next to inquire into the relations between these three distinct objective concepts, corporeal substance, internal quantity, and local or external extension.
83. Corporeal Substance, Quantity and Extension.—The corporeal substance is an essentially composite substance, resulting from the union of two distinct essential constitutive principles. It exists in itself and is the ultimate subject of all the determinations whereby it reveals itself to our senses. Its actual extension in space is a fundamental mode or determination of its reality, but it is a mode which is distinct from the reality itself of the corporeal substance. Aristotle regarded the distinction as real. In his Metaphysics he declares that the three dimensions of bodies are quantities, not substances, that quantity is not a substance, whereas that in which it ultimately inheres is a substance;[357] in his Physics he says that substance is of itself indivisible and is made divisible by its quantity or extension;[358] in his De Anima[359] he observes that [external] quantity is directly perceptible by the senses (sensibile per se) while substance is only indirectly perceptible (sensibile per accidens):[360] from which it is inferred that substance and extension cannot be really identical. Again, St. Thomas argues that a corporeal [pg 312] substance as such, and so far as its essence is concerned, is indifferent to greater or less extension in space, that the whole nature or substance of a man, for instance, is indifferent to, and independent of, his particular size at any point of time, that while he grows from childhood to manhood it is his external quantity that changes, but not his humanity, his human essence, nature, or substance.[361]
Considerations such as these, though they do not indeed amount to cogent proofs of a real distinction between spatial extension and corporeal substance, should make any serious philosopher hesitate to identify these absolutely, as Descartes and his followers did when they declared the essence of corporeal substance to consist in three dimensions of spatial extension. Even looking at the matter from the point of view of natural reason alone, and apart altogether from any light that may be thrown upon it for the Christian philosopher by Divine Revelation, it is only the superficial thinker who will conclude that because extension—which reveals to his intellect through the medium of external sense perception the presence of a corporeal substance—is naturally inseparable from the latter, therefore it is really and absolutely identical with this latter. The philosopher who remembers how little is known for certain about the ultimate, essential constitution of bodies or corporeal substances, will be slow to conclude that the spatially extended mode of their being enters into the constitution of their essence, and is not rather an accidental determination whereby these substances have their integral parts dispersed or extended in space and thus revealed to the human intellect through sense perception.
And if he be a Christian philosopher he will naturally inquire whether any truth of the Christian Revelation will help indirectly to determine the question. Descartes and his followers were Christian philosophers; and hence it was all the more rash and imprudent of them, in spite of what they knew concerning the Blessed Eucharist, to identify the corporeal substance with its spatial extension. They knew that by transubstantiation the bread and wine are changed substantially into the Body and Blood of Christ. But all the appearances or phenomena of bread and wine remain after transubstantiation, the Eucharistic species as they are called, the taste, colour, form, etc., in a word, all the sensible qualities of these substances, including the extension in which they immediately inhere. From the revealed truth that the substances disappear, and from the manifest fact that all their accidents [pg 313] remain, Christian philosophers and theologians have rightly drawn the sufficiently obvious inference that the spatially extended quantity, which immediately supports all the other sensible qualities, must be itself an absolute accident not only really distinct, but by the absolute power of God really separable, from its connatural substance, the bread and the wine respectively; and that this extended quantity remains in this state of actual separation miraculously supported by the direct influence of the Divine Omnipotence. And while Christian philosophers who hold this view can defend it from all charges of inconsistency, unreasonableness and impossibility, Descartes and his followers can defend their particular view only by the admission that in the case of the consecrated Eucharist our senses are deceived. In this view, while no accidents of the bread and wine remain objectively, God Himself produces directly in our minds the subjective, mental states which the bread and wine produced before consecration.[362] This gratuitous aspersion is cast on the trustworthiness of sense perception, simply on account of the preconceived theory identifying the corporeal substance with its extension. According to the common view, on the other hand, the senses are not really deceived. That to which they testify is really there, viz. the whole collection of natural accidents of bread and wine. It is not the function of the senses, but of the intellect, to testify to the presence of the substance. Of course the unbeliever looking at the consecrated species, or the believer who looks at them not knowing that they have been consecrated, thinks that the substance of bread and the substance of wine are there. Each is deceived intellectually, the one by his unbelief of a truth, the other by his ignorance of a fact. If both knew of the fact of consecration, and if the former believed in the effect of it, neither would be deceived.[363]
While the Cartesian view is thus open to such serious objections, the only plausible difficulty against the traditional view is that of conceiving how the reality of a merely accidental mode of being, such as extension, can be sustained in the actual order of things apart from its connatural substance, and yet not become itself eo ipso a substance. Needless to say we have no positive conception of the manner in which the Divine Omnipotence thus sustains extension; but since this latter, being an absolute accident, and not a mere modal determination of the substance, has a reality of its own, the miraculous persistence of this reality cannot be shown to be impossible. Nor is it, in this separated condition, itself a substance, for it still retains its natural aptitude for inherence in its connatural substance; and this aptitude alone, not actual inherence, is of its essence as an accident ([65]): retaining this natural aptitude it cannot possibly become a substance, it cannot be identified with the substantial mode of being which has essentially the very opposite aptitude, that of existing in itself.