Chapter XI. Quantity, Space And Time.
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.
External extension, then, is an absolute accident, really distinct from the corporeal substance, and naturally though not absolutely inseparable from the latter. It is the natural concomitant or consequence of the internal quantity whereby the corporeal substance has in itself a plurality of distinct integral parts. This internal quantity itself is either an aspect of the corporeal substance itself, only virtually distinct from the latter, or else in the strict sense a property, absolutely inseparable, if really distinct, from the substance. Natural experience furnishes no example of a corporeal substance actually existing devoid of internal quantity or internal distinction of integral parts.[364] But scholastic philosophers are not agreed as to whether the corporeal substance is itself and by its own essence a manifold of really distinct integral parts (in which case internal quantity would be merely the aspect under which the essence is thus regarded as an integral whole constituted by a plurality of distinct integral parts; while, looked at as an essence, it would be an essential whole constituted by the union of two essential parts or principles)—or whether it is formally constituted an integral whole, not by its essence (which makes it only an essential whole, an essentially composite substance), but by a property really distinct, though necessarily flowing, from this essence, viz. internal quantity. According to the former view the material principle (materia prima) of the composite corporeal substance is such that the essence resulting from its union with the formative principle (forma substantialis) is necessarily an integral whole with distinguishable integral parts, each of which naturally demands the spatially extended mode of being which external extension de facto confers upon it. According to the latter view, which is that of St. Thomas and his followers generally, the corporeal substance as such has no mode of composition other than essential composition: it is not of itself an integral whole, compounded of distinct or distinguishable integral parts (each of which would be, like the whole, essentially composite): of itself it is indivisible into integral parts: it is, therefore, in [pg 315] this order of being, simple and not composite. It has, no doubt, by reason of its material principle, an absolutely necessary exigence for divisibility into distinct integral parts, for integral composition in other words. But this actual integral composition, this actual divisibility, is the formal effect of a property really distinct from the substantial essence itself; and this property is internal quantity: the connatural, but absolutely separable, complement of this internal quantity being, as in the other view, local or spatial extension.
In both views external extension is an absolute accident of the corporeal substance; and in the Thomist view internal quantity would also appear to be an absolute accident, and not a mere mode.
It is instructive to reflect how far this scholastic doctrine removes us from the Cartesian view which sets up an absolute antithesis between mind or spirit, and matter or body, placing the essence of the former in thought and that of the latter in extension. According to the scholastic view the spiritual substance is an immaterial “actuality” or “form”; it is essentially simple, and not like a corporeal substance an essentially composite substance resulting from the union of a formative principle or “form” with a passive, determinable, material principle. And since it is the material principle that demands the property of internal quantity and the accident of external extension, whereby the corporeal substance becomes an integral whole with its parts extended in space, it follows that the spiritual substance, having no material principle in its constitution, is not only essentially simple—to the exclusion of distinct principles of its essence,—but is also and as a consequence integrally simple, to the exclusion of distinct integral parts, and of the extended or characteristically corporeal mode of occupying space. So far there is contrast between the two great substantial modes of finite being, matter and spirit; but the contrast is by no means an absolute antithesis. For if we look at the essence alone of the corporeal substance it is not of itself actually extended in space: in the Thomist view it is not even of itself divisible into distinct integral parts. It differs from spirit in this that while the latter is essentially simple the former is essentially composite and has by reason of this compositeness a natural aptitude for divisibility into parts and for the extension of these parts in space, an aptitude which spirit does not possess. But the corporeal substance may exist without actual extension, and consequently without any of those other attributes such as impenetrability, solidity, colour, etc., through which it is perceptible to our senses. In this condition, how does it differ from spirit? In being essentially composite, and in being perhaps endowed with distinguishable integral parts.[365] But in this condition the [pg 316] essential mode of its being has a relation to space which closely resembles the mode in which spirit exists in space: it is related to space somewhat in the manner in which the soul is in the space occupied by the body—whole in the whole of this space and whole in every assignable portion of this space. So that after all, different as matter and spirit undoubtedly are, the difference between them is by no means that sort of Cartesian chasm which human thought must for ever fail to bridge.
By virtue of its external extension the corporeal substance exists by having distinguishable parts outside parts in space. We can conceive any perceptible volume of matter as being perfectly continuous, if it has no actual limits or actual distinction of parts within itself, but is one individual being completely filling the whole space within its outer surface; or imperfectly continuous, if while being one and undivided it has within its volume pores or interstices, whether these be empty or filled with some other sort of matter; or as made up of contiguous integral parts if each or these is really distinct and actually divided from every other, while each actually touches with its outer limits the adjacent limits of the parts lying next to it, so that all the internal parts or limits are co-terminous; or as made up of separate, discrete or distant parts no one of which actually touches any other.
It is clear that there must be, in any actually extended volume of matter, ultimate parts which are really continuous—unless we are to hold, with dynamists, that our perception of extension is produced in our minds by the action of extramental points or centres of force which are themselves simple or unextended. But the physical phenomena of contraction, expansion, absorption, undulatory and vibratory motions accompanying our sensations of light, heat and sound, as well as many other physical phenomena, all point to the fact that volumes of matter which are apparently continuous are really porous: the molecular structure of perceptible matter is an accepted physical theory; and scientists also universally accept as a working hypothesis the existence of an imperceptible material medium pervading and filling all real space, though there is no agreement as to the properties [pg 317] with which they suppose this hypothetical medium, the “ether,” to be endowed.
Again, as regards the divisibility of extended matter, it is obvious that if we conceive extension in three dimensions geometrically, mathematically or in the abstract, any such volume or extension is indefinitely divisible in thought. But if we inquire how far any concrete, actually existing volume of matter is divisible, we know in the first place that we cannot divide the body of any actual organic living thing indefinitely without destroying its life, and so its specific character. Nor can we carry on the division of inorganic matter indefinitely for want of sufficiently delicate dividing instruments. But apart from this the science of chemistry points to the fact that every inorganic chemical compound has an ultimate individual unit, the chemical molecule, which we cannot sub-divide without destroying the specific nature of the compound by resolving it into its elements or into less complex compounds. Furthermore, each “elementary” or “chemically simple” body—such as gold, oxygen, carbon, etc.—seems resolvable into units called “atoms,” which appear to be ultimate individual units in the sense that if their mass can be subdivided (as appears possible from researches that have originated in the discovery of radium) the subdivisions are specifically different kinds of matter from that of the atom so divided.
In the inorganic world the perceptible mass of matter is certainly not an individual being, a unum per se, but only a collection of individual atoms or molecules, a unum per accidens. Whether the molecule or the atom of the chemically elementary body is the “individual,” cannot be determined with any degree of certitude. It would appear, however, that every specifically distinct type of inorganic matter, whether compound or elementary, requires for its existence a certain minimal volume, by the sub-division of which the type is substantially changed; and this is manifestly true of organic or living matter: so that matter as it naturally exists would appear not to be indefinitely divisible.
If in a chemically homogeneous mass of inorganic matter (such as carbon or water) the chemical molecule be regarded as the “individual,” this cannot be the case in any organic, living thing, for whatever matter is assimilated into the living substance of such a being eo ipso undergoes substantial change whereby it loses the nature it had and becomes a constituent of the living individual. The substantial, “individual” unity of the organic living being seems to be compatible not merely with qualitative (structural and functional) heterogeneity of parts, but also with (perhaps even complete) spatial separateness [pg 318] of these parts. If the structure of the living body is really “molecular,” i.e. if it has distances between its ultimate integral units, so that these are not in spatial contact, then the fact that the formative, vital principle (forma substantialis, anima) unifies this material manifold, and constitutes it an “individual” by actualizing and vitalizing each and all of the material units, spatially separate as they are,—this fact will help us to realize that the formative principle of the composite corporeal substance has not of itself the spatial, extended mode of being, but that the substance derives the latter from its material principle (materia prima).
84. Place and Space.—From the concept of the volume or actual extension of a body we pass immediately to that of the “place” (locus) which it occupies. We may distinguish between the internal and the external place of a body. By the former we understand the outer (convex) surface of the body itself, regarded as a receptacle containing the volume of the body. If, therefore, there were only one body in existence it would have its own internal place: this is independent of other bodies. Not so, however, the external place; for by the external place of a body we mean the immediately surrounding (concave) surface, formed by the bodies which circumscribe the body in question, and considered formally as an immovable container of this body. This is a free rendering of Aristotle's definition: Place is the first (or immediate) immovable surface (or limit) of that which contains a body: prima immobilis superficies ejus quod continet.[366] If a hollow sphere were filled with water, the inner or concave surface of the sphere would be the “external place” of the water. Not, however, this surface considered materially, but formally as a surface, so that if the sphere could be removed, and another instantaneously substituted for it, the water would still be contained within the same formal surface; its locus externus would remain the same. And, again, it is the containing surface considered as immovable or as circumscribing that definite portion of space, that constitutes the locus externus or “external place” of the located body: so that if the sphere with the water were moved the latter would thereby obtain a new external location, for though the containing surface be still materially and formally the same, it is no longer the same as a locating surface, seeing that it now marks off a portion of space different from that marked off by it before it was moved.
Aristotle's definition defines what is known as the proper external place of a body. From this we distinguish the common [pg 319] external place or location of a body: understanding by the latter, or “locus communis,” the whole collection of spatial relations of the body in question to all the bodies in its immediate neighbourhood. It is by indicating these relations, or some of them, that we assign the Aristotelian category, or extrinsic denomination, Ubi.[367]
Regarded ontologically, the internal place of a body is an absolute accident: it is the accident which gives the latter concrete volume or external extension, and it is not really distinct from the latter. The external place of a body includes in addition the spatial relations of the latter to other bodies, relations grounded in the volumes of those bodies.
It is by reason of these spatial relations with certain bodies, that a being is said to be “present” in a certain place. A corporeal extended substance is said to occupy space circumscriptivé, or by having parts outside parts in the place it occupies. A finite or created spiritual substance is said to occupy space definitivé inasmuch as it can naturally exercise its influence only within certain more or less extended spatial limits: as the human soul does within the confines of the body.[368] The Infinite Being is said to occupy space repletivé. The actual presence of God in all real space, conserving in its existence all created, contingent reality, is called the Divine Ubiquity. The perfection whereby God can be present in other worlds and other spaces which He may actualize is called the Divine Immensity.
The local presence of a finite being to other finite beings is itself a positive perfection—based on its actual extension if it be an extended corporeal substance, or on its power of operating within a certain space if it be a spiritual substance. The fact that in the case of a finite being this local presence is itself limited, is at once a corollary and an index of the finiteness of the being in question. Only the Infinite Being is omnipresent or ubiquitous. But every finite being, whether corporeal or spiritual, from the very fact that it exists at all, must exist somewhere or have some locus internus, and it must have some local presence if there are other corporeal, extended beings in existence. Thus the local presence of a being is a (finite) perfection which seems to be grounded in the very nature itself of the creature.[369]
From the concept of place we pass naturally to the more complex and abstract notion of space. It is, of course, by cognitive processes, both sentient and intellectual, that we come into possession of the abstract concept of space. These processes are subjective [pg 320] in the sense that they are processes of the individual's mental faculties. Distinguishing between the processes and the object or content which is brought into consciousness, or put in presence of the mind, by means of them; and assuming that this object or content is not a mere form or groove of our cognitive activity, not a mere antecedent condition requisite on the mental side for the conscious exercise of this activity on its data, but that on the contrary it is, or involves, an objective, extramental reality apprehended by the mind,—we go on to inquire in what this objective reality consists. In approaching the question we must first note that what is true of every abstract and universal concept is true of the concept of space, viz. that the abstractness and universality (“intentio universalitatis”) of real being, as apprehended by the intellect, are modes or forms of thought, entia rationis, logical conditions and relations which are created by thought, and which exist only in and for thought; while the reality itself is the object apprehended in these modes and under these conditions: Universale est formaliter in mente et fundamentaliter in re. Now through the concept of space we apprehend a reality. Our concept of real space has for its object an actual reality. What is this reality? If space is real, in what does its reality consist? We answer that the reality which we apprehend through this concept is the total amount of the actual extension or magnitude of all created and coexisting bodies; not, however, this total magnitude considered absolutely and in itself, but as endowed with real and mutual relations of all its parts to one another,[370] relations which are apprehended by us as distances, linear, superficial, and voluminal.
Such, then, is the reality corresponding to our concept of real and actual space. But no sooner have we reached this concept than we may look at its object in the abstract, remove mentally all limits from it, and conceive all extended bodies as actually non-existent. What is the result? The result is that we have now present to our minds the possibility of the existence of extended bodies, and a concomitant imagination image (which memory will not allow us to banish from consciousness) of a vast and boundless emptiness, an indefinite and unmeasurable vacuum in which bodies were or may be. The intellectual concept is now not a concept of any actual object, but of a mere possibility: the possibility of a corporeal, extended universe. This is the [pg 321] concept of what we call ideal or possible space; and like the concept of any other possible reality it is derived by us from our experience of actual reality,—in this case from our experience of extended bodies as actually existing. The corporeal universe has not existed from all eternity, but it was possible from all eternity. When we think of that possibility as antecedent to all creation, we are thinking of bodies, and of their extension, as possible; and the concept of their total extension as possible is the concept of ideal or possible space. This concept is, through a psychological necessity, accompanied by an imagination image of what we call imaginary space: the unlimited vacuity which preceded corporeal creation, which would still persist were the latter totally annihilated, which reaches out indefinitely beyond its actual limits, which imagination pictures for us as a receptacle in which bodies may exist but which all the time our reason assures us is actually nothing, being really only the known possibility of corporeal creatures. This familiar notion of an empty receptacle for bodies is what we have in mind when we think of bodies as existing “in space”. Hence we say that space, as conceived by the human mind, is not a mere subjective form of cognition, a mere ens rationis, inasmuch as our concept has a foundation in reality, viz. the actual extension of all existing bodies; nor is it on the other hand simply a real entity, because this actual extension of bodies does not really exist in the manner in which we apprehend it under the abstract concept of space, as a mere possibility, or empty receptacle, of bodies. Space is therefore an ens rationis cum fundamento in re.
A great variety of interesting but abstruse questions arise from the consideration of space; but they belong properly to Cosmology and Natural Theology. For example: Is real space actually infinite in magnitude, or finite? In other words, besides the whole solar system—which is in reality merely one star plus its planets and their satellites,—is there in existence an actually infinite multitude of such stellar worlds? It is not likely that this can ever be determined empirically. Many philosophers maintain that the question must be answered in the negative, inasmuch as an actually infinite multitude is impossible. Others, however, deny that the impossibility of an actually infinite multitude can be proved.[371] Again, within the limits of the actual corporeal universe, are there really vacant spaces, or is all space within these limits actually (or even necessarily) filled with an all-pervading ether or corporeal medium of some sort? How would local motion be possible if all space were full of impenetrable matter? How would the real interaction of [pg 322] distant bodies on one another be possible if there were only vacant space between them? Is the real volume or extension of a corporeal substance (as distinct from its apparent volume, which is supposed to include interstices, or spaces not filled with that body) actually or necessarily unchangeable? Or is the internal quantity of a body actually or necessarily unchangeable? Can more than one individual corporeal substance simultaneously occupy exactly the same space? (This is not possible naturally, for impenetrability is a natural consequence of local extension; but it is possible miraculously—if all the bodies, or all except one, be miraculously deprived of local or spatial extension.) Can the same individual body be present at the same time in totally different and distant places? (Not naturally, of course; but how it can happen even miraculously is a more difficult question than the preceding one. It is in virtue of its actual or local extension that a body is present sensibly in a definite place. Deprived miraculously of this extension it can be simultaneously in several places, as our Blessed Lord's Body is in the Eucharist. But if a body has its natural local extension at one definite place, does this extension so confine its presence to this place that it cannot be simultaneously present—miraculously, and without its local extension—at other places? The most we can say is that the absolute impossibility of this is neither self-evident nor capable of cogent proof. The Body of our Lord has its natural local extension in heaven—for heaven, which will be the abode of the glorified bodies of the blessed after the general resurrection, must be not merely a state or condition, but a place—and at the same time it is sacramentally present in many places on earth.)
85. Time: its Apprehension and Measurement.—If the concept of space is difficult to analyse, and gives rise to some practically insoluble problems, this is still more true of the concept of time. “What, then, is time?” exclaims St. Augustine in his Confessions.[372] “If no one asks me, I know; but if I am asked to explain it, then I do not know!” We reach the notion of space through our external perception of extension by the senses of sight and touch. So also we derive the notion of time from our perception of motion or change, and mainly from our consciousness of change and succession in our own conscious states. The concept of time involves immediately two other concepts, that of duration, and that of succession. Duration, or continuance in existence, is of two kinds, permanent and successive. Permanent duration is the duration of an immutable being, formally and in so far as it is immutable. Successive duration is the continued existence or duration of a being that is subject to change, formally and in so far as it is mutable. Now real change involves a continuous succession of real states, it is a continuous process or fieri; and it is the duration of a being subject [pg 323] to such change that we call time or temporal duration. Had we no consciousness of change, or succession of states, we could have no notion of time; though we might have a notion of unchanging duration if per impossibile our cognitive activity were itself devoid of any succession of conscious states and had for its object only unchanging reality. But since our cognitive activity is de facto successive we can apprehend permanent or unchanging duration, not as it is in itself, but only after the analogy of successive or temporal duration ([86]). The continuous series of successive states involved in change is, therefore, the real and objective content of our notion of time; just as the co-existing total of extension forms the content of our notion of space. The concept of space is the concept of something static; that of time is the concept of something kinetic. Time is the continuity of change: where there is change there is time; without change time would be inconceivable. Change involves succession, and succession involves the temporal elements of “before” and “after,” separated by the indivisible limiting factor called the “now” or “present instant”. The “past” and the “future” are the two parts of time, while the “present instant” is not a part of time, but a point of demarcation at which the future flows into the past. Change is a reality; it is a real mode of the existence of mutable things; but neither the immediately past state, nor the immediately future state of a changing reality, are actual at the present instant: it is only to the permanent, abiding mind, apprehending real change, and endowed with memory and expectation, that the past and the future are actually (and, of course, only ideally, not really) present. And it is only by holding past and future in present consciousness, by distinguishing mentally between them, by counting or measuring the continuous flow of successive states from future to past, through the present instant, that the mind comes into possession of the concept of time.[373] The mind thus apprehends time as the measure of the continuous flow of successive states in things subject to change. As thus apprehended, time is not merely the reality of change: it is the successive continuity or duration of change considered as a measure of change. It is that within which all changes are conceived to happen: just as space is conceived as that within [pg 324] which all extended things are conceived to exist. We have said that without real change or motion there could be no time. We can now add that without a mind to apprehend and measure this motion there could be no time. As St. Thomas declares, following Aristotle: Si non esset anima non esset tempus.[374] For time, as apprehended by means of our abstract and universal concept, is not simply a reality, but a reality endowed with logical relations, or, in other words, a logical entity grounded in reality, an ens rationis cum fundamento in re.
This brings us to Aristotle's classic definition,[375] which is at once pithy and pregnant: Τοῦτο γάρ ἐστιν ὁ χρόνος, ἀριθμὸς κινήσεως κατὰ τὸ πρότερον καὶ ὓστερον: Tempus est numerus motus secundum prius et posterius: Time is the measure of motion or change by what we conceive as before and after, or future and past, in its process. Every change involves its own intrinsic flow of states from future to past. It is by mentally distinguishing these states, and by thus computing, counting, numbering, the continuous flow or change, that we derive from the latter the notion of time.[376] If, then, we consider all created things, all things subject to change, we shall realize that real time commenced with the creation of the first of them and will continue as long as they (or any of them) continue to exist. We thus arrive at a conception of time in general, analogous to that of space: the whole continuous series of successions, in changing things, from future to past, regarded as that in which these changes occur, and which is the measure of them.
Here, too, as in the case of space, we can distinguish real time, which is the total duration of actual changes, from ideal or imaginary time which is the conceived and imagined duration of merely possible changes.
But a more important distinction is that between intrinsic or internal time, or the duration of any concrete mutable reality considered in itself, and extrinsic or external time, which is some other extrinsic temporal duration with which we compare, and by which [pg 325] we may measure, the former duration. Every change or motion has its own internal time; and this is what we have been so far endeavouring to analyse. If two men start at the same instant to walk in the same direction, and if one walk three miles and the other four, while the hands of a watch mark the lapse of an hour, the external time of each walk will be the same, will coincide with one and the same motion of the hands of the watch used as a measure. But the internal time of the four-mile walk will be greater than that of the three-mile walk. The former will be a greater amount of change than the latter; and therefore its internal time, estimated by this amount absolutely, will be greater than that of the latter estimated by its amount absolutely.[377] The greater the amount of a change the greater the internal time-duration or series of successive states which measures this change absolutely.[378]
Just as the category Where is indicated by the spatial relations of a body to other bodies, so the category When is indicated, in regard to any event or process, by its commensuration or comparison with other events or processes.
This brings us to the notion of measurement. To measure anything quantitatively is to apply to it successively some quantitative unit taken as a standard and to count the number of times it contains this unit. This is a process of mentally breaking up continuous quantity or magnitude—whether permanent or successive, i.e. whether extension or motion—into discontinuous quantity or multitude. If the measurement of permanent quantity by spatial units, and the choosing of such [pg 326] units, are difficult processes,[379] those of measuring successive quantity and fixing on temporal units are more difficult still. Is there any natural motion or change of a general character, whereby we can measure (externally) the time-duration of all other changes? The motions of the earth itself—on its axis and around the sun—at once suggest themselves. And these motions form in fact the natural general standard for measuring the time of all other events in the universe. All artificial or mechanical devices, such as hour-glasses, watches, clocks, chronometers, etc., are simply contrivances for the more convenient application of that general and natural standard to all particular events.
It requires a little reflection to realize that all our means of measuring time-duration can only attain to approximate accuracy, inasmuch as our faculties of sense perception, no matter by what devices they are aided, are so limited in range and penetration that fluctuations which fall below the minima sensibilia cannot be detected. It is a necessary condition of any motion used as a standard for time-measurement that it be regular. That the standard motions we actually employ are absolutely regular we have no guarantee. We can test their regularity only up to the point at which our power of detecting irregularity fails.
Reflection will also show that our appreciation of time-duration is also relative, not absolute. It is always a comparison of one flow or current of conscious experiences with another. It is the greater regularity of astronomical motions, as compared with changes or processes experienced as taking place within ourselves, that causes us to fix on the former as the more suitable standard for the measurement of time. “There is indeed,” writes Father Maher,[380] “a certain rhythm in many of the processes of our organic life, such as respiration, circulation, and the recurrent needs of food and sleep, which probably contribute much to our power of estimating duration.... The irregular character and varying duration of conscious states, however, soon bring home to us the unfitness of these subjective phenomena to serve as a standard measure of time.” Moreover, our estimate of duration is largely dependent on the nature of the estimated experiences and of our mental attitude towards them: “A period with plenty of varied incident, such as a fortnight's travel, passes rapidly at the time. Whilst we are interested in each successive experience we have little spare attention to notice the duration [pg 327] of the experience. There is almost complete lapse of the ‘enumerating’ activity. But in retrospect such a period expands, because it is estimated by the number and variety of the impressions which it presents to recollection. On the other hand a dull, monotonous, or unattractive occupation, which leaves much of our mental energy free to advert to its duration, is over-estimated whilst taking place. A couple of hours spent impatiently waiting for a train, a few days in idleness on board ship, a week confined to one's room, are often declared to constitute an ‘age’. But when they are past such periods, being empty of incident, shrink up into very small dimensions.... Similarly, recent intervals are exaggerated compared with equal periods more remote. Whilst as we grow older and new experiences become fewer and less impressive, each year at its close seems shorter than its predecessor.”[381]
From those facts it would seem perfectly legitimate to draw this rather surprising inference: that if the rate of all the changes taking place in the universe were to be suddenly and simultaneously altered in the same direction—all increased or all diminished in the same degree—and if our powers of perception were simultaneously so altered as to be readjusted to this new rate of change, we could not become aware of the alteration.[382] Supposing, for instance, that the rate of motion were doubled, the same amount of change would take place in the new day as actually took place in the old. The external or comparative time of all movements—that is to say, the time of which alone we can have any appreciation—would be the same as of old. The new day would, of course, appear only half as long as the old to a mind not readjusted to the new conditions; but this would still be external time. But would the internal, intrinsic time of each movement be unaltered? It would be the same for the readjusted mind as it was previously for the mind adjusted to these previous conditions. By an unaltered mind, however, by the Divine Mind, for instance, the same amount of motion would be seen to constitute the same movement under both conditions, but to take place twice as quickly under the new conditions as it did under the old. This again, however, involves a comparison, and thus informs us merely of external or relative time. If we identify intrinsic time with amount of change, making the latter the measure of the former, we must conclude that alteration in the rate of a motion does not alter its absolute time: and this is evident when we reflect that the very notion of a rate of motion involves the comparison of the latter with some other motion.[383] Finally, we have no positive conception of the manner in [pg 328] which time duration is related to, or known by, the Divine Eternal Mind, which is present to all time—past, present and future.
Besides the question of the relativity of time, there are many other curious and difficult questions which arise from a consideration of time-duration, but a detailed consideration of them belongs to Cosmology. We will merely indicate a few of them. How far is time reversible, at least in the case of purely mechanical movements?[384] Had time a beginning? We know from Revelation that de facto it had. But can we determine by the light of reason alone whether or not it must have had a beginning? The greatest philosophers are divided as to possibility or impossibility of created reality existing from all eternity. St. Thomas has stated, as his considered opinion, that the impossibility of creatio ab aeterno cannot be proved. If a series of creatures could have existed successively from all eternity, and therefore without any first term of the series, this would involve the possibility of an actually infinite multitude of creatures; but an actually infinite multitude of creatures, whether existing simultaneously or successively, is regarded by most philosophers as being self-contradictory and intrinsically impossible. And this although the Divine Essence, being infinitely imitable ad extra, and being clearly comprehended as such by the Divine Mind, contains virtually the Divine exemplars of an infinite multitude of possible creatures. Those who defend the possibility of an actually infinite multitude of creatures consider this fact of the infinite imitability of the Divine Essence as the ground of this possibility. On the other hand, those who hold that an actually infinite multitude is self-contradictory deny the validity of this argument from possibility to actuality; and they bring forward such serious considerations and arguments in favour of their own view that this latter has been at all times much more commonly advocated than the former one.[385] Will time have an end? All the evidence of the physical sciences confirms the truth of the Christian faith that external time, as measured by the motions of the heavens, will have an end. But the internal or intrinsic time which will be the measure of the activities of immortal creatures will have no end.[386]
86. Duration of Immutable Being: Eternity.—We have seen that duration is the perseverance or continuance of a being in its existence. The duration of the Absolutely Immutable Being is a positive perfection identical with the essence itself of this Being. It is a duration without beginning, without end, without change or succession, a permanent as distinct from a successive duration, for it is the duration of the Necessary Being, whose essence is Pure Actuality. This duration is eternity: an interminable duration existing all together. Aeternitas est interminabilis duratio tota simul existens. This is the common definition of eternity in the proper sense of the term—absolute [pg 329] or necessary eternity. The word “interminabilis” connotes a positive perfection: the exclusion of beginning and end. The word “tota” does not imply that the eternity has parts. The expression “tota simul” excludes the imperfection which is characteristic of time duration, viz. the succession of “before” and “after”. The definition given by Boëtius[387] emphasizes these points, as also the indefectible character of immutable life in the Eternal Being: Aeternitas est interminabilis vitae tota simul et prefecta possessio.
There is, in the next place, a kind of duration which has been called hypothetical, relative, or borrowed eternity: aeternitas hypothetica, relativa, participata, also called by scholastics “aeviternitas”. It is the duration in existence of a being that is contingent, but of its nature incorruptible, immortal, such as the human soul or a pure spirit. Even if such a being existed from all eternity its existence would be contingent, dependent on a real principle distinct from itself: its duration, therefore, would not be eternity in the strict sense. On the other hand, once created by God, its nature would demand conservation without end; nor could it naturally cease to exist, though absolutely speaking it could cease to exist were God to withdraw from it His conserving power. Its duration, therefore, differs from the duration of corporeal creatures which are by nature subject to change, decay, and cessation of their being. A contingent spiritual substance has by nature a beginning to its duration, or at least a duration which is not essential to it but dependent on the Necessary Being, a duration, however, which is naturally without end; whereas the duration of the corporeal being has by nature both a beginning and an end.
But philosophers are not agreed as to the nature and ground of the distinction between these two kinds of duration in contingent beings. No contingent being is self-existent, neither has any contingent being the principle of its own duration in its own essence. Just as it cannot begin to exist of itself, so neither can it continue to exist of itself. At the same time, granted that it has obtained from God actual existence, some kind or degree of duration, of continuance in that existence, seems to be naturally due to its essence. Otherwise conservation would be not only really but formally a continued creation. It is such indeed on the part of God: in God there is no variety of activity. But on the part of the creature, the preservation of the latter in existence, and therefore some degree of duration, seems to be due to it on the hypothesis that it has been brought into existence at all. The conserving influence of God is to its duration in existence what the concurring influence of God is to [pg 330] the exercise of its activities.[388] In this sense the duration of a finite being in existence is a positive perfection which we may regard as a property of its nature. But is this perfection or property of the creature which we call duration, (a) essentially successive in all creatures, spiritual as well as corporeal? And (b) is it really identical with their actual existence (or with the reality of whatever change or actualization occurs to their existence), or it is a mode of this existence or change, really distinct from the latter and conferring upon the latter the perfection of continuity or persistence?
This, at all events, is universally admitted: that we cannot become aware of any duration otherwise than through our apprehension of change; that we have direct knowledge only of successive duration; that we can conceive the permanent duration of immutable reality only after the analogy of successive duration, or as the co-existence of immutable reality with the successive duration of mutable things.
Now some philosophers identify successive duration with change, and hold that successive duration is formally the duration of things subject to change; that in so far as a being is subject to change its duration is successive, and in so far as it is free from change its duration approaches the essentially permanent duration of the Eternal, Immutable Being; that therefore the duration of corporeal, corruptible, mortal beings is par excellence successive or temporal duration (tempus); that spiritual beings, which are substantially immutable, but nevertheless have a successive series of spiritual activities, have a sort of duration more perfect, because more permanent, than mere temporal duration, but less perfect, because less permanent, than eternal duration (aevum, aeviternitas); while the Absolutely Immutable Being alone has perfect permanent duration (aeternitas).[389] It is not clear whether according to this view we should distinguish between the duration of spiritual substances as permanent, and that of their acts as successive; or why we should not attribute permanent duration to corporeal substances and their permanent accidents, confining successive duration formally to motion or change itself. It is, moreover, implied in this view that duration is not any really distinct perfection or mode superadded to the actuality of the being that endures.
Other philosophers hold that all duration of creatures is successive; that [pg 331] no individual creature has a mixture of permanent and successive duration; that this successive duration is really distinct from that which endures by means of it; that it is really distinct even from the reality of change or motion itself; that it is a real mode the formal function of which is to confer on the enduring reality a series of actualities in the order of “succession of posterior to prior,” a series of intrinsic quandocationes (analagous to the intrinsic locations which their extension confers upon bodies in space). These philosophers distinguish between continuous or (indefinitely) divisible successive duration, the (indefinitely divisible) parts of which are “past” and “future,” and the present not a “part” but only an “indivisible limit” between the two parts; and discontinuous or indivisible successive duration, whose parts are separate and indivisible units of duration succeeding one another discontinuously: each part being a real but indivisible duration, so that besides the parts that are past and future, the present is also a part, which is—like an instant of time—indivisible, but which is also—unlike an instant of time—a real duration. The former kind of successive duration they ascribe to corporeal, corruptible creatures; the latter to spiritual, incorruptible creatures. This view is defended with much force and ingenuity by De San in his Cosmologia;[390] where also a full discussion of most of the other questions we have touched upon will be found.