Thomistic Definition of Time.— Time is closely associated with successive continuous quantity; we know it, whether in the ideal or the concrete, as a reality whose parts pass in a continuous succession from ‘future’ to ‘past’. Aristotle and, after him, St. Thomas have defined it: ‘Tempus est numerus motus secundum prius et posterius'. Let us try and elucidate this pregnant definition.
Connexion Between Time and Movement.— According to these two philosophers time is closely connected with continuous movement; it is indeed its measure, or perhaps better, a breaking up of it, a numbering—numerus motus. Now does this close connexion as a matter of fact seem to be borne out by experience? Yes : in the first place, for example, it is by the movement of the earth round its axis that we have our standard of measuring the duration of contingent things and the events and actions of our lives. Again, if it happens that we are intensely absorbed in some occupation and no longer have attention for the various movements or changes taking place around or within us, we lose all sense of time. And should we try to reflect, we find we are incapable of calculating even approximately the time that has elapsed, unless we apply our memory to recall one by one the things which have happened during the interval in question. Lastly, to represent time we often make use of the metaphor of a line, extending indefinitely into the past, running uninterruptedly through the continuous development of an ever elusive present and stretching without limit into the future.
[ST. THOMAS, Opusc. De tempore, c. 2.— In IV physic., lect. 17. On the subject of Time see also Balmès, Fundamental Philosophy III, trs. Brownson (New York, 5864); SPENCER, Principles of Psychology II (London, 1881r); BERGSON. Matter and Memory, trs. PAUL and PALMER (London, 1911)]
Why Movement Suggests the Idea of Time.— Movement (motus) properly so called presents two features; (a) Firstly it is the corning into actuality of something which is capable of being realized tending to be further realized, or something perfectible tending to be perfected; an actuality therefore which has a twofold relationship, viz, to the potentiality whose actualization it initiates and to the yet further perfection in which the potentiality finds its completion or by which it may be even replaced ~ Now so understood, movement is an uninterrupted progress bearing the characteristic of unity proper to all continuous quantity, whether successive or permanent Under this aspect movement is not identical with time nor does it appear to suggest the idea of time). In fact, as we have just said, it is impossible to notice the elapse of time whilst the mind is so absorbed that it cannot take heed of the different phases which really break up its apparent unity.
(b) Secondly, movement possesses another characteristic which is no less essential. Although it does not consist in a collection of parts actually distinct from one another, it nevertheless contains, because it is continuous quantity, the foundation of discrete quantity or of number; it is virtually multiple, in this sense that by a simple extrinsic designation one can separate it out into an indefinite number of parts that when viewed by the mind become really and truly actual parts. Movement, then, subjected to a simple mental division becomes a number or a multitude. The parts of this multitude, however, have this distinctive feature, that they are perceived in the movement whose constituent elements follow one another according to a relation of before and after, of past and future.
What our perception of time consists in is in perceiving in this continuous foundation which is real movement parts that succeed one another without interruption and are linked together according to a fixed and invariable relation of before and after: ‘cum enim intelligimus extrema diversa alicuj us medii, et anima dicat, illa esse duo nunc, hoc prius, illud posterius, quasi numerando prius et postius in motu, tunc hoc dicimus esse tempus’. The ‘numerus motus of which St. Thomas speaks consists, then, of the parts of the division made by the mind in movement. The two words ‘prius’ and ‘posterius’ express the two aspects under which these parts are related to one another and come before the mind. The term ‘motus’ points out the continuous movement or the real and undivided thread which is presented to the mind for division.
Thus time is made up of two elements, the one formal, namely number (numerus), the other material, namely movement (motus).
Distinction Between Time and Movement — Between these two notions there is only a logical distinction 88~ As a matter of fact concrete time and movement are one and the same reality. For although continuous movement does not at once appear before the mind under the formal aspect of temporal duration, as it has first to submit it to a process of mental division which brings out the notion of succession, the progressive development of a before and after; nevertheless this division is not a real one, but belongs to the mental order and makes no change in the objective reality of the movement.
Abstractions Necessary for the Mind to arrive at the Universal Idea of Time.—The identification of real time with continuous movement does not at first sight seem to be compatible with our ordinary conception of time. We represent to ourselves the duration of time as a single duration, regularly successive and always the same in its continuous prolongation. Whereas, on the other hand, there is a great variety of movements, such as rapid, slow, uniform, vibratory, undulatory, etc. How reconcile contradictory attributes in one and the same thing?
These opposite features are seen to be consistent with one another when we take into account the many abstractions that the mind makes in order to form its concept of time.
1 First of all our mind in perceiving in movement the idea of time abstracts from the qualitative element that is there, from what kind of movement it is. Movement may be quantitative, purely local, or qualitative, according as its result is an increase or diminution of quantity, a simple change in position in space, or a modification in quality. To all these three kinds of movement the notion of time applies equally.
2 Next, the concept of time has nothing to do with the special modes of a determined movement. If it is a question of local movement, it is evident that the direction and the successive directions of the movement which produce undulatory, vibratory or other movements, in no way enter into the idea of time.
3 Again, in the original conception of time, the mind abstracts also from the manner in which the parts of the movement succeed one another, the mode which differentiates it into slow or rapid movements. This is proved by the fact that the idea of rapidity or slowness presupposes a relationship between time and the space covered. A movement is more rapid just in proportion as it covers a greater space in a fixed time. From this it is clear that the idea of rapidity and the opposite idea of slowness become intelligible to us only if we already possess the two ideas of space and time; and hence they cannot be the object of the first conception of temporal duration.
When all these abstractions have been made, what is there that remains in the movement we perceive to give our idea of time an objective reality? It is the continuous succession, the flow of the parts some of which are anterior and others posterior. This is the object of the abstract and universal concept of the mind, a concept which is applicable to every kind of continuous movement, whatever be its nature, its mode of succession or its quality.
The Parts of Temporal Duration.—There are three parts in time, the present, the past and the future. The p resent is essentially fleeting. The moment we consciously examine it, it is already in the past. It is impossible to conceive it without putting it into relation with the past which precedes it and of which it will immediately go to form a part, and with the future which follows it and which will immediately replace it. Situated thus between the past and the future, it comes before us as a link, constantly moving, which unites them and disappears with them without interruption.
The other two parts, the past and the future, constitute the intrinsic elements of time. They are essentially relative, since to conceive them as such we have to connect them with the fleeting present. Compared with the real present which is actually passing, all previous parts are once and for all past, all succeeding parts are really to come.
Hence it follows that time has but an imperfect reality. Of the three kinds of parts that go to form it, the one no longer exists, for it is the past; the other is not yet in existence, for it is the future; there only remains the fleeting present, which has a momentary existence. Therefore a duration of time, however small it may be, requires the bringing of the memory into play, that is to say, the simultaneous representation of a whole of which only one part enjoys a reality and that a fleeting one.
Various Acceptations of the Notion of Time.—
SPACE — INTERNAL PLACE
Definition of Internal Place.— Every natural body possesses a certain volume and occupies a determined position, a place properly its own, a change of which constitutes local movement. This portion of space occupied and measured by the real volume of a body is its internal place.
If a material body undergoes a displacement before our eyes, the image of its movement appears to us under the form of a series of positions successively occupied and abandoned. Each of these positions we call a movable or transient place. If the body passes to a state of rest, in so doing it acquires a place of its own, relatively immovable and always proportionate to its real dimensions.
Reality and Nature of Internal Place.—Bodies are indifferent with regard to space; they do not require one particular place rather than another, and yet they cannot exist without occupying some one place determined in all its points. How can we account for the fact that every body, which thus shows a general indifference with regard to all the possible places of the world, does actually occupy an individual place reserved to itself? This taking of possession is due, in our opinion, to a real accident that belongs to the body, which we shall henceforth call its localizing accident or the ‘ intrinsic whereness’ (ubicatio) of a body.
First proof .— The state of rest is not the same as that of motion: apart from any consideration of the mind, the simple displacement in space of a body that is independent of its causes imposes itself upon us as a real phenomenon, perhaps even as the one least liable to sense-illusion. We must then recognize, unless we are willing to avow a radical subjectivism, that not only movement but every part or stage of the movement marks a real change in a body. Now, we ask, what is the precise reality which suffers this change? It cannot be the body’s substance nor can it be one of those accidental properties such as weight, colour, physical or chemical energies: for we have no experience of such a modillcation, seeing that a body in motion remains ever itself as well as keeps all its properties the same throughout, excepting perhaps for some alteration for which we can always discover a cause other than the movement itself. Hence there must be some other reality over and above, whose successive, continuous changes constitute the mobile reality of movement; one that we cannot but suppose to be a special real accident whose proper function is to localize the body and ~nfine it to this or that part of space. Indeed, since movement is continuous change of position or place, it can only exist if place, whereof it is the change, exists too; if place is not real, movement is an illusion. Every material being, then, appropriates a fixed part of space in virtue of a localizing accident which determines its natural indetermination or indifference and fixes it in a position proper to itself and exclusively its own. When the body is at rest, this accident is stable and unchanged like the place it determines; when the body is in motion, it undergoes continuous modifications and to these is due the body’s successive series of positions or places that we understand by ‘movement’. Considered in its whole nature, movement has a twofold formality, the one invisible and alone real, namely the continuous changing or incessant renewal of the localizing accident of the body; the other, the succession of positions which the moving subject occupies and then abandons in its path. The latter is the sense-perceived manifestation of the internal and unseen reality of movement.
Second proof.— Between the various bodies of the universe there exist many relations of distance, and these we must regard as objective and real, seeing that by geometry and astronomy we measure and compare them and, in gauging their respective extents, rely on our judgments having more than a mere subjective validity. Now these relations of distance between bodies so clearly marked and carefully estimated are continually changing; bodies move away from one another and approach nearer to one another; distances increase and diminish. We have the clearest evidence of these real changes, indispensable as they are both for the general development of the universe and the continuation of order on our own globe. The only question to determine is, In what precise reality do they take place?
Every relation necessarily implies two terms and, if it is a mutual one, an objective reason as its foundation (Gen. Meta. 108 ff.). In order that a new relation of distance may exist between two bodies, a real change must have been brought about in the bases of this relation; if not, how can we say that the bodies are really nearer or further apart, seeing that relation as such does not exist but draws its whole reality from the two terms which are its foundation? Now in a real change of distance, the only reality that changes is the actual position of the bodies, i.e. their internal place ; the distance diminishes or increases because the bodies leave their respective places to occupy new ones. Therefore, unless we are going to deny the objective character of the change, we must admit that localization proceeds from a mobile accident whose essential r6le is to determine a body in a certain position in space. In this case, to every spatial change there corresponds in the body a parallel modification of the localizing accident; and new relations of distance have an objective aspect because they rest on new foundations, viz., the intrinsic localizing accidents (ubicationes) they acquire as the result of their movement.
Conclusion.—Internal place, considered under its formal aspect, is the portion of space circumscribed by the mass of a body. Considered in its concrete reality, it is a real accident with the function of circumscribing the volume of a material thing and of giving it its peculiar spatial position.
II. EXTERNAL PLACE
Definition.— Had only one single material substance been created, it would still have had its own internal place. Yet it would have been impossible to determine the position of this body, for the reason that all spatial determination is necessarily relative. The position of a thing is settled by certain guiding-marks, or rather by certain relations established between the body in question and those which surround it. Hence in common language ‘place’ signifies more than the portion of space occupied by the real volume of a material being; it iteans its whereabouts or the surroundings in which it is. So viewed, place is external to the body, and is accordingly known as external place. This external place of a body we may define more strictly as the immediate circumference or the first immovable surface which circumscribes a body.
Analysis of this Definition.—If a hollow vessel is filled with water, to the question, ‘Where is this water? the spontaneous reply is, ‘In the vessel’. This latter serves for the liquid it contains as a true place, a place exterior to the body within it. Here we have a first and fundamental property of place, namely the aptitude to contain within itself a determined volume.
Next, it is clear that by very reason of its character as a recipient, the vessel must be an individual thing distinct from the thing contained in it, since to contain and to be contained are two contrary attributes implying different subjects. This distinction is a second property of place.
Moreover, if we inquire what precisely in the vessel it is which plays the part of recipient, we find it to be only its internal surface. It is a matter of indifference whether it is made of cut-glass or of common glass, or of iron or wood, or whether its sides are fragile or solid; so long as it can contain, it keeps its essential role independently of these and other accessory circumstances. Accordingly we may define external place as the immediate material circumference which surrounds a body, the first surface which a material substance encounters at the limits of its extension. Here we are to notice two elements, the one material, the internal surface; the other formal, the interval or capacity circumscribed. These two elements are indivisibly united in the concept of real place: for the internal surface can be called place only if it has the aptitude to contain, that is to say, if there are relations of distance between the walls of the vessel; and the capacity of the vessel or the distance between its walls is a definite capacity only if it is circumscribed by real limits, by an enveloping surface.
Aristotle adds as a fourth condition that the containing surface be considered as immovable. Relative immobility is indispensable for the constitution of external place as conceived by us. How, indeed, do we represent the movement of a body except as a removal from one place into another; the body moves, but the place it abandons remains unmoved. There is however just this difficulty that, if all the beings in the universe are subject to movement, where are we to find this immobility? There are two ways of considering the surface of a localizing body: either we may consider it as a concrete, individual material thing, and then it constitutes a place that is essentially mobile; or we may leave out of consideration all its individual characteristics and conceive it merely as the surface, of any body whatsoever, capable of circumscribing such and such a volume. Looked at in this latter way, the place always keeps its identity in spite of the many different bodies that follow one another in it and fulfil the same office there.
In order to allow external place a tru&relative immobility it is sufficient to conceive it as related to certain fixed and invariable points, such as the poles and the centre of the earth. As these terms of comparison remain always the same, we are easily enabled to perceive when bodies change their places as well as the identity of the places which they change. In every point~ this definition of Aristotle has the support of empirical data.
Kinds of External Place.—The place we have just defined is called
by Aristotle Proper place. It signifies the material surface or
circumference which immediately fits its content and encloses that alone.
It is, we may say, the typical form of external place. By common place
is meant that which contains several bodies, such as a room full of
furniture: a name that justly applies, but with a sense derived from the
first acceptation.
III. SPACE
Facts of Experience.— To stand on a railway bridge and watch an express train pass by so quickly that scarcely any part of it is seen distinctly, provokes the remark that it flies through space; where by space we mean distance and to fly through it to cover a great distance in a short time. Again, I may say that my study is a very pleasant one, that it is pleasing to gaze upon because of the light and the space, the notion of space being used in the sense of roominess, of interval enclosed by the walls of the place. Once more, we speak of the early mist being melted by the first warm rays of the sun into vapour which slowly rises until it is dissipated in space, meaning to say that it loses itself in the immense capacity or interval that separates the earth from what we speak of as the vault of heaven.
Vary the examples as you will, analyze the various ways that this term is constantly applied by science or ordinary speech, and you will always find that it contains the idea of distance or interval, of real or apparent void, comprised within certain definite limits.
Analysis of the Facts, and Definition of Space.— If we carefully reflect upon this concept of space, we discover in it two elements, one a formal element, the relation of distance, the capacity, or the relative void comprised within the bodies that limit it; another, a material element, namely the bodies, or more exactly, the surfaces of the bodies that by their distance from one another make a real or apparent void.
We may, then, define real or concrete space as a relation of distance in three dimensions, determined by the respective positions of the bodies that limit it.
In point of fact, every definite interval is always limited by extended bodies; and between two extended things, however small they may be, there intervenes some room that is measurable according to three dimensions. If the exact sciences, however, notably geometry, deal sometimes with spaces that are of only one or two dimensions—such as a line or a surface— these extents do not really exist apart from the mind, but are the result of a process of abstraction by which it picks out from among several real objective facts one or other of the three dimensions, while disregarding how inseparably connected they are in the world of reality.
Connexion Between Space and External and Internal Place.— 1. The analysis of space and external place shows the two notions to come really to the same thing. In each we find the same constituent elements, a material element or the bodies that limit the distance, and a formal element or the interval itself, the distance or capacity. If they are different ideas it is because they differently emphasize one or other of the two elements which they embody; in the idea of ‘space’ prominence is given to the relation of distance, in that of ‘external place’ to the concrete limits or terminal surfaces. Yet just as every definite interval presupposes real limits, so every set of real limits implies a definite interval.
2 Internal place’ is also closely allied with ‘space’ inasmuch as the internal places of material substances are the foundations or the formal limits of the spatial relations. For the determination and the extent of these relations depends entirely on the positions occupied by the bodies limiting them; thus, every change in one or other of these positions involves a corresponding change in the distance between them, in other words, in the space. If, then, space enjoys a real existence, however imperfect this reality may be, it is due to these internal places. If a change in spatial relations appears to us as an objective fact, it is only the existence of localizing accidents that give us the reason of it. In brief, the reality of these accidents is the objective foundation of spatial relations.
Is There Only One Space ?—
1. In the real world we distinguish as many particular spaces from
one another as there are intervals or distances marked out by concrete
limits.
2. Yet, among this innumerable multitude of real spaces the whole series of which makes up the extension of the material world, there is one which seems to have a special claim to be called ‘space ‘—that unmatched and unmeasured, immense interval which stretches from the earth to the vault of heaven. Because it is so imposing on account of its unique dimensions and of its part in the economy of the universe, it occupies a special place in our imagination and in our language and we call it simply ‘space’.
3. Outside the world of real things there is still another acceptation of the idea of space. As our senses bring us in touch with concrete and particular spaces, our intellect works upon these data of experience and, by disregarding both the size of the different intervals perceived and the individual nature of the bodies that bound them, retains of the concrete representation only the essential note of limited distance. This is a purely intellectual concept with an indefinite range o f application; it forms an abstract type not determined to correspond to any particular interval but applicable to any interval whatsoever. It is what we call ideal or possible space. The unity and the universality it possesses depend on the fact that it is an abstraction and exists only in the mind.
4. The last form of space we meet with is imaginary space.— The abstractive power of the mind has always to be assisted by representations of the imaginative faculty. When therefore the concept of ideal space is being formed by the mind, an image, more or less vague, accompanies it and serves as a support. Now as distance abstractly conceived is indefinitely elastic, as it can be stretched as far as we wish and the movable limits our intelligence assigns to it are co-extensive with it, the imagination, in playing its part in this work of extension, furnishes under an abstract form a vague and indeterminate image of the extension, it pushes further and further back the horizons it meets, until of abstract space we have a vague concrete image made by the imagination and the illusion that it is something real, independent of all bodies that exist. Such is the genesis and the nature of imaginary space. Like absolute time it has no existence except in our subjective representations.
Does the Notion of Space imply a Vacuum or a Plenum?
Space, as such, is indifferent to either of these attributes; whether matter is one continuous whole stretching from the earth to the heavens or whether this immense interval is void of all material reality, space remains exactly the same. Neither a vacuum nor a plenum makes any change in its nature, since this relation of distance according to three dimensions owes both itself and its extent, not to anything within, but to the respective positions of the boundaries that mark its limits. In other words, if there is no change in the limits that mark a place, the capacity or the physical possibility of a definite thing being within it remains the same.
No doubt the notion of space always awakens the idea of a certain vacuity, but the vacuum indicated by the notion of space is not synonymous with the absence of all matter. It is essentially relative to the two bodies which in every case determine the relation of distance. There cannot, indeed, be any space without interval; but between the extreme limits of any particular interval there are any number of positions where these two limits do not exist. Here we have then a relative void, inseparable from distance, although a void which does not exclude the presence of material bodies, with which it is unconcerned.
Thus are two seemingly contradictory facts explained: every representation of space the mind makes contains the idea of a relative vacuum, and yet neither a vacuum nor a plenum are conditions of the real existence of space.