CHAPTER 6

Origin of the idea of time

764. We have seen how we perceive our body in the first two subjective ways. We must now speak about the third, the extrasubjective way, which is valid for all bodies as external agents applied to our corporeal sensories. Even our own body can be perceived, not only as ours, but as any external body.
However, before examining this third way, we must mention some abstract ideas that can be obtained, at least in part, from the body perceived subjectively.(144) They are the ideas of time, movement and space.

765. In fact, time is connected with all the actions and experiences we are aware of; movement does not require our exterior senses for its perception, because our locomotive faculty is an internal, subjective faculty whose existence is confirmed by our consciousness; lastly space or extension also is a mode of our corporeal, subjective feeling(145) from which it cannot be separated, although we can distinguish it mentally in our own feeling just as we can note its mode of being in any other ens, even if the mode is per se inseparably united to being.
The starting point for these three ideas of time, movement and space is found in the ideas we have so far discussed. However, it will help if we make use also of our exterior senses and extrasubjective perception of bodies, so as not to separate what our mind customarily sees as united.

766. When we perform an action we are limited in two ways.(146) The immediate, interior feeling by which we are conscious of performing the action informs us of this double limitation.
The first limitation is the level of intensity in the action; the second is its duration. The words 'intensity' and 'duration' indicate the limitations in their abstract state, after they have been mentally separated by us from the internal and external actions they are limiting and made into two mental entia.

767. We can increase the intensity and duration of our actions up to a certain point, and we can imagine them increasing indefinitely. Successive duration is the idea of time.

768. Just as my present action has successive duration, so has every other action done by myself or others.
Comparison of the duration of one action with that of other actions gives a certain relationship, called the measure of time.

769. The measure of time is generally based on an important, uniform, constant and easily noticed action, such as the movement of the earth on its axis around the sun. The parts of this movement form the parts of common measures of time: years, months, days, etc. Any action at all could have been chosen, provided the duration of all other actions was related to it.

770. I can increase or decrease the duration of my own actions. But if I want to retain the same quantity of action in a shortened duration, I must compensate with greater intensity; and if I increase the duration, I must reduce the intensity. There is therefore an invariable relationship between the duration and intensity of the action.
In motion, intensity is velocity, which is greater in direct proportion to the distance covered and in indirect proportion to the time taken to cover the distance; hence we have the formula or

771. The constancy of this relationship is founded on two constant data: 1. the constant quantity of the desired effect or action; and 2. the limited quantity of forces involved, which is also constant and given.
Thus, a law founded in the nature of things establishes that within a certain duration, only a particular, fixed intensity can produce a determined quantity of action.

772. Let us now suppose that the duration of a desired action is fixed but not its quantity and intensity. By applying various levels of intensity to the duration, we have various quantities of actions or effects proportionate to the levels of intensity. The general result is that for any duration, the quantity of action will be exactly proportionate to the intensity of the action; this gives us the idea of the uniformity of time. No matter what is done within a fixed duration, there is a constant relationship between the intensity of the action and its quantity; where little has been done, more can be achieved, provided the intensity is heightened. In short, I can think the possibility of doing something within a certain duration by means of a determined intensity of action; the same applies to any similar duration.

773. We can express the relationship between quantity, intensity and duration of action by the formula:, where T = duration, S intensity, and Q quantity. This is valid where there is only one agent; if Q there are several agents, then the formula is, where M is the number of agents.

774. What has been said about actions attested as our own by consciousness can also be said about actions we perceive, but of which we are not the authors.
In this case, time is a limitation not only of actions but also of passive experiences. Passive experience and action are very often the same fact considered from opposite points of view.

775. The limitation we have called 'successive duration' can be abstracted from all the actions and passive experiences of finite beings. If we then add the idea of possibility (of a possible action, that is) which, as we have said, is innate in us, we have the pure idea of time, that is, of time in a possible, but not real action.

776. We perceive successive duration as 'a possibility that a certain quantity of action can be obtained by means of a certain level of intensity.' This is the idea of time in general, the pure idea, given by observation.

777. Granted constant intensity, quantity of action is the measure of time, while uniformity of time means simply 'the same quantity obtained by a constant level of intensity.'

778. This quantity of action, obtained by a constant level of intensity, can be conceived as repeated an indefinite number of times, if we use the idea of possibility. Hence the idea of pure, indefinitely long time composed of: 1. the idea of possibility, which is per se indefinite; and 2. the (abstract) idea of one of the two limitations to which successive actions are subject.

779. Anything subject to succession begins, grows, comes to perfection and then deteriorates and perishes. But at whatever moment we observe this process, we find a determinate state. Indeed, according to the principle of contradiction, there cannot be a part or perfection that is and is not at the same time. Let us take for example a baby cutting a tooth, or an adolescent's facial hair changing into a beard. In answer to the question 'Has the tooth come or the beard grown?' we can indeed reply 'Not yet, but it is beginning.' Nevertheless, although the word 'beginning' involves a mental relationship with the future state of the thing, that is, when the tooth is formed or the beard grown, the early form of the tooth and the first growth of hair already exist as such. Their state is not something between being and not-being.

780. This simple observation of fact leads us to the remarkable but true conclusion that all that happens, happens in an instant - provided we understand 'all that happens' to mean not something composite, that is, an already formed nature (which always attracts our attention), but that thing whatever it may be (a part of nature or an element) which is at each instant. This thing, whatever it may be, which finds itself in being in a given instant is perfect relative to itself, relative to its own existence, although it may be imperfect considered as part of something greater of which it is an element or outline or beginning.

781. However a serious difficulty now presents itself. If all that happens, happens in an instant, what is the origin of continuous time? Is this idea of time obtained by abstraction from what happens, from actions? When we think a series of things which happen, each one of which happens in an instant, we perceive a series of points, a succession of instants, but never continuous time.

782. Let us return to the example of the growth of hair and see whether observation alone offers us an idea of time containing the characteristic of true continuity.
Suppose one hair has taken two months to grow ten centimetres.
This growth is an action which we call composite because it consists of many little actions of shorter duration.
The same would be true for the production of any other kind of thing: the unfolding of a flower, the sculpting of a bas-relief; any event whatever that gave or changed the being of anything, would be called a composite action because it could always be mentally subdivided into many parts which would be so many lesser actions or events.

We must first note carefully that the time taken by the hair to grow maintains a constant proportion to all the other actions done within the two months, as we mentioned above (cf. 764-765 [766-773]), that is, taking into account the intensity of the action.
With the intensity of the action fixed for two months, any entity acting within this period can give only one quantity of action or determinate effect.
Let us see how this composite, successive action, or total effect, can be thought as divided into instants during the two month period.

Suppose we distribute the instants in such a way that the hair has grown 10 cm. in 5,184,000 instants. In each of these instants it will have acquired its corresponding tiny increase. Now, if at the end of two months the hair's length must not exceed 10 cm., the interval between the instants of its growth must be determinate. If we presume the interval is uniform, it will be exactly one second.
Intervals as small as these (or smaller) would completely escape our observation and could not be measured. They can be measured only by reasoning, that is, by knowledge of the total effect or quantity of action taking place in a any fixed, observable length of time, like the two months. The measure of the quantity of action is the comparison with the other quantities of action within the same length of time.

Let us return to the little intervals we suppose exist. In themselves they are not observable, because as such they are a negation, a cessation of action. They are observable only through the relationship between the different frequency of instants in different actions. If we could observe the successive, instantaneous growth we have supposed takes place every second in the hair, we would not be able to measure each of the seconds by observation of the action alone, unless we compared them with the intervals of something happening in us, like our heart beat or a degree of tiredness. On the other hand, if we compared different actions, like the growth of an old man's hair and a young boy's, we would notice that while the old man's grows a certain amount, the boy's grows two or three times that amount. This would give us a measure of the interval: it would be the quantity of action (the intensity being uniform) taking place in the course of two instants. The measure of the intervals, granted it is observable, would simply be the relationship between the quantity or total effect of different causes acting within two instants. It would not differ in any way, therefore, from the measure of a noticeable duration or series of instants, at the end of which we compare greater quantities of actions or total effects large enough to be observed.

So far we have shown: 1. everything happens by instants; 2. the idea of time given by observation is an interconnection of these events, that is, of the quantities of actions within the instants. We can therefore conclude that 'any observation, even an observation so acute and penetrating as to be beyond our capabilities, could never directly offer our mind the idea of a continuous time, that is, of a continuous succession. It would supply only the idea of a series of instants of greater or less proximity to each other and their relationship'.
Nevertheless, we do have the idea of a continuous time, although observation has not explained it. We must therefore look elsewhere for it.

783. We now separate our conceptions of time given directly by observation from those we form by abstract reasoning, which itself starts from observation.
Observation presents matters of fact to our understanding, that is, to our faculty of judgment. Ideas express pure possibilities, not matters of fact. We must not arrogantly disdain pure ideas that express simple possibilities as the custom was in the last century, although possibilities must be kept distinct from cognitions of real things and facts.
Ideas or possibilities are important for two reasons: 1. we cannot reason without them, even about things of fact, as we learn from the theory of the origin of ideas, which shows how possibility is necessarily mingled in every idea (cf. 470); 2. reason can sometimes establish which element in possible contradictions is true.

The greatest mistake, however, is to combine what is possible in a thing with what is fact; this falsifies method itself that is the means of finding the truth.
In our case, therefore, we must carefully distinguish ideas of time obtained directly by observation and presenting us with facts,(147) from ideas that express only simple possibilities.

784. Only large actions are observable because any action, divided and reduced below a certain minimum, escapes observation.
The relationship of the quantity of these large actions (with due regard for the intensity involved) can be observed.(148)
Granted the same intensity, the different quantity is followed by a circumstance enabling observation to provide us with the knowledge of time.
An action of smaller quantity (the intensity still being uniform) is finished and observable at an instant in which we cannot observe the action of larger quantity, that is, the total effect, because it is not yet finished.

This explains the aptitude of the smaller action, part of the large action, to be observed at the time when the large action, composed of a more or less long succession, is not yet fully present to us. We call this aptitude the successive duration of an action. It is the same as the idea of time offered by observation.

785. Up till now we have dealt only with the fact. So, granted the fact, what are the possibilities that present themselves to our mind? We must remember that, in deducing possibilities, our mind goes as far as it can, right to the point where it sees contradiction.

I. First, our mind observes many real actions happening between any two given instants. These actions, although differing in quantity, maintain a certain relationship. By abstraction the mind thinks these real actions as simply possible and thus forms the pure idea of time (cf. 775); it thinks that between two given instants(149) certain quantities of action can take place having a certain relationship with their respective intensities and amongst themselves.

786. II. Next, the mind considers that the various large actions it observes are longer and shorter, that is, between two given instants, an action is sometimes repeated twice, three times or even a thousand times. Mentally therefore, we think the possibility of indefinite repetition of the action, even beyond the two instants, and see the action no longer as real but as a never-ending possibility. Hence we have the indefinite length of pure time, which is only a mental possibility. The mind sees no contradiction in the indefinite repetition of any action no matter how many times it has been performed in the past.

787. III. Noticing longer and shorter actions amongst those we can observe, we realise that while one action is being done, another is repeated many times. Our mind then reasons as follows: the shorter is repeated twice, three times, a thousand times, while the longer action is performed only once, but at the instant when the shorter action is completed for the first time, only a part of the longer action is done. Hence our mind thinks an action to be the result of many parts or else a composite of many smaller actions. It is true that a very short action escapes our observation but we then think of the possibility of a powerful observation, beyond human capacity. Such a thought, which contains no contradiction, enables us to see the possibility of an action shorter than the minimum we can observe. We recognise the possibility of indefinitely shorter actions because our mind finds no contradiction in any action, however short. This is the source of our idea of the indefinite divisibility of time.

788. IV. The indefinite divisibility of time is only the mental possibility of identifying a series of ever-closer instants and thinking of ever-shorter actions, whose beginning and end are precisely the instants of the sequence, just as the ends of a line are its points. But we are still without the idea of continuity which we are seeking. We must therefore consider how this idea also is a mental possibility to be identified carefully because of its importance and difficulty.

789. We have seen that large actions producing something have to be subdivided into smaller actions, and that the minute intervals separating these little actions from each other completely escape our observation. Thus new existences, that is, the total effect of countless tiny actions, are presented to us as a product of a single, truly continuous action (cf. 784-788). But this is only what appears, and consequently observation offers us a phenomenal idea of the continuity of time. That the idea is purely phenomenal and apparent is shown by our proof that everything necessarily happens by instants (cf. 779-781). A series of instants can never be identified in a continuous time, no matter how close to each other they are.

790. Because this truth is so important, I want to reinforce it with another proof which, leading us to the principle of contradiction, shows that the idea of a perfect continuity of time or the continuous production of a large observable effect contains an immanent contradiction. As we said, the mind moves freely in its world of possibility until it encounters something contradictory, about which it cannot think because a contradiction is impossibility itself. I now add that continuity in succession is a contradiction, and therefore impossible to be thought. The proof is as follows.

First proposition: 'To think the existence of an indeterminate number is a contradiction.'

An idea of an existing number means the number must be determinate. The fact that I think of a number means the number itself is determinate; if it were not, I could not think of it as a number. It would no longer be a particular number but number in general, a purely mental being. For instance, if I write the series of cardinal numbers 1, 2, 3, 4, 5, etc. and suppose it continued, this series is the formula expressing and including all possible particular numbers. If I then think of a particular number, I must necessarily think a number contained in the formula. But all the numbers of the series are determinate; each number is itself: 3 is 3, not 2 or 4. The specific essence of number is such that it must be determinate, and therefore an indeterminate number does not and cannot exist.

Second proposition: 'For a number of things to exist, the number has to be determinate. Therefore it must be finite.'

If a number is determinate, it must include the idea of finite being, because to be determinate, as I have said, means that the number is itself, neither more nor less; its existence must not be confused with the number preceding or following it in the series. No number can be chosen outside the series, since the series contains all particular numbers, and any number chosen from the series will always be the preceding number increased by one unit. But the preceding number is also finite, which is true for all the preceding numbers right back to the beginning: every number equals its preceding number plus one, and the whole series is a sum of finite numbers. Thus every particular number must be finite in such a way that the idea of particular number includes the idea of finite number. The existence therefore of an infinite number of things is an absurdity.

Third proposition: 'A succession of things infinite in number is a contradiction.'

The explanation of this proposition is found in the two preceding propositions.
A succession of things infinite in number cannot be thought because to think an infinite number involves contradiction.
What cannot be thought because of the contradiction involved is not possible.
Therefore a succession of things infinite in number is impossible, that is, it involves contradiction.

Fourth proposition: 'The production of an entity by means of a continuous, successive action gives a succession of things infinite in number.'

I can assign an indefinite number of instants in a continuous succession but I fully understand that this number of instants, no matter how large, can never form or diminish a continuum in any way. An instant has no length; it is a perfect point without any continuous length whatsoever. Mentally I can assign and abstract any number of instants in a continuous time but I do not diminish the length of time by the smallest fraction; I have not abstracted any length from it but assigned a number of points in it that have no length at all. Thinking like this, I conclude that, although the same continuous length still remains (divided into parts maybe, but with each part continuous), I could never finally exhaust this length even if I multiplied the instants to infinity: an infinite number of non-lengths can never make a length. However, this nature of the continuum does not involve contradiction because it does not contain an infinite number of points which I only imagine or make myself imagine in it.(150) Such a nature may be mysterious but it contains no intrinsic repugnance or contradiction.

On the other hand, I maintain that, granted a continuous succession (which is our case), there would be no question of being able to note mentally an indefinite number of instants but of having to distinguish in reality a truly infinite number of instants in this succession.
In fact, the instant in which a thing is, is distinguished in reality from the preceding instant when the thing is not.

Let us suppose that the hair in our previous example has grown 10 cm. with a continuous movement. The time required to do this can be divided by me into any number of instants. No matter how many points I freely imagine present in a continuum, there is also a corresponding real division in fact. Let us take the second, third and fourth instants of the series I have imagined; the hair is longer in the fourth than it is in the third, and longer in the third than in the second, if the growth is continuous. No matter how small, this difference is real, so that the growth in the third instant did not exist in the second instant, and the growth in the fourth did not exist in the third. So these little growths or differences exist at different instants and are therefore really distinct from each other. Now if the growth is continuous I am able not only to increase the number of instants indefinitely but also to see that they would not exhaust the continuum even when increased ad infinitum.

But what proves my thesis is this: granted a continuous, successive increase, the division into an infinite number of instants, which I am not able to make, would be made by nature herself, which would be absurd. In fact, we have seen that, when I assign a large number of instants in the continuous growth of the hair, they presuppose a real division in nature and an equal number of differences in the hair, and therefore a real number of different states and lengths. It is not I who have divided the hair into a fixed number of instants and created the differences; the differences exist independently of my mind. I see I can multiply the number of instants at will and find differences really distinct from each other. The number of instants, even if infinite, does not equal the continuum; for this reason I also see that an infinite number of really distinct differences should correspond to this infinite number, and each of these would have its own continuous length. If then a successive, continuous growth takes place, an infinite number of differences or lengths have to be distinguished in time in an infinite number of instants through which the hair has successively passed. We note that, if this result involves contradiction, the contradiction comes only from the infinite number, such that, granted the premisses, the infinite number is necessary; and if the infinite number is absurd, as it in fact is, we must say that the premisses contain absurdity.

Fifth proposition: 'The production of an ens with continuous succession is absurd.'

This is a corollary of the third and fourth propositions and is therefore demonstrated.
Our final conclusion, then, is that the continuity of time as given by observation is purely phenomenal and illusory because reason proves it to be impossible.

791. Although we have no idea of the real continuity of time by observation, we do have an idea of its abstract continuity; a confused idea obtained by considering the possibilities of things.
While one observable action is taking place between any two instants, that is, within the space of time in which an observable action takes place, we can also see a large number of other shorter or longer actions happening or at least beginning. Now let us consider the beginning of these other actions: the instant in which they start is not determined by their nature. We think therefore of the possibility of their commencement at any instant within the space of time of the initial observable action. Thus the whole of this space of time has no particle of time relative to the commencement of another action, which is different from any another particle; it has no interval of any sort. Rather, we can fix a point anywhere for this other action to start. This aptitude possessed by the initial space of time - its perfect equality and indifference to any starting point within it, its absence of interval and exclusion at any instant - is precisely that which provides us with the abstract idea we have of the continuity of time. In effect, the idea is reduced to the possibility of assigning the beginning or end of an action indifferently to all the thinkable points in a certain space of time.

792. But we said that this abstract idea of continuity is confused because, although we find on analysis that an action can begin at any instant we choose, the instants cannot be totalled together or result in any continuity of time.

793. Absurdity is that which involves contradiction; mystery is that which is inexplicable.
No matter how often sophists confuse the two concepts, they remain distinct. What is absurd must be rejected as false; what is mysterious, far from having to be rejected, frequently cannot be rejected at all. Very often, what is mysterious is a fact, and facts cannot be denied.
If physical nature itself is so full of mysterious facts, how can anyone claim there is no mystery in spiritual nature, which is far more sublime, active, immense, and profound?

794. Although I have shown that a continuum in succession is absurd, I believe that the concept of a simple continuum, which is mysterious but not absurd, definitely exists in reality. So, while I have rejected a continuum in succession, I have neither the right nor power to reject the continuum in nature, because its concept implies no evident contradiction. And just as I have proved that a continuum in time is absurd, I shall also prove the non-absurdity of a continuum in space and of duration without succession.

795. An action, an ens, the essence of an ens endures, and sometimes changelessly.
In the existence of an unchanging essence there is duration, but not the succession assignable to actions and entia which have been produced and generated but not yet perfected.
Although there is no succession in the duration of a completed ens, there can still be a continuum. The possibility of a continuum in a succession is excluded in only one case, that is, when its presence would mean, as we have seen, an infinite number of things really distinct from each other, which implies an absurdity.

796. The existence of God, of our soul, and of all things that endure, is continuous.
On the other hand succession, as found in what is generated, is not continuous, and it is this that gives the idea and measure of time.
However, it is difficult for us to think duration without succession because, as I have said so often, we are accustomed to seeking enlightenment for our thoughts from change and limitation.

797. The idea of time is the idea of a succession related to duration.
Succession is found only in passing, transient actions, that is, in the production, generation and change in things.
The idea of being that constitutes our intellect, is unchangeable, simple, and always the same. It is not subject in any way therefore to time.

798. Consequently the idea of time is not obtained a priori, as Kant thought, but only a posteriori, from finite things perceived as changeable, that is, by the use of reason.

799. This clarifies even more the ancient truth that the intellect in its superior part is outside time(151) and, when reasoning a priori, abstracts from time, which it does not find within itself. I mean that it does not find time in its first constitutive idea, in the analysis of which alone consists the matter of its a priori reasoning.(152)

(144) Our mind makes this abstraction only when it is sufficiently developed. This happens only through the use of our exterior senses. But this does not prevent the body, subjectively perceived, from being the foundation of the abstractions we are discussing.

(145) This is all we have discovered so far about extension; later we shall understand its nature better and see that it exists not only in the subject but also in the agent.

(146) Life, which also has the limitation of duration, is the first action we feel ourselves doing. Hence the feeling of time is included in the fundamental feeling. But the analysis of this feeling is difficult, and here I need only mention what is necessary for my purpose.

(147) These cognitions are perceptions of things composed of ideas and judgments. Ideas separated from judgments, and not subject to any other action, express possibilities, some of which have been actuated in reality.

(148) Previously conceived, of course, by our intelligence because only intelligence observes relationships, as I demonstrated in vol. 1, 180-187.

(149) These instants are only the beginning and term of a possible composite action taken as a norm.

(150) Later, when I speak about the continuum in space, it will be more clearly seen that the concept of a continuum is not repugnant in itself.

(151) Properly speaking the intellect is the superior part. St. Thomas says: Supremum in nostra cognitione non est ratio, sed intellectus, qui est rationis origo [Intellect is the highest part in our knowledge, not reasoning; the intellect is the origin of reasoning] (C. Gent. I, 57).

(152) St. Thomas, too, deduces the idea of time a posteriori, from phantasms: Ex ea parte qua se (intellectus) ad phantasmata convertit, compositioni et divisioni intellectus adjungitur tempus [By turning to phantasms the intellect adds time to its composition and division]. This explains why the Fathers of the Church speak so eloquently about the noblest part of the human mind; century by century they all repeat those expressions, consecrated by a constant tradition, which assert that our mind is joined to eternal and immutable things and enjoys the vision of an unchangeable truth. As St. Bonaventure says, it sees sempiternalia, et sempiternaliter [eternal things eternally] (Itin. mentis, etc.).