ON TIME.
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CHAPTER I.
IMPORTANCE AND DIFFICULTY OF THE SUBJECT.
1. The explanation of the idea of time is not a matter of mere curiosity, but of the highest importance. To convince ourselves of this we have only to consider that the explanation of the whole edifice of human cognitions is based upon it. The most fundamental and indispensable principle which supports all others, includes the idea of time. A thing cannot be and not be at the same time: "impossibile est idem simul esse et non esse." The impossibility of being and of not-being regards only the simul, the same time. Therefore, the idea of time necessarily enters into the very principle of contradiction.
2. The idea of time is involved in all our perceptions; it extends to many more objects than does the idea of space. We estimate not only the movements of bodies by time, but also the operations of the mind. We know that a series of thoughts may be measured by time the same as a series of corporal movements.
3. The idea of succession necessarily enters into that of time, and vice versa, the idea of time into that of succession. We may conceive that one thing succeeds another; but this would be impossible without succession, without a before and after, that is, without time. This reasoning, apparently vicious, shows, perhaps, that we must not explain the ideas of time and succession, the one by the other, since they are identical.
4. Time does not seem to be distinct from things; for who can imagine duration without that which lasts, or a succession without that which succeeds? Is it a substance? Is it a modification inherent in things, or distinct from them? Whatever is something exists; and yet we nowhere meet time existing. Its nature is composed of instants divisible to infinity, essentially successive, and consequently incapable of simultaneousness. Imagine the minutest instant you can, and it does not exist, for it is composed of others infinitely minute, which cannot exist united. To conceive an existing time, we must conceive it as actual, and in order to do this, we must surprise it in an indivisible instant; but even this is not time; it involves no succession; it is not duration, containing a before and an after.
5. Nothing is easier than to calculate time, and nothing more difficult than to conceive it in its essence. As to the former the learned and the ignorant are on the same footing; both have equally clear ideas; the latter is excessively difficult even to the most eminent men. The passage in the Confessiones of St. Augustine, in which the Holy Doctor endeavors to penetrate this mystery is well known.
CHAPTER II.
IS TIME THE MEASURE OF MOVEMENT?
6. Time is said by many philosophers to be the measure of movement. This idea is fruitful, but it needs to be illustrated.
When we measure movement we refer to something fixed. Thus we measure the rapidity with which we have traversed a certain space by noticing the time denoted by a watch. But how do we measure time by a watch? By the space passed over by the hand on the dial. If we reflect carefully, we shall see that this is purely conventional, or rather, that it depends upon an arbitrary condition. For if we suppose the time marked to be an hour, the space passed over by the minute hand, that is, the circumference of the dial, has no relation with the hour except what the artificer gave it by so constructing the watch that the minute hand would make one revolution every hour. If the watchmaker had constructed it differently, as he did the hour hand, the time would be the same, but the space passed over is very different.
7. The time, therefore, indicated by the watch is no measure, save as itself is subject to another measure; consequently it is not the primitive measure. The same can evidently be said of all other watches which must have been regulated one after another, until we come to the first of all watches. There was no other watch to regulate this; it follows, therefore, that no one of the measures furnished by art is the primitive measure.
8. Not finding this measure in the works of man, we must seek it in nature; and here we discover fixed measures. If we regard the course of the sun, and take for unity the time it requires from the time it leaves the meridian until it returns, we shall have the day; this divided into twenty-four parts gives us the hours. Here we have a great watch which will serve to regulate all others.
9. Nevertheless, however lightly we reflect upon this, we cannot help seeing that the solution is not so satisfactory as it seems at first sight.
Solar time and sidereal time do not agree. Thus, if we note the moment when a star is in the meridian conjointly with the sun, we shall the next day see that the star reaches the meridian a little before the sun. Which is right? Has the star taken just twenty-four hours, or the sun? If time be a fixed thing independently of movement, neither of these measures corresponds exactly to time.
10. This argument, which may be called practical, is corroborated by another purely theoretical. If we take celestial movement for the measure of time, will it be true that whenever the movement, which serves as the rule, shall be verified, that there has passed a fixed and determinate time? If we be answered in the affirmative, we must infer, that even were this movement to be accelerated or retarded, as, for instance, if a solar revolution were to be made with a half, or with twice its ordinary velocity, it would continue to mark the same time, which, however, is absurd. If it be said that the movement is supposed to be uniform, we reply, that this is a begging of the question. Uniformity of movement consists in equal times recurring after equal intervals. Did time, then, in its nature depend upon the movement of the sun, or of any star, as primitive measure, neither uniformity nor variety would have any meaning. If the space of twenty-four hours depended upon a revolution's being made, no matter in what manner whether at a snail's pace, or with the velocity of light, we should never have more or less than twenty-four hours. But if these depend upon another measure, if prior to them, there was a time which measured the velocity of movement, and determined whether it had been accelerated or retarded, then the movement of the stars is not the primitive measure; they are in the same category as our watches, they marked the time passed, but time has not passed because they mark it. Time is the measure of their movement, not their movement the measure of time. Movement is in time, not time in movement.
11. To appeal to the movement of the superior heavens, is evidently no solution of this difficulty, for what has been said of the sun, may also be said of the remotest star in the firmament. Whether we appeal to annual, solar, or sidereal movements, the same difficulty remains. Would sidereal years be the same, if the movement be made with greater or less velocity. If they would, an absurdity would follow; if not, this is not the primitive measure.
12. Moreover, we perceive, when considering movement, that we seem to conceive of greater and less velocity; and thus the idea of time, of necessity, enters into that of velocity, since velocity is the relation of space passed over in a given time. The idea of time is therefore prior to, consequently independent of, every particular measure.
13. We measure time by movement, and in order to measure the velocity of movement we need that of time. Here then, perhaps, is a vicious circle; but possibly this only shows that these are correlative ideas, the one explanatory of the other; or, rather, they are different aspects of one and the same idea. The difficulty of separating them, and the intimate union which unites them on the one hand as much as it divides them on the other, confirms this conjecture. To show this, we ask, what time has passed? Two hours. How do we know this? By our time-piece. But what if it be too fast or too slow? The measure fails. This time is thus to us as a fixed measure, prior to that of the watch by which we undertake to measure it. But what are these two hours, if we abstract the measure of the watch, that also of the stars, and every other measure? Two hours, in the abstract, can be found in no category of real or possible beings; and we cannot, without a measure, give any idea of them, nor form one for ourselves. The idea of hour refers to a determinate movement of known bodies; and this in its turn refers to others; and finally, we come to one in which we can discover no reason why it should be exempted from the general law to which the others are subject. No farther reference being possible, all measure fails; and this failing, time, by the force of analysis, vanishes.
14. Therefore, the referring of time to movement, explains nothing; it only expresses a thing known, and that is, the mutual relation between time and movement, a relation known to the unlearned, and of constant and common use; but the philosophic idea stands intact; the same difficulty remains; what is time?
SIMILARITIES AND DIFFERENCES BETWEEN TIME AND SPACE.
15. Time seems to us to be something fixed. An hour is neither more nor less than an hour, no matter how our time-pieces go, or the world itself; just as a cubic foot of space is always a cubic foot, neither more nor less, whether occupied or not occupied by bodies.
16. Time exists independent of all movement, of all succession; if it is something absolute, has a determinate value of its own, is applicable to all that changes without itself changing, the measure of all succession without itself being measured, what is it? That it is something accidental cannot be reconciled with its immutability and universality. Every thing lives in it, but it lives in nothing; every thing dies in it, but death has no power over it. When the substance perishes, the accident perishes; but time continues the same although no substance exist. Before all created beings, we conceive ages and ages, that is, time; and after the destruction, the annihilation of all beings, we still conceive a successive although unending succession, which is time. The idea, then, of time, does not demand that of the universe; it existed before it, and will survive it: but without time the universe is inconceivable.
17. The idea of time seems to be independent of the idea of any being; of all duration in it; every thing may endure in it; but it does not begin or end with what endures in itself; it is applicable to all that endures, but it is not itself an endurable thing. We imagine it to be one in the multiple, uniform in the various, fixed in the movable, eternal in the perishable; and it even seems to contain some features of the attributes of Divinity; but it is, on the other hand, essentially despoiled of every property excepting that of succession in its abstractest signification. It is essentially sterile, has no power of its own, no condition of being or action, and consequently leads to the highest imaginations of what a pure idea really is, an abstraction, which, like space, we have imagined in the presence of things.
18. The points of similarity between time and space are worthy of our attention. Both are infinite, immovable; both are a general measure; both essentially composed of continuous and inseparable parts. Limit them you cannot, determine any limit you chose, and beyond it you will see an ocean extended. Your powers are impotent; beyond the highest heaven are unbounded abysses of space; before the beginning of things there was a long chain of interminable ages.
In vain would you undertake to move space; you can only move yourself in it, or survey its various points. Its points are all fixed; you may mark out distances and directions with respect to them, but you cannot change them. The result will be analogous if you attempt to move time. The present instant is not the one just past, nor the one next to succeed; they are of necessity distinct, and of necessity exclude each other. Their very nature is to succeed each other. If their place be changed with respect to time, it ceases to be the same. Imagine, if you can, that to-morrow is to-day, that to-day is yesterday. It is impossible for that which was at a certain time not to have then been; but this would not be impossible if time could be moved; for in order that what was yesterday may not be, it is necessary to convert yesterday into to-morrow; but this would be an absurdity. The past, the present, and the future, are essentially distinct things.
A simple space, a space without parts, is no space at all, it is a contradiction; neither is a simple time, a time without parts, a time, but is a contradiction.
A space whose parts are not continuous, is not a space; neither is a time whose parts are not continuous, a time. The parts of space are inseparable; you may distinguish them one from another, count them one after the other, compare them one with another, and consider them one after another, but you cannot separate them. All imaginable bodies may exist in the apartment where we write, one or many, at rest or in motion; but the space which we conceive is one, fixed, and always the same; we can estimate its extent in cubic feet, if we choose, but these feet are fixed and inseparable; we cannot separate one cubic foot from another, even if we would; for even while we annihilate it, it is present to us, and in the same distance that we need in order to conceive separation. We cannot conceive separation, if we do not conceive distance; nor conceive distance, if we do not conceive space. We separate bodies from each other, but not one space from another. Space remains with the same continuity when bodies are separated, and it is by this continuity remaining unalterable that we measure the extent of their separation. The same happens with time; it is a chain which cannot be broken. Can we conceive three successive, immediate instants, A, B, C, and then suppress B? Certainly not; such a suppression would be impossible, or it would be a poor diversion. We destroy B in our caprice, and A and C are continuous; since being only separated by B, when it disappears the extremes meet. But in this case it is no longer A, but B, for B is the instant which precedes C. We have no other distinction than that of priority with respect to C, and continuity with A. When, then, by the imaginary disappearance of B, A is brought into contact with C, it is converted into B. Moreover, A is not only connected with C, but is preceded by others; if, then, by the disappearance of B, it makes a step, so also must the whole infinite chain which precedes it. Each one is then a soldier, or rather no soldiery is possible, for we have taken an instant from the infinite chain, and so rendered it finite. Or, more distinctly; can we conceive yesterday or to-morrow without to-day, a future or a past without the present? Evidently we cannot. Time, then, is essentially composed of inseparable parts.
19. This similarity between time and space naturally leads us to believe that time is an abstract idea just as space is. What we have said of space is applicable to time, only with a few modifications exacted by the very nature of the thing. It can in no case be without utility, in scientific investigations, to approximate and compare these great ideas, which are as immense receptacles wherein our mind deposits its treasures. The actual corporeal universe, and all possible universes, are included in the idea of space; and all finite beings, corporeal or incorporeal, are included in that of time.
20. We may well suspect that these ideas, so intimately united to our perceptions, are formed in a similar manner; for it is probable that they belong to the order of those primitive laws which govern the development of our intellect.
21. The similarity between space and time must not make us ignore the differences which distinguish them.
I. All the parts of space are co-existent; otherwise, that continuity which is essential to them, would be inconceivable. Time is composed of successive parts; to imagine them co-existent, is to destroy the essence of time.
II. Space refers solely to the corporeal world, under only one aspect, that of continuity. Time extends to all that is successive, corporeal or incorporeal.
III. Consequently, the idea of space exists only in the geometrical order, of which it is the basis. The idea of time is mingled with every thing, and more especially with our own acts.
IV. Our soul, when reflecting upon itself, can totally prescind space, and forget all its relations with extended objects; but it cannot prescind time, which it finds necessary even to its own operations.
This last difference is a great help to the understanding in what the idea of time consists; and we venture to recommend it to the attention and memory of the reader.
CHAPTER IV.
DEFINITION OF TIME.
22. Time is duration; but duration without something which endures, is an absurdity. There can then be no time without something existing. The duration which we conceive, after reducing every thing to nihility, is a vain imagination; it is not an idea, but is rather in contradiction with ideas.
An important consequence flows from this; it is, that time in itself, cannot be defined with absolute elimination of every thing to which it refers. Time, then, has no proper existence; and separated from beings is annihilated.
23. Hence, also, it follows that that infinity which we attribute to time, has no rational foundation. We have no other reason to affirm this infinity than a vague conception, which presents it as such; but we cannot fail to perceive that this conception also exists, even if we suppose all to be reduced to nothing. If, then, there is in this supposition a vain diversion of the imagination, it is not an idea, but a contradiction with ideas; and what has once deceived us, no longer deserves any credit. Those infinite ages of time which we conceive prior to the creation, are not nothing; they are an imaginary time, similar to an imaginary space.
24. Time has no necessary relation with movement, since if nothing were to move, or even no bodies to exist, we should nevertheless conceive time in the succession of operations of our soul. This last is indispensable; we must have some succession of things in order to conceive time. If we suppose nothing to change or to be altered, a being subject to no external or internal change, having one single thought always the same, one single will always the same, having no succession of ideas or acts of any kind whatever, we conceive nothing to which the idea of time is applicable.
Time is a measure; but what is it to measure in a being of this kind? Succession? But there is no succession. Duration? But what is there to measure in a duration always the same, which is only the same being? Duration must have parts given to it before it can be measured; but what parts has it? Those of time? But this would be a begging of the question, since time is applied to it when we are inquiring whether time is applicable to it. When theologians say that the existence of God cannot be measured by time, that there is no succession in eternity, but that all is united in a single point, they utter a profound truth; and Clarke, before ridiculing it, should have studied to understand it.
25. Time commences with mutable things; if they perish, it perishes with them. There is no succession without mutation; and consequently, no time.
26. What, then, is time? The succession of things considered in the abstract.
What is succession? Being and not-being. A thing exists; it ceases to exist; here we have succession. Whenever time can be calculated, there is succession; and whenever succession can be calculated a being and a not-being are considered. The perception of this relation, of this being and not-being, is the idea of time.
27. Time cannot exist without being and not-being; because in this, succession consists; wherever there is succession, there is some mutation; and there is no mutation without something being in another manner, and this other manner is not possible unless the prior manner ceases to be.
Substances, modifications, and appearances have no succession without this being and not-being. What is motion? The succession of the positions of a body with respect to various points; and this succession is verified by occupying some of these positions and destroying others. What is the succession of thoughts or affections of our mind? The not-being of some which were, and the being of others which were not.
28. Time, then, in things, is their succession, their being and not-being. Time in the understanding, is the perception of this mutation, this being and not-being.
TIME IS NOTHING ABSOLUTE.
29. Is time something absolute? The definition given in the last chapter shows clearly enough that it is not. Time in things is not being only, nor not-being only, but the relation of being and not-being. Time in the understanding, is the perception of this relation.
The measure of time is nothing else than the comparison of mutations among themselves. To us, those mutations which seem to be unalterably uniform serve as the primitive measure. For this we have taken the movement of the sun. This movement varies when compared with that of the stars, and ceases to be the primitive measure when referred to this: and it was upon this the scholastics rested when they taught that the movement of the first heavens was the primitive measure of time.
30. But what if the velocity of the sun were augmented, and it should make its revolution in one half of its time? Would the hours continue the same? We distinguish. If this alteration should be verified solely in the solar movement, we should perceive the discordance between this and all other movements; and perceiving this alteration in the sun, we should continue to refer our hours as things fixed to other measures, to our own movements, to our time-pieces, or to other heavenly bodies.
But if we suppose every thing to be changed at one and the same time, and in the same proportion; the movement of all the heavens and of every thing terrestrial to be doubly accelerated, but in such a way as not to increase the rapidity of our thoughts; we should indeed discover an alteration, but we should not know whether to attribute it to the world or to ourselves; we should perceive a discrepancy between our thoughts and these movements, but should not know whether these were accelerated or our thoughts retarded.
If this rapidity be also communicated to us, so that such or such a series of thoughts formerly corresponding to so many minutes is now made in one half the number, we should then witness a perfect correspondence in all things; we could perceive no mutation. An hour, for example, is to us only the perception of the relation of certain mutations: so long as this relation continues the same, there will be no alteration in the hour.
31. To take away from time every idea of absolute, seems an absurdity to the imagination, but not to reason. This case will make this evident. Not the man, the best skilled in perceiving the succession of time, can, if he look at no time-piece, nor refer to any measure for twelve hours, say whether eleven hours and a half or twelve hours have passed. If he live long in this way, he will become totally incapable of estimating time; if locked up in a dark dungeon for several months, he will believe he has spent years there. The idea, therefore, of the measure of time, is nothing absolute; it is essentially relative; it is the perception of the relations between various mutations. So long as these relations remain whole and intact, time will be to us the same.
DIFFICULTIES IN THE EXPLANATION OF VELOCITY.
32. Here arises a serious difficulty: if time be nothing absolute, greater or less velocity is inexplicable. This seems to result even from what we have said, that if the relation of movements be not changed, any augmentation or diminution of velocity is impossible; because, if velocity be in necessary relation to time, and time itself be nothing but the relation of mutations, it is inconceivable how time, and consequently how velocity, can be changed without changing the relation of mutations. Thus it would be impossible for the velocity of the whole mechanism of the universe to be changed, just as it would be absurd to say that the stars and every thing that exists may now experience the same changes of velocity. This would destroy the very idea of velocity; at least if taken as something absolute, wherein different grades may be considered.
33. Let us now examine this difficulty, which indeed deserves to be examined, for it seems to contradict our most common ideas.
First of all, we must premise that velocity is not something absolute, but a relation. Physicists and mathematicians express it by a fraction whose numerator is the space run over and whose denominator is the time consumed. Making V the velocity, S the space, and T the time, we shall have V = S/T. This shows the velocity to be essentially a relation; for it cannot be otherwise expressed than by the ratio of the space to the time.
34. This mathematic formula expresses the idea we all have of velocity; it expresses in three letters what the unlettered man repeatedly says to himself. The velocity of two horses is ascertained not solely by the space they have passed over, nor solely by the time they have consumed in their career, but by the greater or less space passed over in a given time; or by the longer or shorter time required to pass over a given space.
To deny, then, to velocity an absolute nature, is nothing new; for we all of us make it essentially consist in a relation.
35. In the expression V = S/T two terms enter, space and time. Viewing the former in the real order, abstraction made of that of phenomena, we more easily come to regard it as something fixed; and we comprehend it in a given case without any relation. A foot is at all times a foot; and a yard, a yard. These are quantities existing in reality; and if we refer them to other quantities, it is only to make sure that they are so; not because their reality depends upon the relation. A cubic foot of water is not a cubic foot because the measure so says, but on the contrary, the measure so says because there is a cubit foot. The measure itself is also an absolute quantity; and in general, all extensions are absolute, for otherwise, we should be obliged to seek measure of measure, and so on to infinity. True, to call things large or small depends upon comparison; but this does not change their own quantity. The diameter of the earth, compared with an inch measure, is immense; but it is an almost imperceptible point compared with the distance of the fixed stars; yet this does not prevent the inch measure, the diameter of the earth, and the distance to the fixed stars, from being values in themselves determinate, and independent of each other.[27]
If the denominator in S/T were a quantity of the same kind as space, that is, having determinate values, existing and conceivable by themselves alone, the velocity, although still a relation, might also have determinate values, not indeed, wholly absolute, but only in the supposition that the two terms, S and T, having fixed values, are compared. Thus, if we require a velocity of 4, we have only to take a fixed quantity of space, and another fixed quantity of time, having the relation to each other of 4 to 1; and this is quite easy, when S and T are both absolute quantities. If, in this supposition, an acceleration or delay be required in the whole universe, nothing more would be required than to augment or diminish the time in which each part would have to traverse its respective space. But from the difficulties which we have on the one hand seen presented to the consideration of time as an absolute thing, and from the fact that, on the other hand, no solid proof can be adduced to show such a property to have any foundation, it follows that we know not how to consider velocity as absolute, even in the sense above explained.
36. Hence a consequence not less important than striking, as to the possibility of a universal acceleration or retardation. If we would have an acceleration or retardation of the whole machine of the universe, and should abandon all motion to which we might refer time, should at once change all, not excluding the operations of our own soul, we should have a problem proposed to us that appears insolvable, nothing less than the realization of an impossibility; the relation of many terms would have to be changed without undergoing any change. If velocity be only the relation of space and time, and time only the relation of spaces traversed, it is the same thing to change them all in the same proportion, and not to change them at all; it is to leave every thing as it is.
37. The singularity of such consequences ought not to be a sufficient excuse for abandoning them. We must not forget that we are examining the common ideas of time and velocity in their most transcendental aspect, and that it is by no means astonishing that our mind finds itself, as it leaves its ordinary walks, in an entirely new atmosphere, wherein it seems to discover contradictions. When we examine the ideas of time and velocity, we unwittingly fall into the error of uniting them in the same explanation. We would prescind them; but this we do only with great difficulty, and we often fall into a vicious circle. Hence it is that when, by a great effort, we succeed in really prescinding, the consequences that follow seem contradictory; but this apparent contradiction arises solely from our not having persevered with due firmness in our prescision; and as, in this case, the understanding starts from two different suppositions, whereas it believes that it starts from one alone, the results seem to it contradictory, which in reality they may not be. The same thing occurs in the examination of the idea of space.[28]
CHAPTER VII.
FUNDAMENTAL EXPLANATION OF SUCCESSION.
38. The reasons that destroy the absolute nature of time, inasmuch as it is subject to measure, do not seem fully to obviate another difficulty, arising from the consideration of time in itself. If indeed time be succession, what is this succession? It is evident that things succeed each other; but if there be no before or after, that is, time existing before succession, since succession consists in some things coming after others, what is the meaning of succeeding each other? Thus, time is explained by succession, and succession by time. What is afterwards but a part of time that is in relation with a heretofore?
39. What we said in the fourth chapter does not seem completely to solve the difficulty; for being and not-being do not form succession, save only inasmuch as one comes after the other, that is, inasmuch as it presupposes the time to be explained already to exist. There may be a simultaneous being and not-being of distinct things; and there is in one and the same thing no repugnance between being and not-being, if not referred to the same time. In such a case, therefore, this is always presupposed so to be; since in one and the same thing, being and not-being are inconceivable unless at different instants of time. Hence it follows that being and not-being do not sufficiently explain time.
40. This difficulty is indeed grave; and we must, in order to solve it, elaborate a fundamental explanation of succession. This we shall endeavor to do, and without in any sense supposing the idea of time.
41. There are things which exclude, and things which do not exclude each other. When we have existence of things which exclude each other, we have succession. If in a line a————b————c, a body be at a, it cannot pass to b, without ceasing to be at a. The situation at b excludes that at a; and so also that at c excludes that at b. When we see things exist notwithstanding this reciprocal exclusion, we find succession.
42. Succession is, in reality, the existence of things mentally exclusive of each other. What each involves is the being of that which excludes, and the not-being of that which is excluded.
43. This exclusion prevails in all variations; and therefore, we find succession in every variation. Variation is the mutation of states; the loss of one, and the acquisition of another; therefore, there is exclusion, for being excludes not-being, and not-being, being.
44. When we perceive these distinctions, these exclusions realized, we perceive succession, time. When we compute these exclusions, these distinctions in which distinct and exclusive things are offered to us, such as being and not-being, we compute time.
45. Here arises a difficulty. If succession involves exclusion, and there is no succession without exclusion, it follows that things which do not exclude each other are simultaneous; and from this we infer the absurdity of saying, that the things happening in the time of Adam, which do not exclude those of our own time, are simultaneous. The motion of the plants of Paradise excludes not that of plants in gardens now existing; this motion, then, is simultaneous with that; the motion that was then is the present; and the present motion was then; which is inconceivably absurd.
This difficulty is serious: it seems to be based upon a reason founded in evident truths; but it is not impossible to give a solution of it.
46. Were there to exist one thing which excluded nothing, and was excluded by nothing, it would be simultaneous with every thing. Know you what this thing is? There is but one, God. It is therefore that the theologians say, with great truth, and with a profoundness which has not, perhaps, been at all times understood even by those who have made the remark, that God is present to all times; that to him there is no succession, no before or after; that to him every thing is present, is now.
47. Of God alone is this true; in all else there is some exclusion, being and not-being, and therefore succession. Let us now, for example, examine how the motion of the plants in our gardens is excluded by that of the garden of Eden. How are those of our gardens moved? By existing, and also by being subject to conditions necessary to motion. How do they exist? By a development of the germs they themselves contain. What is this development? A series of motions, of being and of not-being, and consequently of things that exclude each other. There is, then, no simultaneousness between those of the garden of Eden and those of our own gardens; for between the former and the first germ, there was no mediation other than the movement of the first development; whereas, between the movements of those of our gardens and the first germ, many others have intervened. Here we have exclusion, being and not-being. The number of exclusions necessary to existence is very different in the two cases; therefore, there is no simultaneousness. Considering all the developments, and all the changes of the orb, as a dilated series of terms interlaced by a mutual dependence, as in fact they are by the laws of nature; and calling these terms A, B, C, D, E,—N, the plants of the garden of Eden belong to the term A, and those of ours, to the term N.
48. The non-simultaneousness of motion is proved in the same manner as the non-simultaneousness of existence, for motion is a manner of existing. Moreover, the air which agitates the plants of our gardens has been moved by another, and this other by yet another; and these motions, subject to all the fixed and constant laws of nature, are all interlinked from the very first motion, just as the wheels are interlocked in a system of machinery. But as the curvature of one wheel is not that of the other, so these motions are different, and exclude one another down to the last, which is the air which moves the present plants.
49. This explanation of succession and time, throws much light on the idea of eternity; and shows that eternity, or the simultaneousness of all existence, belongs only to the immutable being. All mutable beings, which necessarily imply a transition from not-being to being, and from being to not-being, involve a succession, if not in their substance, at least in their modifications.
50. This explains how the idea of time is found in almost all our conceptions, and is expressed in all languages. Man continually perceives being and not-being in all around him. He perceives it within him, in the multitude of his thoughts and affections; at one time agreeing, at another disagreeing; sometimes connected, and sometimes separated; but always distinguished from one another, always producing different modifications in the mind: they therefore exclude each other, and cannot co-exist; because the existence of one excludes the existence of the other.
CHAPTER VIII.
WHAT IS CO-EXISTENCE?
51. If the succession of time involves exclusion, there must be co-existence where there is no exclusion: therefore, supposing that God has created other worlds, they must necessarily be contemporaneous with the present; for it is evident that they would not be excluded; and as they have not the mutual relation of cause and effect like the phenomena of the present world, we cannot apply to them the explanation which we gave to show that the motion of the plants of Paradise was not contemporaneous with the motion of the plants in our gardens. We must, therefore, hold that it would have been impossible for another world to exist before the present world; and that though God might create as many beings as he pleased, yet, so long as they do not exclude each other, they must be contemporaneous.
52. This difficulty is not easy to solve, unless we have perfectly understood the meaning of the word exclusion. By exclusion is meant, not only the intrinsical repugnance of one being to another, but that, for one reason or another, whether intrinsical or extrinsical, the existence of one implies the negation of the existence of the other. This explanation solves the difficulty.
53. Two worlds, entirely independent of one another, could have been subjected to this exclusion by the will of God. God can create one without creating the other; in this case, we find the existence of the first and the negation of the existence of the other. God can cease to preserve the first, and create the second; we then find the existence of the second and the negation of the first. In both these cases, there is before and after, a succession in existence. God can create both; we can conceive the existence of both without the negation of the existence of either; this is co-existence.
54. We shall understand the whole question much better, if we examine for a moment the meaning of co-existence. Two beings co-exist, or exist at the same time, when there is no succession of one to the other, when both exist, when there is not the existence of one and the negation of the other. In order to conceive co-existence, we need only conceive the existence of two beings: we form the idea of succession, by combining with the idea of the existence of one the idea of the negation of the other. The co-existence of two beings is their existence; their succession is the being of one, and the not-being of the other. Being refers only to the present; the past and the future are not being. That only is which is, not that which was, or which will be. There is a profound truth, a sound philosophy, and an admirable ontology in those words of the sacred text: "I am who am. He who is, hath sent me to you."
55. Without being and not-being, there is no succession, there is no time, there is only the present, there is eternity. To a being immutable in itself, and in all its acts, one in its intelligence, one in its will, always its own object, unchangeable, in the plenitude of its being, without any kind of negation,—to such a being there is neither before nor after; there is only now. If you give to it the succession of instants, you apply to it, without any ground, the work of your imagination. Reflect well on the meaning of before and after, in that which can change in nothing, by nothing, and for nothing, and you will see that succession is in this case a word without any meaning. We attribute to it succession because we judge the object by our perceptions, and our perceptions are successive; they have an alternative of being and not-being, even when applied to an immutable object.
56. Every one may experience this in his own mind. Conceive two beings to exist; add to this thought nothing accessory, neither the negation of being, nor of time, nor of any thing else,—merely conceive the existence of two beings, and see if any thing is wanting to complete your idea of their co-existence. If, on the contrary, you wish to perceive succession, or difference of instants, you must perceive the existence of one, and the negation of the existence of the other. Therefore, the idea of co-existence is simple, and implies only the existence of the beings, but the idea of succession is composed of the combination of being with not-being.
57. I must here call attention to the fruitfulness of the idea of being, which, combined with the idea of not-being, furnishes the idea of time. We have before seen, that the ideas of unity and number were favored in the same manner, and we shall soon have occasion to observe, how, from the ideas of being and not-being, spring others, which, although secondary in respect to these, are the most important of all the ideas which the human mind possesses. I call attention to this, from a desire that the reader may become accustomed to refer all ideas to a few points where they are united, not by a factitious chain imposed by arbitrary methods, but by the internal nature of things themselves. What extension is, in relation to sensible intuitions, the idea of being is, in relation to conceptions. The intuition of extension, and the idea of being, are the two fundamental points in all ideological and ontological science; they are two primitive data possessed by the mind, by means of which it can solve all problems, either in the sensible order, or in the purely intellectual. Regarded from this point of view, every thing becomes clear, and is arranged in the most logical order, because it is the order of nature.
58. I wish to make one observation on the method which I have followed in this work. I did not think it well to explain separately my opinion of these general connections of all ideas; for then it would have been necessary to treat philosophy in a systematic order, placing at the beginning what ought to be at the end, and trying to establish as a preliminary doctrine, what ought only to be the result of a collection of doctrines. To attain my object, it was necessary to go on analyzing in succession facts and ideas, without reference to system, without doing violence to them, in order to make them conform to a system, but only examining them, in order to ascertain their result. This, undoubtedly, is the best method. We thus obtain the knowledge of truth as a fruit of our labors on facts, and are not obliged to alter objects for the sake of forcing them to bend to the author's opinion. After the application which we have been making of the ideas of being, and not-being, to one of the most abstruse points of metaphysics, it is not out of place to call the reader's attention to this for a moment, so that he may be able to see the connection of doctrines.
PRESENT, PAST, AND FUTURE.
59. After explaining the idea of co-existence, we came to the definition of the various relations which time presents. They are principally three: present, past, and future. All others are combinations of these.
60. The present is the only absolute time: by this I mean, that it needs no relation, in order to be conceived. The present is conceived without relation to the past or to the future. Neither the past nor the future can be conceived without relation to the present.
61. The past is an essentially relative idea. When we speak of the past, we have to take some point to which it refers, and in respect to which we say it is past. This point is the present, either in reality, or in the ideal order; that is to say, that by the understanding, we place ourselves in that point, and make it present to us, and in reference to it, we speak of the past.
To prove that the idea of past is essentially relative, we may observe, that by varying the points of reference, the past may cease to be considered as such, and may be presented as present or future. Speaking of the events of the time of Alexander, they are presented to us as past, because we consider them in relation to the present moment; but if we are speaking of the empire of Sesostris, the epoch of Alexander ceases to be past, and is converted into future. If we were relating events contemporary with the deeds of Alexander, this epoch would cease to be past or future, and would become present.
The past, therefore, is always in reference to a present point, taken in the course of time, and it is only in respect to this, that any thing is said to have been, to be past; without this relation, the idea of past is absurd, and it is impossible to conceive it.
62. What is the relation of past? According to the definition which we have given of time, when we perceive the being of any thing, and then its not-being, and the being of something else, we say the first is past in relation to the second.
63. What would take place, then, if we should perceive the being of something, and then its not-being, without relation to any other being? This hypothesis is absurd; for we must always have this other being, if we perceive being and not-being.
But it may be replied that we may suppose the disappearance of ourselves, and then the objection would be good. Even though we should disappear, there would still remain intelligences capable of perceiving being and not-being. If there were no finite intelligence, there would still be the infinite intelligence.
64. Here arises a new difficulty; for it may be asked whether the thing would be passed with relation to the infinite intelligence. If we admit that it would be, we seem to introduce time with the duration of God, by which we destroy his eternity, which excludes all succession. If we say that to the eyes of the infinite intelligence the thing would not be past, then it would not be past in reality; for things are as God knows them. Then there would be the idea of being and of not-being, and still there would not be the idea of past. This difficulty arises from a confusion of terms.
Let us suppose that God had created only one being, and this being had ceased to exist; and let us see what would be the result of this hypothesis. God knows the existence and the non-existence of the object. This intellectual act is most simple; there can be no succession in it. There is properly no past with respect to God, and applied to the object this idea can only mean its non-existence in relation to its existence which is destroyed. When the ideas are presented in this light it is easy to understand that there is no past in God, but that there is the knowledge of past things.
65. On this hypothesis, how can the time of only one creature be measured? By its changes. But if it has none? On this imaginary supposition there would be no time.
This conclusion is absolutely necessary, although it may at first sight seem strange. We must either abandon our definition of time, or else admit that there is no time where there is no change.
66. Whatever conclusions we form on questions founded on imaginary suppositions, this, at least, is certain—that the idea of past is essentially relative, and that on no supposition can we conceive the past, if we take from it all relation. The expression has been implies both being and not-being,—the succession which constitutes time. In this relation the order is such that not-being is perceived after being, and this is why it is called past.
67. The idea of the future is also relative to the present. The future is inconceivable without this relation. The future is that which is to come,—that which is to be with respect to a real or hypothetical now; for we may apply to the future what we said of the past, that it is changed by changing the point of its reference. The future for us will be past to those who come after us; that which was future to those past, is present or past to us.
The point of reference of the future is always a present moment; it cannot be referred to the past as its ultimate term; for it is in itself referred equally to the present.
68. Therefore all that we find in the idea of time that is absolute is the present. The present needs no relation. It not only needs none, but it admits none. We can neither refer it to the past nor to the future, because these two times both presuppose the idea of the present, without which they cannot even be conceived.
69. Time is a chain whose links are infinitely divisible. There is no time which we cannot divide into other times. The indivisible instant represents something analogous to the indivisible point; a limit which we approach without ever reaching, an unextended element producing extension. A geometrical point must be moved in order to generate a line; but no motion is conceived as possible unless we presuppose space in which the point moves; or in other words, when we treat of the generation of extension, we commence by presupposing it. A similar thing happens in relation to time. We imagine an indivisible instant, from the fluxion of which results the continuity of duration which we call time. But this fluxion is impossible, unless we suppose a time in which it flows. We wish to examine the generation of time, and we suppose it already existing, prolonged infinitely, as an immense line on which the fluxion of the instant takes place. What are we to infer from these apparent contradictions? Nothing but a strong confirmation of the doctrine which we have established.
Time distinguished from things is nothing. Duration in the abstract, distinguished from that which endures, is a being of reason,—a work which our understanding produces from the materials furnished by reality. All being is present. That which is not present is not-being. The present instant, the now, is the reality of the thing; it is not sufficient to constitute time, but it is necessary to time. There can be present without either past or future; but there can be neither past nor future without the present. When besides being there is not-being, and this relation is perceived, time begins. To conceive past and future without the alternation of being and not-being, as a sort of line infinitely produced in two opposite directions, is to take an empty play of the phantasy for a philosophical idea, and to apply to time the illusion of imaginary space.
70. Therefore, if there is only being, there is only absolute, present duration; therefore no past nor future, and, consequently, no time. Time is in its essence a successive, flowing quantity; it cannot be seized in its actuality; for it is always divisible, and every division in time constitutes past and future. This is a demonstration that time is a mere relation, and in so far as it is in things, it only expresses being and not-being.
APPLICATION OF THE PRECEDING DOCTRINE TO SEVERAL IMPORTANT QUESTIONS.
71. This theory will be much better understood by its application to the solution of several questions.
I. How long a time had passed before the creation? None. As there was no succession, there was only the present, the eternity of God. All else that we imagine is a mere illusion, contrary to sound philosophy.
II. Was it possible for another world to have existed when this world's existence began? Undoubtedly it was; this would only require that God had created it, without creating this world; it would only require the being of the one and the not-being of the other. And as there was not-being because there was no creation, it follows that if God had created the one without creating the other, and had ceased to preserve the first when he created the second, there would have been succession and priority of time.
III. Here is another question which is somewhat strange, and at first seems very difficult. Was the existence of a world prior to this possible in any time? or, in other words, could another world have ceased to exist some time before the beginning of the existence of this world? This question implies a contradiction. It supposes an interval of time, that is, of succession, without any thing to succeed. If a world had ceased to exist, and no new world should exist, there would be nothing but God; there would then be no succession, there would be only eternity. To ask, therefore, how long a time they were apart, is to suppose that there is time, where there is none. The proper answer is, that the question is absurd.
But we shall be asked, were they distant, or were they not? There is no distance of time where there is no time; this distance is a mere illusion, by which we imagine time, while, by the state of the question, we suppose that there is no time.
Then it may be objected, that the two successive worlds must be necessarily immediate, that is to say, that the first instant of one must be immediately connected with the last instant of the other. I deny it. For immediateness of instants supposes the succession of beings mutually connected in a certain order; the two worlds in question would have no mutual relation; consequently, there would be neither distance nor immediateness between them.
But, it may be replied, there is no medium between being and not-being, and distance being the negation of immediateness, and immediateness the negation of distance, by denying one, we affirm the other; they must, therefore, either be distant or immediate. This reply also supposes something which we deny. It speaks of distance and immediateness, that is, of time, as though it were something positive, distinct from the beings themselves. The principle, that every thing is, or is not, quodlibet est vel non est, is applicable only when there is something; but when there is nothing, there is no disjunctive. The time of the two worlds is nothing, as distinguished from them; it is the succession of their respective phenomena; the succession of the two worlds, the one to the other, is nothing distinguished from them; it is the being of the one, and the negation of the other, and the being of the second and the negation of the first. God sees this; an intelligent creature would also see it, if he could survive the annihilation of the first world. To the eyes of God, who sees the reality, succession would be simply the respective existence and non-existence of the two objects. The intelligent creature would say, that the two worlds are immediate, if to the perception of the last instant of the annihilated world, the perception of a new existing world had followed without another intermediate perception; and he would say, that there is distance, if he had experienced various perceptions between the annihilation of the old and the perception of the new creation. The measure of this time would be taken from the changes of perceptions of this creature, and would be longer or shorter, according to the number of these perceptions.
72. The idea of time is essentially relative, as it is the ordered perception of being and not-being. The mere perception of one of the two extremes, would not be sufficient to produce the idea of time in our mind; for this idea necessarily implies comparison. The same is true of the idea of space, which has always a great resemblance to time. We cannot conceive space, or extension of any kind, without juxtaposition; that is to say, without relations of various objects. Multiplicity necessarily enters into the ideas of both space and time. Hence, we may say, that if we conceive a being, absolutely simple, with no multiplicity, either in its essence, or in its acts, but in which all is identified with its essence, there is no room for the ideas of space and time; and, consequently, they are mere fictions of the imagination, when we attribute to them any thing real, beyond the corporeal world, and before the existence of the created.
CHAPTER XI.
THE ANALYSIS OF THE IDEA OF TIME CONFIRMS ITS RESEMBLANCE TO THE IDEA OF SPACE.
73. Having explained the idea of time, and applied it to the most difficult questions, we may explain this doctrine still farther, by examining what we have already intimated concerning the resemblance between time and space.[29] There is analogy in the difficulties; analogy in the definitions of both ideas; analogy in the illusions which hinder the knowledge of the truth. What we announced before with respect to these two ideas, considering the idea of time as only what it appeared at first sight, we may now assert as the secure result of analytical investigations. I call attention in particular to the following parallel, because it greatly explains the ideas of both.
74. Space is nothing in itself, distinguished from bodies; it is only the extension of bodies: time is nothing in itself, distinguished from things. It is only the succession of things.
75. The idea of space is the idea of extension in general; the idea of time is the idea of succession in general.
76. Where there are no bodies, there is no space: where there are no things which succeed each other, there is no time.
77. An infinite space, before the existence of bodies, or outside of bodies, is an illusion of the imagination: an infinite time before the existence of things, or outside of them, is also an illusion.
78. Space is continuous: so is time.
79. One part of space excludes all others; one part of time also excludes all others.
80. A pure space, in which bodies are situated, is imaginary: a succession, a time, in which things succeed, is also imaginary.
81. That which is entirely simple has no need of space, and can exist without it: that which is immutable has no need of time, and can exist without it.
82. The simple and infinite is present to all points of space, without losing its infinity: the immutable and infinite is present to all instants of time, without altering its eternity.
83. Two things are distant in space, because there are bodies placed between them; this distance is only the extension of the bodies themselves: two beings are distant in time, because there are other beings placed between them; this distance is the existence of the beings which are placed between.
84. Extension needs no other extension, in which to be placed, otherwise we should have a processus in infinitum: the succession of things, for the same reason, needs no other succession in which to succeed.
85. Just as we form the idea of continued succession in space by distinguishing different parts of extension, and perceiving that one excludes the others, so we also form the idea of continued succession of time by distinguishing different facts and perceiving that one excludes the others.
86. In order to form determinate ideas of the parts of space, we must take a measure and refer to it: to form an idea of the parts of time we also need a measure. The measure of space is the extension of some body which we know: the measure of time is some series of changes which we know. To measure space we seek for fixed things, as far as possible; for the want of something better, men have recourse to the parts of the body, the hand, the foot, the yard, and the pace, which give an approximate, if not an exact measure. The exact sciences having advanced, they have taken for their measure the forty-millionth part of the meridian of the earth: time is measured by the motion of the celestial bodies, by the diurnal motion, the lunar, solar, and sidereal year.
87. The idea of number is necessary in order to determine space and compare its different parts: the same idea is necessary in the same manner to time. The discrete quantity explains the continuous.
RELATIONS OF THE IDEA OF TIME TO EXPERIENCE.
88. If time is nothing distinct from things, how does it happen that we conceive it in the abstract, independently of things themselves? How does it happen that it presents itself to us as an absolute being, subject to no transformation or motion, while within it every thing is moved and transformed? If it is a subjective fact, why do we apply it to things? If it is objective, why is it mingled with all our perceptions? Because it contains a necessity sufficient to be the object of science.
The idea of time, whatever it may be, seems prior to all perception of transformation, the consciousness of all internal acts included. It is impossible for us to know any of these things, unless time serves as a receptacle in which we may place our own changes and those of others.
89. The idea of time is not the result of observation; for in that case it would be the expression of a contingent fact, and could not be the principle of science. We measure time with the same exactness as we do space, and it is one of the most fundamental ideas of the exact sciences, in so far as they have any application to the objects of nature.
90. It might seem to follow from this that the idea of time is innate in our mind; and that it is prior to all ideas, and even sensations; for both are necessarily involved in successive duration.
91. The necessity of the idea of time seems to prove that time is independent of transitory things; in this case we are obliged to convert it into a purely subjective fact, or else to grant it an objective reality, independent of that which is changeable. By the former we destroy it; by the latter we make it an attribute of the divinity. To deny time is to deny the light of the sun; to raise it to the rank of an attribute of divinity is to admit change in an immutable being. If we make it purely subjective, we deny it; if objective, we make it divine: is there no middle way?
92. I agree that the idea of time is not derived from mere experience; for experience could not furnish an element so solid and so fixed, on which we may with perfect security rest all the observations of science. Still less can it be maintained, that the idea of time is derived from purely sensible experience, or that it is in itself a sensation.
93. The idea of time is not a sensation; for it is relative, and sensation is an affection of our being, without any reference to or comparison with any thing. When we experience sensations, if we had only the sensitive faculty, we should be limited to pure sensation, without any consideration of before or after, or any relation of any kind. Sensation, being limited to certain objects, cannot, like the idea of time, extend to all objects. By time, we measure not only the external world, but also the internal; not only the affections of the body, but also the most concealed and abstract actions of our mind. Time is, in itself, succession, and, in our mind, it is the perception of this succession; it cannot, therefore, present any object to the mind; even when time refers to objects, and is, as it were, the link between them, it is not itself either these objects themselves, nor the intuition of them. The idea of the time which measures the succession of a sound or of a sight, clearly is not either the sound or the sight, but the perception of their succession, of their connection. If it were the sight alone, or the sound alone, either the sight or the sound would alone be sufficient in order to perceive time, which is absurd; for there is no time without succession, and consequently there can be no time which measures two sensations without these sensations. The idea of time is independent of either of the two; it is superior to them; it is a sort of universal form, independent of this or that matter; so that, if after the sound, instead of the sight, another sound should be perceived by us, the measure of the succession would be the same, and this measure is nothing more than the idea of time. Sensations being mere contingent facts, cannot be the foundation of necessary and universal truths, they cannot serve as the basis of a science. But the idea of time is one of the principal ideas in all the physical sciences, and, like extension, is subjected to a very rigorous calculation; therefore, it is not a sensation, and it is not derived from sensation.
94. Purely experimental cognitions are confined to the sphere of experience; the idea of time extends to the whole real and possible order, it teaches us not only what is, but what may, and what must be; its relations are of absolute necessity, and may be subjected to the strictest calculation; therefore it contains something more than the elements furnished by sensible or insensible experience. It is not otherwise possible to explain the necessity which it involves, or to pass beyond a collection of contingent facts to arrive at the possession of an element of science.
95. Let us observe, as we pass, that here is found another proof that the system of Condillac is neither true nor subsistent. His system has been found insufficient to explain any fundamental idea, and it does not explain the idea of time, any more than the rest, although it seems as though this idea must have the most intimate relations to the sensible order.
96. If the idea of time is not merely experimental, how explain the priority and necessity of time?
KANT'S OPINION.
97. Kant uses the same theory to explain time that he used to explain space. Time, according to him, is nothing in itself, neither is it any thing in things; it is a subjective condition of intuition, a form of the internal sense, by means of which phenomena are presented to us as successive, just as space was the form by which they are presented as continuous. To speak frankly, it seems to me that this is saying nothing; it affirms a well-known fact, but does not explain it. Who does not know that what we perceive we perceive in succession—that we perceive even our own perceptions in succession? But what is succession? This is what he ought to have explained.
98. Kant says that time is only in us; but I should like to ask him, if succession is only in us. He pretends that we know nothing of the external world, but that we perceive certain appearances, or phenomena; but he does not deny that beyond the appearance there may be a reality. If this reality is possible, changes are possible in it; and change cannot be conceived without succession, nor succession without time.
99. According to Kant, the ideas of space and time are À priori, they cannot be empirical, or experimental; for in that case they could not be the basis of science; we could only affirm what we had experienced, and this only with respect to the cases in which we have experienced it. This is true, and I have demonstrated it in the last chapter; but, conceding this priority, it proves nothing in favor of Kant's system. The ideas of space and time, although À priori, may nevertheless correspond to something in reality, as follows from the theory by which I have explained them.
100. Time is not any thing which subsists by itself, but it is not equally certain that it does not belong, as an objective determination, to things, and that nothing remains of it, if we abstract it from all the subjective impressions of intuition. I have demonstrated that time does not subsist by itself, and that a duration without any thing which endures, is an absurdity; but it does not follow from this that the order represented by the idea of time is not something real in the objects. Abstracting it from our intuition, there still remains something which verifies the propositions by which we express the properties of time.
101. The German philosopher makes time purely subjective, and relies on the following argument: "If time were a condition belonging to the things themselves, or an order, it could not precede the objects as a condition of them, and be known and perceived À priori by synthetical judgments. This last is easily explained if time is nothing but the subjective condition under which all intuitions are possible in us. For then this form of the internal intuition can be represented before the objects, and consequently À priori....
"If we abstract our manner of perceiving ourselves internally, and of embracing, by means of this intuition, all external intuitions in the faculty of representation, and consequently take objects just as they may be in themselves, time is nothing....
"I can say that my representations are successive, but this only means that we are conscious of them in a succession,—that is, in a form of the internal sense. Time would not therefore be any thing in itself, nor a determination inherent in things."[30]
102. It is easy to see that the philosopher is struggling between two difficulties. The first is, how to explain the necessity involved in the idea of time, if he makes it proceed from experience. The second is, how, if it is not derived from experience, it can be found really in things, or, at least, how we can know that it is found in them.
Hence, he concludes, that it is not possible to save the necessity involved in the idea of time, unless by making it a purely subjective fact, a form of an intuition, entirely independent of the reality of things.
It seems to me, that by attending to the principles established above, we can give an objective value to time, independently of our intuition, and explain its relations to experience, without destroying the necessity contained in its idea.
CHAPTER XIV.
FUNDAMENTAL EXPLANATION OF THE OBJECTIVE POSSIBILITY AND OF THE NECESSITY OF THE IDEA OF TIME.
103. Things in themselves, abstracted from our intuition, are susceptible of change. Where there is change, there is succession, and where there is succession, there is a certain order in the things which succeed,—an order which is really in the things themselves, although it does not subsist by itself, separated from them.
Kant might object to this, that perhaps the changes are not in things, but in the phenomena, or the manner in which they are presented to our intuition. But he cannot deny, that whether these changes are in the reality, or not, they are, at least, possible, independently of the phenomena. Therefore, he asserts, without reason, that time in the things is nothing, and that it is only the form of our internal sense. If he admits the possibility of real changes, he must also admit the possibility of a real time; if he denies that it is possible for the things in themselves to be really changed, we would ask him how he came to know this impossibility,—he, who limits all our knowledge to the purely phenomenal order. We cannot know that a thing is impossible in an order, if we know nothing of this order; if Kant maintains that we know nothing of things in themselves, he cannot prove that we know the impossibility of their really changing.
104. It is then demonstrated that time, or a real order in things, is, at least, possible. Therefore, we cannot say that time is a purely subjective condition, to which nothing can correspond in the reality.
105. Admitting the possibility of an objective value of the idea of time, not only in reference to the purely phenomenal order, but also to the transcendental, or rather to things considered in themselves, and abstracted from our intuition; we shall see how the objectiveness of the idea of time and its relations to experience can be shown, without destroying the intrinsic necessity which makes it one of the principal elements of the exact sciences.
106. Time, considered in things, is the order of their being, and their not-being. The idea of time is the perception of this order in its greatest generality and abstracted from the objects which are contained in it. As our understanding evidently can consider a purely possible order of things, the idea of time extends to the possibility as well as the reality. This is why we conceive time before and after the present world, similar to the space which we imagine beyond the limits of the universe. The idea of being, elevated to a purely possible region, in which it is abstracted from all individual phenomena, is freed from the instability to which the objects of our experience are subject: it can then be an absolutely necessary element of science; for it expresses a relation which is not affected by any thing contingent. These observations are a solution of all difficulties.
IMPORTANT COROLLARIES.
107. Is the idea of time derived from experience? This question is answered by what we said of the idea of being. It is not a type existing previous to all sensation and to all intellectual act; it is a perception of being and not-being which accompanies all our acts, but is not presented to us separately until reflection eliminates from it all that does not belong to it. This perception is the exercise of an innate activity, which is subjected to the conditions of experience in all that concerns the beginning and the continuation of its acts, but not with respect to its laws which are characteristic of it, and correspond to the pure intellectual order. This activity is unfolded in the presence of causes or occasions which excite it, and its exercise ceases when these conditions are wanting; but while the activity acts, it exercises its functions in accordance with fixed laws which are independent of the objects exciting it.
108. It is therefore clear that the idea of time is not strictly derived from experience, except inasmuch as the mind is excited to develop its activity by experience. Neither is it entirely independent of experience; for without experience we should have no knowledge of change, and consequently the intellect would not perceive the order of being and not-being, in which the essence of time consists.
109. Hence the idea of time is not a form of the sensibility, but of the pure intellectual order; and although it descends to the field of sensible experience, it does so after the manner of other general conceptions.
110. The idea of time is one of the most universal and indeterminate ideas which our mind possesses; for it is the combination of the two most general and most indeterminate ideas, being and not-being. Here is the reason why the idea of time is common to all men, and is presented to us as a form of all our conceptions and of all the objects known.
The ideas of being and not-being, entering as primitive elements into all our perceptions, generate the idea of time. We therefore find this idea in the inmost recesses of our soul as a condition from which we cannot withdraw ourselves, and from which we exempt the Infinite Being himself only by an effort of reflection.
111. The transition from the purely intellectual order to the field of experience takes place in the idea of time, in the same manner as in the other intellectual conceptions. I have, therefore, nothing to add to what I have already said on this point when explaining it elsewhere.[31]
CHAPTER XVI.
PURE IDEAL TIME AND EMPYRICAL TIME.
112. Time is not only conceived as a general order of change, or as a relation of being and not-being; but also as something fixed, which can be measured with exactness. Thus, before the creation of the world, we conceive not only an abstract order, or time, but a time composed of years, of centuries, or some other terms. But this, if we closely examine it, is only an idea in which we conceive the phenomena of experience under a general view, taking them out of actuality and contemplating them in the sphere of possibility. Neither the years nor the centuries existed when there was nothing by which they could be measured. If we imagine a sort of vague line of duration prolonged to infinity, abstracting it from the measure and the object measured, we become the sport of our imagination, and are entangled in contradictions from which it is difficult to extricate ourselves.
113. The pure and abstract idea of time admits no measure; it is a mere relation of being and not-being. The measure is possible only when the idea of time is combined with the phenomena of experience.
Subject as we are to change, and situated amid beings as changeable as ourselves, we should certainly fall into the greatest confusion of our ideas, if in this ebb and flow of external as well as internal existences which appear to us, we had not the greatest facility in referring them to fixed measures, which are the thread that guides us in this labyrinth of continual variations.
114. Two things are required for this measure: first, a suitable phenomenon, and secondly, the idea of number. The common idea of time which serves for the ordinary purposes of life of these three elements: the pure idea of time, or the relation of being and not-being; secondly, a suitable phenomenon to which we apply this pure idea; and thirdly, the numeration of the changes of this phenomenon. Apply this observation to all the measures of time, and you will find these three elements always sufficient, but always indispensable also.
115. From this we deduce the necessity of time, even considered empirically; for it involves two ideas, the one metaphysical, and the other mathematical, applied to a fact. The metaphysical idea is the relation of being and not-being; the mathematical idea is number; and the fact is the sensible phenomenon, as, for example, the solar, or human motion. Metaphysics and arithmetic take charge of the absolute certainty; the fact observed answers for the experimental certainty; and as, on the other hand, this phenomenon is supposed to be certain, because, in case it were necessary we could abstract it from the reality, and attend only to the possibility; it follows that time, even considered empirically, may become the object of the exact sciences.
116. This theory does not make time a purely subjective condition, nor grant it a nature independent of things; it reconciles the pure intellectual order with the order of experience; and places man in communication with the real world, without creating a contradiction in his ideas.
RELATIONS OF THE IDEA OF TIME AND THE PRINCIPLE OF CONTRADICTION.
117. Let us explain the true meaning of the principle of contradiction. "It is impossible for any thing to be and not be at the same time." The connection of the ideas contained in this principle seems at first sight to be explained without any difficulty; so that, to raise questions as to its true sense is to place ourselves in contradiction with one of the fundamental truths on which rests the edifice of our knowledge. For, if there be any doubt as to the true meaning of the principle, it may be understood in several ways, and then there will be another doubt as to whether the generality of men understand it as they ought to, and whether, consequently, it is for them a solid foundation of knowledge.
This difficulty ceases to be one when we reflect that the most evident axioms may be considered in two manners: empirically, or scientifically; or in other words, inasmuch as they are the application, or the object of analytical examination. In the first manner, they are equally certain and equally clear to all men; in the second, they are subject to difficulties. The principle,—things equal to a third are equal to each other,—considered empirically, is absolutely certain and evident to all men: all men, from the wisest to the most ignorant, compare things with a third, when they wish to ascertain their equality or inequality; this is only an application of the principle. If you ask them the reason of this proceeding, although they may not enunciate the axiom in its precise terms, they refer to it in different ways: "These two tables are equal, because I have measured them, and they are each four feet square." Probably the generality of men, not accustomed to reflect on their knowledge, would not express the principle in universal and precise terms; as, "These two tables are equal, because they have a common measure, and things equal to a third are equal to each other." Yet they are just as clearly certain of the principle, and apply it, without any danger of error, in all real and possible cases. This is what I call the empirical knowledge of principles,—a knowledge which is perfect in the direct order, and is defective only in the reflex order.[32]
It is very easy to reconcile the difficulty in the analysis of the principle, with its clearness when applied to ordinary purposes, or to those of science. Thus, in the example given, the analysis of the term equal leads to the analysis of the term quantity: reflection can discover in this difficulties which, although they do not disturb mankind in the possession of truth, are difficulties notwithstanding. Geometry is undoubtedly a science perfectly evident and certain; but who can deny that the idea of extension presents serious difficulties, when examined before the tribunal of metaphysics? Universal arithmetic is, beyond all doubt, a science; yet the ideas of quantity and number, which are indispensable to it, give rise to the most abstruse questions of metaphysics and ideology. In general, it may be said that there is no branch of our knowledge which is exempt from difficulties, considered in its root; but these difficulties, arising from reflection, do not in any way lessen the certainty of direct knowledge.
Hence it is no objection that the analysis of the principle of contradiction presents difficulties; nor are we therefore to fear for the firmness of the edifice of our knowledge. It would be of no service to us not to attend to these difficulties, if they really existed; a difficulty does not vanish because we shut our eyes so as not to see it. Let us not, therefore, vainly fear to examine the true sense of the principle of contradiction.
118. It seems that this principle either does not exist, or has no meaning, unless we presuppose the idea of time; and, on the other hand, we cannot conceive time, unless we presuppose the principle of contradiction. Do we thus fall into a vicious circle, and this too in the fundamental principle of all our knowledge? This is a difficulty which I shall first develop and present more clearly.
The principle of contradiction presupposes the idea of time, because there would be no contradiction if being and not-being were not referred to the same time. This last condition is altogether indispensable; for, suppressing the simultaneousness, there is no contradiction in a thing both being and not-being. Not only is there no contradiction in this, but it is a thing which we constantly meet with, in every thing around us. We see being and not-being in things which pass from existence to non-existence, or from non-existence to existence.
Although the simultaneousness may not be expressed in the principle of contradiction, it is always understood, so that we should gain nothing by adopting Kant's formula.[33] In whatever terms the principle may be enunciated, it is always true that the same thing cannot both be and not be at the same time, but may very well be at one time and not be at another time.
The idea of time is therefore necessary in order that the contradiction may follow in some cases, and disappear in others. If the time implies simultaneousness, it generates the contradiction; if it implies succession, it destroys the contradiction; because being and not-being are impossible, unless we presuppose a successive duration, among the different parts of which, things that would otherwise be contradictory are distributed.
119. The idea of time also presupposes the principle of contradiction; for, if time, in things, is only being and not-being, and in the intellect, the perception of this being and not-being; we cannot perceive time without having perceived being and not-being; and as these ideas, without succession, involve a contradiction, we must perceive the principle of contradiction when we perceive time. I have said that succession implies the mutual exclusion of the things which succeed; now, the first exclusion is the principle of contradiction: in perceiving time, we perceive succession; therefore we have already perceived the contradiction.
120. These remarks might incline us to believe it necessary to choose between a vicious circle, which is inadmissible in the foundation of all our knowledge, and an explanation of time, independently of being and not-being. If we conceived time as existing by itself, as a sort of line prolonged to infinity; as a form of things, but distinct from them all; as a vague capacity in which successive beings might be placed, just as we situate co-existences in space,—then the idea of time would not be explained by the principle of contradiction, and we could only say that it was completed by it. "When we say that it is impossible for the same thing to be and not be at the same time, but that it is possible for the same thing to be and not be at different times, the contradiction is affirmed or taken away, accordingly as the being and not-being are referred to the same point or to different points in this vague extension, this infinite line, which we call successive duration, and in which we conceive changeable things to be distributed." This explanation is convenient; but it has a defect, that it cannot stand a philosophical examination, as we have seen in the preceding chapters. We must therefore have recourse to another class of considerations.
121. To solve this difficulty, it is necessary to determine precisely the meaning of our ideas. The expression of vicious circle is improperly applied to this case. If we understand this, the whole difficulty is solved at once. In explaining things, which are not identical, a circle is a defect, and is called vicious; but when two things are identical at bottom, although they appear distinct, because presented under various aspects, it is impossible to explain one without stumbling, so to speak, on the other, or to approach one without meeting the other. Because they are presented under different aspects we are led to believe them distinct; but examining them analytically, we abstract the difference of aspect, and penetrate to the reality, and discover the point where they are united, or, rather, where they are absolutely identified.
122. We may draw from these observations a criterion which we may use in a great many cases. When, in explaining two objects, we find ourselves led alternately from the one to the other, without any possibility of avoiding a circle, we may suspect that objects, which appear distinct, are not so in reality, and that the objects presented to the eyes of our understanding are not two objects, but only one object perceived in different ways.
123. This is true in the present instance. In explaining the principle of contradiction we encounter the idea of time, and in defining time we encounter the principle of contradiction, or the ideas of being and not-being. This is a circle, but an inevitable one; and therefore it ceases to be vicious.
124. What is the meaning of the principle of contradiction? Its true meaning is, that being excludes not-being, and not-being excludes being; that the nature of these conceptions is such that the affirmation of one implies the negation of the other, not only in the order of our ideas, but in reality. Let us call A any being whatever: the principle of contradiction means that A excludes not-A, and not-A excludes A. If we think A, the conception of not-A disappears; and if we think not-A, the conception of A disappears. If we affirm A in reality, we deny not-A, and if we affirm not-A in reality, we deny A. This is the true meaning of the principle of contradiction. If we reflect, we shall find that, as far as possible, we have abstracted the idea of time; for we have only considered the mutual exclusion of A and not-A, in reference to a simul, an indivisible point of duration, which, involving no succession, does not give us the idea of time. I said, as far as possible; because as soon as we think A and not-A, the idea of succession, and consequently of time, arises in our mind.
125. A and not-A imply contradiction; but not so that they absolutely cannot be realized. The exclusion is conditional; that is, it exists as long as the contradictory extremes are simultaneous, or referred to an indivisible now; but we discover no intrinsic necessity of existence in the idea of A: consequently, although we know that while A is, not-A cannot be, we can very well conceive that A may cease to be, and not-A may begin to be. There is, in, that case, no contradiction, and we can easily reconcile in our mind the two ideas of A and not-A, by referring them to different instants.
126. Hence the perception of time implies the perception of beings that are not necessary,—of beings which, when they exist, may cease to exist, and when they do not exist, may begin to exist. The difference between necessary and contingent being is, that the existence of the former absolutely excludes its non-existence, while the existence of the latter excludes its non-existence only conditionally, or on the supposition of simultaneousness.
127. This is why the principle of contradiction requires the condition of time. The objects which we perceive are changeable; there is nothing either in their nature or in their modifications which involves existence. If they are, they may cease to be; and if this change does not constantly occur in their substance, it does in their accidents. Therefore we cannot affirm the absolute, but only the conditional contradiction of their being and not-being; it exists only on the supposition of simultaneousness.
128. If we conceived only necessary being, we could have no idea of time: its existence absolutely excludes its non-existence, and therefore the contradiction would be always absolute, never conditional.
129. A most important consequence results from this analysis. The perception of time with us implies the perception of the non-necessity of things. When we perceive a being which is not necessary, we perceive a being which may cease to be, in which case we have the idea of succession, of real or possible time. Here another reflection arises which is also important: the idea of time is the idea of contingency: the consciousness of time is the consciousness of our weakness.
130. The idea of time is so deep in our mind, that without it we could not form the idea of the me. The consciousness of the identity of the me supposes a link[34] which it is impossible to find without memory. Memory necessarily involves the relation of past, and, consequently, the idea of time.
SUMMING UP.
Let us collect together the doctrines of the preceding chapters.
131. Time is a question difficult to explain. Whoever denies this difficulty shows that he has meditated but superficially on the matter.
132. Motion is measured by time; but it is not a sufficient definition of time to call it the measure of motion.
133. It is impossible to find a primitive measure of motion; we must, at last, take some measure or another, and although arbitrarily chosen, we must refer motion to it. It should be the most uniform measure possible.
134. The resemblance between the ideas of time and space creates a suspicion that they ought to be explained in a similar manner.
135. There is no duration without something which endures; therefore there is no duration separate from things. If nothing existed, there could be no duration.
136. There is no succession without things which succeed: therefore succession cannot be realized as a form independent of things, although it may be conceived in the abstract by itself.
137. Time implies before and after, and, consequently, succession. It is succession itself, because in conceiving succession, we conceive time.
138. Succession involves the exclusion of some things by others. This exclusion may either be founded on the essence of things, or be derived from an external cause.
139. Time, therefore, involves exclusion: it is the general idea of the order of changes, or of the mutual relation of being and not-being.
140. If there were no change there would be no time.
141. No time had passed before the existence of the world. There was no other duration than eternity.
142. Eternity is the existence of the infinite being, without any alteration either actual or possible.
143. Time is not any thing absolute and independent of things, but is really in them. It is the order between being and not-being.
144. Co-existence is merely the existence of various beings. To conceive many beings without the idea of the negation of being, is to have the perception of co-existence.
145. Time may be considered under three aspects; the present, the past, and the future. All other relations of time, differently expressed in different idioms, are only combinations of these.
146. The present is the only absolute time: it is conceived without relation to the past or the future; but the past and the future are not conceived without relation to the present.
147. The idea of present accompanies the very idea of being; or rather, it is confounded with the idea of existence; that which has no present existence is not being.
148. The idea of past time is the perception of not-being, or of a being that has been destroyed, in relation to a present being: the idea of future time is the perception of a possible being proceeding from a cause already determined, and in relation to a present being.
149. The idea of time is excited by experience; but it cannot be called a fact of mere observation; for this would be opposed to its intrinsic necessity, by virtue of which it is the object of the exact sciences.
150. Still less can we say, that this idea is confined to the sensible order, since it includes every manner of change in general, whether sensible or supersensible.
151. The idea of time being the perception of the order between being and not-being, this relation, considered in general, belongs to the pure intellectual order. The transition to experience is realized in the same manner as in other general and indeterminate conceptions.
152. It is necessary to make a distinction between pure ideal time and empirical time: pure ideal time is the relation between being and not-being, considered in the greatest generality and the most complete indeterminateness; empirical time is the same relation subjected to a sensible measure.
153. To measure this succession, three things are necessary, and their union forms the idea of empirical time. They are, first, the pure idea of being and not-being, or of change; secondly, the application of this idea to a sensible phenomenon, as, for example, the solar motion; and thirdly, the idea of number applied to the determining of the changes of this phenomenon.
154. We thus conceive why empirical time implies a true necessity, and is the object of science. Of the three elements which compose it, the first is a metaphysical idea, the second, a mathematical idea, and the third, a fact of observation, to which these ideas are applied. If this fact be not real, it must, at least, be possible, in order to save the necessity of the calculation which is based upon it.
155. There is a close relation between the idea of time and the principle of contradiction. Each is explained by the other, yet this is not a vicious circle. The principle of contradiction consists in the mutual exclusion of being and not-being, and the idea of time is the perception of the order between being and not-being. Analysis must therefore lead to a part which is identical in both, to the comparison of the ideas of being and not-being.
156. Without the idea of time, memory would be impossible; consequently also, the unity of consciousness.
A GLANCE AT THE IDEAS OF SPACE, NUMBER, AND TIME.
157. We may now mark out and determine with perfect exactness the necessary elements which form the object of the natural and exact sciences. This is not only curious, but highly important; for it presents under the simplest aspect, an immense field of knowledge, the limits of which expand, as we advance; so that, it is impossible to assign a limit to progress.
158. Space, number, and time, are the three elements of all the natural and exact sciences. All else contained in them pertains to mere experience, to the order of contingent facts, which involve no necessity, and cannot strictly be the objects of science.
159. Universal arithmetic is founded on the idea of numbers, geometry on that of space, and the idea of time places us in communication with the sensible world, so as to determine the relations of its phenomena. These phenomena are isolated contingent facts, and cannot become the object of science, until subjected to the general ideas of space, number, and time.
160. Hence, there are two parts in every natural science; the theoretic, and the experimental. The former is founded on necessary ideas, the latter on contingent facts; the first without the second, would not come down to the real world; the second without the first, would not rise to the regions of science.
161. The natural sciences merit the name of science, in proportion to the quantity of necessary elements which they contain, and the closeness of the connection by which they unite with them contingent facts. But as no natural science can be conceived, without contingent facts, so there is none entirely free from the contingency which they communicate.
162. These observations reveal a great simplicity in the elements of science, and we may push this simplicity much farther, if we recollect what has been said when analyzing the ideas of number and time.
163. The idea of number arises from the idea of being and not-being: the same is also true of the idea of time; therefore, at bottom, these ideas are but one, though presented under different aspects.
164. Hence, all the natural and exact sciences may be reduced to two elements: the intuition of extension, and the general conception of being. Extension is the basis of all sensible intuitions: externally, it is a necessary condition of the relations which we conceive in the corporeal world; internally, it is a perception, without which the sensibility could not represent external objects. The conception of being, is the basis of all conceptions; developed in different ways, it generates the ideas of number and time; and these, combined with extension, constitute the necessary part of all the natural and exact sciences.
165. The ideas of space, number, and time are common to all men; the proof that they are identical to all is, that, in their application, all are led to the same results, and in speaking of them they all use the same expressions. All men measure space, and its various dimensions; they all count, they all conceive time: why, then, is there so great difficulty in explaining these ideas? why such difference of opinion among philosophers? Here we have a confirmation of what we have said[35] of the strength of direct perception, and the weakness of reflex. When we content ourselves with the direct perception of space, of number, and of time, our ideas are clear, and the understanding feels its strength and energy, it extends the sphere of its knowledge beyond all limits, and raises the edifice of the mathematical and exact sciences. But as soon as it turns upon itself, and, leaving the direct perception, passes to the reflex, endeavoring to perceive its perception, its strength fails, and it falls into a confusion which gives rise to interminable disputes. We scarce perceive that idea, which, a moment ago, we applied to every thing, which penetrated all our cognitions, and circulated, like our life, through all our perceptions; but in its isolation, and its purity, it continually escapes from us; mingled with all things, we see that it is something distinct from them; we separate it from one, and it unites with another; we make an effort to cut it off from all that is not itself, and the mind feels a kind of dizziness come over it, every thing vanishes from before it, and, unable to reach the reality, it is forced to be contented with names, which it pronounces and repeats a thousand times, turning over in them the little reality which they contain.
167. One of the causes of this weakness and of the errors which are its ordinary consequence, is, as I have before said, our mad desire of representing every idea as an internal form, or image, whereas we ought to consider that in many cases there is only a perception, a simple act in the lowest depth of our mind,—an act, which can be represented by nothing, which resembles nothing, and which cannot be explained in words, because it cannot be decomposed, and it is only present as a simple fact of consciousness. But this fact of consciousness is an active fact; by it we penetrate into things, and see what they have in common, and separate it from what is particular, establishing in our mind, as it were, a central, culminating point, from which we contemplate the internal and the external world, and roam through the boundless regions of possibility.
