Kitabı oku: «Fundamental Philosophy, Vol. 2 (of 2)», sayfa 16

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.

CHAPTER V.
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.

CHAPTER VI.
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.