Showing posts with label duration. Show all posts
Showing posts with label duration. Show all posts

14 Jul 2017

Bergson (5.2.1-5.2.15) La pensée et le mouvant / Creative Mind, “[All reality is change and movement, which is absolutely indivisible]”, summary

 

by Corry Shores

 

[Search Blog Here. Index tabs are found at the bottom of the left column.]

 

[Central Entry Directory]

[Zeno’s Paradox, entry directory]

[Bergson, entry directory]

[Bergson, La pensée et le mouvant / Creative Mind, entry directory]

 

[The following is summary. Boldface in quotation and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos. Citations give the pages for the 1938 French edition first; then the 1946 English second, and the 1965 English third.  Section and paragraph divisions follow those in the French edition; enumerations except for chapter numbers are my own.]

 

 

 

Summary of

 

Henri Bergson

 

La pensée et le mouvant:

Essais et conférences

 

[An Introduction to Metaphysics:]

The Creative Mind

 

5. La perception du changement / The Perception of Change

 

5.2. Deuxième conférence / Second Lecture

 

5.2.1-5.2.15

[All reality is change and movement, which is absolutely indivisible.]

 

 

 

Brief summary:

All reality is change. We have an inner mental life that is a flux not of distinct states but of continuous qualitative variation. And what we experience in the world are not invariable objects undergoing a series of discrete states. Rather, there is just pure durational change itself as the only substantiality, and there are not invariable things doing the changing. This means that all change and movement is absolutely indivisible. We cannot then say that a physical motion had spatialized parts to it. The movement is entire and durational (thus non-spatial) while it is happening. Only after the motion is complete can we examine the space traveled and then, if we want, divide that traveled space. But to divide the motion up, like in Zeno’s paradoxes, is to confuse movement and duration with space, which are incommensurable. So by committing this confusion we may derive Zeno’s paradoxes of motion. The evidence for the indivisibility of motion and change is phenomenological: we experience our own bodily motions as such. It is only on account of practical needs that we artificially divide the world and our mind up into immobilities. Also, we rely heavily on our vision, which is prone to artificially carve up the world into things that subsist as they move and change. But we should instead appeal to our hearing for information about real duration and change. When we hear a melody, for example, we experience a pure, indivisible, continuous variation without an invariable object as a substrate for that variation.

 

 

 

Summary

 

5.2.1

[All change and all movement is absolutely indivisible.]

 

Bergson asks us to break our normal habits of thinking so that we may contemplate “the direct perception of change and mobility” / “la percep-| tion directe du changement et de la mobilité” (157|158 / 167 / 142). He continues, “We || shall think of all change, all movement, as being absolutely indivisible” / “Nous nous représenterons tout changement, tout mouvement, comme absolument indivisibles” (158 / 167||168 / 142, emphasis in original).

 

 

5.2.2

[The motion of our hand from point A to B is a simple movement.]

 

Bergson has us consider if we move our hand from point A to B. The movement that transpires is “simple” [which may mean that it is indivisible, or complex in a non-divisible way somehow.]

Let us begin with movement. I have my hand at point A. I move it over to point B, traversing the interval AB. I say that this movement from A to B is by nature simple.

 

Commençons par le mouvement. J’ai la main au point A. Je la transporte au point B, parcourant l’intervalle AB. Je dis que ce mouvement de A en B est chose simple.

(158 / 168 / 142)

 

 

 

5.2.3

[If our hand makes no pause in its motion, it feels unitary and indivisible to us. If it does make a pause, then it does not feel like it was one motion with distinct phases; rather, it feels like two indivisible motions.]

 

We feel this action as being singular and indivisible. Suppose we pause at an intermediary point. How would that feel to us? As one divided motion? No, it would feel like two distinct motions. So long as it is a moving without pause, it feels indivisible.

But of this each one of us has the immediate sensation. No doubt while we are moving our hand from A to B we say to ourselves that we could stop it at an intermediary point, but in that case we should not have to do with the same movement. There would no longer be a single movement from A to B; there would be, by hypothesis, two movements, with an interval. Neither from within, through the muscular sense, nor from without ||| through sight, should we still have the same perception. If I leave my movement from A to B as it is, I feel it undivided and must declare it to be indivisible.

 

Mais c’est de quoi chacun de nous a la sensation immédiate. Sans doute, pendant que nous portons notre main de A en B, nous nous disons que nous pourrions l’arrêter en un point intermédiaire, mais nous n’aurions plus affaire alors au même mouvement. Il n’y aurait plus un mouvement unique de A en B ; il y aurait, par hypothèse, deux mouvements, avec un intervalle d’arrêt. Ni du dedans, par le sens musculaire, ni du dehors par la vue, nous n’aurions encore la même perception. Si nous laissons notre mouvement de A en B tel qu’il est, nous le sentons indivisé et nous devons le déclarer indivisible.

(158 / 168 / 142|||143)

 

 

5.2.4

[Because motion traverses space, we mistakenly think that the motion is divisible like the space is. But it is not. And we cannot say that the motion ever occupies a point of space at an instant of time. For, suppose we did divide the motion into smaller and smaller intervals. We would never arrive upon a point in space or time but only upon intervals of decreasing size. So while moving, the object is always passing through points; and it only occupies a point when it stops. Nonetheless, in reality, there is no rest; there is only change and motion. What appears to be at rest is simply moving at pace with our attention and thus seems like it is not moving or changing, like two trains moving side-by-side, making each train appear stationary to the other.]

 

Bergson will now address our tendency to want to divide up the motion into parts corresponding to spatial intervals the movement traversed. {1} We can divide the spatial interval AB into as many parts as we want. Since the movement traversed this space, we can divide the movement into as many parts as we wish, corresponding to the internal spatial intervals traversed. {2} At each instant of the motion, the hand occupied a determinate point. On the basis of these points, which correlate to instants of the motion, we can divide the motion into stages corresponding to the divided spatial intervals. Bergson then begins his responses to this sort of approach of dividing motion by means of space. He first asks {a} how can movement be applied to the traversed space? {b} And note that the space is immobile, but the movement is mobile. So how do you make something immobile coincide with something mobile? {c} How can a moving object be both moving and occupy a determinate point? If it is moving, it can only be said to be passing through a point. Were it to occupy a point, it would have stopped. [Let us take note briefly of what we may consider a correction and clarification Bertrand Russell makes with regard to this idea that to occupy a point is to be at rest. (See the entries for Bertrand Russell at the Zeno’s Paradox directory.) Russell notes that it is not enough to simply occupy a point to constitute rest. You need to remain at that point as time passes. But I think if we extract some of Bergson’s insight here, we can see a problem even with Russell’s at-at definition of motion. For Russell, there are never immediately successive points, because there is always another between any two. Now suppose we begin with one motion. And suppose we divide it into smaller and smaller intervals. Would we ever arrive upon its occupation of a point during an instant using this method? No. For no matter how small the interval, in Russell’s thinking, there is always a smaller one. And since there is no smallest decomposition, you never have occupation at a point; you only have smaller and smaller passings-through of sets of points. Thus if we begin with a unitary motion, we can never decompose it into parts that simply occupy a singular position at a singular instant. So, insofar as Russell has us think of a moving object occupying a determinate point in space, he is not dealing with a part of motion but rather with the space traversed by that motion.] Bergson further clarifies this notion of unitary motion. We think of any undivided motion as a “bound”, which endures for whatever duration of the motion, which can be any size interval, no matter how small or large. As a singular bound, it is indecomposable. But, after the bound has finished, we see that it traversed an extent of space. Since space is infinitely divisible, we imagine the motion to be so as well. But we are in error as soon as we think that we can really divide the motion up this way into immobilities. Bergson then makes the remarkable claim that in reality there are no immobilities. Whatever we consider to be an immobility is really just a movement that is going at pace alongside a moving point of reference: “when two trains move at the same speed, in the ||| same direction, on parallel tracks: each of the two trains is then immovable to the travellers seated in the other” (159 / 169 / 143|||144). [I am not entirely sure how to conceive the way this transpires in life. Perhaps the idea is that suppose we have something that we think is immobile. In reality it is changing. But it is changing at pace with our flow of awareness, perhaps. Consult the quotation to follow.]

It is true that, when I watch my hand going from A to B and describing the interval AB, I say: “The interval AB can be divided into as many parts as I wish, therefore the movement from A to B can be divided into as many parts as I like, since this movement is applied exactly upon this interval.” Or again: “At each instant of its trajection, the mobile passes through a certain point, therefore one can distinguish in the movement as many stages as one likes, therefore the movement is infinitely divisible.” But let us reflect for a moment. How could the movement be applied upon the space it traverses? How can something moving coincide with something immobile? How could the moving object be in a point of its trajectory passage? It passes through, or in other terms, it could be there. It would be there if it || stopped; but if it should stop there, it would no longer be the same movement we were dealing with. It is always by a single bound that a passing is completed, when there is no break in the passage. The bound may last a few seconds, or days, months, years: it matters little. The moment it is one single bound, it is indecomposable. Only, once the passage is effected, as the trajectory is space and space is indefinitely divisible, we imagine that movement itself is indefinitely divisible. We like to imagine it because, in a movement, it is not the change of position which interests us, it is the positions themselves, the one the movement has left, the one it will take, the one it would take if it stopped on the way. We need immobility, and the more we succeed in imagining movement as coinciding with the immobilities of the points of space through which it passes, the better we think we understand it. To tell the truth, there never is real immobility, if we understand by that an absence of movement. Movement is reality itself, and what we call immobility is a certain state of things analogous to that produced when two trains move at the same speed, in the ||| same direction, on parallel tracks: each of the two trains is then immovable to the travellers seated in the other. But a situation of this kind which, after all, is exceptional, seems to us to be the regular and normal situation, because it is what permits us to act upon things and also permits things to act upon us: the travellers in the two trains can hold out their hands to one another through the door and talk to one another only if they are “immobile,” that is to say, if they are going in the same direction at the same speed. “Immobility” being the prerequisite for our action, we set it up as a reality, we make || of it an absolute, and we see in movement something which is superimposed. Nothing is more legitimate in practice. But when we transport this habit of mind into the domain of speculation, we fail to recognize the true reality, we deliberately create insoluble problems, we close our eyes to what is most living in the real.

 

Il est vrai que, lorsque je regarde ma main allant de A en B et décrivant l’intervalle AB, je me dis : « l’intervalle AB peut se diviser en autant de parties que je le veux, donc le mouvement de A en B peut se diviser en autant de parties qu’il me plaît, puisque ce mouvement s’applique sur cet intervalle. » Ou bien encore : « à chaque instant de son trajet, le mobile passe en un certain point, donc on peut distinguer dans le mouvement autant d’étapes qu’on voudra, donc le mouvement est infiniment divisible. » Mais réfléchissons-y un instant. Comment le mouvement pourrait-il s’appliquer sur l’espace qu’il parcourt ? comment du mouvant coïnciderait-il avec de l’immobile ? comment l’objet qui se meut serait-il en un point de son trajet ? Il y passe, ou, en d’autres termes, il pourrait y être. Il y serait s’il s’y arrêtait ; mais, s’il s’y arrêtait, ce n’est plus au même mouvement | que nous aurions affaire. C’est toujours d’un seul bond qu’un trajet est parcouru, quand il n’y a pas d’arrêt sur le trajet. Le bond peut durer quelques secondes, ou des jours, des mois, des années : peu importe. Du moment qu’il est unique, il est indécomposable. Seulement, une fois le trajet effectué, comme la trajectoire est espace et que l’espace est indéfiniment divisible, nous nous figurons que le mouvement lui-même est divisible indéfiniment. Nous aimons à nous le figurer, parce que, dans un mouvement, ce n’est pas le changement de position qui nous intéresse, ce sont les positions elles-mêmes, celle que le mobile a quittée, celle qu’il prendra, celle qu’il prendrait s’il s’arrêtait en route. Nous avons besoin d’immobilité, et plus nous réussirons à nous représenter le mouvement comme coïncidant avec les immobilités des points de l’espace qu’il parcourt, mieux nous croirons le comprendre. A vrai dire, il n’y a jamais d’immobilité véritable, si nous entendons par là une absence de mouvement. Le mouvement est la réalité même, et ce que nous appelons immobilité est un certain état de choses analogue à ce qui se produit quand deux trains marchent avec la même vitesse, dans le même sens, sur deux voies parallèles : chacun des deux trains est alors immobile pour les voyageurs assis dans l’autre. Mais une situation de ce genre, qui est en somme exceptionnelle, nous semble être la situation régulière et normale, parce que c’est celle qui nous permet d’agir sur les choses et qui permet aussi aux choses d’agir sur nous : les voyageurs des deux trains ne peuvent se tendre la main par la portière et causer ensemble que s’ils sont « immobiles », c’est-à-dire s’ils marchent dans le même sens avec la même vitesse. L’ «immobilité » étant ce dont notre action a besoin, nous l’érigeons en réalité, nous en faisons un absolu, et nous voyons dans le mouvement | quelque chose qui s’y surajoute. Rien de plus légitime dans la pratique. Mais lorsque nous transportons cette habitude d’esprit dans le domaine de la spéculation, nous méconnaissons la réalité vraie, nous créons, de gaieté de cœur, des problèmes insolubles, nous fermons les yeux à ce qu’il y a de plus vivant dans le réel.

(158|160 / 168||170 / 143|||144)

 

 

5.2.5

[Zeno’s paradoxes of motion confuse the space traversed, which is divisible, with the motion, which is not. For example, Achilles is said to never overtake the Tortoise, because the Tortoise is constantly creating new distances for Achilles to cross. But Achilles’ own motion was not composed of infinitely many movements that endlessly decrease in size. It was made of a series of indivisible steps.]

 

Zeno’s paradoxes of motion confuse movement with the space traversed. Or if they do not make such a simplistic equivalence, they at least treat movement as being divisible like space is, without taking into account that movement is articulated in unitary segments. [Recall the paradox of Achilles and the Tortoise (described at section II.F of this entry, and discussed by Bergson in Time and Free Will §70, Matter and Memory section 4.2.6, and Creative Evolution section 4.5.10.) The Tortoise has a head start at the beginning of its race with Achilles. For Achilles to overtake the Tortoise, he must first arrive upon the Tortoise’s starting position. But by the time he gets there, the Tortoise has already advanced a little further. So now Achilles must arrive upon the Tortoise’s new position. But again, upon arriving upon it, the Tortoise will be further. So long as the Tortoise keeps moving, it will always create a new, more distant position for Achilles to cross. Thus Achilles will never overtake the Tortoise while it keeps moving.] Bergson recalls Zeno’s paradox of Achilles and the Tortoise, where “Achilles, they say, will never overtake the tortoise he is pursuing, for when he arrives at the point where the tortoise was the latter will have had time to go further, and so on indefinitely.” Bergson notes that there have been a great variety of refutations, but he proposes a simple one. He says we need to ask Achilles after he in fact overtakes the Tortoise, how did he do it? He would say that Zeno’s description does not match the way the event transpired. He did not first arrive upon the Tortoises’ first position, then second position, and on and on. Rather, Achilles will say that he took a series of steps until finally overtaking the Tortoise. So his course was a series of indivisible actions. These are the only parts we can divide his whole course into. We should not, like Zeno, divide the acts indefinitely like spatial parts corresponding to the spatial locations of the race track, because the acts are not immobilities like space and they cannot be coordinated point-by-point with an immobility like space.

I need not recall the arguments of Zeno of Elea. They all involve the confusion of movement with the space covered, or at least the conviction that one can treat movement as one treats space, divide it without taking account of its articulations. Achilles, they say, will never overtake the tortoise he is pursuing, for when he arrives at the point where the tortoise was the latter will have had time to go further, and so on indefinitely. Philosophers have refuted this argument in numerous ways, and ways so different that each of these refutations deprives the others of the right to be considered definitive. There would have been, nevertheless, a very simple means of making short work of the difficulty: that would have been to question Achilles. For since Achilles finally catches up to the tortoise and even passes it, he must know better than anyone else how he goes about it. The ancient philosopher who demonstrated the possibility of movement by walking was right: his only mistake was to make the gesture without adding a commentary. Suppose then we ask Achilles to comment on his race: here, doubtless, is what he will answer: “Zeno insists that I go from the point where I am to the point the tortoise ||| has left, from that point to the next point it has left, etc., etc.; that is his procedure for making me run. But I go about it otherwise. I take a first step, then a second, and so on: finally, after a certain number of steps, || I take a last one by which I skip ahead of the tortoise. I thus accomplish a series of indivisible acts. My course is the series of these acts. You can distinguish its parts by the number of steps it involves. But you have not the right to disarticulate it according to another law, or to suppose it articulated in another way. To proceed as Zeno does is to admit that the race can be arbitrarily broken up like the space which has been covered; it is to believe that the passage is in reality applied to the trajectory; it is making movement and immobility coincide and consequently confusing one with the other.”

 

Je n’ai pas besoin de vous rappeler les arguments de Zénon d’Élée. Tous impliquent la confusion du mouvement avec l’espace parcouru, ou tout au moins la conviction qu’on peut traiter le mouvement comme on traite l’espace, le diviser sans tenir compte de ses articulations. Achille, nous dit-on, n’atteindra jamais la tortue qu’il poursuit, car lorsqu’il arrivera au point où était la tortue, celle-ci aura eu le temps de marcher, et ainsi de suite indéfiniment. Les philosophes ont réfuté cet argument de bien des manières, et de manières si différentes que chacune de ces réfutations enlève aux autres le droit de se croire définitives. Il y aurait eu pourtant un moyen très simple de trancher la difficulté : c’eût été d’interroger Achille. Car, puisqu’Achille finit par rejoindre la tortue et même par la dépasser, il doit savoir, mieux que personne, comment il s’y prend. Le philosophe ancien qui démontrait la possibilité du mouvement en marchant était dans le vrai : son seul tort fut de faire le geste sans y joindre un commentaire. Demandons alors à Achille de commenter sa course : voici, sans aucun doute, ce qu’il nous répondra. « Zénon veut que je me rende du point où je suis au point que la tortue a quitté, de celui-ci au point qu’elle a quitté encore, etc. ; c’est ainsi qu’il procède pour me faire courir. Mais moi, pour courir, je m’y prends autrement. Je fais un premier pas, puis un second, et ainsi de suite : finalement, après un certain nombre de pas, j’en fais un dernier par lequel j’enjambe la tortue. J’accomplis | ainsi une série d’actes indivisibles. Ma course est la série de ces actes. Autant elle comprend de pas, autant vous pouvez y distinguer de parties. Mais vous n’avez pas le droit de la désarticuler selon une autre loi, ni de la supposer articulée d’une autre manière. Procéder comme le fait Zénon, c’est admettre que la course peut être décomposée arbitrairement, comme l’espace parcouru ; c’est croire que le trajet s’applique réellement contre la trajectoire ; c’est faire coïncider et par conséquent confondre ensemble mouvement et immobilité. »

(160|161 / 170||171 / 144|||145)

 

 

5.2.6

[Under this erroneous understanding that confuses movement with traversed space, we hold two incompatible metaphysical assumptions: {1} motion is fundamentally a passage between points, and thus it is fundamentally a mobility transpiring between immobilities, and {2} motion is decomposable into nothing more than positions dividing passages (into immobilities), and it is recomposable by taking all these positions together.]

 

Bergson says that this method of decomposition that confuses motion with traversed space is our usual way of understanding movement. It treats motion as if it were constituted by immobilities (spatial positions). And we think we can reconstitute movement by adding all the immobilities together. But at the same time that we decompose movement into positions, we assume as well that there is a passage between any two positions. Yet, how do we conceptualize this passage? By saying it is composed of yet more positions. We want to be able to have both concepts, that there is a mobile passage and that the passage is made of immobile positions. But as we can see, they are conceptually irreconcilable. [Bergson again ends with the notion that immobility is perhaps not even real.]

But that is precisely what our usual method consists in. We argue about movement as though it were made of immobilities and, when we look at it, it is with immobilities that we reconstitute it. Movement for us is a position, then another position, and so on indefinitely. We say, it is true, that there must be something else, and that from one position to another there is the passage by which the interval is cleared. But as soon as we fix our attention on this passage, we immediately make of it a series of positions, even though we still admit that between two successive positions one must indeed assume a passage. We put this passage off indefinitely the moment we have to consider it. We admit that it exists, we give it a name; that is enough for us: once that point has been satisfactorily settled we turn to the positions preferring to deal with them alone. We have an instinctive fear of those difficulties which the vision of movement as movement would arouse in our thought; and quite rightly, once we have loaded movement down with immobilities. If movement is not everything, it is nothing; and if to begin with we have sup- || posed that immobility can be a reality, movement will slip through our fingers when we think we have it.

 

Mais en cela consiste précisément notre méthode habituelle. Nous raisonnons sur le mouvement comme s’il était fait d’immobilités, et, quand nous le regardons, c’est avec des immobilités que nous le reconstituons. Le mouvement est pour nous une position, puis une nouvelle position, et ainsi de suite indéfiniment. Nous nous disons bien, il est vrai, qu’il doit y avoir autre chose, et que, d’une position à une position, il y a le passage par lequel se franchit l’intervalle. Mais, dès que nous fixons notre attention sur ce passage, vite nous en faisons une série de positions, quittes à reconnaître encore qu’entre deux positions successives il faut bien supposer un passage. Ce passage, nous reculons indéfiniment le moment de l’envisager. Nous admettons qu’il existe, nous lui donnons un nom, cela nous suffit : une fois en règle de ce côté, nous nous tournons vers les positions et nous préférons n’avoir affaire qu’à elles. Nous avons instinctivement peur des difficultés que susciterait à notre pensée la vision du mouvement dans ce qu’il a de mouvant ; et nous avons raison, du moment que le mouvement a été chargé par nous d’immobilités. Si le mouvement n’est pas tout, il n’est rien ; et si nous avons d’abord posé que l’immobilité peut être une réalité, le mouvement | glissera entre nos doigts quand nous croirons le tenir.

(161|162 / 171||172 / 145)

 

 

5.2.7

[In fact, all real change is indivisible. We erroneously think that change can be divided into states because indivisible change in the world is practically coordinated with the indivisible change of our inner experience. When our actions need to intervene in the world or when for other practical reasons we coordinate events in the world with events in our minds, we artificially designate stable states in the changes outside and inside us.]

 

Bergson says that this applies to any sort of change whatsoever: “All real change is an indivisible change” / “Tout changement réel est un changement indivisible”. Bergson then explains how it is that we come to erroneously understand real change as being divisible. [His first idea here might be the following, but check the quotation below. We suppose there is some change happening in the world. Let us imagine that we are heating water to a boil. So out in the world there is continuous qualitative change of the water. At the same time, our mind is in a flux of consciousness. These two fluxes flow together in simultaneity (see for example Ch.3 of Duration and Simultaneity.) Now, as the water comes to boil, we get anxious because it might overboil, so we lift the pan off the fire. We then want to say that there were distinct states of the water, namely,  it being below boiling, it being at boiling, and it cooling below boiling. These states correspond to states of our mind: our waiting for it to boil, our alarm when it boils, and our relief when it cools. But in reality, Bergson seems to be saying, the water was never in some determinate, stable state. It was always changing. And our mind was not in any determinate, stable state. It was always a flux of consciousness. But we came to regard the water having states corresponding to the appropriate actions we made with regard to it, and these actions that divided the change serve to mark off seemingly distinct and stable inner states of our experience of the change. So it is simply for practical reasons (our needing to boil the water but not too much) that cause us to delineate states of change in the world and in our inner life. But these immobilities are not really inherent to the world and our mind.]

I have spoken of movement; but I could say the same for any change whatever. All real change is an indivisible change. We like to treat it as a series of distinct states which form, as it were, a line in time. That is perfectly natural. If change is continuous in us and also in things, on the other hand, in order that the uninterrupted change which each of us calls “me” may act upon the uninterrupted change that we call a “thing,” these two changes must find themselves, with regard to one another, in a situation like that of the two trains referred to above. We say, for example, that an object changes color, and that change here consists in a series of shades which would be the constitutive elements of change and which, themselves, would not change. But in the first place, if each shade has any objective existence at all, it is an infinitely rapid oscillation, it is change. And in the second place, the perception we have of it, to the extent that it is subjective, is only an isolated, abstract aspect of the general state of our person, and this state as a whole is constantly changing and causing this so-called invariable perception to participate in its change; in fact, there is no perception which is not constantly being modified. So that color, outside of us, is mobility itself, and our own person is also mobility. But the whole mechanism of our perception of things, like the mechanism of our action upon things has been regulated in such a way as to bring about, between the external and the internal mobility, a situation comparable to that of our two trains, – more complicated, perhaps, but of the same kind: when the || two changes, that of the object and that of the subject, take place under particular conditions, they produce the particular appearance that we call a “state.” And once in possession of “states,” our mind recomposes change with them. I repeat, there is nothing more natural: the breaking up of change into states enables us to act upon things, and it is useful in a practical sense to be interested in the states rather than in the change itself. But what is favourable to action in this case would ||| be fatal to speculation. If you imagine a change as being really composed of states, you at once cause insoluble metaphysical problems to arise. They deal only with appearances. You have closed your eyes to true reality.

 

J’ai parlé du mouvement ; mais j’en dirais autant de n’importe quel changement. Tout changement réel est un changement indivisible. Nous aimons à le traiter comme une série d’états distincts qui s’aligneraient, en quelque sorte, dans le temps. C’est naturel encore. Si le changement est continuel en nous et continuel aussi dans les choses, en revanche, pour que le changement ininterrompu que chacun de nous appelle « moi » puisse agir sur le changement ininterrompu que nous appelons une « chose », il faut que ces deux changements se trouvent, l’un par rapport à l’autre, dans une situation analogue à celle des deux trains dont nous parlions tout à l’heure. Nous disons par exemple qu’un objet change de couleur, et que le changement consiste ici dans une série de teintes qui seraient les éléments constitutifs du changement et qui, elles, ne changeraient pas. Mais, d’abord, ce qui existe objectivement de chaque teinte, c’est une oscillation infiniment rapide, c’est du changement. Et, d’autre part, la perception que nous en avons, dans ce qu’elle a de subjectif, n’est qu’un aspect isolé, abstrait, de l’état général de notre personne, lequel change globalement sans cesse et fait participer à son changement cette perception dite invariable : en fait, il n’y a pas de perception qui ne se modifie à chaque instant. De sorte que la couleur, en dehors de nous, est la mobilité même, et que notre propre personne est mobilité encore. Mais tout le mécanisme de notre perception des choses, comme celui de notre action sur les choses, a été réglé de manière à amener ici, entre la mobilité externe et la mobilité intérieure, une situation comparable à celle de nos deux trains, - plus compliquée, sans doute, mais du même genre : quand les deux changements, celui de l’objet et celui du sujet, ont lieu dans ces conditions particulières, | ils suscitent l’apparence particulière que nous appelons un « état ». Et, une fois en possession d’ « états », notre esprit recompose avec eux le changement. Rien de plus naturel, je le répète : le morcelage du changement en états nous met à même d’agir sur les choses, et il est pratiquement utile de s’intéresser aux états plutôt qu’au changement lui-même. Mais ce qui favorise ici l’action serait mortel à la spéculation. Représentez-vous un changement comme réellement composé d’états : du même coup vous faites surgir des problèmes métaphysiques insolubles. Ils ne portent que sur des apparences. Vous avez fermé les yeux à la réalité vraie.

(162|163 / 172||173 / 146|||147)

 

 

5.2.8

[We can know that change is indivisible, because when we witness it, we experience it as such. Also, all is change, and there are no invariable objects doing those changes.]

 

Bergson offers as proof that whenever we directly view change or a movement, we have a feeling of absolute individuality. Bergson now makes the point that although there are changes, that is all there is. There are no invariable objects undergoing the changes. Even in movements there are no invariable objects that are doing the moving.

I shall not press the point. Let each of us undertake the experiment, let him give himself the direct vision of a change, of a movement: he will have a feeling of absolute indivisibility. I come then to the second point, closely allied to the first. There are changes, but there are underneath the change no things which change: change has no need of a support. There are movements, but there is no inert or invariable object which moves: movement does not imply a mobile.

Je n’insisterai pas davantage. Que chacun de nous fasse l’expérience, qu’il se donne la vision directe d’un changement, d’un mouvement : il aura un sentiment d’absolue indivisibilité. J’arrive alors au second point, qui est très voisin du premier. Il y a des changements, mais il n’y a pas, sous le change­ment, de choses qui changent : le changement n’a pas besoin d’un support. Il y a des mouvements, mais il n’y a pas d’objet inerte, invariable, qui se meuve : le mouvement n’implique pas un mobile.

(163 / 173 / 147, italics in the original, boldface mine)

 

 

5.2.9

[Our vision distinguishes things that come to appear as invariable objects persisting through their changes. But our sense of hearing only gives us the changes. For example, when we hear a melody, the “object” here is the melodic change itself.]

 

Bergson says that we develop the erroneous notion of invariable objects subsisting through change from our primary reliance on vision. Our sight separates things in our visual field, and we come to take those distinguished things as invariable figures. Sight thus prepares the sense of touch for our interactions with the world. But the other senses are better able to give us the world in changefulness. When we hear a melody, we do not perceive an invariable object that is changing but rather the change “is the thing itself”. We know this is so, because if you stop the melody at one point or at another, it is a different thing in each case. So there is no one melody that subsists throughout its changes. And we should not think of the melody being composed of the notes pictured in the score. For this is to understand it as a visualizable object with spatial properties.

It is difficult to picture things in this way, because the sense ‘par excellence’ is the sense of sight, and because the eye has developed the habit of separating, in the visual field, the relatively invariable figures which are then supposed to change place without changing form, movement is taken as super-added to the mobile as an accident. It is, in fact, useful to have to deal in daily life with objects which are stable and, as it were, responsible, to which one can address oneself as to persons. The sense of sight contrives to take things in this way: as an ad- || vance-guard for the sense of touch, it prepares our action upon the external world. But we already have less difficulty in perceiving movement and change as independent realities if we appeal to the sense of hearing. Let us listen to a melody, allowing ourselves to be lulled by it: do we not have the clear perception of a movement which is not attached to a mobile, of a change without anything changing? This change is enough, it is the thing itself. And even if it takes time, it is still indivisible; if the melody stopped sooner it would no longer be the same sonorous whole, it would be another, equally indivisible. We have, no doubt, a tendency to divide it and to picture, instead of the uninterrupted continuity of melody, a juxtaposition of distinct notes. But why? Because we are thinking of the discontinuous series of efforts we should be making to recompose approximately ||| the sound heard if we were doing the singing, and also because our auditory perception has acquired the habit of absorbing visual images. We therefore listen to the melody through the vision which an orchestra-leader would have of it as he watched its score. We picture notes placed next to one another upon an imaginary piece of paper. We think of a keyboard upon which some one is playing, of the bow going up and down, of the musicians, each one playing his part along with the others. If we do not dwell on these spatial images, pure change remains, sufficient unto itself, in no way divided, in no way attached to a “thing” which changes.

 

On a de la peine à se représenter ainsi les choses, parce que le sens par excellence est celui de la vue, et que l’œil a pris l’habitude de découper, dans l’ensemble du champ visuel, des figures relativement invariables qui sont censées | alors se déplacer sans se déformer : le mouvement se surajouterait au mobile comme un accident. Il est en effet utile d’avoir affaire, tous les jours, à des objets stables et, en quelque sorte, responsables, auxquels on s’adresse comme à des personnes. Le sens de la vue s’arrange pour prendre les choses de ce biais : éclaireur du toucher, il prépare notre action sur le monde exté­rieur. Mais déjà nous aurons moins de peine à percevoir le mouvement et le changement comme des réalités indépendantes si nous nous adressons au sens de l’ouïe. Écoutons une mélodie en nous laissant bercer par elle : n’avons-nous pas la perception nette d’un mouvement qui n’est pas attaché à un mobile, d’un changement sans rien qui change ? Ce changement se suffit, il est la chose même. Et il a beau prendre du temps, il est indivisible : si la mélodie s’arrêtait plus tôt, ce ne serait plus la même masse sonore ; c’en serait une autre, égale­ment indivisible. Sans doute nous avons une tendance à la diviser et à nous représenter, au lieu de la continuité ininterrompue de la mélodie, une juxtapo­sition de notes distinctes. Mais pourquoi ? Parce que nous pensons à la série discontinue d’efforts que nous ferions pour recomposer approximativement le son entendu en chantant nous-mêmes, et aussi parce que notre perception auditive a pris l’habitude de s’imprégner d’images visuelles. Nous écoutons alors la mélodie à travers la vision qu’en aurait un chef d’orchestre regardant sa partition. Nous nous représentons des notes juxtaposées à des notes sur une feuille de papier imaginaire. Nous pensons à un clavier sur lequel on joue, à l’archet qui va et qui vient, au musicien dont chacun donne sa partie à côté des autres. Faisons abstraction de ces images spatiales : il reste le changement pur, se suffisant à lui-même, nullement divisé, nullement attaché à une « chose » qui change.

(163|164 / 173||174 / 147|||148)

 

 

5.2.10

[Science decomposes things down into smaller and smaller particles understood increasingly in terms of their movements and vibrations. When we see something, we might think it is an invariable object. But that image is composed of tiny dots of color, each itself a light frequency and thus a movement.]

 

Bergson returns to sight to make the point that it is not necessary for us to only see invariable objects. Science decomposes things down into smaller and smaller things, understood more in terms of their motion than their substantiality. Bergson then notes that when we see something moving, the parts of our vision are colored spots, which are made of a “series of extremely rapid vibrations”. [I am not certain, but perhaps he is referring to something like the frequency of the light waves. See 165 / 175 / 148.]

 

 

5.2.11

[Change itself is the only thing with any substantiality in the sense of being something that endures. There are no other invariabilities. We see this with our inner life, which is a pure continuous flux like a melody. We are mistaken to think that there is a series of discrete and distinct psychic states modifying an invariable ego as substrate.]

 

Bergson says that we most encounter the “substantiality” of change in our inner life. [By substantiality he does not mean the invariable objects but change itself being the only thing that could qualify as a substrate, because change itself is the only thing that endures.] He says that certain theories of personality assume two things about consciousness, both being incorrect, and as a result they encounter a number of conceptual problems. The first incorrect assumption is that we have “a series of distinct psychological states, each one invariable”. [He also says that this series of states is thought to produce  variations of the ego by their very succession”. It is not stated whether or not the ego’s variations are a series of discrete invariable states, but I would guess they would be, as that is the form the cause takes.] The second incorrect assumption is that we have an invariable ego which “would serve as support” for the psychic variations. He first wonders how the unity of the ego could meet up with the multiplicity of the psychic variations. He next wonders how either one could have duration. Consider the flux of psychic states. Here change is superadded (s’y surajoute). [I am not sure what is meant here. I am going to guess it is the following, but please consult the text. There is only flux, which means at any present there is a variation. But what it is varying against is not present. In order to say there was change, we need to add to the present variation the past and/or future situations in order to say that a change transpires. Thus it is hard to say how the flux has duration, because in itself it is only a present variation and not something that itself endures.] Now consider the invariable ego. The ego is made of elements which do not change. [I am not sure what those elements are. Perhaps they are psychic structures of some kind.] So if its elements are invariable, how can it be said to endure? [Apparently only variable things can endure, but I am not sure why. Perhaps invariable things like structures are not temporal but some sort of idealized abstraction.] Bergson then claims that neither assumption is true. There is only the continuously varying “melody” of our inner life, and this is what constitutes our personality. [In other words, we have no stable ego.]

But nowhere is the substantiality of change so visible, so palpable as in the domain of the inner life. Difficulties and contradictions of every kind to which the theories of personality have led come from our having imagined, on the one hand, a series of distinct psychological ||| states, each one invariable, which would produce the variations of the ego by their very succession, and on the other hand an ego, no less invariable, which would serve as support for them. How could this unity and this multiplicity meet? How, without either of them having duration – the first because change is something superadded, the second because it is made up of elements which do not change – how could they constitute an ego which endures? But the truth is that there is neither a || rigid, immovable substratum nor distinct states passing over it like actors on a stage. There is simply the continuous melody of our inner life, – a melody which is going on and will go on, indivisible, from the beginning to the end of our conscious existence. Our personality is precisely that.

 

Mais nulle part la substantialité du changement n’est aussi visible, aussi palpable, que dans le domaine de la vie intérieure. Les difficultés et contra­dictions de tout genre auxquelles ont abouti les théories de la personnalité viennent de ce qu’on s’est représenté, d’une part, une série d’états psycholo­giques distincts, chacun invariable, qui produiraient les variations du moi par leur succession même, et d’autre part un moi, non moins invariable, qui leur servirait de support. Comment cette unité et cette multiplicité pourraient-elles se rejoindre ? comment, ne durant ni l’une ni l’autre – la première parce que le changement est quelque chose qui s’y surajoute, la seconde parce qui elle est faite d’éléments qui ne changent pas – pourraient-elles constituer un moi qui dure ? Mais la vérité est qu’il n’y a ni un substratum rigide immuable ni des états distincts qui y passent comme des acteurs sur une scène. Il y a simple­ment la mélodie continue de notre vie intérieure, – mélodie qui se poursuit et se poursuivra, indivisible, du commencement à la fin de notre existence consciente. Notre personnalité est cela même.

(165-166 / 175-176 / 148-149)

 

 

5.2.12

[This indivisible continuity of change that we directly experience as being fundamental to our awareness is real duration or time proper. But we normally conceive time erroneously as being spatial, like the note symbols of a melody juxtaposed simultaneously side-by-side on the musical staff.]

 

Bergson has been describing an “indivisible continuity of change”. He claims that “this is precisely what constitutes true duration.” Many might object that this notion of duration is “something inexpressible and mysterious.” But in fact this duration is “the clearest thing in the world” [because we experience it directly every moment of our consciousness.] We can think of real duration as time, so long as we qualify that it is “time perceived as indivisible.” [Now, time is often understood as being a matter of succession.] But although duration is time, we should not think of it as succession. Succession is understood as a matter of moments coming before and after, each being set beside the other. [Bergson might here, when mentioning simultaneity, be noting that this setting beside one another of moments makes them simultaneous when really they are not. See the quote below.] When we hear a melody, we have the impression that it cannot be broken up. So we should not think of the melody being broken up into notes set side-by-side and thus not in terms of this spatialized sort of succession. By putting the note symbols into the space of the musical staff, we might erroneously come to believe that the melody itself is something composed of spatially simultaneous parts. Bergson then acknowledges that we normally live our lives in the spatialized time. But real duration is something going on deep inside us. His last point might be that real duration is a single, universal time that happens exclusively in the present and that makes possible the extending changes we notice inside and outside us.]

This indivisible continuity of change is precisely what constitutes true duration. I cannot here enter into the detailed examination of a question I have dealt with elsewhere. I shall confine myself therefore to saying, in reply to those for whom this “real duration” is something inexpressible and mysterious, that it is the clearest thing in the world: real duration is what we have always called time, but time perceived as indivisible. That time implies succession I do not deny. But that succession is first presented to our consciousness, like the distinction of a “before” and “after” set side by side, is what I cannot admit. When we listen to a melody we have the purest impression of succession we could possibly have, – an impression as far removed as possible from that of simultaneity, – and yet it is the very continuity of the melody and the impossibility of breaking it up which make that impression upon us. If we cut it up into distinct notes, into so many “befores” and “afters,” we are bringing spatial images into it and impregnating the succession with simultaneity: in space, and only in space, is there a clear-cut distinction of parts external to one another. I recognize moreover that it is in spatialized time that we ordinarily place ourselves. We have no interest in listening to the uninterrupted ||| humming of life’s depths. And yet, that is where real duration is. Thanks to it, the more or less lengthy changes || we witness within us and in the external world, take place in a single identical time.

 

C’est justement cette continuité indivisible de changement qui constitue la durée vraie. Je ne puis entrer ici dans l’examen approfondi d’une question que j’ai traitée ailleurs. Je me bornerai donc à dire, pour répondre à ceux qui voient dans cette durée « réelle » je ne sais quoi d’ineffable et de mystérieux, qu’elle est la chose la plus claire du monde : la durée réelle est ce que l’on a toujours appelé le temps, mais le temps perçu comme indivisible. Que le temps impli­que la succession, je n’en disconviens pas. Mais que la succession se présente d’abord à notre conscience comme la distinction d’un « avant » et d’un « après » juxtaposés, c’est ce que je ne saurais accorder. Quand nous écoutons une mélodie, nous avons la plus pure impression de succession que nous puissions avoir, – une impression aussi éloignée que possible de celle de la simultanéité, – et pourtant c’est la continuité même de la mélodie et l’impos­sibilité de la décomposer qui font sur nous cette impression. Si nous la découpons en notes distinctes, en autant d’ « avant » et d’« après » qu’il nous plaît, c’est que nous y mêlons des images spatiales et que nous imprégnons la succession de simultanéité : dans l’espace, et dans l’espace seulement, il y a distinction nette de parties extérieures les unes aux autres. Je reconnais d’ailleurs que c’est dans le temps | spatialisé que nous nous plaçons d’ordinaire. Nous n’avons aucun intérêt à écouter le bourdonnement ininterrompu de la vie profonde. Et pourtant la durée réelle est là. C’est grâce à elle que prennent place dans un seul et même temps les changements plus ou moins longs aux­quels nous assistons en nous et dans le monde extérieur.

(166-167 / 176-177 / 149-150)

 

 

5.2.13

[Only change is real. There are no invariable things doing the changing.]

 

So both internal and external reality is “mobility itself”. There is change without things doing the changing.

Thus, whether it is a question of the internal or the external, of ourselves or of things, reality is mobility itself. That is what I was expressing when I said that there is change, but that there are not things which change.

 

Ainsi, qu’il s’agisse du dedans ou du dehors, de nous ou des choses, la réalité est la mobilité même. C’est ce que j’exprimais en disant qu’il y a du changement, mais qu’il n’y a pas de choses qui changent.

(167 / 177 / 150)

 

 

5.2.14

[Some might feel dizzy when contemplating the idea that reality has no fixed points of immobility. But we can obtain a sense of orientation by seeing that change itself is the most substantial and durable thing possible.]

 

Many will object to the notion that all is change, because they will not be able to deal with the disorienting feeling. Bergson assures such people that they can ground their sense of reality in change itself, which is “the most substantial and durable thing possible”.

Before the spectacle of this universal mobility there may be some who will be seized with dizziness. They are accustomed to terra firma; they cannot get used to the rolling and pitching. They must have “fixed” points to which they can attach thought and existence. They think that if everything passes, nothing exists; and that if reality is mobility, it has already ceased to exist at the moment one thinks it, – it eludes thought. The material world, they say, is going to disintegrate, and the mind will drown in the torrent-like flow of things. – Let them be reassured! Change, if they consent to look directly at it without an interposed veil, will very quickly appear to them to be the most substantial and durable thing possible. Its solidity is infinitely superior to that of a fixity which is only an ephemeral arrangement between mobilities. I have come, in fact, to the third point to which I should like to draw your attention.

 

Devant le spectacle de cette mobilité universelle, quelques-uns d’entre nous seront pris de vertige. Ils sont habitués à la terre ferme ; ils ne peuvent se faire au roulis et au tangage. Il leur faut des points « fixes » auxquels attacher la pensée et l’existence. Ils estiment que si tout passe, rien n’existe ; et que si la réalité est mobilité, elle n’est déjà plus au moment où on la pense, elle échappe à la pensée. Le monde matériel, disent-ils, va se dissoudre, et l’esprit se noyer dans le flux torrentueux des choses. – Qu’ils se rassurent ! Le changement, s’ils consentent à le regarder directement, sans voile interposé, leur apparaîtra bien vite comme ce qu’il peut y avoir au monde de plus substantiel et de plus durable. Sa solidité est infiniment supérieure à celle d’une fixité qui n’est qu’un arrangement éphémère entre des mobilités. J’arrive ici, en effet, au troisième point sur lequel je voulais attirer votre attention.

(167 / 177 / 150)

 

 

5.2.15

[We need to change our notion of the past, which says that just the present is real and that the past can only survive when remembered in the present.]

 

Bergson says that if we accept that “change is real and even constitutive of reality”, we will need to understand the past differently than we normally do. Usually we think that only the present exists, and the past can only survive when it is remembered in the present. In a sense, memory would be “storing them [certain parts of the past] away in a kind of box.” Bergson says this is a “profound mistake” (167-167 / 177-178 / 150-151).

 

 

[Sections 5.2.16-5.2.23 are excluded from this summary.]

 

 

 

 

 

Bergson, Henri. 1938 [3rd edition, 1990]. La pensée et le mouvant: Essais et conférences. Paris: Quadridge / PUF.

Available online at:

http://catalogue.bnf.fr/ark:/12148/cb372379203

Another version available at:

http://classiques.uqac.ca/classiques/bergson_henri/pensee_mouvant/pensee_mouvant.html

 

Bergson, Henri. 1946. The Creative Mind. English translation by Mabelle L. Andison. Westport, Connecticut: Greenwood.

 

Bergson, Henri. 1965. An Introduction to Metaphysics: The Creative Mind. English translation by Mabelle L. Andison. Totowa, New Jersey: Rowman & Allanheld.

 

 

 

.

25 May 2017

Bergson (4.2) Matter and Memory, “Indivisibility of Movement,” summary

 

by Corry Shores

 

[Search Blog Here. Index tabs are found at the bottom of the left column.]

 

[Central Entry Directory]

[Zeno’s Paradox, entry directory]

[Bergson, entry directory]

[Bergson’s Matter and Memory, entry directory]

 

[The following is summary. Boldface in quotation and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos. Citations give the pages for the 1939 French edition first; then the 2004 English. Or they will indicate the publication’s date before the page number. Paragraph enumerations and section divisions follow those in the French edition.]

 

 

Summary of

 

Henri Bergson

 

Matière et mémoire

Matter and Memory

 

Ch.4

De la délimitation et de la fixation des images. Perception et matière. Âme et corps.

The Delimiting and Fixing of Images. Perception and Matter. Soul and Body

 

4.2

Tout mouvement est indivisible

Indivisibility of Movement

 

 

Brief summary:

We often think of motion as having parts corresponding to the space it travels through and to the length of time it takes to complete. But in fact, movement is absolutely indivisible, spatially and temporally. We find evidence of its indivisibility both in our experience and in the absurdities of Zeno’s paradoxes. {1} In our experiences of our own actions, like of our hands moving from point A to point B, we feel it as one continuous, unified (although complex) action that we are aware of during a unified and flowing act of consciousness. We do not experience our hand’s motion as divisible into smaller segments, and surely not infinitely divisible. However, after the action is completed, we think abstractly about the space covered, and we understand it as having the properties of a geometrical line. We thereby conclude that our hand occupied an infinite series of points or positions in the course of its movement. We furthermore think that to each position there corresponds an indivisible instant of time when it was there. But in reality, given the indivisibility of motion, we can only say that while it is moving, it indeterminately does so as it changes place through duration. And if we artificially do make cuts in time and try to coordinate them to points in space, the best we can say is that at some moment the object is passing at some point. It never determinately occupies a point. Under this artificial view where we abstractly divide up time, we must [use paraconsistent reasoning to] claim that at some instant the object occupies not simply one point. The only way an object can determinately occupy a single position is if it stops moving. So Bergson distinguishes (under this artificialized view of the abstract time and space of movement): {1} passage at a point, from {2} halting at a point. The other evidence we have of the indivisibility of motion is the absurdity of Zeno’s paradoxes; in other words, the reason his conclusions are absurd is because he begins with the false assumption that the space or the time of motion can be thought of as being apart from the motion itself and as having the geometrical properties of a line. In “the Dichotomy” and “Achilles” arguments, the space traversed is infinitely divided; but we should have begun by assuming it cannot be, thereby avoiding the absurd conclusions. In “the Arrow” argument, the points or positions that the arrow passes through are understood spatially and thus as immobile. Zeno’s error then is that he wrongly took this also to mean that the arrow’s motion is composed of immobile poses at each point. Instead, we should have assumed either that the motion cannot be decomposed into component positions, or if we do admit of such an abstraction, we cannot say that at some instant it is determinately in (or halting at) one position; rather we should say that it is covering more than (or passing at) one position. And in “the Stadium” argument, Zeno wrongly assumes that the durations of the movements are not inherent to them but are rather determined by the objects’ speeds in relation to the relative distances covered. He also wrongly assumes that there is not one duration common to all movements, as for example the single flowing duration of an observer of the entire situation.

 

 

 

 

Summary

 

“Movement is indivisible; it is only the trajectory of a moving body that is divisible”

 

4.2.1

[It is a fact that every movement is absolutely indivisible.]

 

Bergson says that the following claim is not a hypothesis, but is rather a fact often mistaken for a hypothesis [or somehow confused with hypotheses related to it]: “Every movement, inasmuch as it is a passage from rest to rest, is absolutely indivisible”.

I. - Tout mouvement, en tant que passage d'un repos à un repos, est absolument indivisible.

Il ne s’agit pas ici d’une hypothèse, mais d’un fait, qu’une hypothèse recou­vre généralement.

(1939: 209. Text copied from UQAC)

 

I. – Every movement, inasmuch as it is a passage from rest to rest, is absolutely indivisible.

This is not an hypothesis, but a fact, generally masked by an hypothesis.

(2004: 246. Text copied from Mead Project)

 

 

4.2.2

[When we move our hand from point A to B, we are conscious of a single act of a unified, indivisible motion. The spatial path the hand produced is infinitely divisible, and we are tempted to say the motion is too.]

 

Bergson demonstrates this by having us consider a motion of our hand, which we move from point A to B. We are consciously aware of a single act made of one continuous motion and not of a segmented set of motions. Our vision detects a line between points A and B, which are divisible, however. We are tempted at first to say that the motion is divisible like the space traversed.

Voici, par exemple, ma main posée au point A. Je la porte au point B, parcourant d’un trait l’intervalle. Il y a dans ce mouvement, tout à la fois, une image qui frappe ma vue et un acte que ma conscience musculaire saisit. Ma conscience me donne la sensation intérieure d’un fait simple, car en A était le repos, en B est le repos encore, et entre A et B se place un acte indivisible ou tout au moins indivisé, passage du repos au repos, qui est le mouvement même. Mais ma vue perçoit le mouvement sous forme d’une ligne AB qui se parcourt, et cette ligne, comme tout espace, est indéfiniment décompo- | sable. Il semble donc d’abord que je puisse, comme je voudrai, tenir ce mouvement pour multiple ou pour indivisible, selon que je l’envisage dans l’espace ou dans le temps, comme une image qui se dessine hors de moi ou comme un acte que j’accomplis moi-même.

(1939: 209-210. Text copied from UQAC)

 

Here, for example, is my hand, placed at the point A. I carry it to the point B, passing at one stroke through the interval between them. There are two things in this movement: an image which I see, and an act of which my muscular sense makes my consciousness aware. My consciousness gives me the inward feeling of a single fact, for in A was rest, in B there is again rest, and between A and B is placed an indivisible or at least an undivided act, the passage from rest to rest, which is movement itself. But my sight perceives the movement in the form of a line AB which is traversed and this line, like all space, may be indefinitely divided. It seems then, at first sight, that I may at will take this movement to be multiple or indivisible, according as I consider it in space or in time, as an image which takes shape outside of me or as an act which I am myself accomplishing.

(2004: 246. Text copied from Mead Project)

 

 

4.2.3

[Were a moving object to occupy a determinate position, it would actually not be in motion; for, objects in motion occupy space indeterminately. We must distinguish occupation at a point, which is what happens when a moving object stops its motion, from passage at a point, which happens when a moving object is still in motion in a certain area. Motion is not divisible like space is. (Instead, we must think of a moving object always as going beyond any of the points it is located at during some ((small)) interval of time.)]

 

[His next points are very important, but I may not restate them perfectly well. He writes: “Yet, when I put aside all preconceived ideas, I soon perceive that ... even my sight takes in the movement from A to B as an indivisible whole, and that if it divides anything, it is the line supposed to have been traversed, and not the movement traversing it”. Maybe the idea here is that the line traversed by the hand is a mathematical abstraction projected upon the real space of the motion, and that we did not directly perceive it; we rather only perceived the motion itself as it was happening. His next point is the important one here. He seems to distinguish occupation at a position (or point) and passage at (or through or across) a position or point: “It is indeed true that my hand does not go from A to B without passing through the intermediate positions, and that these intermediate points resemble stages, as numerous as you please, all along the route ; but there is, between the divisions so marked out and stages properly so called, this capital difference, that at a stage we halt, whereas at these points the moving body passes.” It is still not perfectly clear to me what it means to pass at a point rather than to halt at a point. To halt at the point means to determinately occupy it, with that occupation being no different than were it at rest at that point. The only way I have so far to understand passage at a point is that it is not determinately occupying it like it would at rest, meaning perhaps that it is both there and not there at the same time, or at least that it is there and near there at the same time. Does this mean that at a certain moment it occupies a fuzzy or blurry region where no precise location can be specified? In that case, passing at a point would still mean residing throughout a small surrounding region, or in other words, occupying many positions at once. Bergson next writes: “Now a passage is a movement and a halt is an immobility. The halt interrupts the movement ; the passage is one with the movement itself.” It is clear how the halt interrupts the movement. But what does it mean for the passage being one with the movement? If he means “passage” as the total passage, that would not seem interesting to say (‘the movement from A to B is the passage from A to B’), and it would not make “passage” be parallel to “halt”, which happens at a point. So perhaps he means “passage” here as passage at a point or at least passage in the region of some point. Were that the case, then it would mean that passage at (or around) a point is one with the whole movement itself, and this is a much more interesting claim, although not one I fully comprehend. It would suggest that although we might want to say the object at a certain time is at a certain location,  it would be more accurate to say that it is passing that location, and that passage is not distinguishable or disentangleable from the whole motion enveloping that part. Let us pursue this concept. Is this so, because ... {1} The whole movement occupies an indivisible block of time, and thus we cannot pinpoint some instant where it is at some location. Rather, during a block of time it is within a block of space. We might call it the “block-block” theory of motion, in keeping with Russell’s “at-at” theory. (This interpretation stays closely to the wording “the passage is one with the movement itself”. But it seems odd to say that the duration of time admits of no partition where the position of the object cannot be narrowed down. If we watch an ant move across a sidewalk while cars drive down the adjacent road, surely we can say that after so many cars go by, the ant is still on the first half of the sidewalk, and after so many more go by, it is on the other half. In other words, even if I see the motion of the ant as unified, it is not so obvious to me that the space-time locations cannot at least be distinguished relative to one another. And surely we are not saying that during a certain passage of time, it is always in all locations all throughout that time. The object is in some region at one phase and another region at another phase. So I am not convinced yet that Bergson is making a generalized block-block conception.) (Or is the passage the same as the whole movement for the reason that ...) {2} Because the object is always in motion, it cannot be determinately located at any point; for, then it is at rest. It must instead, at some instant, be indeterminately at some point. One reason this could be is that at some instant, it is located at more that one point, or it is located between successive points in an infinitesimal interval. He next writes: “When I see the moving body pass any point, I conceive, no doubt, that it might stop there;” (here we are thinking of the motion in its present activity, and we think at any moment it might stop at its given location) “and even when it does not stop there, I incline to consider its passage as an arrest, though infinitely short, because I must have at least the time to think of it;” (and even though its motion does not pause, we think that we might have caught it at an infinitely brief part of its movement where it occupies a specific position. But I do not know what he means by “because I must have at least the time to think of it.” Perhaps he means that at some moment we think of it being there, and since that thought occupies a moment we might assume the motion we observe also can be contained in that moment of thought. But I doubt that is the meaning, however;) “but it is only my imagination which stops there, and what the moving body has to do is, on the contrary, to move.” (This might mean that as we are watching the movement, we imagine its continuously varying location in space, and since our imagination of that movement can pause, we assume the movement can be understood as having very brief pauses where it occupies a determinate position, corresponding to where our imagination stops following the progress.) “As every point of space necessarily appears to me fixed, I find it extremely difficult not to attribute to the moving body itself the immobility of the point with which, for a moment, I make it coincide ; it seems to me, then, when I reconstitute the total movement, that the moving body has stayed an infinitely short time at every point of its trajectory.” (So because we imagine these positions during its motion, we then think we can reconstitute the motion by connecting the fabricated points or positions.) “But we must not confound the data of the senses, which perceive the movement, with the artifice of the mind, which recomposes it. The senses, left to themselves, present to us the real movement, between two real halts, as a solid [247|248] and undivided whole. The division is the work of our imagination, of which indeed the office is to fix the moving images of our ordinary experience, like the instantaneous flash which illuminates a stormy landscape by night.” (These passages reiterate the point that the senses perceive the unified whole of the motion, but the imagination is what artificially creates the cuts dividing it. The interesting part here is the vibrant metaphor of the flash of lightning giving us a snapshot of a dark stormy scene being like the way the imagination makes instantaneous immobile snapshots of activity).]

Toutefois, en écartant toute idée préconçue, je m’aperçois bien vite que je n’ai pas le choix, que ma vue elle-même saisit le mouvement de A en B comme un tout indivisible, et que si elle divise quelque chose, c’est la ligne supposée parcourue et non pas le mouvement qui la parcourt. Il est bien vrai que ma main ne va pas de A en B sans traverser les positions intermédiaires, et que ces points intermédiaires ressemblent à des étapes, en nombre aussi grand qu’on voudra, disposées tout le long de la route ; mais il y a entre les divisions ainsi marquées et des étapes proprement dites cette différence capitale qu’à une étape on s’arrête, au lieu qu’ici le mobile passe. Or le passage est un mouvement, et l’arrêt une immobilité. L’arrêt interrompt le mouvement ; le passage ne fait qu’un avec le mouvement même. Quand je vois le mobile passer en un point, je conçois sans doute qu’il puisse s’y arrêter ; et lors même qu’il ne s’y arrête pas, j’incline à considérer son passage comme un repos infiniment court, parce qu’il me faut au moins le temps d’y penser; mais c’est mon imagination seule qui se repose ici, et le rôle du mobile est au contraire de se mouvoir. Tout point de l’espace m’apparaissant nécessairement comme fixe, j’ai bien de la peine à ne pas attribuer au mobile lui-même l’immobilité du point avec lequel je le fais pour un moment coïncider ; il me semble alors, quand je reconstitue le mouvement total, que le mobile a stationné un temps infiniment court à tous les points de sa trajectoire. | Mais il ne faudrait pas con­fondre les données des sens, qui perçoivent le mouvement, avec les artifices de l’esprit qui le recompose. Les sens, laissés à eux-mêmes, nous présentent le mouvement réel, entre deux arrêts réels, comme un tout solide et indivisé. La division est l’œuvre de l’imagination, qui a justement pour fonction de fixer les images mouvantes de notre expérience ordinaire, comme l’éclair instantané qui illumine pendant la nuit une scène d’orage.

(1939: 210-211. Text copied from UQAC)

 

Yet, when I put aside all preconceived ideas, I soon perceive that I have no such choice, that even my sight takes in the movement from A to B as an indivisible whole, and that if it divides anything, it is the line supposed to have been traversed, and not the movement traversing it. It is indeed [246|247] true that my hand does not go from A to B without passing through the intermediate positions, and that these intermediate points resemble stages, as numerous as you please, all along the route ; but there is, between the divisions so marked out and stages properly so called, this capital difference, that at a stage we halt, whereas at these points the moving body passes. Now a passage is a movement and a halt is an immobility. The halt interrupts the movement ; the passage is one with the movement itself. When I see the moving body pass any point, I conceive, no doubt, that it might stop there; and even when it does not stop there, I incline to consider its passage as an arrest, though infinitely short, because I must have at least the time to think of it; but it is only my imagination which stops there, and what the moving body has to do is, on the contrary, to move. As every point of space necessarily appears to me fixed, I find it extremely difficult not to attribute to the moving body itself the immobility of the point with which, for a moment, I make it coincide ; it seems to me, then, when I reconstitute the total movement, that the moving body has stayed an infinitely short time at every point of its trajectory. But we must not confound the data of the senses, which perceive the movement, with the artifice of the mind, which recomposes it. The senses, left to themselves, present to us the real movement, between two real halts, as a solid[247|248] and undivided whole. The division is the work of our imagination, of which indeed the office is to fix the moving images of our ordinary experience, like the instantaneous flash which illuminates a stormy landscape by night.

(2004: 246-248. Text copied from Mead Project)

 

 

 

4.2.4

[Again, we mistake the line traced by the object with the motion that did the tracing. The motion is not divisible into immobile spatial points.]

 

[Bergson restates these notions: the line that we think the moving object draws is divisible and composed of points which are immobile, but the movement itself is not made of such rests and never determinately occupied these points.]

Nous saisissons ici, dans son principe même, l’illusion qui accompagne et recouvre la perception du mouvement réel. Le mouvement consiste visible­ment à passer d’un point à un autre, et par suite à traverser de l’espace. Or l’espace traversé est divisible à l’infini, et comme le mouvement s’applique, pour ainsi dire, le long de la ligne qu’il parcourt, il paraît solidaire de cette ligne et divisible comme elle. Ne l’a-t-il pas dessinée lui-même ? N’en a-t-il pas traversé, tour à tour, les points successifs et juxtaposés ? Oui sans doute, mais ces points n’ont de réalité que dans une ligne tracée, c’est-à-dire immo­bile ; et par cela seul que vous vous représentez le mouvement, tour à tour, en ces différents points, vous l’y arrêtez nécessairement; vos positions successi­ves ne sont, au fond, que des arrêts imaginaires. Vous substituez la trajectoire au trajet, et parce que le trajet est sous-tendu par la trajectoire, vous croyez qu’il coïncide avec elle. Mais comment un progrès coïnciderait-il avec une chose, un mouvement avec une immobilité ?

(1939: 211. Text copied from UQAC)

 

We discover here, at its outset, the illusion which accompanies and masks the perception of real movement. Movement visibly consists in passing from one point to another, and consequently in traversing space. Now the space which is traversed is infinitely divisible ; and as the movement is, so to speak, applied to the line along which it passes, it appears to be one with this line and, like it, divisible. Has not the movement itself drawn the line ? Has it not traversed in turn the successive and juxtaposed points of that line ? Yes, no doubt, but these points have no reality except in a line drawn, that is to say motionless; and by the very fact that you represent the movement to yourself successively in these different points, you necessarily arrest it in each of them ; your successive positions are, at bottom, only so many imaginary halts. You substitute the path for the journey, and because the journey is subtended by the path you think that the two coincide. But how should a progress coincide with a thing, a movement with an immobility ?

(2004: 248. Text copied from Mead Project)

 

 

4.2.5

[We want to think that there is a continuous correlation between the geometricized spatial trail of the moving object and the temporal duration of that motion. But duration is something alive and active in the present, and what happens in that duration is not determined by past moments, just as the motion is not either. So in truth, duration is not continuously correlated with the spatialized trail. That furthermore means that we cannot correlate the indivisible points in the geometricized trail with indivisible instants in the duration of the motion. (Instead, we should see the duration of the motion as the living present of that movement, which has no parts to be divided.)]

 

[We now get a clear statement from Bergson that there can be no real indivisible instants. Let us go part by part. “What facilitates this illusion is that we distinguish moments in the course of duration, like halts in the passage of the moving body.” (The illusion I think is the illusion that motion is made of the spatial points that the imagination projects upon it.) “Even if we grant that the movement from one point to another forms an undivided whole, this movement nevertheless takes a certain time;” (I am not sure why it is formulated this way as if there is a conceptual tension between a movement being whole and it lasting a duration of time, but that is the point here;) “so that if we carve out of this duration an indivisible instant, it seems that the moving body must occupy, at that precise moment, a certain position, which thus stands out from the whole.” (So since we have established a correlation between the temporal and spatial extents of the motion, and since this correlation is continuous with the motion, we think that if we pinpoint some precise indivisible moment in time, we will find the object at some precise spatial location. Note here that he portrays this understanding of the instant as seeing it as standing outside the flow of the motion’s duration. In other words, the temporality of the motion is such that it is internally “organized” or integrated, and any attempt to pinpoint a precise moment would be to extract it from that internal integration somehow and thus to no longer make it a real part of that duration.) “The indivisibility of motion implies, then, the impossibility of real instants;” (Here he is saying that if the motion is indivisible, this means it must be both spatially and temporally indivisible. I am not entirely sure I understand why, but it might be because the correlation between time and space is continuous, and we are assigning them both the same properties of a geometrical continuum like  a line. For the same reason it never occupies a determinate point of space it also does not occupy a determinate point in time. If that is the case, then perhaps he is giving a “block-block” theory of motion where the best we can say is that a unified act of motion involves a block of time and a block of space, but no further determinations can be made whatsoever regarding more precise locations and phases within those blocks;) “and indeed, a very brief analysis of the idea of duration will show us both why we attribute instants to duration and why it cannot have any.” (He continues:) “Suppose a simple movement like that of my hand when it goes from A to B. This passage is given to my consciousness as an undivided whole.” (This is the same example before of the hand moving from A to B, only now there is emphasis on our consciousness of this passage.) “No doubt it endures ; but this duration, which in fact coincides with the aspect which the movement has inwardly for my consciousness, is, like it, whole and undivided.” (So the movement of the hand is undivided, and so too is the duration of its motion, corresponding to the undivided duration of our consciousness of the motion.) “Now, while it presents itself, qua movement, as a simple fact, it describes in space a trajectory which I may consider, for purposes of simplification, as a geometrical line;” (we have encountered this notion many times. The hand traces a path in space, and that traced path can be understood as a geometrical line;) “and the extremities of this line, considered as abstract limits, are no longer lines, but indivisible points.” (The idea here seems to be that the traced line has ends to it, which as terminations of the line, are not lines but are rather points.) “Now, if the line, which the moving body has described, measures for me the duration of its movement, must not the point, where the line ends, symbolize for me a terminus of this duration ?” (He seems to be saying that since we coordinate the spatial extent with the temporal extent, and since the spatial ends are terminations of the line, they must correspond to temporal termination points to the duration.) “And if this point is an indivisible of length, how shall we avoid terminating the duration of the movement by an indivisible of duration ?” (The spatial terminating point is indivisible, so the temporal terminating point must be also ((or else the spatial and temporal extents would not be correlated)).) “If  the total line represents the total duration, the parts of the line must, it seems, correspond to parts of the duration, and the points of the line to moments of time.” (Since the whole temporal and spatial extents correlate, and because that correlation is continuous, that means any part of the one must correspond to its counterpart in the other. It is not stated here if the parts should be understood as intervals or as points, but it would seem to apply to both sorts.) “The indivisibles of duration, or moments of time, are born, then, of the need of symmetry; we come to them naturally as soon as we demand from space an integral presentment of duration.” (I think he is saying that since we make this strict correlation between space to time, that means so long as we think space is made of indivisible points, we must also conceive there being indivisible instants). “– But herein, precisely, lies the error. While the line AB symbolizes the duration already lapsed of the movement from A to B already accomplished, it cannot, motionless, represent the movement in its accomplishment nor duration in its flow.” (I am not entirely sure here, but the idea might be the following. We said before that the line traced can only be understood in this spatial way after the motion is completed and the line is finished. It was not clear why, but that was the claim. Thus this spatial line can only be thought of as corresponding to a finished duration and not to the duration as it is happening. I am still not sure why this is exactly, beside simply appealing to the claim that the motion is indivisible in action but divisible in completion. But why? Does it have something to do with indeterminacy of where it is going or whether it will continue or not? Is it because the motion is in the present ((and is open to unpredictable variation) but the spatial and temporal trail are in the past, which is fixed and determined?) “And from the fact that this line is divisible into parts and that it ends in points, we cannot conclude either that the corresponding duration is composed of separate parts or that it is limited by instants.” (Here he seems to be calling into question the correlation between time and space. He seems to be saying that time must be understood as duration in his sense rather than in the sense of a geometrical sort of line, and thus we cannot say that duration is made of indivisible parts. But most interesting here is to say that the duration does not terminate at instants. Does he mean that it does not terminate? Does he mean that it terminates, but in an indeterminate way?)]

Ce qui facilite ici l’illusion, c’est que nous distinguons des moments dans le cours de la durée, comme des positions sur le trajet du mobile. À supposer que le mouvement d’un point à un autre forme un tout indivisé, ce mouvement n’en remplit [211|212] pas moins un temps déterminé, et il suffit qu’on isole de cette durée un instant indivisible pour que le mobile occupe à ce moment précis une certaine position, qui se détache ainsi de toutes les autres. L’indivisibilité du mouvement implique donc l’impossibilité de l’instant, et une analyse très sommaire de l’idée de durée va nous montrer en effet, tout à la fois, pourquoi nous attribuons à la durée des instants, et comment elle ne saurait en avoir. Soit un mouvement simple, comme le trajet de ma main quand elle se déplace de A en B. Ce trajet est donné à ma conscience comme un tout indivisé. Il dure, sans doute; mais sa durée, qui coïncide d’ailleurs avec l’aspect intérieur qu’il prend pour ma conscience, est compacte et indivisée comme lui. Or, tandis qu’il se présente, en tant que mouvement, comme un fait simple, il décrit dans l’espace une trajectoire que je puis considérer, pour simplifier les choses, comme une ligne géométrique ; et les extrémités de cette ligne, en tant que limites abstraites, ne sont plus des lignes mais des points indivisibles. Or, si la ligne que le mobile a décrite mesure pour moi la durée de son mouve­ment, comment le point où la ligne aboutit ne symboliserait-il pas une extré­mité de cette durée ? Et si ce point est un indivisible de longueur, comment ne pas terminer la durée du trajet par un indivisible de durée ? La ligne totale représentant la durée totale, les parties de cette ligne doivent correspondre, semble-t-il, à des parties de la durée, et les points de la ligne à des moments du temps. Les indivisibles de durée ou moments du temps naissent donc d’un besoin de symétrie; on y aboutit naturellement dès qu’on demande à l’espace une représentation intégrale de la durée. Mais voilà précisément l’erreur. Si la ligne AB symbolise la durée écoulée du mouvement [212|213] accompli de A en B, elle ne peut aucunement, immobile, représenter le mouvement s’accomplissant, la durée s’écoulant ; et de ce que cette ligne est divisible en parties, et de ce qu’elle se termine par des points, on ne doit conclure ni que la durée corres­pondante se compose de parties séparées ni qu’elle soit limitée par des instants.

(1939: 211-213. Text copied from UQAC)

 

What facilitates this illusion is that we distinguish moments in the course of duration, like halts in the passage of the moving body. Even [248|249] if we grant that the movement from one point to another forms an undivided whole, this movement nevertheless takes a certain time ; so that if we carve out of this duration an indivisible instant, it seems that the moving body must occupy, at that precise moment, a certain position, which thus stands out from the whole. The indivisibility of motion implies, then, the impossibility of real instants ; and indeed, a very brief analysis of the idea of duration will show us both why we attribute instants to duration and why it cannot have any. Suppose a simple movement like that of my hand when it goes from A to B. This passage is given to my consciousness as an undivided whole. No doubt it endures ; but this duration, which in fact coincides with the aspect which the movement has inwardly for my consciousness, is, like it, whole and undivided. Now, while it presents itself, qua movement, as a simple fact, it describes in space a trajectory which I may consider, for purposes of simplification, as a geometrical line; and the extremities of this line, considered as abstract limits, are no longer lines, but indivisible points. Now, if the line, which the moving body has described, measures for me the duration of its movement, must not the point, where the line ends, symbolize for me a terminus of this duration ? And if this point is an indivisible of length, how shall we avoid terminating the duration of the movement by an indivisible of duration ? If [249|250]  the total line represents the total duration, the parts of the line must, it seems, correspond to parts of the duration, and the points of the line to moments of time. The indivisibles of duration, or moments of time, are born, then, of the need of symmetry; we come to them naturally as soon as we demand from space an integral presentment of duration. – But herein, precisely, lies the error. While the line AB symbolizes the duration already lapsed of the movement from A to B already accomplished, it cannot, motionless, represent the movement in its accomplishment nor duration in its flow. And from the fact that this line is divisible into parts and that it ends in points, we cannot conclude either that the corresponding duration is composed of separate parts or that it is limited by instants.

(2004: 248-250. Text copied from Mead Project)

 

 

 

“Zeno transfers to the moving body the properties of its trajectory: hence all the difficulties and contradictions”

 

4.2.6

[Zeno’s paradoxes of motion involve a confusion of the space travelled with the motion itself and its real duration. In “the Dichotomy” and “the Achilles” arguments, the space traversed is infinitely divided, forgetting that motion itself cannot be. In “the Arrow” argument, the immobility of the points of the space travelled are wrongly thought to mean that the arrow’s motion is composed of immobile poses at each point. And in “the Stadium” argument, we wrongly think that the duration of the movement should be calculated based on the relative spatial distances covered, and we forget there is one duration that comprehends all the motions involved.]

 

Bergson claims that all of Zeno’s paradoxes of motion result from this error of confusing the properties of real motion and real duration with the properties of geometrical lines. Zeno was guided by common sense to conceive the movement in terms of the trajectory or traversed path, and he was guided by language to conceive of movement and duration in terms of space. Common sense and language, for their own purposes, treat becoming as a thing, and thereby ignore “the interior organization of movement”. In practical life, there are two facts that lead common sense to spatialize the movement: {1} the fact that every movement describes a space (by “describes” perhaps he means draws a path through or at least happens within), and {2} the fact that at every point of this described space the moving thing might stop. Zeno mistakenly holds these to be facts of motion. [Bergson then speaks of Zeno’s four arguments. They are summarized within parts II.C-E at this entry. The first one he calls “the Dichotomy”. I cannot tell if it refers to the paradox I numbered II.D or II.E. In II.D, the moving object, before reaching its destination, must first get half-way there. But before reaching the halfway point, it must get half that way (a quarter of the total distance). Since the distance is infinitely divisible, there is always a new halfway mark set away at some distance. In other words, it can never get past its starting position, because it can never reach a first halfway point. In II.E, we begin by noting that within a finite extent of motion, there are still an infinity of points for the moving body to cross. But arriving upon any point requires a finite amount of time. Thus, to cross the infinity of points within a finite range of motion will still take an infinite amount of time. Bergson describes it as: “By the first argument (the Dichotomy) he supposes the moving body to be at rest, and then considers nothing but the stages, infinite in number, that are along the line to be traversed we cannot imagine, he says, how the body could ever get through the interval between them.” (Note: the Internet Encyclopedia of Philosophy and the Stanford Encyclopedia of Philosophy list the dichotomy argument as the halving one.) Bergson’s comment here is not that we should conclude motion is impossible but rather that it cannot be constructed from a series of immobilities. (Bergson also says that this is “a thing no man ever doubted”, but Russell’s theory of motion  in fact tries to construct movement this way.) Bergson says that the real question is whether or not the moving object passes through an infinity of points. He emphasizes again that the spatial trajectory is infinitely divisible but the movement (or the component movements) is not. The second Zeno argument is “the Achilles argument”. Here the Tortoise leads Achilles at the start of the race. To catch-up, Achilles needs to reach the Tortoise’s advanced position. Suppose he does. By that time, however, the Tortoise has advanced further. So long as they are both moving, the Tortoise will always lead, no matter how far ahead he is. This paradox, Bergson notes, requires that we consider the paths traversed as distinct from their movements and thereby as infinitely divisible. Rather, Achilles running is made of a number of bounds and the Tortoise a number of steps, and since Achilles’ bounds are much greater or faster, he will overtake the Tortoise. Zeno’s third argument is “the Arrow”. Here a moving arrow has a certain length, and that length equals the amount of space (the part of its path of movement) it occupies at any moment. But if it always occupies no more than its own length of space, then it is never moving (because it is never changing location). Here Bergson again reminds us that we are confusing the space of motion with the motion itself. Bergson then turns to Zeno’s fourth argument, “the Stadium”, about which Bergson writes, “which has, we believe, been unjustly disdained, and of which the absurdity is more manifest only because the postulate masked in the three others is here frankly displayed”, then in a footnote he explains what he means. (In this case, you have three objects of equal length and running on parallel tracks, moving past one another. The first one is stationary, and the other two move in opposite directions at the same speed, and coming together like so:

--AAAA--        --AAAA--

BBBB----   =>   --BBBB--

----CCCC        --CCCC--

The conclusion in Aristotle is that “half a given time is equal to double that time” and in Bergson “a duration is the double of itself.”  Think now of just B’s motion in relation to A’s. Suppose it is going one meter per second and each segment is one meter. It traveled two A segments, so it must have taken two seconds. Now consider B’s motion in relation to C’s. In the same motion, it passed four C’s. So it must have also taken four seconds to complete that same motion. (Possibly I have this wrong, but it is not very obvious how we reach the conclusion and thus how we are to portray the situation.) Now, for this to work (at least with how I set it up) and for us to follow what might be Bergson’s point here, we need to look at the assumptions that lead us to this conclusion. {1} The speeds of B and C are constant, and the lengths of A, B, and C are all the same. {2} The duration of the entire event is not absolutized; rather, it is calculated on the basis of the object’s given speed in relation to the distance traveled. {3} the spatial coordinates of the situation are not absolutized but are rather relativized, and thus the distances we use in our calculations are determined by an arbitrary selection of any two of the given bodies. Thus B can be said to move two different distances in the same stroke and thus its motion consumes two different durations. (I am ignoring other possibilities, like we compare the time of B’s movement to that of C, because I think it comes out the same but is less directly paradoxical.) From what I can tell, Bergson’s claim is that Zeno does not think of a real duration shared by all three and given directly to a consciousness aware of the entire event (I am thinking here of the simultaneity notion in Duration and Simultaneity §42 and discussed in Deleuze’s Bergsonism §76.) Bergson instead thinks the duration can be represented in terms of the space covered, as we see in our calculations. In other words, instead of the duration being understood (correctly) as part of all the motions and thus being just as indivisible as they are, duration is instead thought (incorrectly) to be a by-product of the space covered at a certain speed. (I might be misreading, so check the text below.) Bergson concludes this paragraph by reemphasizing that these paradoxes do not do justice to the lived duration of the motion and rather deal with its contorted abstraction in the mind, and he says all this discussion leads us to the conclusion that there are in fact real movements (the topic of the next section).]

Les arguments de Zénon d’Élée n’ont pas d’autre origine que cette illusion. Tous consistent à faire coïncider le temps et le mouvement avec la ligne qui les sous-tend, à leur attribuer les mêmes subdivisions, enfin à les traiter com­me elle. À cette confusion Zénon était encouragé par le sens commun, qui transporte d’ordinaire au mouvement les propriétés de sa trajectoire, et aussi par le langage, qui traduit toujours en espace le mouvement et la durée. Mais le sens commun et le langage sont ici dans leur droit, et même, en quelque sorte, font leur devoir, car envisageant toujours le devenir comme une chose utilisable, ils n’ont pas plus à s’inquiéter de l’organisation intérieure du mouve­ment que l’ouvrier de la structure moléculaire de ses outils. En tenant le mouvement pour divisible comme sa trajectoire, le sens commun exprime simplement les deux faits qui seuls importent dans la vie pratique : 1º que tout mouvement décrit un espace ; 2º qu’on chaque point de cet espace le mobile pourrait s’arrêter. Mais le philosophe qui raisonne sur la nature intime du mouvement est tenu de lui restituer la mobilité qui en est l’essence, et c’est ce que ne fait pas Zénon. Par le premier argument Ca Dichotomie) on suppose le mobile au repos, pour ne plus envisager ensuite que des étapes, en nombre indéfini, sur la ligne qu’il doit parcourir : vous chercheriez vainement, nous dit-on, comment il arriverait à franchir l’intervalle. Mais on prouve [213|214] simple­ment ainsi qu’il est impossible de construire a priori le mouvement avec des immobilités, ce qui n’a jamais fait de doute pour personne. L’unique question est de savoir si, le mouvement étant posé comme un fait, il y a une absurdité en quelque sorte rétrospective à ce qu’un nombre infini de points ait été parcouru. Mais nous ne voyons rien là que de très naturel, puisque le mouvement est un fait indivisé ou une suite de faits indivisés, tandis que la trajectoire est indéfiniment divisible. Dans le second argument (l’Achille), on consent à se donner le mouvement, on l’attribue même à deux mobiles, mais, toujours par la même erreur, on veut que ces mouvements coïncident avec leur trajectoire et soient, comme elle, arbitrairement décomposables. Alors, au lieu de reconnaître que la tortue fait des pas de tortue et Achille des pas d’Achille, de sorte qu’après un certain nombre de ces actes ou sauts indivisibles Achille aura dépassé la tortue, on se croit en droit de désarticuler comme on veut le mouvement d’Achille et comme on veut le mouvement de la tortue : on s’amuse ainsi à reconstruire les deux mouvements selon une loi de formation arbitraire, incompatible avec les conditions fondamentales de la mobilité. Le même sophisme apparaît plus clairement encore dans le troisième argument (la Flèche), qui consiste à conclure, de ce qu’on peut fixer des points sur la trajectoire d’un projectile, qu’on a le droit de distinguer des moments indivi­sibles dans la durée du trajet. Mais le plus instructif des arguments de Zénon est Peut-être le quatrième (le Stade), qu’on a, croyons-nous, bien injustement dédaigné, et dont l’absurdité n’est plus manifeste que parce qu’on y voit étalé dans toute sa franchise le postulat [214|215] dissimulé dans les trois autres1. Sans nous engager ici dans une discussion qui ne serait pas à sa place, bornons-nous à constater que le mouvement immédiatement perçu est un fait très clair, et que les difficultés ou contradictions signalées par l’école d’Élée concernent beau­coup moins le mouvement lui-même qu’une réorganisation artificielle, et non viable, du mouvement par l’esprit. Tirons d’ailleurs la conclusion de tout ce qui précède :

II. – Il y a des mouvements réels.

(1939: 213-215. Text copied from UQAC)

1 Rappelons brièvement cet argument. Soit un mobile qui se déplace avec lune certaine vitesse et qui passe simultanément devant deux corps dont l'un est immobile et dont l'autre se meut à sa rencontre avec la même vitesse que lui. En même temps qu'il parcourt une certaine longueur du premier corps, il franchit naturellement une longueur double du second. D'où Zénon conclut « qu'une durée est double d'elle-même ». - Raisonnement puéril, dit-on, puisque Zénon ne tient pas compte de ce que la vitesse est double, dans un cas, de ce qu'elle est dans l'autre. - D'accord, mais comment, je vous prie, pourrait-il s'en apercevoir ? Que, dans le même temps, un mobile parcoure des longueurs différentes de deux corps dont l'un est en repos et l'autre en mouvement, cela est clair pour celui qui fait de la durée une espèce d'absolu, et la met soit dans la conscience soit dans quelque chose qui participe de la conscience. Pendant qu'une portion déterminée de cette durée con­sciente ou absolue s'écoule, en effet, le même mobile parcourra, le long des deux corps, deux espaces doubles l'un de l'autre, sans qu'on puisse conclure de là qu'une durée est double d'elle-même, puisque la durée reste quelque chose d'indépendant de l'un et l'autre espace. Mais le tort de Zénon, dans tolite son argumentation, est justement de laisser de côté la durée vraie pour n'en considérer que la trace objective dans l'espace. Comment les deux traces laissées par le même mobile ne mériteraient-elles pas alors une égale consi­dération, en tant que mesures de la durée ? Et comment ne représenteraient-elles pas la même durée, lors même qu'elles seraient doubles l'une de l'autre ? En concluant de là qu'une durée « est double d'elle-même » Zénon restait dans la logique de son hypothèse, et son quatrième argument vaut exactement autant que les trois autres.

(1939: 215. Text copied from UQAC)

 

The arguments of Zeno of Elea have no other origin than this illusion. They all consist in making time and movement coincide with the line which underlies them, in attributing to them the same subdivisions as to the line, in short in treating them like that line. In this confusion Zeno was encouraged by common sense, which usually carries over to the movement the properties of its trajectory, and also by language, which always translates movement and duration in terms of space. But common sense and language have a right to do so [250|251] and are even bound to do so, for, since they always regard the becoming as a thing to be made use of, they have no more concern with the interior organization of movement than a workman has with the molecular structure of his tools. In holding movement to be divisible, as its trajectory is, common sense merely expresses the two facts which alone are of importance in practical life: first, that every movement describes a space ; second, that at every point of this space the moving body might stop. But the philosopher who reasons upon the inner nature of movement is bound to restore to it the mobility which is its essence, and this is what Zeno omits to do. By the first argument (the Dichotomy) he supposes the moving body to be at rest, and then considers nothing but the stages, infinite in number, that are along the line to be traversed we cannot imagine, he says, how the body could ever get through the interval between them. But in this way he merely proves that it is impossible to construct, a priori, movement with immobilities, a thing no man ever doubted. The sole question is whether, movement being posited as a fact, there is a sort of retrospective absurdity in assuming that an infinite number of points has been passed through. But at this we need not wonder, since movement is an undivided fact, or a series of undivided facts, whereas the trajectory is infinitely divisible. In the second argument (the Achilles) movement is [251|252] indeed given, it is even attributed to two moving bodies, but, always by the same error, there is an assumption that their movement coincides with their path, and that we may divide it, like the path itself, in any way we please. Then, instead of recognizing that the tortoise has the pace of a tortoise and Achilles the pace of Achilles, so that after a certain number of these indivisible acts or bounds Achilles will have outrun the tortoise, the contention is that we may disarticulate as we will the movement of Achilles and, as we will also, the movement of the tortoise : thus reconstructing both in an arbitrary sway, according to a law of our own which may be incompatible with the real conditions of mobility. The same fallacy appears, yet more evident, in the third argument (the Arrow) which consists in the conclusion that, because it is possible to distinguish points on the path of a moving body, we have the right to distinguish indivisible moments in the duration of its movement. But the most instructive of Zeno's arguments is perhaps the fourth (the Stadium) which has, we believe, been unjustly disdained, and of which the absurdity is more manifest only because the postulate masked in the three others is here frankly displayed.1 Without entering on a dis- [252|253] cussion which would here be out of place, we will content ourselves with observing that motion, as given to spontaneous perception, is a fact which is quite clear, and that the difficulties and contradictions pointed out by the Eleatic school concern far less the living movement itself than a dead and artificial reorganization of movement by the mind. But we now come to the conclusion of all the preceding paragraphs: [253|254]

II. There are real movements.

(2004: 250-253. Text copied from Mead Project)

1 We may here briefly recall this argument. Let there be a moving body which is displaced with a certain velocity, and which passes simultaneously before two bodies, one at rest and the other moving towards it with the same velocity [252|253] as its own. During the same time that it passes a certain length of the first body, it naturally passes double that length of the other. Whence Zeno concludes that ‘a duration is the double of itself.’ A childish argument, it is said, because Zeno takes no account of the fact that the velocity is in the one case double that which it is in the other. – Certainly, but how, I ask, could he be aware of this ? That, in the same time, a moving body passes different lengths of two bodies, of which one is at rest and the other in motion, is clear for him who makes of duration a kind of absolute, and places it either in consciousness or in something which partakes of consciousness. For while a determined portion of this absolute or conscious duration elapses, the same moving body will traverse, as it passes the two bodies, two spaces of which the one is the double of the other, without our being able to conclude from this that a duration is double itself, since duration remains independent of both spaces. But Zeno's error, in all his reasoning, is due to just this fact, that he leaves real duration on one side and considers only its objective track in space. How then should the two lines traced by the same moving body not merit an equal consideration, qua measures of duration ? And how should they not represent the same duration, even though the one is twice the other ? In concluding from this that ‘a duration is the double of itself,’ Zeno was true to the logic of his hypothesis; and his fourth argument is worth exactly as much as the three others.

(2004: 252-253. Text copied from Mead Project)

 

 

 

 

 

 

Texts:

 

Bergson, Henri. 1939 [this one 3rd edn. 1990]. Matière et mémoire: Essai sur la relation du corps à l'esprit. Paris: Quadridge / Presses Universitaires de France.

PDF available online at:

http://catalogue.bnf.fr/ark:/12148/cb37237615p

PDF of 1903 edition at:

http://www.archive.org/details/matireetmmoiree01berggoog

Text copied from 1939 edition at:

http://classiques.uqac.ca/classiques/bergson_henri/matiere_et_memoire/matiere_et_memoire.html


Bergson, Henri. 2004 [says originally published by George Allen & Co., Ltd., London, 1912. But there is 1911 edition (below)]. Matter and Memory. Translated by Nancy Margaret Paul & W. Scott Palmer. Mineola, New York: Dover.

PDF of 1911 edition [8th printing 1970] at:

http://www.archive.org/details/mattermemory00berg

Text copied from 1911 edition at:

https://brocku.ca/MeadProject/Bergson/Bergson_1911b/Bergson_1911_toc.html

[chapter 4:]

https://brocku.ca/MeadProject/Bergson/Bergson_1911b/Bergson_1911_04.html

 

 

.