25 May 2017

Russell’s “The Philosophy of Bergson”, entry directory

 

by Corry Shores

 

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

 

[Central Entry Directory]

[Logic and Semantics, entry directory]

[Bertrand Russell, entry directory]

 

 

 

Entry Directory for

 

Bertrand Russell

 

“The Philosophy of Bergson”

 

 

 

 

 

 

 

Russell, Bertrand. 1912. “The Philosophy of Bergson.” Monist vol. 22, no. 3: pp.321-347.

PDF available at:

https://archive.org/details/jstor-27900381

Online text at:

https://en.wikisource.org/wiki/The_Philosophy_of_Bergson_(Russell)

 

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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

 

 

.

24 May 2017

Bergson (4.5) Creative Evolution, “Form and Becoming [Part 2: Zeno’s Paradoxes],” 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 Creative Evolution, 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 1941 French edition first; then the 1922 English; and finally the 1998 English. Or they will indicate the publication’s date before the page number. Paragraph and section divisions follow those in the French edition.]

 

 

Summary of

 

Henri Bergson

 

L’évolution creatrice

Creative Evolution

 

Ch.4

Le mécanisme cinématographique de la pensée et l'illusion mécanistique. — Coup d'oeil sur l'histoire des systèmes. — Le devenir réel et le faux évolutionisme.

The cinématographical mechanism of thought and the mechanistic illusion – A glance at the history of systems – Real becoming and false evolutionism

 

4.5

Le devenir et la forme

Form and Becoming

[Part 2: Les arguments de Zénon / Zeno’s paradoxes of motion]

 

 

 

Brief summary:

There is no one general Becoming. There are only particularly becomings for all the many instances, and thus Becoming is infinitely varied. We might mistakenly think that two color changes are two sorts of the same type of becoming (two color changes). But really, the change from yellow to green is an entirely different movement or change than from green to blue. Or for evolutionary [or developmental] changes: a change from flower to fruit is a different sort of change than from larva to nymph. Or for extensive changes: the movements involved in eating are different kinds of action than those involved in fighting. We must give conceptual priority to the particular transition or becoming itself, which is individualized, and only secondarily can it be (erroneously) understood as a more general movement and as involving distinct stable and discrete parts. In fact, we immediately and intuitively experience this indivisible flux of reality by means of the durational flux of consciousness. Then, instead of staying true to the proper features of this durational flux, we for practical purposes think we can pinpoint moments in the variation, thereby stabilizing them when in reality they are instable parts of the flow. We further this error by assuming that we can reconstruct the original duration by thinking of it being like an abstract, general, and impersonal movement transpiring between the snapshots, like how the machinery of a film projector moves the images of the film strip, thereby generating the motion of the images. Our actions also are involved in this pattern of understanding, because we are concerned with arrangements in the world corresponding to how our completed actions have influenced those arrangements, and we neglect the continuous variation transpiring between those states of arrangement and completed actions. But we can see that this cinematographic mode of understanding Becoming and change failing to do what it is fundamentally supposed to do, namely, to grasp the particular becomings involved in change. We might think for example that all we need to do is take enough snapshots within an interval of change in order to capture the change that transpired. But this will always fail and duration will always slip through the snapshots. It fails on the finite scale, because duration will always be found between the newest internal intervals created, and each newer intermediary snapshot only creates a new gap to divide. And it fails on an infinitesimal scale where there is an infinitesimal distance between snapshots; for, no additional reified snapshot can be inserted into the infinitesimal gap so to capture the change transpiring in it. So no matter how small we make the interval, even taking it to its mathematical limit, durational becoming and motion will have to slip between the cuts. We see this mistaken, cinematographic conception of Becoming in Zeno’s paradoxes of motion. It could very well be that physical space is divisible into discrete dimensionless points, and that these points can cut out smaller and smaller intervals getting as small as we like. But motion itself is not divisible. In the paradox of the arrow, Zeno thinks that we can pinpoint exact locations where the arrow was at precise points in time. Since at every moment of its motion it is just in one particular location, that means it is never changing place and is thus never in motion, which is absurd. But movement as we said is not divisible like space is, and so the arrow is never found to be fixed to any position within the path of its continuous motion. This erroneous way of understanding Becoming and change also reveals itself in the two other sorts of change (the prior one being extensive), namely, qualitative and evolutionary changes. Consider the evolutionary case of human development where we would say “the child becomes a man”. This assumes there are fixed phases, child and man, and the Becoming between them is like film projector motion producing the motion of the transition. But this conception and linguistic formulation leads to an absurdity. We begin with a child, who is supposed to developmentally glide into adulthood, suggesting that there are intermediary movements rather than an instantaneous developmental jump. But just as soon as we predicate “adult” to the child, it is no longer a child. In other words, it is always one or the other, and this conception of becoming does not account for the gradual transition between them. Instead we should say, “there is becoming from the child to the man”. So if we really want to grasp Becoming in its true nature, we must somehow enter into the process as it is happening, perhaps by using an intuitive rather than a conceptual or abstract mode of consciousness. The Eleatics (who included Parmenides and Zeno of Elea) misconceived reality by using the reifying structures of abstract thought and language, leading them to conclude that becoming is unreal and that sensible motion and change are illusions. Other Greek philosophers (including Plato, Aristotle, the Stoics, and Plotinus) who believed in Forms or Ideas also did so, but in a more tempered way. They acknowledged that sensible reality admits of change, but that we should look deeper for unchanging structures (in intelligible reality) underlying that change, namely, Ideas or Forms. The three senses of the ancient Greek word εἶδος correspond with the three ways of reifying change and of taking a fixed view on flux. {1} Quality, corresponding to qualitative motion and to the adjective. Here there is a snapshot in qualitative flux. {2} Form or essence, corresponding to evolutionary change and to the substantive. In the case of form, there is a period in the flux where there is relatively negligible variation and is thus taken as a more or less homogeneous phase or moment in the development, like ‘child’ or ‘man’. Here there is a fixed section of change from which the other moments are seen as transitions. Essence is like an average of forms, and is thus a fixity in comparison with that formal variety. {3} End or design in the sense of the intention of an action (like a mental design or schema for the action), corresponding to extensional motion and to the verb. Here the action is understood in terms of its completed state and thus of its aim or purpose. Hence it is a fixity as an idea of the action on the basis of which all the action’s motional variation is oriented around or directed toward. Thus the Greek notion of εἶδος involves taking the cinematographic approach to understanding reality.

 

 

 

 

Summary

 

4.5.1

[Becoming is infinitely varied. There is no one single abstract Becoming that is subcategorized by the types of reified states we (erroneously) project upon changes. Rather, each instance of Becoming is its own sort of movement or change, and we see this in the three types of movement: {1} Qualitative: A change from yellow to green is an entirely different movement or change than from green to blue. {2} Evolutionary: A change from flower to fruit is a different sort of change than from larva to nymph. {3} Extensive: The movements involved in eating are different kinds of action than those involved in fighting. So we need to think of becoming in terms of the transition involved, which is entirely different in each particular case, no matter how seeming similar we misconstrue them to be.]

 

[As we saw in the previous section, we ignore the continuous variability of the durational flux of becoming and instead, mostly for practical purposes, fabricate fixities in the flux. But we primarily perceive the flux.] Bergson will now characterize “our natural attitude towards Becoming”. One thing we experience is that “Becoming is infinitely varied”. [There is a profound and fascinating insight here, but I am not sure if I will get it right. The basic idea seems to be that each instance of change is its own sort of becoming. We might say that they are all qualitatively different, or different in kind. Thus we should not abstract from all these different kinds of becoming one Becoming common to all. Rather becoming is infinitely varied. He gives examples for the three kinds of movement: qualitative movement, evolutionary movement, and extensive movement.  {1} Suppose something changes from yellow to green. The infinite variety here is not all the infinite gradations of color between the two. For, he compares the change between yellow and green to something going from green to blue, and he says that each instance of qualitative movement is different. In other words, there are not simply an infinity of qualities (which are erroneously conceived as reified in the first place). There is an infinity of qualitative movements. In order for this to work with the case of color, perhaps we have to acknowledge that no two colors could be exactly the same, on account of them involving their own unique dynamics and circumstances. So that means no color change is identical to another. That might not be right, but the insight I feel we are hitting on in this example is that we need to think of the movements of change as themselves admitting of individuality, particularity, and variety. {2} He then says that the developmental movement from flower to fruit is not the same kind of movement as from larva to nymph and from nymph to adult insect. {3} His final examples are that the actions of eating and of drinking are not like the action of fighting. But despite this infinite variety, perception, intellect, and language all generalize “these profoundly different becomings” into “the single representation of becoming in general, undefined becoming, a mere abstraction which by itself says nothing.” I do not  grasp the next idea. I am going to guess it is the following, but please consult the text below. Consider the case of yellow changing to blue. This is a unique becoming all its own. As such, it cannot be categorized as though it were a subvariety of another type of becoming. However, we have this (erroneous and) vague notion of becoming in general that we suppose all changes to be instances of. And we then subclassify this general becoming according to types of states that characterize changes. So in the case of change from yellow to green, we regard it as a change in color state. But these states are fabricated and imposed upon  a flux that involves no such reified states. (See section 4.4.) This part that I am probably misreading begins, “To this idea, always the same... / A cette idée toujours la même...”]

Que si maintenant on cherchait à caractériser avec plus de précision notre attitude naturelle vis-à-vis du devenir, voici ce qu'on trouverait. Le devenir est infiniment varié Celui qui va du jaune au vert ne ressemble pas à celui qui va du vert au bleu : ce sont des mouvements qualitatifs différents. Celui qui va de la fleur au fruit ne ressemble pas à celui qui va de la larve à la nymphe et de la nymphe à l'insecte parfait : ce sont des mouvements évolutifs différents. L'ac­tion de manger ou de boire ne ressemble pas à l'action de se battre : ce sont des mouvements extensifs différents. Et ces trois genres de mouvement eux-mêmes, qualitatif, évolutif, extensif, diffèrent profondément. L'artifice de notre perception, comme celui | de notre intelligence, comme celui de notre langage, consiste à extraire de ces devenirs très variés la représentation unique du devenir en général, devenir indéterminé, simple abstraction qui par elle-même ne dit rien et à laquelle il est même rare que nous pensions. A cette idée toujours la même, et d'ailleurs obscure ou inconsciente, nous adjoignons alors, dans chaque cas particulier, une ou plusieurs images claires qui représentent des états et qui servent à distinguer tous les devenirs les uns des autres. C'est cette composition d'un état spécifique et déterminé avec le changement en général et indéterminé que nous substituons à la spécificité du changement. Une multiplicité indéfinie de devenirs diversement colorés, pour ainsi dire, passe sous nos yeux : nous nous arrangeons pour voir de simples différences de couleur, c'est-à-dire d'état, sous lesquelles coulerait dans l'obscurité un devenir toujours et partout le même, invariablement incolore.

(1941: 303|304. Copied from UQAC)

 

Now, if we try to characterize more precisely our natural attitude towards Becoming, this is what we find. Becoming is infinitely varied. That which goes from yellow to green is not like that which goes from green to blue: they are different qualitative movements. That which goes from flower to fruit is not like that which goes from larva to nymph and from nymph to perfect insect: they are different evolutionary movements. The action of eating or of drinking is not like the | action of fighting: they are different extensive movements. And these three kinds of movement themselves—qualitative, evolutionary, extensive—differ profoundly. The trick of our perception, like that of our intelligence, like that of our language, consists in extracting from these profoundly different becomings the single representation of becoming in general, undefined becoming, a mere abstraction which by itself says nothing and of which, indeed, it is very rarely that we think. To this idea, always the same, and always obscure or unconscious, we then join, in each particular case, one or several clear images that represent states and which serve to distinguish all becomings from each other. It is this composition of a specified and definite state with change general and undefined that we substitute for the specific change. An infinite multiplicity of becomings variously colored, so to speak, passes before our eyes: we manage so that we see only differences of color, that is to say, differences of state, beneath which there is supposed to flow, hidden from our view, a becoming always and everywhere the same, invariably colorless.

(1922: 320|321; 1998: 304. Copied from Project Gutenberg)

 

 

 

4.5.2

[There are artificial ways we can reconstruct motion. The first is like Turkish shadow puppets where we make figures with joints move on a screen. This does not capture the fluidity of natural motion. The second is the cinematic technique. Here we use a machine to project a series of still frames rapidly enough that it generates the impression of fluid motion. But here the motion is not really in the image figures but is rather in the machine itself, which presents a general, impersonal sort of motion that animates the imagery. We can see the cinematic apparatus as a metaphor for how we incorrectly understand Becoming. We erroneously see it likewise as being a sort of general movement underlying all particular ones and as moving things from one stable state to another.]

 

[Bergson it seems will now discuss different ways to artificially give to our perception the impression of motion. The first sort, it seems to me, might like how motion is created in a magic lantern show or a puppet show (using two-dimensional figures, like in Turkish shadow puppets) but I am not sure.  His example is trying to recreate soldiers marching. (He writes that it “would be to cut out jointed figures representing the soldiers, to give to each of them the movement of marching, a movement varying from individual to individual although common to the human species, and to throw the whole on the screen”). He says that this approach would involve a lot of effort, and it would not do well to “reproduce the suppleness and variety of life” (see the shadow puppets link above.) The second approach is the cinematic one. We “take a series of snapshots of the passing regiment and to throw these instantaneous views on the screen, so that they replace each other very rapidly”. Here we reconstitute the motion by means of the rapid shuffling through the fixed images in each frame. He then says that if we simply looked at the series of still images, one after the other or maybe all at once somehow, we would not see the figures animated. We need the additional, exterior, mechanical motion of the projector to animate the motion. (Note. I am not sure if Bergson is saying that scanning across the series of stills that they would not give the impression of motion. But if he is, then we might take some of Scott McCloud’s findings into consideration to challenge this notion. See chapter 3 of his Understanding Comics, and especially this image demonstration:

 photo McCloud. p.67.2_zpshpqid3sy.jpg

. I think there is such a thing as comics animation, produced by a Gestalt sort of operation. But as we will see, Bergson’s point is that even if the motion we construct is seemingly continuous, real motion and becoming cannot be recreated from connected snapshots; it can only be experienced in its original flow.) This movement of the film reel is not the movement of the soldiers depicted. It is rather a general, impersonal, abstract movement. So we animate the individuals on the screen by hooking them up into the impersonal movement of the cinematic apparatus. It then seems Bergson says that we should consider the cinematic apparatus metaphorically for how our minds reconstitute motion and change. We originally experience it as continuous. But we retain snapshot impressions. Each such impression presents us with an illusory reification in the flux, in the form of a state. Then we conceptualize  Becoming as being like the general, impersonal motion that moves the world from one state to the next or that moves or perception or inner states from one to the next. I may have that wrong, so check the quotation.]

Supposons qu'on veuille reproduire sur un écran une scène animée, le défilé d'un régiment par exemple. Il y aurait une première manière de s'y prendre. Ce serait de découper des figures articulées représentant les soldats, d'imprimer à chacune d'elles le mouvement de la marche, mouvement variable d'individu à individu quoique commun à l'espèce humaine, et de projeter le tout sur l'écran. Il faudrait dépenser à ce petit jeu une somme de travail formidable, et l'on n'obtiendrait d'ailleurs qu'un assez médiocre résultat : com­ment reproduire la souplesse et la variété de la vie ? Maintenant, il y a une seconde manière de procéder, beaucoup plus aisée en même temps que plus efficace. C'est de prendre sur le régiment qui passe une série d'instantanés, et de projeter ces instantanés sur l'écran, de manière qu'ils se remplacent très vite les uns les autres. Ainsi fait le cinématographe. Avec des photographies dont chacune représente le régiment dans une attitude immobile, il reconstitue la mobilité du régiment | qui passe. Il est vrai que, si nous avions affaire aux pho­tographies toutes seules, nous aurions beau les regarder, nous ne les verrions pas s'animer : avec de l'immobilité, même indéfiniment juxtaposée à elle-mê­me, nous ne ferons jamais du mouvement. Pour que les images s'animent, il faut qu'il y ait du mouvement quelque part. Le mouvement existe bien ici, en effet, il est dans l'appareil. C'est parce que la bande cinémato­gra­phique se déroule, amenant, tour à tour, les diverses photographies de la scène à se continuer les unes les autres, que chaque acteur de cette scène reconquiert sa mobilité : il enfile toutes ses attitudes successives sur l'invisible mouve­ment de la bande cinématographique. Le procédé a donc consisté, en somme, à ex­traire de tous les mouvements propres à toutes les figures un mouvement impersonnel, abstrait et simple, le mouvement en général pour ainsi dire, à le mettre dans l'appareil, et à reconstituer l'individualité de chaque mouvement particulier par la composition de ce mouvement anonyme avec les attitudes personnelles. Tel est l'artifice du cinématographe. Et tel est aussi celui de notre connaissance. Au lieu de nous attacher au devenir intérieur des choses, nous nous plaçons en dehors d'elles pour recomposer leur devenir artificielle­ment. Nous prenons des vues quasi instantanées sur la réalité qui passe, et, comme elles sont caractéristiques de cette réalité, il nous suffit de les enfiler le long d'un devenir abstrait, uniforme, invisible, situé au fond de l'appareil de la connaissance, pour imiter ce qu'il y a de caractéristique dans ce devenir lui-même. Perception, intellection, langage procèdent en général ainsi. Qu'il s'agisse de penser le devenir, ou de l'exprimer, ou même de le percevoir, nous ne faisons guère autre chose qu'actionner une espèce de cinématographe inté­rieur. On résumerait donc tout ce qui précède en disant que le mécanisme de notre connaissance usuelle est de nature cinématographique.

(1941: 304|305. Copied from UQAC)

 

Suppose we wish to portray on a screen a living picture, [304||305] such as the marching past of a regiment. There is one way in which it might first occur to us to do it. That would be to cut out jointed figures representing the soldiers, to give to each of them the movement of marching, a movement varying from individual to individual although common to the human species, and to throw the whole on the screen. We should need to spend on this little game an enormous amount of work, and even then we should obtain but a very poor result: how could it, at its best, reproduce the suppleness and variety of life? Now, [321|322] there is another way of proceeding, more easy and at the same time more effective. It is to take a series of snapshots of the passing regiment and to throw these instantaneous views on the screen, so that they replace each other very rapidly. This is what the cinematograph does. With photographs, each of which represents the regiment in a fixed attitude, it reconstitutes the mobility of the regiment marching. It is true that if we had to do with photographs alone, however much we might look at them, we should never see them animated: with immobility set beside immobility, even endlessly, we could never make movement. In order that the pictures may be animated, there must be movement somewhere. The movement does indeed exist here; it is in the apparatus. It is because the film of the cinematograph unrolls, bringing in turn the different photographs of the scene to continue each other, that each actor of the scene recovers his mobility; he strings all his successive attitudes on the invisible movement of the film. The process then consists in extracting from all the movements peculiar to all the figures an impersonal movement abstract and simple, movement in general, so to speak: we put this into the apparatus, and we reconstitute the individuality of each particular movement by combining this nameless movement with the per- [305||306] sonal attitudes. Such is the contrivance of the cinematograph. And such is also that of our knowledge. Instead of attaching ourselves to the inner becoming of things, we place ourselves outside them in order to recompose their becoming artificially. We take snapshots, as it were, of the passing reality, and, as these are characteristic of the reality, we have only to string them on a becoming, abstract, uniform and invisible, situated at the back of [322|323] the apparatus of knowledge, in order to imitate what there is that is characteristic in this becoming itself. Perception, intellection, language so proceed in general. Whether we would think becoming, or express it, or even perceive it, we hardly do anything else than set going a kind of cinematograph inside us. We may therefore sum up what we have been saying in the conclusion that the mechanism of our ordinary knowledge is of a cinematographical kind.

(1922: 321|323; 1998: 304||306. Copied from Project Gutenberg)

 

 

 

4.5.3

[Reality is composed of a network of things mutually affecting one another through their interactions. At any moment, this whole network takes on some arrangement. But no arrangement is stable in its real happening. Yet, our actions have purposes that aim to influence these arrangements. And as we have seen, our actions are enacted with ends in mind and with the processes leading up to them being mostly out of mind. So we come to have a cinematic sort of understanding of the world, based on this pattern of adaptation understood as involving discrete phases. It is like how we care mostly about the arrangements produced by shaking a kaleidoscope, and we are less concerned with the imagery while the shaking is happening.]

 

Bergson further elaborates on this point with the metaphor of a kaleidoscope. [I am not exactly certain, but the idea here might be the following. It seems the sort of kaleidoscope is one where the imagery is altered by shaking the device, perhaps because there are particles suspended in a fluid. Or maybe it involves rotation, but the rotations should be understood somehow as shaking up the arrangement of things causing the imagery. In reality, there are arrangements of bodies, related perhaps by mutually affective interactions. These arrangements are always in flux. Now, our own body and its actions are a part of these arrangements, and we intentionally try to have some effect on them through our actions. And this complex network of many actors all trying to influence the arrangement (or unintentionally doing so) involves a continuous variation in the arrangements. However, since we are dealing with our own actions and body, which we have reified and set into correspondence with artificially reified states in reality’s arrangements, we are less concerned with the continuity of the variation and more so with the arrangement at particular moments. Perhaps those particular moments correspond to the completions of our own actions or with completions of others’ actions affecting us. This is like how when looking through a kaleidoscope, we are interested less in how the images shake up and change and more so with the new arrangement that is produced by that shaking up. So we adapt to the world as though by series of actions that are enacted with ends in mind and with states of the world in mind. We thus adapt to things by concentrating on certain arrangements of them corresponding to completed actions. This is a sort of cinematic pattern of adaptation, because we select moments between which we ignore the real durational variation. Since we base our understanding of the world on how we artificially interact with it in this cinematic way, our knowledge of reality as well has this cinematic character.]

Sur le caractère tout pratique de cette opération il n'y | a pas de doute pos­sible. Chacun de nos actes vise une certaine insertion de notre volonté dans la réalité. C'est, entre notre corps et les autres corps, un arrangement comparable à celui des morceaux de verre qui composent une figure kaléïdoscopique. Notre activité va d'un arrangement à un réarrangement, imprimant chaque fois au kaléidoscope, sans doute, une nouvelle secousse, mais ne s'intéressant pas à la secousse et ne voyant que la nouvelle figure. La connaissance qu'elle se donne de l'opération de la nature doit donc être exactement symétrique de l'intérêt qu'elle prend à sa propre opération. En ce sens on pourrait dire, si ce n'était abuser d'un certain genre de comparaison, que le caractère cinémato­graphique de notre connaissance des choses tient au caractère kaléïdoscopi­que de notre adaptation à elles.

(1941: 305|306. Copied from UQAC)

 

Of the altogether practical character of this operation there is no possible doubt. Each of our acts aims at a certain insertion of our will into the reality. There is, between our body and other bodies, an arrangement like that of the pieces of glass that compose a kaleidoscopic picture. Our activity goes from an arrangement to a rearrangement, each time no doubt giving the kaleidoscope a new shake, but not interesting itself in the shake, and seeing only the new picture. Our knowledge of the operation of nature must be exactly symmetrical, therefore, with the interest we take in our own operation. In this sense we may say, if we are not abusing this kind of illustration, that the cinematographical character of our knowledge of things is due to the kaleidoscopic character of our adaptation to them.

(1922: 323; 1998: 306. Copied from Project Gutenberg)

 

 

 

4.5.4

[In this cinematographical method of acting, perceiving, and knowing, our actions are guided by the knowledge we have of the purposes and situations of completed actions, while at the same time, our knowledge of these artificially discerned completions is based on the nature of our actions. This correspondence between the staccato rhythms of both is grounded in our practical concerns.]

 

[Bergson next seems to be continuing this idea of a cinematographical sort of knowledge being based on practical concerns. His claim is that the “cinematographical method is [...] the only practical method,” and his reasoning for this is that this method “consists in making the general character of knowledge form itself on that of action, while expecting that the detail of each act should depend in its turn on that of knowledge”. I do not follow this reasoning (why is this the only practical method?). I will have to guess here, so please consult the text to follow. We of course have a direct way of understanding the world, using a method of intuition that somehow directly grasps the durational flux of consciousness. But, as we have seen, this is not our default method. For practical reasons, we use the cinematographical method that we have discussed above. There is a sort of circularity somehow in how the method operates. On the one hand, we derive our knowledge of the world on the basis of our patterns of action. Yet on the other hand, our actions are guided by this knowledge. Let us put aside the problem of how this circularity might begin, and let us try to devise an illustration. We previously built from his arm movement example by saying it was done to bring a drink to one’s mouth. If we follow the movement of the arm, we see that it needs to stop before the mouth. For otherwise we slam our face with the glass and fail to drink the contents. So here there is a sort of potential “joint” that we might artificially cleave into this larger process of drinking, which is in larger and larger processes of our life and furthermore of the world at large. But when we decide to drink, we from the beginning have it in mind that we will bring our glass to our mouth. Let me quote so you can see.]

La méthode cinématographique est donc la seule pratique, puisqu'elle consiste à régler l'allure générale de la connaissance sur celle de l'action, en attendant que le détail de chaque acte se règle à son tour sur celui de la connaissance. Pour que l'action soit toujours éclairée, il faut que l'intelligence y soit toujours présente ; mais l'intelligence, pour accompagner ainsi la mar­che de l'activité et en assurer la direction, doit commencer par en adopter le rythme. Discontinue est l'action, comme toute pulsation de vie ; discontinue sera donc la connaissance. Le mécanisme de la faculté de connaître a été construit sur ce plan. Essentiellement pratique, peut-il servir, tel quel, à la spéculation ? Essayons, avec lui, de suivre la réalité dans ses détours, et voyons ce qui va se passer.

(1941: 306. Copied from UQAC)

 

The cinematographical method is therefore the only practical method, since it consists in making the general || character of knowledge form itself on that of action, while expecting that the detail of each act should depend in its turn on that of knowledge. In order that action may always be enlightened, intelligence must always be present in it; but intelligence, in order thus to accompany the progress of activity and ensure its direction, must begin by adopting its rhythm. Action | is discontinuous, like every pulsation of life; discontinuous, therefore, is knowledge. The mechanism of the faculty of knowing has been constructed on this plan. Essentially practical, can it be of use, such as it is, for speculation? Let us try with it to follow reality in its windings, and see what will happen.

(1922: 323|324; 1998: 306||307. Copied from Project Gutenberg)

 

 

 

4.5.5

[No matter now near we make our snapshot cuts, duration will always slip between the cuts.]

 

Bergson continues with this cinematographic approach to becoming. [Instead of using intuition to grasp becoming in its original flux, we instead begin with artificially reified views or takes on it, which we connect with our vague notion of becoming in general, similar to how the motion of the film projector adds motion to the still frames. I am not sure about the next point, but I will guess it is the following. Our notion of becoming in general is like a variable x, because it stands for any particular becoming. But since becoming is infinitely varied (see 4.5.1 above), it is not enough to see any particular becoming in this generalized sense. In other words, we understand nothing of a particular becoming simply by categorizing it as an instance of a general sort of becoming. Yet, in how it is conceived in the cinematic way, we understand the becoming as being a matter of transition between snapshots. Bergson will further analyze this cinematographic understanding of becoming by considering some instance where we say there was a transition between snapshots. He writes: “As I apply the same method, I obtain the same result; a third view merely slips in between the two others. I may begin again as often as I will, I may set views alongside of views for ever, I shall obtain nothing else.” I am not sure exactly what he means, but I will guess. We want to further conceptualize the becoming involved in the transition from snapshot to the next. We do so by thinking of there being yet another snapshot between those two, which displays something from that transition. But this only creates two more intervals of becoming. No matter how many times we insert images, drawing the intervals nearer, we never arrive at the durational process of becoming intervening between the snapshots. Let me quote from Deleuze’s course of 1981-01-20.

Quand, des siècles après, Bergson fera de la durée un concept philosophique, ce sera évidement avec de toutes autres influences. Ce sera en fonction de lui-même avant tout, ce ne sera pas sous l’influence de Spinoza. Pourtant je remarque juste que l’emploi bergsonien de la durée coïncide strictement. Lorsque Bergson essaie de nous faire comprendre ce qu’il appelle “durée”, il dit: vous pouvez considérer des états psychiques aussi proche que vous voulez dans le temps, vous pouvez considérer l’état a et l’état a’ aussi bien séparés par une minute, mais aussi bien par une seconde, par un millième de seconde, c’est à dire vous pouvez faire des coupes, de plus en plus, de plus en plus serrées, de plus en plus proches les unes des autres. Vous aurez beau aller jusqu’à l’infini, dit Bergson, dans votre décomposition du temps, en établissant des coupes de plus en plus rapides, vous n’atteindrez jamais que des états. Et il ajoute que les états c’est toujours de l’espace. Les coupes c’est toujours spatial. Et vous aurez beau rapprocher vos coupes, vous laisserez forcément échapper quelque chose, c’est le passage d’une coupe à une autre, si petit qu’il soit. Or, qu’est-ce qu’il appelle durée, au plus simple? C’est le passage d’une coupe à une autre, c’est le passage d’un état à un autre. Le passage d’un état à un autre n’est pas un état, vous me direz que tout ça ce n’est pas fort, mais c’est un statut du vécu vraiment profond. Car comment parler du passage, du passage d’un état à un autre, sans en faire un état; ça va poser des problèmes d’expression, de style, de mouvement, ça va poser toutes sortes de problèmes. Or la durée c’est ça, c’est le passage vécu d’un état à un autre en tant qu’irréductible à un état comme à l’autre, en tant qu’irréductible à tout état. C’est ce qui se passe entre deux coupes. En un sens la durée c’est toujours derrière notre dos, c’est dans notre dos qu’elle se passe. C’est entre deux clins d’yeux. Si vous voulez une approximation de la durée: je regarde quelqu’un, je regarde quelqu’un, la durée elle n’est ni là ni là. La durée elle est: qu’est-ce qui s’est passé entre les deux. J’aurais beau allé aussi vite que je voudrais, la durée elle va encore plus vite, par définition, comme si elle était affectée d’un coefficient de vitesse variable: aussi vite que j’aille, ma durée va plus vite. Si vite que je passe d’un état à un autre le passage est irréductible aux deux états. C’est ça que toute affection enveloppe.
Je dirais: toute affection enveloppe le passage par lequel on arrive à elle. Ou aussi bien: toute affection enveloppe le passage par lequel on arrive à elle, et par lequel on sort d’elle, vers une autre affection, si proches soient les deux affections considérées. Donc pour avoir ma ligne complète il faudrait que je fasse une ligne à trois temps: a’, a’, a’’; a c’est l’affection instantanée, du moment présent, a’ c’est celle de tout à l’heure, a’’ c’est celle d’après, qui va venir. J’ai beau les rapprocher au maximum il y a toujours quelque chose qui les sépare, à savoir le phénomène du passage. Ce phénomène du passage, en tant que phénomène vécu, c’est la durée [...].

(Deleuze, course of 1981-01-20)

When, centuries later, Bergson will make duration into a philosophical concept, it will obviously be with wholly different influences. It will be according to itself above all, it will not be under the influence of Spinoza. Nevertheless, I am just pointing out that the Bergsonian use of duration coincides strictly. When Bergson tries to make us understand what he calls duration‚, he says: you can consider psychic states as close together as you want in time, you can consider the state A and the state A‚ as separated by a minute, but just as well by a second, by a thousandth of a second, that is you can make more and more cuts, increasingly tight, increasingly close to one another. You may well go to the infinite, says Bergson, in your decomposition of time, by establishing cuts with increasing rapidity, but you will only ever reach states. And he adds that the states are always of space. The cuts are always spatial. And you will have brought your cuts together very well, you will let something necessarily escape, it is the passage from one cut to another, however small it may be. Now, what does he call duration, at its simplest? It is the passage from one cut to another, it is the passage from one state to another. The passage from one state to another is not a state, you will tell me that all of this is not strong, but it is a really profound statute of living. For how can we speak of the passage, the passage from one state to another, without making it a state? This is going to pose problems of expression, of style, of movement, it is going to pose all sorts of problems. Yet duration is that, it is the lived passage from one state to another insofar as it is irreducible to one state as to the other, insofar as it is irreducible to any state. This is what happens between two cuts.

In one sense duration is always behind our backs, it is at our backs that it happens. It is between two blinks of the eye. If you want an approximation of duration: I look at someone, I look at someone, duration is neither here nor there. Duration is: what has happened between the two? Even if I would have gone as quickly as I would like, duration goes even more quickly, by definition, as if it was affected by a variable coefficient of speed: as quickly as I go, my duration goes more quickly. However quickly I pass from one state to another, the passage is irreducible to the two states. It is this that every affection envelops. I would say: every affection envelops the passage by which we arrive at it. Or equally well: every affection envelops the passage by which we arrive at it, and by which we leave it, towards another affection, however close the two affections considered are. So in order to make my line complete it would be necessary for me to make a line of three times: A, A,' A”; A is the instantaneous affection, of the present moment, A' is that of a little while ago, A” is what is going to come. Even though I have brought them together as close as possible, there is always something which separates them, namely the phenomenon of passage. This phenomenon of passage, insofar as it is a lived phenomenon, is duration [...].

(Deleuze, course of 1981-01-20)

But from the wording, I am not sure if the additional snapshots are understood as internally dividing and drawing nearer: “I may begin again as often as I will, I may set views alongside of views for ever, I shall obtain nothing else.” Perhaps he is saying instead that the additional ones come successively one after another, like following sequentially after the most recent one. But in that case I am not sure what point he would be making. He next writes: “The application of the cinematographical method therefore leads to a perpetual recommencement, during which the mind, never able to satisfy itself and never finding where to rest, persuades itself, no doubt, that it imitates by its instability the very movement of the real.” Maybe the idea here is that because we must continually reenact the placement of snapshots that we have thereby captured as a result of our continual failure, we come upon the true flux of reality that should by its nature defy all such attempts to reify it. But, he explains, if we really want to advance in concord with the flux of becoming, we must actually enter into it directly. Yet we will fail insofar as we create partitions and regard becoming as transpiring between them. He then says make the interval between snapshots infinitesimal. Still, becoming and movement will slip between the infinitely near snapshots. This is interesting, as one might say no extensive duration can intervene when the temporal interval is infinitesimal. Perhaps the idea is the following. Each snapshot is an instant. Suppose we have an infinitesimal duration between two instants. We might say that we have captured the duration. But we have not. It is not found in either snapshot. And we cannot give a snapshot form to what transpires within the infinitesimal duration, because no snapshot can be interposed in it. In other words, our effort to capture duration by giving it snapshot form by means of inserting more snapshots between snapshots fails on the finite scale, because duration will always be found between the newest intervals created, and it fails on an infinitesimal scale, because no reified ‘take’ on becoming can be inserted into the infinitesimal gap so to capture it. So no matter how small we make the interval, even taking it to its limit, durational becoming and motion will have to slip between the cuts.]

Sur la continuité d'un certain devenir j'ai pris une série de vues que j'ai reliées entre elles par « le devenir » en général. Mais il est entendu que je ne puis en rester là. Ce qui n'est pas déterminable n'est pas représentable : du « devenir en général » je n'ai qu'une connaissance verbale. Comme la lettre x désigne une certaine inconnue, | quelle qu’elle soit, ainsi mon « devenir en général », toujours le même, symbolise ici une certaine transition sur laquelle j'ai pris des instantanés . de cette transition même il ne m'apprend rien. Je vais donc me concentrer tout entier sur la transition et, entre deux instantanés, chercher ce qui se passe. Mais, puisque j'applique la même méthode, j'arrive au même résultat ; une troisième vue va simplement s'intercaler entre les deux autres. Indéfiniment je recommencerai, et indéfiniment je juxtaposerai des vues à des vues, sans obtenir autre chose. L'application de la méthode cinéma­tographique aboutira donc ici à un perpétuel recommencement, où l'esprit, ne trouvant jamais à se satisfaire et ne voyant nulle part où se poser, se persuade sans doute à lui-même qu'il imite par son instabilité le mouvement même du réel. Mais si, en s'entraînant lui-même au vertige, il finit par se donner l'illu­sion de la mobilité, son opération ne l'a pas fait avancer d'un pas, puisqu'elle le laisse toujours aussi loin du terme. Pour avancer avec la réalité mouvante, c'est en elle qu'il faudrait se replacer. Installez-vous dans le changement, vous saisirez à la fois et le changement lui-même et les états successifs en lesquels il pourrait à tout instant s'immobiliser. Mais avec ces états successifs, aperçus du dehors comme des immobilités réelles et non plus virtuelles, vous ne reconstituerez jamais du mouvement. Appelez-les, selon le cas, qualités, for­mes, positions ou intentions; vous pourrez en multiplier le nombre autant qu'il vous plaira et rapprocher ainsi indéfiniment l'un de l'autre deux états consé­cutifs : vous éprouverez toujours devant le mouvement intermédiaire la déception de l'enfant qui voudrait, en rapprochant l'une de l'autre ses deux mains ouvertes, écraser de la fumée. Le mouvement glissera dans l'intervalle, parce que toute tentative pour reconstituer le changement avec des états implique cette proposition absurde que le mouvement est fait d'immobilités.

(1941: 306|307. Copied from UQAC)

 

I take of the continuity of a particular becoming a series of views, which I connect together by “becoming in general.” But of course I cannot stop there. What is not determinable is not representable: of “becoming in general” I have only a verbal knowledge. As the letter x designates a certain unknown quantity, whatever it may be, so my “becoming in general,” always the same, symbolizes here a certain transition of which I have taken some snapshots; of the transition itself it teaches me nothing. Let me then concentrate myself wholly on the transition, and, between any two snapshots, endeavor to realize what is going on. As I apply the same method, I obtain the same result; a third view merely slips in between the two others. I may begin again as often as I will, I may set views alongside of views for ever, I shall obtain nothing else. The application of the cinematographical method therefore leads to a perpetual recommencement, during which the mind, never able to satisfy itself and never finding where to rest, persuades itself, no doubt, that it imitates by its instability the very movement of the real. But though, by straining itself || to the point of giddiness, it may end by giving itself the illusion of mobility, its operation has not advanced it a step, since it remains as far as ever from its goal. In order to advance with the moving reality, you must replace yourself within it. Install yourself within change, and you will grasp at once both change itself and the successive states in which it might at any instant be immobilized. But with these successive | states, perceived from without as real and no longer as potential immobilities, you will never reconstitute movement. Call them qualities, forms, positions, or intentions, as the case may be, multiply the number of them as you will, let the interval between two consecutive states be infinitely small: before the intervening movement you will always experience the disappointment of the child who tries by clapping his hands together to crush the smoke. The movement slips through the interval, because every attempt to reconstitute change out of states implies the absurd proposition, that movement is made of immobilities.

(1922: 324|325; 1998: 307||308. Copied from Project Gutenberg)

 

 

 

4.5.6

[This insight is found in Zeno of Elea.]

 

This insight has been found in philosophy since its early beginnings with Zeno of Elea, but it was formulated so to serve a different philosophical purpose. [This entry details Zeno’s paradoxes. This is an entry directory of Zeno related entries.]

C'est de quoi la philosophie s'aperçut dès qu'elle ouvrit les yeux. Les argu­ments de Zénon d'Elée, quoiqu'ils aient été formulés dans une intention bien différente, ne disent pas autre chose.

(1941: 308. Copied from UQAC)

 

Philosophy perceived this as soon as it opened its eyes. The arguments of Zeno of Elea, although formulated with a very different intention, have no other meaning.

(1922: 325; 1998: 308. Copied from Project Gutenberg)

 

 

 

4.5.7

[In the Zeno paradox of the arrow, we note that at any moment, it occupies just one position. But that means at no time during its movement is it changing position, and thus it never moves.]

 

We consider Zeno’s paradox of the flying arrow. [Suppose we consider a moment to be absolute durationless, and not even infinitesimally durational, like in the conception from above. A moment would be equivalent to the snapshots or cuts we discussed. As such, in an instant of the arrow’s motion, there is no amount of time during which the arrow can move. So every instant of its motion, it is motionless. There is never a point in time when it is in motion. (I would think here one could make certain replies. We might say that motion always requires more than one instant anyway, and thus it does not matter if there is no one single instant when it is moving. Another reply could be that in one instant, it occupies more than one position, namely, one position and the next possible one following that.)]

Considère-t-on la flèche qui vole ? A chaque instant, dit Zénon, elle est immobile, car elle n'aurait le temps de se mouvoir, c'est-à-dire d'occuper au moins deux positions successives, que si on lui concédait au moins deux instants. A un moment donné, elle est donc au repos en un point donné. Immobile en chaque point de son trajet, elle est, pendant tout le temps qu'elle se meut, immobile.

(1941: 308. Copied from UQAC)

 

Take the flying arrow. At every moment, says Zeno, it is motionless, for it cannot have time to move, that is, to occupy at least two successive positions, unless at least two moments are allowed it. At a given moment, therefore, it is at rest at a given point. Motionless in each point of its course, it is motionless during all the time that it is moving.

(1922: 325; 1998: 308. Copied from Project Gutenberg)

 

 

4.5.8

[Motion cannot be divided. Were it so, there would be a point of rest in the middle of it, and thus it would not be one motion. This means that we cannot say the object occupies a determinate position at a determinate time, because doing so divides the motion.]

 

[Bergson’s next idea is fascinating but tricky to pinpoint. The basic idea here is that motion should be understood as making up a solid and indivisible unity from its start to finish. We cannot pinpoint the object being at a certain position, because doing so treats the motion as divisible, which it is not. In commentary that follows, I struggle with the wording of the text and with finding a precise explication of its concepts. You should skip it unless you are interested in debating the details.] [When the arrow is moving, it never lies at any position of motion. But it is not easy to conceptualize how all of this works for Bergson. One of the claims here is that because the arrow never stops at an intermediary position, it never occupies that position. So it seems one insight we must hold here is that because  movement prevents the occupation of a determinate position, that means we should take one of the following interpretations, if not some other I failed to conceive: {1} The arrow at any instant occupies more than one position. But Bergson it would seem is not conceiving the duration as decomposable into instants, so this is probably not his meaning exactly. {2} The arrow’s movement itself (put aside time and space for now) is not decomposable into parts. If the motion stops in the middle, then restarts and continues to the destination, then yes, it is decomposable into these two sections. But so long as it is moving, that movement, for as long as it endures, is one solid movement that cannot be divided. Now, if the motion itself cannot be decomposed into parts, that means we cannot say it is at some position precisely at some instant, because that would construe the motion as having parts, divided by that instant. (If this is simply the insight here, I find it a bit vague and unconvincing. I would still want to know why as time passed a certain point in time that it is not in a certain position? Is it again because it is in more than one position? Is it that it is impossible to stop time at an instant, and instead we can only have intervals of time and thus intervals of crossed space?) {3} (This one is similar to the prior one.) The motion, as a solid block of indecomposable movement, cannot be said to occupy some position at some time, but rather only an extent of space during an extent of time. (But here I am not sure how to explain why at some point in time there arrow is not at some position, other than to repeat that we can at best say that between two times the arrow was between two positions. I have in mind something like his account of Zeno’s Achilles and Tortoise paradox from Time and Free Will, where Achilles steps are longer than the Tortoise’s.) {4} We need to think of motion in terms of indeterminacy somehow. Whenever something is in motion, its position is always for some reason indeterminable. Maybe we are to think of it as sliding over or past multiple locations, or that it simply could be here or there, but we have no way to make that determination or maybe in physical reality it can have no possible determinate position. (This conception is also too vague for me. Is it indeterminable because it is neither at one position nor another, even though it is in the region of those positions? Is it indeterminable because it occupies more than one determination, which is logically impossible from a certain view and thus defies our techniques to make univocal determinations?) {5} (This one is similar to the prior one.) While the thing is moving, we might think that the laws of physics determine where it will be in the next instant. But while things are moving or changing, there is no guarantee that reality will unfold according to fixed physical laws. These regularities only become apparent after the motion or change is completed and we see where it went. What this means is that somehow, at any moment, were it possible to examine what is going on at such an instant, we would see that the object is expressing multiple virtual paths of movement. Maybe it will accelerate a little or maybe decelerate, maybe it will turn this direction or that. All these tendencies push and pull the arrow, blurring its position in a sense, or at least making it occupy a vague region of positions rather than a determinate one, somehow. (This conception has in mind what Leibniz says about conatus as motion at a point, in “Studies in Physics and the Nature of Body”. I am thinking of the passage: “the [moving] body will fill a part of space greater than itself, or greater than it would fill at rest or if moving more slowly, or if striving in one direction only” {Leibniz 140d}. As far as I recall, the idea might be that the arrow in motion occupies an extent of space longer than its actual length, almost as if it is leaning through a very tiny additional amount of space. And if we think it can be tending in multiple directions and speeds, then we might think of it leaning through a vague region, and thus that its position is indeterminate.) {6} The motion should be understood as a continuous, qualitatively heterogeneous manifold. As such, were we to divide it, we have two new distinct qualitative manifolds rather that the one we started with.  (I am deriving this interpretation from ideas in Deleuze’s Bergsonism. See this part of chapter 2 for example. But I am not sure how to think of physical motion in terms of quality.) {7} We cannot think of the flow of the object’s motion as distinct from the flow of our consciousness and from the flow of reality as duration. So while the motion happens, just as there are no stops in our conscious duration, there are also no stops in the object’s motion. There is instead one continuous and variety-creating unfolding of duration. (This is based partly on this section in Bergsonism.) As this is an important but tricky paragraph, let us go line by line. The interpretation that seems to me to be the best to explain all of them is the following. Motion cannot be decomposed, because the process of becoming involved in it links all the moments together indissolubly and thus all its physical positions are linked together indissolubly, somehow. If we try to pinpoint its location at an instant, we understand that motion as having stopped there and then. For, were it actually in motion, it would be sliding through many points within its interval and never occupying a single one. In other words, consider the point it reaches at the end of its motion. Were it to have instead continued past that end-point, then it never in the first place would have occupied that position; rather it would have been sliding through it. So since the arrow remains in motion through its flight, it never at any instant is located an any point. This is not a satisfactory interpretation, but let us now go part-by-part. “Yes, if we suppose that the arrow can ever be in a point of its course. Yes again, if the arrow, which is moving, ever coincides with a position, which is motionless. But the arrow never is in any point of its course. The most we can say is that it might be there, in this sense, that it passes there and might stop there. It is true that if it did stop there, it would be at rest there, and at this point it is no longer movement that we should have to do with.” Here maybe the idea is that so long as the arrow is in motion, it is never at a point, but it is passing through points that it may stop upon, at which time it would occupy that  point. But that means were it ever to determinately occupy a position, it would no longer be in motion. “ The truth is that if the arrow leaves the point A to fall down at the point B, its movement AB is as simple, as indecomposable, in so far as it is movement, as the tension of the bow that shoots it”. We think of the tension in the bow as one solid thing, and likewise we must think of the arrow’s motion that way. “As the shrapnel, bursting before it falls to the ground, covers the explosive zone with an indivisible danger, so the arrow which goes from A to B displays with a single stroke, although over a certain extent of duration, its indivisible mobility”. Here he seems to be leaving the arrow illustration and dealing with more advanced sorts of explosives (unless the shrapnel results from the arrow’s strike somehow). So maybe this next image is that when there is an explosion, there are fragments of shrapnel. They are relatively small. But they fly through a zone. Anyone in that zone is in danger, since we do not know where the shrapnel will go. So this zone has an indecomposability based on the fact that we do not know what in the zone will be affected by the shrapnel and what will not; so it is all one danger zone. I am not sure, however, why he is using these particular metaphors of the string tension and the shrapnel zone.  “Suppose an elastic stretched from A to B, could you divide its extension? The course of the arrow is this very extension; it is equally simple and equally undivided. It is a single and unique bound.” Maybe the idea with the elastic is that if you cut it, it falls. And maybe we simply take it as a metaphor loosely to indicate that if you cut the arrow’s motion, you lose that thing which you first acknowledged to exist, namely, its motion. “You fix a point C in the interval passed, and say that at a certain moment the arrow was in C. If it had been there, it would have been stopped there, and you would no longer have had a flight from A to B, but two flights, one from A to C and the other from C to B, with an interval of rest”. This claim is important but tricky to grasp. Why is it that a continuous motion cannot be said to be at an intermediary point C and yet still be in motion? It is still not entirely clear to me why these are incompatible conceptions (unless we are claiming that motion requires always being in more that one place at a time). Suppose the object leaves a mark, like dropping something, sometime in its motion. It has just one thing that it drops. That dropped thing will have a position. Why can we not say that the moving object was also at that position the moment it was dropped? Here we can conceive of the object in continuous motion and yet occupying some determinate position during that motion. Or maybe we might think of a croquet ball passing under a hoop. You can tell me that so long as the ball was in motion, it does so within a duration that covers an extent of space rather than any particular position, but my eyes see at one moment it crossing under the hoop. The question is, why does the center of the ball not occupy the center point position of the hoop at some instant? Still the best I can think of is that it is because when it is passing under the hoop, it is occupy a range of locations surrounding that center-point, even if we pinpoint an instant. “A single movement is entirely, by the hypothesis, a movement between two stops; if there are intermediate stops, it is no longer a single movement. At bottom, the illusion arises from this, that the movement, once effected, has laid along its course a motionless trajectory on which we can count as many immobilities as we will. From this we conclude that the movement, whilst being effected, lays at each instant beneath it a position with which it coincides. We do not see that the trajectory is created in one stroke, although a certain time is required for it; and that though we can divide at will the trajectory once created, we cannot divide its creation, which is an act in progress and not a thing”. Here we need to distinguish the movement as an act in creation, which cannot be divided, from the accomplished movement, which can be divided spatially and perhaps also temporally. These lines push me to the interpretation that the indeterminacy of the motion while it is happening is the reason for its indeterminacy of position, were we to somehow consider one present instant of it. Another idea here might be that the motion at any present moment is bound up with its past moments and maybe somehow its future ones as well in such a way that they cannot be segregated. I am not sure how to conceive that, however. “To suppose that the moving body is at a point of its course is to cut the course in two by a snip of the scissors at this point, and to substitute two trajectories for the single trajectory which we were first considering. It is to distinguish two successive acts where, by the hypothesis, there is only one. In short, it is to attribute to the course itself of the arrow everything that can be said of the interval that the arrow has traversed, that is to say, to admit a priori the absurdity that movement coincides with immobility”. I do not understand the last sentence, but the idea here might simply be that we begin by saying there is one motion, but we treat it as two; and, we begin by saying the motion is truly something mobile, and yet we conceive it as nothing but immobility. And generally speaking, we make a mistake when we ascribe the spatial properties of the line (its decomposability into discrete, determinate points) to that of the motion, which does not have these spatial properties.]

Oui, si nous supposons que la flèche puisse jamais être en un point de son trajet. Oui, si la flèche, qui est du mouvant, coïncidait jamais avec une position, qui est de l'immobilité. Mais la flèche n'est jamais en aucun point de son trajet. Tout au plus doit-on dire qu'elle pourrait y être, en ce sens qu'elle y passe et qu'il lui serait loisible de s'y arrêter. Il est vrai que, si elle s'y arrêtait, elle y resterait, et que ce ne serait plus, en ce point, à du mouvement que nous aurions affaire. La vérité est que, si la flèche part du point A pour retomber au point B, son mouvement AB est aussi simple, aussi indécomposable, en tant que mouvement, que la tension de l'arc qui la lance. Comme le shrapnell, éclatant avant de toucher terre, couvre d'un indivisible danger la zone d'explo­sion, ainsi la flèche qui va de A en B déploie d'un seul coup, quoique sur une certaine étendue de durée, son indivisible mobilité. Supposez un élastique que vous tireriez de A en B ; pourriez-vous en diviser l'extension ? La course de la flèche est cette extension même, aussi simple qu'elle, indivisée comme elle. C'est un seul et unique bond. Vous fixez un point C dans l'intervalle parcouru, et vous dites qu'à un certain moment la flèche était en C. Si elle y avait été, c'est qu'elle s'y serait arrêtée, et vous n'auriez plus une course de A en B, mais deux courses, l'une de A en C, | l'autre de C en B, avec un intervalle de repos. Un mouvement unique est tout entier, par hypothèse, mouvement entre deux arrêts : s'il y a des arrêts intermédiaires, ce n'est plus un mouvement unique. Au fond, l'illusion vient de ce que le mouvement, une fois effectué, a déposé le long de son trajet une trajectoire immobile sur laquelle on peut compter autant d'immobilités qu'on voudra. De là on conclut que le mouvement, s'effectuant, déposa à chaque instant au-dessous de lui une position avec laquelle il coïncidait. On ne voit pas que la trajectoire se crée tout d'un coup, encore qu'il lui faille pour cela un certain temps, et que si l'on peut diviser a volonté la trajectoire une fois créée, on ne saurait diviser sa création, qui est un acte en progrès et non pas une chose. Supposer que le mobile est en un point du trajet, c'est, par un coup de ciseau donné en ce point, couper le trajet en deux et substituer deux trajectoires à la trajectoire unique que l'on consi­dérait d'abord. C'est distinguer deux actes successifs là où, par hypothèse, il n'y en a qu'un. Enfin c'est transporter à la course même de la flèche tout ce qui peut se dire de l'intervalle qu'elle a parcouru, c'est-à-dire admettre a priori cette absurdité que le mouvement coïncide avec l'immobile.

(1941: 308|309. Copied from UQAC)

 

Yes, if we suppose that the arrow can ever be in a point of its course. Yes again, if the arrow, which is moving, ever coincides with a position, which is motionless. But the arrow never is in any point of its course. The most we can say is that it might be there, in this sense, that it [308||309] passes there and might stop there. It is true that if it did stop there, it would be at rest there, and at this point it is no longer movement that we should have to do with. The truth is that if the [325|326] arrow leaves the point A to fall down at the point B, its movement AB is as simple, as indecomposable, in so far as it is movement, as the tension of the bow that shoots it. As the shrapnel, bursting before it falls to the ground, covers the explosive zone with an indivisible danger, so the arrow which goes from A to B displays with a single stroke, although over a certain extent of duration, its indivisible mobility. Suppose an elastic stretched from A to B, could you divide its extension? The course of the arrow is this very extension; it is equally simple and equally undivided. It is a single and unique bound. You fix a point C in the interval passed, and say that at a certain moment the arrow was in C. If it had been there, it would have been stopped there, and you would no longer have had a flight from A to B, but two flights, one from A to C and the other from C to B, with an interval of rest. A single movement is entirely, by the hypothesis, a movement between two stops; if there are intermediate stops, it is no longer a single movement. At bottom, the illusion arises from this, that the movement, once effected, has laid along its course a motionless trajectory on which we can count as many immobilities as we will. From this we conclude that the movement, whilst being effected, lays at each instant beneath it a position with which it coincides. We do not see that the trajectory is created in one stroke, although a certain time is required for it; and that though we can divide at will the trajectory once created, we cannot divide its creation, which is an act in progress and not a thing. To suppose that the moving body is at a point of its course is to cut the course in two by a snip of the scissors at this point, [309||310]  and to substitute two trajectories for the single trajectory which we were first considering. [326|327]  It is to distinguish two successive acts where, by the hypothesis, there is only one. In short, it is to attribute to the course itself of the arrow everything that can be said of the interval that the arrow has traversed, that is to say, to admit a priori the absurdity that movement coincides with immobility.

(1922: 325|327; 1998: 308||310. Copied from Project Gutenberg)

 

 

 

4.5.9

[The mistake in all of Zeno’s paradoxes is that the geometrical properties of the line (traversed by the moving object) are attributed to the motion itself. But motion, unlike lines, is not divisible. Hence the absurd conclusions of the paradoxes.]

 

Bergson says that we will not examine Zeno’s other three paradoxes of motion, but we can at least say that they all involve the error of attributing the spatial properties of a line to that of the object’s motion. So we should not assume that motion is divisible like lines are. [The sentence in question here reminds me of the qualitative heterogeneity interpretation we gave above: “The line, for example, may be divided into as many parts as we wish, of any length that we wish, and it is always the same line. From this we conclude that we have the right to suppose the movement articulated as we wish, and that it is always the same movement.”] But this error leads to the absurdities found in Zeno’s paradoxes. [Bergson then seems to appeal to our intuition of duration and motion. Just as our own actions or motions seem absolutely continuous, with no stops, so too should the arrow’s motion be understood as indecomposable. (These lines make me think of the interpretation 7 above, where the unbrokenness has to do with a unified flux of duration including our consciousness and the motion of the arrow, when it is in action: “ the possibility of applying the movement to the line traversed exists only for an observer who keeping outside the movement and seeing at every instant the possibility of a stop, tries to reconstruct the real movement with these possible immobilities. The absurdity vanishes as soon as we adopt by thought the continuity of the real movement, a continuity of which every one of us is conscious whenever he lifts an arm or advances a step”. But it does not correspond entirely.) [His next point seems to be that physical motion, like our bodily movements, have some sort of internal organization that would disallow them from being dissected: “The line traversed by the moving body lends itself to any kind of division, because it has no internal organization. But all movement is articulated inwardly.” Here perhaps he means that there is something like an integrated qualitative variety in the motion, but I am not sure what he means here. In the case of moving our arm, there is the line in space it traverses, but there are also all the internal, constituent motions in the body involved in that motion, and this complex of constituent motions have their own organization that cannot be severed. But I am not sure how to apply this interpretation to simple physical motion like that of arrows. Yet what seems important here is that movements are always articulated, and those articulations are unique in each case and throughout the course of the motion, perhaps like a heterogeneous qualitative manifold.]

Nous ne nous appesantirons pas ici sur les trois autres arguments de Zénon. Nous les avons examinés ailleurs. Bornons-nous à rappeler qu'ils con­sis­tent encore à appliquer le mouvement le long de la ligne parcourue et à sup. poser que ce qui est vrai de la ligne est vrai du mouvement. Par exemple, la ligne peut être divisée en autant de parties qu'on veut, de la grandeur qu'on veut, et c'est toujours la même ligne. De là on conclura qu'on a le droit de supposer le mouvement articulé comme on veut, et que c'est toujours le même mouvement. On obtiendra ainsi une série d'absurdités qui toutes exprimeront la même absurdité fondamentale. Mais la possibilité d'appliquer le mouve­ment sur la ligne parcourue n'existe que | pour un observateur qui, se tenant en dehors du mouvement et envisageant à tout instant la possibilité d'un arrêt, prétend recomposer le mouvement réel avec ces immobilités possibles. Elle s'évanouit dès qu'on adopte par la pensée la continuité du mouvement réel, celle dont chacun de nous a conscience quand il lève le bras ou avance d'un pas. Nous sentons bien alors que la ligne parcourue entre deux arrêts se décrit d'un seul trait indivisible, et qu'on chercherait vainement à pratiquer dans le mouvement qui la trace des divisions correspondant, chacune à chacune, aux divisions arbitrairement choisies de la ligne une fois tracée. La ligne parcou­rue par le mobile se prête à un mode de décomposition quelconque parce qu'elle n'a pas d'organisation interne. Mais tout mouvement est articulé inté­rieu­rement. C'est ou un bond indivisible (qui peut d'ailleurs occuper une très longue durée) ou une série de bonds indivisibles. Faites entrer en ligne de compte les articulations de ce mouvement, ou bien alors ne spéculez pas sur sa nature.

(1941: 309|310. Copied from UQAC)

 

We shall not dwell here on the three other arguments of Zeno. We have examined them elsewhere. It is enough to point out that they all consist in applying the movement to the line traversed, and supposing that what is true of the line is true of the movement. The line, for example, may be divided into as many parts as we wish, of any length that we wish, and it is always the same line. From this we conclude that we have the right to suppose the movement articulated as we wish, and that it is always the same movement. We thus obtain a series of absurdities that all express the same fundamental absurdity. But the possibility of applying the movement to the line traversed exists only for an observer who keeping outside the movement and seeing at every instant the possibility of a stop, tries to reconstruct the real movement with these possible immobilities. The absurdity vanishes as soon as we adopt by thought the continuity of the real movement, a continuity of which every one of us is conscious whenever he lifts an arm or advances a step. We feel then indeed that the line passed over between two stops is described with a single indivisible stroke, and that we seek in vain to practice on the movement, which traces the line, divisions corresponding, each to each, with the divisions arbitrarily chosen of the line once it has been traced. The line traversed by the moving body lends itself to any kind of division, because it has no internal organization. But | || all movement is articulated inwardly. It is either an indivisible bound (which may occupy, nevertheless, a very long duration) or a series of indivisible bounds. Take the articulations of this movement into account, or give up speculating on its nature.

(1922: 327|328; 1998: 310||311. Note: Page breaks at the same word. Copied from Project Gutenberg)

 

 

4.5.10

[The same error is also responsible for the absurdity in Zeno’s paradox of Achilles and the Tortoise. It also incorrectly attributes infinite divisibility to unified motion.]

 

Bergson now turns to Zeno’s paradox of Achilles racing the Tortoise. [In this entry from Bergson’s Time and Free Will, we examine in detail how Bergson’s objection works, using diagrams. Both there as well as here, the idea seems to be the same. Achilles’ and the Tortoise’s motions are made of steps, which more or less can be considered as unified motions or actions all themselves. Achilles’ steps are longer, so of course he can overtake the Tortoise. It is only when we make the error of infinitely dividing up their steps into a series of tiny steps (or phases of steps) that we think Achilles can only advance one point at a time while the Tortoise advances ahead of Achilles point-by-point at pace with him. It is only because Zeno misconceives the motion as having the same geometrical properties as the space traversed, namely, decomposability into an infinity of points, that the absurdity arises.] [Bergson then notes an idea found in François Évellin’s  Infini et quantité (1880). We summarize the main points relevant to Bergson’s treatments here. But in that summary, we are missing the part that is in the footnote of this paragraph. Bergson writes: “we do not consider the sophism of Zeno refuted by the fact that the geometrical progression a(1 + 1/n + 1/n2 + 1/n3 +,... etc.)—in which a designates the initial distance between Achilles and the tortoise, and n the relation of their respective velocities—has a finite sum if n is greater than 1.” A similar formulation is found in the Évellin text on page 73:

image_thumb1

I am not certain, but the idea here might be something like the following. Suppose we want to keep this idea of infinite divisibility, but still say that Achilles overtakes the Tortoise. And also suppose we would be content with an abstract mathematical notion for this explanation. Before we get to Évellin’s conception, let us consider how this solution is presented in Edwards’ and Penney’s Calculus, section 11.1. We will suppose the simple case of the arrow arriving at its destination. To get there, it must go half the distance, than half the distance between there and the end, then half the distance between that new half and the end, and so on.

[a1.jpg]

(Image source: p682 of Edwards and Penney, Calculus)

Since every half can be divided infinitely, it would seem to never be able to arrive, as there is always another half to traverse. But if we sum this infinite series of fractions, we get the finite value 1 (if I am not mistaken, but I could be). Évellin seems to be discussing this sort of tactic, but now with complication that two things are in motion and not just one. He has us think of the Tortoise leading Achilles at first by a meter, but going at a speed one tenth that of Achilles. Now I am not exactly sure why it takes this form:

image_thumb2

but I will guess, and most likely you will need to correct me. The idea here might be that in the first phase of the motion, the difference between them is a ratio of one to 10, in other words, Achilles gets about 90 percent of the way. Then in the next phase, their difference is a ratio of 1 to 100, or in other words Achilles gets 99 percent of the way. And so on. But I am guessing, and also Bergson’s formula is structured slightly differently as:

image_thumb4

Where a  is the initial distance between them. At any rate, Évellin’s point is that this does not work. Because the series is infinite, there is always another partial movement. So while it might work out nicely in mathematics, were it to transpire in the physical world, it would not solve the problem.] [(The following comments were added later.) Upon reexamining the paradox (II.F at this entry), I see something to mention. The paradox it seems is that for Achilles to reach the Tortoise, he first has to reach the Tortoise’s starting point. But upon doing so, the Tortoise has gone a little further. Suppose they are one meter apart, and Achilles goes 1 meters per second and the Tortoise goes 0.1 meter per second. After one second, Achilles is at 1 meter, and the Tortoise is at 1.1 meters. It will then take one tenth of a second for Achilles to get to this newer position of the Tortoise, at which time Achilles is at 1.1 and the Tortoise has now advanced to 1.11. (And so on, with the 1 decimal repeating in this way.) In other words, possibly we are to understand the sum of the infinity of all of Achilles’ incremental catchings-up to total a finite sum equaling wherever the Tortoise would be when Achilles finally meets up. (Possibly in our example it would be the fraction 10/9, but I am not sure. And possibly the percentage idea still works here too, more or less.)]

 

Quand Achille poursuit la tortue, chacun de ses Pas doit être traité comme un indivisible, chaque pas de la tortue aussi. Après un certain nombre de pas, Achille aura enjambé la tortue. Rien n'est plus simple. Si vous tenez a diviser davantage les deux mouvements, distinguez de part et d'autre, dans le trajet d'Achille et dans celui de la tortue, des sous-multiples du pas de chacun d'eux ; mais respectez les articulations naturelles des deux trajets. Tant que vous les respecterez, aucune difficulté ne surgira, parce que vous suivrez les indications de l'expérience. Mais l'artifice de Zénon consiste à recomposer le mouvement d'Achille selon une loi arbitrairement choisie. Achille arriverait d'un premier bond au point où était la tortue, d'un second bond au point où elle s'est transportée pendant qu'il faisait le premier, et ainsi de suite. Dans ce cas, Achille aurait en effet toujours un nouveau bond à faire. | Mais il va sans dire qu'Achille, pour rejoindre la tortue, s'y prend tout autrement. Le mouve­ment considéré par Zénon ne serait l'équivalent du mouvement d'Achille que si l'on pouvait traiter le mouvement comme on traite l'intervalle parcouru, décomposable et recomposable à volonté. Dès qu'on a souscrit à cette première absurdité, toutes les autres s'ensuivent.1

(1941: 310|311. Copied from UQAC)

1 C'est dire que nous ne considérons pas le sophisme de Zénon comme réfuté, par le fait que la progression géométrique

image_thumb

a désigne l'écart initial entre Achille et la tortue, et n le rapport de leurs vitesses respectives, a une somme finie si n est supérieur à l'unité. Sur ce point, nous renvoyons à l'argumentation de M. Évellin, que nous tenons pour décisive (Voir Évellin, Infini et quantité, Paris, 1880, pp. 63-97. Cf.

(1941: 311. Text copied from UQAC. Image from the PUF text.)

 

When Achilles pursues the tortoise, each of his steps must be treated as indivisible, and so must each step of the tortoise. After a certain number of steps, Achilles will have overtaken the tortoise. There is nothing more simple. If you insist on dividing the two motions further, distinguish both on the one side and on the other, in the course of Achilles and in that of the tortoise, the sub-multiples of the steps of each of them; but respect the natural articulations of the two courses. As long as you respect them, no difficulty will arise, because you will follow the indications of experience. But Zeno's device is to reconstruct the movement of Achilles according to a law arbitrarily chosen. Achilles with a first step is supposed to arrive at the point where the tortoise was, with a second step at the point which it has moved to while he was making the first, and so on. In this case, Achilles would always have a new step to take. But obviously, to overtake the tortoise, he goes about it in quite another way. The movement considered by Zeno would only be the equivalent of the movement of Achilles if we could treat the movement as we treat the interval passed through, decomposable and recomposable at will. Once you subscribe to this first absurdity, all the others follow.1

(1922: 328; 1998: 311. Copied from Project Gutenberg)

1 That is, we do not consider the sophism of Zeno refuted by the fact that the geometrical progression a(1 + 1/n + 1/n2 + 1/n3 +,... etc.)—

image_thumb7

in which a designates the initial distance between Achilles and the tortoise, and n the relation of their respective velocities—has a finite sum if n is greater than 1. On this point we may refer to the arguments of F. Evellin, which we regard as conclusive (see Evellin, Infini et quantité, Paris, 1880, pp. 63-97; cf. Revue philosophique, vol. xi., 1881, pp. 564-568). The truth is that mathematics, as we have tried to show in a former work, deals and can deal only with lengths. It has therefore had to seek devices, first, to transfer to the movement, which is not a length, the divisibility of the line passed over, and then to reconcile with experience the idea (contrary to experience and full of absurdities) of a movement that is a length, that is, of a movement placed upon its trajectory and arbitrarily decomposable like it.

(1922: 328; 1998: 311. Copied from Project Gutenberg)

 

 

 

4.5.11

[The same Zeno-like error that we make for extensive movements we also make for evolutionary movements (as well as qualitative ones), and this mistake is reinforced by language. We say “the child becomes a man”. We know the change to be continuous, but the words ‘child’ and ‘man’ designates states or snapshots, between which is the vague verb ‘becomes’ that acts like the impersonal motion of the film projector. Such formulations make the change discontinuous, because as soon as the predicate “adult” is assigned to “child”, it is no longer child, and thus there was no continuity from one state to the next. Instead, we should say, “there is becoming from the child to the man”. ]

 

[Recall from section 4.4 that there are three types of movement or variation: qualitative, evolutionary, and extensive. It seems we have shown how extensive moment is indivisible. Bergson says this applies to the other kinds of motion, but in this paragraph he focuses it seems on the evolutionary kind. We take a person’s growth from child to youth to adult to old age. In reality there was one continuous movement of development. It is only the mind, with the aid of concepts and language, that we think of it having discrete stages where the change has more or less arrested at certain times. Bergson has us consider how we might say, conventionally, “the child becomes a man”. We should not be deceived that there is in fact a reified child and a reified man. Let me quote:  ‘when we posit the subject “child,” the attribute “man” does not yet apply to it, and that, when we express the attribute “man,” it applies no more to the subject “child.”  The reality, which is the transition from childhood to manhood, has slipped between our fingers.’ I am not sure but the point here might be that under such a formulation, we cannot explain the transition, for the following reason. Under this formulation where child is distinct from man, we cannot say it was one thing persisting in both states, or at least, there is no continuous transition between them. There must have been a discontinuous leap. He says that these stops like ‘child’ and ‘man’ are equivalent to the positions of the arrow. He then says something fascinating: ‘The truth is that if language here were molded on reality, we should not say “The child becomes the man,” but “There is becoming from the child to the man”.’ What is interesting here grammatically (or syntactically) is that the subject in the first case is ‘child’ and in the second case is ‘becoming’. If we only think of ‘child’, then as soon as we attribute the predicate “adult” to it, it is no longer a child, and thus there is no continuity from one state to the other. This is one way that language reinforces the inaccuracy of the cinematographic method.]

Rien ne serait plus facile, d'ailleurs, que d'étendre l'argumentation de Zénon au devenir qualitatif et au devenir évolutif. On retrouverait les mêmes contradictions. Que l'enfant devienne adolescent, puis homme mûr, enfin vieillard, cela se comprend quand on considère que l'évolution vitale est ici la réalité même. Enfance, adolescence, maturité, vieillesse sont de simples vues de l'esprit, des arrêts possibles imaginés pour nous, du dehors, le long de la continuité d'un progrès. Donnons-nous au contraire l'enfance, l'adolescence, la maturité et la vieillesse comme des parties intégrantes de l'évolution : elles deviennent des arrêts réels, et nous ne concevons plus comment l'évolution est possible, car des repos juxtaposés n'équivaudront jamais à un mouvement. Comment, avec ce qui est fait, reconstituer ce qui se fait ? Comment, par exemple, de l'enfance une fois posée comme une chose, passera-t-on à l'ado­lescence, alors que, par hypothèse, on s'est donné l'enfance seulement ? Qu'on y regarde de près : on verra [311|312] que notre manière habituelle de parler, laquelle se règle sur notre manière habituelle de penser, nous conduit à de véritables impasses logiques, impasses où nous nous engageons sans inquiétude parce que nous sentons confusément qu'il nous serait toujours loisible d'en sortir; il nous suffirait, en effet, de renoncer aux habitudes cinématographiques de notre intelligence. Quand nous disons « l'enfant devient homme », gardons-nous de trop approfondir le sens littéral de l'expression. Nous trouverions que, lorsque nous posons le sujet « enfant », l'attribut « homme » ne lui convient pas encore, et que, lorsque nous énonçons l'attribut « homme », il ne s'appli­que déjà plus au sujet« enfant». La réalité, qui est la transition de l'enfance à l'âge mûr, nous a glissé entre les doigts. Nous n'avons que les arrêts imagi­naires« enfant» et « homme», et nous sommes tout près de dire que l'un de ces arrêts est l'autre, de même que la flèche de Zénon est, selon ce philosophe, à tous les points du trajet. La vérité est que, si le langage se moulait ici sur le réel, nous ne dirions pas « l'enfant devient homme », mais « il y a devenir de l'enfant à l'homme ». Dans la première proposition, « devient » est un verbe à sens indéterminé, destiné à masquer l'absurdité où l'on tombe en attribuant l'état « homme » au sujet « enfant ». Il se comporte à peu près comme le mouvement, toujours le même, de la bande cinématographique, mouvement caché dans l'appareil et dont le rôle est de superposer l'une à l'autre les images successives pour imiter le mouvement de l'objet réel. Dans la seconde, « deve­nir » est un sujet. Il passe au premier plan. Il est la réalité même : enfance et âge d'homme ne sont plus alors que des arrêts virtuels, simples vues de l'es­prit : nous avons affaire, cette fois, au mouvement objectif lui-même, et non plus à son imitation cinématographique. Mais la première manière de s'expri­mer est seule conforme à nos habitudes de langage. Il faudrait, pour adopter la seconde, se [312|313] soustraire au mécanisme cinémato­graphique de la pensée.

(1941: 311|313. Copied from UQAC)

 

 

Nothing would be easier, now, than to extend Zeno's argument to qualitative becoming and to evolutionary becoming. We should find the same contradictions in these. That the child can become a youth, ripen to maturity and decline to old age, we understand when we consider that vital evolution is here the reality itself. Infancy, adolescence, maturity, old age, are mere views of the mind, possible stops imagined by us, from without, along the continuity of a progress. On the contrary, let childhood, adolescence, maturity and old age be given as integral parts of the evolution, they become real stops, and we can no longer conceive how evolution is possible, for rests placed beside rests will never be equivalent to a movement. How, with what is made, can we reconstitute what is being made? How, for instance, from childhood once posited as a thing, shall we pass to adolescence, when, by the hypothesis, childhood only is given? If we look at it closely, we shall see that our habitual manner of speaking, which is fashioned after our habitual manner of thinking, leads us to actual logical dead-locks—dead-locks to which we allow ourselves to be led without anxiety, because we feel confusedly that we can always get out of them if we like: all that we have to do, in fact, is to give up the cinematographical habits of our intellect. When we say “The child becomes a man,” let us take care not to fathom too deeply the literal | meaning of the expression, or we shall find that, when we posit the subject “child,” the attribute “man” does not yet apply to it, and that, || when we express the attribute “man,” it applies no more to the subject “child.” The reality, which is the transition from childhood to manhood, has slipped between our fingers. We have only the imaginary stops “child” and “man,” and we are very near to saying that one of these stops is the other, just as the arrow of Zeno is, according to that philosopher, at all the points of the course. The truth is that if language here were molded on reality, we should not say “The child becomes the man,” but “There is becoming from the child to the man.” In the first proposition, “becomes” is a verb of indeterminate meaning, intended to mask the absurdity into which we fall when we attribute the state “man” to the subject “child.” It behaves in much the same way as the movement, always the same, of the cinematographical film, a movement hidden in the apparatus and whose function it is to superpose the successive pictures on one another in order to imitate the movement of the real object. In the second proposition, “becoming” is a subject. It comes to the front. It is the reality itself; childhood and manhood are then only possible stops, mere views of the mind; we now have to do with the objective movement itself, and no longer with its cinematographical imitation. But the first manner of expression is alone conformable to our habits of language. We must, in order to adopt the second, escape from the cinematographical mechanism of thought.

(1922: 329|330; 1998: 312|313. Copied from Project Gutenberg)

 

 

 

4.5.12

[Thus we should not think of movement by beginning with immobile sections and building up to the transitions thought to hold between them. Rather we must begin with the flux of conscious duration, and secondarily make artificial cuts if we so choose.]

 

So we encounter these contradictions when we think of movement by beginning with states and building up to a transition. However, there is no contradiction when “we place ourselves along the transition” [perhaps by entering into a direct awareness of the flux of our consciousness] and then secondarily and artificially make cuts in the flow. The reason this is so is that there is always more in the movement than in all the cuts you can possibly make in it: “there is more in the transition than the series of states, that is to say, the possible cuts—more in the movement than the series of positions, that is to say, the possible stops”. In order to attain this direct awareness, we need to go against our normal habits of thought. [The next idea might be that the ancient Greeks instead tried to understand reality as if it conformed to the restrictions of language.]

Il en faudrait faire abstraction complète, pour dissiper d'un seul coup les absurdités théoriques que la question du mouvement soulève. Tout est obscurité, tout est contradiction quand on prétend, avec des états, fabriquer une transition. L'obscurité se dissipe, la contradiction tombe dès qu'on se place le long de la transition, pour y distinguer des états en y pratiquant par la pensée des coupes transversales. C'est qu'il y a plus dans la transition que la série des états, c'est-à-dire des coupes possibles, plus dans le mouvement que la série des positions, c'est-à-dire des arrêts possibles. Seulement, la première manière de voir est conforme aux procédés de l'esprit humain ; la seconde exige au contraire qu'on remonte la pente des habitudes intellectuelles. Faut-il s'étonner si la philosophie a d'abord reculé devant un pareil effort ? Les Grecs avaient confiance dans la nature, confiance dans l'esprit laissé à son inclina­tion naturelle, confiance dans le langage surtout, en tant qu'il extériorise la pensée naturellement. Plutôt que de donner tort à l'alti­tude que prennent, devant le cours des choses, la pensée et le langage, ils aimèrent mieux donner tort au cours des choses.

(1941: 313. Copied from UQAC)

 

We must make complete abstraction of this mechanism, if we wish to get rid at one stroke of the theoretical absurdities that the question of movement raises. All | is obscure, all is contradictory when we try, with states, to build up a transition. The obscurity is cleared up, the contradiction vanishes, as soon as we place ourselves along the transition, in order to distinguish states in it || by making cross cuts therein in thought. The reason is that there is more in the transition than the series of states, that is to say, the possible cuts—more in the movement than the series of positions, that is to say, the possible stops. Only, the first way of looking at things is conformable to the processes of the human mind; the second requires, on the contrary, that we reverse the bent of our intellectual habits. No wonder, then, if philosophy at first recoiled before such an effort. The Greeks trusted to nature, trusted the natural propensity of the mind, trusted language above all, in so far as it naturally externalizes thought. Rather than lay blame on the attitude of thought and language toward the course of things, they preferred to pronounce the course of things itself to be wrong.

(1922: 330|331; 1998: 313|314. Copied from Project Gutenberg)

 

 

 

4.5.13

[The Eleatics (who included Parmenides and Zeno of Elea), instead of trying to understand the durational flux nature of Becoming, made it conform to the reifying patterns of thought and language. They thus deemed Becoming unreal and change and motion illusory. We could soften this view to obtain a Platonic sort, where we say that sensible reality does change, but we should seek a deeper reality of Forms or Ideas that does not change.]

 

Because the Eleatics (who included Parmenides and Zeno of Elea) were unable to manage the way Becoming shocks our reifying habits of thought, they tried to make it conform to language. And since language, which is also reifying, cannot adequately express Becoming’s real durational nature, they came to conclude that Becoming is unreal. Thus they saw change and movement as illusory. [Bergson’s next point I might not get right, but it seems to be the following. We might soften the Eleatic position. We recognize that in fact things in sensible reality do change. But things in intelligible reality (which are reified)  do not change. Furthermore, we would place a priority on the intelligible reality, and say that things should be like intelligible reality and thus even sensible things ought not to change (or would be better if they did not). And so our minds should go beneath qualitative, evolutionary, and extensive becomings to seek out that which defies change, as with the philosophy of Forms or Ideas.]

C'est ce que firent sans ménagement les philosophes de l'école d'Élée. Comme le devenir choque les habitudes de la pensée et s'insère mal dans les cadres du langage, ils le déclarèrent irréel. Dans le mouvement spatial et dans le changement en général ils ne virent qu'illusion pure. On pouvait atténuer cette conclusion sans changer les prémisses, dire que la réalité change, mais qu'elle ne devrait pas changer. L'expérience nous met en présence du devenir, voilà la réalité sensible. Mais la réalité intelligible, celle qui devrait être, est plus réelle encore, et celle-là, dira-t-on, ne change pas. Sous le devenir quali­tatif, sous le devenir évolutif, sous le devenir extensif, l'esprit doit chercher ce qui est réfractaire au changement : la qualité | définissable, la forme ou essen­ce, la fin. Tel fut le principe fondamental de la philosophie qui se développa à travers l'antiquité classique, la philosophie des Formes ou, pour employer un terme plus voisin du grec, la philosophie des Idées.

(1941: 313|314. Copied from UQAC)

 

Such, indeed, was the sentence passed by the philosophers of the Eleatic school. And they passed it without any reservation whatever. As becoming shocks the habits of thought and fits ill into the molds of language, they declared it unreal. In spatial movement and in change in general they saw only pure illusion. This conclusion could be softened down without changing the premisses, by saying that the reality changes, but that it ought not to change. Experience confronts us with becoming: that is sensible reality. But the intelligible reality, that which ought to be, is more real still, and that reality does not change. Beneath the qualitative becoming, beneath the evolutionary becoming, beneath the extensive becoming, the mind must | seek that which defies change, the definable quality, the form or essence, the end. Such was the fundamental principle of the philosophy which developed throughout the classic age, the philosophy of Forms, or, to use a term more akin to the Greek, the philosophy of Ideas.

(1922: 331|332; 1998: 314. Copied from Project Gutenberg)

 

 

4.5.14

[The ancient Greek word for Forms or Ideas is εἶδος. Its three senses correspond with the three sorts of reified motion and the three categories of language corresponding to them. Each case takes a stable  perspective on the instability of Becoming. {1} Quality, corresponding to qualitative motion and to the adjective. Here there is a snapshot in qualitative flux. {2} Form or essence, corresponding to evolutionary change and to the substantive. In the case of form, there is a period in the flux where there is relatively negligible variation and is thus taken as a more or less homogeneous phase or moment in the development, like ‘child’ or ‘man’. Here there is a fixed section of change from which the other moments are seen as transitions. Essence is like an average of forms, and is thus a fixity in comparison with that formal variety. {3} End or design in the sense of the intention of an action (like a mental design or schema for the action), corresponding to extensional motion and to the verb. Here the action is understood in terms of its completed state and thus of its aim or purpose (along with a vague schema or pattern for all its component parts that go unnoticed mostly). Hence it is a fixity as an idea of the action on the basis of which all the action’s motional variation is oriented around or directed toward. Thus the Greek notion of εἶδος involves taking the cinematographic approach to understanding reality.]

 

Bergson now discusses the ancient Greek notion of εἶδος or Idea. Bergson says it means three things: {1} quality, {2} form or essence, and {3} end or design (as in the intention) of the act being performed. Quality is thus related to adjective, form or essence to substantive, and end or design to verb. Bergson then claims we could think of εἶδος more as “the stable view taken of the instability of things”. Quality: this is a moment of becoming [and is thus a stable snapshot from the perspective of which all else is in flux]. Form: this is a moment in evolution [like ‘child’ and ‘adult’]. Essence: this is the average or mean of relatively negligible formal variation (see section  4.4.6). Intention or Mental Design: this is like the notion of the action understood primarily in terms of the completion, end, or purpose of the action, [with perhaps a vague or partly ignored notion of all the component parts of that action. He wrote in section 4.4.2: “the mind is carried immediately to the end, that is to say, to the schematic and simplified vision of the act supposed accomplished.”] Given how in all senses of Idea we are taking a fixed perspective on the flux of becoming, “To reduce things to Ideas is [...]to resolve becoming into its principal moments, each of these being [...] screened from the laws of time and [...] plucked out of eternity”. In other words, this ancient Greek notion of Ideas applies the cinematographic method when analyzing reality.

Le mot eidos, que nous traduisons ici par Idée, a en effet ce triple sens. Il désigne : 1° la qualité, 2° la forme ou essence, 3° le but ou dessein de l'acte s'accomplissant, c'est-à-dire, au fond, le dessin de l'acte sup­posé accompli. Ces trois points de vue sont ceux de l'adjectif, du substan­tif et du verbe, et correspondent aux trois catégories essentielles du langage. Après les explications que nous avons données un peu plus haut, nous pourrions et nous devrions peut-être traduire eidos par « vue » ou plutôt par « moment ». Car eidos est la vue stable prise sur l'instabilité des choses : la qualité qui est un moment du devenir, la forme qui est un moment de l'évolution, l'essence qui est la forme moyenne au-dessus et au-dessous de laquelle les autres formes s'échelonnent comme des altérations de celle-là, enfin le dessein inspirateur de l'acte s'ac­complissant, lequel n'est point autre chose, disions-nous, que le dessin antici­pé de l'action accomplie. Ramener les choses aux Idées consiste donc à résou­dre le devenir en ses principaux moments, chacun de ceux-ci étant d'ailleurs soustrait par hypothèse à la loi du temps et comme cueilli dans l'éternité. C'est dire qu'on aboutit à la philosophie des Idées quand on applique le mécanisme cinématographique de l'intelligence à l'analyse du réel.

(1941: 314. Copied from UQAC. eidos endered as εἶδος in PUF.)

 

The word ειδος, which we translate here by “Idea,” has, || in fact, this threefold meaning. It denotes (1) the quality, (2) the form or essence, (3) the end or design (in the sense of intention) of the act being performed, that is to say, at bottom, the design (in the sense of drawing) of the act supposed accomplished. These three aspects are those of the adjective, substantive and verb, and correspond to the three essential categories of language. After the explanations we have given above, we might, and perhaps we ought to, translate ειδος by “view” or rather by “moment.” For ειδος is the stable view taken of the instability of things: the quality, which is a moment of becoming; the form, which is a moment of evolution; the essence, which is the mean form above and below which the other forms are arranged as alterations of the mean; finally, the intention or mental design which presides over the action being accomplished, and which is nothing else, we said, than the material design, traced out and contemplated beforehand, of the action accomplished. To reduce things to Ideas is therefore to resolve becoming into its principal moments, each of these being, moreover, by the hypothesis, screened from the laws of time and, as it were, plucked out of eternity. That is to say that we end in the philosophy of Ideas when we apply the cinematographical mechanism of the intellect to the analysis of the real.

(1922: 332; 1998: 314||315. Copied from Project Gutenberg)

 

 

 

4.5.15

[Many ancient Greeks took this cinematographic approach to understanding reality.]

 

Bergson says that this ancient Greek view, which is not limited just to the Eleatics and Plato but also to Aristotle, the Stoics, and Plotinus [and perhaps to many coming after], is based on an idea of reality that comes from the cinematographic mode of thinking about change. This view of reality has consequences as well for one’s physics, cosmology, and theology.

Mais, dès qu'on met les Idées immuables au fond de la mouvante réalité, toute une physique, toute une cosmologie, toute une théologie même s'ensui­vent nécessairement. Arrêtons-nous sur ce point. Il n'entre pas dans notre pensée de résumer en quelques pages une philosophie aussi complexe et aussi compréhensive que celle des Grecs. Mais, puisque nous venons de décrire le mécanisme | cinématographique de l'intelligence, il importe que nous mon­trions à quelle représentation du réel le jeu de ce mécanisme aboutit. Cette représentation est précisément, croyons-nous, celle qu'on trouve dans la philo­sophie antique. Les grandes lignes de la doctrine qui s'est développée de Platon à Plotin, en passant par Aristote (et même, dans une certaine mesure, par les stoïciens), n'ont rien d'accidentel, rien de contingent, rien qu'il faille tenir pour une fantaisie de philosophe. Elles dessinent la vision qu'une intelli­gence systématique se donnera de l'universel devenir quand elle le regardera à travers des vues prises de loin en loin sur son écoulement. De sorte qu'au­jourd'hui encore nous philosopherons à la manière des Grecs, nous retrouve­rons, sans avoir besoin de les connaître, telles et telles de leurs conclusions générales, dans l'exacte mesure où nous nous fierons à l'instinct cinémato­graphique de notre pensée.

(1941: 314|315. Copied from UQAC)

 

But, when we put immutable Ideas at the base of the moving reality, a whole physics, a whole cosmology, | a whole theology follows necessarily. We must insist on the point. Not that we mean to summarize in a few pages a philosophy so complex and so comprehensive as that of the Greeks. But, since we have described the cinematographical mechanism of the intellect, it is important that we should show to what idea of reality the play of this mechanism leads. It is the very idea, we believe, that we find in the ancient philosophy. The main lines of the doctrine that was || developed from Plato to Plotinus, passing through Aristotle (and even, in a certain measure, through the Stoics), have nothing accidental, nothing contingent, nothing that must be regarded as a philosopher's fancy. They indicate the vision that a systematic intellect obtains of the universal becoming when regarding it by means of snapshots, taken at intervals, of its flowing. So that, even to-day, we shall philosophize in the manner of the Greeks, we shall rediscover, without needing to know them, such and such of their general conclusions, in the exact proportion that we trust in the cinematographical instinct of our thought.

(1922: 332|333; 1998: 315||316. Copied from Project Gutenberg)

 

 

 

 

 

Texts:

 

Bergson, Henri. 1941. L’évolution créatrice. Paris: Quadridge / Presses Universitaires de France.

Text available at:

http://catalogue.bnf.fr/ark:/12148/cb372376370

Text copied from the 1907 edition, available at:

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

 


Bergson, Henri. 1922. Creative Evolution. Transl. Arthur Mitchell. London: MacMillan and Co.

Available online at:

http://www.archive.org/details/creativeevolutio00berguoft

Text copied from the 1911 edition, available at:

http://www.gutenberg.org/ebooks/26163

 


Bergson, Henri. 1998. Creative Evolution. Transl. Arthur Mitchell. Mineola, New York: Dover.

 

 

 

Also mentioned:

 

Edwards & Penney. Calculus. New Jersey: Prentice Hall, 2002.

 

Évellin, François. Infini et quantité: Étude sur le concept de l’infini en philosophie et dans les sciences. Paris: Librairie Germer Baillière, 1880.

Available online at:

http://www.archive.org/details/infinietquantit00evelgoog

 

Leibniz. Philosophical Papers and Letters. Ed. & Transl. Leroy E. Loemker. Dordrecht: D. Reidel Publishing Company, 1956.

 

McCloud, Scott. Understanding Comics: The Invisible Art. Northampton, Mass.: Kitchen Sink Press, 1993.

 

 

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