30 Dec 2009

Deleuze Cinema Update: Deadly Forking. Joseph Mankiewicz. Cleopatra


by Corry Shores
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Subjective Multiplicity §33. Ch.2.Duration as Immediate Datum. Bergsonism. Deleuze

by Corry Shores
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[The following summarizes parts of Deleuze's Bergsonism. My commentary is in brackets. Paragraph subheadings are my own.]



Gilles Deleuze

Le bergsonisme
Bergsonism

Ch.2
La Durée comme donné immédiate
Duration as Immediate Datum


Previously Deleuze discussed Bergson's notion of objectivity. Something is an object when this happens: we divide it, and both its parts share the same nature. Extending things have this property. We see this exemplified with numbers, which maintain their homogeneous divisibility no matter how many time we divide them.


§33 Subjective Multiplicity

Now, if objectivity is divisible into parts, does that mean that subjectivity involves indivisibility? It seems not. In order for us to have a pure, indivisible subjective state, it would need to be simple rather than complex. For otherwise, we could decompose it into parts. In order to have such a state, it would need to be 'realized,' which means that consciousness would have to have a distinct perception it [perhaps this is because a feeling which is not a part of our consciousness would then not be a conscious state, which is what is under consideration here]. However, when we combine our perception of the state with the state itself, we now have a compound. Bergson writes [and Deleuze quotes]:

a complex feeling will contain a fairly large number of simple elements ; but, as long as these elements do not stand out with perfect clearness, we cannot say that they were completely realized, and, as soon as consciousness has a distinct perception of them, the psychic state which results from their synthesis will have changed for this very reason" (Bergson, Time and Free Will, 84a, see §55).

So no matter what, states of consciousness are complex. If we had a simple state, we might divide it into parts that were of the same kind. But when we split complex states, we obtain parts that are of different natures. Hence it is not that conscious duration is indivisible. In fact, it is. Only, each time it divides, it changes in kind. In this way it is a multiplicity [see this entry for Riemann's influence on Bergson's notion of multiplicity].

So we may distinguish here two types of multiplicities: 1) Numerical multiplicities retain the same nature with each division; 2) Non-numerical multiplicities change in kind with each division.

Bergson explains in §75 of Time and Free Will that we need to distinguish same and other when differentiating qualitative from quantitative multiplicities. First recall Bergson's example of the bell tolling the time while he is engrossed in writing book [See §77, also see §57]. While writing, he did not consciously separate each sound-image of the bell and juxtapose them so that they may be counted. However, hearing four bells, for example, has a certain feeling to it, and this feeling is different from when we hear three or five bells. What we come to count begins first as a feeling. Hence Bergson says that qualitative multiplicities contain number only potentially. [Here Deleuze probes deeper into Bergson's insight and distinguishes other from several. At the basis of Deleuze's idea is that there can be differences that do not immediately express number. So along these lines, we can have an other without there being two things. In other words, we might secondarily come to count and say there are two different things. But primarily these differences were expressed without there firstly being a quantity of two things. Rather, difference itself expresses itself fundamentally. So something can be other to something else, without either being one thing and both being two things. This makes sense when we consider qualitative differences, which are of different kinds, and hence are not inherently grouped together or homogenized to each other in a way that they may be counted as each being one of the same category. Also recall Bergson's examples of the shepherd counting his sheep, in §51 and §52. The shepherd might consider each sheep individually. But he might also disregard their individual differences. This way, he can count them one-by-one, because they are all considered just sheep and no longer unique individuals. So when we see the sheep as individuals, they are different and other to one another, but not yet numbering anything. This is like Bergson's tolling-bell example. We feel numbers before we count them. This is also why for example merchants subtract a cent from a price: 9.99 feels different (and better) than 10.00 (also see §75). In the case of the bell-tolls, four tolls feels different than three tolls, even before we know the quantity of each. We often think that when one thing is different from another, there must be two things. Yet, consider conscious states, at least. In the first place they express difference, and only secondarily do they express there being two distinct and countable different states. You can have otherness without numerical difference. Sometimes it is said that two coke bottles for example are numerically different but qualitatively identical. But two consciousness states are qualitatively different without also being numerically different. As Deleuze writes,] "There is other without there being several; number exists only potentially / Il y a autre, sans qu'il y ait plusieurs; nombre seulement en puissance" (42d/36a).

Now, consciousness is always a continuous multiplicity. And duration is thoroughly heterogeneous. So as it flows, no instant is qualitatively the same as any other instant. Hence duration is actual so long as there is differentiation. And whenever there is differentiation, there is multiplicity. And when there is multiplicity, there is potentially or virtually number. Deleuze writes,

the subjective, or duration, is the virtual. To be more precise, it is the virtual insofar as it is actualized, in the course of being actualized, it is inseparable from the movement of its actualization. For actualization comes about through differentiation, through divergent lines, and creates so many differences in kind by virtue of its own movement. Everything is actual in a numerical multiplicity; everything is not "realized," but everything there is actual. (42-43)

En d'autres termes, le subjectif, ou la durée, c'est le virtuel. Plus précisément, c'est le virtuel en tant qu'il s'actualise, en train de s'actualiser, inséparable du mouvement de son actualisation. Car l'actualisation se fait par différenciation, par lignes divergentes, et crée par son mouvement propre autant de différences de nature. Tout est actuel dans une multiplicité numérique : toute n'y est pas « réalisé », mais tout y est actuel, il n'y a de rapports qu'entre actuels, et de différences, que de degré. (36a.c)

In a virtual multiplicity, you do not yet actually have numerically distinct things. However, in a numerical multiplicity, all the things are actual, and they differ in degree (being more or less). Yet a non-numerical multiplicity, like duration and subjectivity, "plunges into another dimension, which is no longer spatial and is purely temporal: It moves from the virtual to its actualization, it actualizes itself by creating lines of differentiation that correspond to its differences in kind" (43b). We noted that such multiplicities are heterogeneous. And [because they are not numerically distinguishable, they 'melt' into each other and hence] they are continuous multiplicities. As well, [because dividing a virtual multiplicity requires a secondary act, they are not primarily complex aggregates made-up of actual parts, and thus primarily] they are simple.

Now, if duration is thoroughly heterogeneous, that means no one instant is like its immediate neighbor. That would seem to imply that duration is discontinuous. However, [we see that one instant cannot be seen as being numerically distinct from one of its neighbors. Hence in a way,] they are continuously different. So we might normally think that Bergson would encounter contradictions by saying that duration is both heterogeneous and yet continuous. However we see he has here no problem reconciling the two. (43b)



Bergson, Henri. Time and Free Will: An Essay on the Immediate Data of Consciousness, Transl. F. L. Pogson, (New York: Dover Publications, Inc., 2001).

Available online at:http://www.archive.org/details/timeandfreewill00pogsgoog



Deleuze, Gilles. Bergsonism. Transl. Hugh Tomlinson and Barbara Habberjam. New York: Zone Books, 1991.Deleuze, Gilles.

Deleuze, Gilles. Le bergsonisme. Paris : Presses Universitaires de France, 1966.



Objective Divisibility §32. Ch.2.Duration as Immediate Datum. Bergsonism. Deleuze

[The following summarizes parts of Deleuze's Bergsonism. My commentary is in brackets. Paragraph subheadings are my own.]



Gilles Deleuze

Le bergsonisme
Bergsonism

Ch.2
La Durée comme donné immédiate
Duration as Immediate Datum


[For Bergson, duration changes in kind when we divide it. This is because it is thoroughly heterogeneous. But duration does not extend like space does. So we do not have half a duration when we split it. Rather, we have wholly different durations. There are never any self-same phases throughout a duration. It is continuously heterogeneous. (Consider seeing this entry. It discusses Riemann's influence on Bergson's notion of continuous multiplicity.]


§32 Objective Divisibility

[Duration is subjective. But we are also conscious of objective things in the world around us. And these extend in homogeneous space, unlike duration. Hence,] objective things (objects) are divisible, and when we divide them, they do not change in kind. Hence objectivity is what divides by differences in degree. [Deleuze cites Matter and Memory p.273. (Reference to be added later). Bergson writes here: "As long as we are dealing with space, we may carry the division as far as we please; we change in no way, thereby, the nature of what is divided. This is because space, by definition, is outside us; it is because a part of space appears to us to subsist even when we cease to be concerned with it; so that, even when we leave it undivided, we know that it can wait, and that a new effort of our imagination may decompose it when we choose. As, moreover, it never ceases to be space, it always implies juxtaposition and consequently possible division. Abstract space is, indeed, at bottom, no thing but the mental diagram of infinite divisibility. But with duration it is quite otherwise" (Bergson 273c.d).]

Numbers are the model for those things that can divide without changing their nature. Like numbers, objects are numerically divisible into units. Hence an object is a "numerical multiplicity / multiplicité numérique" (41d/34d). In a sense, such numerically divisible things already have the division implied within them. So Deleuze writes: "number has only differences in degree, or that its differences, whether realized or not, are always actual in it / le nombre n'a que des différences de degré, ou que ses différences, réalisées ou non, sont toujours actuelles en lui" (41d/34-35).

Something that does not extend also does not have parts and cannot be divided into parts. So what about the basic numerical units? If they are unities, then can they be divisible? If not, then they would have different degrees of difference within them. Rather, perhaps they might be like heterogeneities which change kind if they are divided. Consider for example when we add two units together. We regard each of these units as indivisible wholes that are combined with each other. So are such units indivisible? But later, we might divide that doubled unit by four. By doing so, we divide each of the previous wholes into halves. So in this way, the unity of the unit is provisional. Bergson says it obtains its unity in the mental act that regards it as such, for the temporary purpose of addition. But then for the purpose of division, the mind then regards the unit as divisible. Bergson writes in Time and Free Will §54, [underlined are the parts that Deleuze quotes]:

by looking more closely into the matter, we shall see that all unity is the unity of a simple act of the mind, and that, as this is an act of unification, there must be some multiplicity for it to unify. No doubt, at the moment at which I think each of these units separately, I look upon it as indivisible, since I am determined to think of its unity alone. But as soon as I put it aside in order to pass to the next, I objectify it, and by that very deed I make it a thing, that is to say, a multiplicity. To convince oneself of this, it is enough to notice that the units by means of which arithmetic forms numbers are provisional units, which can be subdivided without limit, and that each of them is the sum of fractional quantities as small and as numerous as we like to imagine. How could we divide the unit, if it were here that ultimate unity which characterizes a simple act of the mind? How could we split it up into fractions whilst affirming its unity, if we did not regard it implicitly as an extended object, one in intuition but multiple in space? You will never get out of an idea which you have formed anything which you have not put into it; and if the unity by means of which you make up your number is the unity of an act and not of an object, no effort of analysis will bring out of it anything but unity pure and simple. No doubt, when you equate the number 3 to the sum of 1 +1 + 1, nothing prevents you from regarding the units which compose it as indivisible: but the reason is that you do not choose to make use of the multiplicity which is enclosed within each of these units. Indeed, it is probable that the number 3 first assumes to our mind this simpler shape, because we think rather of the way in which we have obtained it than of the use which we might make of it. But we soon perceive that, while all multiplication implies the possibility of treating any number whatever as a provisional unit which can be added to itself, inversely the units in their turn are true numbers which are as big as we like, but are regarded as provisionally indivisible for the purpose of compounding them with one another. Now, the very admission that it is possible to divide the unit into as many parts as we like, shows that we regard it as extended. (Bergson Time and Free Will 80d.82b)



Bergson, Henri. Time and Free Will: An Essay on the Immediate Data of Consciousness, Transl. F. L. Pogson, (New York: Dover Publications, Inc., 2001).

Available online at: http://www.archive.org/details/timeandfreewill00pogsgoog



Deleuze, Gilles. Bergsonism. Transl. Hugh Tomlinson and Barbara Habberjam. New York: Zone Books, 1991.Deleuze, Gilles.

Deleuze, Gilles. Le bergsonisme. Paris : Presses Universitaires de France, 1966.





24 Dec 2009

Bergson's Einstein §74. Ch.4.One or Many Durations? Bergsonism. Deleuze

[The following summarizes parts of Deleuze's Bergsonism. My commentary is in brackets. Paragraph subheadings are my own.]



Gilles Deleuze

Le bergsonisme
Bergsonism

Ch.4.
Une ou plusieurs durées ?
One or Many Durations?


Previously Deleuze discussed Bergson's position on whether there is just one duration or many of them. Bergson often describes duration as a heterogeneous qualitative multiplicity. So we might expect him to say that there are many durations. Oddly, Bergson holds that there is just one duration. This is his monist hypothesis of time.



§74 Bergson's Einstein

Deleuze wonders how we might account for Bergson's surprising position. It is the product of Bergson's confrontation with Einstein's relativity theory. Both Einstein and Bergson draw their notion of multiplicity from Riemann. However, they come to opposing positions regarding whether there is a plurality or unity of time.

Deleuze will review Bergson's summary of Einstein's relativity theory. [It can be found in greater detail in the first chapter of Bergson's Duration and Simultaneity].

We in the first place conceive of bodies in motion. [Their movement is reciprocal. While in a steadily moving train, we walk around and feel as though we are on stable ground. But we might observe through the window a person along the track rapidly coming-and-going. For us on the train, the person is in motion. But for this same person observing the train from the ground, the locomotive is the moving body, while she remains immobilized, standing on firm ground. This can be explained using Newtonian physics. But when dealing with the speed of light, we encounter a problem. First consider a man walking on a boat. He feels himself travel at the speed of his gait. But a woman on the docks sees him travel not just his walking speed, but also she adds to that the speed of the boat. So the walking-man's speed depends on the perspective of reference. This is not so for light. It goes the same speed for the person on the boat as it does for the person observing from the dock. But this is strange, because for the man on the boat, the light goes a certain distance. But for the woman on the dock, it goes a different distance; for, the boat moves underneath the light, in a sense. To explain how the light goes the same speed for different distances, Einstein theorized that] time dilates and space contracts [on a moving body, from the perspective of the reference position, which is provisionally considered as immobile, so that accurate calculations are made that will accord with all other moving systems, which also must take this phenomenon into account. But as a result of the distortions in time, what seems simultaneous on the boat is really not so from the perspective of the woman on the dock. Hence] simultaneities in mobile systems are not so for fixed ones. Einstein also theorized that motion, rest, and acceleration are all relative. [So for the woman on the dock, the boat-man is moving and is wrong about his simultaneities. But for him, his own boat is stable, and the dock moves away from him. So for the boat observer, what seems to be simultaneities on the dock for the dock person are not simultaneities for the boat person. Thus,] "these contractions of extensity, these dilations of time, these ruptures of simultaneity become absolutely reciprocal" (Deleuze 79bc). [So we have one time for the boat person, which he thinks differs for the time on the dock. Yet the person on the dock has her own time, which likewise she thinks differs from the boat's time. Hence] "there would be a multiplicity of times, a plurality of times, with different speeds of flow, all real, each one peculiar to a system of reference" (79c).

Now, if we want to situate a point somewhere, we need to indicate both its spatial and temporal position. So the only unity of time is the fourth temporal dimension united with its spatial dimensions [see this entry on the Mankowski diagrams for this correlation between time and space]. But this unity does not hold universally throughout the cosmos. The relations between time and space for moving bodies depend upon the relative speed of the observer. So in this way "It is precisely this Space-Time block that actually divides up into space and into time in an infinity of ways, each one peculiar to a system" (79d). [All of this is Bergson's summary of Einstein's theory of relativity. Bergson builds from the same premises to conclude that there is only one duration, and not the plurality that Einstein posits].


Deleuze, Gilles. Bergsonism. Transl. Hugh Tomlinson and Barbara Habberjam. New York: Zone Books, 1991.Deleuze, Gilles.

Deleuze, Gilles. Le bergsonisme. Paris : Presses Universitaires de France, 1966.

Entry Directory. Bergsonism. Deleuze




Gilles Deleuze

Le bergsonisme
Bergsonism

Ch.2.
La durée comme donnée immédiate
Duration as Immediate Datum






Ch.4.
Une ou plusieurs durées ?
One or Many Durations?












Deleuze, Gilles. Bergsonism. Transl. Hugh Tomlinson and Barbara Habberjam. New York: Zone Books, 1991.Deleuze, Gilles.

Le bergsonisme. Paris : Presses Universitaires de France, 1966.


One or Many Hypotheses of Duration? §73. Ch.4.One or Many Durations? Bergsonism. Deleuze


by Corry Shores
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[The following summarizes parts of Deleuze's Bergsonism. My commentary is in brackets. Paragraph subheadings are my own.]



Gilles Deleuze

Le bergsonisme
Bergsonism

Ch.4.
Une ou plusieurs durées ?
One or Many Durations?


§73
One or Many Hypotheses of Duration?

Deleuze wonders if for Bergson, there is one duration shared by all consciousnesses, or if there are as many durations as there are minds. Deleuze notes that in Duration and Simultaneity, Bergson addresses three possibilities. [For more detail, see §35 of Duration and Simultaneity]

1) Generalized Pluralism
According to this theory, each conscious being experiences a rhythm of duration; yet, every individual experiences durational rhythm in their own unique way. Hence this would be a radical multiplicity of Time. Bergson claims he once advanced this hypothesis. ["We once advanced a theory of that kind with regard to living species. We distinguished durations of higher and lower tension, characteristic of different levels of consciousness, ranging over the animal kingdom" (Bergson, DS 31), again, see §35 of Ch.3]. Yet, Bergson goes on to say that he did not then realize that we could as well extend this hypothesis to the material world, such that it posits different durations for the many material things in the world around us. This is the basis for the next hypothesis.

2) Limited Pluralism
Under this view, we would not say that the things outside us experience a duration that is absolutely different from our own. Rather, exterior things participate in our duration and give it emphasis. [For more on this participation, see the pendulum example in Time and Free Will §68]. But the way they partake in our conscious experience of duration is mysterious. This is because there is some "inexpressible ground" to external objects [§144] that is responsible for the conversion from their exterior non-durational character into our conscious awareness of them changing through time. So this thesis is partly a condensation of ideas from Time and Free Will. In Creative Evolution Bergson says that things participate in our consciousness on account of all things belonging to the Whole of the universe [reference to be added later]. Nonetheless, the nature of the Whole along with our relation to it remains mysterious. Thus Bergson suggests another hypothesis.

3) Monism
"There is only a single time, a single duration, in which everything would participate, including our consciousnesses, including living beings, including the whole material world" / "il n'y aurait qu'un seul temps, une seule durée, auquel tout participerait, y compris nos consciences, y compris les vivants, y compris le tout du monde matériel" (Deleuze 78c/78c).

In footnote 13 [first note of page 78 in the French text], Deleuze recognizes that in Matter and Memory, Bergson speaks of a plurality of rhythms [reference to be added later]. Different minds experience different 'tensions.' Bergson writes:

In reality there is no one rhythm of duration; it is possible to imagine many different rhythms which, slower or faster, measure the degree of tension or relaxation of different kinds of consciousness, and thereby fix their respective places in the scale of being. To conceive of durations of different tensions is perhaps both difficult and strange to our mind, because we have acquired the useful habit of substituting for the true duration, lived by consciousness, an homogeneous and independent Time; but, in the first place, it is easy, as we have shown, to detect the illusion which renders such a thought foreign to us, and, secondly, this idea has in its favour, at bottom, the tacit agreement of our consciousness. Do we not sometimes perceive in ourselves, in sleep, two contemporaneous and distinct persons of whom one sleeps a few minutes, while the other's dream fills days and weeks? And would not the whole of history be contained in a very short time for a consciousness at a higher degree of tension than our own, which should watch the development of humanity while contracting it, so to speak, into the great phases of its evolution? (275d)

En réalité, il n'y a pas un rythme unique de la durée; on peut imaginer bien des rythmes différents, qui, plus lents ou plus rapides, mesureraient le degré de tension ou de relâchement des consciences, et, par là, fixeraient leurs places respectives dans la série des êtres. Celte représentation de durées à élasticité inégale est peut-être pénible pour notre esprit, qui a contracté l'habitude utile de substituer à la durée vraie, vécue par la conscience, un temps homogène et indépendant; mais d'abord il est facile, comme nous l'avons montré, de démasquer l'illusion qui rend une telle représentation pénible, et ensuite cette idée a pour elle, au fond, l’assentiment tacite de notre conscience. Ne nous arrive-t-il pas de percevoir en nous, pendant notre sommeil, deux personnes contemporaines et distinctes dont l'une dort quelques minutes tandis que le rêve de l'autre occupe des jours et des semaines? Et l'histoire tout entière ne tiendrait-elle pas en un temps très court pour une conscience plus tendue que la nôtre, qui assisterait au développement de l'humanité en le contractant, pour ainsi dire, dans les grandes phases de son évolution? (231b.d)

However, Deleuze explains that this multiplicity of rhythms comes to be termed the plurality of fluxes in Duration & Simultaneity. And we shall see that these fluxes are unified into one duration.

Yet, this is surprising. We would have expected from Bergson that he would consider duration to be a multiplicity. For in Time and Free Will he characterizes duration as a thoroughly heterogeneous multiplicity [See for example §65, §68, and §69].




Deleuze, Gilles. Bergsonism. Transl. Hugh Tomlinson and Barbara Habberjam. New York: Zone Books, 1991.Deleuze, Gilles.

Le bergsonisme. Paris : Presses Universitaires de France, 1966.





23 Dec 2009

Change without Duration. §144. In the External World We Find Not Duration but Simultaneity. Ch2. Time and Free Will. Bergson


by Corry Shores
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Change without Duration


Henri Bergson

Essai sur les données immédiates de la conscience
Time and Free Will: An Essay on the Immediate Data of Consciousness

Part CXVI: No Duration in the External World

§144 In the External World We Find Not Duration but Simultaneity




Bergson asks, what sort of duration exists outside us? He replies that there is merely the present, or we could say, simultaneity.

Now, exterior things change. And there are moments to these changes.

[But what makes one moment succeed another is that the previous one was retained and found to come before the following moment. Yet, this requires there be some consciousness to perform that retention. Hence] the moments of the changes in external things do not succeed each one another. They fall in succession only "for a consciousness which keeps them in mind" (227a).

When we observe the world around us at a given moment, we see "a whole system of simultaneous positions; of the simultaneities which have preceded them nothing remains" (227ab). [Yet it is common to think of succeeding moments falling along a line of time. This makes a prior moment and a later one coincide with each other on that same line. Hence] "To put duration in space is really to contradict oneself and place succession within simultaneity" (227b). Because external things do not have moments which succeed each other, we cannot say that they endure through time. Instead, there is something mysterious about external things which makes the matter more complex. Our own mind experiences a flowing duration. When we view external things, there will be different moments of our inner duration during which we are perceiving the objects. Each moment of our inner consciousness will always correspond to a perception of change in the external object we are observing. Bergson says that there is something we cannot grasp about external objects which causes us to perceive them as changing durationally, even though they do not endure.

Hence we must not say that external things endure, but rather that there is in them some inexpressible reason in virtue of which we cannot examine them at successive moments of our own duration without observing that they have changed. (227bc, boldface mine)

Il ne faut donc pas dire que les choses extérieures durent, mais plutôt qu'il y a en elles quelque inexprimable raison en vertu de laquelle nous ne saurions les considérer à des moments successifs de notre durée sans constater qu'elles ont changé. (175a.b, boldface mine)

We would only say the exterior changes involve succession only if we give succession a different meaning. [Bergson notes that science and common sense agree on this meaning. Reference to be added later].

In consciousness, however, moments melt into each other. [See §64 and §66 for description of how the notes of a melody melt into each other]. Bergson writes then,

Thus in consciousness we find states which succeed, without being distinguished from one another; and in space simultaneities which, without succeeding, are distinguished from one another, in the sense that one has ceased to exist when the other appears. Outside us, mutual externality without succession; within us, succession without mutual externality. (227c.d)

Ainsi, dans la conscience, nous trouvons des états qui se succèdent sans se distinguer ; et, dans l'espace, des simultanéités qui, sans se succéder, se distinguent, en ce sens que l'une n'est plus quand l'autre paraît. — En dehors de nous, extériorité réciproque sans succession : au dedans, succession sans extériorité réciproque. (175bc)




[Directory of other entries in this series.]


Images from the pages summarized above, in the English Translation [click on the image for an enlargement]:




Images from the pages summarized above, in the original French [click on the image for an enlargement]:







Bergson, Henri. Time and Free Will: An Essay on the Immediate Data of Consciousness, Transl. F. L. Pogson, (New York: Dover Publications, Inc., 2001). Available online at: http://www.archive.org/details/timeandfreewill00pogsgoog


Bergson, Henri. Essai sur les données immédiates de la conscience. Originally published Paris: Les Presses universitaires de France, 1888. Available online at: http://www.archive.org/details/essaisurlesdonn00berguoft