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Gilles Deleuze
Différence et répétition
Difference and Repetition
Chapitre II: La répétition pour elle-même
Chapter II: Repetition for Itself
First paragraph of the chapter.
Deleuze begins with one of Hume's theses regarding repetition. To understand this notion, we need to review Hume's theory of causal relations. We begin with one of his examples.
Some cannot resist fire's seduction. What power does this beauty possess? We reach into it. And we burn. Yet we try again. Touch & Burn. Touch & Burn. Touch & Burn. Touch... AB, AB, AB, A.... Soon our hands become disinclined to touch the fire. As they near it, our minds cannot but invoke the past impressions of heat.
'Tis therefore by EXPERIENCE only, that we can infer the existence of one object from that of another. The nature of experience is this. We remember to have had frequent instances of the existence of one species of objects; and also remember, that the individuals of another species of objects have always attended them, and have existed in a regular order of contiguity and succession with regard to them. Thus we remember, to have seen that species of object we call flame, and to have felt that species of sensation we call heat. Without any farther ceremony, we call the one cause and the other effect, and infer the existence of the one from that of the other. In all those instances, from which we learn the conjunction of particular causes and effects, both the causes and effects have been perceiv'd by the senses, and are remember'd. But in all cases, wherein we reason concerning them, there is only one perceiv'd or remember'd, and the other is supply'd in conformity to our past experience. (Hume, A Treatise of Human Nature, 87bc)
This relation is their CONSTANT CONJUNCTION. (§205, 87c)
Each repetition of the constantly conjoined objects leaves an entirely new impression. For there will always be slight differences even between the most similar repeated causal pairings, if only on account of their different places in the succession.
the repetition is not in every particular the same, but produces a new impression, and by that means the idea. (§333, 155d)
Ideas are merely faint remnants of sense-impressions. So each impression is already an idea [§§11-17]. When we continuously find two impressions taken together, like fire and heat, their ideas become conjoined in the mind as well. Thus when we sense one, it may evoke the idea of the other [§18].
From this constant conjunction of resembling perceptions I immediately conclude, that there is a great connexion betwixt our correspondent impressions and ideas, and that the existence of the one has a considerable influence upon that of the other. Such a constant conjunction, in such an infinite number of instances, can never arise from chance; but clearly proves a dependence of the impressions on the ideas, or of the ideas on the impressions. (4d)
The constant conjunction of our resembling perceptions, is a convincing proof, that the one are the causes of the other; and this priority of the impressions is an equal proof, that our impressions are the causes of our ideas, not our ideas of our impressions. (§18, 5a)
There enters nothing into this operation of the mind but a present impression, a lively idea, and a relation or association in the fancy betwixt the impression and idea (§234, 101d)
After many repetitions of AB together, soon we need only A to infer the existence of B.
For after a frequent repetition, I find, that upon the appearance of one of the objects, the mind is determin'd by custom to consider its usual attendant, and to consider it in a stronger light upon account of its relation to the first object. 'Tis this impression, then, or determination, which affords me the idea of necessity. (§333, 156 emphasis mine)
Each time we experience the conjunction of Fire & Heat (A & B), the idea becomes more vivid in our minds. It is like we take a blade and score the image deeper in our minds each time we experience it. In fact, Hume has us envision that it is as though our imaginations take a pencil and tally the 'score' for each time the two are found conjoined. That way, if there are exceptions, then we may still infer the idea of B from the sensation of A.
These agreeing images unite together, and render the idea more strong and lively, not only than a mere fiction of the imagination, but also than any idea, which is supported by a lesser number of experiments. Each new experiment is as a new stroke of the pencil, which bestows an additional vivacity on the colours without either multiplying or enlarging the figure. (§298, 135a, emphasis mine)
Each repeated instance adds a force or power of our inference from one to the other.
The efficacy or energy of causes is neither plac'd in the causes themselves, nor in the deity, nor in the concurrence of these two principles; but belongs entirely to the soul, which considers the union of two or more objects in all past instances. 'Tis here that the real power of causes is plac'd along with their connexion and necessity. (§355, 166b)
So even though each instance of AB is different, they still unite into a common impression. To grasp this, Hume has us imagine a dice throw. In the past, we have found that we have rolled each number just as many times as the others. So the force of our tendency to call to mind each of the six numbers is equally the same. Then Hume has us imagine that we place one symbol on the first four numbers, and another symbol on the last two. We will then be inclined to bet on the symbol for the first four numbers. This is not because we use our reason to calculate the probabilities. Rather, because the symbol is the same on each, all those images combine their forces of association.
'Tis evident that where several sides have the same figure inscrib'd on them, they must concur in their influence on the mind, and must unite upon one image or idea of a figure all those divided impulses, that were dispers'd over the several sides, upon which that figure is inscrib'd. (129d, emphasis mine)
...
'tis evident, that the impulses belonging to all these sides must re-unite in that one figure, and become stronger and more forcible by the union. (§287, 130a emphasis mine)
The reason that the contraction of similar instances increases the force of our tendency to associate them is because their vivacity increases with a greater number of contracted similar instances.
The vivacity of the idea is always proportionable to the degrees of the impulse or tendency to the transition; and belief is the same with the vivacity of the idea. (§287, 130b emphasis mine)
So not only do all the A's contract with the other A's, and the B's contract with the other B's, but also all the A's contract with the B's. Now clearly each time we experience a repetition of AB, this changes the way our mind's operate. For, each recurrence increases our tendencies of association. Nonetheless, each instance has no effect on the other repetitions.
To illustrate this last point, Hume has us imagine that we see a billiard ball strike another one. Motion communicates. We see recurrent instances of one ball hitting another, and causing the second one to fly-off. In our childhood we witnessed this. And many years later today we see it as well. Each is an instance of causation. But consider when it happened many years ago. Did it have any causal effect on the instance we see today? No. The balls settle. Then we strike them again. One instance has no influence on the other repetitions.
These impulses have no influence on each other. They are entirely divided by time and place; and the one might have existed and communicated motion, tho' the other never had been in being. (§350, 164bc)
One repeated instance can exist independently of the other. Hence:
'Tis certain that this repetition of similar objects in similar situations produces nothing new either in these objects, or in any external body. (§350, 164b, boldface mine)
Deleuze's offers his formulation of Hume's thesis:
Repetition changes nothing in the object repeated, but does change something in the mind which contemplates it. (Deleuze 70a)
La répétition ne change rien dans l'objet qui se répète, mais elle change quelque chose dans l'esprit qui la contemple. (98b)
So each day, there are new instances of billiard balls colliding. But the collisions of yesterday, or the previous game, have no influence on each other. There is "a perfect independence on the part of each presentation" (70a).
Now, if something is a repetition of something else, then it is not simultaneous. It must come after, otherwise it is a concurrence and not a repetition. [Deleuze calls this the "rule of discontinuity or instantaneity in repetition." He might be referring to Leibniz's Law of Continuity. For example, Leibniz uses his law to refute Descartes' second law of nature. Descartes says that if two unequal bodies collide, the smaller will deflect and the larger will continue in its direction. This might be easy to imagine when the bodies are very different in mass. But Leibniz has us think of the bodies beginning as very different, and then gradually they become equal to each other. When they are equal they both deflect. When one is only very slightly less than the other, still wouldn't both deflect? In fact they do. Leibniz Law of Continuity says that as the conditions change continuously, the results should change continuously also. Thus as we bring the bodies' masses closer to each other, their results should gradually come closer to the resemble the result when they are equal. Leibniz formulation is: when two hypothetical conditions or two different data continuously approach each other until the one at last passes into the other, then the results sought for must also approach each other continuously until one at last passes over into the other, and vice versa. (Leibniz, "Critical Thoughts on the General Part of the Principles of Descartes," 397d)
Clearly Deleuze is speaking of something quite different. However, he does seem to be saying that one event does not approach the other until it at last passes into the other. This would be to conceive time as continuous. But as we will see, Deleuze's theory of phenomemal contraction is based on a conception of time as made-up of discrete parts. Hence there is no law of continuity to temporal events, but instead there is a law of discontinuity.] As Hume explains,
It is a property inseparable from time, and which in a manner constitutes its essence, that each of its parts succeeds another, and that none of them, however contiguous, can ever be co-existent. For the same reason, that the year 1737 cannot concur with the present year 1738. every moment must be distinct from, and posterior or antecedent to another. (§69, 31b)
Deleuze will further explain Hume's thesis that repetition changes nothing in the repeated thing, but only changes the mind. To do so, he will make use of Leibniz concept of mens momentanea, which we can translate as momentary mind, momentaneous mind, or if we want, instantaneous mind. This concept is based on Leibniz theory of conatus. To grasp Leibniz' idea, we need to first understand these basic concepts. [After this enumeration we explain them in more detail.]
1) There are things that extend, namely, time and distance (extension itself). So there are durations that extend and objects that extend. Also, there are motions that extend in both time and distance jointly. Time, distance, and motion all have a beginning. But that beginning itself does not extend. In fact, motion first begins without extending in time or distance. But for something's motion to begin extending through time and distance, it must have a tendency. This tendency is not extensive. It is an internal tending that if released would extend. But by itself it just is an internal tendency that has not been externalized. In other words, it is an intensity implicit in the motional body, and it has not yet been made explicit as time and distance extensions. These intensities are what Leibniz calls conatus.
2) A conatus of one body may transfer into another body. Also, there may be more than one contrary conatus in a single body in an instant (just as we might imagine a tug-of-war that pulls the rope in two directions at once).
3) Although there can be more than one conatus at a time in a single body, they can only reside together for just an inextensive and indivisible instant of time (a temporal intensity).
4) This is the case for bodies. But minds have memory. And sensation can be viewed as a body striking our sense organs. So we receive conatuses. They impress upon our minds. These impressions accumulate. So our minds can contain contrary conatuses for longer than an instant. But the body can only retain them for just a moment. For that reason, bodies are momentary minds, or mens momentanea.
Beginnings are Intense
We first explain how Leibniz concludes that beginnings do not extend.
He notes that if something extends, then it extends from one end to another end. So it has a beginning and an end. He then asks if some extended thing's beginning is itself extended. No, he answers, beginning's do not extend.
In short, his explanation is that
a) extended things have extensive parts; but
b) a beginning does not have parts; therefore
c) a beginning cannot be an extended thing.
To illustrate, he has us first imagine line ab.
Line ab extends. It has a beginning a and an end b. It must also have a middle then. We will find middle-point c half-way between the endpoints.
This creates another extended segment, line ac. It too must have a middle-point. So half-way between a and c we place point d.
Now we have extended-line ad. So let's place point e in the middle.
We can imagine placing middle-points repeatedly, moving toward a.
Now, if a line has parts, then only one of them can be a beginning. And the beginning itself cannot have more parts within it. We are taking the left-side of the line to be its beginning. And we see there are many parts on that left side. So there are many candidates for the beginning. To see which one is the beginning, we need to see that
1) it is on the lefter-most side of the line, and
2) it does not have any more parts within it. For, if it did, then the beginning is to be found in the lefter-most part within that composite part. So the whole composite piece cannot be the beginning, because it has parts, and one of those inner parts itself is exclusively the beginning.
So we may use this criteria to devise a test. We
I)
Examine a candidate.
II)
See if we can remove from it a part on the right-side.
IIIa)
If we can remove a part on the right-side, then the beginning is to be found in the left-side part.
IIIb)
If we try to remove anything from the candidate, but find that any possible removal leaves nothing left, then it must be the beginning. For, it is on the lefter-most side and it is not made-up of parts.
Let's put this criteria in practice on our divided line:
Our first candidate is line ac. We can remove from the right-side line dc, which leaves line ad. So the beginning must lie in ad.
Now ad is our candidate. We remove ed from the right, and ae remains. So ae is our new candidate. We keep repeating this process.
But so long as our beginning is an extended part of the line, it will be divisible. However, any divisible piece cannot itself be the beginning. Thus something's beginning cannot be extensive.
So nothing is a beginning from which something on the right side can be removed. But that from which nothing extended can be removed is unextended. Therefore the beginning of body, space, motion or time – namely, a point, conatus, or instant – is either nothing which is absurd, or unextended, which was to be demonstrated. (Leibniz, Theory of Abstract Motion, 140a, emphasis mine)
Now let's imagine there is a ball upon a hilltop. It would roll down the hillside, except we rest our hand on it to keep it in place. The ball extends in space. So we know that it's front side has an inextensive beginning. Now we lift our hand quickly. The ball remains paused it seems for an instant before beginning to roll down. While supporting the ball with our hands, we felt that it "wanted" to roll down the hill. It had a "tendency" that it kept within itself. That is to say, it had an "intensity." Recall also that the instant we lifted our hands, it sort-of paused before rolling. In fact, let's imagine the very instant we set it free. This moment is the "beginning" of that duration happening right after it is liberated from our restraint. We know already that beginnings are inextensive. This holds for time too. So we are considering the inextensive instant of time at the beginning of the ball's freedom. We also know that it had a tendency to move while we restrained it. That tendency did not go away the instant we freed the ball. So for that first instant, the ball was beginning its motion. It did not move through extensive space. But its inextensive beginning was tending forward.
Imagine that the ball were made of wood. It would be moving with so much of an intensity in that instant. But if it were made of iron, it would have been beginning its motion with an even greater internal tendency. This greater inextensive magnitude at the beginning of motion Leibniz calls conatus. In fact, conatus is both the beginning and the end of motion.
Now we need to imagine a very small wooden ball colliding with a large stationary iron ball. The wooden ball does not push through the iron ball. So at that point of collision, it seems to stop its motion. Now recall when we restrained the ball at the top of the hill. The ball did not move, but it still "wanted" or tended-towards moving through our hand. And if it were heavy enough, it would have pushed through our hand. But we kept it still while it "struggled" to move forward. The same holds for that instant when the little wooden ball impacts the large iron ball. It still is "tending" in its motion forward through the iron ball, even though it is not actually moving into the iron ball's extensive space. We know that two solid extended things cannot both be in the same place at the same time. But, recall that the edge of both balls are inextensive, so the edge of one may penetrate the edge of the other, because they never took up extended space to begin with.
Now perhaps we noticed that when the two balls collided, the larger iron ball "shuddered" or seemed to be affected somehow, even though it did not move. For, the smaller wooden ball transfers its tendency to move-forward into the larger ball. So whether we notice any movement or not, the larger ball in that instant also tended in the direction of the smaller ball's motion. The smaller body could have been a speck of dust that the breeze blows upon the steel ball. Still the dust's conatus will transfer into the larger object and cause it to tend in its motion. Only, the effect is too subtle for our senses to perceive.
So when the collision involves one moving body and one stationary body, there is only one conatus tending in one direction.
Now, suppose we had two iron balls both moving toward each other. What will happen when they collide?
Let's illustrate this event to find out. Body c and body d are moving toward each other.
And they continue toward each other.
And then they collide.
At the moment of collision, the two bodies are still
1) striving forward,
2) transferring their conatus, and thus
3) striving backwards
all in the same moment.
Hence there may be many contrary conatuses in the same body at the same time. But only for a moment, because immediately after their exchanged-conatuses are co-present, the balls bounce back away from each other, carrying the other's conatus with them.
The Intensity of Sensation
Now let's imagine that we are at the bottom of a valley. Someone rolls a ball from the hill on our right side. It impacts us. It's conatus transfers to our body, and we move slightly to the left. We keep this in mind, and stay ready for another ball to come from our right side. But that causes us to miss a ball coming from our left side. It hits us. And it transfers its conatus to our body, which lurches to the right. But now we are vigilant for balls coming from either side. Why? Because we remember the conatus moving through us right-to-left, and we also remember the conatus pushing through us from left-to-right. In other words, our mind retains both conatuses. We saw that when the two iron balls collided, there were contrary conatuses in each single ball. But this was only for an instant. After that, each ball reflects the other way. Then there is only one conatus in each. However, our mind retains contrary conatuses for longer than an instant. In fact, our memories allow us to retain such impressions for all our lives. Objects like steel balls, however, only retain multiple conatuses for just one instant. So on the one hand, bodies are like minds, because they retain tendencies. But on the other hand, they only do so momentarily. Hence they are minds for only a moment. Leibniz calls them mens momentanea, which we may translate as momentary minds. [click image to enlarge]
Deleuze evokes this idea to help us understand the role of the mind in making repetition out of difference. For, our bodies can only experience a conjunction of conatuses for an instant. If there were to be another instance of such a conjunction, then they would have to happen in another instant ["the year 1737 cannot concur with the present year 1738. every moment must be distinct from, and posterior or antecedent to another." (§69, 31b). We noted before that Deleuze calls this the "rule of discontinuity or instantaneity in repetition."] So from the perspective of our bodies, there cannot be repetition. Each impact is utterly different from all those prior to it. But our minds may retain such concurrences. So a previous one may be taken along with a present one.
Hence the present collision of billiard balls is completely different from the previous one. They have no influence on each other. One exists independently of the other. But we consider them to be the same. So for there to be a repetition, there must be an absolute difference. Otherwise there would not be another occurrence to group with the previous one.
Yet, if there are only repetitions in our minds, then there is no recurrence in itself. Rather, it seems only by means of our subjectivity that things are considered repetitions. Deleuze asks if this is repetition's "for-itself." We wonder then, is repetition merely a construction of our imaginations, or is it a real event?
Deleuze, Gilles. Différence et répétition. Paris: Presses Universitaires de France, 1968
Deleuze, Gilles, Difference & Repetition. Transl. Paul Patton. New York: Columbia University Press, 1994.
Hume, David. A Treatise of Human Nature. Ed. L.A Selby-Bigge. Oxford: Clarendon Press, 1979.
Leibniz. "Critical Thoughts on the General Part of the Principles of Descartes." in Philosophical Papers and Letters. Ed. & Transl. Leroy E. Loemker. Dordrecht: D. Reidel Publishing Company, 1956
Leibniz. "Studies in Physics and the Nature of Body. 1, The Theory of Abstract Motion: Fundamental Principles." in Philosophical Papers and Letters. Ed. & Transl. Leroy E. Loemker. Dordrecht: D. Reidel Publishing Company, 1956.
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