17 Aug 2015

Somers-Hall, (4.4), Deleuze’s Difference and Repetition, ‘4.4 First Example: Atomism as a Physical Idea (184/232–3)’, summary

by Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH and Difference and Repetition as DR.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text

Chapter 4. Ideas and the Synthesis of Difference


4.4 First Example: Atomism as a Physical Idea (184/232–3)



Brief summary:
For Deleuze, differential calculus exhibits certain critical features of “the Idea”: 1) the parts are determined through (and not prior to) their differential reciprocal relations, 2) the parts become determined only together by and as these reciprocal relations, and 3) there must be a variety of possible ways these spatio-temporal relations can manifest. Deleuze gives three examples in philosophy which seem to fulfill these criteria. The first is Epicurus’ and Lucretius’ atomistic model of the world. They say the world is made of atoms which move so fast downward through a void that their motions cannot even be perceived. And the atoms would never interact were it not for their tendency to make spontaneous deviations (clinamen) from their directly downward course, which causes them to collide into one another. Such mutually colliding atoms might continue doing so, forming a compound. Their collisions cause them somehow to appear to vibrate at a speed slower enough to be perceptible, and this is how atoms can generate the sensible qualities of the objects they compose. Thus we see how this model satisfies the three criteria for Ideas: 1) on their own, the atoms are not sensibly determinable; 2) but they can become so when they enter into differential relations with one another; and 3) there are many spatio-temporal ways they may enter into such reciprocal relations. Yet, because their relations are understood too much in terms of sensible determinations, this model does not fully exemplify Deleuze’s notion of the Idea.




As we noted before, Deleuze will give three examples of attempts “to develop a wider calculus” (143). The first is the attempt by the atomists, “notably Epicurus in his Letter to Herodotus and Lucretius in his De Rerum Natura” (143). Deleuze provides a much more elaborated version of this account in the appendix to Logic of Sense entitled, “The Simulacrum and Ancient Philosophy” (143). [I am not sure I completely grasp the ideas of the atom to follow, so I will quote them to be sure. It seems we can picture the atoms in the following way. The first thing we should keep in mind is that the speed of something is only limited by what resists that speed. Therefore, something moving without resistance has no limit to its speed. It is moving infinitely fast in a sense. Atoms seem to be small particles, and since they are moving in a void, there is nothing to resist their movement, and thus they move “quickly as thought,” covering “every comprehensible distance in an inconceivably short time.” The next thing to note is that they all seem to be moving downward, since they are heavy, but I am not sure what is the center of “gravity” to which they are moving. Perhaps it is the world, and they are raining down upon it. The next thing to note is that visible objects are compounds made up of different related atoms of different shapes. The reason why the object is visible, it seems, is because within the compound, instead of the atoms moving downward, they are instead bouncing around, all going in different directions. And perhaps all the countering motions appear to subtract somehow from one another, thereby making the object seem to be made of particles moving at a slower rate and vibrating. (I am guessing that is what this sentence means: “Atoms in these compound structures appear to move at a perceptible rate, but this is simply due to the fact that as their directions differ, the atoms ‘vibrate’, leading to a perceptible average motion”. Another possibility is that since their directions differ, the movement of each ends up being confined in a certain location where they appear to vibrate. In this case I am not sure I understand however how this makes them appear to be moving slower, since their rate of “vibration” I would think would be just as fast as their motion.) But we have a problem at this point. If the atoms were all moving downward at an infinite speed, then they will not be bumping into each other and causing them to move any direction other than downward. However, in visible objects, we see that atoms are indeed interacting with one another. The explanation for this is that the atoms each on their own, that is, without first being influenced by other atoms, swerve spontaneously from their direct downward course, thereby colliding with others. Let me quote:]

Epicurus claims that the universe is composed of two kinds of entities: atoms and void. While the atoms vary in size, they are all below the threshold of perception. Since resistance slows bodies down, and there is no resistance within the void, the atom’s ‘passage through the void, when it takes place without meeting any bodies which might collide, accomplishes every comprehensible distance in an inconceivably short time’. They move ‘quick as thought’ (Epicurus 1926: 37). These atoms have shapes, and the structure of the visible world is explained by their combination into compound structures. Atoms in these compound structures appear to move at a perceptible rate, but this is simply due to the fact that as their directions differ, the atoms ‘vibrate’, leading to a perceptible average motion. Given that it is ‘essential that atoms be related to other atoms at the heart of structures which are actualised in sensible composites’, we need to ask what allows this relation to take place. Lucretius gives | the following account of how atoms enter into relations with one another [The following up to citation is Lucretius quotation]:

In this connection, I am anxious that you should grasp a further point: when the atoms are being drawn downward through the void by their property of weight, at absolutely unpredictable times and places they deflect slightly from their straight course, to a degree that could be described as no more than a shift of movement. If they were not apt to swerve, all would fall downward through the unfathomable void like drops of rain; no collisions between primary elements would occur, and no blows would be effected, with the result that nature would never have created anything. (Lucretius 2001: 40–1)

It is through this swerve (clinamen) that atoms come into contact with one another.

[Next we seem to be seeing how Deleuze finds ways that this model of the atoms has features that follow the three criteria for Ideas. We first note that the atoms are not localizable, and this is because the void provides no resistance. I do not quite grasp the reasoning there. It seems the idea is that you need resistance to be localized. It is possible I do not understand what is meant by ‘localized’ here. I will suppose it means that the atoms are everywhere or global in some other sense. This is analogous to how the differential is undetermined and thus lacking in the determinations that would be needed for them to be sensible on their own. The next analogy is that the atoms, like the differentials, can only be sensible (and determinate) when they form reciprocal differential relations. These relations, we noted, are possible on account of the clinamen that allows the atoms to collide. Thirdly, since the atoms can form a variety of relations, and because they exist in space and time, they can thus actualize diverse spatio-temporal relationships. Now, although the atoms fulfill these three criteria for Ideas, they are too tied to sensible determinations to count as Ideas for Deleuze.]

Deleuze’s analysis of this situation begins with the claim that since the void provides no resistance, it is not the case that the atoms simply have an undefined location. Rather, moving at the speed of thought, they are strictly speaking ‘non-localisable’. In this sense, they operate much like the differential, dx, in that they are undetermined, lacking one of the key characteristics of ‘sensible form’. Second, they can only be given in sensibility though a reciprocal relation formed between them, just as it is only through the differential relation dy/dx that differentials become determinate. In the case of atomism, this reciprocal relation is provided by the clinamen, which allows a collection of atoms to take on sensible significance. Finally, as the atoms are capable of forming diverse relationships amongst themselves, they can be ‘actualised in diverse spatio-temporal relationships’ (DR 183/231). Atomism therefore appears to meet Deleuze’s criteria for the Idea. In fact, however, Deleuze claims it fails to exemplify the Idea fully, because the atom is still too tied to sensible determinations. Epicurus’ account of its nature is based on an analogy with sensible bodies: ‘We must suppose that the atoms do not possess any of the qualities belonging to perceptible things, except shape, weight and size, and all that necessarily goes with shape’ (Epicurus 1926: 31).

[I might be misunderstanding the final point, but it seems that the notion here is that although the atoms are described in a way which suggests they can be understood without relation to sensible bodies, they in the end are understood negatively as lacking the features of sensible bodies. But I am not sure I am getting the point there.]

Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.

Or if otherwise noted:

Deleuze, Gilles. Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.

Epicurus (1926), ‘Letter to Herodotus’, in Cyril Bailey (ed.), Epicurus: The Extant Remains, Oxford: Clarendon Press, 18–55.






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