#thefourfold

Author: Magda Wisniowska – March, 2021.

Much of the appeal of Arjen Kleinherenbrink’s book lies in the single-mindedness of his argument. From the start we are told in no uncertain terms that many, if not most, of Deleuze’s ontological interpretations are incorrect, and that his machine ontology has been fundamentally misunderstood. Why? Because all these interpretations tend to posit a single continuous virtual realm. Depending on who you read, this realm consists of either those dynamic processes  underlying the discontinuity of concrete entities; a virtuality characterised as the one true real and causal agent of an only apparent existence; or a single intensive force accounting for all change (Kleinherenbrink 31-7). And in light of what Kleinherenbrink calls the ‘externality thesis’ it makes sense to posit such a continuous, active, virtual realm. For if all entities in our world of things are discontinuous and separate individuals, something else must account for these things to be able to change, to relate to each other, and to produce and create. Things would then be the manifestation of the one creative force, in actuality apparently discontinuous, but continuous in their virtuality; entities mere intersections in something much more vast and powerful than themselves. This is our proverbial tablecloth (see Sad Mondays 13). 

As Kleinherenbrink argues, the problem with ontological interpretations positing a continuous virtual realm is that they cannot be adequately reconciled with Deleuze’s machine thesis. ‘Everything is a machine’ Deleuze repeatedly states, but everything is not a machine, if there is something other than the machine, of which the machine is an expression. In these ontologies of the virtual, the being of mechanic entities is dissolved into something non-ontic, which nevertheless is presented as a realm in which things really and truly ‘are’ (Kleinherenbrink 32). We are very much reminded here of the Spinozian argument relating to God’s causality. We might recall how earlier, I argued that Spinoza’s is an immanent rather than transient God, meaning that his God neither acts on something other than himself nor does he create something other than himself (see Sad Mondays 6b i). If in Spinoza there is only the one God, the one Substance, then everything God creates must remains in God. Everything partakes in God. Here the analogy is of the world as God’s facial expression (Sad Mondays 6b i). 

For Kleinherenbrink however, Spinoza’s philosophy must also be rejected, as it too falls back on continuity. No matter our expression in modes — we are all part of God’s continuous being. So what does Kleinherenbrink propose? Instead of reality being divided into, on the one hand, a continuous virtual, and on the other, a discontinuous actual realm of entities, he proposes a second, mechanic ontology of a private virtual (36). Each machine, he claims, has this private virtual aspect, divided as it is, through an internal difference in kind, between the virtual and the actual. So with every machine there is an aspect that we can encounter, and an aspect that remains hidden to us, which is non-relational. Furthermore, Kleinherenbrink divides both the virtual and the actual aspect of the thing into the ‘one’ and the ‘multiple’ (38-9). On the virtual side of the machine, each entity has to be both one and multiple, or as Kleinherenbrink attributes to Deleuze’s reading of Leibniz, ‘one to be this, but multiple to distinguish this from that’ (39). Similarly on the actual side of the machine, each entity is also one and multiple. ‘One is this encounter’ that we relate to, but this same encounter is also ‘multiple in the sense of having qualities distinguishing this from that’ (39). I very much like the simple starkness of Kleinherenbrink’s first diagram, which he copies from Deleuze’s The Fold. I reproduce it below:

These few lines are meant to represent the fourfold of the machine, both virtual and actual, one and many, but ultimately, individual, isolated, non-relational. A more accurate diagram perhaps would be:

Which in turn brings us to Kleinherenbrink’s second diagram, following quick on the heels of the first.

In this much more complex elaboration of the fourfold, Kleinherenbrink draws on a number of Deleuze’s texts, each with its own idiosyncratic vocabulary. To explore the private virtual of the machine we encounter concepts of ‘sense,’ ‘body,’ ‘qualities’ and ‘idea’ as well as such familiar Deleuzian concepts as the ‘body without organs,’ the ‘problem,’ the ‘event,’ or ‘intensive matter’ — all of which I want to leave aside for now to concentrate only on one interpretation. For at this point of his argument Kleinherenbrink’s thinking of the fourfold owes the most to an early 1967 discussion at the French Society of Philosophy, a transcript of which has been republished in Desert Islands in 2002. Under debate here are the parameters of what Deleuze calls the idea, or rather, more accurately, of the thing of the idea. This for Deleuze does not consist of a ‘what’ but of a multitude of determinations: ‘how,’ ‘how much,’ ‘where and when’ and ‘what case.’ What is crucial is that already then, the fourfold is at play, as identified by the moderator of the discussion and president of the society, Jean Wahl.

Deleuze begins the discussion by identifying the thing through its two distinguishing traits. The first concerns the qualities that specify it as a thing, the second, the extension that the thing occupies, an organisation of internal and external parts. So on the one hand, there is the synthesis of qualification and specification, on the other hand, the synthesis of partition and organisation. Crucially, the one depends on the other, there being no qualities without extension, no species without parts. In the mathematical language that Deleuze uses, this is differentiation, with its two correlative aspects, and it does remind one of a graph, the vertical marking the difference in y, the horizontal, the difference in x, together representing the rate of change. But Deleuze argues that underlying specification and organisation are spatio-temporal dynamisms, an intensive spatium pre-existing every quality and extension. This would be in Deleuze’s mathematical language, the differential, the rate of change at any one single point. And the determinations of the intensive field are what corresponds to the multiplicity of questions of how, when, where, who. 

Jean Wahl identifies Deleuze’s thing as a fourfold, because Deleuze shows that the dynamisms controlling differentiation — the specification and partition that actualise the thing of the idea — are derived from the two aspects of the differential — differential relations and their concomitant points. That the differential has two aspects might have eluded my description of the differential as the rate of change at any single point, but this is what, mathematically speaking, the differential consists of: differential relations existing only through reciprocal determinations, and singularities, points corresponding to these relations. Thus the thing of the idea is only ever actualised when differential relations are incarnated in species or qualities and concomitant points in the extension corresponding to these qualities. Or  as my diagram shows:

What we have here is a very abstract system, but which nevertheless corresponds to many, not so abstract systems, found in our everyday world. The differential is the phonemes distinguishing one sound from another in language, the physical particles making up matter, the biological genes carrying the instructions of how protein is made.