Abstract
This paper introduces Deleuze’s philosophy of becoming in a system theoretic framework and proposes an alternative ontological foundation to the study of systems and complex systems in particular. A brief critique of systems theory and the difficulties apparent in it is proposed as an introduction to the discussion. Following is an overview aimed at providing access to the ‘big picture’ of Deleuze’s revolutionary philosophical system with emphasis on a system theoretic approach and terminology. The major concepts of Deleuze’s ontology—difference, virtuality, multiplicity, assemblages, quasi-causation, becoming (individuation), intensity and progressive determination are introduced and discussed. Deleuze’s work is a radical departure from the dogma of western philosophy that guides the foundations of science and systems theory. It replaces identity with difference and being with becoming; in other words, it provides systems theory with an ontological ground based on change, heterogeneity and the inexhaustible novelty-producing process that underlies all phenomena. The conceptual tools made available by this philosophy seem to capture the fundamental aspects of complexity and complex systems much better than the current conceptual system that is based on static transcendent ontological entities.
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Notes
This revolutionary approach causes more than a slight discomfort to many orthodox analytical philosophers that often describe Deleuze’s work as obscure, inconsistent and highly speculative.
The contrast between becoming and being can be traced back to the influential works of Heraclitus and Parmenides, but it is only in the work of philosophers such as Nietzsche, Bergson and prominently in Deleuze’s that becoming regains primacy.
Typological categories bestow ontological status on generalizations through the concept of species.
The term modification is used here to emphasize that Deleuze’s novel conceptualization of substance does not contradict, negate or oppose Spinoza’s concept. Deleuze rather introduces a difference, a novelty and by that he reaffirms Spinoza’s concept, as all affirmations are repetitions and every repetition is a repetition of a difference.
Embryonic is used here to make clear that the virtual is not populated by possible or potential existences that are fully formed and just need to be ‘realized’. Embryonic comes to mean a not yet formed expression. Yet even this metaphor captures only approximately the meaning of a virtual expression.
Ordinal distances measure the degree of dissimilarity between differential elements. They can be compared but a difference between ordinal distances cannot be cancelled because they are not quantifiable measures. For example one can know that A is more different from B than C is from D, but there is no meaning to ask how much it is more different. This becomes important when two series of differences are related via a third series of differences, which is the manner by which differences connect on the virtual plane to form a continuum.
The word ‘instance’ is used here to signify something akin to an instantiation of a variable. An instance is any product of determination but not necessarily fully determined. Yet every instance is unique.
This has implications for the very understanding of time and its relation to change.
We will later see that these trajectories constitute a multiplicity.
In Sect. 6.2 we will see that certain differences are more significant than others and are therefore called singularities or virtual events. They are important because they are ‘turning points’ in the process of becoming that bring forth actualizations and therefore have a distinct signature on both virtual topography and actual outcomes.
Initial point or initial condition of a system is a practical and arbitrary imposition made by an external observer. A dynamic system does not have privileged initial conditions of any kind. An initial condition marks only the state of the system when observation began.
Conventionally the differential dx is derived from X and therefore secondary to it. In Deleuze’s analysis of the philosophical meaning of calculus, the differential dx is primary in the ontological sense. The differential dx corresponds to the kind of difference described in the previous section.
These intrinsic variables are just differentiated elements of pure change. There is no indication in multiplicity as to what they represent in an actual system. Dimensionality is the number of distinct intrinsic differences whose reciprocally determining relations describe the multiplicity or a virtual event. A multiplicity therefore encompasses multiple (indefinite) paths of individuation. The integer number of dimensions is still a point of weakness in this development of the concept because it presupposes a kind of distinctiveness that is reminiscent of that which exists in fixed identities. This difficulty can be overcome by introducing fractal dimensions but the development of this idea is beyond the scope of this paper.
Protevi (2010, p. 13) remarks: “So the interesting sense of realism for Deleuze is that the world has structure, but that structure is the structure of multiply realizable processes, not the structure of fully individuated things which result from those processes.” But realizable processes are not enough to account for reality. The process of becoming that integrates the virtual and the actual is the necessary and sufficient account.
This proposition is extended later.
The fact that trajectories are computed by performing mathematical integration over the vector field can be deceiving. There is a deep philosophical significance to this integration. It is part of the individuating process that must be carried out to actualize anything.
For Deleuze multiplicities are distinct but obscure. While becoming actual phenomena they undergo a philosophical phase transition and become clear (observable, not hidden, given to representation) yet confused because what is apparent in actuality is clear but never expresses to the fullest the hidden pattern that connects each manifest to the whole of the virtual plane (Deleuze 1994, pp. 213–214; DeLanda 2005, p. 16).
Even when systems do have a mathematical model, it is impossible, in most cases, to compute the distribution of singularities. Such computation is achievable only in extremely simplified cases. But having even a qualitative and partial knowledge of such distribution may already contribute much to the understanding of a system.
Interest is intrinsic to multiplicities in the form of singularities. A singularity need not be interesting for something. Interest in this sense is immanent.
A series of differences is a collection of consecutive differences (a trajectory) that embodies a partial identity. A variable of a multiplicity or a mathematical combination of such variables can be expressed as a series of differences that reflect (or are implied by) a certain type of behaviour in the dynamics of actual systems associated with the said multiplicity.
Higher order differences represent the inherent ‘depth’ of the virtual dimension because they embody even less identity compared to the lower order differences to which they relate.
An interesting approach to assemblages can be found in Kauffman (1990). Kauffman’s strings and random grammars can be understood in terms of differences and multiplicities.
The major source of the flexibility of assemblages is that the nature of connections among virtual differential elements is topological and not metric.
Beyond multiplicities there are assemblages that retain a partial structure which is pre-individual, and beyond them there is a continuum of difference with ever diminishing structural content—an open-ended ‘wilderness’ of pure potentiality. See also footnote 34.
A compelling example is physical vacuum that undergoes quantum fluctuations.
Intensive differences must not be confused with external phenomenal differences, which distinguish between actual (formed) individuals and are based on representational identities.
Intensive differences must not be confused with external phenomenal differences, which distinguish between actual (formed) individuals and are based on representational identities.
To characterize something as black we must disregard an indefinite number of shades and nuances and the indefinite relations these may hold in perception to shades and nuances of other colours etc.
These assemblages imply of course the meshing of multiplicities at the virtual dimension.
Additionally, certain events can introduce new intensities and involve new assemblages, and hence dynamically modify the individuating field (a man runs into the water and starts swimming).
‘Select’ is only partially appropriate here because there is no selective criterion involved. This is rather an intractable chance event.
The communication of the series is an effect of a determination of trajectory in the multiplicity that underlies the mediating series.
The concept of unilateral determination of differences is particularly powerful in that it allows the virtual plane to include all potential connections but in various degrees of distinctiveness. The continuum of distinctiveness never falls into the ultimate static condition of ‘containing all possibilities’: Distinct features (connections) can indefinitely differentiate from an indistinct ground while they can also disappear into a featureless ground. The profound meaning of difference is exactly this: a metaphysically dynamic and indefinitely creative existence.
“The reason of the sensible, the condition of that which appears is not space and time but the Unequal in itself...” See Sect. 7.1.
Deleuze’s concept of repetition draws also from Hume’s idea on habits see Deleuze (1991).
Systems involving quantum effects are a special case. The wave function is still deterministic; only its measurements require probabilistic considerations. This is a topic for further research.
Less determined limits of diversity must not be confused with chaotic behaviours. Chaotic attractors for example may still belong to well-determined limits of diversity.
See Gontier (2007) on the idea of universal symbiogenesis.
The term basically means making the contour of the idea more distinct and definite. For example, if all the houses of a certain neighbourhood are painted with one distinct colour it makes this neighbourhood more territorialized. De-territorialization means the opposite: making the contour of an idea less distinct and definite.
See Protevi (2012, pp. 251–254) on assemblages and niche construction.
See Andriani and Cohen (2013) on the role of exaptation in biological and technological innovation.
Carnap and the Vienna Circle that operated in the 1920s had a tremendous influence on the scientific paradigm during the twentieth century.
This involves of course a critique on the famous ‘Cogito’ with implications on the nature of ‘self’ and ‘I’: the thinker is individuated in thought always fragmented and incomplete.
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Weinbaum, D.R. Complexity and the Philosophy of Becoming. Found Sci 20, 283–322 (2015). https://doi.org/10.1007/s10699-014-9370-2
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DOI: https://doi.org/10.1007/s10699-014-9370-2