From Continuity to Becoming

Leibniz, Deleuze and the Logic of Individuation

Through the looking glass of Leibniz’s differential relation: instead of identity, we see limits of variation; instead of rest, we discern infinitely small movement; instead of coincidence, we detect infinitely small distance; and instead of equality, we notice infinitely small inequality. Even the circle transforms into a polygon with infinitely many sides. What previously seemed static becomes animated through an endless process of variation. In the world governed by differential relations, concepts are no longer built on immovable identities but rather on continuous movement towards their vanishing edge.

This is one of the primary philosophical inspirations of Deleuze’s famous concept of becoming. It is not that the polygon merely resembles a circle but rather that it enters an infinite movement of becoming the circle. And this movement is unceasing. From an ordinary perspective, what is understood as rest is still movement carried to its infinitesimal limit. Becoming is not a transition from one state to another but rather a continuous movement that serves as the skeleton for any apparent state or object.

Through this, an entire new domain of analysis opens up that is no longer governed by identities understood as self-same static formations. In fact, from this point of view, the conventional understanding of identity is a closure, a dead end insofar as it merely posits each term as what it is. In this context, analysis is no longer a mere unpacking of what is already given in a concept (as we discussed in From Identity to Totality), but rather an infinite movement, an ongoing process passing through forms.

​The Differential Unconscious and the Limits of Continuity

It is based on this differential logic that Deleuze and Guattari develop their concept of the unconscious in Anti-Oedipus, which no longer operates through opposition, conflict, and repression. It is no longer regarded as a drama of antagonistic forces but rather as a field of differential relations, governed by continuity and vanishing differences. Passage of intensities into one another, their mutation and redistribution without crystallization into fixed identities, becomes more prominent than analysis of the opposing tendencies.

The contrast with the Freudian model, where the unconscious is fundamentally organized around conflict, prohibition, and repression, is apparent here. For Deleuze and Guattari, this model is too closely aligned philosophically with Kant and Hegel, where negation, contradiction, and synthesis are fundamental laws of psychic dynamics. For Deleuze and Guattari, the unconscious is fundamentally positive and productive. It does not move by opposing and negating but rather by continuously differentiating itself from within.

Yet if we were to push this differential logic to its end, we will find ourselves forced to return to Leibniz. The very continuity that allows difference to unfold positively threatens to dissolve the conceptual difference on which Leibniz insists. At this point, we need to pinpoint what seems like a tension internal to Leibniz’s thought. On the one hand, the principle of the identity of indiscernibles asserts that every difference is internally composed and conceptually irreducible. Each difference has its concept that is irreducible to any other. On the other hand, the law of continuity insists that things change and transform continuously through infinitely small differences that are unassignable as discrete terms. As a result, we have a difference that is at once fully conceptual and yet infinitely divisible, well beyond conceptual grasp.

​Singularity and the Logic of Individuation

Following Daniel Smith’s and Manuel DeLanda’s reading, Deleuze approaches this problem through the mathematical notion of singularity. In mathematics, we can distinguish between ordinary and singular points. For example, a square has four singular points and an infinite number of ordinary points. A singular point signifies a change of behavior of a surface. Whereas ordinary points are regular and well-behaved, changing at a steady rate, singular points are disruptive, values change unevenly, signs change, and rates of variation become irregular.

For Deleuze, continuum and singularity are not opposites. A continuum is no other than a prolongation of singularity in the form of ordinary points until it meets another singularity. Seen in this light, continuity is not a smoothing over difference but rather its advancement. Difference does not vanish in continuity; it persists even if in a diluted form until it reaches a threshold, another singularity.

The model of determination that Deleuze builds from this is no longer grounded in fixed identity but rather in individuation. Any determination can be seen as a multiplicity or manifold that is a composition of the singular and the ordinary. What something is is inseparable from how it is individuated.

This model is equally applicable to mathematical and physical entities. For example, in physical systems, singular points appear as points of phase change: condensation, coagulation, and boiling. These are not to be seen as external impositions but rather as internal thresholds where the system’s behavior shifts. Even if the overall continuity of the system is preserved, something decisive is taking place. The system’s individuation proceeds not through the dialectic of opposition and negation but rather through crossing critical points within its own field of variation.

The same model can be applied even to sentient and living systems. In this context, singularities can be seen as points of affective transition, entering joy or sadness, shifting in sensitivities that reorganize the field of experience. In living systems, singularities appear as passages towards strengthening or weakening, birth and death, growth and decay. In each case, individuation can be observed as an interplay between singular events and ordinary continuities that carry forward their effects.

Determination is not a fixation of identity but rather a tracing of how a multiplicity holds together, how the passage from one regime of variation to another takes place, how difference persists within continuity without final resolution.

In Deleuze’s reading, this Leibnizian system produces a transcendental field that is a-theological, a-cosmic, and pre-individual that operates with a transcendental logic that is irreducible to the formal logic of predication. This transcendental logic operates prior to the attribution of properties to subjects. Determination no longer consists in saying what something is but rather in tracing the differential field within which something is individuated.

This model seems especially suitable for a world in which none of the historically dominant determinants can be taken for granted anymore. Normative frameworks no longer stabilize experience as they once did; traditions have lost their function as reliable coordinates, and even what once were seen as simple empirical givens are appearing increasingly fragile.

In these conditions, a model of transcendental multiplicities articulated through singularities that is a-theological, a-cosmic, and pre-individual may prove particularly relevant precisely because it does not rely on fixed identities or transcendent guarantees; it remains capable of describing and perhaps even anticipating emerging patterns within a field of intensities and differences. It allows us to think of determination without relying on foundations and analyzing continuity without thereby erasing difference.