research
Every concept draws a line through the world. This research program studies three things: the line itself, the conditions that determine where it falls, and what happens to everything it excludes.
The work operates across three registers: formal structure, cognitive process, and social organization. What follows is not a summary of results but a map of the questions — organized around three operations that recur everywhere concept formation occurs.
Foundation
Three operations
Distinction
The transmissible form that appears when pressure crystallizes into something that can be recognized. Both what we know and what there is. Identical with representation.
Index
The set of parameters that orient a distinction — scope, resolution, measurement, locus, rules for sameness. Change any one and you change what the distinction captures.
Remainder
What any finite form excludes from an infinite field. It does not disappear. It persists as pressure, driving the next cycle of change.
01
Distinction
A distinction is what appears when pressure crystallizes into transmissible form. Not a label applied to a pre-existing difference — the line itself. Every concept, every category, every measurement is a distinction, and every distinction draws a partition through the world.
Distinction is both epistemic and ontological. It is how we know — the partition through which we see — and what is — the partition as a feature of the world. These are not two senses of the word. They are the same operation seen from two directions. A concept is a distinction. A representation is a distinction. The identity is exact.
Every distinction is inherently recursive: it requires an index — a set of parameters that orient the partition — and each of those parameters is itself a distinction. There is no ground floor.
Properties
- Epistemic + Ontological
- How we know and what is — simultaneously
- Recursive
- Every distinction requires an index, whose parameters are themselves distinctions
- Dyadic
- Requires two systems under shared pressure to emerge
- Identical with representation
- The structure of all representation is distinction
02
Index
The index is the condition of possibility for distinction — the orientation that determines what can be distinguished at all. It consists of five parameters. Change any one, and you change what the distinction captures.
Every measuring instrument, every classification scheme, every perceptual apparatus operates through an index. The index is never neutral. It is a set of choices that produce consequences.
Scope
What domain does the distinction apply to?
A distinction must know its jurisdiction. A medical diagnosis applies to bodies, not buildings. A color term applies to surfaces, not sounds. Scope determines the field within which the partition operates — and everything outside that field is structurally invisible to it.
Locus
Where is the distinction located?
The same phenomenon can be distinguished at different sites — in the object, in the observer, in the instrument, in the institution. Where you locate the distinction changes what it means. A tremor in the hand is one thing for a neurologist and another for a painter. Locus is the root of categorization.
Resolution
At what grain does the distinction hold?
A satellite image at one meter per pixel and the same scene at one centimeter per pixel produce different worlds. Resolution is not a matter of precision — it is a choice about what counts as a difference. Below the resolution threshold, variation is noise. Above it, variation is signal.
Measurement
How is membership determined?
Every classification needs a procedure for deciding what falls on which side. The procedure is never innocent. What a census counts depends on the categories it deploys. What a diagnostic manual recognizes depends on the threshold it sets. Measurement is the operational face of distinction — the place where theory meets apparatus.
Illustrated in: "From Borrowed Templates to Working Models" — on how scientific fields mature through the stabilization of their measurement procedures. Leibniz University Hannover, April 2026.
Rules for sameness
When are two instances 'the same'?
Identity is not given — it is imposed by the index. Two performances of the same score, two prints from the same negative, two speakers of the same dialect: sameness is a policy, not a discovery. The rules for sameness determine the granularity of the world the distinction can see.
03
Remainder
What any finite form excludes from an infinite field does not disappear. It persists at the boundary, accumulating, exerting force. This structural consequence of distinction as such — the remainder — is not waste, noise, or error. It is the material that drives the next cycle of change.
A negative prompt pushes away what the model should not produce, but the excluded content shapes the image from the outside. A diagnostic category excludes edge cases, but the edge cases organize. A census counts what its categories permit, and everything else accumulates as political pressure. Remainder is structural. It is produced by the act of distinction itself, and it is never inert.
Consequences
Declinations
Relations
Cut and fold
Cut and fold are not separate operations — they are two relations that every distinction bears simultaneously. It partitions a field — the cut. And it nests inside other distinctions — the fold. These two relations generate the entire architecture.
Cut
Distinction’s relation to the field
A cut is a distinction considered from the outside — as a partition that divides a domain into what is captured and what is excluded. Every cut produces two sides and a remainder. The cut is where distinction meets the world.
The cut is the spatial metaphor: a line drawn through territory.
Fold
Distinction’s relation to other distinctions
A fold is a distinction considered from the inside — as a nesting of one distinction within another. When one distinction includes another as a component, it folds it. Folds produce hierarchy, policy, and structure.
Explored in: “The Fold as Dialogue” (University of Konstanz, June 2026) and “Folding Contradiction” (UNILOG 7, Cusco, 2025).
Structure
Policy and stabilization
A policy is a cluster of folds that hang together — a set of distinctions that mutually reinforce one another to form a coherent framework. A scientific paradigm is a policy. A photographic style is a policy. A legal code is a policy. Each determines what can be seen, measured, and acted upon within its jurisdiction.
Stabilization is what happens when a policy achieves coherence under pressure. It is not permanence — it is the condition of being held in place by the forces acting on it. A stabilized distinction is one that resists perturbation, not because it is true, but because the system has organized itself around it.
The gradient from fabrication to truth-tracking is resilience — how well a stabilized distinction survives contact with what it did not anticipate. A fragile stabilization shatters at the first counter-example. A resilient one absorbs perturbation and updates.
Illustrated in: “From Borrowed Templates to Working Models” — on how scientific fields develop from borrowed distinction-policies to native stabilization procedures. Leibniz University Hannover, April 2026.
Logic
Contradiction
Contradiction is not a primitive. It is the outcome of an index policy — the point where the same distinction, under aligned parameters, yields mutually exclusive sides.
Contradiction as index outcome
Two measurement procedures applied to the same domain can produce contradictory results — not because the world is contradictory, but because the indices are incompatible. Contradiction is diagnostic. It tells you where your index policies collide.
Managing contradiction through folding
Rather than eliminating contradiction or ignoring it, the fold-based architecture manages contradiction by containing it — folding the contradictory distinctions into a structure that preserves both without collapsing. Reasoning proceeds as recursive management of bounded contradiction.
Formalized in: “Folding Contradiction” and “Contradiction as Cognitive Resource” — UNILOG 7, Cusco, 2025.
Access
Opacity and shimmer
Opacity
Opacity is the gradient of access to the index of a distinction. It is not a property of the object — it is relational. What is opaque to one measurement apparatus may be transparent to another.
Naturalization is opacity at its limit — the point where the index becomes invisible to those operating within it. The constraint appears as topology. The apparatus disappears into the landscape.
Shimmer
Shimmer is what happens at the boundary before stabilization settles. It is the oscillation between folded and unfolded states — the moment when the field has not yet decided which partition will hold.
Shimmer is also the trace of what was excluded. In aesthetic experience, shimmer is the quality of a surface that holds more than its category permits — the remainder made visible without being captured.
Dynamics
Value, pressure, policy
What makes distinction necessary in the first place? Pressure — and pressure comes from value. Something matters, and because it matters, it must be distinguished from what does not.
01
Value
Something matters. A difference makes a difference. Value is what creates the demand for a response — the source of pressure. Without value, no distinction is necessary.
02
Pressure
Value creates pressure, and pressure demands distinction. The organism must partition its environment. The institution must classify its cases. Pressure is the engine of concept formation.
03
Policy
The response to pressure is a policy — a structured cluster of distinctions that governs how the system partitions its domain. Policy is not a single decision but an architecture of decisions.
01
Value
Something matters. A difference makes a difference. Value is what creates the demand for a response — the source of pressure. Without value, no distinction is necessary.
02
Pressure
Value creates pressure, and pressure demands distinction. The organism must partition its environment. The institution must classify its cases. Pressure is the engine of concept formation.
03
Policy
The response to pressure is a policy — a structured cluster of distinctions that governs how the system partitions its domain. Policy is not a single decision but an architecture of decisions.
T-failure
Commitment and realization
When a policy stabilizes, it commits you to outcomes not yet realized. A consistent position — one that does not contradict itself — is not thereby a true position. The gap between what is consistent and what is true is not a defect. It is the structural space within which the future remains open.
Commitment
What the policy commits you to
Realization
What actually holds
This is the formal basis for the non-factivity of consistency: that something is permitted by the framework does not mean it is the case. The settlement commits; reality decides. Between the two lies everything that matters about the future.
Formalized in: “The Failure of Reflection” — on the gap between commitment and realization as the habitable space of the future. ENS Paris (Derrida Today), July 2026.
Dynamics
Metabolism
The three operations do not sit still. They constitute a cycle: every fold produces a remainder; every remainder presses back; every press-back restructures the fold. This is metabolism — the engine that keeps living systems from crystallizing.
Fold
inclusion
Unfold
restructuring
Remainder
exclusion
Pressure
accumulation
Systems that produce no remainder have nothing left to metabolize. They are crystallized — perfectly ordered, perfectly dead. Systems that cannot contain their remainder explode into incoherence. The metabolic cycle is the narrow path between these two endpoints.
Explored in computational context: “Folding with the Machine” — on the recursive co-construction between human and machine systems. Under review.
Emergence
The two-body problem
A distinction is not made by a single system. It is recognized between two systems under shared pressure. One differentiates; the other reads the differentiation as signal. This is the two-body hypothesis — the claim that the minimal unit of concept formation is not one mind but two.
System A
Differentiates
Produces a variation in the field — a perturbation, a mark, a pressure differential. Not yet a concept. Not yet transmissible. A difference that has not been read.
System B
Recognizes
Reads the variation as signal — as a difference that makes a difference. The distinction crystallizes between the two systems. Neither one alone produces it.
Work from this program has been presented or is forthcoming at:
UNILOG 7 (Cusco) · Leibniz University Hannover · University of Konstanz · ENS Paris (Derrida Today) · VISION_E (Politecnico di Torino) · ESPACE art actuel (Montréal)