Every ontology starts with something that already exists. Aristotle starts with substances. Leibniz starts with monads. Set theory starts with sets. Object-oriented programming starts with objects. Database design starts with tables. In every case, the first move is the same: here is a thing, and here is another thing, and now let us describe how they relate.
But what was there before the first thing? Before the first entity was carved out, named, given properties, and connected to other entities — what existed? This is not a mystical question. It is a structural one, and how you answer it determines everything that follows.
Three traditions, one question
Three very different thinkers confronted this question directly, and their answers converge in a way that none of them could have anticipated.
Nagarjuna, writing in India around 150 CE, argued that dependent origination goes all the way down. Nothing exists independently. Everything arises in dependence on conditions. But if nothing is self-standing, then what do the relations differentiate from? There must be something prior to differentiation — not a substance, not a thing, but the capacity for things to arise. He called it sunyata, usually translated as emptiness. The translation is misleading. Emptiness here is not absence. It is fullness so complete that no single description can exhaust it. It is the undifferentiated ground from which all differentiation occurs.
Alain Badiou, writing in France in the late twentieth century, arrived at a structurally identical position from within Western mathematics. His term is inconsistent multiplicity — pure being, before any operation has structured it into countable units. For Badiou, the fundamental act of any ontology is the count-for-one: the operation that takes the uncountable and makes it countable, that carves discrete entities from a multiplicity that is, in itself, prior to discreteness. Every ontology is a count-for-one. It is a particular way of structuring what was there before structure.
Alan Turing, writing in England in 1936, gave us the most concrete image of the same idea, though he was not trying to do philosophy. Before a Turing machine writes its first symbol, the tape exists — infinite, blank, real. The tape is not nothing. It is the medium that makes inscription possible. When the machine writes its first symbol, it does not create the tape. It differentiates one location from the rest. That first mark is the first entity — and everything the machine subsequently computes builds on that initial differentiation. The blank tape is the pre-ontological ground of computation.
What these three share
Nagarjuna's emptiness, Badiou's inconsistent multiplicity, and Turing's blank tape are not the same concept. They come from different centuries, different disciplines, different questions. But they share a structure.
In all three cases, the thing before structure is not nothing. It is not chaos. And it is not a substance. It is potential — undifferentiated capacity for differentiation. You cannot represent it within the ontology, because representing it is the act of differentiating. The moment you describe it, you have already made the first cut. But you can know it is there, because every first entity presupposes it. Something had to be there for the first mark to differentiate from.
Think of it this way. You walk into a dark room. You cannot see anything. But the room is not empty — it is full of furniture, walls, air, dimensions. When you switch on a flashlight, you do not create the room. You illuminate one part of it. The beam picks out a chair and leaves everything else in darkness. That chair is your first entity. The darkness is not nothing. It is everything the beam has not yet reached.
The schema as a count-for-one
This matters concretely, not just philosophically.
Every database begins with a schema — a decision about what kinds of entities exist and how they relate. A hospital database has patients, doctors, diagnoses, treatments. A library database has books, authors, subjects, holdings. The schema determines what the system can see. If the hospital schema has no entity for "patient's family," then the family is invisible to the system — not nonexistent, just uncountable within this particular count-for-one.
The schema is not a neutral mirror of reality. It is a cut. It carves the world into these entities and not those. Every entity it creates is real — patients really do exist, books really do exist. But the entities it does not create are not thereby nonexistent. They are the mess that this particular structuring has not reached. The patient's anxiety. The book's smell. The relationship between a diagnosis and the weather on the day it was made. These are not nonsense. They are the darkness the flashlight has not illuminated.
Every schema is partial. Every ontology is a particular cut into an inexhaustible ground.
The smallest possible cut
If every ontology is a cut, then the question becomes: how much should you cut?
Traditional ontologies cut a lot. The Basic Formal Ontology (BFO), widely used in biomedical informatics, defines 36 primitive relations: part-of, has-participant, located-in, precedes, and so on. Each relation is a separate decision about how the world is structured. Each one forecloses alternatives. If "located-in" is a primitive, then the ontology has already decided that spatial containment is a fundamental kind of relationship, different in kind from temporal precedence or part-whole composition. Maybe it is. But maybe it is not, and by making it a primitive you have made it impossible to discover that it is not.
The one-relation ontology makes a different bet. One relation: belongs-to. A directed dependence. The kind of dependence — spatial, temporal, compositional, causal — is not encoded in the relation type. It is encoded as a qualifier, and the qualifier is itself an entity in the same graph, subject to the same single relation. "Located-in" becomes a quality of a belonging, not a primitive of the system.
Every ontology is a particular cut into an inexhaustible ground. The less you assume at the start, the more remains accessible to future differentiation.A 36-relation ontology has already made 36 decisions about how to carve the world. A one-relation ontology has made one. The mess is closer. The pre-ontological ground has not been pushed as far away. This does not make the one-relation ontology "truer" — it makes it more open. It preserves more of the darkness for future flashlights.
Openness as infinity
There is a further structural consequence. In the one-relation ontology, the vocabulary of qualities — the ways things can relate — has no closure axiom. There is no fixed list of qualities. The graph grows as new domains are encountered. When the system meets a kind of relationship it has not seen before, it creates a new quality node. The vocabulary is finite at any moment but unbounded in principle.
This is infinity, but not the kind you might expect. Not a completed infinity — not an actually infinite set laid out all at once. It is openness: the absence of a bound. Like a Turing tape. At any step of computation, the tape has a finite number of marks on it. But there is no step at which you run out of tape. The tape is not infinite in the sense that it exists all at once in its entirety. It is infinite in the sense that it never ends.
The ontology works the same way. It is not infinite. It is open. And openness is the structural condition for being able to encounter what you have not yet differentiated. A closed ontology — one with a fixed set of entity types and relation types — can only recognize what it was designed to recognize. An open ontology can grow to meet what it finds. The pre-ontological ground remains accessible, not because the ontology is incomplete (though it always is), but because incompleteness is built into its architecture as a feature rather than a defect.
The first cut and its blind spot
The first entity is not the beginning. It is the first differentiation of something that was already there. Nagarjuna knew this. Badiou formalized it. Turing built a machine that demonstrates it every time it starts.
The interesting question is not "what are the right entities?" Every working ontology has entities that are right enough for its purposes. The interesting question is: what are we unable to see because of how we made the first cut?
Every schema has a blind spot — the mess it structured away. The patient the hospital cannot see because the schema has no field for what is wrong. The book the library cannot find because the catalog has no category for what it is about. The relationship the knowledge graph cannot represent because it falls between the primitives.
The blind spot is not an error. It is the structural consequence of having made a cut at all. You cannot illuminate the whole room at once. The flashlight has a beam, and the beam has edges, and beyond the edges is the darkness that makes the beam possible.
The best schemas are the ones that know this. The ones that build in the awareness that the darkness exists, that the cut was a choice, that the entities it created are real but not exhaustive. The ones that leave room — structurally, architecturally — for the next flashlight to point somewhere new.
Nagarjuna's Mulamadhyamakakarika (c. 150 CE) develops the doctrine of sunyata (emptiness) and dependent origination. Alain Badiou's "Being and Event" (1988) formalizes the concept of inconsistent multiplicity and the count-for-one using Zermelo-Fraenkel set theory. Alan Turing's "On Computable Numbers, with an Application to the Entscheidungsproblem" (1936) introduces the tape machine. None of these authors were in dialogue with each other. The convergence is structural.