When the net moves

Imagine a fishing net stretched between four posts. Mark one intersection with a bead. Pull the upper-left post. The bead moves, although nothing inside the bead instructs it to move. Its position is produced by tensions distributed through the net.

The obvious lesson is relational: the bead is where it is because other things are where they are. A less obvious question follows. Are the tensions themselves fixed properties? Each tension depends on the material, the knots, the posts, the pull, the weather and the boundary we chose when we called this section of cord a net. Replacing isolated objects with relations does not end the search for intrinsic nature. It can simply move the supposed intrinsic nature from the bead into the lines.

Madhyamaka begins from a related pressure on explanation. The target is svabhāva, often translated as intrinsic nature, own-nature or self-existence. A thing with svabhāva would be what it is from its own side, not through causes, parts, contrasts, cognition or designation. Nāgārjuna's arguments repeatedly ask whether familiar phenomena can bear that burden.

A cause cannot be a cause without an effect. A whole cannot be the same as its parts, wholly different from them, or located as an extra component beside them. A long object is long relative to a comparison and a measure. A person is not found as an independent owner behind body, memory, intention and social recognition. Yet causes work, wholes are repaired, lengths are measured and people keep promises. Emptiness removes self-establishment, not conventional efficacy.

The distinction between conventional and ultimate truth matters here. Conventional truth is not a pile of false appearances awaiting replacement by an ultimate substance. It includes the transactions through which language, causation, inference and ethical practice function. Ultimate analysis asks whether anything in those transactions is self-established. It does not uncover a more basic object called emptiness.

That last point prevents the first major error in comparison. Emptiness is not a hidden relational medium. If relations were the final furniture of reality, they would inherit the very independence denied to objects. Madhyamaka analysis also asks what makes a relation a relation, where its terms begin, and which conceptual practice identifies it.

flowchart TD
  A["When the net moves"] --> B["Emptiness without hidden relations"]
  B --> C["Where relational semantics stops"]
  C --> D["The four-dependence audit"]
  D -. "re-test" .-> A
  classDef first fill:#0a1424,stroke:#5B5CF6,stroke-width:2px,color:#e6f3ff
  classDef step fill:#0a1424,stroke:#3f7da0,stroke-width:1px,color:#e6f3ff
  class A first
  class B,C,D step

Emptiness without hidden relations

Suppose we accept that a word gains significance through its place in a language. Have we reached Madhyamaka? Only if we forget to ask what constitutes the language, the places and the relation called “gains significance”.

Madhyamaka literature analyses several forms of dependence. Three recur prominently: dependence on causes and conditions, dependence of wholes on parts, and dependence on conceptual designation. For semantic systems, a fourth dependency deserves separate visibility: contrast. “Hot” is intelligible against “cold”, “urgent” against “routine”, and “safe” against a reference class of risks. This fourth item is a practical extension for semantic analysis, not a claim that Nāgārjuna taught a four-part engineering framework.

Why say these dependencies do not “bottom out”? Consider a causal relation. To identify a cause, we need a time window, a candidate effect, a background set of conditions and some account of what would happen under intervention. Change the window and a trigger becomes a background condition. Change the effect and the relevant cause set changes. The relation is not imaginary, but neither does it arrive pre-cut with its own complete boundary.

Mereological dependence has the same structure. A document can be decomposed into pages, clauses, tokens, database fields or evidential propositions. None is the uniquely correct set of parts for every task. Conceptual dependence adds the rules by which an investigator recognises a clause, a person or a risk category. Contrastive dependence adds the alternatives against which a distinction matters. A dependency is real enough to support intervention while still depending on a specified grain, purpose and comparison.

This matters because engineers often use “relational” as if it named one sufficient mechanism. In practice, relations are typed. Co-occurrence, causation, legal entitlement, similarity, temporal succession and social recognition support different inferences. A model that stores one type cannot silently claim another. The question is never only whether two items are connected. It is what kind of connection is represented, what generated it and which action that connection may licence.

The figure expresses the paper's central mechanism. A label is reified when a system treats it as invariant under interventions that alter what made it meaningful. The familiar failure is to freeze the node: “this applicant is intrinsically high priority”. A subtler failure freezes the edges: “the label is relational, so its meaning is secured by the current graph”. But the graph depends on data history, feature construction, contrast classes, policy and use.

Edge reification is the mistaken belief that a fixed relation structure has escaped intrinsic nature. It is the reason a system can be thoroughly relational and still be brittle.

This boundary is familiar in debates about the symbol grounding problem and about models trained only on linguistic form. Harnad asked how symbols acquire non-symbolic grounding rather than merely circulating among symbols. Bender and Koller distinguished success at modelling form from evidence of communicative meaning tied to intention and world states. Those arguments are contested, especially as models become multimodal and tool-using. Their load-bearing point remains narrower: more internal relations do not automatically identify the relation that counts as reference.

Where relational semantics stops

Relational semantics succeeds because context matters. It fails when context is compressed into one privileged snapshot and then mistaken for the thing itself.

“Relational semantics” names several positions, not one formal doctrine. Structural linguistics treats values as differences within a system. Distributional semantics learns representations from patterns of occurrence. Inferential approaches connect meaning to what follows from a claim and what licences it. Use-oriented approaches connect meaning to practices. Modern contextual encoders compute a representation for a token from its surrounding sequence rather than assigning one vector to every occurrence.

These are not trivial achievements. Harris's distributional work made linguistic structure empirically tractable. Word-vector methods captured many syntactic and semantic regularities. Contextual representations showed that the same token occupies different geometric positions in different sentences. Ethayarajh found that upper-layer representations in BERT, ELMo and GPT-2 were substantially context-specific rather than recoverable as a single static vector.

Context sensitivity is evidence against a sealed lexical essence. It is not evidence that every dependency relevant to meaning is inside the model.

Four ways a relational model can still reify

First, the graph can be permuted. Rename every internal node consistently and the formal relation structure can remain isomorphic. The system preserves its internal predictions, but the permutation alone does not tell an external user which node concerns medicine, rain or debt. Structure constrains interpretation without always determining reference.

Second, the graph can preserve a bad history. Caliskan, Bryson and Narayanan showed that word embeddings trained on ordinary corpora recovered human-like associations, including problematic racial and gender patterns. The representations were relationally faithful to their data. That faithfulness did not make every recovered relation true, fair or fit for action.

Third, the context boundary can be wrong. A model can condition on every token in a document while missing a policy change, a new authority, a changed population or a purpose constraint. “Long context” is not the same as the right context. The model may be context-sensitive inside the wrong boundary.

Fourth, the metric can become the meaning. Cosine proximity is a geometric relation. A release decision may require causal relevance, legal entitlement, temporal validity or human endorsement. Treating high similarity as semantic sufficiency confuses a convenient measure with the relation the decision actually needs.

stateDiagram-v2
  [*] --> Claim
  state "The cup that became a paperweight" as Claim
  state "A four-vector example you can<br/>calculate mentally" as Test
  state "Four ways a relational model<br/>can still reify" as Revision
  Claim --> Test: expose mechanism
  Test --> Decision: evidence survives
  Test --> Revision: rival survives
  Revision --> Claim: narrow or rebuild
  Decision --> [*]

The four-dependence audit

The engineering consequence is not to delete labels. It is to attach every consequential label to the dependencies that make it valid, then test the label under interventions on those dependencies.

The proposed instrument is the 4D Dependence Audit. It converts a philosophical warning into four operational questions. The names are chosen for memory rather than textual fidelity.

Drivers are the causal and historical conditions that produced the representation: training data, sensors, sampling, policy versions, incentives and feedback. Decomposition is the choice of parts and system boundary: tokens, features, documents, people, components and aggregation rules. Differences are the contrasts that give a label discriminative force: classes, neighbours, thresholds, baselines and counterfactual alternatives. Designation is the practice that names and uses the label: purpose, authorised user, legal rule, workflow and action consequence.

From intuition to a testable score

Let a label's current meaning be written as:

Here x is the item being represented and c is the declared operating context. The equation does not claim that meaning is numerically reducible. It forces the system owner to name the inputs on which a semantic judgement depends.

For each dimension, score sensitivity s from 0 to 4 and evidence coverage e from 0 to 4. Sensitivity asks how much a plausible change could alter the action. Coverage asks how well the system can detect, reproduce and test that dependency. With equal weights, a simple triage score is:

If designation has sensitivity 4 and coverage 0, it contributes the maximum risk. If decomposition has sensitivity 2 and coverage 3, it contributes little. Suppose the four pairs are (4,1), (2,3), (3,2) and (4,0). With equal weights, R is 0.56. That is a high triage result: the label should not be reused without revalidation or an abstention gate.

The score assumes ordinal ratings and chosen weights are decision-useful. They are not probabilities. Remove that assumption and the audit still works as a structured comparison: the highest sensitivity with the weakest evidence identifies the first intervention to run.

The lab tests whether a label has high decision sensitivity where evidence is weak. It encodes four assumptions: the operating context can be declared, dependencies can be separately discussed, ratings are ordinally meaningful, and higher sensitivity with lower evidence justifies stronger control.

A low result permits scoped reuse only inside the declared context, with an expiry and monitoring rule. A high result permits no adverse inference about the person or object; it means the system owner lacks enough evidence to treat the label as portable. If an intervention leaves outcomes stable, confidence in that specific invariance rises. If outcomes change, the label must be recalibrated, remapped or withdrawn.

The tool cannot establish metaphysical emptiness, genuine understanding, fairness, reference or consciousness. It can expose where a decision has mistaken a conditioned representation for a context-free fact.

How the audit enters an operating system

Begin before model evaluation, not after a failure. The product owner writes the exact action sentence: “This label permits this actor to take this action for this purpose until this condition expires.” That sentence fixes the designation to be audited. Without it, reviewers will discuss abstract model quality while imagining different consequences.

Next, the data and engineering owners construct the driver and decomposition records. The driver record versions training sources, temporal cutoffs, sampling choices, feedback channels and policy inputs. The decomposition record names the candidate system and its parts: which documents count, how records are joined, which population is represented, and whether the model, retrieval layer, rules and human operator are inside or outside the assessed boundary.

The domain owner then defines differences. What are the nearest alternative labels? Which threshold separates them? Which reference population makes “high”, “similar” or “urgent” meaningful? The team designs at least one intervention that could cause a justified label to change and one that should leave it invariant. A test suite that contains only invariance cases rewards semantic rigidity.

Finally, the authority layer turns audit results into release behaviour. A changed high-sensitivity dependency can trigger one of four typed responses: continue within scope, require review, revalidate, or abstain. The response and its evidence become a decision receipt. After execution, readback records whether the intended queue placement, message or transaction occurred. This separation stops a plausible label from being treated as a verified effect.

Do not average away a red dimension. A well-documented data history does not compensate for an unauthorised purpose. Excellent policy documentation does not compensate for a changed population boundary. The total score supports triage, but hard gates belong to individual dependencies whose failure can cause irreversible harm.

/** Ratings are ordinal, 0..4. Weights must sum to 1. */
function reificationRisk(dimensions, weights) {
  const terms = Object.keys(dimensions).map((name) => {
    const { sensitivity, evidence } = dimensions[name];
    if (![sensitivity, evidence].every(Number.isFinite)) {
      throw new TypeError(`Missing numeric rating for ${name}`);
    }
    if (sensitivity < 0 || sensitivity > 4 || evidence < 0 || evidence > 4) {
      throw new RangeError(`Ratings for ${name} must be between 0 and 4`);
    }
    return weights[name] * sensitivity * (4 - evidence) / 16;
  });
  return terms.reduce((sum, term) => sum + term, 0);
}

A testable research hypothesis

The smallest experiment uses synthetic tasks. Generate a label under one configuration, then independently shift its data-generating history, feature boundary, contrast class and action rule. Compare two systems: a fixed relational classifier, and the same classifier wrapped with a 4D manifest, targeted interventions and abstention. Measure decision error, calibration, unsafe action rate, abstention cost and revalidation burden.

• Strengthening result: the wrapped system lowers unsafe actions under matched in-context performance, especially when ordinary feature drift is small.
• Weakening result: the audit adds cost without improving calibration or catching failures beyond existing provenance and policy controls.
• Rival explanation: any gain may come from better metadata and change management, not from the Madhyamaka comparison.
• Do not apply: the full gate is excessive for low-consequence labels whose purpose, boundary and data source are deliberately fixed.
• Smallest useful implementation: a versioned dependency manifest, one intervention test per high-sensitivity dimension, an expiry and an abstention rule.

sequenceDiagram
  participant Q as Question
  participant M as Mechanism
  participant E as Evidence
  participant D as Decision
  Q->>M: When the net moves
  M->>E: The cup that became a paperweight
  E-->>M: compare rival explanations
  E->>D: Govern the conditions under which the relation works
  D-->>Q: revise scope or act

Govern the conditions under which the relation works

Stop asking whether a representation is relational. Ask which dependencies make it valid now, which intervention could change its use, and who has authority to act on it.

The opening system failed because it preserved a score while losing the configuration that made the score actionable. A conventional machine-learning review might check data drift, predictive performance and reproducibility. Those checks matter. They can all pass while the purpose, contrast class or authorised action has changed.

A consequential label should therefore ship with a dependency manifest, rather than only a model card. The manifest names its drivers, decomposition, differences and designation. Each high-sensitivity dependency receives an intervention test, a change trigger, an owner and an expiry. The label remains a proposal until authority validates the current policy and permitted context. A verified outcome is recorded separately from the proposal.

For philosophy, the decision is equally concrete. Do not translate Madhyamaka as “everything is relations”. That phrase sounds anti-essentialist while quietly granting essence to the network. The more faithful comparison is methodological: examine what a phenomenon depends on, then examine whether the supposed dependencies have been exempted from the same analysis.

This does not make the world unusable. It makes use more precise. A chariot can carry a traveller without possessing a final chariot-core. A word can guide action without containing an isolated meaning atom. A model can support a decision without its label becoming a context-free fact.

In a review meeting, this changes the first question. Instead of asking whether the model “understands” the label, ask which dependency was last tested. Instead of asking whether two systems agree, ask whether they depend on independent evidence. Instead of treating a stable score as continuity, ask whether the action sentence, reference class and temporal entitlement are unchanged. These questions turn an abstract anti-essentialism into release criteria that can be owned, versioned and challenged.

The middle move is neither to worship the node nor to worship the edge. It is to govern the conditions under which the relation works.