Derivation and inheritance give starting warrant; discriminating evidence or proof earns scope

Type: kb/types/note.md · Tags: learning-theory, discovery, foundations

A reusable decomposition claims more than adequacy for its originating case. It claims that its categories will continue to mark consequential boundaries elsewhere. A one-off partition need not make this claim. Once a decomposition is proposed for reuse, however, merely displaying or applying its categories does not establish their explanatory-reach. Use tests a decomposition only in the context exercised.

Provenance determines whether a scope claim begins with support and where further testing should focus. Derivation from independently supported constraints gives conditional starting warrant. Inheritance from a tested source ontology gives transferred starting warrant, conditional on a bridge to the target domain. A boundary fixed by neither is underdetermined. Pragmatic or abductive reasons may recommend it, but they do not warrant its scope.

These are starting positions, not earned scope. Discriminating evidence earns scope only across the empirical domains and failure modes it covers. Proof earns scope only within the formal domain specified by its axioms and formalization.

Three provenance states locate what remains untested

Derivation applies when independently supported causal, operational, or formal constraints fix the axes and the cells follow from them. Its warrant is conditional: if these axes remain operative, these cells remain exhaustive. Axes chosen only because they produce a desired split remain underdetermined, even when the cells follow mechanically.

Testing a derivation therefore targets its antecedent and its constraint-to-boundary dependence. Establish that the named constraints hold, then vary them and ask whether the boundaries change as predicted. When the claim and domain are fully formalized, a proof may instead establish exhaustiveness over every state admitted by that formal domain. It cannot establish that the axioms describe a target outside the domain.

Inheritance applies when a decomposition is borrowed together with evidence from a source domain. That evidence transfers only to the extent that the source testing was discriminating: the ontology survived cases that relevant rivals would have handled differently or that could have exposed a boundary failure. Longevity and repeated use are poor proxies because an ontology can persist without being challenged.

The target-domain test therefore focuses on a bridge. The borrower must show both that the source testing was discriminating and that the constraints that made its boundaries consequential still hold at the target. Matching a few named constraints is insufficient if an omitted modifier could change the boundaries.

Underdetermined choice is the residue that neither route fixes. Convenience, symmetry, simplicity, or a mechanism-preserving analogy may justify a provisional preference. Such reasons can make one decomposition more worth testing than another, but they supply neither the conditional warrant of derivation nor the transferred evidence of inheritance. The boundary should remain cheap to replace, and a boundary-preserving rival demotes any claim that it was inherited.

These states attach to individual axes and boundaries, not necessarily to a whole decomposition. One decomposition may derive some boundaries, inherit others, and choose the rest. A single label for the artifact hides the obligations that remain untested.

Scope is earned only over the domain tested or proved

Evidence is discriminating when an encounter could settle a disagreement between live rival decompositions or expose a scope-relevant boundary failure. Passing a confirmatory case that every rival also passes adds little. A held-out comparison, intervention, or risky prediction can be discriminating before deployment; “use” is not a special epistemic category.

One successful context earns support for that context. Repeated successes extend the record to the contexts checked. They warrant an unobserved class only when the tested sample has a stated relation to that class, such as justified coverage, sampling, independence, or an invariant mechanism. Surface variety and sample count alone do not satisfy reach-assessment.

Proof provides a non-empirical route. A theorem, invariant, type property, or exhaustive model check can establish a decomposition's scope across its specified formal domain without an empirical encounter. This is genuine earned scope inside the model. The model-to-world bridge remains a separate claim, because formal reach is bounded by its causal and proof obligations.

The practical question is therefore not whether a decomposition has been used. It is what scope the decomposition claims, what kind of test fits the claim's representational form, and what domain that test actually covers.

Provenance and retained rationale answer different questions

Retained rationale records what each boundary answers to: an inherited constraint, a local requirement, or an underdetermined choice. Provenance records why that boundary's scope claim begins with support: derivation, inheritance, or neither. The classifications overlap but do not map one-to-one.

Derivation can operate on either of the first two rationale slots. A boundary may follow from a substrate constraint or from one application's local requirements. For example, scenario decomposition derives boundaries from problem-local context needs without borrowing them from another domain. Its conditional warrant extends only to problems that share those needs. Inheritance instead records where a rationale and its evidence came from; it does not determine which rationale slot every borrowed boundary occupies.

The distinction matters because a provenance label is useful only when the record makes its obligations checkable. A derivation record must state the constraint and its predicted effect on the boundary. An inheritance record must state the source test and the target bridge. Without those details, the label names an obligation but provides no way to test it.

Two recorded instances

The representational-form decomposition is derived from the axes of consequence assignment and localization. Those axes generate three occupied cells, an explicit empty fourth cell, and the read/test/probe rule. Its starting warrant applies only while the axes remain consequential. A formal proof could establish the generated cells inside a formalization; empirical use must still test whether the axes mark consequential distinctions in a target system.

Reflective system is inherited from prior reflection research. Its definition records the inherited criteria separately from Commonplace's local extension. Applying those criteria outside the source setting therefore carries a bridge obligation: the causal connection and self-representation constraints must still distinguish the target cases that the definition claims to cover.

Scope

  • The quality of inherited testing remains difficult for a borrower to audit. A mature ontology may have survived because no relevant rival or boundary case was tried.
  • Abductive support is not a fourth provenance state. It can rank underdetermined candidates, but it does not erase the distinction between a boundary fixed by constraints, one carrying source evidence, and one still awaiting either route.
  • Proof establishes scope only relative to a formal domain. Empirical transfer beyond that domain requires a model-to-world bridge.
  • Commonplace's two recorded instances show that conditional and transferred obligations can be made auditable. They do not show that recording provenance produces better decompositions or that the framework itself transfers.

Open Questions

  • What evidence makes source testing auditable when a borrower cannot rerun the source field's cases?
  • Which coverage, sampling, or invariance conditions let a set of discriminating contexts warrant a claim over an unobserved class?
  • Can intervention on the stated constraint reliably distinguish a fresh derivation from a post-hoc rationalization of a borrowed split?

Relevant Notes: