docs/subject-reduction.md
Attacking Subject
Subject attacked with the methodology used throughout. Eighteen candidates across eight domains, seven reductions attempted, layers kept separate.
Outcome: "Subject" is not one thing. Three of its four classes reduce constructively. Continuants resist — by a consistently diagnosed mechanism, not by accident. Identity itself decomposes into lineage plus convention. And the persistence law is found to govern the subject layer too, which predicts a case already independently observed.
1. The falsification ledger
| # | Candidate | Domain | Classification | Reduces to |
|---|---|---|---|---|
| 1 | employee | organizations | role (4) | person + employment state |
| 2 | team | organizations | persistent identity (2) + boundary (3) | resists — membership is a state, the bearer is not |
| 3 | department | organizations | persistent identity (2) + boundary (3) | resists |
| 4 | meeting | organizations | reified episode (2/8) | episode of a state |
| 5 | shipment | transportation | ambiguous — two subjects in one word | parcel (continuant) + shipping (episode) |
| 6 | storm | physics | reified episode | episode of regional state |
| 7 | conversation | organizations | reified episode | episode over participants |
| 8 | disease | biology | conflation — type vs instance | influenza = a value; the infection = an episode |
| 9 | nation | organizations | persistent identity (2) | resists — survives total population replacement |
| 10 | ecosystem | biology | observational convenience (7) | a projection artifact — no fact settles where a forest ends |
| 11 | software service | software | persistent identity (2) | resists — survives complete code replacement |
| 12 | repository | software | persistent identity (2) | resists; forking is the fission case |
| 13 | molecule | chemistry | persistent identity (2) + boundary | resists; dissociation is fission |
| 14 | packet | software | persistent identity, short extent | resists; fragmentation is fission |
| 15 | planet | astronomy | persistent identity (2) | resists — but "is a planet" is convention (Pluto) |
| 16 | orbit | astronomy | relation mistaken for entity (5) | a state over a tuple |
| 17 | project | organizations | reified episode + role-bearing boundary | episode of a state |
| 18 | payment | economics | occurrence promoted to subject | zero-extent subject |
The ledger's first result is that the question was malformed. "Subject" names at least four structurally different things, and asking whether it reduces produced no answer for six rounds because three of the four reduce and one does not.
2. The reductions that succeed — and what moved
Roles → states over a continuant. Employee is not a thing; it is a person under an employment state. Row 1 reduces cleanly, and what moved is exact: the role became a state, the person remained a subject. Nothing was lost, and one subject was removed.
Relations → states over tuples. Orbit is a relation between a body and what
it orbits. This routes through the elimination of relation in
truth-kinds.md and needs no new machinery. What moved: an
entity became a 2-ary state.
Reified episodes → episodes of states. Meeting, storm, conversation, project — and, from dimension-algebra.md, journey and infection. What moved: the subject became an episode, and its name became a label on that episode.
Observational conveniences → projection artifacts. Ecosystem is the clean case: nothing in reality settles where a forest ends. The boundary is drawn by an observer for a purpose. What moved: out of ontology entirely, into projection.
A conflation, not a reduction. Disease names two different things —
influenza is a value on a dimension, while "Alice's infection" is an
episode. Row 8 is not one subject that reduces; it is two things sharing a
word. Same defect shape as shipment, and the same warning as before: classifying
from vocabulary inherits natural language's conflations.
3. The reduction that fails, and exactly how
Continuants — team, nation, service, repository, molecule, packet, planet — resist every attempted reduction, and the resistance has one mechanism.
| Reduction | Fails because |
|---|---|
| subject → boundary | a boundary gives a set, and sets do not survive membership change. A team persists as members leave; a nation through total population replacement |
| subject → episode | an episode is an episode of a state of something. It needs a bearer, so it presupposes a subject |
| subject → equivalence class over observations | requires knowing which observations co-refer — which is what a subject is |
| subject → lineage over bundles of co-located truths | requires spatiotemporal location as prior; location is a dimension whose subject is the thing being located |
| subject → persistence | "X persists" is not statable without X |
Every route terminates in the same place: each proposed reduction requires a co-reference relation, and co-reference is what a subject is. That is not five independent failures; it is one failure appearing five times.
That matters for how much the result is worth. A reduction failing for five unrelated reasons would suggest we had not found the right one. A reduction failing for the same reason five times identifies the phenomenon that resists: co-reference.
4. Identity decomposes
The four candidate criteria, each tested against known hard cases:
| Criterion | Fails on |
|---|---|
| continuity | gaps — a disassembled engine, a suspended process, an unobserved parcel in transit |
| boundary | part-replacement — Ship of Theseus, a nation's population, a service's code |
| causal persistence | fission — both halves are causally continuous with the original |
| equivalence over observations | circular unless the relation is independently given |
The first two fail on different cases. The third and fourth fail on the same one, and so does every other criterion tried: fission and fusion, where the relation is not one-to-one. An amoeba divides. A company spins off. A repository is forked. A molecule dissociates. A packet fragments.
Identity as an equivalence relation is transitive and therefore one-to-one — and so it is structurally too strong to describe what actually happens. What survives fission is not identity but a many-to-many lineage over stages.
Identity = lineage (ontological) + a selection rule (convention).
Lineage is a causal graph and is a fact about the world. The selection rule — which branch keeps the name — is a decision, and no fact determines it.
This explains why identity has felt slippery through six rounds: it fuses a real structure with a convention and presents the pair as one thing.
And it predicts that any system handling fission must supply a naming convention its ontology cannot justify. Confirmed in three domains independently: git names a fork by fiat; corporate spinoffs are settled by legal decision; species naming is settled by committee. None derives the answer; all three decide it.
5. The persistence law governs the subject layer too
Subjects turn out to carry a persistence extent, exactly as truths do:
| Extent | Subject class | Examples |
|---|---|---|
| until-change | continuant | planet, molecule, repository, team |
| bounded episode | reified episode | storm, meeting, journey |
| zero | occurrence-as-subject | payment, commit, collision |
This generates the prediction the objective asked for. If the same binary law applies, zero-extent subjects must exist — subjects that are instantaneous and yet bear states. They do: a commit has an author and a message; a payment has a status. truth-kinds.md recorded "occurrences become subjects" as a curiosity three rounds ago. It is not a curiosity. It is predicted.
Same shape as the unary-occurrence prediction in minimal-ontology.md: a structural claim, made before looking, confirmed against something already present.
The "bounded episode" row is not a third value of the law — per dimension-algebra.md, a state episode already has finite duration, so this is until-change applied to a subject whose defining state ends.
6. Layers
The objective requires these kept apart, and for Subject they diverge sharply.
| Layer | Standing |
|---|---|
| ontology | continuants resist reduction; roles, relations, episodes and boundaries do not |
| canonical representation | a SubjectRef — kind, subtype, authority, path |
| computational derivation | none. The system derives no subject identity whatsoever |
| projection | subtype — documented "carries display and provenance and never identity semantics" |
| presentation | naming, labelling, the selection rule after fission |
The third row is the finding. subject.ts documents authority as "the
system of record that owns this identifier." Subject identity is imported, in
full, from an external authority — the system has no mechanism to decide that
two URNs co-refer, and none to represent one subject becoming two.
The aliasing gap recorded in identity-axes.md is the fusion case. Fission has no representation at all. They are one gap: co-reference is delegated, and delegation is invisible in the type.
That is the correct place for it to live — an open system cannot derive co-reference — but it should be recorded as a stated import, not as an absence nobody named.
A predicted defect, found
dimension-algebra.md established that a mutually exclusive
classification placed in a key breaks functionality. urn() is:
`${ref.kind}:${ref.authority}/${ref.path}`
kind is inside the identity. Subject kind is a mutually exclusive
classification — one of six — and classifications change. Pluto is the canonical
case: reclassification alters the URN, so the same object becomes a different
subject and its history splits at the moment of reclassification.
This is the same defect as conditionIdentity and placement@at, now found at
the subject layer, and it was predicted by the law before the file was read.
Third instance of one error.
Recorded, not fixed, per standing instruction.
7. Standing
| Concept | Verdict |
|---|---|
| Subject as a single concept | eliminated — four structurally different things |
| roles, relations-as-entities, reified episodes, observational boundaries | reduced constructively |
| continuant | resists — one diagnosed mechanism, five routes |
| identity | decomposes — lineage (ontological) + selection rule (convention) |
| persistence law | extends to subjects; predicts zero-extent subjects, confirmed |
Continuant is not promoted. One round of sustained attack is not the standard this investigation has used, and the objective explicitly warns against promoting on first failure.
What would falsify the residue: an independent co-reference criterion — one that decides whether two observations are about the same thing without presupposing the thing. Every route above failed at exactly that point, so that is the single thing to attack next.
What is still not established
- The co-reference circularity is diagnosed, not proved inescapable.
- The ledger classifies 18 candidates, which is support, not derivation. The lineage decomposition is the one structural claim here.
capabilityremains untouched — six rounds. It is now by a wide margin the oldest unexamined assumption in the taxonomy.
Nothing implemented.