TheoryTHY-2026-0004v0.1

Probability is not Bayesian; Bayes cannot self-authorize its premises

A system can be stochastic, probabilistic or probability-shaped without performing Bayesian conditionalization, and can look Bayesian without a real prior, likelihood or posterior. A layered vocabulary (stochastic, probabilistic, Bayesian-like, exact, approximate, generalized Bayesian) and a Bayesian authenticity test check whether an update is substantively Bayesian or merely redescribed as such; and the update rule itself — prior, likelihood, hypothesis space — needs a justification that Bayes' rule does not supply (Papers 09–10).

Research status: PRELIMINARY a first formalisation or observation exists
Evidence level: E0 Concept only
Data basis: THEORY Theoretical reasoning only; no measurement.
Version: 0.1
Updated: 2026-09-08
Created: 2026-09-10
Domain: Formal AI, Reasoning
Program: PRG-2026-0001 Adaptive Epistemic Systems
Authors: Neo.K (EveMissLab)
AI collaborators: Sol (GPT-5.6, OpenAI ChatGPT)

Claims

claims: 'This is a probabilistic system' and 'this is a Bayesian system' are not equivalent statements.
Bayesian updating is one belief-revision operator among several; the epistemic router should choose the operator explicitly and record its provenance.

Predictions

predictions: An adaptive epistemic router beats AlwaysBayes, AlwaysLogic and AlwaysRobust across mixed domains only if operator choice is explicit and traced (Paper 11 §86).

Falsification / failure conditions

falsification_conditions: Fixed Bayesian updating dominates every mixed-domain test at equal cost.

Known limitations

known_limitations: Formal/conceptual so far; the AER-0 router implements four operators but no mixed-domain routing benchmark has been run.

Relations

Source	Relation	Target	Status	ID
`RES-2026-0001` Blind derivation of an adaptive epistemic architecture	`develops`	`THY-2026-0004` Probability is not Bayesian; Bayes cannot self-authorize its premises	`ACTIVE`	`REL-2026-0013`
`RES-2026-0002` PACC conjecture — do non-probabilistic primitives converge to probability-like structure?	`develops`	`THY-2026-0004` Probability is not Bayesian; Bayes cannot self-authorize its premises	`ACTIVE`	`REL-2026-0014`
`PAP-2026-0009` Paper 09 — Probability is not Bayesian	`formalizes`	`THY-2026-0004` Probability is not Bayesian; Bayes cannot self-authorize its premises	`ACTIVE`	`REL-2026-0042`
`PAP-2026-0010` Paper 10 — Bayes within Bayes: who authorizes the update rule?	`formalizes`	`THY-2026-0004` Probability is not Bayesian; Bayes cannot self-authorize its premises	`ACTIVE`	`REL-2026-0045`

History and provenance

Canonical URL

https://evemisslab.com/ai/theory/THY-2026-0004/

Machine-readable

/ai/theory/THY-2026-0004/index.json

Snapshot

AI-SNAPSHOT-v0.1-fe85b9694a45

Provenance

source: EveMissLab research collection: Adaptive Epistemic Systems (真本體論13)
extracted_by: Splice (Claude Code), reading the canonical UTF-8 sources and each lab's own result reports
extracted_at: 2026-09-11
generator: tools/extract_aes/extract.py
claim_boundary: status, evidence level and result type follow the source artifact's own stated claim boundary; nothing is upgraded beyond what the report supports