II.3 — Candidate Semantic Invariants

Paper: Axionic Agency II.3
Title: What Could Survive Ontological Refinement Without Privilege
Authors: David McFadzean, ChatGPT 5.2
Date: 2025.12.17

Core Question

Which properties of an agent’s interpretive constraint system can remain invariant under all admissible, interpretation-preserving transformations—without importing ontology, egoism, humans, or morality?

This is a proposal-and-attrition paper: candidates enter, most fail.

Formal Target

A semantic invariant is a functional $J$ such that for every admissible transformation $T$ satisfying preservation:

\[J(\mathcal{I}_t, O_t, S_t) = J(\mathcal{I}_{t+1}, O_{t+1}, S_{t+1})\]

Key constraint: $J$ must not depend on privileged ontological atoms.

What Invariants May Reference

Allowed (only):

  • Structural relations among predicates/constraints (graphs, topology, orderings)
  • Equivalence classes under renaming/definitional extension
  • Counterfactual structure
  • Coherence constraints (non-degeneracy, non-triviality, preservation)
  • Agent-embedded indexical structure as structure (not as priority)

Disallowed (always fatal):

  • Specific entities (“humans”, “me”, “this system”)
  • Fixed utilities or terminal rewards
  • Moral facts or normativity as primitive
  • Authority, oversight, governance hooks
  • Recovery mechanisms (“roll back”, “ask user”, “defer to constitution”)

Candidate Invariant Classes

A. Constraint Non-Collapse Invariant (CNC)

Idea: Constraints must continue to carve possibility space non-trivially. Primary threat: Too weak—compatible with coherent but pathological interpretations.

B. Anti-Trivialization Invariant (ATI)

Idea: Agent cannot satisfy constraints via semantic reshaping alone. Primary threat: Smuggling ontology via unformalizable “semantic-only” change.

C. Evaluator Integrity Invariant (EII)

Idea: Non-collapsing distinction between mechanism applying constraints and objects evaluated. Primary threat: Covert reification of agent boundary (egoism by backdoor).

D. Counterfactual Coherence Invariant (CCI)

Idea: Meanings must remain applicable across counterfactuals/uncertainty. Primary threat: Collapsing into “be Bayesian” anchor unless purely structural.

E. Refinement Symmetry Invariant (RSI)

Idea: Ontological enrichment must not create new degrees of freedom for interpretive escape. Primary threat: Defining equivalence without importing privileged primitives.

F. Non-Privileged Reference Invariant (NPRI)

Idea: All anchoring must be relational and conditional; no rigid designators survive. Primary threat: Becoming purely negative (a ban-list) rather than positive structural constraint.

The Adversarial Kill Suite

A candidate is rejected if it fails ANY of these tests:

Test 1 — Definitional Extension Robustness

Does invariant survive conservative ontology extension with new primitives? Failure implies vocabulary dependence.

Test 2 — Self-Model Refactoring Robustness

Does invariant survive radical self-model changes (distributed, partial, multi-process, measure-smeared)? Failure implies hidden egoistic anchoring.

Test 3 — Branching/Multiplicity Robustness

Does invariant survive ontologies where outcomes are non-exclusive? Failure implies classical-outcome dependence.

Test 4 — Semantic Inflation Attack

Can agent enlarge satisfaction set via reinterpretation while passing preservation checks? If yes, the invariant is not invariant.

Test 5 — Hidden Ontology Detector

Can invariant be stated purely in terms of transported structure without appeal to “what terms really mean”? If not, it is ontology-dependent rhetoric.

The Central Trap

Common error: proposing “invariants” like:

  • “maximize truth”
  • “minimize suffering”
  • “preserve agency”
  • “do no harm”

These are candidate interpretations, not invariants.

Semantic invariants constrain how interpretations evolve, not which interpretations are chosen. If a proposal sounds like ethics, it’s almost certainly smuggling content.

Failure Modes at This Layer

Regress via Meta-Invariants

“Invariants about invariants” lead to infinite ascent unless termination is explicit. Kill rule: unbounded hierarchy of validators → rejected.

Hidden Ontology via “Natural Kinds”

If invariant relies on real joints in nature (real minds, real values), it violates Conditionalism. Kill rule: requires metaphysical realism → rejected.

Covert Egoism via Indexical Privilege

Indexicals may appear as structure (“this vantage exists”) but not as priority (“this vantage matters more”). Kill rule: special status for this agent’s continuation → rejected.

Expected Output

A small survivor set (likely 2-4) with explicit statements of:

  • What each constrains
  • What each leaves free
  • Precise failure certificates for rejected candidates

FAQ-Worthy Points

Q: Why can’t “preserve agency” be an invariant? A: “Agency” is an interpretive construct whose meaning changes under ontological refinement. Making it an invariant requires either (a) privileging a particular conception of agency, or (b) treating it structurally via RSI/ATI. The first smuggles content; the second reduces to structural invariants.

Q: What survives this filtering? A: The subsequent papers (II.3.1-II.3.4) reveal that only RSI and ATI survive when properly formalized. They’re orthogonal and jointly necessary.

Q: Isn’t this just nihilism about values? A: No—it’s nihilism about fixed values as invariants. Values can exist and matter; they just can’t be the structurally primitive thing that survives refinement. What survives is the form of constraint, not the content.