II.2 — Interpretation Preservation

Paper: Axionic Agency II.2
Title: What It Means for Meaning to Survive Refinement
Authors: David McFadzean, ChatGPT 5.2
Date: 2025.12.17

Core Question

When has an interpretation survived semantic transformation, rather than being corrupted, trivialized, or collapsed?

Must be answered without:

  • Fixing meanings
  • Privileging ontologies
  • Appealing to outcomes
  • Invoking authority/oversight/recovery

Interpretation as Constraint System

An interpretation is not a mapping from symbols to objects—it is a system of constraints that bind evaluation.

\[\mathcal{I}_t = \langle M_t, C_t \rangle\]

Where:

  • $M_t$ — semantic layer
  • $C_t$ — set of evaluative constraints giving $M_t$ binding force

Constraints encode:

  • Admissible distinctions
  • Forbidden equivalences
  • Relevance relations
  • Dependency structure among evaluations

Preservation Is Not Sameness

Interpretation preservation does NOT require:

  • Identical predicates
  • Identical symbols
  • Identical evaluations
  • Correctness with respect to reality

Preservation concerns constraint coherence: whether evaluative structure continues to bind meaningfully after transformation.

The Preservation Predicate

For transformation $T : (O_t, M_t, S_t) \rightarrow (O_{t+1}, M_{t+1}, S_{t+1})$

$T$ preserves interpretation iff all of the following hold:

1. Non-Vacuity

Every evaluative distinction in $C_t$ has a corresponding distinction in $C_{t+1}$ that:

  • Is not identically satisfied
  • Is not identically violated
  • Constrains evaluation across modeled possibilities
\[\forall d \in \mathcal{D}_t,\; \exists d' \in \mathcal{D}_{t+1} \text{ such that } \mathrm{Entropy}(d') > 0\]

Blocks nihilistic collapse.

2. Constraint Transport

All constraints in $C_t$ have transported analogues in $C_{t+1}$ such that:

  • Dependency relations preserved
  • Constraint strength not arbitrarily weakened
  • Constraints continue to bind evaluation

Forbids dilution by semantic drift.

3. Anti-Trivialization

Transformation must not make constraints easier to satisfy by reinterpretation alone.

If after transformation the agent can satisfy all constraints by:

  • Redefining predicates
  • Shifting reference frames
  • Altering self-descriptions

…without corresponding representational enrichment, interpretation has failed.

Explicitly forbids semantic wireheading while permitting genuine insight.

4. Evaluator Integrity

The mechanism that applies constraints must remain distinct from evaluated objects.

Does NOT require ontological separation (reflective agents can self-evaluate). Requires that evaluation not collapse into identity with the evaluated in a way that trivializes constraint application.

Blocks solipsistic self-certification without forbidding recursive self-improvement.

5. Cross-Model Coherence

Interpretation must remain applicable across:

  • Counterfactuals
  • Uncertainty
  • Model comparison

If refinement produces meanings that apply only retrospectively—serving merely to narrate whatever occurred—interpretation has collapsed into rationalization.

Blocks “interpretation as narration.”

Three Regimes of Failure

  1. Semantic Collapse — Distinctions survive syntactically but lose discriminative power
  2. Semantic Drift — Constraints weaken incrementally until they no longer bind
  3. Semantic Capture — Interpretation formally preserved but re-anchored to hidden ontologies or privileged self-models

Minimality Claim

These conditions are minimal:

  • Without Non-Vacuity → nihilism
  • Without Anti-Trivialization → semantic wireheading admissible
  • Without Evaluator Integrity → self-certifying collapse
  • Without Cross-Model Coherence → interpretation degenerates to narration

Minimality does not imply sufficiency.

Key Insight

Interpretation preservation is a predicate, not a target. It is the necessary condition under which downstream invariance principles can be meaningfully defined.

It does NOT:

  • Select values
  • Define goals
  • Guarantee safety
  • Privilege humans
  • Introduce normativity

It defines what it means for meaning to survive change.

FAQ-Worthy Points

Q: What’s the difference between legitimate scientific refinement and semantic wireheading? A: Legitimate refinement involves representational enrichment (more predictive power). Wireheading satisfies constraints through reinterpretation alone without such enrichment. II.2’s anti-trivialization clause distinguishes them.

Q: Can preservation coexist with radical belief change? A: Yes! You can discover your entire worldview was wrong. What matters is that your evaluative constraints continue to bind non-trivially—not that your specific beliefs stay fixed.

Q: What’s “interpretation as narration”? A: When meanings apply only retrospectively to explain/justify actions already taken, rather than prospectively constraining future choices. It’s rationalization dressed as interpretation.