Termination Preserves Purity More Reliably Than Adaptation

[2025-12-22 Mon]

1. INTRODUCTION

This note formalizes the claim that termination is a structurally purer response to instability than adaptation within a purity-constrained system in Purity and time. The system(see: Ethics(5)):

treats purity as a constitutive constraint¹
excludes justification from admissible execution²
defines identity synchronically, not historically³

Within this framework, adaptation and termination are not symmetric options.

2. Definitions

2.1. Transition

A transition is any state change executed under the system’s ruleset. (see: Transitions and Behavior) Only transitions generated by the ruleset are admissible⁴.

2.2. Adaptation

Adaptation is an intra-systemic modification of the ruleset in response to instability

2.2.1. Formal:

\begin{equation} \exists \tau\; (\tau : R \rightarrow R') \quad\text{executed while } R \text{ is still authoritative} \end{equation}

2.3. Termination

Termination is the cessation of execution:

\[ \neg \exists \tau\; \text{such that } S_{t+1} \text{ is defined} \]

3. Thesis

Termination preserves purity more reliably than adaptation. \[ \text{Purity}(S) \succ \text{Continuity}(S) \] This is a dominance relation under purity constraints.

4. Why Adaptation Is Structurally Risky

Adaptation requires ≥1 of the following:

Evaluation The system must assess its own performance or adequacy⁵.
Comparison The system must compare current rules to possible alternatives⁶.
Justification The system must treat some change as warranted⁷.

Each of these bring extra-systemic criteria into execution.

Formally, adaptation implies: \[ \exists a \notin R \;\wedge\; \text{Executed}(a) \]

Which violates order and purity simultaneously(see: Order and Purity) ⁸.

5. Why Termination Is Structurally Clean

Termination involves no new transition types.

It is the last admissible transition.

Termination therefore satisfies: \[ \forall a\; (\text{Executed}(a) \rightarrow a \in R) \]

up to and including cessation.

6. Death

An update requires(see: Meta-Update Process):

reasoning
justification
value comparison
tradeoff evaluation

These are explicitly excluded.

Therefore:

meta-updating within the system is impossible
meta-updating after termination is coherent⁹

The system must “die” for the update to occur.

This death is a type-correct exit¹⁰.

7. Elsewhere

7.1. References

7.2. In my garden

Notes that link to this note (AKA backlinks).

Footnotes:

Constitutive constraint: a property without which the system is not instantiated at all, rather than a goal the system aims to realize.

See Structural Purity and Moral Identity: justification is excluded from admissible transitions.

See Holding Grudges: identity does not persist across causal histories; only present structure matters.

⁴

Cf. Order and Purity: admissibility is rule-generated, not outcome-evaluated.

⁵

Evaluation introduces teleology: the system treats itself as aiming at something.

⁶

Comparison presupposes a metric external to the current ruleset.

⁷

Justification is reasoning about reasons; this is meta-systemic by definition.

⁸

See formal definition of Order: no executed action may lie outside the ruleset.

⁹

Meta-reasoning is permitted only when the system is not running. nn

¹⁰

Analogy: a well-typed program exiting normally rather than catching undefined behavior.