Order and Purity
* journal philosophy ethics work frontier1. Background.
In Ethics(5), we use terms like 'order', and in Structural Purity and Moral Identity we use 'purity'. What do we mean when we say this?
2. Definition of ORDER
2.1. Informal
Order is the property of a system whose state-transitions are fully determined by its ruleset, without contradiction, bypass, or uncontrolled coupling to external inputs. They are non-contradictory and predictable. Order excludes impulsive, ad-hoc, or exception-based transitions.
2.2. Formal
\[ \text{Order}(S,t) \;\overset{\mathrm{def}}{:=}\; \forall C_1, C_2 \; \big( C_1 \equiv C_2 \;\wedge\; R_t \Rightarrow A_t(C_1) = A_t(C_2) \big) \]
Where:
- \(C_i\) are contexts
- \(R_t\) is the active ruleset at time \(t\)
- \(A_t(C)\) is the action selected under context \(C\)
Order therefore implies:
\[ \neg \exists a \; \big( a \notin R \;\wedge\; \text{Executed}(a) \big) \]
3. Definition of PURITY
3.1. Informal
Purity is the invariant property that all admissible transitions preserve order, non-coercion, symmetry, and boundary integrity, independent of outcomes. Purity means: no contaminating transition is allowed into the system.
3.2. Formal (Minimal)
\[ \text{Purity}(S) \;\overset{\mathrm{def}}{:=}\; \forall a \in \text{Actions}(S): \text{Admissible}(a) \Rightarrow \text{Preserve}(a,S) \]
Where preservation expands as:
\begin{equation} \text{Preserve}(a,S) \;\iff\; \begin{cases} \neg \text{Coerce}(a) \\ \neg \text{Asymmetry}(a) \\ \neg \text{Destabilize}(a,S) \\ \neg \text{BoundaryLeak}(a,S,E) \end{cases} \end{equation}4. Relation Between Order and Purity
Order is not sufficient for purity.
Purity = Order + Constraint Closure.
Formally: \[ \text{Purity}(S) \Rightarrow \text{Order}(S) \]
But: \[ \text{Order}(S) \;\not\Rightarrow\; \text{Purity}(S) \]
A system can be orderly and still:
- coerce consistently
- dominate symmetrically
- violate boundaries predictably
5. Why Purity Is Not a Value
Purity is posited as an axiom of admissibility:
\[ \mathcal{P}:\quad \text{Transitions violating purity are excluded from the action space} \]
No justification follows. No persuasion is attempted. No universality is claimed. Violating purity means it is no longer this system.
This avoids:
- moralism
- ego-defense
- justificatory regress
6. Elsewhere
6.1. References
6.2. In my garden
Notes that link to this note (AKA backlinks).