Axiom Hierarchy — Bedrock vs Derived
Axiom Hierarchy — Bedrock vs Derived
§SELF — oip-axiom-hierarchy
What this page is: the dependency ordering the twelve axioms were missing. What it explains: A0 cannot fully self-justify without circularity; bedrock is admitted; derived axioms are prosecuted by bedrock. Why read it: reflexive incompleteness (Gödel-adjacent; you published the no-go shape) demands a named un-prosecutable floor.
Bedrock (asserted — load-bearing — cannot self-justify without circularity)
| ID | Name | Role | |---|---|---| | A0 | Inversion | Validity test: concepts face negation. Bedrock of method. | | A11 | Receipt is the proof | Validity test for claims about systems: checkable record. Bedrock of evidence. (If A11 is not numbered in a given edition, the same role is held by the receipt principle in OIP + what-is-receipt-is-proof.) |
We admit: A0 cannot be proven by A0 without circularity. Its negation ("untested claims are fine in adversarial environments") is rejected as operational suicide, not as a theorem inside the system. That is the price of a floor.
Derived / prosecuted by bedrock
| ID | Prosecuted by | How | |---|---|---| | A1–A3 | A0 | Survive negation tests in ground book | | A4 | A0 + declared choice | Meta-ethical atom is chosen; rivals named on A4 | | A5 | A0 + A4 | Prejudice contamination | | A6–A7 | A0 | Structural/recurrence | | A8 | A0 + A5 | Must compose: A8×A5 | | A9+ | A0 + A11 | Downstream operational |
What we refuse
All twelve floating at the same level as if each were self-proving. That is the trap.
Links
- A0 · A4 · A5 · A8
- Twelve axioms
- No-go theorems