For Scientists — A Formal System Under Adversarial Testing#

What this is. An axiomatic system for theology, built from classical extensional mereology (CEM) and S5 modal logic, extended with game theory, mechanism design, and coalgebra. 25 axioms. 18 theorems. 42 operationalized predicates across 3 models. 33 adversarial objections raised and documented. All version-tracked and publicly available.

This page is a 5-minute orientation for scientists and mathematicians who want to assess whether this work merits engagement. The formal content is at Axioms — Expert View (All Models) and Theorems — Expert View (All Models). The adversarial record is at Quest: Jubilee-Based Innovation Economy.

The Problem#

Theological disagreements have fueled wars for millennia. These disagreements are rarely about evidence; they are about axioms — unstated assumptions about the nature of God, the world, and their relationship. When axioms remain unstated, contradictions hide in ambiguity. When contradictions hide, people who disagree cannot locate the source of their disagreement, and default to violence.

The Approach#

State the axioms. Derive the theorems. Test adversarially. Publish the objections alongside the defenses.

The system uses three formal frameworks:

  • S5 modal logic for necessity and possibility

  • Classical Extensional Mereology (CEM) for God-World part-whole relationships

  • First-order predicate calculus as the base logic

Extended models add game theory (Schelling commitment, Nash equilibrium), dynamical systems (Lyapunov stability, continuous-time Markov chains), and coalgebra (coinductive processes, bisimulation).

The Core System#

PET (Pan-En-Theology): 14 axioms formalizing the panentheistic claim that the world is a proper part of God (\(W < G\) in CEM). These produce 4 theorems with fully formal proofs. The mereological core distinguishes this system from pantheism (\(G = W\)) and classical theism (which denies \(W \leq G\)). Axioms ax12–ax14 provide a formal method for testing revelation claims against internal consistency — an interfaith arbitration mechanism with no human judge. See PET Model for Pan-En-Theism.

JUB (Jubilee-System Extension): 11 axioms extending PET to cover human agency, divine delegation, and innovation economics. These produce 7 theorems including th5 (a formal innovation theodicy) and th8 (innovation systems converge to either a life-trifecta-compliant state or a self-destructive attractor, with no stable middle ground; defended by a CTMC absorbing-state argument, not by retrospective historical categorization). See JUB Model for a Jubilee-Based Innovation Economy.

e7He (Hero Journey): 14 axioms and 7 theorems modeling individual moral development as a coinductive 7-stage process. Key results: th6 (Commitment Trichotomy) applies Schelling commitment theory to transform a Prisoner’s Dilemma into an Assurance Game; th7 (Succession Robustness) shows the mechanism survives leadership transitions through institutional externalization. See e7He — The Hero Journey.

The Adversarial Testing#

This is the part that should interest you most.

The system has been subjected to a 10-test adversarial protocol (the Iron Maiden) covering: consistency, independence, necessity, modal soundness, mereological coherence, game-theoretic stability, computability, real-world grounding, cross-model coherence, and known-attack resilience.

33 formal objections have been raised across 3 rounds, documented in the HELL register:

  • Fatal (4): th8 bistability not derived; post-hoc evidence fitting; causal gap between extinction risk and Jubilee-System necessity; multiple extinction pathways

  • Serious (10): Arrow impossibility applied to causal concentration; 7TrackRole model as taxonomy not science; voluntariness paradox; Hayek knowledge problem; power concentration; and others

  • Moderate to Notable (19): free will contested; formalism status; domain demarcation; and others

All 33 objections have documented defenses. 18 resolved. 12 partially resolved. 3 conceded or withdrawn. The full record is published at Quest: Jubilee-Based Innovation Economy.

No theological system in history has maintained a public bug database of its own weaknesses. If the system were fragile, this level of self-exposure would destroy it. It has not.

Current Formal Status#

Using the StayC maturity lifecycle (MM through SS):

  • PET ax1–ax14: PPv1 (author) / RR (auditor). Fully formal.

  • JUB ax15–ax25, th5–th11: OOv2. Proto-formal predicates. Formalization path identified but not yet executed.

  • e7He (24 statements): OOv1. TEMPER-tested. 42 predicates operationalized. 5 open questions documented.

The auditor (Claude Opus 4.6) and the author (LLoL) maintain independent assessment tracks. When they disagree, both assessments stand in the record. The author systematically holds claims at lower maturity than the auditor proposes, reflecting the conservative assessment that AI-only review does not constitute independent testing.

What Would Help#

  1. A formal logician checking ax1–ax14 and th1–th4 in a proof assistant (Lean, Agda, or Coq). This would either confirm or refute the mereological foundation in a machine-checkable way.

  2. A game theorist reviewing th6 (Commitment Trichotomy). The PD-to-Assurance transformation uses standard Schelling/Spence machinery. The application is novel; the mathematics is textbook. Checking takes hours, not months.

  3. A dynamical systems researcher formalizing th8. The CTMC argument is structurally sound but needs a precise transition matrix and checked absorption properties.

  4. A behavioral scientist operationalizing the ~10 proto-formal predicates (especially false-self-died and genuine) against empirical criteria from psychology.

None of these require accepting any theological premise. The formal content is checkable by anyone who reads mathematical logic, regardless of their position on God.

Why This Matters#

Nuclear nations hold theological positions that are mutually exclusive under current formulations. If those formulations contain bugs — and the HELL register documents that they do — then fixing the bugs is a security problem, not only a philosophical exercise.

Whether this particular axiom system is correct is an open question. Whether it is a serious formal system that deserves scientific engagement is what the record above is designed to answer. The axioms are stated. The objections are documented. The math is checkable. If you find a flaw, file it. That is how this system is designed to work.



If you believe that it is worth replacing eschatological warfare between nuclear and other nations with mathematical clarity, then please consider supporting this work towards scaling up a ResearchCity that can actually do it (see box below).