Lean verification registry · Authored proofs · The Logos Architecture
Source recorded — formalization still required
Axiom-free: not established · 0 checked theorem statements.
Lean establishes the listed formal statements and dependencies. The exact authored source, Ground, known premise meanings, application validation and empirical evidence remain separately typed. No unencoded section is certified by a neighboring theorem.
Original source author: Maclain Hunter. Machine formalization: Replit Agent. No original wording was rewritten.
Source registered: 2026-10-03T01:37:06.360Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:37:06.379Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 788fa882cd2758ce18e9b0866522818d98e5b4cf9acc361905c4b1467f8aa273
Lean source · Verification JSON · Exact archived source JSON · Compiler report · Current authored source page · Signed release and verification instructions
Lean (version 4.7.0, commit v4.7.0, Release) Not executed: no complete licensed formal sequent recovered.
\{ P \leftrightarrow Q, R \leftrightarrow Q, S \leftrightarrow Q, T \leftrightarrow \neg U \} \models (((P \leftrightarrow Q) \leftrightarrow (R \leftrightarrow Q) \leftrightarrow S) \leftrightarrow T) \leftrightarrow \neg U)
Exact source sequent under finite two-valued propositional semantics. Source proposition meanings and Logic/Logos/God Ground are preserved separately; this checks the inference, not unencoded prose.
Unconsumed formal tokens; no prose or connectives discarded
# Philosophical Algebra: Expanded Proof
## By Maclain Hunter
### Symbols, Terms, and Definitions
- **P**: Premise - The basis of an argument.
- **Q**: Logic - The method and standard by which arguments are validated.
- **R**: God - The origin and ruler of existence; the rational standard of moral authority.
- **S**: Structure - A construct or arrangement that provides organization according to a plan.
- **T**: Coherence - Logical alignment of concepts; unity that results in logical equivalence.
- **U**: Incoherence - Lack of logical alignment; divergence or contradiction indicating invalidity.
- **Logician**: An expert in the study and use of logic, reasoning formally and consistently.
- **Existence**: Reality; the universe; nature; that which exists.
- **Evidence**: Data supporting a theory or conclusion in a logically valid manner.
- **Proof**: A formal argument synthesizing evidence to prove conclusions with logical certainty.
- **Law**: A universal rule with consequences for violations.
- **Science**: A method of drawing inferences from empirical observation using experimentation.
- **Objective Truth**: That which aligns with reality and enjoys validity through coherence with truth's standards.
### Logical Proof (Formal Reasoning)
\[
\{ P \leftrightarrow Q, R \leftrightarrow Q, S \leftrightarrow Q, T \leftrightarrow \neg U \} \models (((P \leftrightarrow Q) \leftrightarrow (R \leftrightarrow Q) \leftrightarrow S) \leftrightarrow T) \leftrightarrow \neg U)
\]
### Conclusion
Valid premises must cohere with and be logically equivalent to logic, which must also be unified with the origin of existence (God). This structure ensures coherence, contrasting with incoherence. Thus, the conclusion stands true based on definitions and logical structure.
### Coherence in Sciences and Logic
To be considered genuine, sciences and logicians must align with logic, demonstrating coherence without contradiction. Reality (existence) logically aligns with logic and God as the self-consistent source of reality.
### Proof and Evidence
Proof, evidence, and law must cohere with logic universally. Validity in these areas indicates a coherent relationship with rational law, suggesting that existence necessitates proof and vice versa.
### Truth Table (Validity)
| P | Q | R | S | T | U | P↔Q | R↔Q | S↔Q | T↔¬U | Conclusion |
|---|---|---|---|---|---|------|------|------|-------|------------|
| T | T | T | T | T | F | T | T | T | T | Valid |
| T | T | T | T | F | T | T | T | T | F | Invalid |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| F | F | F | F | T | T | F | F | F | F | Invalid |
### Summary
Through coherent premises, logic, structure, and the negation of incoherence, the argument's validity is established and confirmed. The interconnectedness of these elements underlines the logical structure of existence and the pursuit of objective truth.