{"slug":"hunter-rules-of-logic-science-proof","identifier":"hunter-rules-of-logic-science-proof","title":"The Rule(s) of Logic and Logic Applied to Logic, Science, and Proof by Maclain Hunter","author":"Maclain Hunter","sourceSha256":"9a721430954eafb053405f7db703d2158b367d1000a39c0598cf1e3e3b8f913a","sourceKind":"authored-foundational-record","recordedAt":"2026-10-02T14:38:29.622Z","recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:42:29.891Z","status":"partial","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.inference_2","HunterAuthored.inference_4","HunterAuthored.inference_5","HunterAuthored.inference_7","HunterAuthored.inference_8","HunterAuthored.source_identity_rule"],"units":[{"id":"inference_1","sourceStatement":"{1, 1 <-> 2, 2 <-> 3, 4 <-> 5, 5 <-> 6, 6 <-> 7}\n|= (((1 & 2) & (3 & 4) & 5) & 6) & 7","sourceOffset":3407,"scope":"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.","variables":["1","2","3","4","5","6","7"],"premises":["1","1 <-> 2","2 <-> 3","4 <-> 5","5 <-> 6","6 <-> 7"],"conclusion":"(((1 & 2) & (3 & 4) & 5) & 6) & 7","status":"countermodel","countermodel":{"1":true,"2":true,"3":true,"4":false,"5":false,"6":false,"7":false},"reason":"The written sequent alone has a countermodel. No authored wording or unstated premise was changed.","kernelStatus":"not_checked"},{"id":"inference_2","sourceStatement":"{P, P <-> P, P <-> ~Q} |= P & ~Q","sourceOffset":7840,"scope":"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.","variables":["P","Q"],"premises":["P","P <-> P","P <-> ~Q"],"conclusion":"P & ~Q","status":"candidate","leanStatement":"theorem inference_2 (v0 v1 : Bool) :\n    ((!((v0 && (v0 == v0)) && (v0 == (!v1)))) || (v0 && (!v1))) = true := by\n  cases v0 <;> cases v1 <;> decide\n#print axioms inference_2\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_2"},{"id":"inference_3","sourceStatement":"{P, P -> Q} |= P and it leads to logical contradiction. It amounts to saying Logic is “not Logic” which is not Logic (Valid Order and Reasoning). To assume God (Logos) is not God (Logic) would mean that God’s output (Reality - All Existence) is not Reality (what Logic entails).","sourceOffset":7918,"scope":"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.","variables":[],"premises":[],"conclusion":"","status":"unsupported","reason":"Unsupported formal syntax near \". It amounts to saying Logic is “not Logic” w\"","kernelStatus":"not_checked"},{"id":"inference_4","sourceStatement":"{P <-> Q, Q <-> R} |= (P <-> Q) & (Q <-> R)","sourceOffset":9412,"scope":"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.","variables":["P","Q","R"],"premises":["P <-> Q","Q <-> R"],"conclusion":"(P <-> Q) & (Q <-> R)","status":"candidate","leanStatement":"theorem inference_4 (v0 v1 v2 : Bool) :\n    ((!((v0 == v1) && (v1 == v2))) || ((v0 == v1) && (v1 == v2))) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> decide\n#print axioms inference_4\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_4"},{"id":"inference_5","sourceStatement":"{P, P -> Q, Q -> R, R -> S, S -> T} |= ((P & Q) & (R & S)) & T","sourceOffset":12522,"scope":"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.","variables":["P","Q","R","S","T"],"premises":["P","P -> Q","Q -> R","R -> S","S -> T"],"conclusion":"((P & Q) & (R & S)) & T","status":"candidate","leanStatement":"theorem inference_5 (v0 v1 v2 v3 v4 : Bool) :\n    ((!((((v0 && ((!v0) || v1)) && ((!v1) || v2)) && ((!v2) || v3)) && ((!v3) || v4))) || (((v0 && v1) && (v2 && v3)) && v4)) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> cases v4 <;> decide\n#print axioms inference_5\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_5"},{"id":"inference_6","sourceStatement":"{LL <-> LS} |= LL & LS","sourceOffset":14864,"scope":"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.","variables":["LL","LS"],"premises":["LL <-> LS"],"conclusion":"LL & LS","status":"countermodel","countermodel":{"LL":false,"LS":false},"reason":"The written sequent alone has a countermodel. No authored wording or unstated premise was changed.","kernelStatus":"not_checked"},{"id":"inference_7","sourceStatement":"{P, P -> Q, Q -> R, R -> S, S -> T, T -> U, U -> V} |= (((P & Q) & (R & S) & T) & U) & V","sourceOffset":16894,"scope":"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.","variables":["P","Q","R","S","T","U","V"],"premises":["P","P -> Q","Q -> R","R -> S","S -> T","T -> U","U -> V"],"conclusion":"(((P & Q) & (R & S) & T) & U) & V","status":"candidate","leanStatement":"theorem inference_7 (v0 v1 v2 v3 v4 v5 v6 : Bool) :\n    ((!((((((v0 && ((!v0) || v1)) && ((!v1) || v2)) && ((!v2) || v3)) && ((!v3) || v4)) && ((!v4) || v5)) && ((!v5) || v6))) || (((((v0 && v1) && (v2 && v3)) && v4) && v5) && v6)) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> cases v4 <;> cases v5 <;> cases v6 <;> decide\n#print axioms inference_7\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_7"},{"id":"inference_8","sourceStatement":"{P1, P2, P3, P4} |= (P1 & P2) & (P3 & P4)","sourceOffset":17894,"scope":"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.","variables":["P1","P2","P3","P4"],"premises":["P1","P2","P3","P4"],"conclusion":"(P1 & P2) & (P3 & P4)","status":"candidate","leanStatement":"theorem inference_8 (v0 v1 v2 v3 : Bool) :\n    ((!(((v0 && v1) && v2) && v3)) || ((v0 && v1) && (v2 && v3))) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> decide\n#print axioms inference_8\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_8"},{"id":"source_identity_rule","sourceStatement":"Law of Identity","sourceOffset":188,"scope":"The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.","status":"candidate","variables":[],"premises":[],"conclusion":"∀ (α : Type) (a : α), a = a","leanStatement":"theorem source_identity_rule (α : Type) (a : α) : a = a := rfl\n#print axioms source_identity_rule\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.source_identity_rule"}],"files":{"source.json":{"sha256":"7c038326d254e0bc55e3759ae4ed7daffe422a0fddd58676442ebf53b3200df9","bytes":19939},"Proof.lean":{"sha256":"07683b66598bae415a0140aea9283fdac45cb1b88e793416a1bba445a78fe100","bytes":1675},"lean-check.txt":{"sha256":"f7147632b8cdf7e8a4669af00efd4f866c629251cbfa28b166f6be529a37fb26","bytes":419}},"boundary":"Lean establishes the listed formal statements and dependencies. The exact authored source, Ground, known premise meanings, application validation and empirical evidence remain separately typed. 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