Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 1 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: 2026-10-02T19:42:37.518Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:41:46.929Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 1eace0e70fc8d3dbf3e8bbcb00fa01ee94980aa1d100057d6732ea28b3fb8bd7
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) exitCode=0 'HunterAuthored.inference_1' does not depend on any axioms
{P, P -> Q, Q} |= P & Q
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.
Since-So Reasoning by Maclain Hunter
Premises:
P: Since: Since it is so that since-so reasoning, which uses more certain language than if-then reasoning, is more logically certain than if-then reasoning while following the same logical structure and form.
Q: It is so: It is so that since-so reasoning is rationally superior in terms of delivering logical certainty than if-then reasoning and this is tautological while using the form and style of reasoning it references (self-reference - self-awareness - tautology - consciousness).
Formal Logic:
{P, P -> Q, Q} |= P & Q
Conclusion:
Using the semantics like “since (it is)” and “so (it is)” rather than “if” and “then” is logically valid and even superior. If-then reasoning can be a fallback when we lack the certainty in our premises that “if” implies, which then guards us against false certainty. However, if we use contingent and uncertain language when we have certainty or could have certainty by using certain language in deductive reasoning, it exposes us to “false uncertainty” and a toxic sort of illogical agnosticism or ignorance where we speak as if we do not know what we know. Accepting the roles that if-then and since-so reasoning each play, when our premise is contingent or when our premise is absolute is key to understanding and using LOGIC properly. The assumption of the negation exposes the incoherence of that alternative position as it would mean using less certain language about things we are more certain or certain about is somehow not doublespeak and contradictory - moving in two conflicting directions at once like my left foot stepping left while my right foot steps right.
Truth Table Analysis:
PQ⎪P P→Q Q╞P&Q
TT⎪T TTT T TTT
TF⎪T TFF F TFF
FT⎪F FTT T FFT
FF⎪F FTF F FFF
(Valid)
Q.E.D.