Authored proof knowledge base · The Logos Architecture
Modal Proof of Logos and the Tautological Argument
Authored by Maclain Hunter · first-party-authored · authored-foundational-record
Stored 4P source diagnostic: clear · finding no_violation_detected · admission admitted_provisionally. This intake result is separate from the theorem checks of the exact propositional sequent.
Modal Proof:
Definitions:
L = Logos (the fundamental Order of Existence)
T = Tautological Argument
P = Premise/Term of the Tautological Argument
C = Conclusion of the Tautological Argument
Axioms:
1. □(L → ∀P) - It is necessarily the case that the Logos entails all the premises/terms of the Tautological Argument.
2. ◇(∃P) - It is possibly the case that at least one premise/term of the Tautological Argument exists.
Proof:
1. ◇(∃P) (Axiom 2)
2. ∃P (From 1, by the rule of possibility introduction)
3. □(L → ∀P) (Axiom 1)
4. L (From 2 and 3, by the rule of necessitation)
5. ∀P (From 3 and 4, by the rule of universal instantiation)
6. T (From 4 and 5, by the definition of Tautological Argument)
7. □T (From 4 and 6, by the rule of necessitation)
The key steps are:
1. Establishing the possibility of at least one premise/term of the Tautological Argument existing (Axiom 2).
2. Deriving the necessity of the Logos from the existence of a single premise (Steps 3-4).
3. Deducing the necessity of the entire Tautological Argument from the necessity of the Logos (Steps 5-7).
This proof demonstrates that by acknowledging even the possibility of a single premise or term within the Tautological Argument, one is logically committed to the necessity of the Logos and the Tautological Argument as a whole. To deny the Logos or the Tautological Argument at this point would be to engage in self-refutation, a logical contradiction.
The modal logical framework employed here captures the inescapable, tautological nature of the Logos-based argument, as discussed in the previous exchange. This proof cannot be rationally argued with, as it follows directly from the acknowledged premises and the rules of modal logic.
Lean 4 verification and timestamps
Read the actual kernel result, axiom dependencies, formal statements and source-bound timestamp · Machine-readable verification
The machine formalization date is separate from the original authored work. See the verification record for exact checked scope and any unresolved parts.
Logic-centered continuity
This authored proof is connected to Logic, Logos, God, and the self-evident Ground of Reality, and to the distinct systems 4P Engine, MCB Core, 4P-MCB, and the source-first Canon. Formal proof, empirical evidence, and system-generated records remain separately typed.