Aristotelian Logic — The first formal system of reasoning — and the default assumption in almost every philosophy debate today.
Eastern Logical Traditions — The convergence proof: independent civilizations, no contact, same structural insights — centuries before the West caught up.
Emergence, Convergence, and the Strange Loop — The vault’s metaphysical position, stated explicitly: what logic is, why it works, why it doesn’t need God, and what it can’t prove about itself.
Intuitionistic Logic — What if truth requires proof? Drop the excluded middle and logic becomes constructive — and accidentally invents the theoretical foundation of programming.
Non-Classical Logics — What happens when you challenge the other axioms? Contradictions that don’t explode, truth that comes in degrees, and premises that must actually be relevant.
Quantum Logic — The other non-classical logics were invented by philosophers.
The Formal Revolution (1847–1931) — In 84 years, logic went from a philosophical discipline to the foundation of mathematics, computing, and the limits of knowledge itself.
The Translation Problem — Formal logic is only as good as the translation from reality into symbols.
The Regress Problem — Agrippa’s trilemma and the performative escape; logic’s axioms aren’t assumed, they’re constitutive of reasoning.
The Absoluteness Claim — the case against “the laws of logic are absolute, therefore God” made without Gödel or self-reference; unbundles the three laws into a tautology, a bookkeeping rule, and one empirical bet
Formal Systems and Approximation — the Euclid worked example — what a formal system is, Saccheri deriving hyperbolic geometry and refusing it, Beltrami’s relative-consistency model, and the extension that matters: a proposition is as idealized as a point
The Consistency Defeater — never claim his system is inconsistent — claim a proof is worth only your confidence the system never contradicts itself; the printing machine, the parity move, and the substantive-or-safe fork
The SQL Argument — the opener — three-valued SQL, NULL = NULL is not TRUE, and the breakfast-next-Tuesday fork that makes the epistemic rescue cost him free will
Theorems With Absurd Readings — argue from theorems, not mistakes — the drinker paradox worked line by line, and explosion as a valid proof of God and of no-God
Logics In Production — rival consistent logics that ship — excluded middle as an opt-in axiom in Coq/Lean, fuzzy control walked through with its own refutation, independent civilizations
Malpass vs Dyer — TAG and the Laws of Logic — the 2019 technical version: concedes alternative formal systems, claims Gödel as an ally, denies being an Aristotelian; the later corpus drops every technical thread
The Parity Move — apply the “account for your foundation” demand symmetrically; kills the uniqueness claim, not the conclusion. Euthyphro is the moral instance; the leveler is the door, not the room
What Is a Number? — von Neumann vs. Zermelo ordinals; two incompatible sevens, identical arithmetic; the Benacerraf datum and structuralism
The Blind Pill (Ruelas vs. AVG) — a coiner defending his definition against a clip of himself; a “dilemma” whose two answers get their consequences by stipulation