The method-war, run as code
For ninety years the fight over economic method — Austrian a-priorism against logical positivism — has been conducted in prose. Here it is conducted in the interpreter: every claim below is a check, and Axioma returns a verdict. The distinction that decides it — a priori vs. empirical — runs on two orthogonal axes Axioma tracks for every fact: its grounding tier (how it was derived) and its kind (what it draws on). Distilled from the 10-assertion showcase.
A footnote history left in place: the quarrel ran through one family — Ludwig von Mises, a-priorist economist, against his brother Richard von Mises, of the Vienna Circle. Ayer is Richard's argument in English.
Ayer's verification principle, turned on itself
The criterion: a statement is meaningful iff it is analytic or empirically verifiable. It is not a vacuous stamp — a genuine empirical claim does pass. But apply it to the principle itself, which no observation can confirm, and by its own test the principle is a pseudo-statement. Logical positivism fails its own criterion.
The action axiom is not an empty tautology
The standard charge (Samuelson, Nozick, Blaug): praxeology's axiom — humans act — is true by definition, hence says nothing. Tested on the positivists' own analytic machinery (truth over every state-description), a real tautology is L-true; the action axiom is not. It is substantive — yet no observation verifies it either, so Ayer's classifier files it as pseudo. That is the fault line: the synthetic a priori box Ayer's two-way criterion denies exists.
Pure praxeology is a priori — Mises vindicated
From the action axiom, deduce: an actor has time preference, therefore interest exists. Every step is a strict rule, so the conclusion is a derived theorem — and because no observation enters its support, its kind stays a-priori (logical). For the pure theory, Mises is right: economic law without experience.
Applied economics is empirical — Ayer vindicated
Now Austrian Business Cycle Theory over a specific economy: a credit expansion → malinvestment → an unsustainable boom → the bust. The deductive form is identical (still a theorem), but the moment it names an actual observed credit expansion, the whole chain inherits empirical content. Applied Austrian economics is not pure a priori — and Axioma marks the seam automatically, on the kind axis, without touching the tier.
What the interpreter settled — and what it didn't
No executable system can end a ninety-year dispute. What it can do is make the assertions decidable, disprove specific sub-claims on each side's own terms, and locate the one question that remains genuinely open.
“the action axiom is an empty tautology” — it is not analytic (L-true = false). It says something.
“the verification principle is itself meaningful” — it is pseudo by its own test.
“applied Austrian economics is pure a priori” — the ABCT bust carries kind empirical.
“pure praxeology is a priori” — the deductive core stays kind logical, tier theorem.
Whether the synthetic-a-priori box the action axiom occupies is real (Kant, Mises) or an illusion (Ayer, Quine). The engine forces the axiom into that box; it cannot decide whether the box exists.
The honest headline is not “Mises wins” or “Ayer wins.” Each is right about a different half — Mises about the deductive core, Ayer about empirical application — and Axioma draws the seam between them per proposition, which neither could do in prose.
Run the whole argument
The full ten-assertion adjudication lives in the repo and runs in the sweep. Fork it, change the economy, add a premise — and watch the a priori / empirical line move with it.