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Axiomatik der Ökonomik — MoMaT-A working draft online

· 5 min read
Renée Menéndez
Renée Menéndez
OiC.OS
Viktor Winschel
Viktor Winschel
OiC.OS

What is money? Martin Hellwig diagnosed in 1993, and again in 2018, that monetary theory has no conceptual foundations: the word "money" stands for at least four different things — legal tender, medium of exchange, macroeconomic aggregate, unit of account — without the difference ever being formalised. We read that as a type error: the same word for different types.

Our answer is now online as a working draft (PDF): Axiomatik der Ökonomik — Von Schuld- und Erfüllungsverträgen mit Geld, Zinsen und Lernen zum Topos der Wirtschaftspolitik. Citation: MoMaT-A.

This is the German monograph of the MoMaT program — Monetary Macro Accounting Theory. It builds on forty years of Renée Menéndez's work on credit-money capitalism, work by Viktor Winschel since 1996 on monetary theory, compositional game theory, and categorical semantics, and about a decade of joint development since 2018.

The idea in one sentence​

Accounting is not an appendix to price theory. Double and quadruple entry, gauge invariance, and the three languages AccCat (accounting), DecCat (decisions), and GovCat (governance) are the geometry in which economic behaviour must live — from a household ledger to central-bank settlement.

Ten structural results​

1. A universal economic space. The axiomatics defines a minimal space — analogous to a Riemannian manifold — through which every behavioural theory must factor. Consistency of the books is not one constraint among others; it is the coordinate system of economics.

2. Noether's theorem of accounting. From symmetry follows invariance. At the micro level every entry balances: debtor and creditor T-accounts must match across quadruple entry (QEB) over paired double-entry (DEB) systems. Aggregated to the macro level, the same law says that the world as a whole is not indebted: the sum of all claims equals the sum of all obligations, because every claim is someone else's liability. There are no net financial positions in a closed economy.

3. Gauge invariance. A gauge structure formalises coordinate and unit independence — the freedom to re-express accounts in another currency or valuation without changing their economic content. This is where Hellwig's type error becomes visible: "euro" and "unit" are not strings but objects of different types.

4. Profit and earnings sharing. With gauge invariance and quadruple entry in place, a division of profit and of results appears as coherent institutional design — not as an afterthought bolted onto marginal productivity.

5. Distribution becomes discussable — on a firm footing. Only after QEB, gauge invariance, and the accounting Noether theorem are established can distribution questions be posed rigorously: wages, profit, risk premia, product shares. The framework separates what the books require from any particular distributional ideology.

6. Three types of money and the absorption hierarchy. Money is not homogeneous. Typed as giral (book) money, reserves, and cash (G → R → C), it reveals the risk-absorption ladder of the economy: firms absorb risk first through retained earnings, then commercial banks, then the central bank as lender of last resort.

7. Endogenous interest. The interest rate is endogenous — a risk-insurance premium, not a policy dial and not a rent on idle gold. Interest bans and "money breeding money" without production become empty categories in this geometry.

8. Fiat money is inherently stable. Money backed by institutional invariants is not merely "more stable than gold" — it is stable by construction, through quadruple-entry closure. Commodity money carries no such guarantee. Stability is an institutional invariant, not a scarcity of metal.

9. Cash as terminal settlement. In the axiomatics there is no untyped "money". Cash (C) is the terminal object — the settlement standard that discharges debt relations. Clearing and settlement are primary; exchange is secondary. A barter market with a Walrasian auctioneer has nothing to settle.

10. Financial and real endowment together drive the dynamics. Neoclassical equilibrium theory lets the real endowment alone determine outcomes. Here the cycle is generated by financial and real endowment together: there is no production without prior financial endowment — credit, contracts, booking. The dynamics is a hylomorphism. Investment unfolds (a coalgebra: it opens a tree of production, credit, and contracts into the future); demand and settlement fold it back (an algebra: revenue, profit, or loss). Demand validates investment, ex post. Failed validation writes off and constrains the next cycle; successful validation closes the books and funds the next unfold. That loop is how the system learns — cycle by cycle — and why market economies, for all their faults, remain the most adaptive institutional setup humanity has built: they let promises be made into the future, test them against reality, book the result, and begin again.

Comments and collaboration: contact@oicos.systems.