Ludwig von Mises, Bemerkungen über die mathematische Behandlung nationalökonomischer Probleme

First published in 1953, this methodological essay presents a selective, explicitly aphoristic critique of mathematical economics. After a preliminary statement of scope, Mises proceeds through measurement, decision theory, equilibrium equations, and scientific analogies. His central contention is that mathematical economics mistakes historical observations for measurable constants and descriptions of hypothetical equilibrium for explanations of human action.

The section on measurement challenges the positivist aspiration to make economics exact by following the natural sciences. Henry Schultz’s statistical investigation of demand, Mises argues, concerns particular commodities in specified places and periods, not invariant relations between quantities and prices. Such findings belong to economic history; their interpretation requires theoretical propositions that historical observation cannot itself establish. The conceptual basis of this distinction is his account of valuation:

Das Werturteil mißt nicht, es skaliert.

English translation: The value judgment does not measure, it grades on a scale.

Valuation ranks alternatives rather than measuring equivalent magnitudes. Action follows from preferring one condition to another, and exchange presupposes differences in valuation rather than equality. Mises consequently distinguishes monetary prices from measurements of an underlying quantity of value:

Preise werden nicht in Geld gemessen; sie bestehen in Geld.

English translation: Prices are not measured in money; they consist in money.

Concrete prices are historical data, while numerical statements about future prices remain speculative. For Mises, the absence of constants in human action prevents economics from reproducing the transition from qualitative to quantitative knowledge achieved in chemistry.

The discussion of decision theory carries this argument into business practice. Mises characterizes mathematical prescriptions as algebraic generalizations of commercial arithmetic whose apparent precision leaves the decisive entrepreneurial judgment untouched. Inventory decisions, for example, depend on expectations about future circumstances, not merely on formal optimization. His objection concerns the uncertainty constitutive of action:

Wie Marx und allen Sozialisten fehlt den mathematischen Nationalökonomen die Erkenntnis, daß menschliches Handeln mit künftigen Verhältnissen zu tun hat, über die nichts Sicheres bekannt ist.

English translation: Like Marx and all socialists, the mathematical economists lack the insight that human action has to do with future conditions about which nothing certain is known.

The polemical comparison serves a specific methodological claim: removing uncertainty changes the object under investigation. Mises likewise rejects the Cowles Commission’s appeal to numerical values remaining reasonably constant over several years. Whether they did remain stable can only be established retrospectively; that makes the procedure a treatment of historical data rather than a secure basis for prediction.

The longest section qualifies the critique by defending a legitimate use of abstraction. Mises’s “gleichmäßige Wirtschaft” is an imaginary economy in which production repeats and all price-determining data remain unchanged. Although unrealizable, this construction helps isolate the consequences of changing one factor while holding others constant. Where controlled experiments are unavailable, such thought constructions clarify entrepreneurship, profit, and loss. His objection is therefore not to hypothetical models as such, but to confusing their heuristic function with a mathematical account of actual market processes.

Equilibrium equations, he argues, restate relationships already articulated verbally without supplying either empirically usable constants or an explanation of how actors bring about adjustment. Unlike equations of mechanics, they describe a hypothetical endpoint rather than movement through successive states. The positive explanatory task is stated succinctly:

Die Katallaktik hat zu zeigen, wie aus dem Handeln der Wirtschafter die Marktpreise hervorgehen.

English translation: Catallactics has to show how market prices arise out of the action of the economizing individuals.

This is the essay’s governing contrast: explaining the emergence of prices from action versus symbolically representing a condition in which the relevant adjustments have ceased. Even a mathematical path toward equilibrium would not, in Mises’s view, establish a conceptual correspondence with the choices constituting the market process.

The final section broadens the criticism into an attack on intellectual fashion. Institutional support, journals, congresses, and government patronage cannot substitute for demonstrable results or answers to methodological objections. Mises compares the mechanical analogy favored by mathematical economists with earlier attempts to understand society as a biological organism. The comparison closes the essay by presenting borrowed scientific prestige as a recurring temptation. Its enduring methodological relevance lies in the distinctions it presses between historical regularity and theoretical law, calculation and uncertain judgment, and equilibrium description and causal explanation.