Operational Concepts and Mental Constructs in Model and Theory Formation

This source is best summarized as an edited symposium volume on models, not as a single essay by Fritz Machlup. Its chapters ask how “model” changes meaning as it passes from mathematical logic into physics, economics, and the social sciences. Freudenthal’s framing presents the volume as a comparative inquiry; Apostel seeks a formal account of models in non-formal sciences; Beth and Suppes connect the discussion to logical semantics and mathematical model theory; contributors such as Braithwaite, Bunge, Hesse, Nagel, and Black treat models as interpreted systems, analogies, idealizations, or explanatory instruments. Machlup’s chapter belongs to this wider sequence by asking how far operational definitions can serve model and theory formation in economics.

When Einstein invented the Special Theory of Relativity he developed as a by-product a new type of concept or definition.

The collection’s center of gravity is the relation between formal structure and empirical interpretation. In the formal chapters, models are not miniature copies of reality but structures satisfying relations, axioms, or rules of correspondence. The philosophical chapters complicate this logical picture: a model may clarify a theory, transfer relations from a familiar domain to an unfamiliar one, or idealize away irrelevant detail. Across the volume, the same term therefore names several activities: representation, calculation, analogy, simplification, and empirical coordination.

Machlup’s chapter makes the methodological problem sharpest for social science. He accepts the value of operations for measurement, especially where data must be recorded and compared, but rejects the stronger operationalist doctrine that a concept is meaningful only if synonymous with a concrete operation. His reading of Bridgman is sympathetic to the origin of operationalism in physics yet critical of its overextension.

Bridgman could not possibly have meant what he said about mental operations.

The economic cases show why the volume cannot rest with a narrow measurement theory. Terms such as firm, industry, price, demand, cost, and output require empirical counterparts, yet none is exhausted by the statistical series, questionnaires, ledgers, or market quotations used to approximate it. Suppes’s and Apostel’s more formal accounts explain how structures may be related to target systems; Machlup’s examples show why that relation is never automatic.

The logical relationship between mental constructs and mental models is quite simple: models are made up of interrelated constructs.

Machlup’s contribution also clarifies the social-scientific role of idealization. A competitive market, a homogeneous commodity, or a profit-maximizing firm may not be directly observable in purified form, but such constructs can organize explanation when connected to imperfect data. In this respect his chapter complements the volume’s treatments of analogy and formalization: models are neither mere pictures nor mere collections of observations, but arrangements of selected relations made useful by inquiry.

A mental construct is a concept designed for purposes of analytical reasoning that cannot be adequately defined or circumscribed in terms of observables or in terms of operations with recorded data derived from observation.

Taken as a whole, the volume argues for a plural and layered account of scientific representation. Mathematical contributors emphasize structure; philosophers of empirical science emphasize interpretation and analogy; social-science contributors emphasize operational difficulty and the necessity of constructs. Machlup’s chapter is thus not the whole work but a culminating economic case study within it. Its defense of mental constructs reinforces the volume’s broader conclusion: models become scientifically valuable not by copying reality or by reducing all terms to operations, but by linking formal relations, idealized concepts, and responsible empirical use.