Fritz Machlup, “Issues in Methodology—Discussion” (1952)

Fritz Machlup’s contribution to this published conference discussion addresses three connected methodological questions: the use of mathematics, the role of realism, and the proper occasion for synthesis. Responding chiefly to Paul Samuelson and Kenneth Boulding, he argues for analytical tools chosen according to the problem under investigation. Mathematics is valuable without being universally adequate; unrealistic assumptions can be illuminating; and interdisciplinary synthesis belongs to the explanation of concrete situations rather than the construction of an all-purpose general theory. The contribution moves from the limits of analytical language to the design of economic models, then to the relation between specialized knowledge and its application.

Machlup accepts Samuelson’s claim that mathematics is a language, sometimes superior to ordinary language, but rejects the implication that everything worth understanding can be expressed mathematically. His humorous examples—algebraic renderings of names, love letters, and Samuelson’s own delivery—prepare a substantive objection:

And, to come to the real issue, I submit that the basic human attitudes that underlie economic conduct—and must be understood if we are to understand economics—cannot be described and analyzed exclusively in mathematical language.

The objection concerns exclusivity, not mathematical analysis itself. Machlup also defends inquiry into the “essence” and qualitative aspects of phenomena against Samuelson’s dismissal of such questions as pseudo-problems. Clarifying what one is talking about is a legitimate preliminary to making analytical statements. Different languages can reveal different problems, while translation between them may expose some apparent problems as spurious. His recommendation of “polylingistic scholarship” therefore combines conceptual openness with critical scrutiny: neither mathematical nor verbal formulation has an unconditional monopoly on understanding.

The discussion of realism develops the same resistance to methodological monopoly. Machlup rejects the criticism that mathematical models are defective simply because their assumptions are unrealistic. His examples distinguish the recognized complexity of conduct from the selective representation needed to analyze it. Consumer theory acknowledges multiple ends even when graphical exposition reduces choice to two alternatives. Labor-supply analysis can isolate income and leisure while omitting differences in working and living conditions. Likewise, economists can recognize businessmen’s concern with comfort, risk, status, patriotism, and workmanship while employing a profit-maximizing model for particular questions.

The addition of "admittedly realistic" variables into analytical models can be defended only if they significantly modify the results.

Simplification is justified by what it enables the economist to learn. Additional detail must earn its place analytically, rather than merely resemble familiar experience. This is not a defense of every simplified model: different questions require different degrees of complexity. Machlup’s agreement that richer assumptions may be necessary for some purposes leads to his central correction of Boulding’s discussion of the firm.

What he does not say, and in my opinion should say, is that there is not one theory of the firm but that there are many.

The textbook theory of the firm serves static price and distribution analysis. Its inability to explain investment, dividends, managerial power, or growth does not by itself establish a defect in that function. Equipping one model for every conceivable business decision would make it unnecessarily cumbersome, like a universal implement combining several distinct tools. The relevant comparison is between models designed for particular tasks, not between a simplified theory and an exhaustive depiction of business life.

Drawing on discussions with Edith Penrose, Machlup extends this argument from the choice of variables to the identity of the object being modeled. “The firm” changes meaning across problems: it may be identified through assets, a balance sheet, an entrepreneur, managers, controlling persons, equity ownership, or a corporate charter. These alternatives affect what counts as continuity, survival, or death. Consequently, biological analogies and survival theories cannot be assessed without specifying the entity whose survival is at issue. The apparent mystery of a firm’s demise may disappear—or become meaningless—under a different definition. Conceptual clarification thus returns as a prerequisite of useful analysis.

Machlup agrees with Boulding that more realistic theories of the firm may have little effect on static price analysis, but doubts that integrating models into a more realistic whole necessarily accelerates economic dynamics. His governing distinction is between realism and relevance: resemblance to someone’s experience does not establish analytical usefulness.

The final section separates two questions often confused in calls for synthesis: whether knowledge is sufficiently mature to combine, and whether combination serves the task at hand. Machlup rejects waiting for perfected disciplines, since knowledge will always remain incomplete. Yet this does not justify merging general theories in advance of their application.

The time to synthesize is when we wish to explain or diagnose particular situations or to predict or control particular events.

Concrete cases require different combinations of disciplinary knowledge; no universal “knowledge mix” can anticipate them all. The contribution’s enduring methodological point is that specialization and synthesis are complementary when properly situated. Keep analytical tools distinct while developing them, then combine their findings when a specific explanatory or practical problem demands it.