Joseph Schumpeter (1883-1950) likened the rigorous mathematical formulation of economic causality set forth by Léon Walras (1834-1910) to an ocean liner amid the small boats of other theories. Contemporary economic historian Ben Seligman records certain doubts that have subsequently arisen about the mathematical adequacy of Walras’ system:

Credit for the first precise theoretical formulation of interdependence must go, naturally, to Léon Walras. In his system, as we have noted, were utility functions, supply and demand functions, and coefficients of production, such that it was theoretically possible to establish the prices of goods and the amounts that entered upon the market. But this was all pure theory, and Walras doubted that his system would ever exhibit empirical usefulness, for it was unlikely that the necessary statistical data would ever become available. Nor did Pareto or Barone believe that numerical content could be given to general equilibrium theory. For a long time it was questioned whether the Walrasian system could be ‘solved’, that is that there was a unique and determined equilibrium. Not until the 1930’s did the noted mathematician, Abraham Wald, demonstrate the feasibility of such a solution. Despite Walras’ tâtonnements, [literally ‘a groping’ as for equilibrium prices] there was no assurance in his model that equilibrium would be restored after a disturbance. As Wald indicated, only one path of equilibrium at best existed in Walras’ theory. Pareto's analysis was somewhat richer in content, in that he sought to employ varying technological coefficients rather than single linear homogeneous production functions. And in Hicks and Samuelson one finds an attempt to have the system respond to changes in parameters. ¹

These dispositions are troubling from the standpoint of SFEcon on several counts: 1) we find the problem of interdependence among economic sectors inseparable from any sensible formulation of macroeconomics; 2) our utility functions are coextensive with our supply and demand schedules; 3) we see no possibility of economic decision making based on linear homogeneous technical and utility tradeoffs of the sort used by Walras; 4) we presume to have created mechanisms by which Walras’ equilibrium comes to be expressed in excruciating quantitative detail; and 5) to have demonstrated this equilibrium to be efficiently restored from displacements in any direction.

Our preferences therefore run to greater affinity with Walras’ own estimation of his place in economic science:

In any case, the establishment sooner or later of economics as an exact science is no longer in our hands and need not concern us. It is already perfectly clear that economics, like astronomy and mechanics, is both an empirical and rational science. As for those economists who do not know any mathematics, who do not even know what is meant by mathematics and yet have taken the stand that mathematics cannot possibly serve to elucidate economic principles, let them go their way repeating that “human liberty will never allow itself to be cast into equations” or that “mathematics ignores frictions which are everything in social science” and other equally forceful and flowery phrases. They can never prevent the theory of the determination of prices under free competition from becoming a mathematical theory. Hence they will always have to face the alternative of either steering clear of this discipline and consequently elaborating a theory of applied economics without recourse to a theory of pure economics or tackling the problems of pure economics without the necessary equipment, thus producing not only very bad pure economics but also very bad mathematics.²

Unfortunately those who followed Walras have generally concluded his formulations to be 1) precise enough, given the limited extent to which mathematical rigor might avail the economist, because 2) full scientific rigor is impossible for economics’ subject matter. Where modern economics is fixated by a ‘never’ on one side of its scientific pretentions and an ‘already’ on the other side, Walras clearly invites us to think in terms of a ‘not yet’.
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¹      Ben B. Seligman: Main Currents, 1963: pp. 434-435.
²      Léon Walras: preface to his Elements, 1877.
        [Emphases are in the original.]