This paper is an exploration of the genesis of Paul Samuelson's Foundations of Economic Analysis (1947) from the perspective of his commitment to Edwin B. Wilson's mathematics. The paper sheds new lights on Samuelson's Foundations at two levels. First, Wilson's foundational ideas, embodied in maxims that abound in Samuelson's book such as "Mathematics is a Language" or "operationally meaningful theorems," unified the chapters of Foundations and gave a sense of unity to Samuelson's economics, which was not necessarily and systematically mathematically consistent. Second, Wilson influenced certain theoretical concerns of Samuelson's economics. Particularly, Samuelson adopted Wilson's definition of a stable equilibrium position of a system in terms of discrete inequalities. Following Wilson, Samuelson developed correspondences between the continuous and the discrete in order to translate the mathematics of the continuous of new-classical economics into formulas of discrete magnitudes. In Foundations, the local and the discrete provided the best way of operationalizing marginal and differential calculus. The discrete resonated intuitively with data; the continuous did not.
Samuelson E. B. Wilson Foundations of Economic Analysis Mathematics Is a Language Operationally Meaningful Theorems Equilibrium