Weight of Argument at Work: Formalizing Keynes’s Bridge from the _Treatise on Probability_ to the _General Theory_

Keynes’s weight of argument, the robustness of evidence behind a probability estimate, has long been read as an ancestor of Ellsberg’s ambiguity and Walley’s imprecise probabilities, but has resisted formalization surviving Keynes’s own test cases. This paper makes three contributions. First, Keynes’s two-urn example refutes the standard formalization of weight as the complement of an imprecise-probability interval’s width, treating weight instead as an independent evidential primitive. Second, under a tractable specialization of Smith’s credal-set framework, it proves an investment’s temperament-sensitivity is non-increasing in weight, turning Chapter 12’s “state of confidence” into a demonstrated result, and that the Chapter 17 liquidity premium falls monotonically in weight. Third, reading Sraffa’s notes on Chapter 17, it locates the chapter’s textual instability where Sraffa identified the argument’s weakest step, and supplies the missing formal conditions. The paper situates these results within the imprecise-probability lineage from de Finetti to Walley.