Revisiting the century-old Keynes-Ramsey dispute: a lattice-theoretic reinterpretation and a coherent solution.

This paper aims to formalize the abstract algebraic difference between Keynes's and Ramsey's theories of probability. Drawing on the foundational paper of Birkhoff and von Newmann (1936) on quantum mechanics, the algebraic-axiomatic properties underpinning the relation between belief and probability in Keynesian and Ramseyan theories are identified. The paper demonstrates that a specific class of abstract algebras - bounded distributive lattice - can represent Keynes's problem while sharing key properties with traditional Ramsey's probability theory. By introducing the notion of an interval probability measure and assuming a model of uncertainty, Keynesian uncertain beliefs can be represented as isomorphic probability intervals. This provides a coherent resolution to Ramsey's long-standing challenge and reconciles the two approaches within a unified algebraic framework.