Incomparability in Keynes's Logical Theory of Probability and Quantum Probability: From the Limits of Frequency Theory to Condition-Dependent Probability Structures

This article reassesses the conditions under which frequency-based reasoning is warranted within J. M. Keynes's logical theory of probability, with particular attention to repeatability, independence relative to evidence, and homogeneity. Drawing on Keynes and Carabelli, it reconstructs six modes of probability relations distinguished by the possibilities of numerical measurement and ordering, rather than by degrees along a single scale. Incomparability, indeterminate probability, and the limiting case of ignorance are carefully separated. The relationship to quantum probability is a restricted formal and methodological correspondence between evidence-dependent logical relations and quantum quantities defined relative to preparation, pre-selection, post-selection, and measurement arrangements. ABL probabilities, weak values, and Kirkwood–Dirac quasiprobabilities remain distinct mathematical objects. Keynesian incomparability is neither quantum contextuality nor nonadjacency in an exclusivity graph. Three proposed research tasks concern an order cone, a noncontextual feasibility cone, and conditions for a nontrivial mapping between them; no general correspondence theorem is claimed. Finally, the paper distinguishes the assessment of probability relations from practical judgment, in which an agent must justify an action and take responsibility for its consequences under incomplete knowledge.