Determinacy as a Two-Place Relation: The Category Mistake in Quantum Interpretation, and the Dissolution of the Paradox Set

A realist about quantum mechanics wants two things the standard interpretations will not sell together: enough counterfactual structure to say what an unperformed experiment would have shown, and no hidden valuation for the Bell theorems to kill. This paper argues that both can be had, and that having them follows from one correction. The claim’s shape should be fixed at the outset: given four commitments stated in advance, monadic determinacy cannot be recovered without contradiction or empirical inadequacy. The commitments are not themselves forced—a reader may decline them, and §6 prices the doors that declining opens. What is forced is the consequence. Following Spekkens’s diagnosis that quantum interpretation is stalled on a category mistake, the paper identifies the entry: determinacy has been treated as a one-place property that facts have or lack, when it is a two-place relation between an attribute and an information state. Two results carry the paper. The first is a no-go: the two-place structure cannot be deflated back into determinate-but-unknown values. A deflation must place its determinate values either inside a persisting state, where they contradict that state’s own content, or outside every state, where their image is a single-sample-space model of exactly the kind the quantum statistics exclude. The second is a yield: the same correction, fixed in advance and applied with nothing added per case, dissolves the standard paradox set—delayed choice, the cat, Wigner’s friend, EPR, PBR, the proper/improper mixture—each dissolution graded, with Frauchiger–Renner marked as the contested case. The paper closes by naming the squares still blank.