Not Derivation But Statability

Contemporary logic separates a language from its interpretation, but it has nowhere to separate what there is from how what there is is grasped. The cost is not obscurity but unstatability: error, fiction, generality, sense, conceptual crisis and discovery can be reported and not written down, and so cannot be disagreed about precisely. This essay sets out a framework which carries two coordinates — an object, and the content it is grasped under — and adds no logic whatever. Its models leave the relation between the coordinates neither injective nor functional, and those two failures prove to be the problem of universals and the problem of sense: Ockham and Frege at work on one relation from opposite ends. Three consequences follow. A contradiction can be located rather than tolerated, which is what Bohr's atom and the unreformed infinitesimal require. Inference from absence becomes a crossing between the coordinates, and the price of the crossing is nameable. And once the framework is set in motion, what it forces is not consequence but availability, which is indexed to a state and fails cut. There is no axiomatisation here, no consequence relation, and no completeness result. What is offered is statability, not derivation.