If the primary intension is not recoverable through pure a priori reasoning—as Williamson's externalist cases suggest—the context dimension cannot reliably encode analyticity, undermining the claim that the framework handles necessity-analyticity divergence in general.

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Externalism(Philosophy of linguistics): The view that the forms of actually attested expressions — sentences, phrases, syllables, and systems of such units — are the proper object of linguistic inquiry
Necessity-analyticity divergence(used in philosophy of language and metaphysics): The philosophical problem that some statements are necessarily true but not analytic (true based purely on definitions), which challenges traditional theories about how meaning and truth work.
Williamson: # Williamson Williamson most commonly refers to Timothy Williamson, a prominent British philosopher known for his work on knowledge, logic, and language. He's influential in contemporary philosophy for arguing that knowledge is more fundamental than belief and that traditional definitions of knowledge may be too restrictive. His ideas have shaped how philosophers think about what it means to know something and how language relates to reality.
a priori reasoning(Broader than deductively valid inferences from a priori premises; includes any non-empirical inference)

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