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In order to block controversial predictions of 2D semantics (The Nesting Problem), Chalmers and Rabern (2014) propose adding an additional constriction called “the liveness constraint” in definitions of epistemic modals. Without this constraint, all scenario-world pairs counterfactual to a scenario-world pair considered as actual in a 2D matrix for a contingent a priori proposition ϕ appear problematic for 2D semantics. This is because, although it is false that ϕ in such pairs, it is a priori true that ϕ. I consider two versions of 2D semantics, those with unstructured and structured intensions. I argue that the unstructured version of 2D semantics is over-simplified and due to this, it has controversial predictions for counterfactual scenario-world pairs – the definition of epistemic conceivability with the liveness constraint causes some contingent propositions to appear inconceivable in counterfactual scenario-world pairs, while some other contingent propositions remain conceivable. In turn, the structured version of the 2D account of propositions has no explanation of how it is possible to possess purely qualitative knowledge without its being dependent on a particular individual or on a particular actual world.
