Conceivability, Possibility and Two-Dimensional Semantics

Kripke (1980) famously separates the metaphysical and epistemic modal domains, with supposed necessary a posteriori identity statements such as ‘Hesperus is Phosphorus’, appearing to create an irreconcilable gap between conceivability and possibility. In response to this problem, David Chalmers (2002, 2004a, 2006) uses two-dimensional modal semantics (2DS) to claim that conceivability entails possibility. Specifically, Chalmers makes five claims: 1. metaphysical is ’secondary’, ’horizontal’ or counterfactual modality; 2. conceivability is epistemic possibility; 3. epistemic is ’primary’, ’diagonal’ or ’counteractual’ modality; 4. possibility consists in metaphysical and/or epistemic modalities;