Higher-Order Counterfactual Logic

This paper axiomatizes higher-order counterfactual logic, proves the equivalence of various of its fragments to existing higher-order modal systems, and establishes some of its metaphysically significant implications. Most controversially, it entails that logically equivalent expressions can be substituted in the antecedents of counterfactuals, that all counterpossibles are vacuously true, that the Barcan and Converse Barcan both hold, and that everything necessarily exists