Does Standard Modal Logic Adequately Represent Metaphysics?

Dana Goswick (University of Melbourne)

Abstract: Standard alethic modal logic accepts the equivalence of necessarily and not possibly not ([]∂≡~◊~∂).  Standard deontic logic accepts the equivalence of obligatory to and not permissible not to (OB∂≡~PE~∂).  Standard tense logic accepts the equivalence of has at all times and has not at some time not (H∂≡~P~∂).  I argue that the purposes of metaphysics are not best served by standard alethic modal logic.  In so arguing, I exploit the structural similarities between standard alethic modal logic and standard deontic and tense logic.  In section I, I argue that counterexamples arise to OB∂≡~PE~∂, H∂≡~P~∂, and []∂≡~◊~∂.  In section II, I suggest two ways of modifying standard modal logic to block the counterexamples.