Being Necessary Really Isn't the Same As Being Not Possibly Not

Dana Goswick (University of Melbourne)

In standard modal logic, □ ≡ ~◊~ and ◊ ≡ ~□~.  In standard tense-logic, where □ is taken to stand for “at all times” and ◊ is taken to stand for “at some time”, these equivalences are also taken to hold.  In Time and Modality, Arthur Prior argues that—despite their prima facie plausibility—these equivalences fail to hold.  In particular, he argues that not some time not is weaker than at all times and that not at all times not is weaker than at some time.  I’ll, first, examine the motivation for and plausibility of Prior's rejection of the standard equivalences.  Then, I’ll present analogous motivations for adopting a modal logic which denies these standard equivalences, and examine the plausibility of such a non-standard modal logic.