Metaphysical Principles in Modal Free Logic

Free logic is a non-classical logical system that rejects some of the rules of standard logic‎. ‎While the importance of free logic has been discussed a lot‎, ‎its significance in modal logics has been largely overlooked‎. ‎In this paper‎, ‎I aim to highlight the importance of free logic in modal logics (and also in temporal logic)‎. ‎In classical modal logic‎, ‎many metaphysical principles are proven which are philosophically controversial‎, ‎such as Barcan formulas‎, ‎Buridan formula‎, ‎converse Barcan formula‎. ‎These formulas in modal free logic are equivalent to two strong metaphysical principles‎: ‎Necessitism (i.e‎. ‎“all beings are necessary”) and Actualism (meaning “all possibilities are existent”)‎. ‎These two principles appear in temporal free logic as new metaphysical principles‎: ‎eternalism (i.e‎. ‎“all material beings are permanent”) and presentism (meaning “all past and future things are present”)‎. ‎Since these principles as well as Barcan and Buridan formulas are provable in modal and temporal “classical” logics‎, ‎they are equivalent in thesee classical logics‎. ‎I show (i) that these principles are unprovable in “free” logics‎, ‎(ii) that their relationships and proportions can be obtained‎, ‎and (iii) that adding each of them as metaphysical principles to modal and temporal free logics has what consequences.