A Leibnizian Logic of Possible Laws

Abstract

The so-called Principle of Plenitude was ascribed to Leibniz by A. O. Lovejoy in The Great Chain of Being: A Study of the History of an Idea (1936). Its temporal version states that what holds always, holds necessarily (or that no genuine possibility can remain unfulfilled). This temporal formulation is the subject of the current paper. Lovejoy’s idea was criticised by Hintikka. The latter supported his criticisms by referring to specific Leibnizian notions of absolute and hypothetical necessities interpreted in a possible-worlds semantics. In the paper, Hintikka’s interpretative suggestions are developed and enriched with a temporal component that is present in the characteristics of the real world given by Leibniz. We use in our approach the Leibnizian idea that change is primary to time and the idea that there are possible laws that characterize worlds other than the real one. We formulate a modal propositional logic with three primitive operators for change, temporal constancy, and possible lawlikeness. We give its axiomatics and show that our logic is complete with respect to the given semantics of possible worlds. Finally, we show that the counterparts of the considered versions of the Principle of Plenitude are falsified in this semantics and the same applies to the counterpart of Leibnizian necessarianism.