On Weak Ground

Though the study of grounding is still in the early stages, Kit Fine, in ”The Pure Logic of Ground”, has made a seminal attempt at formalization. Formalization of this sort is supposed to bring clarity and precision to our theorizing, as it has to the study of other metaphysically important phenomena, like modality and vagueness. Unfortunately, as I will argue, Fine ties the formal treatment of grounding to the obscure notion of a weak ground. The obscurity of weak ground, together with its centrality in Fine’s system, threatens to undermine the extent to which this formalization offers clarity and precision. In this paper, I show how to overcome this problem. I describe a system, the logic of strict ground (LSG) and demonstrate its adequacy; I specify a translation scheme for interpreting Fine’s weak grounding claims; I show that the interpretation verifies all of the principles of Fine’s system; and I show that derivability in Fine’s system can be exactly characterized in terms of derivability in LSG. I conclude that Fine’s system is reducible to LSG. A number of contemporary metaphysicians are exploring the nature and uses of a phenomenon known as grounding. These thinkers link grounding to a certain kind of explanation. Philosophers and scientists are fond of asking for explanations of this kind: “In virtue of what is murder wrong?” “In virtue of what am I justified in believing that I have hands?” “What makes gravity such a weak force?” Each question sets the stage for a more or less familiar ongoing research program. Each question calls for an explanation. A correct answer to each question will tell us which are the facts in virtue of which something is the case. In general, the facts that ground a given fact are the facts in virtue of which that fact obtains. 1Enthusiasts of grounding agree that facts may ground other facts, but they split on