Philosophers have spilled a lot of ink over the past few years exploring the nature and significance of grounding. Grounding is supposed to be a certain relation of dependence and determination among facts. This relation is linked with a certain kind of explanation. It is targeted by the sort of explanations we give sometimes when we say that some facts obtain in virtue of other facts and when we ask what makes something the case. When, for instance, ethicists ask what makes murder wrong, epistemologists ask what makes my belief that I have hands justified, chemists ask what makes alcohol miscible in water, and physicists ask what makes gravity so weak, they are asking after the worldly conditions on which the facts in question depend, and by which they are determined.What, though, is the nature of grounding? Though there is much disagreement over the details, some rough points of consensus over some of its formal features have emerged. Kit Fine has offered an exact treatment of these formal features of grounding (Fine, 2012a). He specifies a language in which grounding claims may be expressed, proposes a system of axioms which capture the relevant formal features, offers a semantics which interprets grounding claims expressible in the language, and shows that his axioms are sound and complete for his semantics.As we shall see, however, there are reasons for dissatisfaction with Fine's semantics. We could, of course, avoid the unacceptable results by simply dropping the ambition to provide a semantics for those grounding claims expressible in Fine's language. We might then affirm the principles of the pure logic of ground without offering any formally specified conception of what grounding claims say or under what conditions they are true.In this paper I show that there is another approach available. I offer a formally specified, model-theoretic semantics for Fine's language, for which a certain natural axiomatization of the pure logic of ground is sound and complete. The semantics is motivated by ideas already present in the grounding literature, so it offers a plausible candidate for an exact specification of an intended interpretation of grounding claims. I also show how the semantics I offer avoids problems faced by Fine's semantics.
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.
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