What is Weak Ground?
Kit Fine, in The Pure Logic of Ground, has made a seminal attempt at formalizing the notion of ground. Fine ties the formal treatment of grounding to the notion of a weak ground. Formalization of this sort is supposed to bring clarity and precision to our theorizing. Unfortunately, as I will argue, it's not clear what weak ground is. I review five alternative explanations of the idea, and argue that none of them are ultimately satisfactory. I close by outlining a more complicated explanation of the notion that turns out to be more satisfactory. 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. 1 Enthusiasts of grounding agree that facts may ground other facts, but they split on whether grounding relates things other than facts; Schaffer [2009] contends that it does, and Fine [2001, 2012] disagrees. If Schaffer is correct, then Fine’s formal treatment of ground may be incomplete. I take no stand on this dispute here. Fine also argues in [Fine, 2001] that, strictly speaking, we don’t need to reify facts and claim that grounding is a relation between them in order to give a theory of ground; we may instead treat talk of grounding’s being a relation between facts as a mere fa con de parler. We should formalize our theory of ground by appeal to sentential operators which do not pick out any relation, and whose arguments, semantically speaking, do not pick out some special category of entity. According to Fine, the logical Essays Philos (2013) 14:1 deRosset | 8 Though the study of grounding is still in the early stages, Kit Fine, in “The Pure Logic of Ground” [Fine, 2012], 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 notion of a weak ground, and it is not clear what that notion comes to. Weak Ground in the Pure Logic of Ground In Fine’s system, which he calls the pure logic of ground (PLG), grounding claims vary along two independent axes: (i) a grounding claim may either be partial or full; and (ii) it may either be strict or weak. There are thus four types of grounding claim in Fine’s system. Corresponding to each type of grounding claim is an operator in the language of PLG: