Emptying a Paradox of Ground

Abstract

Sometimes a fact can play a role in a grounding explanation, but the particular content of that fact make no difference to the explanation-any fact would do in its place. I call these facts vacuous grounds. I show that applying the distinction between-vacuous grounds allows us to give a principled solution to Kit Fine and Stephen Kramer's paradox of (reflexive) ground. This paradox shows that on minimal assumptions about grounding and minimal assumptions about logic, we can show that grounding is reflexive, contra the intuitive character of grounds. I argue that we should never have accepted that grounding is irreflexive in the first place; the intuitions that support the irreflexive intuition plausibly only require that grounding be non-vacuously irreflexive. Fine and Kramer's paradox relies, essentially, on a case of vacuous grounding and is thus no problem for this account. Keywords Grounding · Paradoxes of ground · IrreflexivityInterest in the putatively explanatory relation of metaphysical grounding and, in particular, its "logic" has recently been the focus of much attention. 1 Grounding has often been taken to be a strict partial order-i.e. to be an irreflexive, asymmetric, transitive relation. However, there have been important challenges to the claim that 1 See [24] for a recent survey, [7,26,27] for the kick-off of the contemporary research program, and [23,26] for a defense of the coherence of the notion and that it is an explanatory relation.

Structure by proxy, with an application to grounding

“…Note that this is in some ways a more pressing problem than the previous one: In response to the problems with quantificational grounds, one may consider simply allowing for exceptions to the irreflexivity of ground. This is the response proposed by Correia (2014) and Woods (2018). In the present case, we would have to allow every truth to ground itself.…”

On higher-order logical grounds

“…E.g., Correia (2014, pp. 54-55) and Woods (2018) accept the conclusion of the argument, and give up the irreflexivity of ground, while Fine (2010) considers a number of di↵erent responses, some of which require rejecting classical inferences. Krämer (2013) notes that many of the responses which Fine considers are not applicable to the very simple form of the problem arising from (9S), and suggests that restricting (9S) to predicative instances (instances in which does not itself involve propositional quantifiers) is the only plausible response available, apart from giving up irreflexivity.…”

In Defense of the (Moderate) Disunity of Grounding

“…One might of course reject the theory of decycling and deal with puzzles of grounding like the one presented by (U) in some other way. While this is not the place to argue for this in detail, it is noteworthy that the otherwise quite different approaches to the puzzles of grounding proposed Litland (), Fine (), Woods (2017), and deRosset (n.d.) all agree on taking a cycle‐tolerant relation as basic.…”