Debunking Logical Ground: Distinguishing Metaphysics from Semantics

Abstract

Many philosophers take purportedly logical cases of ground (such as a true disjunction being grounded in its true disjunct(s)) to be obvious cases, and indeed such cases have been used to motivate the existence of and importance of ground. I argue against this. I do so by motivating two kinds of semantic determination relations. Intuitions of logical ground track these semantic relations. Moreover, our knowledge of semantics for (e.g.) first order logic can explain why we have such intuitions. And, I argue, neither semantic relation can be a species of ground even on a quite broad conception of what ground is. Hence, without a positive argument for taking so-called ‘logical ground’ to be something distinct from a semantic determination relation, we should cease treating logical cases as cases of ground.

Formal explanations as logical derivations

“…While much has been done in order to define satisfactory logical grounding rules, no thorough study of the resulting notion of formal explanation and of the relationship between grounding rules and logical rules exists. Some even contest the legitimacy of considering logical grounding as different from logical consequence, see for instance the arguments presented by McSweeney (2020). We will show in this paper that there is a sensible notion of grounding based on Bolzano's Abfolge 4 which can be clearly and formally distinguished from logical entailment, but still induces a notion of formal explanation which determines a meaningful subclass of the class of logical derivations.…”

“…In particular, we will consider the notion of complete logical grounding introduced by Poggiolesi (2016) and based on Bolzano's analysis of Abfolge, and we will study the resulting notion of formal explanation, that is, of derivation constructed by only employing the grounding rules that characterise this notion of logical grounding. Our 1 See Betti (2010); Correia (2014); Correia and Schnieder (2012); Fine (2012a); Korbmacher (2018b); McSweeney (2020); Poggiolesi (2016); Rosen (2010); Rumberg (2013); Schnieder (2011);Sider (2018).…”

Ground first: against the proof-theoretic definition of ground

“…One where the disjunction of p, q is grounded in whichever one of p, and q is the case and another where the disjunction of p, q is grounded also in p, q, if they are both the case. 37 Second, McSweeney (2020) has recently objected that our intuitions about cases of logical ground-for instance, that a proposition grounds its double negation-can be explained away as really being intuitions about "meaning-determination" or "truth-determination". She argues that while there is reason to think that the truth value (meaning) of a disjunction is determined by the truth values (meanings) of the disjuncts there is no reason to think that disjunctions are metaphysically grounded in their disjuncts.…”

Grounding, Quantifiers, and Paradoxes

“…The notion of grounding has recently received increasing attention in different areas of philosophy: from explanation, to metaphysical dependence and fundamentality, to the analysis of logico-linguistic operators [3,7,8,14,21,22,25,26,28,30,32,33]. Grounding is usually conceived as an objective and explanatory relation.…”

“…However, regardless of how the grounding relation is captured, a major hard problem remains: characterizing the grounds of universal and existential formulae [21,22,29,36]. There exist several different attempts to formalize the relations between quantifiers and their grounds [7,13,32], but, as it has been shown in [12,18], each of these attempts fails to enforce the irreflexivity of grounding in some very natural contexts of application.…”