Ground First: Against the Proof-Theoretic Definition of Ground * Jon Erling Litland [This paper is forthcoming in Synthese. Please cite the published version.] Abstract This paper evaluates the proof-theoretic definition of ground developed by Poggiolesi in a range of recent publications and argues that her proposed definition fails. The paper then outlines an alternative approach where logical consequence relations and the logical operations are defined in terms of ground. Keywords: Ground, Logic, Proof-Theory, Definition 1 Introduction What is the relationship between ground, proof, and consequence? In a series of recent publications 1 Francesca Poggiolesi and her collaborators have proposed that ground should be defined in terms of logical consequence and complexity, the idea being that the grounded is both a consequence of and is more complex than its grounds. Most of this paper is taken up by the negative task of refuting this account of ground. But the paper also makes a positive proposal: instead of defining ground in terms of consequence we should rather define both consequence (in general) and the logical operations (in particular) in terms of ground. For the reader’s benefit here is an overview of the paper. § 2 introduces notation and terminology. § 3 then presents Poggiolesi’s proposed definition of complete immediate (formal) ground. § 4 develops the main argument against her account. It begins by observing that she has, at best, defined the grounding relation for conjunctive, disjunctive, and negated propositions. § 4.1 then raises a general worry about how the account can be extended to accommodate other types of logically complex propositions. Supposing that this in fact can be done, § 4.2 raises the philosophically fundamental objection that the enumerative nature of the resulting definition means both that it cannot capture what is common to distinct cases of ground * Thanks to Ray Buchanan for helpful advice on drafts of this paper. Thanks also to a number of especially conscientious referees whose meticulous comments have greatly improved the paper both in structure and content. 1 See Poggiolesi 2016a,b, 2018, 2020a,b,c,d Poggiolesi and Francez 2021 and Rossi, Poggiolesi, and Genco 2021. 1