PURE LOGIC OF ITERATED FULL GROUND
Jon Erling Litland · The Review of Symbolic Logic · 2018
Abstract This article develops the Pure Logic of Iterated Full Ground (plifg), a logic of ground that can deal with claims of the form “ϕgrounds that (ψgroundsθ)”—what we call iterated grounding claims. The core idea is that some truths Γ ground a truthϕwhen there is an explanatory argument (of a certain sort) from premisses Γ to conclusionϕ. By developing a deductive system that distinguishes between explanatory and nonexplanatory arguments we can give introduction rules for operators for factive and nonfactive full ground, as well as for a propositional “identity” connective. Elimination rules are then found by using a proof-theoretic inversion principle.