WHAT STANDS BETWEEN GROUNDING RULES AND LOGICAL RULES IS THE EXCLUDED MIDDLE

Abstract The distinction between the proofs that only certify the truth of their conclusion and those that also display the reasons why their conclusion holds has a long philosophical history. In the contemporary literature, the grounding relation—an objective, explanatory relation which is tightly connected with the notion of reason—is receiving considerable attention in several fields of philosophy. While much work is being devoted to characterising logical grounding in terms of deduction rules, no in-depth study focusing on the difference between grounding rules and logical rules exists. In this work, we analyse the relation between logical grounding and classical logic by focusing on the technical and conceptual differences that distinguish grounding rules and logical rules. The calculus employed to conduct the analysis provides moreover a strong confirmation of the fact that grounding derivations are logical derivations of a certain kind, without trivialising the distinction between grounding and logical rules, explanatory and non-explanatory parts of a derivation. By a further formal analysis, we negatively answer the question concerning the possible correspondence between grounding rules and intuitionistic logical rules.