(Conceptual) explanations in logic

Abstract To explain phenomena in the world is a central human activity and one of the main goals of rational inquiry. There are several types of explanation: one can explain by drawing an analogy, as one can explain by dwelling on the causes (see e.g. see [Woodward (2004, Making Things Happen: A Theory of Causal Explanation. Oxford University Press, Oxford)]. Amongst these different kinds of explanation, in the last decade, philosophers have become receptive to those explanations that explain by providing the reasons (or the grounds) why a statement is true; these explanations are often called conceptual explanations (e.g. see [Betti (2010, Explanation in metaphysics and Bolzano's theory of ground and consequence. Logique et analyse, 211:281316)]). The main aim of the paper is to propose a logical account of conceptual explanations. We will do so by using the resources of proof theory, in particular sequent rules analogous to deep inferences ([e.g. see Brunnler (2004, Deep Inference and Symmetry in Classical Proofs. Logoc Verlag)]). The results we provide not only shed light on conceptual explanations themselves, but also on the role that logic and logical tools might play in the burgeoning field of inquiry concerning explanations. Indeed, we conclude the paper by underlining interesting links between the present research and some other existing works on explanations and logic that have arise in recent years, e.g. see [Arieli et al. (2022, Explainable logic-based argumentation. Computational Models of Argument, 353:3243); Darwiche and Hirth (2023, On the (complete) reasons behind decisions. Journal of Logic Language and Information, 32:6388); Piazza, Pulcini, and Sabatini (2023, Abduction as deductive saturation: a proof-theoretic inquiry. Journal of Philosophical Logic, 52:15751602)]. For here it is for the empirical scientist to know the fact and for the mathematical to know the reason why (our emphasis) [Aristotle (1993, Posterior Analytics. Oxford University Press, Oxford)].