Shogo Tsuboi

This paper investigates the logic of grounding, a non-causal explanatory relation. While the study of this field is flourishing, it is still in its early stages. This paper contributes to the literature by presenting $\mathcal{G}_\mathbf{LWG}$, a novel sequent calculus for weak full grounding. While it provides a sequent-style presentation of the existing axiomatic system $\mathbf{LWG}$ proposed by Adam Lovett, our calculus is balanced and avoids the ad-hoc rules contained in $\mathbf{LWG}$. An important fact shown in this paper is that if a sequent $\Gamma \Rightarrow \Delta$ is derivable in $\mathcal{G}_\mathbf{LWG}$, then any variable occurring positively (or negatively) in $\Gamma$ also occurs positively (or negatively) in $\Delta$. This highlights a deep connection between grounding and variable inclusion. This property, in particular, suggests a similarity to Rohan French's sequent calculus for analytic containment, $\mathcal{G}_\mathbf{AC}$. Indeed, we demonstrate that $\mathcal{G}_\mathbf{LWG}$ is the negation dual of $\mathcal{G}_\mathbf{AC}$. The paper concludes by proving the equivalence between $\mathcal{G}_\mathbf{LWG}$ and $\mathbf{LWG}$.

There is a widely accepted claim that necessary truths lack truthmakers. The (implicit) argument for this claim hinges on the ideas that necessary truths hold regardless of what exists, and that truth depends on the existence of its truthmaker. By analyzing the role of dependence in truthmaking, the claim that necessary truths cannot have truthmakers is challenged. I distinguish two senses of “dependence” and argue that necessary truths can have a “productive” kind of truthmaker. Finally, I propose an account of truthmakers for a certain class of necessary truths──metaphysical necessities──based on essentialism.