In spite of its significance for everyday and philosophical discourse, the explanatory connective has not received much treatment in the philosophy of logic. The present paper develops a logic for based on systematic connections between and the truth-functional connectives.

The dogma that the propositional logic of metaphysical modality is S5 is rebutted. The author exposes fallacies in standard arguments supporting S5, arguing that propositional metaphysical modal logic is weaker even than both S4 and B, and is instead the minimal and weak metaphysical-modal logic T.

Fundamentality plays a pivotal role in discussions of ontology, supervenience, and possibility, and other key topics in metaphysics. However, there are two different ways of characterising the fundamental: as that which is not grounded, and as that which is the ground of everything else. I show that whether these two characterisations pick out the same property turns on a principle—which I call “Dichotomy”—that is of independent interest in the theory of ground: that everything is either fully grounded or not even (...) partially grounded. I then argue that Dichotomy fails: some facts have partial grounds that cannot be complemented to a full ground. Rejecting Dichotomy opens the door to recognising a bifurcation in our notion of fundamentality. I sketch some of the far-reaching metaphysical consequences this might have, with reference to big-picture views such as Humeanism. Since Dichotomy is entailed by the standard account of partial ground, according to which partial grounds are subpluralities of full grounds, a non-standard account is needed. In a technical “Appendix”, I show that truthmaker semantics furnishes such an account, and identify a semantic condition that corresponds to Dichotomy. (shrink)

A lot of research has recently been done on the topic of ground, and in particular on the logic of ground. According to a broad consensus in that debate, ground is hyperintensional in the sense that even logically equivalent truths may differ with respect to what grounds them, and what they ground. This renders pressing the question of what we may take to be the ground-theoretic content of a true statement, i.e. that aspect of the statement’s overall content to which (...) ground is sensitive. I propose a novel answer to this question, namely that ground tracks how, rather than just by what, a statement is made true. I develop that answer in the form of a formal theory of ground-theoretic content and show how the resulting framework may be used to articulate plausible theories of ground, including in particular a popular account of the grounds of truth-functionally complex truths that has proved difficult to accommodate on alternative views of content. (shrink)

A lot of research has recently been done on the topic of ground, and in particular on the logic of ground. According to a broad consensus in that debate, ground is hyperintensional in the sense that even logically equivalent truths may differ with respect to what grounds them, and what they ground. This renders pressing the question of what we may take to be the ground-theoretic content of a true statement, i.e. that aspect of the statement’s overall content to which (...) ground is sensitive. I propose a novel answer to this question, namely that ground tracks how, rather than just by what, a statement is made true. I develop that answer in the form of a formal theory of ground-theoretic content and show how the resulting framework may be used to articulate plausible theories of ground, including in particular a popular account of the grounds of truth-functionally complex truths that has proved difficult to accommodate on alternative views of content. (shrink)

Say that two sentences are ground-theoretically equivalent iff they are interchangeable salva veritate in grounding contexts. Notoriously, ground-theoretic equivalence is a hyperintensional matter: even logically equivalent sentences may fail to be interchangeable in grounding contexts. Still, there seem to be some substantive, general principles of ground-theoretic equivalence. For example, it seems plausible that any sentences of the form A∧B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A \wedge B$$\end{document} and B∧A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B (...) \wedge A$$\end{document} are ground-theoretically equivalent. What, then, are in general the conditions for two sentences to stand in the relation of ground-theoretic equivalence, and what are the logical features of that relation? This paper develops and defends an answer to these questions based on the mode-ified truthmaker theory of content presented in my recent paper ‘Towards a theory of ground-theoretic content’ :785–814, 2018). (shrink)

In his 2010 paper ‘Grounding and Truth-Functions’, Fabrice Correia has developed the first and so far only proposal for a logic of ground based on a worldly conception of facts. In this paper, we show that the logic allows the derivation of implausible grounding claims. We then generalize these results and draw some conclusions concerning the structural features of ground and its associated notion of relevance, which has so far not received the attention it deserves.

This chapter explains the basic framework of truthmaker or 'exact' semantics, an approach to semantics that has recently received a growing amount of interest, and discusses a number of different applications within philosophy and linguistics. The idea of truthmaking is the idea of something on the side of the world ‐ a fact, perhaps, or a state of affairs ‐ verifying, or making true, something on the side of language or thought ‐ a statement, perhaps, or a proposition. The chapter (...) focuses on the ultimate truthmakers, on what in the world ultimately makes something true, and the question of how the truthmakers make the statements of our language true is of no great concern. It also focuses on the immediate truthmakers, and the question of how they make the statements of the language true will be of greatest concern. (shrink)

I propose a new semantics for intuitionistic logic, which is a cross between the construction-oriented semantics of Brouwer-Heyting-Kolmogorov and the condition-oriented semantics of Kripke. The new semantics shows how there might be a common semantical underpinning for intuitionistic and classical logic and how intuitionistic logic might thereby be tied to a realist conception of the relationship between language and the world.

I lay down a system of structural rules for various notions of ground and establish soundness and completeness.

I develop a basic theory of content within the framework of truthmaker semantics and, in the second part, consider some of the applications to subject matter, common content, logical subtraction and ground.

I identify a notion of logical grounding, clarify it, and show how it can be used (i) to characterise various consequence relations, and (ii) to give a precise syntactic account of the notion of “groundedness” at work in the literature on the paradoxes of truth.

I give a semantic characterisation of a system for the logic of grounding similar to the system introduced by Kit Fine in his “Guide to Ground”, as well as a semantic characterisation of a variant of that system which excludes the possibility of what Fine calls ‘zero-grounding’.

How does metaphysical grounding interact with the truth-functions? I argue that the answer varies according to whether one has a worldly conception or a conceptual conception of grounding. I then put forward a logic of worldly grounding and give it an adequate semantic characterisation.