Could the Grounds's Grounding the Grounded Ground the Grounded?

I show that any predicational theory of (partial) ground that ex- tends a standard theory of syntax and that proves some commonly accepted principles for partial ground is inconsistent. I suggest a way to obtain a consistent, type-free, predicational theory of ground.

Oxford Studies in Metaphysics, 2017

The Problem of Iterated Ground is to explain what grounds truths about ground: if Γ grounds φ, what grounds that Γ grounds φ? This paper develops a novel solution to this problem. The basic idea is to connect ground to explanatory arguments. By developing a rigorous account of explanatory arguments we can equip operators for factive and non-factive ground with natural introduction and elimination rules. A satisfactory account of iterated ground falls directly out of the resulting logic: nonfactive grounding claims, if true, are zero-grounded in the sense of Fine.  Introduction If Γ 's being the case grounds φ's being the case, what grounds that Γ 's being the case grounds φ's being the case?  This is the Problem of Iterated Ground. (Dasgupta c; Bennett ; and deRosset ) have grappled with this problem from the point of view of metaphysics. But iterated ground is a problem not just for metaphysicians: the existing logics of ground  have had nothing to say about such iterated grounding claims. In this paper I propose a novel account of iterated ground and develop a logic of iterated ground. The account-what I will call the Zero-Grounding Account (zga for short)-is based Material from this paper has been presented at a reading group at Harvard University, the University of Texas at Austin, a conference on grounding at the University of Nottingham, a workshop at CSMN, a workshop on Ground and Groundedness at Munich and at the  meeting of the Eastern division of the APA. I'm grateful to members of the audience at all those places. I am very grateful to Michael Raven, Shamik Dasgupta, Øystein Linnebo, and Jönne Kriener for comments on earlier drafts of this material. Special thanks to Louis deRosset for extended discussions of the logics sketched in this paper and to Kit Fine for several suggestions that led to technical improvements. I am also very grateful for the detailed and very helpful comments I received from several anonymous reviewers.  Here Γ are some (true) propositions and φ is a (true) proposition. For the official formulation of claims of ground, see §  below. In the interest of readability I will not distinguish carefully between use and mention throughout.  Fine b; Correia , ; Schnieder ; Poggiolesi forthcoming.

Journal of Philosophical Logic, 2019

I explore the logic of ground. I first develop a logic of weak ground. This logic strengthens the logic of weak ground presented by Fine in his ‘Guide to Ground.’ This logic, I argue, generates many plausible principles which Fine’s system leaves out. I then derive from this a logic of strict ground. I argue that there is a strong abductive case for adopting this logic. It’s elegant, parsimonious and explanatorily powerful. Yet, so I suggest, adopting it has important consequences. First, it means we should think of ground as a type of identity. Second, it means we should reject much of Fine’s logic of strict ground. I also show how the logic I develop connects to other systems in the literature. It is definitionally equivalent both to Angell’s logic of analytic containment and to Correia’s system G.

I set up a system of structural rules for reasoning about ground and prove soundness and completeness for an appropriate truthmaker semantics.

Journal of Philosophical Logic, 2017

This is part two of a two-part paper, in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. This allows me to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we extend the base theory from the first part of the paper with hierarchically typed truth-predicates and principles about the interaction of partial ground and truth. We show that our theory is a proof-theoretically conservative extension of the ramified theory of positive truth up to 0 and thus is consistent. We argue that this theory provides a natural solution to Fine's " puzzle of ground " about the interaction of truth and ground. Finally, we show that if we drop the typing of our truth-predicate, we run into similar paradoxes as in the case of truth: we get ground-theoretical paradoxes of self-reference.

Sometimes we can have a fact playing a role in a grounding explanation, but where the particular content of that fact makes no difference to the explanation---any fact would do in its place. I call these facts vacuous grounds. I show that applying the distinction between vacuous and non-vacuous grounds allows us to give a principled solution to Kit Fine and Stephen Kramer's paradox of (reflexive) ground. This paradox shows that on minimal assumptions about grounding and minimal assumptions about logic, we can show that grounding is reflexive, contra the intuitive character of grounds. I argue that we should never have accepted that grounding is irreflexive in the first place; the intuitions that support the irreflexive intuition plausibly only require that grounding be non-vacuously irreflexive. Fine and Kramer's paradox relies, essentially, on a case of vacuous grounding and is thus no problem for this account.

Thought: A Journal of Philosophy, 2013

Many philosophers have recently been impressed by an argument to the effect that all grounding facts about “derivative entities”—e.g. the facts expressed by the (let us suppose) true sentences ‘the fact that Beijing is a concrete entity is grounded in the fact that its parts are concrete’ and ‘the fact that there are cities is grounded in the fact that p’, where ‘p’ is a suitable sentence couched in the language of particle physics—must themselves be grounded. This argument relies on a principle, Purity, which states that facts about derivative entities are non-fundamental. Purity is questionable. In this paper, I introduce a new argument—the argument from Settledness—for a similar conclusion but which does not rely on Purity. The conclusion of the new argument is that every “thick” grounding fact is grounded, where a grounding fact [F is grounded in G, H, …] is said to be thick when at least one of F, G, H, … is a fact—a condition that is automatically satisfied if grounding is factive. After introducing the argument, I compare it with the argument from Purity, and I assess its cogency relative to the relevant accounts of the connections between grounding and fundamentality that are available in the literature.

This is part one of a two-part paper in which we develop an axiomatic theory of the relation of partial ground. The main novelty is that we use a binary ground predicate rather than an operator to formalize ground. This allows us to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we develop an axiomatization of the relation of partial ground over the truths of arithmetic and show that the theory is a proof-theoretically conservative extension of the theory of positive truth. We also construct models for the theory and draw some conclusions for the semantics of conceptualist ground.

A popular principle about grounding, "Internality", says that if A grounds B, then necessarily, if A and B obtain, then A grounds B. I argue that Internality is false. Its falsity reveals a distinctive, new kind of explanation, which I call "ennobling". Its falsity also entails that every previously proposed theory of what grounds grounding facts is false. I construct a new theory.