Grounding Ground

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.

This paper evaluates the proof-theoretic definition of ground developed by Poggiolesi in a range of recent publications and argues that her proposed definition fails. The paper then outlines an alternative approach where logical consequence relations and the logical operations are defined in terms of ground.

Philosophers have spilled a lot of ink over the past few years exploring the nature and significance of grounding. Kit Fine has made several seminal contributions to this discussion, including an exact treatment of the formal features of grounding [Fine, 2012a]. He has specified a language in which grounding claims may be expressed, proposed a system of axioms which capture the relevant formal features, and offered a semantics which interprets the language. Unfortunately, the semantics Fine offers faces a number of problems. In this paper, I review the problems and offer an alternative that avoids them. I offer a semantics for the pure logic of ground that is motivated by ideas already present in the grounding literature, and for which a natural axiomatization capturing central formal features of grounding is sound and complete. I also show how the semantics I offer avoids the problems faced by Fine’s semantics.

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.

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.

Journal of Philosophical Logic, 2017

Studies on the logic of grounding , i.e. of the notion of one truth or fact holding in virtue of others, are currently flourishing. These studies vary significantly in their objets. They are not all concerned with the same notion: while most focus on metaphysical grounding, others are about logical grounding, which may be seen as a subtype of the other, more familiar notion. They also do not all assume the same conception of grounding: some assume a worldly conception, and others a conceptual or representational conception. And finally, they do not all focus on the same kind of logical features of grounding: some are concerned with the pure logic of grounding, and others with its applied or impure logic. In this paper, I put forward an impure logic of metaphysical grounding, where grounding is understood in a representational way.

We provide a semantics and proof of completeness for the impure logic of ground.

Dag Prawitz's theory of grounds proposes a fresh approach to valid inferences. Its main aim is to clarify nature and reasons of their epistemic power. The notion of ground is taken to denote what one is in possession of when in a state of evidence, and valid inferences are described in terms of operations that make us pass from grounds we already have to new grounds. Thanks to a rigorously developed proof-as-chains conception, the ground-theoretic framework permits Prawitz to overcome some conceptual difficulties of his earlier proof-theoretic explanation. Though from different points of view, anyway, the two accounts share an issue of recognizability of relevant operational properties.

I develop two logics (pplg and pnlg) of grounding which can deal with iterated grounding claims. The logics are developed in naturaldeduction form and the grounding operators are equipped with bothintroduction and elimination rules. I prove normalization results for pplg and pnlg and determine their relationship to Fine’s Pure Logic of Ground.