Though the study of grounding is still in the early stages, Kit Fine, in ”The Pure Logic of Ground”, has made a seminal attempt at formalization. Formalization of this sort is supposed to bring clarity and precision to our theorizing, as it has to the study of other metaphysically important phenomena, like modality and vagueness. Unfortunately, as I will argue, Fine ties the formal treatment of grounding to the obscure notion of a weak ground. The obscurity of weak ground, together (...) with its centrality in Fine’s system, threatens to undermine the extent to which this formalization offers clarity and precision. In this paper, I show how to overcome this problem. I describe a system, the logic of strict ground (LSG) and demonstrate its adequacy; I specify a translation scheme for interpreting Fine’s weak grounding claims; I show that the interpretation verifies all of the principles of Fine’s system; and I show that derivability in Fine’s system can be exactly characterized in terms of derivability in LSG. I conclude that Fine’s system is reducible to LSG. (shrink)

In this paper I explore irrealist alternatives to orthodox realism about grounding, and claim that at least some of these alternatives represent fertile areas for future discussion.

I develop a graph-theoretic model theory for pure and iterative grounding logics.

A raft of new philosophical problems concerning truth have recently been discovered by several theorists. These problems concern the question of how ascriptions of truth are to be grounded. Most previous commentators have taken the problems to shed light on the theory of ground. In this paper, I argue that they also shed light on the theory of truth. In particular, I argue that the notion of ground can be deployed to clearly articulate one strand of deflationary thinking about truth, (...) according to which truth is “metaphysically lightweight.” I offer a ground-theoretic explication of the lightness of truth and show how it yields a novel solution to the problems concerning how truth is grounded. So, the theory of truth and the theory of ground interact fruitfully: we can apply the notion of ground to offer a clear explication of the deflationist claim that truth is “metaphysically lightweight” that both captures the motivations for that claim and solves the problems. (shrink)

Seemingly natural principles about the logic of ground generate cycles of ground; how can this be if ground is asymmetric? The goal of the theory of decycling is to find systematic and principled ways of getting rid of such cycles of ground. In this paper—drawing on graph-theoretic and topological ideas—I develop a general framework in which various theories of decycling can be compared. This allows us to improve on proposals made earlier by Fine and Litland. However, it turns out that (...) there is no unique method of decycling. An important upshot is that the notion of asymmetric ground may be indeterminate. (shrink)

Reality is hierarchically structured, or so proponents of the metaphysical posit of grounding argue. The less fundamental facts obtain in virtue of, or are grounded in, the more fundamental facts. But what exactly is it for one fact to be more fundamental than another? The aim of this paper is to provide a measure of relative fundamentality. I develop and defend an account of the metaphysical hierarchy that assigns to each fact a set of ordinals representing the levels on which (...) it occurs. The account allows one to compare any two facts with respect to their fundamentality and it uses immediate grounding as its sole primitive. In the first section, I will set the stage and point to some shortcomings of a rival account proposed by Karen Bennett. The second section will present my own proposal and the third section will discuss how it can be extended to non-foundationalist settings. The fourth section discusses potential objections. (shrink)

This paper focuses on the concept of collective essence: that some truths are essential to many items taken together. For example, that it is essential to conjunction and negation that they are truth-functionally complete. The concept of collective essence is one of the main innovations of recent work on the theory of essence. In a sense, this innovation is natural, since we make all sorts of plural predications. It stands to reason that there should be a distinction between essential and (...) accidental plural predications if there is a distinction among singular predications. In this paper I defend the view that the concept of collective essence is governed by the principle of Monotonicity: that something is essential to some items only if it is essential to any items to which they belong. (shrink)

Could φ’s partially grounding ψ itself be a partial ground for ψ? I show that it follows from commonly accepted principles in the logic of ground that this sometimes happens. It also follows from commonly accepted principles that this never happens. I show that this inconsistency turns on different principles than the puzzles of ground already discussed in the literature, and I propose a way of resolving the inconsistency.

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 of the paper is the of use of 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 PT of positive truth. We construct models for the theory and draw some conclusions for the semantics of conceptualist ground. (shrink)

The scientific successes of the last 400 years strongly suggest a picture on which our scientific theories exhibit a layered structure of dependence and determination. Economics is dependent on and determined by psychology; psychology in its turn is, plausibly, dependent on and determined by biology; and so it goes. It is tempting to explain this layered structure of dependence and determination among our theories by appeal to a corresponding layered structure of dependence and determination among the entities putatively treated by (...) those theories. In this paper, I argue that we can resist this temptation: we can explain the sense in which, e.g., the biological truths are dependent on and determined by chemical truths without appealing to properly biological or chemical entities. This opens the door to a view on which, though there are more truths than just the purely physical truths, there are no entities, states, or properties other than the purely physical entities, states, and properties. I argue that some familiar strategies to explicate the idea of a layered structure of theories by appeal to reduction, ground, and truthmaking encounter difficulties. I then show how these difficulties point the way to a more satisfactory treatment which appeals to something very close to the notion of ground. Finally, I show how this treatment provides a theoretical setting in which we might fruitfully frame debates about which entities there really are. (shrink)

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’.

I provide and defend two natural accounts of fundamentality for facts that do justice to the idea that the “degree of fundamentality” enjoyed by a fact is a matter of how far, from a ground-theoretic perspective, the fact is from the ungrounded facts.

A logic of grounding where what is grounded can be a collection of truths is a “many-many” logic of ground. The idea that grounding might be irreducibly many-many has recently been suggested by Dasgupta. In this paper I present a range of novel philosophical and logical reasons for being interested in many-many logics of ground. I then show how Fine’s State-Space semantics for the Pure Logic of Ground can be extended to the many-many case, giving rise to the Pure Logic (...) of Many-Many Ground. In the second, more technical, part of the paper, I do two things. First, I present an alternative formalization of plg; this allows us to simplify Fine’s completeness proof for plg. Second, I formalize plmmg using an infinitary sequent calculus and prove that this formalization is sound and complete. (shrink)

It is widely acknowledged that some truths or facts don’t have a minimal full ground [see e.g. Fine ]. Every full ground of them contains a smaller full ground. In this paper I’ll propose a minimality constraint on immediate grounding and I’ll show that it doesn’t fall prey to the arguments that tell against an unqualified minimality constraint. Furthermore, the assumption that all cases of grounding can be understood in terms of immediate grounding will be defended. This assumption guarantees that (...) the proposed minimality constraint is significant for all cases of grounding. With its help one can get a clear grip on the relevance of grounding, a feature that will be put to use in the penultimate section. (shrink)

Many non-naturalists about the normative want to endorse the view that some normative facts hold in virtue of both non-normative facts and normative principles. In this paper, I argue that non-naturalism is inconsistent with this thesis, due to the nature of normative principles and their grounds. I then consider two ways in which the nonnaturalist position could be modified or expanded to solve this problem. No solution, it turns out, is without its problems. I end by considering how the non-naturalist (...) can deny that normative facts obtain partially in virtue of principles. (shrink)

I introduce a proof system for the logic of relative fundamentality, as well as a natural semantics with respect to which the system is both sound and complete. I then “modalise” the logic, and finally I discuss the properties of grounding given a suggested account of this notion in terms of necessity and relative fundamentality.

Fine (2012) is a pluralist about grounding. He holds that there are three fundamentally distinct notions of grounding: metaphysical, normative, and natural. Berker (2017) argues for monism on the grounds that the pluralist cannot account for certain principles describing how the distinct notions of grounding interact. This paper defends pluralism. By building on work by Fine (2010) and Litland (2015) I show how the pluralist can systematically account for Berker's interaction principles.