Kit Fine, in "The Pure Logic of Ground", has made a seminal attempt at formalizing the notion of ground. Fine ties the formal treatment of grounding to the notion of a weak ground. Formalization of this sort is supposed to bring clarity and precision to our theorizing. Unfortunately, as I will argue, it's not clear what weak ground is. I review five alternative explanations of the idea, and argue that none of them are ultimately satisfactory. I close by outlining a (...) more complicated explanation of the notion that turns out to be more satisfactory. (shrink)

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)

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’.

Metaphysicians of a certain stripe are almost unanimously of the view that grounding is necessarily irreflexive, asymmetric, transitive, and well-founded. They deny the possibility of circles of ground and, therewith, the possibility of species of metaphysical coherentism. But what's so bad about circles of ground? One problem for coherentism might be that it ushers in anti-foundationalism: grounding loops give rise to infinite regresses. And this is bad because infinite grounding regresses are vicious. This article argues that circles of ground do (...) not necessarily give rise to infinite regresses, and where they do, those regresses are not necessarily vicious. (shrink)

Recently much has been made of the grounding relation, and of the idea that it is intimately tied to fundamentality. If A grounds B, then A is more fundamental than B (though not vice versa ), and A is ungrounded if and only if it is fundamental full stop—absolutely fundamental. But here is a puzzle: is grounding itself absolutely fundamental?

It is my aim in this paper to show that the contemporary assimilation of essence to modality is fundamentally misguided and that, as a consequence, the corresponding conception of metaphysics should be given up. It is not my view that the modal account fails to capture anything which might reasonably be called a concept of essence. My point, rather, is that the notion of essence which is of central importance to the metaphysics of identity is not to be understood in (...) modal terms or even to be regarded as extensionally equivalent to a modal notion. The one notion is, if I am right, a highly refined version of the other; it is like a sieve which performs a similar function but with a much finer mesh. (shrink)

The article introduces and defends the Nomological Account of ground, a reductive account of the notion of metaphysical explanation in terms of the laws of metaphysics. The paper presents three desiderata that a theory of ground should meet: it should explain the modal force of ground, the generality of ground, and the interplay between ground and certain mereological notions. The bulk of the paper develops the Nomological Account and argues that it meets the three desiderata. The Nomological Account relies on (...) two central notions: the notion of a ‘law of metaphysics’ and the notion of ‘determination via the laws’. The paper offers the constructional conception of the laws of metaphysics, on which the metaphysical laws are general principles that characterize construction–operations such as composition, constitution, or set-formation. The role of determination in the account is explained and some reductive approaches to the notion are sketched. The case for the Nomological Account presented in this article is also a case for the laws of metaphysics. Since the Nomological Account offers a promising approach to metaphysical explanation we should take the laws of metaphysics seriously. (shrink)

The paper explores a deductive-nomological account of metaphysical explanation: some truths metaphysically explain, or ground, another truth just in case the laws of metaphysics determine the latter truth on the basis of the former. I develop and motivate a specific conception of metaphysical laws, on which they are general rules that regulate the existence and features of derivative entities. I propose an analysis of the notion of ‘determination via the laws’, based on a restricted form of logical entailment. I argue (...) that the DN-account of ground can be defended against the well-known objections to the DN-approach to scientific explanation. The goal of the paper is to show that the DN-account of metaphysical explanation is a well-motivated and defensible theory. (shrink)

It has recently been suggested that a distinctive metaphysical relation— ‘Grounding’—is ultimately at issue in contexts in which some goings-on are said to hold ‘in virtue of’’, be ‘metaphysically dependent on’, or be ‘nothing over and above’ some others. Grounding is supposed to do good work in illuminating metaphysical dependence. I argue that Grounding is also unsuited to do this work. To start, Grounding alone cannot do this work, for bare claims of Grounding leave open such basic questions as whether (...) Grounded goings-on exist, whether they are reducible to or rather distinct from Grounding goings-on, whether they are efficacious, and so on; but in the absence of answers to such basic questions, we are not in position to assess the associated claim or theses concerning metaphysical dependence. There is no avoiding appeal to the specific metaphysical relations typically at issue in investigations into dependence—for example, type or token identity, functional realization, classical mereological parthood, the set membership relation, the proper subset relation, the determinable/determinate relation, and so on—which are capable of answering these questions. But, I argue, once the specific relations are on the scene, there is no need for Grounding. (shrink)

I problematize Grounding-based formulations of physicalism. More specifically, I argue, first, that motivations for adopting a Grounding-based formulation of physicalism are unsound; second, that a Grounding-based formulation lacks illuminating content, and that attempts to imbue Grounding with content by taking it to be a strict partial order are unuseful and problematic ; third, that conceptions of Grounding as constitutively connected to metaphysical explanation conflate metaphysics and epistemology, are ultimately either circular or self-undermining, and controversially assume that physical dependence is incompatible (...) with explanatory gaps; fourth, that in order to appropriately distinguish physicalism from strong emergentism, a Grounding-based formulation must introduce one and likely two primitives in addition to Grounding; and fifth, that understanding physical dependence in terms of Grounding gives rise to ‘spandrel’ questions, including, e.g., “What Grounds Grounding?”, which arise only due to the overly abstract nature of Grounding. (shrink)

It has been suggested that many philosophical theses—physicalism, normative naturalism, phenomenalism, and so on—should be understood in terms of ground. Against this, Ted Sider (2011) has argued that ground is ill-suited for this purpose. Here I develop Sider’s objection and offer a response. In doing so I develop a view about the role of ground in philosophy, and about the content of these distinctively philosophical theses.

The framework of natural deduction is extended by permitting rules as assumptions which may be discharged in the course of a derivation. this leads to the concept of rules of higher levels and to a general schema for introduction and elimination rules for arbitrary n-ary sentential operators. with respect to this schema, (functional) completeness "or", "if..then" and absurdity is proved.

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.

Inferentialism claims that expressions are meaningful by virtue of rules governing their use. In particular, logical expressions are autonomous if given meaning by their introduction-rules, rules specifying the grounds for assertion of propositions containing them. If the elimination-rules do no more, and no less, than is justified by the introduction-rules, the rules satisfy what Prawitz, following Lorenzen, called an inversion principle. This connection between rules leads to a general form of elimination-rule, and when the rules have this form, they may (...) be said to exhibit “general-elimination” harmony. Ge-harmony ensures that the meaning of a logical expression is clearly visible in its I-rule, and that the I- and E-rules are coherent, in encapsulating the same meaning. However, it does not ensure that the resulting logical system is normalizable, nor that it satisfies the conservative extension property, nor that it is consistent. Thus harmony should not be identified with any of these notions. (shrink)

The aim of this paper is to provide a definition of the the notion of complete and immediate formal grounding through the concepts of derivability and complexity. It will be shown that this definition yields a subtle and precise analysis of the concept of grounding in several paradigmatic cases.

In Poggiolesi we have introduced a rigorous definition of the notion of complete and immediate formal grounding; in the present paper our aim is to construct a logic for the notion of complete and immediate formal grounding based on that definition. Our logic will have the form of a calculus of natural deduction, will be proved to be sound and complete and will allow us to have fine-grained grounding principles.

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)

I discuss three recent counterexamples to the transitivity of grounding due to Jonathan Schaffer. I argue that the counterexamples don’t work and draw some conclusions about the relationship between grounding and explanation.

Most authors on metaphysical grounding have taken full grounding to be an internal relation in the sense that it's necessary that if the grounds and the grounded both obtain, then the grounds ground the grounded. The negative part of this essay exploits empirical and provably nonparadoxical self-reference to prove conclusively that even immediate full grounding isn't an internal relation in this sense. The positive, second part of this essay uses the notion of a “completely satisfactory explanation” to shed light on (...) the logic of ground in the presence of self-reference. This allows us to develop a satisfactory logic of ground and recover a sense in which grounding is still an internal relation. (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.

Metaphysical grounding is standardly taken to be irreflexive: nothing grounds itself. Kit Fine has presented some puzzles that appear to contradict this principle. I construct a particularly simple variant of those puzzles that is independent of several of the assumptions required by Fine, instead employing quantification into sentence position. Various possible responses to Fine's puzzles thus turn out to apply only in a restricted range of cases.

The article explores the irreflexivity of metaphysical dependence in the physical structure of reality. It stresses that the word dependence denotes quasi-ireflexivity which affects the metaphysical relations of a physical structure. It focuses on the view that irreflexivity assumption has been made without discussion of the dependence relations on the structure of reality.

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

I describe some paradoxes of ground and relate them to the semantic paradoxes.

This paper is an investigation of the general logic of "identifications", claims such as 'To be a vixen is to be a female fox', 'To be human is to be a rational animal', and 'To be just is to help one's friends and harm one's enemies', many of which are of great importance to philosophers. I advocate understanding such claims as expressing higher-order identity, and discuss a variety of different general laws which they might be thought to obey. [New version: (...) Nov. 4th, 2016]. (shrink)

This paper argues that ground is irreducibly plural: a group of facts can be grounded together, as a collective, even though no member of the group has a ground on its own. This kind of plural grounding is applied to the metaphysics of individuals and quantities, yielding a “structuralist” view in each case. Some more general implications of plural grounding are also discussed.

A compelling idea holds that reality has a layered structure. We often disagree about what inhabits the bottom layer, but we agree that higher up we find chemical, biological, geological, psychological, sociological, economic, /etc./, entities: molecules, human beings, diamonds, mental states, cities, interest rates, and so on. How is this intuitive talk of a layered structure of entities to be understood? Traditionally, philosophers have proposed to understand layered structure in terms of either reduction or supervenience. But these traditional views face (...) well-known problems. A plausible alternative is that layered structure is to be explicated by appeal to explanations of a certain sort, termed / grounding explanations/. Grounding explanations tell us what obtains in virtue of what. Unfortunately, the use of grounding explanations to articulate the layered conception faces a problem, which I call /the collapse/. The collapse turns on the question of how to ground the facts stated by the explanations themselves. In this paper I make a suggestion about how to ground explanations that avoids the collapse. Briefly, the suggestion is that the fact stated by a grounding explanation is grounded in its /explanans/. (shrink)

This paper distinguishes two kinds of realist issue -- the issue of whether the propositions of a given domain are factual and the issue of whether they are fundamental. It criticizes previous accounts of what these issues come to and suggests that they are to be understood in terms of a basic metaphysical concept of reality. This leaves open the question of how such issues are to be resolved; and it is argued that this may be done through consideration of (...) what grounds the facts of a given domain, when fundamentality is in question, and what grounds our engagement with the putative facts, when factuality is in question. (shrink)

Interest surges in a distinctively metaphysical notion of ground. But a Schism has emerged between Orthodoxy’s view of ground as inducing a strict partial order structure on reality and Heresy’s rejection of this view. What’s at stake is the structure of reality (for proponents of ground), or even ground itself (for those who think this Schism casts doubt upon its coherence). I defend Orthodoxy against Heresy.

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.