This paper develops a novel theory of abstraction—what we call collective abstraction. The theory solves a notorious problem for noneliminative structuralism. The noneliminative structuralist holds that in addition to various isomorphic systems there is a pure structure that can be abstracted from each of these systems; but existing accounts of abstraction fail for nonrigid systems like the complex numbers. The problem with the existing accounts is that they attempt to define a unique abstraction operation. The theory of collective abstraction instead (...) simultaneously defines a collection of distinct abstraction operations, each of which maps a system to its corresponding pure structure. The theory is precisely formulated in an essentialist language. This allows us to throw new light on the question to what extent structuralists are committed to symmetric dependence. Finally, we apply the theory of collective abstraction to solve a problem about converse relations. (shrink)

This paper establishes a sound and complete semantics for the impure logic of ground. Fine (Review of Symbolic Logic, 5(1), 1–25, 2012a) sets out a system for the pure logic of ground, one in which the formulas between which ground-theoretic claims hold have no internal logical complexity; and it provides a sound and complete semantics for the system. Fine (2012b) [§§6-8] sets out a system for an impure logic of ground, one that extends the rules of the original pure system (...) with rules for the truth-functional connectives, the first-order quantifiers, and λ-abstraction. However, no semantics has yet been provided for this system. The present paper partly fills this lacuna by providing a sound and complete semantics for a system GG containing the truth-functional operators that is closely related to the truth-functional part of the system of Fine (2012b). (shrink)

This paper develops and defends a new argument against physicalist views of consciousness: the inconceivability argument. The argument has two main premises. First, it is not (ideally, positively) conceivable that phenomenal truths are grounded in physical truths. (For example, one cannot positively conceive of a situation in which someone has a vivid experience of pink wholly in virtue of the movements of colorless, insentient atoms.) Second, (ideal, positive) inconceivability is a guide to falsity. I attempt to show that the inconceivability (...) argument enjoys a significant advantage over the more familiar conceivability argument. One can reasonably endorse the inconceivability argument without endorsing the conceivability argument, but one cannot reasonably endorse the conceivability argument without also endorsing the inconceivability argument. (shrink)

A fundamental fact is “pure” just in case it has no grounded entities—ex. Tokyo, President Biden, the River Nile, {Socrates}, etc.—among its constituents. Purity is the thesis that every fundamental fact is pure. I argue that Purity is false. My argument begins with a familiar conditional: if Purity is true, then there are no fundamental “grounding facts” or facts about what grounds what. This conditional is accepted by virtually all of Purity’s defenders. However, I argue that it is also the (...) first step toward Purity’s undoing. For, if every grounding fact has a ground, then some grounded entities have “groundmates” or distinct grounded entities that share their full grounds. But, if there are groundmates, then Purity is false. So Purity leads to a contradiction. Therefore, it is false. I close by noting that my argument against Purity also gives us a powerful reason to think that some grounding facts are fundamental. (shrink)

The aim of this paper is to introduce, elucidate and defend the usefulness of a variant of grounding, or metaphysical explanation, that has the feature that the grounds explain of some states of affairs that one of them obtains without explaining which one obtains. I will dub this variant arbitrary grounding. After informally elucidating the basic idea in the first section, I will provide three metaphysical hypotheses that are best formulated in terms of arbitrary grounding in the second section. The (...) third section will be concerned with the relation between arbitrary grounding and non-arbitrary grounding. The fourth section will compare arbitrary grounding to two extant proposals in the literature. (shrink)

How is grounding related to metaphysical explanation? The standard view is that the former somehow “backs”, “undergirds” or “underlies” the latter. This view fits into a general picture of explanation, according to which explanations in general hold in virtue of a certain elite group of “explanatory relations” or “determinative relations” that back them. This paper turns the standard view on its head: grounding doesn't “back” metaphysical explanation but is in an important sense downstream from it. I call this view “grounding (...) idealism”, since it structurally resembles an analogous view about causation that is known as “causal idealism” and has been endorsed by philosophers like Michael Scriven and Philip Kitcher. I formulate a specific version of grounding idealism, Metaphysical Explanation‐First Idealism (MEFI), according to which the semantic value of ‘grounding’ is an abundant, gerrymandered relation settled by the metaphysical explanation facts. Then I offer some theoretical considerations that support MEFI over rival accounts of the relation between grounding and metaphysical explanation. Finally, I address the question of what role is left for grounding to play, if not that of “backing” metaphysical explanations. (shrink)

Grounding and explanation are said to be intimately connected. Some even maintain that grounding just is a form of explanation. But grounding and explanation also seem importantly different—on the face of it, the former is ‘worldy’ or ‘objective’ while the latter isn’t. In this paper, we develop and respond to an argument to the effect that there is no way to fruitfully address this tension that retains orthodox views about grounding and explanation but doesn’t undermine a central piece of methodology, (...) namely that explanation is a guide to ground. (shrink)

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)

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 of what grounds grounding: the ennobling theory.

Discussion of partial grounds that aren't parts of full grounds; definition of full grounding in terms of partial grounding.

In his insightful and challenging paper, Jonathan Schaffer argues against a distinction I make in The Ant Trap (Epstein 2015) and related articles. I argue that in addition to the widely discussed “grounding” relation, there is a different kind of metaphysical determination I name “anchoring.” Grounding and anchoring are distinct, and both need to be a part of full explanations of how facts are metaphysically determined. Schaffer argues instead that anchoring is a species of grounding. The crux of his argument (...) comes in the last sections of his paper, in his discussion of “exportation,” the relations strategy, and the definitions strategy. I am inclined to agree that Schaffer’s interesting strategies offer the best choices for the philosopher who wants to insist that anchoring is a species of grounding. But both, I will argue, are fatally flawed. I do not take the separation of anchors from grounds lightly, but find the evidence in its favor overwhelming. And once the distinction is made, I find anchoring to be a powerful practical tool in metaphysics. Philosophy and Phenomenological Research, Volume 99, Issue 3, Page 768-781, November 2019. (shrink)

Discussion of the relevance of grounding to substantiveness, theory-choice, and “location problems” in metaphysics.

Contingent negative existentials give rise to a notorious paradox. I formulate a version in terms of metaphysical grounding: nonexistence can't be fundamental, but nothing can ground it. I then argue for a new kind of solution, expanding on work by Kit Fine. The key idea is that negative existentials are contingently zero-grounded – that is to say, they are grounded, but not by anything, and only in the right conditions. If this is correct, it follows that grounding cannot be an (...) internal relation, and that no complete account of reality can be purely fundamental. (shrink)

Some people think that grounding is a type of identity. And some people think that grounding connections hold necessarily. I show that, under plausible assumptions, if grounding is a type of identity, then grounding connections hold necessarily.

The Question of Iterated Grounding (QIG) asks what grounds the grounding facts. Although the question received a lot of attention in the past few years, it is usually discussed independently of another important issue: the connection between metaphysical explanation and the relation or relations that supposedly “back” it. I will show that once we get clear on the distinction between metaphysical explanation and the relation(s) backing it, we can distinguish no fewer than four questions lumped under QIG. I will also (...) argue that given some plausible assumptions about what it would take for a relation to back metaphysical explanation, many salient views about grounding allow us to give “easy” answers to these questions—easy in the sense that we can straightforwardly derive them from the respective conception of grounding without getting into the sorts of complexities that typically inform answers to QIG. The paper's main upshot is that we cannot expect to make much progress on QIG without first addressing the difficult issue of how exactly grounding is related to metaphysical explanation. (shrink)

I argue that one’s views about which “metaphysical laws” obtain—including laws about what is identical with what, about what is reducible to what, and about what grounds what—can be used to deflect or neutralize the threat posed by a debunking explanation. I use a well-known debunking argument in the metaphysics of material objects as a case study. Then, after defending the proposed strategy from the charge of question-begging, I close by showing how the proposed strategy can be used by certain (...) moral realists to resist the evolutionary debunking arguments. (shrink)

I am very grateful to Stephan Leuenberger, Erica Shumener and Naomi Thompson for their excellent and thoughtful commentaries on Making Things Up. I have learned a lot from thinking through their replies. As it happens, they focus on pretty disparate aspects of the book: necessitation, relative fundamentality, and what builds the building facts, respectively. I will thus engage with their remarks separately.

The notion of fundamentality, as it is used in metaphysics, aims to capture the idea that there is something basic or primitive in the world. This metaphysical notion is related to the vernacular use of “fundamental”, but philosophers have also put forward various technical definitions of the notion. Among the most influential of these is the definition of absolute fundamentality in terms of ontological independence or ungroundedness. Accordingly, the notion of fundamentality is often associated with these two other technical notions.

This article develops the Pure Logic of Iterated Full Ground (PLIFG), a logic of ground that can deal with claims of the form “ϕ grounds that (ψ grounds θ)”—what we call iterated grounding claims. The core idea is that some truths Γ ground a truth ϕ when there is an explanatory argument (of a certain sort) from premisses Γ to conclusion ϕ. By developing a deductive system that distinguishes between explanatory and nonexplanatory arguments we can give introduction rules for operators (...) for factive and nonfactive full ground, as well as for a propositional “identity” connective. Elimination rules are then found by using a proof-theoretic inversion principle. (shrink)

Moral properties are explained by other properties. And moral principles tell us about moral properties. How are these two ideas related? In particular, is the truth of a given moral principle part of what explains why a given action has a given moral property? I argue “No.” If moral principles are merely concerned with the extension of moral properties across all possible worlds, then they cannot be partial explainers of facts about the instantiation of those properties, since in general necessitation (...) does not suffice for explanation. And if moral principles are themselves about what explains the moral properties under their purview, then by their own lights they are not needed in order to explain those moral properties’ instantiation—unless, that is, the principles exhibit an objectionable form of metaphysical circularity. So moral principles cannot explain why individual actions have moral properties. Nor, I also argue, can they explain why certain other factors explain why those actions have the moral properties that they do, or in some other way govern or mediate such first-order explanations of particular moral facts. When it comes to the explanation of an individual action’s specific moral features, moral principles are explanatorily idle. (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.

Sometimes a fact can play a role in a grounding explanation, but the particular content of that fact make 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 grounds allows us to give a principled solution to Kit Fine and Stephen Kramer’s paradox of 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. (shrink)

I argue—contra moderate grounding pluralists such as Kit Fine and more extreme grounding pluralists such as Jessica Wilson—that there is fundamentally only one grounding/in-virtue-of relation. I also argue that this single relation is indispensable for normative theorizing—that we can’t make sense of, for example, the debate over consequentialism without it. It follows from what I argue that there is no metaethically-pure normative ethics.

Characterization of a form of explanation involving grounding on the model of mechanistic causal explanation.

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)

Proponents of grounding often describe the notion as "metaphysical causation" involving determination and production relations similar to causation. This paper argues that the similarities between grounding and causation are merely superficial. I show that there are several sorts of causation that have no analogue in grounding; that the type of "bringing into existence" that both involve is extremely different; and that the synchronicity of ground and the diachronicity of causation make them too different to be explanatorily intertwined.

There is a tension in our theorizing about laws of nature: our practice of using and reasoning with laws of nature suggests that laws are universal generalizations, but if laws are universal generalizations then we face the problem of explanatory circularity. In this paper I elucidate this tension and show how it motivates a view of laws that I call Minimal Anti-Humeanism. This view says that the laws are the universal generalizations that are not grounded in their instances. I argue (...) that this view has a variety of advantages that could make it attractive to people with both Humean and anti-Humean inclinations. (shrink)

Discussion of a metaphysical sense of 'inheritance' and cognate notions relevant to fundamentality.

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)

According to the perceptual model, our knowledge of others' minds is a form of perceptual knowledge. We know, for example, that Jones is angry because we can literally see that he is. In this essay, I argue that mental states do not have the kind of distinctive looks that could sufficiently justify perceptual knowledge of others’ mentality. I present a puzzle that can arise with respect to mental states that I claim does not arise for non-mental properties like being an (...) apple and argue that this is explained by the fact that the looks of non-mental properties adhere to a certain explanatory principle that does not hold for mental states. This shows, I argue, that, even if we think mental states do have looks, these cannot offer sufficient grounds for perceptual knowledge of others' minds. In the final section of the essay, I suggest an alternative way of thinking about our knowledge of others' minds and about the sorts of looks or appearances that might be associated with mental states. (shrink)

General discussion of grounding, including its formal features, relations to other notions, and applications. (Originally published 2014; revised 2021).

A premise of the Leibnizian cosmological argument from contingency says that no contingent fact can explain why there are any contingent facts at all. David Hume and Paul Edwards famously denied this premise, arguing that if every fact has an explanation in terms of further facts ad infinitum, then they all do. This is known as the Hume–Edwards Principle (HEP). In this paper, I examine the cosmological argument from contingency within a framework of metaphysical explanation or ground and defend a (...) ground-theoretic version of HEP which says, roughly, that the plurality of contingent facts is grounded in its members. (shrink)

Our aim in this paper is to extend the semantics for the kind of logic of ground developed in (deRosset and Fine, 2023). In that paper, we very briefly suggested a way of treating universal and existential quantification over a fixed domain of objects. Here we explore some options for extending the treatment to allow for a variable domain of objects.

The physicalist credo is that the world is physical. But some phenomena, such as minds, morals, and mathematics, appear to be nonphysical. While an uncompromising physicalism would reject these, a conciliatory physicalism needn’t if it can account for them in terms of an underlying physical basis. Any such account must refer to the nonphysical. But won’t this unavoidable reference to the nonphysical conflict with the physicalist credo? This essay aims to clarify this problem and introduce a novel solution that relies (...) on a distinction between “circumstantial” facts that are based in the circumstances and “acircumstantial” facts that are not. This is used in two ways. First, physicalism is restricted to circumstantial facts: only they must have a physical basis that does not refer to the nonphysical. Second, facts accounting for the nonphysical are not restricted to the circumstantial: they may refer to the nonphysical if they are acircumstantial. Facts about how the physical accounts for the nonphysical therefore do not conflict with the physicalist’s credo. This provides a credible answer to what physicalism could be. (shrink)

The idea that some objects are metaphysically “cheap” has wide appeal. An influential version of the idea builds on abstractionist views in the philosophy of mathematics, on which numbers and other mathematical objects are abstracted from other phenomena. For example, Hume’s Principle states that two collections have the same number just in case they are equinumerous, in the sense that they can be correlated one-to-one: (HP) #xx=#yy iff xx≈yy. The principal aim of this article is to use the notion of (...) grounding to develop this sort of abstractionism. The appeal to grounding enables a unified response to the two main challenges that confront abstractionism. First, we must explicate the metaphor of meta- physical “cheapness.” Second, we must rebut the “bad company” objection, which rejects abstraction principles like (HP) as tarnished by their similarity to inconsistent principles like Frege’s Basic Law V. By enforcing a simple requirement that all abstraction be properly grounded, we propose a unified solution to these two hard, and prima facie unrelated, problems. On our view, grounded abstraction simultaneously ensures “cheap” abstracta and permissible abstraction. (shrink)

Many hope that our values, purged of messy human contingency, could aspire to correspond with mind-independent, rationally obligatory, and eternal ethical facts. But if the arguments of this thesis are on the right track, we should reject the search for non-natural and mind-independent moral truths.

Abstract:Skepticism about grounding is the view that ground-theoretic concepts shouldn’t be used in meta­physical theorizing. Possible reasons for adopting this attitude are numerous: perhaps grounding is unintelligible; or perhaps it’s never instantiated; or perhaps it’s just too heterogeneous to be theor­­­­­etically useful. Unfortunately, as currently pursued the debate between grounding enthusiasts and skeptics is insufficiently structured. This paper’s purpose is to impose a measure of conceptual rigor on the debate by offering an opinionated taxonomy of views with a reasonable claim (...) to being “skeptical.” I argue that carving up logical space into pro- and anti-grounding views isn’t especially helpful; rather, we should recognize various degrees of ground-theoretic involvement depending on how inflationary our understanding of the theoretical term ‘ground’ is. (shrink)

I will use paradox as a guide to metaphysical grounding, a kind of non-causal explanation that has recently shown itself to play a pivotal role in philosophical inquiry. Specifically, I will analyze the grounding structure of the Predestination paradox, the regresses of Carroll and Bradley, Russell's paradox and the Liar, Yablo's paradox, Zeno's paradoxes, and a novel omega plus one variant of Yablo's paradox, and thus find reason for the following: We should continue to characterize grounding as asymmetrical and irreflexive. (...) We should change our understanding of the transitivity of grounding in a certain sense. We should require foundationality in a new, generalized sense, that has well-foundedness as its limit case. Meta-grounding is important. The polarity of grounding can be crucial. Thus we will learn a lot about structural properties of grounding from considering the various paradoxes. On the way, grounding will also turn out to be relevant to the diagnosis (if not the solution) of paradox. All the paradoxes under consideration will turn out to be breaches of some standard requirement on grounding, which makes uniform solutions of large groups of these paradoxes more desirable. In sum, bringing together paradox and grounding will be shown to be of considerable value to philosophy.1. (shrink)

Current views of metaphysical ground suggest that a true conjunction is immediately grounded in its conjuncts, and only its conjuncts. Similar principles are suggested for disjunction and universal quantification. Here, it is shown that these principles are jointly inconsistent: They require that there is a distinct truth for any plurality of truths. By a variant of Cantor’s Theorem, such a fine-grained individuation of truths is inconsistent. This shows that the notion of grounding is either not in good standing, or that (...) natural assumptions about it need to be revised. (shrink)

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.

The aim of this study is to address the “Grounding Grounding Problem,” that is, the question as to what, if anything, grounds facts about grounding. I aim to show that, if a seemingly plausible principle of modal recombination between fundamental facts and the principle customarily called “Entailment” are assumed, it is possible to prove not only that grounding facts featuring fundamental, contingent grounds are derivative but also that either they are partially grounded in the grounds they feature or they are (...) “abysses”. (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)

Abstraction principles and grounding can be combined in a natural way Modality: metaphysics, logic, and epistemology, Oxford University Press, Oxford, pp 109–136, 2010; Schwartzkopff in Grazer philosophische studien 82:353–373, 2011). However, some ground-theoretic abstraction principles entail that there are circles of partial ground :775–801, 2017). I call this problem auto-abstraction. In this paper I sketch a solution. Sections 1 and 2 are introductory. In Sect. 3 I start comparing different solutions to the problem. In Sect. 4 I contend that the (...) thesis that the right-hand side of an abstraction principle is prior to its left-hand side motivates an independence constraint, and that this constraint leads to predicative restrictions on the acceptable instances of ground-theoretic abstraction principles. In Sect. 5 I argue that auto-abstraction is acceptable unless the left-hand side is essentially grounded by the right-hand side. In Sect. 6 I highlight several parallelisms between auto-abstraction and the puzzles of ground. I finally compare my solution with the strategies listed in Sect. 3. (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)

I argue that libertarian paternalism is in fact paternalism, or hard paternalism, rather than a form of soft paternalism. I do so on the basis of an analysis of the paternalist act according to which the paternalist act needn’t violate the will of the agent who is the target of that act and the paternalist actor need only suspect that her action may improve the welfare of that target. The paper considers and rejects interpretations of libertarian paternalism as soft paternalism. (...) I then provide an outline as to how libertarian paternalism may be reformed in light of the finding that current libertarian paternalism is hard paternalism. The proposal is to require that the enactment of libertarian paternalist policies be conditional on opinion polling indicating support for those policies from the agents they target. (shrink)

Argument that priority monism is best understood as being a contingent thesis.

There has been much recent interest in a distinctively metaphysical kind of determinative explanation: ground. This paper concerns various skeptical challenges to ground’s relevance to metaphysics, such as that it is an empty posit, that the work it is supposed to do is appropriated by other notions, and that it is inapt for specific issues it should serve. I argue against these challenges. My strategy is both critical and constructive. Critical because I argue that versions of these challenges raised by (...) Elizabeth Barnes, Kathrin Koslicki, Mari Mikkola, and Jessica Wilson are not persuasive. Constructive because we may nevertheless learn from them new work for ground. (shrink)