This paper concerns an epistemological objection against mathematical platonism, due to Hartry Field.The argument poses an explanatory challenge – the challenge to explain the reliability of our mathematical beliefs – which the platonist, it’s argued, cannot meet. Is the objection compelling? Philosophers disagree, but they also disagree on (and are sometimes very unclear about) how the objection should be understood. Here I distinguish some options, and highlight some gaps that need to be filled in on the potentially most compelling version (...) of the argument. (shrink)

First-order normative theories concerning what’s right and wrong, good and bad, etc. and metanormative theories concerning the nature of first-order normative thought and talk are widely regarded as independent theoretical enterprises. This paper argues that several debates in metanormative theory involve views that have first-order normative implications, even as the implications in question may not be immediately recognizable as normative. I first make my claim more precise by outlining a general recipe for generating this result. I then apply this recipe (...) to three debates in metaethics: the modal status of basic normative principles, normative vagueness and indeterminacy, and the determination of reference for normative predicates. In each case I argue that certain views on each issue carry first-order normative commitments, in accordance with my recipe. (shrink)

According to an intuitive picture of relevant entailment, an entailment is relevant if all the formulas it contains contribute to its validity. In this paper, we provide a ground-theoretic analysis of this notion of contribution, and as a result of relevant entailment. We build a system of bilateral logical grounding within which we can derive classical entailment and analyze the contribution of premises and conclusions, in terms of a certain type of connection between their respective logical grounds. The resulting framework (...) is shown to have a strong unifying and explanatory power by bringing together the notions of grounding and relevance and explaining the commonalities and differences between alternative contribution-based accounts of relevance. (shrink)

This book is in honour of Professor Anna-Sofia Maurin on her 50th birthday. It consists of eighteen essays on metaphysical issues written by Swedish and international scholars.

It is commonly held that p is a reason for A to ϕ only if p explains why A ought to ϕ. I argue that this view must be rejected because there are reasons for A to ϕ that would be redundant in any ex...

[This paper is available as open access from the publisher.] Normative theories aim to explain why things have the normative features they have. This paper argues that, contrary to some plausible existing views, one important kind of normative explanations which first-order normative theories aim to formulate and defend can fail to transmit downward along chains of metaphysical determination of normative facts by non-normative facts. Normative explanation is plausibly subject to a kind of a justification condition whose satisfaction may fail to (...) transmit along the relevant kind of metaphysical hierarchy. A broader aim of the paper is to contribute to systematic theorizing about normative explanation: whereas there has been a great deal of work on scientific explanation, there has been little by way of systematic exploration of what sort of explanations normative theories aim to formulate and defend. (shrink)

What does it mean that some proposition follows from others? The standard way of spelling out the notion proceeds in modal terms: x follows from y iff necessarily, if y is true, so is x. But although this yields a useful and manageable account of consequence, it fails to capture certain aspects of our pre-theoretical understanding of consequence. In this paper, an alternative notion of logical consequence, based on the idea of grounding, is developed.

What grounds the facts about what is identical to/distinct from what? A natural answer is: the facts about what exists. Despite its prima facie appeal, this view has received surprisingly little attention in the literature. Moreover, those who have discussed it have been inclined to reject it because of the following important challenge: why should the existence of some individuals ground their identity in some cases and their distinctness in others? (Burgess 2012, Shumener 2020b). This paper offers a sustained defense (...) of the view. The first half provides some positive motivations in terms of other natural principles involving ground. The second half considers various ways of distilling the challenge into a precise objection to the view, and argues that none of the resulting objections proves persuasive. (shrink)

According to an increasingly popular view among philosophers of science, both causal and non-causal explanations can be accounted for by a single theory: the counterfactual theory of explanation. A kind of non-causal explanation that has gained much attention recently but that this theory seems unable to account for are grounding explanations. Reutlinger :239-256, 2017) has argued that, despite these appearances to the contrary, such explanations are covered by his version of the counterfactual theory. His idea is supported by recent work (...) on grounding by Schaffer and Wilson who claim there to be a tight connection between grounding and counterfactual dependence. The present paper evaluates the prospects of the idea. We show that there is only a weak sense in which grounding explanations convey information about counterfactual dependencies, and that this fact cannot plausibly be taken to reveal a distinctive feature that grounding explanations share with other kinds of explanations. (shrink)

Explanatory realism is the view that explanations work by providing information about relations of productive determination such as causation or grounding. The view has gained considerable popularity in the last decades, especially in the context of metaphysical debates about non-causal explanation. What makes the view particularly attractive is that it fits nicely with the idea that not all explanations are causal whilst avoiding an implausible pluralism about explanation. Another attractive feature of the view is that it allows explanation to be (...) a partially epistemic, context-dependent phenomenon. In spite of its attractiveness, explanatory realism has recently been subject to criticism. In particular, Taylor :197–219, 2018). has presented four types of explanation that the view allegedly cannot account for. This paper defends explanatory realism against Taylor’s challenges. We will show that Taylor’s counterexamples are either explanations that turn out to provide information about entities standing in productive determination relations or that they are not genuine explanations in the first place. (shrink)

Grounding pluralism is the view that there are multiple kinds of grounding. In this essay, I motivate and defend an explanation-theoretic view of grounding pluralism. Specifically, I argue that there are two kinds of grounding: why-grounding—which tells us why things are the case—and how-grounding—which tells us how things are the case.

It is common to think that grounding is necessary in the sense that: if P grounds Q, then necessarily: if P, then Q. Though most accept this principle, some give counterexamples to it. Instead of straightforwardly arguing for, or against, necessity, I explain the sense in which grounding is necessary and contingent. I argue that there are two kinds of grounding: what-grounding and why-grounding, where the former kind is necessary while the latter is contingent.

Many philosophers have been attracted to the idea of using the logical form of a true sentence as a guide to the metaphysical grounds of the fact stated by that sentence. This paper looks at a particular instance of that idea: the widely accepted principle that disjunctions are grounded in their true disjuncts. I will argue that an unrestricted version of this principle has several problematic consequences and that it’s not obvious how the principle might be restricted in order to (...) avoid them. My suggestion is that, instead of trying to restrict the principle, we should distinguish between metaphysical and conceptual grounds and take the principle to apply exclusively to the latter. This suggestion, if correct, carries over to other prominent attempts at using logical form as a guide to ground. (shrink)

ABSTRACTWhile extant replies to Jonathan Schaffer’s putative counterexamples to the transitivity of grounding have made significant strides against the charge of transitivity failure, the replies pay insufficient attention to the common structure of the counterexamples, overlooking a deeper structural feature that contributes to their prima facie plausibility. Putative counterexamples to the transitivity of grounding, I argue, trade on the distinction between what I call ‘rigid’ and ‘non-rigid’ grounding, and confusion over how rigid and non-rigid grounding react when combined pumps the (...) intuition that the counterexamples’ chained conclusions are false. The rigid/non-rigid grounding distinction also reveals plausible weakening inference rules that have been overlooked in treatments of the logic of grounding. (shrink)

Humeans about laws maintain that laws of nature are nothing over and above the complete distribution of non-modal, categorical properties in spacetime. ‘Humean compatibilists’ argue that if Humeanism about laws is true, then agents in a deterministic world can do otherwise than they are lawfully determined to do because of the distinctive nature of Humean laws. More specifically, they reject a central premise of the Consequence argument by maintaining that deterministic laws of nature are ‘up to us’. In this paper, (...) we present a new argument for Humean compatibilism. We argue that Humeans about laws indeed have resources for defending compatibilism that non-Humeans lack. Moreover, we show that utilizing these resources does not lead to objectionable consequences. Humeans about laws should thus embrace Humean compatibilism. (shrink)

A lot of research has recently been done on the topic of ground, and in particular on the logic of ground. According to a broad consensus in that debate, ground is hyperintensional in the sense that even logically equivalent truths may differ with respect to what grounds them, and what they ground. This renders pressing the question of what we may take to be the ground-theoretic content of a true statement, i.e. that aspect of the statement’s overall content to which (...) ground is sensitive. I propose a novel answer to this question, namely that ground tracks how, rather than just by what, a statement is made true. I develop that answer in the form of a formal theory of ground-theoretic content and show how the resulting framework may be used to articulate plausible theories of ground, including in particular a popular account of the grounds of truth-functionally complex truths that has proved difficult to accommodate on alternative views of content. (shrink)

A lot of research has recently been done on the topic of ground, and in particular on the logic of ground. According to a broad consensus in that debate, ground is hyperintensional in the sense that even logically equivalent truths may differ with respect to what grounds them, and what they ground. This renders pressing the question of what we may take to be the ground-theoretic content of a true statement, i.e. that aspect of the statement’s overall content to which (...) ground is sensitive. I propose a novel answer to this question, namely that ground tracks how, rather than just by what, a statement is made true. I develop that answer in the form of a formal theory of ground-theoretic content and show how the resulting framework may be used to articulate plausible theories of ground, including in particular a popular account of the grounds of truth-functionally complex truths that has proved difficult to accommodate on alternative views of content. (shrink)

Say that two sentences are ground-theoretically equivalent iff they are interchangeable salva veritate in grounding contexts. Notoriously, ground-theoretic equivalence is a hyperintensional matter: even logically equivalent sentences may fail to be interchangeable in grounding contexts. Still, there seem to be some substantive, general principles of ground-theoretic equivalence. For example, it seems plausible that any sentences of the form A∧B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A \wedge B$$\end{document} and B∧A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B (...) \wedge A$$\end{document} are ground-theoretically equivalent. What, then, are in general the conditions for two sentences to stand in the relation of ground-theoretic equivalence, and what are the logical features of that relation? This paper develops and defends an answer to these questions based on the mode-ified truthmaker theory of content presented in my recent paper ‘Towards a theory of ground-theoretic content’ :785–814, 2018). (shrink)

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)

Grounding necessitarianism (GN) is the view that full grounds necessitate what they ground. Although GN has been rather popular among philosophers, it faces important counterexamples: For instance, A=[Socrates died] fully grounds C=[Xanthippe became a widow]. However, A fails to necessitate C: A could have obtained together with B=[Socrates and Xanthippe were never married], without C obtaining. In many cases, the debate essentially reduces to whether A indeed fully grounds C – as the contingentist claims – or if instead C is (...) fully grounded in A+, namely A plus some supplementary fact S (e.g. [Xanthippe was married to Socrates]) – as the necessitarian claims. Both sides typically agree that A+ necessitates C, while A does not; they disagree on whether A or A+ fully grounds C. This paper offers a novel defence of the claim that, in these typical cases, unlike A+, A fails to fully ground C – thereby bringing further support to GN. First and foremost, unlike A+, A fails to fully ground C because it fails to contain just what is relevant to do so, in two distinct senses – explanatory and generative relevance. Second, going for A, rather than A+, as a full ground undermines not just grounding necessitarianism, but modally weaker views which even contingentists may want to preserve. (shrink)

The aim of this paper is to argue for some useful distinctions in the theory of grounding. I do so by first introducing the notion of grounding, discussing some of its features, and arguing that grounds must play some role in bringing about what they ground (sec.1). I then argue that there are various distinct roles a fact may play in bringing about another, and more particularly that we should distinguish between three such roles; enablers, partial grounds, and facts that (...) partly ground (sec. 2). Finally, I present two theoretical advantages to incorporating these distinctions into our theory of grounding. Namely, that it reframes, and arguably dissolves, the contingentist-necessitarian debate (sec. 3), and that it helps to elegantly deal with the purported counterexamples to the transitivity of grounding and thus maintain the plausible elements of the assumption that grounding is a transitive relation (sec.4). (shrink)

Although much technical and philosophical attention has been given to relevance logics, the notion of relevance itself is generally left at an intuitive level. It is difficult to find in the literature an explicit account of relevance in formal reasoning. In this article I offer a formal explication of the notion of relevance in deductive logic and argue that this notion has an interesting place in the study of classical logic. The main idea is that a premise is relevant to (...) an argument when it contributes to the validity of that argument. I then argue that the sequents which best embody this ideal of relevance are the so-called perfect sequents—that is, sequents which are valid but have no proper subsequents that are valid. Church’s theorem entails that there is no recursively axiomatizable proof-system that proves all and only the perfect sequents, so the project that emerges from studying perfection in classical logic is not one of finding a perfect subsystem of classical logic, but is rather a comparative study of classifying subsystems of classical logic according to how well they approximate the ideal of perfection. (shrink)

Our concern in this paper lies with a common argument from racial discrimination to realism about races: some people are discriminated against for being members of a particular race (i.e., racial discrimination exists), so some people must be members of that race (i.e., races exist). Error theorists have long responded that we can explain racial discrimination in terms of racial attitudes alone, so we need not explain it in terms of race itself. But to date there has been little detailed (...) discussion of whether it is better to explain racial discrimination in terms of race or in terms of racial attitudes alone. Our goal is to offer a novel and detailed argument in defense of explaining racial discrimination in terms of racial attitudes alone, by attending to the neglected phenomenon of misperception discrimination, which involves differential treatment due to misperceived race. We argue that the discriminatory action in misperception cases must be explained in the same way as cases where (according to the realist) the victim’s race is accurately perceived. Thus, the victim’s actual race cannot provide the best explanation. The main upshot of our argument is that explanatory arguments from racial discrimination to realism about race fail. (shrink)

Whether or not we are able to do x is on many philosophical accounts of our moral practice relevant for whether we are responsible for not doing x or for being excusable for not having done x. In this paper I will examine how such accounts are affected by whether a Humean or non-Humean account of laws is presupposed. More particularly, I will argue that (on one interpretation) Humean conceptions of laws, while able to avoid the consequence argument, run into (...) what might be called “the problem of radical freedom”: Humean laws fail to constrain what we can do. By contrast, non-Humean laws (and Humean laws on a second interpretation) avoid the problem of radical freedom but have no easy way out of the consequence argument. (shrink)

I survey the philosophical literature on grounding explanation and its connection to metaphysical ground.