The Metaphysics of Moral Explanations 1 Daniel Fogal (NYU) and Olle Risberg (Uppsala) [​Note​: A slightly shorter version of this paper appears in ​Oxford Studies in Metaethics​, Vol. 15. The​ text in green​ was cut from the final version due to space constraints.] 1 Introduction What are the aims of first-order moral inquiry, or normative inquiry more generally? One aim is to specify which actions are right and which actions are wrong. But that's not enough; another aim is to ​explain ​why ​the right actions are right and the wrong ones are wrong. How, more exactly, do such explanations work? On one natural view, the full explanation of why a particular action was wrong (or right or good or bad, etc.) involves two kinds of facts: (i) a particular 'natural' or 'descriptive' fact-perhaps it was a lie, for instance, or failed to maximize well-being-and (ii) a general moral fact-that it is wrong to lie, for instance, or to not maximize well-being. Call the latter facts ​moral principles​. Despite the naturalness of this view, the precise nature and structure of the relevant principles, and the form of explanation involved, is not yet well understood. What's more, the view that moral principles play an explanatory role has recently been attacked. Selim Berker (forthcoming-a), for example, argues that moral principles can instead be viewed as ​mere ​summaries of the explanatory relations that obtain between particular moral and non-moral facts, with the principles themselves being explanatorily inert. Similarly, Mark Schroeder (2005) argues that Ralph Cudworth's objection against theological voluntarism-which crucially involves appeal to explanatory moral principles-threatens to generalize so as to rule out the possibility of "perfectly general explanatory moral theories" (2005, 3). Our aim in this paper is to defend the explanatory role of moral principles by arguing that it best accommodates some intuitive claims about moral metaphysics. Indeed, while we focus on morality, parallel claims are plausible with respect to normative principles and explanations more generally. We begin by presenting the relevant 'data points' (§2) before outlining, in general terms, how our favored view captures them (§3). We then argue that the view that moral principles aren't explanatory in this way falls short (§4)-in particular, it fails to explain the supervience of moral facts on ​natural facts. Next we discuss two competing accounts of what, more precisely, moral principles are like: ​the nomic view ​(§5) and ​moral 1 Thanks to Selim Berker, Matti Eklund, David Faraci, Martin Glazier, Jaakko Hirvelä, John Keller, David Mark Kovacs, Stephanie Leary, Michael Raven, Henrik Rydéhn, Jonathan Shaheen, Knut Skarsaune, Bart Streumer, Mark van Roojen, Pekka Väyrynen, Daniel Wodak, and audiences at UNC Chapel Hill, College of William & Mary, and University of Wisconsin-Madison. Risberg's work was supported by Helge Ax:son Johnson's Foundation, Hultengren's Foundation, The Royal Swedish Academy of Letters, History and Antiquities, The Salén Foundation, Sixten Gemzéus' Foundation, Thun's Grant Foundation, and Värmland's nation in Uppsala. 1 platonism ​(§6). Finally, we consider the sense in which moral principles are metaphysically necessary (§7). 2 The data We'll begin by presenting three claims we think any fully satisfactory metaethical theory should explain, or otherwise accommodate in a principled manner. Although none are completely uncontroversial, theories that explain them will, other things being equal, enjoy an advantage over those that don't (and even more so over theories which are incompatible with them). The first data point is that moral facts supervene upon purely natural (or descriptive or whatever) facts. Suppose that Matti is a good person. Besides being good, he also has numerous natural properties (including relational ones) that are connected to goodness in the following way: anyone who is descriptively just like Matti will also be good. Indeed, if Matti is good, it's ​impossible for someone to possess all and only his natural properties without also being good. Generalizing, the supervenience relation that holds between 'the natural' and 'the moral' is standardly formulated as follows, where ​M is the family of moral properties, ​N is the family of natural properties, and ☐ is metaphysical necessity: Data point (i): ​Strong Supervenience (∀​F​ in ​M​)(∀​x​)[​Fx​ → (∃​G​ in ​N​)(​Gx​ & ☐(∀​y​)(​Gy​ → F​y​))] 2 In English: for every moral property ​F​, if something is ​F​, then that thing has some (possibly quite complex!) natural property ​G such that, by metaphysical necessity, everything that is ​G​ is also ​F​. Strong Supervenience has long been treated as something like a fixed point, though recently it's been called into question. We'll nonetheless assume that its rejection 3 comes as a cost. There are three things to note about Strong Supervenience. First, despite being standardly glossed (as we did above) as expressing a relation between 'the moral' and 'the natural', the relevant pattern of covariation only concerns properties of ​particular things. (The higher-order quantifiers quantify over moral and natural properties while the first-order quantifiers quantify over particular bearers of those properties.) We'll return to this point. 2 Cf. McPherson (2015), ​Leary (2017), Dreier (1992)​. Strong Supervenience is standardly assumed to hold of necessity, either metaphysical or conceptual (or both). We assume it at least holds of metaphysical necessity. 3 See, e.g., Rosen (forthcoming)​, Fine (2005), Hattiangadi (2018), and Roberts (2018)​. Rosen nonetheless remains committed to a form of supervenience that involves 'normative' rather than metaphysical necessity, and so faces the analogous task of explaining why it holds. ​(For criticism of the notion of normative necessity, see Lange 2018) There are also extreme forms of particularism which are incompatible with supervenience. Arguably, however, such views are ​too​ extreme. 2 Second, there's controversy over how to characterize the supervenience base. At a minimum, we assume the relevant family of properties (​N​) is closed under property conjunction and property disjunction ​(cf. e.g. Bader 2017) and restricted to repeatable properties (cf. Atiq forthcoming). In general, the goal is to strip base 4 properties of their particularity. Although there are several additional complications, everyone should acknowledge that there is some ​truth in the neighborhood, though how exactly one formulates it may depend on one's other commitments. 5 Third, Strong Supervenience doesn't entail that particular moral facts are explained by or obtain in virtue of natural facts. Indeed, supervenience claims in general are silent as to which, if any, explanatory relations obtain between the relevant kinds of facts. Nevertheless, the modal correlation specified by Strong Supervenience isn't 6 the only interesting relation that holds between particular moral and natural facts. An explanatory relation also seems to hold: when (e.g.) a person is good or an action is wrong, there are natural features of those entities that ​make ​the person good and the action wrong. Hence the second data point: Data point (ii): ​Particular moral facts are at least partly (and at least ultimately) explained by particular natural facts. We say 'at least ultimately' because some particular moral facts may obtain in virtue of other particular moral facts. In such cases, those other moral facts are in turn explained (at least ultimately) by particular natural facts. 7 4 Following Atiq (forthcoming), we can say that a property ​B is "repeatable" when, necessarily, if ​x ​is ​B then it's metaphysically possible for there to be an entity ​y ​such that ​y is distinct from ​x ​and ​y ​is ​B​. This rules out inclusion of haecceitistic properties, such the property of being Barack Obama. We agree with Atiq that an adequate account of the supervenience base should entail that it is possible for distinct individuals to be "base-identical". This restriction may not give us everything we want, however, since presumably we also want to rule out properties like that of being an Obama, which are repeatable insofar as Barak has it, Michelle has it, etc., even though their "descriptive twins" do not. (Thanks to Selim Berker for this point.) 5 In particular, it is disputed how exactly one should characterize the family of subvenient facts. Instead of "natural" or "descriptive" facts, some philosophers opt for (among other things) "base" or "not-normativity-involving" facts. Which option that is most plausible depends to a large extent on other metaethical issues, however (cf. Sturgeon (2009), so we're setting these questions aside. 6 On the difference between supervenience and explanation, see DePaul (1987), Bliss and Trogdon (2014), and Berker (2018). For dissent, see Kovacs (forthcoming). 7 It may seem that some particular moral facts resist such explanation-for example, consider the fact that Matti is such that if he tells a lie, then he does something prima facie wrong. Insofar as the explanation of such normative "Cambridge facts" differs from the typical case, though, they seem to be exceptions to a general norm. Another particular moral fact that may not seem to be explained by natural facts is the fact that the fact lying violates the Categorical Imperative is a reason against Matti's lying yesterday. However, reasons-claims arguably require separate treatment, since they themselves seem to be explanatory claims of a certain kind (Fogal 2016), not entirely unlike claims about a particular action being pro tanto right or ​wrong ​in virtue of ​a given natural fact. (Thanks to Selim Berker for (versions of) these apparent counterexamples.) 3 Some additional clarifications are in order. First, what is meant by 'particular moral fact'? A particular moral fact is a moral fact about a particular (dated, non-repeatable) thing, such as a particular action, person, or state of affairs. Besides particular moral facts, there are also general, non-particular moral facts, such as that pain is bad or that lying is pro tanto wrong. This intuitive distinction is surprisingly often overlooked.​ ​For example, Pekka Väyrynen (2013) writes in a related context: [It] is very common to think that actions and other things have their normative and evaluative properties ​in virtue of their non-normative, non-evaluative properties. It is similarly very common for those who are allergic to talk of normative properties nonetheless to agree that things are good or bad, or right or wrong, ​because of some non-normative properties. There is, in other words, a strong intuition that normative facts are dependent on and explained by other facts. Call this 'the dependence intuition'. (p. 155; italics in original) Though we agree with the spirit of the dependence intuition, this is a potentially misleading formulation of it insofar as it suggests that ​every ​moral (or normative) fact is explained by other facts. This matters because while ​particular moral facts plausibly depend (at least in part) on natural facts in this way, it's far less clear that ​general moral facts-e.g., fundamental moral principles-also so depend. So while Väyrynen is right that there's a strong intuition in the vicinity, it only applies to a subset of the moral facts-i.e., the particular ones. We'll return to this issue below. Second, what is meant by 'explained'? The kind of explanation we have in mind is ​metaphysical explanation (or what is commonly called 'grounding'). One distinguishing feature of such explanations is that they are non-causal. Suppose, for example, that we want to know why the barn is red. There are at least two questions 8 we might be interested in. The first is what ​made it the case that the barn is red. The fact that, say, someone painted it yesterday would help provide an answer-it would help causally explain why the barn is red. The second question concerns what presently makes ​it the case that the barn is red. Here historical facts are irrelevant. Instead, what matters are contemporaneous facts, such as the fact that the barn is crimson. This fact non-causally explains why the barn is red. , 9 10 We also take metaphysical explanation to be ​objective ​, roughly in the sense of being mindor stance-independent. Impressionistically put, objective explanations 11 involve explanatory relations-whether they be causal, nomic, metaphysical, or something else-that obtain 'out there' in the world. This is different from the more familiar, pragmatic notion of an explanation, understood as the sort of thing we 8 Cf. Glazier (2016, 11). 9 We count present facts about the past and timeless facts as contemporaneous. 10 Although causal explanations are paradigmatically diachronic and non-causal explanations are paradigmatically synchronic, there may be exceptions. 11 We treat this as a stipulation. It's therefore immune to challenges by Thompson (2016) and Miller and Norton (forthcoming), who seem to collapse the 'makes sense of why' vs. 'makes it the case' distinction. 4 standardly ask for and provide concerning a variety of subject matters (and which can in that sense be causal or non-causal), and whose success depends on "facts about the interests, beliefs or other features of the psychology of those providing or receiving the explanation [or] the 'context' in which the explanation occurs" (Woodward 2014, §6.1). In slogan form, we can distinguish between 'explains' in the sense of ​makes it the case ​and 'explains' in the sense of ​makes sense of why it's the case. Although knowing 12 what made or makes something the case will often help make sense of why it's the case, objective and pragmatic explanations are not neatly aligned. It might be objected that focusing on metaphysical explanation prejudges certain metaethical disputes, such as whether expressivism is true. Insofar as there's a conflict, however, the problem lies with those views. After all, everyone needs a story about the metaphysical-seeming judgments we make about moral matters, including judgments about what makes actions right, wrong, etc. If expressivists can provide such a story, the seeming conflict disappears. If they can't, that's a problem for their 13 view. The third clarification concerns what is meant by 'partly explains'. The relevant contrast here is the notion of a ​full explanation. Almost all the explanations we actually provide-i.e. pragmatic explanations-are partial rather than full. If you purchase a pet, and someone asks you why, you might say that you're lonely. While sensible as a reply, the fact that you're lonely doesn't ​by itself ​explain your purchase. Instead, its explanatory import depends on a bunch of background facts that are taken for granted, such as that you don't want to be lonely, that you believe a pet will make you less lonely, etc. Your loneliness is thus only a part, and indeed a rather small part, of what fully explains your action. This illustrates a general feature of our explanatory practice: rather than providing a full explanation, we're typically content to highlight one or two notable factors, trusting our interlocutors to fill in the rest. Providing the full explanatory story is typically laborious, if possible at all, and unnecessary. Here, finally, is our third data point: Data point (iii): ​Moral principles are explanatory in nature. This claim is motivated, in part, by the observation that a moral theory merely consisting of a ​list of all particular actions that are right or wrong is incomplete. We also want to know ​why they're on the list. General moral principles answer that question. Some care is needed, however. For as Berker (forthcoming-a) notes, moral principles might be explanatory in either of two ways. Suppose it's always wrong to lie. According to Berker, this principle is explanatory only in the sense that it specifies a natural property-i.e., being a lie-such that any particular act with that property is wrong fully because it is a lie. On this view, moral principles can be viewed as mere summaries ​of patterns of particular explanatory relations, with the principles themselves being explanatorily inert. As we'll put it, such principles are merely 12 More nuance is called for, but we lack space to provide it. Suffice it to say, ordinary explanation-talk is both messy and context-sensitive (cf. Lewis 1986; Jenkins 2008). 13 For discussion, see Berker (forthcoming-b) and Toppinen (2018). 5 explanatory in content​-they specify ​which particular natural facts explain which particular moral facts and that's it. Berker's view thus resembles 'Humean' accounts of laws of nature, according to which natural laws are mere summaries of patterns among particulars. Yet the view is also ​non ​-Humean insofar as the relevant patterns involve instantiations of a hyperintensional explanatory relation, not mere co-occurrence of distinct facts or properties. This view-call it ​Hyperintensional Humeanism​-is effectively what you get if you take data point (ii), which concerns the explanation of particular moral facts by natural facts, to be more fundamental than data point (iii), which concerns the explanatory nature of moral principles. The salient alternative is that the truth of the principle that lying is wrong ​itself ​plays a role in explaining particular moral facts involving lying, with the fact that the action was a lie only partly explaining why it's wrong. On this view, moral principles are ​explanatory in ​role-​they themselves help explain particular moral facts. Data point (iii) is 14 neutral with respect to whether such principles are explanatory in role or in content. 3 Explaining the data To recap, here are the data points: Data point (i): ​Strong Supervenience-for every moral property ​F ​, if something is ​F​, then that thing has some natural property ​G such that, by metaphysical necessity, everything that is ​G​ is also ​F​. Data point (ii): ​Particular moral facts are at least partly explained by natural facts. Data point (iii): ​Moral principles are explanatory in nature. A unified account of these data points is desirable. The most natural way of providing one is to view some data points as more fundamental than others. But which ones? We doubt (i) is most fundamental. As is standardly recognized, supervenience is "not a 'deep' metaphysical relation" but "a 'surface' relation that reports a pattern of property covariation, suggesting the presence of an interesting dependency relation that might explain it" (Kim 1993: 167). Supervenience theses thus ​call for explanation rather than provide them. So ideally, (i) can be accounted for in terms of (ii) or (iii) or both. We think the best way of making sense of (i) is by opting for the package of (ii) together with the interpretation of (iii) on which moral principles are explanatory in role. On this view, explanations of particular moral facts involve three main ingredients: Explanans:​ particular natural fact(s) (e.g. ​a​ is a lie). Principle:​ general explanatory moral principle (e.g. lying is wrong). Explanandum:​ particular moral fact (e.g. ​a ​ is wrong). 14 Berker calls such principles 'explanation-serving' and principles that are explanatory in content 'explanation-involving'. 6 The explanandum is fully explained by the explanans together with the moral principle, though (as we'll see) the exact role played by principles will depend partly on how they are formulated. But for now this outline of the tripartite structure of moral explanations will suffice. Alternative terminological choices might be made. Schaffer (2017a), for example, emphasizes the importance of the tripartite structure of metaphysical explanations by distinguishing between the 'source', 'link', and 'result' in an explanation. As he notes, when "there are three roles involved, nothing but confusion can arise from insisting on only using two classificatory boxes" (20). Causal explanations illustrate this point: while causal laws plausibly help explain particular effects, laws aren't themselves causes. Causes and laws play different roles in the full explanation of whatever is caused. We agree, although we've supplemented the explanans​/​explanandum ideology rather than jettison it. The tripartite account of moral explanations incorporates data points (ii) and (iii): particular moral facts are explained by particular natural facts together with general moral principles. Given the substantive but plausible assumption that the 15 fundamental moral principles obtain of metaphysical necessity (if at all), making sense of strong supervenience-data point (i)-is straightforward. (We'll return to this assumption in §7.) We'll call this the ​Divide & Conquer ​(or ​D&C​) ​strategy. Essentially, Strong Supervenience states that the moral properties of some particular things cannot differ unless their natural properties differ. On the tripartite account, the moral properties of particular things depend on two things: (a) which natural properties they have and (b) which moral principles obtain. Regarding (a), it's trivial that two things cannot differ in their natural properties without differing in their natural properties. Regarding (b), it's also trivial that two things cannot differ with respect to which moral principles obtain, because such principles can't differ period​-they obtain of necessity and so trivially supervene on everything. Hence, a particular thing's moral properties depend on two things-(a) and (b)-both of which 15 Our account thus resembles what Schroeder (2005) calls "the Standard Model" of normative explanations​, where such explanations "[subsume] specific obligations in context to more general obligations, by appeal to specific features of the agent's circumstances" (2014, 3). [A]lthough we agree this is an intuitive idea, ​we think the tripartite account is more perspicuous ​than Schroeder's Standard Model. Especially important here is the distinction between particular and general normative facts (cf. sect. 2), since some of Schroeder's discussion seems to overlook it. For example, Schroeder apparently holds that every "perfectly general explanatory moral theory" is in the business of explaining why particular agents ought to perform certain action-types (2005, 3). What we perform in the first instance, however, are ​token ​actions, and the moral status of such actions is also-arguably even primarily-something moral theories should explain. Other times, something like the general-particular distinction figures in Schroeder's discussion of the Standard Model, but is not clearly separated from other distinctions, such as the one between explained and unexplained moral facts, or the one between moral facts that are 'wholly distinct' from non-moral facts and those that aren't (cf. 'pure' moral facts; 2014, ch. 6). Contra Schroeder, then, we doubt the Standard Model-at least as he formulates it-is widely accepted among moral philosophers. Reinterpreted along our lines, though, we think it's both widely accepted and highly plausible. 7 supervene on the thing's natural properties for trivial reasons. It's therefore no surprise that moral properties of particular things can't differ unless their natural properties differ. 16 We take the claim just explained to be the 'core' supervenience claim. But as David Faraci (2017) emphasizes, Strong Supervenience also entails a ​necessitation claim: no particular thing can have a moral property unless it also has some natural property. Making sense of this isn't difficult, however, as its falsity would require something to have a moral property without having any natural properties at all. And given the very broad sense of 'natural' at issue, this seems impossible. Every action, for example, will at least have the natural property of being an action, however featureless it might otherwise be. Similarly, Cartesian souls, even if empirically inaccessible, will still have properties such as being conscious, or, indeed, being Cartesian souls. This suggests that every particular thing will have some natural property or other, and ​a fortiori ​, that every particular thing with a moral property will also have a natural property. 17 It might be worried that an account of Strong Supervenience that posits non-contingent explanatory moral principles fails to make genuine progress, since such principles merely restate (in a slightly different guise) the problematic truth that was supposed to be accounted for. But that's false: supervenience theses say nothing 18 about explanation, so principles concerning the latter can't be restatements of the former. Although several recent explanations of supervenience resemble the D&C strategy, none are fully satisfactory. Enoch (2011), for instance, takes the basic normative facts to be "norms" that hold with metaphysical necessity, and thereby explain Strong Supervenience. But Enoch says little about what norms are or how they explain particular normative facts. We'll consider some answers to this question in §§5-6. One account takes the fundamental moral facts to concern ​kinds ​rather than 19 particulars. Both Skarsaune (2015) and, more briefly, Schroeder (2014, §6.6) appeal to this idea in explanations of supervenience, though neither pays sufficient attention to data points (ii) and (iii). Scanlon (2014), in contrast, holds that supervenience is explained by "pure" normative facts of the form '∀x(​R​(​p​, ​x​, ​c​, ​a ​))', which reads: for all agents ​x​, in circumstance ​c​, fact ​p is a reason to do ​a​. However, for reasons discussed in §4, the use of universal generalisations in formulating moral principles is problematic.​ 20 16 At least in general, if ​X​ depends on ​Y​ and ​Y​ trivially supervenes on ​Z​ then it should be no surprise that ​X​ supervenes on ​Z​. 17 We suspect Faraci's real concern is why it's "impossible for normative properties to be ungrounded" (2017, 315)-i.e., data point (ii), not (i). 18 Cf. McPherson (2012) on "bruteness revenge". 19 Enoch (forthcoming) advocates a form of 'grounding pluralism'. For reasons to be skeptical, see Enoch (forthcoming), n. 21. In our view, the best way to develop Enoch's 2011 account is instead along the lines that we'll consider in section 5. 20 Schroeder (2015) suggests that the quantifier and the person variable x are redundant, and that Scanlon's proposal can be read 'R(p, c, a)' without loss. And indeed, that is the formulation Scanlon uses in the manuscript for his 2009 Locke Lectures, on which the 8 While the proposals just considered are all pursued in defense of some form of non-naturalism, the D&C strategy itself is neutral regarding the naturalism/non-naturalism dispute, and indeed regarding most other metaethical disputes. In particular, even if it's always possible to explain why a particular thing has a certain moral property, it doesn't follow that the moral properties themselves-i.e., ​what it is to have a certain moral property-can be explained. 21 That's a point of contention dividing naturalists and non-naturalists, and one to be decided on other grounds. More generally, the D&C strategy is neutral concerning the status, specific content, number, complexity, and explanation (if any) of the relevant moral principles. This is a feature, not a bug: it focuses the debate precisely where it should be (and to some extent always has been)-namely, on the fundamental moral principles, if such there be. Given the foregoing, the attention garnered by Strong Supervenience (and its ilk) in recent decades looks rather misplaced. It has often been held, for example, that non-naturalists have a hard time explaining moral supervenience. But if the D&C strategy is successful, that's false. This is just one example of how focusing on supervenience while neglecting the more fundamental data points (ii) and (iii) can be distorting. Other examples are furnished by various attempted explanations of supervenience-many of which are naturalist-friendly-that are either silent about or, worse, in tension with the other data points. To illustrate: ● Naturalistic identity-theses make sense of supervenience but are harder to reconcile with the data points about moral explanation-i.e. (ii) and (iii). Although things that differ morally must differ naturally if moral properties just ​are natural properties, if rightness is, say, identical to happiness-maximizing, it's hard to see how actions can be right ​in virtue of being happiness-maximizing, since nothing explains itself. ​(cf. McNaughton & Rawling 2003) ● Expressivist explanations of supervenience have often centered on the idea that our moral practice wouldn't fulfill its 'function' of, e.g., coordinating behavior if our moral views didn't respect supervenience (cf. Blackburn 1984). For example, Mitchell (2017) attributes to Blackburn the view that "it is practically necessary that everyone conform their evaluations to a supervenience constraint: without it, we lapse into practical and discursive chaos...". ​Even if this thesis makes sense of supervenience, it's silent concerning data points (ii) and (iii). book is based. Thus understood, Scanlon's view is a version of platonism, which we discuss in section 6. 21 As Leary (ms) argues, this distinction was recognized by G.E. Moore (1942, 588). See also Rydéhn (2019) on "opaque grounding" (which we'll return to below) and Rosen (2010, sect. 13) on "Moorean connections". By distinguishing between explaining why something is ​F ​and explaining what it is to be ​F​, we think one can also avoid Berker's revisionary result that "almost all contemporary metaethical views (other than nihilism) end up counting as a form of non-naturalism about the normative" (forthcoming-a, 29) and Heathwood's (2012) related view. 9 While there are various things adherents of such views might say in response, our main complaint concerns the focus of the debate. For as Berker (2018) argues, the 22 notion of moral supervenience was first introduced and motivated with reference to claims concerning ​both ​co-variance-data point (i)-and explanation-data point (ii). In one of the earliest discussions, for example, R. M. Hare notes that if two things differ in goodness "there must be some further difference between them to ​make one good and the other not..." (1952, 81; emphasis added). The modal formalizations of supervenience that subsequently became dominant replaced this dual-focus with a single-minded one-they express co-variation claims and that's it. This coincided with general philosophical suspicion of heavier-weight notions like metaphysical explanation, but times have changed. Both of Hare's original motivations are relevant, and accounts that don't make sense of moral explanations fail to capture what motivated the focus on supervenience in the first place. To sum up so far: taking moral principles to be explanatory in role helps provide a unified account of the data points. The next task is to investigate the nature and structure of such principles. Doing so is not straightforward-for as we'll see, the most common way to formulate moral principles makes it hard to see how they could be explanatory in role, rather than merely in content. 4 Moral principles are not merely explanatory in content Moral principles are commonly formulated as universal generalizations. Berker (forthcoming-a) defends this view, arguing that "the most naive way of formulating moral principles (...) is also the best, namely one that uses no materials other than a wide-scope necessity operator, standard quantification, mundane indicative conditionals, and the full grounding [i.e. metaphysical explanation] relation" (26). The utilitarian principle is thus formulated as follows ('B' for 'Berker'): (U​B​) Necessarily, an action is required if and only if, and fully because, it maximizes happiness. It'll be useful to pay attention to some details of this formulation. While Berker says statements like this one are necessitated universal generalizations, or necessitated universally generalized indicative (bi)conditionals, (U​B​) doesn't explicitly involve 22 For example, in order to make progress in explaining data point (ii), expressivists might help themselves to the account of normative explanation suggested by Berker (forthcoming-b)-of which both he and we are ultimately skeptical. It's also possible to simply deny one of our data points and seek to explain away the relevant intuition(s). As noted above, however, we think such views will be less plausible, other things being equal. For example, while our concern has been the broadly metaphysical sense of 'explains', there may be other senses of the word that advocates of identity theses can invoke if they want to say that some facts explain themselves. For instance, one might say 'Joe is a bachelor because he is an unmarried eligible male' in attempting to elucidate the notion of a bachelor (see Kovacs 2018, sect. 4). The present point is just that moral explanations don't strike us as mere attempts at elucidation. We'll return to the relation between explanatory and identificational claims in section 6.1. 10 universal generalization. Rather, it uses the indefinite 'an action' which (as we'll further discuss in §5.1) can be used in importantly different ways. Let's nonetheless assume that (U​B​) can be paraphrased as follows: (U​B​*) Necessarily, for all actions ​x​, ​x is required if and only if, and fully because, ​x​ maximizes happiness. (U​B​*) states a general fact-call it '[U​B​*]'-that is explanatory in content, but not role: it states that whenever some particular action is morally required, that fact is fully 'grounded' in its maximizing happiness. Given the common assumption that 23 universal generalizations obtain at least partly in virtue of their instances, [U​B​*] obtains (if at all) in virtue of ​this ​action being required because it maximizes happiness, ​that ​action being required because it maximizes happiness, and so on for each possible required action (perhaps together with a totality fact). [U​B​*] thus 24 summarizes, and is explained by, instantiations of the grounding relation between particular facts about happiness-maximizing and particular facts about moral obligatoriness-[U​B​*] itself plays no explanatory role. Indeed, given that 25 metaphysical explanations are irreflexive and transitive, [U​B​*] ​can't explain the facts about moral obligatoriness. This gets us Hyperintensional Humeanism, per above. The problem, however, is that Hyperintensional Humeanism has trouble making sense of supervenience-i.e. data point (i). To see why, let ​D be the set of Matti's natural properties. Assuming he's good, Strong Supervenience allows us to infer that every other possible entity with the properties in ​D is also good. But if we take (ii) to be more fundamental than (iii), it's not clear why that inference is sound. On Berker's view, there are some natural properties in ​D such that the fact that Matti has those properties fully explains the fact that he's good. Call those natural properties ​D​*. Given ​grounding necessitarianism​-i.e., the thesis that if some facts ​Γ fully explain the fact [​Q ​], then it's necessary that if ​Γ obtain then [​Q​] obtains-it follows that, necessarily, if Matti is ​D​* then he is good. But it doesn't follow that if, 26 say, ​Folke has the properties in ​D (and thus the ones in ​D​*) then Folke is good. That's 23 Following Berker (following Rosen), we'll use square brackets to denote facts. We'll also sometimes use them to denote fact schemata-context will disambiguate. 24 It's actually a hard question what the 'instances' of [U​B​*] are, though one we can't ​fully address here. ​For instance, rather than facts of the form [​x is required because ​a is happiness-maximizing], it might be better to view instances of [U​B​*] as particular facts of the form [​x is required if and only if and because ​a is happiness-maximizing]. This would complicate things, however, especially if such facts can obtain even if the relevant action ​is neither happiness-maximizing nor required. Fortunately these sorts of complications have little bearing on the question of whether Berker's view makes sense of supervenience. 25 This is true even when the relevant universal generalizations are 'non-accidental' and necessitated. For this reason we are skeptical of various formulations floated by Rosen (2017). ​Rosen focuses on formulations of laws that have the form ​☐​∀​x​(​Gx ​→ ​Fx​), where ​G is a descriptive property, ​F is a normative property, the arrow stands for material conditional, and the box stands for so-called 'normative necessity'. 26 Grounding necessitarianism is not universally accepted (see, e.g., Leuenberger 2014 and Skiles 2015). But in this context, rejecting necessitarianism would only make it more difficult to see how Berker's view could make sense of why Strong Supervenience is true. 11 because Berker takes the grounding relation to hold between wholly particular natural facts (e.g., that Matti is ​D​*) and wholly particular moral facts (e.g., that Matti is good). As a result, nothing entitles us to generalize from facts about the natural and moral properties of one particular entity to those of another. In other words, even if the ​properties in ​D ​are repeatable, the ​subjects ​instantiating them-i.e, Matti and Folke-remain particular and non-repeatable. And generalizations from facts about one particular to another is precisely what the supervenience thesis captures: if someone with the properties in ​D​ is good, then ​anyone ​with those properties is good. Of course, ​if a principle like (U​B​*) is true for goodness, it follows that goodness supervenes on the natural properties specified by that principle. But the point is that given Berker's underlying metaphysics, there's no reason to expect there to be true principles of that form, and hence no reason to expect supervenience to be true. Whether going from the wholly particular to the general secures such principles depends on what the various patterns among wholly particular facts across possible worlds happen to look like. Hence, the Hyperintensional Humean's principles (and thus supervenience) ends up hostage to a kind of modal miracle. In other words, although principles like (U​B​*), if true, would secure supervenience, they would do so in the wrong way-rather than being made sense of in a principled fashion, it would still look like a mystery that the Humean mosaic necessarily turns out to give rise to them. This worry resembles some of the traditional complaints in the literature on moral supervenience, though the present situation is in one regard even worse. For while the traditional worry is that it's 27 mysterious why particular moral facts should necessarily align with particular natural facts in the way specified by Strong Supervenience, the worry now concerns not only those facts but also particular instances of the grounding-relation between them. In response, Hyperintensional Humeans might appeal to a principle like Formality (Rosen 2010, 131). Simplifying somewhat, this principle states that [​a is ​F​] fully grounds [​a is ​G​] only if any fact of the form [​x is ​F​] fully grounds [​x is ​G​]. Given Formality, the fact that Matti is good because he is ​D​* entails that Folke is also good because he is ​D​*. However, the same problem seems to arise. For why should Hyperintensional Humeans expect Formality to be true? Given their other commitments, they cannot consistently claim that this general principle (or something like it) is ​itself ​explanatory in role. Instead, whether Formality is true would also seem to depend on what the modal mosaic happens to look like. Rather than vindicating Strong Supervenience, then, Formality is hostage to the same sort of modal miracle. These problems are avoided if moral principles are explanatory in role. On this view, Matti's being ​D ​* doesn't fully explain why he's good-a general moral principle also plays a role. If particular facts about goodness are always partly explained by such principles, it's clear why we can infer that Folke, who is also ​D​, must likewise be good. So we not only get Strong Supervenience but also a 27 See, e.g., Skarsaune (2015, 267). ​There are also other worries about supervenience which we don't have in mind here-for instance, the one associated with Blackburn (1984) that it's mysterious why moral facts ​weakly ​supervene upon natural facts without ​strongly doing so. 12 counterpart of Formality-at least in the moral case-for more-or-less the same reasons. 28 The arguments just given rely on several assumptions which could be rejected, such as that (necessitated) universal generalizations are explained by their (non-necessitated) instances, that (U​B​) is correctly paraphrased as a universal generalization, and so on. But once these assumptions are rejected, it becomes unclear what the Hyperintensional Humean view is, and whether the main ingredients in principles like (U​B​)-i.e. "standard" quantification, indicative conditionals, and so on-are really as "naive" as Berker claims them to be. We won't consider those questions here. Instead, in what follows we'll focus on two accounts that treat moral principles as explanatory in role, rather than merely in content. 5 The nomic view of moral explanations The nomic view of moral explanations is modeled on what we'll call the law-based view of grounding explanations. By 'grounding explanations' we mean cases in which a particular fact obtains in virtue of others (its 'grounds'), with the latter being more fundamental than the former. Standard examples include: (i) Mental facts obtain because of neurophysiological facts. (ii) The fact that the ball is red and round obtains in virtue of the fact that it is red and the fact that it is round. (iii) Socrates was pale because he was this specific skin tone. The nature of grounding explanations is a matter of controversy. One issue concerns the existence of general metaphysical principles, or 'laws', and what role (if any) they play. According to the law-based view, metaphysical laws play an ineliminable role in grounding explanations. On this view, the full metaphysical account of, say, Socrates' being pale extends beyond his having a certain skin tone-the general fact that having that skin tone makes one pale is also relevant. Even if metaphysical laws exist and play an explanatory role, the precise role they play is disputed. Should we treat laws as ​part of grounding explanations, for example, or instead as merely 'underlying' or 'backing' or 'governing' such explanations? (And what's the difference?) We'll set such questions aside. What matters for our purposes is what unites law-based theorists-namely, that metaphysical laws play ​some essential role in metaphysical explanations. The law-based view of grounding explanations can thus be seen as a generalized version of the tripartite view of moral explanations above: 28 In support of Formality, Rosen notes that it seems "particular grounding facts must always be subsumable under general laws... It would be interesting to know why this is so." (2010, 132) The idea that the general laws are explanatory in role is, we think, a natural answer to this question. 13 Grounds:​ particular fact(s). Metaphysical Law:​ general explanatory principle. Explanandum:​ particular fact. Discussions about grounding explanations are complicated, however, by the fact that the word 'ground(s)' is often used in different ways. For some, for ​A to ground ​B is for ​A to metaphysically explain ​B​, whereas for others, for ​A to ground ​B is for there to be a metaphysical relation between ​A and ​B that 'backs' explanations. What's more, 29 many theorists-including Berker-take the grounding relation to hold between particular facts. But on the law-based view, it's a mistake to focus exclusively on relations between particular facts, just as on law-based views of causal explanation it's a mistake to focus exclusively on relations between individual events. In both cases laws also matter. To minimize confusion we'll mostly avoid using 'ground(s)' as a verb, preferring instead to use it as a noun to pick out the explanan(s) of grounding explanations (per above) on analogy with the use of 'cause(s)' as a noun. (This terminological issue will re-arise in responding to Berker in §5.1.) While the law-based view of grounding explanations is plausible, we won't be defending it here. Our primary concern is instead with the nomic view of moral 30 explanations. What motivates the nomic view is the idea that the general principles or 'laws' that help explain moral facts should be understood in the same way as those thought (rightly or wrongly) to figure in grounding explanations elsewhere. The main difference is that moral laws involve moral properties whereas non-moral laws don't-a difference in content rather than form. Although the nomic view is a natural companion to the law-based view, neither entails the other. One might accept the nomic view while rejecting the law-based view in general; alternatively, one might accept the law-based view while rejecting the nomic view (by, e.g., denying that moral explanations are grounding explanations). How, then, are metaphysical and/or moral laws to be understood? There are different ways of trying to capture their characteristic features, such as their generality and directionality, but the proposal we find most congenial is from Glazier (2016). He writes: [A metaphysical law] clearly has a sort of generality, but it is a general fact that is not explained by its instances. Since this sort of generality is not achieved through quantification, it must instead be achieved through another variable-binding operator. I therefore propose that we recognize a new operator '<<' [that] bind[s] any number of variables, since our intuitive understanding of a general metaphysical-explanatory connection does not support any relevant limit. And because a fact may be metaphysically explained by any number of other facts, the operator should also be variably polyadic 'on the left'. (25) Thus, according to Glazier, a statement of a law will be of the form 29 Raven (2015) calls the first view 'unionism' and the second view 'separatism'. 30 Instead, see Kment (2014), Wilsch (2016), Glazier (2016), and Schaffer (2017a, 2017b). 14 φ​1​,..., ​φ​n​ <<​α1​,..., ​αm​ ψ where ​φ​1​,..., ​φ​n​, ​ψ are sentences, and ​α​1​,..., α​m are variables that the '<<'-operator binds. We can therefore express the law connecting, say, an arbitrary thing's being crimson and its being red as: Crimson​: x​ is crimson <<​x​ ​x ​ is red In terms of facts: ​Crimson ​states the general explanatory connection that holds between facts of the form [​x ​is crimson] and facts of the form [​x ​is red]. This connection obtains non-vacuously even in possible worlds in which nothing is either crimson or red. Though Glazier doesn't discuss moral principles, the nomicist can use the '<<'-operator to formulate the utilitarian principle as follows ('N' for 'Nomic'): (U​N​) x​ maximizes happiness <<​x​ ​x ​ is morally required (U​N​) states the general explanatory connection that holds between facts of the form [​x maximizes happiness] and facts of the form [​x is morally required]. Other principles can be formulated similarly. The nomic view is thus an independently-motivated implementation of the tripartite view of moral explanations presented in §3, thereby capturing data points (i)-(iii) as desired. 5.1 Berker's objections Berker (forthcoming-a) considers but rejects the nomic view of moral explanations. One worry concerns the relationship between metaphysics and language. He writes: [It] is basically impossible to express [Glazier's] operator in natural language. Such a result would be surprising (...) Natural language is like water: over time it tends to adjust itself and flow toward the metaphysically and normatively relevant cracks in nature. (24) Following this analogy, Berker urges "caution when there is such a large disconnect between a posited fundamental feature of reality and the everyday language with which we talk about that reality." (24) We take the analogy with water to be inapt. Carnap (1963) provides a better analogy: [N]atural language is like a crude, primitive pocket knife, very useful for a hundred different purposes. But for certain specific purposes, special tools are more efficient (...) If we find that the pocket knife is too crude for a given purpose and creates deficient products, we shall try to discover the cause for the failure, and then either use the knife more skillfully, or replace it for this special purpose by a more suitable tool, or even invent a new one. (938) 15 That is, natural language has many virtues, but for specialized purposes-like describing fundamental features of reality-it often fails to constitute the best tool. Fortunately, its adaptability and flexibility enables us to give voice to novel concepts easily, whether by introducing a new term or else by giving an old term a new meaning. In neither case does natural language adjust itself so as to "flow toward the metaphysically relevant cracks in nature"-​we ​ adjust ​it ​ to do that. The same is true of the generality that is characteristic of laws. While Berker may be right that "English doesn't mark a difference between the sort of generality featured in ['That an action breaks a promise makes it the case that it is prima facie wrong'] and the sort featured in a sentence such as 'That an action breaks a promise is not something its agent always knows'" (forthcoming: 25), we don't view this as an obstacle or an objection. It's a familiar point that simplicity of surface grammar often masks a multitude of ways in which a sentence can be used. For example, sentences of the form 'A(n) ​F is ​G​' can plausibly be used to express universal generalizations ('A human can't fly'), exception-permitting generalizations ('A dog has four legs'), claims about specific individuals ('A cat is over there'), and full or partial definitions ('A bachelor is an unmarried male', 'A vixen is a fox'). The indefinite is also used to express variable-binding term operators like Hilbert's ε ​(cf. Woods 2014), and arbitrary reference more generally (e.g. 'Let John be a German'; cf. Breckenridge & Magidor 2012). So: we can do lots of stuff with indefinites. Definitions are particularly relevant, since-as we'll see in §6.1-they seem to involve the same kind of generality that laws do and similarly require special-purpose operators for perspicuous representation. Berker has a second objection. As he notes, "Glazier often summarizes his proposed laws using 'makes the case'-talk, which he takes to be a 'generic placeholder' that 'perhaps... should be replaced by something like 'determines' or even 'grounds''" (Berker forthcoming-a, 24). If we take such glosses seriously, we might think that (U​N​) can be reformulated as follows: (U​N​*) That an action maximizes happiness makes it the case that it is morally required. However, if 'makes it the case' in (U​N​*) picks out the grounding-relation, Berker thinks we face a dilemma. If this locution denotes ​full grounding, the moral principle becomes explanatorily redundant-the fact that the action maximized happiness by itself fully explains that it is right. On the other hand, if 'makes it the case' only denotes ​partial grounding, Berker thinks (U​N​*) ceases to qualify as a statement of moral law, since when looking for such laws "we are looking for [a] specification of ​all the partial grounds" (25). On this horn, Berker thinks, (U​N​) is better informally put as follows: (U​N​**) That an action maximizes happiness, together with this very moral law, fully makes it the case that the action is morally required. 16 But this is metaphysically circular​. ​And that's implausible. The upshot is that whether we take 'makes it the case' to denote full or partial grounding, the view that moral principles are explanatory in role runs into trouble. There's a lot that might be said in response to Berker's dilemma. We'll limit ourselves to two remarks. To begin with, we need to be careful with 31 'ground(s)'/'makes-it-the-case'-talk. On the law-based view, grounding explanations have a tripartite structure: grounds, general explanatory principle, and explanandum. If 'fully grounds' means 'constitutes the explanans and connection of', then Berker is right that (U​N​) doesn't entail that A​'s maximizing happiness fully grounds ​A ​'s being morally required. But (U​N​) still legitimately 'qualifies as a statement of moral law' since it specifies all the relevant (i.e. particular-level) explanantia, or what we earlier called 'grounds'. If, on the other hand, 'fully grounds' means 'constitutes the explanans (but not the connection)', then the entailment may well hold. But we'll still need an explanatory connection, and it's not clear why (U​N​) couldn't state that connection without redundancy. Regarding the second horn, we think the nomicist is within their rights taking the notion of metaphysical law as an ideological primitive. So although something like (U​N​**) may approximate a statement of law, it's not maximally perspicuous. There's no reason to expect that laws could be perspicuously expressed in non-canonical (including self-referential) terms. Worries about circularity and/or redundancy therefore don't seem probative. 6 Moral platonism Although the nomic view is attractive, it's not the only way moral principles might be explanatory in role. To illustrate, we'll consider an alternative: ​moral platonism​. 32 Whereas the nomic view centers on the notion of a moral law, the platonist view of moral explanations centers on the distinction between particular-applying and kind-applying moral properties. The former are properties of ​particulars (datable, non-repeatable things), while the latter are properties of ​kinds or ​types ​of things (timeless things with multiple instances). Initial motivation comes from language: We not only say things like 'Matti is good' but also things like 'Pleasure is good.' On the face of it, whereas the predicate 'is good' applies to a particular (Matti) in the former, it applies to a kind ​(pleasure) in the latter. The same is true of other moral terms. That moral predicates have genuinely kind-applying senses is further supported by facts about co-predication-sentences that conjoin moral predicates with predicates that apply primarily, if not exclusively, to kinds (e.g. 'Lying is wrong yet widespread') are acceptable (Skarsaune 2015, 255). The fact that moral predicates like 'good' apply both to kinds and particulars is plausibly a case of polysemy-i.e. distinct but related meanings. This is supported by the zeugmatic nature of sentences that apply a single predicate to both 31 Thanks to Martin Glazier for discussion. 32 The platonist view is defended and motivated more fully by Skarsaune (2015)​, who also discusses the linguistic motivation for it in more detail. For an earlier proposal along these lines, see Forrest (1986). 17 particular-applying and kind-applying noun phrases-'MLK's assassination was wrong, and so is lying', for example, feels a bit like a pun (cf. Skarsaune 2015, 258). Or consider the following lists of things that are bad: KINDS: pain, suffering, unrequited love PARTICULARS: the pain you felt yesterday, the war in Syria, Bill's cheating on Hillary MIXED: pain, the pain you felt yesterday, suffering, the war in Syria, unrequited love, Bill's cheating on Hillary We find KINDS and PARTICULARS much more natural than MIXED, despite the diversity of subjects within each. Indeed, the polysemy of moral predicates isn't surprising, as the distinction between particularand kind-applying senses arises with many non-normative predicates, with certain sentences being ambiguous between the different readings. For example, 'That's a famous pen' might be used to claim that a particular ​pen is itself famous (e.g. Einstein's Waterman pen) or merely is an instance of a famous kind​ ​of pen (e.g a Fischer Space Pen). What is the relationship between kindand particular-applying senses of predicates? In the non-normative case, kind-applying predicates are usually understood in terms of the particular-applying ones. Consider the sentence 'There was a dinosaur species that was 50 feet tall' (Skarsaune 2015, 257). Intuitively, to say that a species was 50 feet tall is to say that its adult members were (normally, approximately) 50 feet tall. But Skarsaune argues that the opposite relationship holds in the normative case: kind-applying predicates (and corresponding concepts) are basic and particular-applying ones derivative. This broadly linguistic thesis might then be taken as a guide to metaphysics, with particular-applying moral properties being analyzed in terms of kind-applying ones. This gives us moral platonism. According to platonism, moral terms like 'good', 'wrong', and 'obligatory' stand for two distinct but intimately connected properties. One property-call it 'goodness​kind​'-applies to kinds or types of things. The other-call it 'goodness​part​'-applies to particulars. Particular-applying moral properties are then metaphysically analyzed (in a sense to be explained below) in terms of more fundamental kind-applying ones: for a particular thing to be good​part is just for it to be a token of a good​kind ​kind; for a particular action to be wrong​part ​is just for it to be a token of a wrong​kind ​action-type; and so on. The basic moral properties are thus 'second-order'-their relationship to their bearers is instantiation​, ​rather than, say, necessitation (a la Armstrong 1983). 33 33 Rosen (2017: sect. 6.12) briefly considers an Armstrong-like view on which natural properties like ​being a lie ​stand in a 'normative grounding'-relation ('M'), rather than instantiation, to moral properties like ​being wrong ​(cf. Murphy 2011)​. ​The fundamental moral facts have the following form: M(​being a lie, ​being wrong​)​. ​Rosen goes on to suggest that the M-relation is essentially such that if such a fact obtains and particular action is a lie, then its being a lie together with lying being M-related to wrongness metaphysically grounds the action's being wrong (2017: 156). Thus, unlike platonism, Rosen's proposal focuses exclusively on particular-applying moral properties and so fails to explain the application of moral terms to kinds. Worries also arise about the multiplication of 18 Platonism straightforwardly accommodates data points (ii) and (iii) concerning the role of descriptive facts and moral principles, respectively, in moral explanations. The Rossian principle of Fidelity, for example, can be formulated as follows ('P' for 'platonism'): (PF​P​) ​Lying is (pro tanto) wrong​kind Assuming that to be a wrong​part ​action is just to be an action of a wrong​kind kind, (PF​P​) guarantees that every instance of lying is wrong​part​. For given (PF​P​), every particular lie will be an instance of a wrong​kind kind. This in turn will be explained by (a) the action's being an instance of lying (a particular natural fact) and (b) lying being wrong​kind (a general moral fact). ​This fits the basic tripartite structure of explanation outlined in §3. The platonist-like the nomicist-can thus adopt a version of the D&C strategy to make sense of data point (i), Strong Supervenience. 34 6.1 Metaphysical analysis It's worth clarifying the notion of metaphysical analysis being appealed to in describing how, given platonism, firstand second-order moral properties are related. It's sometimes thought, for example, that such analyses constitute a distinctive form of metaphysical explanation, stating what ​a fact or property 'consists in' (as opposed to, say, what they are 'grounded' in). Analyses are canonically expressed by sentences like 'To be ​F is to be ​G ​' and 'For something ​to be ​F is for it to be ​G ​'. One might agree with Plato, for instance, that to be virtuous is to have a well-ordered soul, or with Aristotle's more recent proposal that to be human is to be a rational animal. More mundanely, one might think that to be a vixen is to be a female fox. One complication is that 'To be ​F is to be ​G ​' allows at least two readings. On what we'll call the ​symmetric reading, claims of that form express 'generalized identities' (cf. Linnebo 2014, Rayo 2014), or what Dorr (2016) calls 'identifications'. We can formalize generalized identities by introducing a 'no-difference' operator, ≡, indexed by zero or more variables, which takes two open or closed sentences and yields another. As Corriea and Skiles (2019, 644) note, where ​p and ​q are open or closed sentences, p​ ≡ ​q grounding-relations, since the view posits two very different kinds of such relations, one of which (i.e. metaphysical) holds between facts while the other (i.e. normative) holds between properties. 34 Platonism doesn't entail that every true sentence of the form 'kind K is good' states an explanatory principle. ​For instance, as Berker (p.c.) notes, if 'Lying is pro tanto wrong' is true, then 'Lying-on-a-Tuesday is pro tanto wrong' is plausibly also true. But the latter arguably doesn't state an explanatory principle. While it's hard to say exactly how the relevant distinction should be drawn, this is neither surprising nor particularly problematic-​[s]imilar issues arise with respect to kind-predication and property inheritance more generally (cf. Liebesman and Magidor 2017). 19 can be read as 'For it to be the case that ​p (just) is for it to be the case that ​q​'. Similarly, where ​F​ and ​G ​ are monadic predicates, Fx ​ ≡​x​ ​Gx can be read as 'For a thing to be ​F (just) is for it to be ​G​'. More generally, statements of the form p​ ≡​x,y,...​ ​q can be read as 'For some things ​x,y ​,... to be such that ​p is for them to be such that ​q​'. For example, Vixen ​(​x​) ≡​x​ ​Female-fox​(​x ​) (For a thing to be a vixen is for it to be a female fox) Like the familiar objectual identity operator (e.g. Superman = Clark Kent), the generalized identity operator is reflexive, symmetric, and transitive. The above claim thus entails that: Female-fox ​(​x ​) ≡​x​ ​Vixen​(​x ​) (For a thing to be a female fox is for it to be a vixen) In contrast, on the ​asymmetric reading, 'To be ​F is to be ​G ​' expresses a general grounding claim, or 'metaphysical law' per above. So, for example: Female(x), Fox(x) ​<<​x​ Vixen(x) (A thing's being female together with its being a fox make it the case that it's a vixen) While the word 'reduction' has been used in many different ways, symmetric readings of 'To be ​F is to be ​G ​' clearly count as reductive insofar as they involve property identities (or something close). But they aren't explanatory, given that metaphysical explanation is asymmetric. In contrast, while asymmetric readings are explanatory, they're not straightforwardly reductive, since the facts related remain distinct. As the vixen example illustrates, there are often identificational truths in the vicinity of general grounding claims, and when there are the corresponding grounding claim is natural to accept. But the grounding claim neither is nor entails an identificational claim. Much the same can be said of sentences of the form 'To be ​F is in part to be ​G​', such as 'To be a vixen is in part to be a fox'. On one reading, they are general statements about what partially explains what. (Vixen-facts are partially explained by fox-facts.) On the other, they provide partial analyses. (For something to be a vixen is in part for it to be a fox.)​ 35 35 Thus, contra Schroeder (2005, 2007) and others, we don't think metaphysical analyses constitute a distinctive, reductive form of metaphysical explanation. On one reading, the 20 Note that statements of generalized identities, like statements of metaphysical laws, exhibit a kind of generality that entails but isn't identical to universal generalization, standardly understood. Whether they are true or false, for instance, doesn't depend on whether the leftor right-hand sides are satisfied: even if there are no vixens, it's still non-vacuously true that to be a vixen is to be a female fox. Distinguishing metaphysical grounding from metaphysical analysis leaves room for what Rydéhn (2019, ch. 3) calls 'metaphysically opaque grounding'. Simplifying slightly, this is the relation that holds when [​P ​] is the ground of [​Q​] without being involved in the metaphysical analysis or essence of [​Q ​]. This possibility conflicts with the commonly accepted idea that grounding guarantees a high degree of metaphysical intimacy. It has been claimed, for example, that if [​P​] is the ground of [​Q​], then [​Q ​] is 'nothing over and above' [​P ​]. This purported platitude is far from obvious, however, and arguably rests on a conflation of explanatory and identificational notions. (Compare: few people think effects are 'nothing over and above' their causes.) Although one might think that general grounding claims, or metaphysical laws, are always accompanied by identificational facts, this requires argument. After all, it would seem to rule out various non-reductive metaphysical theses, including versions of metaethical non-naturalism and mind-body dualism. On the nomic view, for example, the non-naturalist will view natural facts as being 'opaque' grounds of particular moral facts, explaining ​why ​but not ​what it is ​for particular actions to be right or wrong, good or bad, etc. Using the above machinery, we can formulate the platonist view of the relation between particular and general facts about (e.g.) wrongness as follows: x​ is wrong​part​ ≡​x​ ​x​ is a token of a wrong​kind​ kind (For a particular thing to be wrong is for it to be a token of a kind that is wrong) As noted above, generalized identity statements often guarantee certain general grounding claims. For example, given (PF​P​), it's plausible that: Lying is wrong​kind​, ​x​ is an instance of lying <<​x​ ​x ​ is wrong​part (Lying being wrong​kind​ and ​x ​ being a lie together make it that ​x ​ is wrong​part​) This is a metaphysical law that, on the law-based view of grounding explanations, does explanatory work. Moral platonism is thus compatible with the law-based view of grounding explanation, though it's a competitor to the nomic view of moral explanations. The difference between platonism and the nomic view mainly concerns the relation between metaphysical laws and substantive moral principles. On platonism, the relevant moral principles are not metaphysical laws but rather facts relevant claims are reductive but not explanatory; on the other, they are explanatory but not reductive (at least not on their own). We leave open the possibility of defining broader, non-identificational notions of reduction that supplement the grounding claim with, say, essentialist claims. See, e.g., Rydéhn's (2019, ch. 3) development of Schroeder's (2005, 2007) proposal. 21 involving kind-applying moral properties (e.g., the principle that lying is wrong takes the form [wrong​kind​(lying)]). Metaphysical laws merely connect the moral principles plus the relevant natural facts with the explanandum in a transparent way. On the nomic view, by contrast, the substantive moral principle is the law-like connection between natural and moral facts itself (e.g. [​x​ is lie <<​x​ ​x​ is wrong]). 7 Necessity We've mostly ignored the modal status of the fundamental moral principles. As noted above, the D&C strategy for explaining Strong Supervenience assumes the relevant principles are metaphysically necessary, and non-naturalists will insist these principles are not only ​morally fundamental, but fundamental ​simpliciter ​. As a result, despite making sense of supervenience, they'll still be committed to there being ​some brute necessary 'connections' between the natural and non-natural. This is hardly 36 surprising-it's simply the bullet non-naturalists bite. Nonetheless, at least two things can be said in closing. First, although non-naturalism will (unsurprisingly) violate various 'Humean' metaphysical principles, the details matter. Take, for instance, the so-called 'Modest Humean' principle that "[c]ommitment to brute necessary connections between discontinuous properties counts significantly against a view" (McPherson 2012). Very different things might be meant by 'connections'-at a minimum, we should distinguish co-occurrence (iff), general 'making' (<<​x​) and instantiation (is). If the non-naturalist was forced to accept the necessary co-occurrence of particular moral and natural facts as brute, that would be bad. But they don't-as we've seen, they can make sense of such co-occurrence, and hence supervenience, by appeal to explanatory-in-role moral principles. Whatever worries that remain won't be worries about ​supervenience ​-they'll be about something else. 37 Another important issue concerns the sense in which the fundamental moral principles obtain 'of (metaphysical) necessity'. We think that, given certain assumptions about possible worlds, it's plausible for naturalists and non-naturalists alike to view the relevant principles as being ​transcendental ​in the sense of Fine (2005, ch. 9), not (merely) necessary. The intuitive idea is that transcendental truths obtain independently of​-rather than ​in ​-all worlds. Merely necessary truths, in contrast, depend on how things turn out in each world, coming out true every time. For example, seven's being prime is plausibly transcendental, while a truth like ​P∨¬P is merely necessary-in some worlds it's true because ​P is while in others it's true because ​¬P​ is. 36 We take Shafer-Landau's (2003) view that instances of moral properties are fully constituted by natural ones to be a form of naturalism, just as the view that instances of mental properties are fully constituted by physical properties is a form of physicalism (cf. Väyrynen 2017). 37 We're not suggesting that positing general explanatory principles is a metaphysical get-out-of-jail-free card. What's needed is independent support for positing them, which there is in the moral case. 22 The distinction between transcendental and merely necessary truths requires a more restrictive notion of necessity and truth-in-a-world than is standard. On Fine's alternative conception, a possible world is not to be viewed as a "totality of facts, or of how things might ​be​, but [instead as] the totality of circumstances, or of how things might ​turn out​" (2005, 325). While the totality of circumstances (roughly, substances and their properties and relations) varies between worlds, the transcendental facts form "the invariable framework within which the variation takes place" (325-6). Put in terms of logical form, while transcendental truths entail necessitated (or 'box'-ed) ones, they aren't themselves necessitated. Like Fine, we doubt there's a need to choose between the more restrictive modal concepts and the more expansive ones. Different modal notions may be useful for different purposes. However, when it comes to the modal status of many philosophical theses-including fundamental moral principles-we think the more fine-grained concepts are most suitable. The analogies between morality and mathematics help illustrate this point. According to Ross (1930), for example, "[t]he moral order... is just as much part of the fundamental nature of the universe [and, we may add, of any possible universe...] as is the spatial or numerical structure expressed in the axioms of geometry or arithmetic" (29-30). We doubt Ross is best interpreted as claiming that the relevant moral and mathematical facts are merely necessary-i.e. dependent on the circumstances in each world and coming out true every time. 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