Metaphysical and Conceptual Grounding

Abstract

In this paper, I clarify the relation between two types of grounding: metaphysical andconceptual. Metaphysical grounding relates entities at more and less fundamentalontological levels. Conceptual grounding relates semantically primitive sentencesand semantically derivative sentences. It is important to distinguish these relationsgiven that both types of grounding can underwrite non-causal “in-virtue-of” claims.In this paper, I argue that conceptual and metaphysical grounding are exclusive: ifa given in-virtue-of claim involves conceptual grounding, then it does not involvemetaphysical grounding. I then present two heuristics for deciding which type ofgrounding is relevant to a given case. These heuristics suggest that certain proposedcases of metaphysical grounding may not actually involve metaphysical groundingat all.

Keywords: metaphysical grounding, conceptual grounding, non-causal explanation

1 Introduction

Recently, many theorists have claimed that the world has an ordered, hierarchical struc-ture. Entities at lower ontological levels are said to metaphysically ground entities athigher ontological levels.1 It has also recently been claimed that our language has anordered, hierarchical structure. Semantically primitive sentences are said to conceptuallyground less primitive sentences.2 It is often emphasized that metaphysical grounding isa relation between things out in the world, not a relation between our sentences. But Iwill argue that not enough care has been taken to distinguish these two types of ground-ing. Conflating these relations is easy to do, given that both types of grounding areexpressed by non-causal “in-virtue-of” claims.

In section 2, I will argue that there are indeed two distinct grounding relations ex-pressed by non-causal “in-virtue of” claims. In sections 3-4, I will argue that conceptualand metaphysical grounding are exclusive: if a given in-virtue-of claim involves concep-tual grounding, then it does not involve metaphysical grounding. In section 5, I will givesome heuristics for deciding which type of grounding is relevant in a given case. Theseheuristics suggest that many proposed cases of metaphysical grounding may not involvemetaphysical grounding at all. I will conclude by explaining why these results shouldinterest both supporters and detractors of the study of metaphysical grounding.

1See, e.g., Schaffer (2009), Audi (2012a).2See Chalmers (2012, 452-460).

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2 Distinct types of grounding

I will begin by describing metaphysical and conceptual grounding and the explanatorywork each is supposed to perform.

2.1 Metaphysical grounding

I will follow the common strategy of introducing metaphysical grounding with examples:3

[Chem] The H2O molecule exists in virtue of the fact that there are hydrogen and oxygen atomsarranged in a certain way.

[Sets] {Socrates} exists in virtue of the fact that Socrates exists.[Shape] x is roughly spherical in virtue of its having determinate shape R.[Fragile] x is fragile in virtue of its molecular arrangement and the physical laws.[Harm] x’s action is wrong in virtue of its being done with the sole motive to cause harm.[Pain] x is in pain in virtue of the fact that x is in brain state P .

For example, [Shape] is said to correspond to a metaphysical grounding relationbetween the fact x’s having determinate shape R and the fact x’s being roughly spherical.

These examples have an important role in the literature because they are supposed toprovide an intuitive grip on the notion of metaphysical grounding.4 They are also usedto motivate two types of explanatory work that metaphysical grounding is supposed toperform. First, metaphysical grounding is supposed to underwrite cases of metaphysicalexplanation. For example, in [Chem], we explain the fact that there is an H2O moleculeby appealing to the fact that there are hydrogen and oxygen atoms arranged in a certainway. It is claimed that, just as we need the causal relation to underwrite cases of causalexplanation, so too we need metaphysical grounding to underwrite cases of metaphysicalexplanation.5

Second, metaphysical grounding is posited to accommodate intuitions about meta-physical priority.6 For example, it intuitively seems that the individual Socrates is morefundamental than the singleton set {Socrates}. But we cannot accommodate this intu-ition using familiar tools like supervenience, since Socrates and {Socrates} supervene oneach other. Accordingly, it has been argued that metaphysical grounding is needed tocapture the fine-grainedness of metaphysical priority.7

I will adopt two assumptions about metaphysical grounding in the discussion ahead.First, I will assume the common view that metaphysical grounding relates facts (i.e.,

3For ease of presentation, I have adjusted these examples to give them a common form. The examplesare from (in order): Schaffer (2012, 125), Fine (1995, 271), Schaffer (2012, 126), Rosen (2010, 110), Fine(2012b, 1), and Clark & Liggins (2012, 812).

4For discussion, see Schaffer (2009, 375-376).5See Audi (2012a, 687-688) for this view. One might instead say that metaphysical grounding is just

identical to metaphysical explanation (see Trogdon (2013, section 3) for discussion). The distinctionbetween these views will not be relevant to the arguments ahead.

6See Clark & Liggins (2012, 813).7It is commonly supposed that metaphysical grounding straightforwardly implies supervenience. But

see Leuenberger (2013) and Skiles (2014) for more nuanced discussion.

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obtaining states of affairs).8 Facts are individuated by the objects and properties com-posing them. Second, I will assume that metaphysical grounding is unitary, i.e., thatthere is a single dependence relation corresponding to all cases of metaphysical expla-nation.9 Of course, there is one sense in which I am a “pluralist” about grounding: Iwill argue that metaphysical and conceptual grounding are distinct relations. But thisis consistent with the assumption that all cases of metaphysical dependence are unified.(In this sense, the pluralism I defend differs from the pluralist views of Wilson (2014)and Koslicki (2015).)

2.2 Conceptual grounding

Metaphysical grounding relates items on different ontological levels; it concerns the struc-ture of the world. In contrast, conceptual grounding relates items on different semanticlevels; it concerns the meanings of our linguistic expressions. Here I will assume thatconceptual grounding takes interpreted sentences as its relata.10

Just as above, instances of conceptual grounding can be expressed by non-causalin-virtue-of claims:

[Fox] x is a vixen in virtue of the fact that x is a female fox.[Chair] x is a piece of furniture in virtue of the fact that x is a chair.[Bald] x is bald in virtue of the fact that x has exactly 20 hairs.[Gene] x is a gene in virtue of the fact that x fills the functional role of storing and

transmitting hereditary information from one generation to the next.

For example, [Fox] corresponds to a conceptual grounding relation between the sentences‘x is a female fox’ and ‘x is a vixen’.11 Notice that, with these examples, the form ofconceptual grounding claims parallels the form of the metaphysical grounding claimsfrom 2.1; this choice simplifies the formulation of the main theses in section 3.

Intuitively, a sentence A is conceptually grounded by a sentence B when the sentence‘If B, then A’ is a conceptual truth, some expressions in B are semantically prior to thecorresponding expressions in A, and no expressions in A are semantically prior to thecorresponding expressions in B. For the purposes of this paper, it will be fine to rely on

8See, e.g., Rosen (2010, 114) and Audi (2012a, 693). Other theorists, such as Schaffer (2009, 375-376),claim that metaphysical grounding takes different types of entities as relata. Other theorists, such asCorreia (2010) and Fine (2012a), express metaphysical grounding claims using sentential operators.

The arguments ahead should generalize to any view on which metaphysical grounding is a relationthat takes worldly entities (e.g., properties) as relata. These arguments may not be available on certainversions of the operator approach; see fn. 35 for discussion.

9See Trogdon (2013, section 2) for discussion.10One could also define a relation of conceptual grounding for Fregean propositions, for thoughts, etc.

(I thank an anonymous referee for this observation). The discussion ahead should not depend on thischoice. But it is interesting to consider which type of conceptual grounding is comparatively fundamental.This question may be related to the dispute over the relative primacy of mental representation vs. publiclanguage meaning.

11When speaking strictly, I will say that [Fox] corresponds to a case of conceptual grounding (just as[Chem] corresponds to a case of metaphysical grounding). But more colloquially, I will speak of [Fox] asa case of conceptual grounding.

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examples like those above to provide a working grip on the notion of conceptual ground-ing, just as examples from 2.1 provided a working grip on the notion of metaphysicalgrounding.12

But there are various ways to make the notion of conceptual grounding more precise.For example: according to anchored inferentialism (see Chalmers (2012, 464-465)), themeaning of a (non-primitive) term C is constituted by its inferential connections to thoseterms that are semantically prior to C.13 For example, it is plausible that the meaning ofthe term ‘vixen’ is constituted by certain obvious inferential links to the more primitiveterms ‘female’ and ‘fox’. (By contrast, on this account, the term ‘fox’ is not individuatedby its links to the less-primitive term ‘vixen’.) If we adopt this account, we can say thata sentence A is conceptually grounded by a sentence B when the sentence ‘If B, thenA’ is a conceptual truth and the constitutive inferential roles of the terms in A providecompetent speakers with a warrant for asserting A on the supposition that B.

However one chooses to precisify the notion of conceptual grounding, it requires the“foundationalist” assumption that certain linguistic expressions are semantically priorto others. But conceptual grounding does not require that the terms in the conceptuallygrounded sentence have precise definitions. For example, let ¬S be the sentence ‘It isnot the case that Smith knows that: either Jones owns a Ford or Brown is in Barcelona’.Let D be the conjunction of the following sentences:

Smith is justified in believing that Jones owns a Ford. Originally, Smith hasno beliefs about Brown’s location. By making a logical inference from hisbelief that Jones owns a Ford, Smith forms the belief: Jones owns a Fordor Brown is in Barcelona. In fact, Jones does not own a Ford. But in fact,Brown happens to be in Barcelona.

It seems that competent speakers can immediately judge that ¬S is true when presentedwith D. The same goes for all other cases in the Gettier literature: the entire progress ofthis literature depended on our ability to make these immediate judgments in responseto cases. What can explain our ability to make these judgments? Here’s one plausibleexplanation: it is partially constitutive of the meaning of the term ‘knows’ that one isdisposed to judge that ¬S when presented with D (and similarly for other cases). Inother words, the sentence ‘If D, then ¬S’ is plausibly a conceptual truth. This suggeststhat, even if the term ‘knowledge’ cannot be given a precise definition, there is still aconceptual link between ‘knowledge’-sentences and sentences describing subjects’ beliefstates.

12The present analysis imples that ‘x is a female fox and y is a female fox’ conceptually grounds ‘xis a vixen’. To address this case, I will stipulate as a further condition that B conceptually grounds Aonly if the sentence ‘A in virtue of the fact that B’ is genuinely explanatory. (One might also rule outthis case with a minimality condition to the effect that B conceptually grounds A only if there is no φsuch that (i) A is conceptually grounded by φ and (ii) φ is a proper part of B. I thank an anonymousreferee for this suggestion.)

13Throughout this paper, I will rely on examples like [Fox], [Chair], etc. to provide the reader withan intuitive grip on the notion of semantic priority. See Chalmers (2012) for discussion.

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Conceptual grounding is supposed to perform analogous theoretical work to meta-physical grounding. First: conceptual grounding is needed to underwrite cases of con-ceptual explanation.14 For example, to describe the explanatory force of [Fox], we mightsay: “what it means for x to be a vixen just is for x to be a female fox”; this explanationseems semantic, not metaphysical or causal.15 Second, conceptual grounding is neededto accommodate intuitions about semantic priority. For example, even if ‘knowledge’cannot be given an explicit definition, there is an intuitive sense in which ‘knowledge’-sentences seem semantically derivative from sentences describing beliefs.16

To head off any potential confusion, it is worth contrasting the claim that the aboveexamples involve conceptual grounding from two other claims encountered in the litera-ture. First: conceptual grounding is unrelated to the dispute over whether metaphysicalgrounding claims should be expressed using predicates or using sentential operators (seefn. 8). This is a debate about the logical form of metaphysical dependence claims;in contrast, conceptual grounding concerns the semantic links between our sentences.Second: proponents of metaphysical grounding sometimes distinguish “conceptual” and“worldly” views of facts; these views disagree over whether, e.g., x’s being water andx’s being H2O are distinct facts.17 But this is a question about the fine-grainednessof the metaphysical grounding relation, not a question about conceptual grounding. Toclaim that there is conceptual grounding is not to claim that the metaphysical groundingrelation takes conceptual facts as its relata.18

2.3 The independence of conceptual grounding

I have emphasized that metaphysical and conceptual grounding are two distinct rela-tions. One concerns the metaphysical structure of the world while the other concernsthe meanings of our sentences. Nonetheless, some philosophers might wonder whetherinstances of conceptual grounding turn out to be instances of metaphysical grounding,so that we do not need to treat them as independent phenomena. (For example, per-haps sentence A conceptually grounds sentence B just in case the fact expressed by Ametaphysically grounds the fact expressed by B.) To rule out this possibility, it sufficesto give instances of conceptual grounding for which there is no corresponding instanceof metaphysical grounding. Here is the simplest example of this type:

[Bach] x is a bachelor in virtue of the fact that x is an unmarried male.19

14For discussion of conceptual explanation, see Schnieder (2006, 405-406).15To see the difference between semantic explanation and metaphysical explanation, contrast [Fox]

with a case like [Chem]. We would not say that “what it means for an H2O molecule to exist just is forthere to be hydrogen and oxygen atoms arranged in a certain way.”

16If the reader disagrees, the case [Bald] also plausibly exhibits conceptual priority without explicitdefinition. I further discuss the ‘knowledge’ case in 5.1.

17Proponents of worldly facts include Correia (2010, 258-259) and Audi (2012b, 3.5). Rosen (2010)and Fine (2012a) seem to adopt a finer-grained conception of facts.

18While these claims are meant to be distinct, some philosophers may worry that conceptual groundingis just a form of the fine-grained conception of metaphysical grounding. I address this concern in thenext sub-section with the example [Bach].

19I intend for [Bach] to be distinguished from a case of “conjunctive grounding” like [Bach∗]: x is

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As it happens, [Bach] is sometimes cited as a case of (fine-grained) metaphysical ground-ing in the literature.20 But I think that, once conceptual grounding is recognized as alive option, this view no longer seems attractive. Here is a simple argument to push thisintuition.

Suppose a community is just like our community except that they do not possessthe expression ‘bachelor’: they always use the expression ‘unmarried male’. So thesespeakers never form the belief that x is a bachelor.21 Do we think that these speakersare missing something about the world’s structure insofar as they lack this belief? Ofcourse not: these speakers have just as complete an account of the world’s structurethat we do. We just have another way of speaking. This suggests that there is nothingmetaphysical about [Bach].22

For further support, I observe that the fact F1: x’s being a bachelor and the fact F2:x’s being an unmarried man have exactly the same explanatory profile. In other words,for any fact other than F1 and F2, that fact will stand in exactly the same explanatoryrelations to both F1 and F2. This again suggests that F1 and F2 are just identical facts.23

Besides failing to respect our intuitions in the above thought experiment, anyonewho insists on viewing [Bach] as involving metaphysical grounding must either reject (a)the claim that ‘being a bachelor ’ and ‘being an unmarried male’ are just two names fora single property or (b) the claim that metaphysical grounding is irreflexive.24 But withconceptual grounding on the table, there is no need to deny either of these claims.

Could we say that conceptual grounding is a form of metaphysical grounding thatrelates facts about sentences? In response: if asked about the metaphysical groundsof facts involving the sentence ‘x is a bachelor’ (e.g., the fact that the sentence ‘x is abachelor ’ has the meaning that it does, the fact that the sentence ‘x is a bachelor’ istrue, etc.), we might have pointed to facts about its constituent expressions, or perhapsfacts about our linguistic practices. But we would not have said such facts are meta-physically grounded by facts about another sentence (i.e., ‘x is an unmarried male’).These sentences are certainly linked, but the link is semantic, not metaphysical.25

unmarried and male in virtue of the fact that x is unmarried and the fact that x is male. [Bach∗]is explicitly distinguished from [Bach] in the literature (see, e.g., Chalmers (2012, 454)). This seemsappropriate, since [Bach] and [Bach∗] have different explanatory force: in [Bach] the emphasis is on‘bachelor’, while in [Bach∗] the emphasis is on ‘and’. I will argue that conceptual grounding is neededto account for the distinctive explanatory force in [Bach].

20See, e.g., Rosen (2010, 124).21Here, I am assuming a fine-grained categorization of beliefs on which the belief that x is a bachelor

is distinct from the belief that x is an unmarried male.22Note: this argument stands even on a deflationary account of facts and of the metaphysical grounding

relation. See 3.3.23I thank an anonymous referee for suggesting this line of argument.24For discussion of these responses, see Rosen (2010, 124) and Jenkins (2011, 169), respectively.25As an alternative, we might consider whether the meanings of the concepts expressed in a concep-

tually grounded sentence are metaphysically grounded in the meanings of the concepts expressed in theconceptually grounding sentence (I thank an anonymous referee for this suggestion). If successful, thisaccount might provide a means of precisifying the notion of semantic priority discussed in 2.2. This ac-count would also further support the claim that there is an important difference between the in-virtue-ofclaims found in 2.1 and 2.2.

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Of course, someone could stipulate that they intend to use ‘metaphysical grounding’as a catch-all term that applies in any case of non-causal explanation. But why try tomake room for [Bach] under this banner? To insist on grouping these cases togetherdoes not somehow unify them; it merely obscures an important distinction between twodifferent phenomena.

3 The relation between metaphysical and conceptual grounding

In the last section, I argued that instances of conceptual grounding do not reduce toinstances of metaphysical grounding. This shows that we need to distinguish whichtype(s) of grounding are relevant for a given non-causal in-virtue-of claim. In this section,I will consider whether we can establish any general results about the relation betweenmetaphysical and conceptual grounding. I will first briefly consider a proposal fromChalmers (2012) before defending an alternative proposal.

3.1 The Conceptual/Metaphysical Thesis

Chalmers (2012, 453) claims that metaphysical and conceptual grounding correspondover a certain restricted range of cases:

Conceptual/Metaphysical (C/M) Thesis: Suppose an in-virtue-of claimV involves only super-rigid expressions. Then V involves metaphysical ground-ing iff it involves conceptual grounding.

Roughly, an expression is super-rigid when it takes the same extension across all epis-temic and metaphysical possibilities. For example, Chalmers suggests that the expres-sions ‘zero’, ‘wise’, and ‘cause’ are super-rigid (366-369). In contrast, the expression‘water’ is arguably non-super-rigid (since, according to many philosophers, ‘water’ wouldhave referred to XYZ on the epistemic possibility that the water-like liquid in our envi-ronment turned out to be XYZ).

Without the super-rigidity restriction, there would be a clear class of counterexamplesto C/M. For example, consider [Gene]: ‘x is a gene in virtue of the fact that x fills thefunctional role of storing and transmitting hereditary information from one generationto the next’. Since ‘is a gene’ expresses whatever property happens to fill the functionalrole of storing and transmitting hereditary information, the fact x’s being an gene isplausibly identical to the fact x’s being R, where R is whatever property happens tofill this role. In other words: lifting the super-rigidity requirement allows us to regard‘x’s being a gene’ and ‘x’s being R’ as referring to the same fact. And because thesefacts are identical, [Gene] plausibly involves conceptual but not metaphysical grounding(see 2.3). Speaking more generally: in-virtue-of claims with non-super-rigid terms ofteninvolve two different ways of describing the same worldly fact and so do not involvemetaphysical grounding.

(Some readers may be skeptical of the notion of super-rigidity and the use Chalmersputs to it in the C/M thesis. But I will set these worries aside. This is because my own

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view of the relation between conceptual and metaphysical grounding—the GroundingExclusion Thesis—does not rely on this notion.)

3.2 The Grounding Exclusion Thesis

Because metaphysical grounding is supposed to be independent of our language, manytheorists will immediately worry about counterexamples in the left-to-right direction ofC/M: cases of metaphysical grounding without conceptual grounding. For this reason,Chalmers’ defense of C/M focuses on counterexamples of this sort. But upon reflection,we see that there are clear counterexamples in the right-to-left direction: cases of con-ceptual grounding without metaphysical grounding. For example, the bachelor examplefrom 2.3 is one such case.26

To exclude such cases, one might try to restrict C/M further. But I think that thepressures against viewing [Bach] as a case of metaphysical grounding actually apply muchmore generally. In fact, I will defend the opposite view that conceptual and metaphysicalgrounding are exclusive:

Grounding Exclusion (GE) Thesis: If an in-virtue-of claim V involvesconceptual grounding, then V does not involve metaphysical grounding.

In 2.3, I showed that there are at least some cases where metaphysical and conceptualgrounding do not coincide. GE, by contrast, states that these two grounding relationsnever underwrite the same in-virtue-of claim.

3.3 Preliminary notes

Here are three notes on the argument for GE presented in section 4.Substantive metaphysical grounding : On the standard view, there are substan-

tive truths to discover about what metaphysically grounds what. On an alternativedeflationary conception, truths about metaphysical grounding are merely conceptualtruths (see Chalmers (2012, 458)). In the arguments ahead, I assume a non-deflationaryconception of metaphysical grounding since this is the most common view in the litera-ture. I will consider the alternative deflationary conception in 4.4.

Subject-predicate form : In my arguments, I will restrict attention to in-virtue-ofclaims with the form V ≡ ‘x is β in virtue of the fact that x is α’. In such cases, wecan call the property expressed by ‘is β’ a c-grounded property, and we can call theproperty expressed by ‘is α’ a c-grounding property.27 So, for example, being bald is c-grounded while having 20 hairs is c-grounding (n.b.: one should not read any implicationsabout metaphysical fundamentality into these terms). This restriction will simplify

26This case falls within the scope of C/M because Chalmers (2012) considers ‘bachelor’, ‘unmarried’,and ‘male’ to be super-rigid terms (453-454). I note that [Bach] will be a counterexample to C/M evenon a deflationary conception of metaphysical grounding—see 4.4.

27Of course, conceptual grounding is a relation between sentences, not properties. I introduce this termjust to keep track of the property corresponding to the predicate in a conceptually grounded sentence.Note that a property’s status as c-grounded will be relative to the in-virtue-of claim under consideration.

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presentation since we can focus on cases where, intuitively, the focus is on properties (asopposed to other ontological categories). But later, I will explain why the arguments forGE are extendable to other cases.

Restrictions: In the arguments ahead, I will appeal to some implicit restrictions onhow we must view the objects and properties involved in metaphysical grounding claims.In this note, I will explain these restrictions. Focusing on properties first, consider thefollowing proposed case of metaphysical grounding:

[Shape] x is roughly spherical in virtue of the fact that x has determinate shape R

I will use the label “lightweight” to subsume deflationary and (class or predicate) nom-inalist views of properties. I will now explain why adopting a lightweight view of thec-grounded property being roughly spherical is incompatible with viewing [Shape] as acase of metaphysical grounding.28

(i) Deflationism : According to deflationary theorists, properties are mere “shad-ows of predicates”: there is no more to their metaphysical nature than what is correctlyassertible of them in ordinary language.29 In particular, there are no truths to discoverabout whether deflationary properties are involved in metaphysical grounding relations.For this reason, a deflationary view of the property being roughly spherical is incompat-ible with viewing [Shape] as a case of metaphysical grounding (at least as the relation istypically conceived). (For further discussion, see Schaffer (2009, 360), who also claimsthat we should reject a deflationary view of the entities involved in grounding relations.)

Some deflationists claim that there is a sense in which properties are derivative fromour linguistic practices (see Schiffer (1996, 161)). So one might adopt a view on whichdeflationary properties are metaphysically grounded in our linguistic practices. Buteven if this is correct, the deflationist will still deny that x ’s being roughly spherical ismetaphysically grounded by x ’s having determinate shape R (which is what is neededfor [Shape] to involve metaphysical grounding).

(ii) Class nominalism : Suppose we identify being roughly spherical with a cer-tain set of individuals {x1, x2, . . . , xn}. Then to say that [Shape] involves metaphysicalgrounding is to say that x’s having determinate shape R metaphysically grounds x’sbeing a member of the set {x1, x2, . . . , xn}.30 But this seems wrong. It is not clear whatmetaphysically explains facts about x’s membership in {x1, x2, . . . , xn}. Perhaps fact

28 Note that, throughout this paper, I assume that it is possible to take different stances towardsdifferent types of properties. So, for example, I assume that one can adopt a deflationary view of beingroughly spherical while adopting a heavyweight view of having determinate shape R. I think that adoptinga lightweight view of the c-grounding property having determinate shape R is also incompatible withviewing [Shape] as a case of metaphysical grounding. But in this section, I discuss only the c-groundedproperty because I focus on this type of property in the arguments of section 4.

29Says Schiffer (1996, 159): “there’s nothing more to the nature of properties ... than is determined byour [property-hypostatizing] linguistic practices. What we can learn about them is what our linguisticpractices license us to learn about them.”

30Because some nominalists do not countenance facts, we should perhaps view the metaphysicalgrounding relata in some other way for present purposes. This technicality does not affect the cur-rent point.

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about x’s membership in a given collection of individuals has no metaphysical expla-nation. Or perhaps such facts are metaphysically explained by an axiom of impure settheory. But whatever the case, it is certainly not explained by the fact that x has acertain determinate shape R.

Of course, the class nominalist can accept some instances of metaphysical ground-ing; for example, perhaps the class nominalist will say that x’s being a member of{x1, x2, . . . , xn} grounds x’s having the property being roughly spherical. But even ifshe accepts this claim, the class nominalist will not view [Shape] itself as a case ofmetaphysical grounding.

(iii) Predicate nominalism : Similar remarks apply to other “reductive” versions ofnominalism. For example, suppose we identify being roughly spherical with the predicate‘is roughly spherical’. Then to say that [Shape] involves metaphysical grounding is to saythat x’s having determinate shape R metaphysically grounds P ≡ x’s falling under thepredicate ‘is roughly spherical’. But this seems wrong. Facts about what our predicatesapply to are instead metaphysically explained by facts about our linguistic practices.31

I group (i)-(iii) together under the label “lightweight” because of an important fea-ture they have in common. As I discuss in section 4, proponents claim that we canestablish a priori that lightweight properties are instantiated.32 By contrast, on morestandard views, establishing that a property is instantiated is typically thought to re-quire substantive argument.33 For simplicity, we can use the label “heavyweight” as acatch-all term for any property of this sort (that is: any property not identified witha set, a predicate, or a deflationary item). So, for example, the heavyweight label willsubsume views where properties are identified with tropes, ante rem universals, in rebusuniversals, bundles of causal powers, and so on.

(It is worth noting that, in addition to lightweight and heavyweight views, one couldalso endorse eliminativism. But if the property being roughly spherical does not exist,there are no rough sphericality facts to be related by metaphysical grounding. So elim-inativism is incompatible with viewing [Shape] as a case of metaphysical grounding aswell. I will set eliminativism aside in the discussion ahead.)

Notes (i)-(iii) show that the properties involved in metaphysical grounding claimscannot be lightweight entities. Analogous remarks apply to objects. There are defla-tionist views of objects, and these views are incompatible with metaphysical groundingfor the same reasons given above. In summary: the properties and objects involvedin cases like [Shape] cannot be lightweight if we are to view such cases as involving

31Perhaps one could have the view that x’s shape partially contributes to the metaphysical explanationof P, in addition to facts about our linguistic practices. But even on this view, [Shape] itself will notcount as a case of metaphysical grounding.

32See, e.g., Schiffer (2003, ch. 2). More precisely, proponents claim that we can have conditional apriori knowledge that lightweight properties are instantiated. By conditionally a priori, I mean that itis a priori to infer that lightweight properties are instantiated in a case C once one has been given abasic empirical description of C. For further discussion, see fn. 40.

33See Swoyer (1999) for discussion.

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metaphysical grounding.34 I will appeal to this result in the next section.35

4 Arguments for Grounding Exclusion

Schaffer (2009, 357-360) claims that metaphysics should focus on fundamentality ques-tions because existence questions are obvious. For example, the following “pleonasticargument” is said to establish the existence of the property knowing that p:

1*. John knows that p.2*. John has the property knowing that p. (“pleonastic inference” from 1)3*. Therefore: the property knowing that p exists. (generalization from 2)

While this style of argument is controversial, I agree with Schaffer that it successfullyestablishes the existence of a certain property. But I disagree with Schaffer that the aboveargument specifically establishes the existence of a heavyweight property (see Schaffer(2009, 357-358)). Indeed, it is often been claimed that pleonastic arguments supportlightweight views of properties.36 It has been said, for example, that we can make senseof the obvious inference from (1*) to (2*) if knowing that p is a mere deflationary item(or a mere set, etc.). But if knowing that p is something more than this, how could thisinference be obvious (as Schaffer claims)?

If it is true that pleonastic arguments for an item x support a lightweight viewof x, this might threaten the entire project of metaphysical grounding. This is be-cause pleonastic arguments are available for many types of items in our ontology, andlightweight views are incompatible with metaphysical grounding (see 3.3).

But in fact, I think this argument is too quick. This is because certain linguisticexpressions may themselves carry more substantial ontological commitments. As a casein point, it is at least plausible that ‘x has spin 1/2’ is only true if x has a certainheavyweight microphysical property.37 If this is right, then the pleonastic inference fromthis sentence does not show that having spin 1/2 is lightweight.

34Audi (2012a, 708-709) similarly claims that grounded facts must be something “over and above”grounding facts. While Audi’s focus is on showing that eliminativism is incompatible with metaphysicalgrounding, I have argued that deflationism and (class and predicate) nominalism are likewise incompat-ible.

35 This paper assumes that metaphysical grounding relates facts (see 2.1). But the discussion shouldgeneralize to views with other worldly entities (e.g., properties, objects) as relata, since the heavy-weight/lightweight distinction is available on those views as well. The situation is not as clear on theoperator approach (see fn. 8). Some operator-proponents accept that metaphysical grounding claimscorrespond to relations between facts (see Correia (2010, 254) for discussion). These theorists can acceptthe heavyweight/lightweight distinction and, accordingly, the section 4 arguments. But other proponentsdeny that metaphysical grounding is even a genuine relation. For such theorists, further arguments willbe needed to establish GE.

36See, e.g., Thomasson (2001, 320) and Schiffer (2003, ch. 2).37For example, one might think that ‘has spin 1/2’ carries heavyweight ontological commitment be-

cause this type of expression figures in statements of laws of nature. More generally, philosophers haveidentified various types of explanatory work that are thought to determine when a given predicate car-ries heavyweight ontological commitment (see, e.g., Swoyer (1999)). I discuss these types of explanatorywork in 5.2.

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For this reason, I will not rely on any general argument for lightweight propertieswhen defending GE. Instead, I will provide an independent argument for thinking thatc-grounded properties in particular are lightweight (even though c-grounding propertiesneed not be).38 In 4.1, I give a positive argument in support of the lightweight statusof c-grounded properties. In 4.2, I respond to variety of possible arguments for insteadviewing c-grounded properties as heavyweight.

4.1 The apriority argument

I will illustrate the apriority argument by considering the case of [Mass]. I assume that[Mass] involves conceptual grounding, since there is almost certainly a conceptual linkbetween the sentence F ≡ ‘x has the property having a mass of 2g ’ and the sentence F ′

≡ ‘x has the property having a mass’.

[Mass] x has a mass in virtue of the fact that x has a mass of 2g.

Let’s grant, as is plausible enough, that x’s property having a mass of 2g is heavyweight(as is required to view [Mass] as a case of metaphysical grounding). What about theproperty having a mass? As explained above: if the property having a mass is somethingmore than a mere set, predicate, or deflationary item, then its instantiation requiresargument.39 But here is the puzzle: within ordinary language, we can infer a priori thatx has the property having a mass from the fact that x has the property having a massof 2g.40

This raises an epistemic tension for the theorist who would view [Mass] as a case ofmetaphysical grounding. Given the apriority of the inference from F to F ′, why would wethink that the term ‘having a mass’ refers to anything other than a lightweight entity?A more substantial referent would be implausible from an epistemological standpoint(unless one views the inference from F to F ′ as some sort of synthetic a priori truth).41

By contrast, the apriority of the inference from F to F ′ is compatible with viewinghaving a mass as a set. Suppose that having a mass is identified with the set of thingsfalling under the predicate ‘has a mass’. Then there is no puzzle: it is a priori in ordinarylanguage for a subject who knows that x has a mass of 2g to infer that x is a member

38N.b.: here, as in 3.3, I assume that it is possible for some properties to be lightweight while othersare not.

39See, e.g., Swoyer (1999). I discuss the types of arguments used to establish the instantiation ofheavyweight properties in 4.2.

40On current usage, a sentence is a priori when it can be known conclusively (i.e., with certainty)on the basis of reflection that is independent of experience (see Chalmers (2012, 41) for discussion ofconclusive apriority). The relevant notion of apriority is also conditionalized. While F ′ is not a priorisimpliciter ; it an be known a priori conditional on the assumption that F (see Chalmers (2012, 55-56)for discussion).

41This is not to suggest that any a priori inference suggests lightweight properties (or conceptualgrounding); I clarify which types of a priori inferences are in tension with metaphysical grounding in5.1.

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of the set of things falling under the predicate ‘has a mass’. Similar remarks if having amass is viewed as a predicate or a deflationary item.42

So, in order to be compatible with ordinary epistemology, it is most plausible to saythat ‘having a mass’ refers to some kind of lightweight property.43 And given the discus-sion of 3.3, this in turn suggests that [Mass] does not involve metaphysical grounding.Analogous remarks apply for other c-grounded properties.44

(N.b.: while I have argued that a priori inferences involving conceptual groundingsupport a lightweight view of c-grounded properties, there are other types of a prioriinferences that do not involve conceptual grounding. These latter inferences may notsupport lightweight ontological commitments. I return to discuss this issue in 5.1.)

4.2 c-grounded properties and explanatory work

In 4.1, I offered a positive argument for the lightweight status of c-grounded properties.In this sub-section, I will rebut a variety of arguments that philosophers might give forinstead viewing c-grounded properties as heavyweight.

In order to show that there is a heavyweight property P , the standard strategy is toargue that P is needed to perform certain important explanatory work. It is then arguedthat P could not perform this explanatory work if it were a mere lightweight entity. Butin this section, I will argue that this argument fails in the case of c-grounded properties.The upshot will be that there are no reasons to view c-grounded properties as anythingmore than lightweight entities, which will in turn support GE.

Of course, it is outside the scope of this paper to consider all the types of explanatorywork that properties have been posited to perform. For this reason, I have tried to select

42Suppone one is antecedently convinced that having a mass is heavyweight. Then one might try toargue that, because having a mass is heavyweight, the inference from F to F ′is not (in fact) a priori,thus blocking the argument.

I provide a response to this objection in 4.2 (under the heading “scientific practice”). But regardless,anyone offering this line will have to deny that [Mass] involves conceptual grounding. So even if it wassuccessful, this objection would not threaten the argument for GE, which is a conditional thesis: if anin-virtue-of claim involves conceptual grounding, then it does not involve metaphysical grounding.

43It is important to recognize that viewing [Mass] as a case of conceptual grounding does not requireone to accept any specific view of the property having a mass. It is compatible with this view to adopteither a deflationary or a nominalist view of having a mass, or else to adopt an eliminativist stancetowards this property (see 3.3).

44The present argument is different from the deflationist’s argument (see 4.0) in important ways. First:the apriority argument does not rely on the inference from ‘x has a mass’ to ‘x has the property havinga mass’; instead it relies on the inference from F to F ′. Because F involves a determinate property,it avoids the worry that the basic sentence builds in heavyweight commitments (see 4.0). (In fact, theapriority argument assumes that F does carry heavyweight commitment, but this commitment is to adeterminate property, not a determinable.) Second: the present argument invokes apriority rather thanobviousness. This ensures that F ′ can be established purely as a result of an inference from F ; in otherwords, asserting that F ′ does not require that one accept any background assumption to the effect thatit is obvious that x has a heavyweight determinable. (Even if we ignore this last point, I think it shouldbe clear that F ′ does not obviously carry commitment to a heavyweight determinable (as opposed to alightweight one). Indeed, the very existence of the literature on the status of determinables shows thatthe instantiation of heavyweight determinables is not generally considered obvious.)

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examples that are representative of the arguments typically given in the literature.Truthmaking : Properties are sometimes posited to serve in accounts of the truth-

makers for our sentences.45 For example, it has been claimed that we need to posit theproperty of negative charge in order to explain the truth of sentences like ‘X is negativelycharged’. One might claim that heavyweight c-grounded properties are similarly neededfor truthmaking.

In response: while some heavyweight properties may be needed for truthmaking, itis not the case that for every predicate in a true sentence, there has to be a heavyweightproperty that figures in truthmakers for predications of that predicate (but in no othertruthmakers). And there is a specific reason to doubt that heavyweight c-grounded prop-erties are needed for truthmaking. Because sentences expressing c-grounded propertiesare conceptually entailed by sentences expressing c-grounding properties, the truthmak-ers for the latter sentences will already be sufficient to serve as truthmakers for theformer sentences. So: while we may need heavyweight properties eventually, we do notneed to posit additional heavyweight c-grounded properties.46

Scientific practice : Theorists sometimes argue that c-grounded properties areneeded to account for various aspects of scientific practice. For example, Wilson (2012,5) notes that determinable properties like being in a low entropy state figure cruciallyin scientific explanations. Scientists explain the final state of a system by noting thatsystems naturally proceed from low entropy to high entropy states. Wilson argues thatwe can only make sense of this practice if we posit properties like being in a low entropystate to serve as the “ontological ground” of this explanation. (Note that, because thesentence ‘X is in a low entropy state’ is plausibly definitionally entailed by sentencesdescribing the underlying physical state of the system’s component particles, being in alow entropy state is plausibly a c-grounded property.)

While Wilson’s argument may support the existence of the property being in a lowentropy state, it does not support the claim that this property is anything more than alightweight entity. Wilson posits determinables so that they can serve as the denotationsof certain property terms used in scientific theories and explanations. But here is theproblem: within scientific discourse, ‘being in a low entropy state’ is a c-grounded prop-erty term. And the discussion of 4.1 shows that such terms refer to lightweight entities.So if anything, Wilson’s argument establishes that we need lightweight determinableproperties to account for various aspects of scientific practice.

Wilson (2012) does not explicitly discuss the a priori entailment of determinableproperties. But how might she respond? I will consider two possibilities. First: Wilsonmight argue that, because determinables are needed to perform substantive work inscientific practice, it cannot really be the case that they are a priori entailed fromdeterminate properties. In response: this inference is obviously treated as a priori bypracticing scientists. But then I think it would be presumptuous for philosophers to try

45See, e.g., Armstrong (1997).46The claim that c-grounded properties are not required for truthmaking aligns with Heil’s (2004, 6)

rejection of the view that “the character of reality can be ‘read off’ our linguistic representations”; wedo not need distinct properties involved in truthmaking for every predicate in our language.

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to “correct” scientists about this aspect of scientists’ own area of inquiry.47

Second: Wilson might accept the apriority of the inference, but deny the premisethat there cannot be a priori entailment of heavyweight properties. While interesting,I think this response is undermined by Wilson’s original argument. This argument wasa substantive, empirical argument relying on premises about actual scientific practice.The fact that Wilson provides such an argument suggests that there is in fact no a priorientailment of heavyweight properties.

Wilson’s argument is just one example of a scientific argument for positing c-groundedproperties. But the above response will be applicable to any argument in which c-grounded properties are posited in order to serve as the denotation of property termsused in scientific theories and explanations.

Resemblance : Properties are often invoked to explain similarity.48 But even ifthese arguments are successful in certain cases, we do not need c-grounded propertiesto explain resemblance. To illustrate this, I will use the entropy example from before.Suppose that X and Y are both in a low entropy state. How do we best explain thissimilarity between them? One possible explanation is that X and Y both instantiatesome sui generis property that explains their similarity. But with conceptual grounding,we have a better explanation. Conceptual grounding suggests that the similarity in virtueof which we apply the predicate ‘is in a low entropy state’ to both X and Y is a similaritythat is “already present” in the facts described by the more basic sentences (i.e., thefacts about the relative positions of the particles, etc.). In other words, it is because ofa similarity in the c-grounding properties of X and Y that we are able to judge a priorito apply ‘is in a low entropy state’ to both X and Y on the basis of the c-groundingsentences. So we don’t need to appeal to a c-grounded property to explain this similarity.

Causal powers: Suppose Sophie the pigeon is trained to peck at various shades ofred. Now suppose Sophie pecks at something scarlet. What causes Sophie’s pecking: theinstance of scarlet or the instance of red? The intuitive answer is supposed to be: theinstance of red (since Sophie would have pecked at other shades of red). So philosophershave posited c-grounded properties (such as redness) in order to serve as the bearers ofcausal powers.49

The response to this argument is the same as the response to Wilson’s argumentabove. Notice that the Sophie example relies on our ordinary intuitions about the causeof the pecking in the described case. In other words: when we judge that redness causesthe pecking, we are employing the ordinary expression ‘redness’. But if redness is ac-grounded property, then the term ‘redness’ refers to a lightweight entity (see 4.1).So even if the Sophie case supports the claim that c-grounded properties have causalpowers, it does not support the claim that c-grounded properties are anything more than

47One may still have the intuition that, if being in a low entropy state scientifically explains anything,then it must be heavyweight. But this intuition plausibly derives from the assumption that scientificexplanations correspond to genuine causal relations (I thank an anonymous referee for suggesting thisresponse). Against this assumption, many philosophers have argued that certain scientific explanationsare merely pragmatic. See, e.g., Jackson & Pettit (1990).

48See Swoyer (1999, 107)49This argument is originally from Yablo (1992). See Swoyer (1999, 107) for relevant discussion.

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lightweight entities.How can redness have causal powers if it is merely lightweight? One possibility is

that broadly causal explanations do not perfectly track causal relations, so that figuringin a causal explanation does not imply heavyweight metaphysical status.50

An objection : One might think that, in principle, we can perform all of the abovetypes of explanatory work just with the fundamental facts. If so, then one might worrythat the arguments of this sub-section overgeneralize to all cases of metaphysical ground-ing. (I thank an anonymous referee for pressing this point.) Here are two responses:

(1) With the exception of truthmaking, the above arguments appealed to a specificfeature of c-grounded properties: their a priori entailment from c-grounding properties.For example, when discussing resemblance, I appealed to the claim that we can judge apriori to apply ‘is in a low entropy state’ to a system when given a description of thatsystem using the c-grounding sentences. Similarly, the discussions of causal powers andscientific practice appealed to the apriority argument of 4.1, which itself appealed to thea priori entailment of c-grounded properties. So these arguments do not support thegeneral thesis that only fundamental properties are heavyweight. And indeed, there areplausible counterexamples to this thesis. For example, suppose that the physical groundsthe phenomenal. Many materialists will grant that it is possible that subjects with verydifferent physical states nonetheless share, e.g., a phenomenal pain state. It is plausiblethat, to account for this resemblance, we need to countenance heavyweight phenomenalproperties. Audi (2012a) discusses a variety of other possible counterexamples (involving,e.g., normative properties, semantic properties, etc.).

(2) Even if the 4.2 arguments did apply generally to all non-fundamental properties,there may be other types of reasons for viewing certain non-fundamental properties asheavyweight. For example: even if heavyweight phenomenal properties are not neededto perform any explanatory work, there is independent support for them: we (plausibly)can introspect such properties in conscious experience. (Of course, this type of consider-ation is inapplicable to c-grounded properties, which we cannot introspect in consciousexperience.51)

Summary : Given the above discussion, I conclude that the standard arguments forshowing that a property is heavyweight fail in the case of c-grounded properties. Whilethe above arguments do not definitively establish this result, they at least put the burdenof proof on the metaphysical grounding theorists invoking such properties to show thatc-grounded properties are something more than mere sets or shadows of predicates. Heil(2009, 309-210) suggests that it would be an inappropriate “linguisticizing of philosophy”to expect a correspondence between predicates and (heavyweight) relations. This sectionsuggests that we should adopt a similar stance towards c-grounded properties.

50I thank an anonymous referee for this suggestion.51I think the most plausible arguments for heavyweight c-grounded properties are considerations re-

lating to explanatory work, which is why I have focused on these arguments in this section.

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4.3 Summary

I have argued that we should not assign heavyweight status to c-grounded properties.Given the restrictions on properties involved in metaphysical grounding relations (see3.3), this supports the GE thesis.

For ease of presentation, I have focused on in-virtue-of claims with the form ‘x is βin virtue of the fact that x is α’. But analogous arguments should apply to other casesas well. For example, Thomasson (2007, 164-165) claims that the sentence ‘There is achair’ is conceptually entailed by the sentence ‘There are particles arranged chairwise’.If she is right, then [Chair] will be a case of conceptual grounding:

[Chair] There is a chair in virtue of the fact that there are particles arrangedchairwise.

Does [Chair] also involve metaphysical grounding? Thomasson (2009, 467) appeals to theapriority of the above inference to argue that items like chairs have no “real metaphysicalnature” for metaphysics to discover (this is just a version of the apriority argument givenin 4.1). But if chairs have no real metaphysical nature to discover, then debates aboutwhether parts metaphysically ground wholes or wholes metaphysically ground partsare misguided. So if [Chair] involves conceptual grounding, then it is not a case ofmetaphysical grounding.

4.4 Objections

I will now consider two further ways a theorist might resist GE. It is possible to adopta deflationary stance where truths about metaphysical grounding are mere conceptualtruths (see Chalmers (2012, 458)). So in arguing for GE, a deflationist may object thatI am trying to deny conceptual truths. My response to this worry is simply to say that,as I intend to use the term ‘metaphysical grounding’, truths about metaphysical ground-ing are not supposed to be conceptual truths. Most theorists who study metaphysicalgrounding are not deflationists: their stated goal is to discover substantive truths aboutmetaphysical dependence.

A second way to resist GE would be to claim that c-grounded properties are morethan mere sets or deflationary items, but to insist that their instantiation is a priorinonetheless. For example, Schaffer (2009, 360) says: “I take entities [involved in ground-ing claims] to be full-blown “heavyweight” entries on the roster of entities, and merelyadd that their existence is obvious.” If a philosopher claims that the existence of theseentities is not merely obvious, but also a priori, then she can reject GE.

But in response, I want to re-emphasize that there is nothing in Schaffer’s argumentsthat suggests that the relevant items are anything more than lightweight properties. Soanyone who wants to reject GE has the burden of showing that c-grounded propertyterms do not refer to mere lightweight entities. But the discussion of 4.1 and 4.2 supportthe opposite conclusion.

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5 Heuristics

If GE is true, it becomes important to distinguish instances of metaphysical and con-ceptual grounding. Conflating these relations may lead to mistaken conclusions aboutmetaphysical structure. In this section, I will consider two heuristics for distinguishingeach type of case.

5.1 The Scrutability Heuristic

I will illustrate the scrutability heuristic by considering the following alleged case ofmetaphysical grounding:

[Know] x knows that p in virtue of facts about the causes, evidence, truth,etc. of x’s belief that p (Fine 2012a, 53)

In 2.2, I made the following observation: when we are told sufficient information abouta subject’s belief state, we are (across a variety of ordinary cases) able to infer a prioriwhether or not that subject has knowledge. With this epistemic result in hand, we canuse inference to the best explanation to support conceptual grounding in the case of[Know]. What explains the fact that we can often infer a priori whether x knows thatp when given a description of x’s belief state? If [Know] involves conceptual grounding,we have an elegant explanation: it is constitutive of competence with the term ‘knows’that one is disposed to make these inferences. This motivates the following heuristic:

Scrutability heuristic: Consider a (genuinely explanatory) in-virtue-ofclaim V : ‘S1 in virtue of the fact that S2’. If sentences involving thesame family of terms52 as S1 are inferable a priori from sentencesinvolving the same family of terms as S2, this is evidence that Vinvolves conceptual grounding.

So, for example, since ‘knowledge’ sentences are inferable a priori from sentences de-scribing belief states, the scrutability heuristic suggests that, in fact, [Know] involvesconceptual grounding.

It is worth noting that not all a priori inferences suggest conceptual grounding. Forexample, suppose ‘2+2=4’ is inferable a priori from ‘John is tall’. This would onlybe because ‘2+2=4’ is a priori simpliciter. The restriction to “genuinely explanatory”in-virtue-of claims helps to exclude such cases.

More generally, I have made the scrutability heuristic defeasible in order to allowfor the possibility that conceptual grounding does not provide the best explanation ofscrutability in all cases. For example, one interesting case to consider is: ‘∃xFx invirtue of the fact that Fa’. Many philosophers (including myself) will view this as a

52The intuitive distinctions between “families of terms” will directly mirror the distinctions drawnbetween domains of facts in the literature on metaphysical grounding (i.e., the type of distinction drawnwhen it is claimed that physical facts metaphysically ground phenomenal facts, etc.).

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straightforward case of conceptual grounding: it is constitutive of competence with theexistential quantifier that one is disposed to infer something of the form ‘∃xFx’ fromsomething of the form ‘Fa’. But some philosophers instead claim that logical inferencesare justified by “rational intuition” (for discussion, see, e.g., Dogramaci (2013)). If thereindeed cases where rational intuition provide the best explanation of scrutability, thenthese will be cases where the heuristic is defeated. (My own view is that there are nosuch cases.)

I call this the “scrutability heuristic” because of recent work from Chalmers (2012)on scrutability theses. A scrutability thesis is a claim that sentences of a certain family ofvocabulary are trivially inferable from sentences of another family of vocabulary: exactlythe type of result relevant to the scrutability heuristic.

5.2 The Vagueness Heuristic

I will illustrate the second heuristic by considering the following alleged case of meta-physical grounding:

[Shape] x is roughly spherical in virtue of the fact that x has determinate shape R

I will argue that the vagueness of the predicate ‘is roughly spherical’ supports the viewthat, in fact, [Shape] involves conceptual grounding.53

Suppose that it is indeterminate whether x is roughly spherical when x has deter-minate shape Ri. On the standard linguistic theory of vagueness, this indeterminacyis attributable to linguistic imprecision. So to eliminate the indeterminacy, we canstipulate whether or not the predicate ‘is roughly spherical’ applies to shape Ri. But ifwhether Ri counts as roughly spherical merely depends on this type of semantic decision,this suggests that ‘rough-sphericality’-sentences are conceptually linked to ‘determinateshape’-sentences. This in turn supports viewing [Shape] as a case of conceptual ground-ing, since [Shape] employs expressions from these two families of terms.

The above argument does not show that all vagueness indicates conceptual ground-ing. For example, consider [Pain]: ‘x is in pain in virtue of the fact that x is in brain stateP ’. Because the predicate ‘is in pain’ is vague, there is a case of conceptual groundingin the vicinity: T ≡ ‘x is in pain in virtue of the fact that x has a pricking sensationof degree 7’.54 But notice that T is different from [Pain]. T involves vague and precisephenomenal predicates. But [Pain] involves phenomenal and neuroscientific predicates.

So even if we were to precisify the phenomenal predicate in [Pain], there would stillbe an in-virtue-of claim left over: ‘x has a pricking sensation of degree 7 in virtue of x’sbeing in brain state P ’. This was the non-causal explanation that originally interestedus in the case of [Pain]. For this reason, the vagueness of ‘is in pain’ does not suggestthat [Pain] itself involves conceptual grounding.55

The above discussion motivates the following heuristic:

53If [Shape] is indeed a case of conceptual grounding, it is because the term ‘R’ (which picks out acertain determinate shape) is semantically prior to the expression ’is roughly spherical’—see 2.2.

54I thank an anonymous referee for this example.55Of course, if we know that subjects in a certain borderline pain state are in brain state Pi, we could

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Vagueness heuristic: Consider a (genuinely explanatory) in-virtue-of claimV : ‘S1 in virtue of the fact that S2’. If:

(a) S1 is indeterminate in some situation L due to a vague expressionin S1 and

(b) a subject with no further empirical information could precisify S1by stipulating its truth when given a description of L that onlyemploys vocabulary from the same family as in S2,

then this is evidence that V involves conceptual grounding.

For example, in [Shape], S1 is indeterminate in the situation described by C: ‘x hasdeterminate shape Ri’. Since a subject can simply stipulate that Ri is roughly sphericalwithout needing any further empirical information, the vagueness heuristic suggests that[Shape] involves conceptual grounding. In contrast, the vagueness in [Pain] does notsuggest conceptual grounding because of condition (b).

5.3 A test case

I will illustrate the heuristics with the following case:

[Cause] x causes y in virtue of facts about the Humean mosaic and laws ofnature.56

There have been many attempts to analyze the term ‘cause’. But every proposal seemsto face counterexamples. These failures have led certain philosophers to suggest that wereorient our approach to theorizing about causation. Instead of focusing on the term‘cause’, we should instead focus on the causal relation itself, investigating its patterns ofmetaphysical dependence. Here is a representative quotation from Schaffer (2007):

I suspect that many philosophers have really been interested in a concep-tual analysis of causation because they thought the issue was of ontologicalmoment. ... [But the] conceptual order — the order of definitions in ourminds — need not match the ontological order — the order of dependenciesin nature. (873)

But the move from the failure of conceptual analysis to the study of the metaphysicalgrounds of causation may be premature. This is because, even if ‘cause’ cannot begiven a definition, there is still strong support for the claim that causal sentences areconceptually grounded. I will support this claim with the above heuristics.

Scrutability heuristic: The very counterexamples that tell against the analyz-ability of the term ‘cause’ actually support the claim that ‘cause’ stands in a priori

precisify ‘is in pain’ by stipulating that anyone in Pi is in pain. But this stipulation is only possible ifwe possess empirical knowledge about the connections between brain states and conscious states. Forthis reason, the possibility of such stipulations does not suggest conceptual grounding in [Pain].

56Schaffer (2007, 873-874) considers this possible example of metaphysical grounding (although hedoesn’t endorse it).

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inferential connections to more basic terms. For example, let E be the sentence ‘Suzy’sthrow caused the bottle to shatter’. Let F be the conjunction of the following sentences:

“Billy and Suzy throw rocks at a bottle. Suzy throws first, or maybe shethrows harder. Her rock arrives first. The bottle shatters. When Billy’s rockgets to where the bottle used to be, there is nothing there but flying shards ofglass. Without Suzy’s throw, the impact of Billy’s rock on the intact bottlewould have [shattered the bottle]. But, thanks to Suzy’s preempting throw,that impact never happens.” (Lewis (2004, 82))

It seems that competent speakers can infer a priori that E is true when presentedwith F . The same goes for other cases in the literature on causation (e.g., preemptioncases, overdetermination cases, etc.). The entire progress of this literature dependedon our ability to make a priori inferences about what causes what when presentedwith descriptions of cases. Taken together, these cases suggest that: when we are toldsufficient information about a situation without using the term ‘cause’, we can infer apriori whether x causes y.57

What explains our ability to make these a priori inferences? With conceptual ground-ing, we have an elegant explanation: it is constitutive of competence with the term ‘cause’that one is disposed to make these inferences.

Vagueness heuristic: There are many cases where we lack firm intuitions aboutwhether x causes y. For example, let G be the conjunction of the following sentences:‘Two assassins, Captain and Assistant, are on a mission to kill Victim. Upon spottingVictim, Captain yells “Fire!”, and Assistant fires. Overhearing the order, Victim ducksand survives unscathed.’58 In the case described by G, we lack firm intuitions about P :‘The captain’s yelling “Fire!” caused Victim to survive’.

One might think that there is still an objective fact about the truth of P in this case.But this can be resisted with a thought experiment. Imagine two communities A andB that agree with us on almost all of our ordinary causal judgments. But, while we areundecided about P , A-speakers have robust intuitions that P is true while B-speakershave robust intuitions that P is false. What should we say about the dispute betweenA-speakers and B-speakers over P? It seems most plausible to say that this disputeis merely verbal: A-speakers and B-speakers simply use the term ‘cause’ in slightlydifferent ways, such that P is true for A-speakers and false for B-speakers. But if this isright, it suggests that P is indeterminate on our use of the term ‘cause’. So condition(a) of the vagueness heuristic is met.

To precisify P , we would simply stipulate its truth given the description G of thecase; no further empirical information would be required. So it is plausible that condition

57Non-humeans about causation (such as Tooley (1990)) claim that, even after fixing the laws andthe Humean base, there can still be differences in what causes what. These philosophers may denythe applicability of the scrutability heuristic to the present case. While I find this implausible, there isno need to address this issue. This is because the present section only seeks to establish a conditionalconclusion: if [Cause] involves grounding at all, the grounding in question is conceptual. Non-humeanswill simply deny the antecedent.

58This example is from Hitchcock (2003, 10).

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(b) is also met and that the vagueness heuristic supports viewing [Cause] as a case ofconceptual grounding.

Summary : Both heuristics suggest that, if [Cause] involves grounding at all, thegrounding in question is conceptual. So metaphysical grounding isn’t the proper method-ological approach for theorizing about causation.

5.4 How widespread is conceptual grounding?

It is outside the scope of this paper to apply the heuristics to further cases. But my ownview is that many other alleged cases of metaphysical grounding are better interpretedas involving conceptual grounding. Examples I have discussed in this paper include[Shape], [Know], and [Cause]. From the original list of examples, I am inclined to saythat [Fragile] and [Harm] involve conceptual grounding as well. In contrast, the bestcandidates for metaphysical grounding are [Chem], [Pain], and perhaps [Sets]. But theseexamples are controversial and deserve fuller discussion.

6 Conclusion: philosophical payoffs

In this paper, I have argued that metaphysical and conceptual grounding are exclusiveand have offered two heuristics to identify which type of grounding is operative in agiven case. I will now mention some payoffs of the above discussion.

First, and most importantly, I have argued that metaphysical grounding is not theonly way to make sense of non-causal in-virtue-of claims. Deflationist and reduction-ist views can equally well account for cases of non-causal explanation by appealing toconceptual grounding.

Second, the above discussion shows that before we ask questions of the form ‘Does Xground Y ?’, we first need to ask: ‘Is there a semantic link between the expressions ‘X’and ‘Y ’? In answering this question, we find that many alleged cases of metaphysicalgrounding actually involve conceptual grounding.

Finally, the above discussion should be of interest to theorists who are skeptical ofmetaphysical grounding. One way to object to metaphysical grounding is to challengeproposed examples of it.59 And with the GE thesis, we have a general strategy forchallenging such cases: use the heuristics to show that a given in-virtue-of claim actuallyinvolves conceptual grounding. It has been outside the scope of this paper to apply theseheuristics to a wide variety of cases. But my own view is that most proposed cases ofmetaphysical grounding are actually cases of conceptual grounding. If this is correct,the heuristics may help justify skepticism about the notion of metaphysical groundingitself.

59See, e.g., Hofweber (2009). Raven (2012) defends certain alleged examples of metaphysical ground-ing.

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