ORIGINAL ARTICLE Against Grounding Necessitarianism Alexander Skiles Received: 17 September 2013 / Accepted: 18 August 2014 / Published online: 10 September 2014  Springer Science+Business Media Dordrecht 2014 Abstract Can there be grounding without necessitation? Can a fact obtain wholly in virtue of metaphysically more fundamental facts, even though there are possible worlds at which the latter facts obtain but not the former? It is an orthodoxy in recent literature about the nature of grounding, and in first-order philosophical disputes about what grounds what, that the answer is no. I will argue that the correct answer is yes. I present two novel arguments against grounding necessitarianism, and show that grounding contingentism is fully compatible with the various explanatory roles that grounding is widely thought to play. 1 Introduction A fact is grounded when there are metaphysically more fundamental facts that it non-causally derives from-that make it the case; that bring it about-as when the fragility of a vase is said to be grounded in facts about its crystalline microstructure, or when the wrongness of lying is said to be grounded in facts about the physical and psychological harm it causes. Although distinct, grounding is similar to causation insofar as they are both relationships of production: just as an event may occur wholly in virtue of events that cause it, a fact may obtain wholly in virtue of facts that ground it. Or as Jonathan Schaffer has put it, ''grounding is something like metaphysical causation. Roughly speaking, just as causation links the world across A. Skiles (&) Institut de Philosophie, Université de Neuchâtel, Espace Louis-Agassiz 1, 2000 Neuchâtel, Switzerland e-mail: alexander.j.skiles@gmail.com 123 Erkenn (2015) 80:717–751 DOI 10.1007/s10670-014-9669-y time, grounding links the world across levels'', producing facts upward from the more fundamental levels to the less (2012a, p. 122).1 A fact, [p], is necessitated by a collection of facts, C, just when any time and (metaphysically possible) world at which all the facts in C obtain is also a time and world at which [p] obtains.2 The question I wish to address in what follows is this: can there be grounding without necessitation? Most philosophers answer this question with a resounding no, and thus endorse the thesis I call grounding necessitarianism: that for any time t and world w, if [p] is grounded in C at t and w, then [p] is necessitated by C. The minority who answer yes endorse the thesis I call grounding contingentism. Contingentists do not make the radical claim that no fact is necessitated by the facts that ground it: for instance, they typically agree with their necessitarian rivals that the conjunction [p ^ q] is both grounded in and necessitated by the collection of its conjuncts, [p] and [q]. Rather, contingentists merely deny that every possible instance of grounding carries such strong modal import.3 In this paper I challenge the necessitarian orthodoxy, and give the contingentist alternative its proper due. After discussing some preliminaries about the notion of grounding I will be working with in §2, I argue that there are at least two varieties of grounding without necessitation. In §3, I argue that scenarios familiar from literature on the metaphysics of material composition-namely, those modeled on the infamous 'ship of Theseus'-constitute one variety. In §4, I argue that a certain class of accidental generalizations constitutes another. In §5, I consider the best arguments in favor of necessitarianism in existing literature on the metaphysics of fundamentality, and show how the contingentist is able to resist them. Finally, in §6 I conclude by briefly outlining how taking the contingentist perspective seriously can substantively impact a number of important philosophical disputes in which grounding plays a central role. 2 Some Preliminaries on Grounding Although my topic is grounding, a comprehensive treatment of the competing accounts of its nature and of the proper regimentation of grounding statements is 1 For influential discussions of the relevant sense of ''ground'', its role in philosophical inquiry, and defense of its coherence, see Fine (2001), Correia (2005), Schaffer (2009), and Rosen (2010). For a more pessimistic take, see Wilson (forthcoming). 2 I adopt formalism from Rosen (2010). Brackets indicate facts: for any true sentence ''p'', let ''[p]'' rigidly denote the fact that p. If ''C'' is a plural term rigidly denoting one or more facts, then a fact is in C iff it is identical to one of the facts that ''C'' rigidly denotes. (I will say more about what facts are and how they interlock with grounding in §2.) I interchange statements about necessity and possibility with statements about worlds purely for convenience. 3 Explicit proponents of necessitarianism include Correia (2005), Witmer et al. (2005), deRosset (2010, 2013a, b), Rosen (2010), Audi (2012a, b), Trogdon (2013), and Dasgupta (2014), while Barker (2012), Bennett (2011) and Cameron (forthcoming) endorse principles that entail it. Fine (2012) is subtly different: although he claims that every variety of grounding requires necessitation, the variety of necessity required need not be metaphysical necessity. Explicit contingentists include Dancy (2004), Bricker (2006), Schnieder (2006), Zangwill (2008), Schaffer (2010a), Leuenberger (2013), and Chudnoff (2013, manuscript). 718 A. Skiles 123 beyond what I can carry out here. Since differences between these accounts subtly effect how necessitarianism and contingentism are stated and appraised, instead I will briefly sketch a 'default' framework-one amenable to necessitarians-and note how my arguments apply within alternative frameworks elsewhere in the paper.4 What is it for a fact to be grounded? A answer to this question would clearly be useful for adjudicating the necessitarian/contingentist debate, yet it is another orthodoxy about grounding that no reductive analysis can be given. (Like necessitarianism, this is an orthodoxy I ultimately reject-I return to this matter when addressing an objection to contingentism in §5.) Nonetheless, we can instead rely upon our intuitive judgments about what grounds what. Just as our intuitive judgments about what causes what provide defeasible evidence for and against claims about how the relation of causation is distributed, similarly with the relation of grounding. The judgments I have in mind are characteristically elicited by familiar philosophical queries like ''What is it in virtue of which lying is immoral?'', or ''What makes it the case that a true belief is also knowledge?'', where causal, epistemic, or agential readings are either understood to be off-topic (as when questioner and audience both know that lying is immoral, contrary to an epistemic reading), or explicitly canceled (as when the questioner emphasizes that she is querying about the metaphysically more fundamental facts that turn a true belief into knowledge, contrary to a causal or agential reading). To illustrate the framework I will work within, consider two grounding statements that meet the intuitive 'smell test', where s is the shirt I am now wearing (cf. Rosen 2010, pp. 117 and 129): (1E) [s is blue] is grounded at t and w in [s is cyan] and [being cyan is a determinate of being blue] (2E) [Obama is a Democrat ^ Romney is a Republican] is grounded at t and w in [Obama is a Democrat] and [Romney is a Republican] As I understand it, grounding is factive: (1E) is true, for instance, only if each fact entering into this relationship obtains at t and w (for short: on this particular occasion). The reason I take grounding to be indexed to a time and a world is that a single fact may have different grounds on different occasions, and may lack grounds altogether on other occasions. Were my shirt turquoise rather than cyan, the grounds of [s is blue] would differ accordingly; if it were maroon, then [s is blue] would not obtain, and therefore would not be grounded on that occasion (assuming, again, that grounding is factive).5 And what goes for (1E) goes for (2E) as well. In general, I 4 The framework most closely resembles the one developed in Rosen (2010), although he includes ''the Entailment Principle'' (ibid., 118), which is equivalent to necessitarianism. Given that Rosen's is a popular 'out-of-the-box' framework for theorizing about grounding in first-order applications (cf. Whitcomb 2012), my arguments are notable even if they do not extend to alternative frameworks. For a state-of-the-art overview of options pertaining to the nature, logic, and semantics of grounding, see the introduction to Correia and Schnieder (2012). 5 Rather than indexing the grounding relation, one might instead capture either the modal or temporal variability of grounding by embedding the indices into the facts that grounding relates. On one such alternative view, grounding holds simpliciter over a domain of facts fully specified with respect to a time and world; according to this view, what is grounded is not [s is green], but rather [s is green at 9 October Against Grounding Necessitarianism 719 123 will assume that there is a single relation of grounding between facts ascribed by grounding statements regardless of which ontological categories the facts related by grounding happen to concern: mental, moral, and modal facts-or facts regarding any other subject matter-are grounded in the very same way (if, that is, they are grounded at all).6 At times I will employ the notion of partial grounding: when a collection of facts contributes to the grounding of another fact, as when [Obama is a Democrat] contributes to the grounding of [Obama is a Democrat ^ Romney is a Republican]. I will assume that [p] is partially grounded in C iff C is a subcollection of some collection of facts, C*, that fully grounds [p]. Clearly, necessitarianism is not to be understood as a claim about partial grounding: barring unexpected necessary connections between party affiliations, [Obama is a Democrat] fails to necessitate [Romney is a Republican] and thus fails to necessitate their conjunction. I will construe statements of the form ''[p] is grounded in [q1], [q2], etc.'' as ascribing a relational predicate, the relata of which are entities I have been calling facts. I wish to remain neutral about what kinds of entities facts are. But for reasons of space, I will treat facts as true 'Russellian' propositions with individuals, properties, relations, quantifiers, logical connectives, and so forth as constituents, structured in the manner depicted.7 These two assumptions will play no essential role in the arguments to come, however. To avoid ontological commitment to facts, some take ''it's being the case that __ is grounded in its being the case that ..., its being the case that ..., etc.'' to be a sentential operator that, when combined with a sequence of statements ''p'', ''q1'', ''q2'', etc., yields a truth-evaluable grounding statement. Proponents of this view may apply standard paraphrase procedures throughout the following discussion.8 I will not assume that grounding only relates facts: grounding may well hold between the members of any one or more ontological categories. The necessitarian versus contingentist dispute as I have formulated it is silent about the modal implications of grounding beyond the realm of facts (if grounding extends beyond the realm of facts at all). Nonetheless, since most necessitarians deny that grounding Footnote 5 continued 2012 in w@]. Such a view would follow from combining the claim that facts are true propositions (e.g., Rosen 2010, p. 114; see below) with the claim that propositions are fully time and world specific (e.g., Schaffer 2012b). If this alternative view were true, then the necessitarian thesis would require reformulation in order to avoid trivialization: [s is green at 9 October 2012 in w@] obtains at every world, and thus is trivially necessitated by any collection of facts. Say that a fact is fixed iff of the form [p at t and w], and let Ct,w be any collection of facts fixed to t and w. Then grounding necessitarianism should be understood as the view that for any t and any w, if [p at t in w] is grounded in Ct,w, then for any t* and any w*, if all the fixed facts in Ct*,w* obtain then so does [p at t* in w*]. All of my arguments apply within this alternative framework. Similar comments apply to a 'mixed' view which instead takes a world-indexed grounding relation to hold between facts with embedded temporal indices, although I shall largely set these and other variants aside. 6 See Trogdon (2013) for a discussion of different varieties of grounding pluralism. 7 On a rival view, grounding instead holds only between worldly 'states-of-affairs' that serve as truthmakers for true propositions: cf. Audi (2012a, b). 8 Cf. Correia (2010, §1.1). 720 A. Skiles 123 relates anything other than facts, I will set aside arguments that build on putative cases of grounding between other kinds of entities.9 Finally, I will make a couple of assumptions about the logical form of grounding statements: namely, that ''...is grounded in...'' is a non-contrastive predicate that must be flanked by a single fact on the left-hand side. At points I will briefly discuss how my arguments are affected when these assumptions are relaxed.10 3 Against Grounding Necessitarianism: Theseus-Style Rearrangement It is natural to think of ordinary composites-macroscopic items of everyday experience like trees, tables, and tigers-as somehow 'ontologically dependent' on the existence and features of the many parts that compose them.11 For instance, Conee and Sider (2005, p. 68) point to this phenomenon to help convey what ontological dependence is more generally: The idea eludes precise definition, but it has one clear sort of illustration. Consider a tuna salad sandwich. At any given time, the sandwich derives its existence from the existence of the bread, the tuna salad, and any other ingredients that compose it. Without them, it would be nothing. The sandwich's ingredients do not cause it to exist. Rather, they give it existence directly. The sandwich 'ontologically depends' on its ingredients. The relevant variety of ontological dependence is notoriously slippery to capture. It is too strong a constraint to say (as Conee and Sider do here) that it ''would be nothing'' without the existence of these particular ingredients: destroying the tomatoes, e.g., does not destroy the sandwich. Yet it is too weak a constraint to say that the sandwich ''would be nothing'' without the existence of some or other ingredients of the relevant kinds: it ontologically depends upon its own ingredients, not those of a distinct yet similarly constructed sandwich. To capture ontological dependence of this variety, an attractive strategy instead appeals to grounding: for x to ontologically depend upon the ys is for there to be a collection of facts about the ys that the existence of x is grounded in.12 In this section, I will argue that the ontological dependence of ordinary composites on their parts is a case of grounding without necessitation. I will make use of some terminology. Suppose that o is an ordinary object composed of a collection of objects, the as, at time t. Say that a collection of facts, C, is an arrangement of the as iff each fact in C solely concerns the intrinsic properties of, or causal and spatial relations holding between, the as. Say that the as are in this arrangement at t iff all facts in C obtain at t. Finally, say that a scenario of 9 Schaffer (2010a, §4) constructs such an argument. 10 Schaffer (2012) and Dasgupta (2014) criticize the first and second assumptions respectively. 11 By ''part'' I mean proper part: x is a part that is distinct from y. By ''composes'' I mean properly composes: each of the xs is a proper part of y, and each part of y shares a part in common with ('overlaps') some of the xs. 12 See Correia (2005) and Schnieder (2006) for accounts of ontological dependence along these lines. Against Grounding Necessitarianism 721 123 rearrangement with respect to such a C is any temporal interval during the history of a world at which the as are in an arrangement at some initial short duration t of that interval, in that arrangement at a concluding short duration t* of that same interval, but are not in that arrangement between t and t*. The argument against necessitarianism may then be formulated as follows, where o is some ordinary composite composed of the as: The rearrangement argument against grounding necessitarianism: (P1) The existence of o is grounded in C, some arrangement of the as, at t. (P2) There are scenarios of rearrangement with respect to C at the end of which o does not exist. Thus: Grounding necessitarianism is false. Call this the rearrangement argument. The thought behind it is simple: even though the existence of at least one possible ordinary composite is grounded in the arrangement of its parts at one time, it is possible for these parts to 'scatter' and come back into that arrangement at another time without that ordinary composite existing as a result. Since necessitarianism entails that it must exist if its parts are in that arrangement, the view is false. The scenario of rearrangement I will focus upon-call it the sandwich of Theseus-is a spin on a widely discussed case in literature on the metaphysics of material composition. Let ''o'' pick out a particular tuna sandwich. Suppose that in an earlier epoch, the existence of o is grounded in an arrangement of its parts, the as (call this arrangement ''C''). At a later epoch, one of the as (call it ''a1'') is sloughed off and replaced with a duplicate (call it ''b1''). There is now a sandwich composed of b1, a2, ..., an; this sandwich (call it ''o1'') is presumably identical to o. Suppose this process of gradual replacement repeats so that eventually in a later epoch, we are left with two sandwiches: one (call it ''on'') identical to o and composed of b1, b2, ..., bn, but also another sandwich (call it ''oR'', for replacement) composed of a1, a2,..., an and placed in the same arrangement, C, they were in when they composed o in the earlier epoch. Finally, o is destroyed, leaving oR unscathed. Although all the facts inC obtain during this later epoch, [o exists] does not; hence although the existence of owas grounded in these facts about its parts, they do not necessitate o's existence.13,14 In setting up this Theseus-style scenario, I have assumed that the existence of an ordinary composite is grounded in an arrangement of its spatial parts, which compose it not atemporally but rather relative to a given time.15 But similar 13 DeRosset (2013b) independently discusses a version of this argument, but takes it to undermine the claim that o is grounded in an arrangement of its parts. He considers several strategies for supplementing these facts in order to yield necessitating grounds that I will discuss momentarily. 14 Another scenario of rearrangement is the recycling scenario (cf. McKay 1986). Suppose that in an earlier epoch the existence of o is grounded in C. Afterward, o rots and as a result permanently ceases to exist as the as scatter throughout the environment. But millennia afterward in a later epoch, the as come back into the arrangement they were once in during the earlier epoch, composing a new sandwich distinct from the original. Here again, it seems plausible to say that all the facts in C obtain during this later epoch, [o exists] does not. 15 I will also assume that composition fails to be contingent in the following sense: if the as are in some arrangement when they compose o, then necessarily, the as compose at least some object whenever they 722 A. Skiles 123 scenarios can be constructed if instead it is assumed that its existence is grounded in facts about the temporal parts that compose it atemporally. Instead of imagining the replacement of spatial parts across a sequence of times, we imagine the replacement of temporal parts across a sequence of worlds. Suppose that in world w, the existence of o is grounded in an arrangement of its temporal parts, the as (call this arrangement ''C''). Next consider a world w1 at one of the as (call it ''a1'') has been replaced by a duplicate (call it ''b1''). Hence in w1, there is a sandwich composed of b1, a2, ..., an; this sandwich, call it ''o1'', is presumably identical to o. Suppose this sequence of worlds has as its final member a world wn that contains two sandwiches: one (call it ''on'') identical to o and atemporally composed of the bs, but also another (call it ''oR'') atemporally composed of the as in the same arrangement, C, as they were when composing o in the first world of the sequence. Finally, imagine a world exactly like the previous in the sequence except that o and the bs that compose it do not exist, with no other differences to oR and the as. Although all the facts in C obtain at this world, [o exists] does not. Hence, although the existence of o would have been grounded in these facts at one world, they do not necessitate o's existence.16 That said, given the clear structural similarities between the two cases, for simplicity's sake I will focus on the first Theseus-style case and the mereological assumptions used to state it (and suppress time/world indexing mereological notions whenever possible). Broadly speaking, the necessitarian can resist the rearrangement argument in one of two ways. One strategy is to reject that there is any arrangement of an ordinary composite's parts that its existence could be grounded in: facts about the intrinsic properties of and causal and spatial relations between its parts are just not enough. This is to deny (P1). The other strategy is to claim that the relevant ordinary composite does exist at the end of the scenario of rearrangement described above. This is to deny (P2). In the following two subsections, I will defend the rearrangement argument against both kinds of response. 3.1 In Defense of (P1) One obvious way to reject (P1) is to deny that o exists. If o does not exist, then the existence of o cannot be grounded in an arrangement of the as, contrary to (P1). This response is available to only the most extreme proponents of compositional nihilism-the thesis that there are no composites-whereas less extreme (and more popular) theses in the neighborhood of compositional nihilism do not escape. One way to be less extreme is to deny the existence of ordinary composites except for living organisms (cf. van Inwagen 1990), or except for those possessing nonredundant causal powers (cf. Merricks 2001). But if there are scenarios of Footnote 15 continued are in that arrangement. This is a friendly concession to the necessitarian: if composition were contingent, then one could argue that [o exists] is not necessitated by the arrangement of the as without recourse to scenarios of rearrangement. For defense of the contingency of composition, see Cameron (2007). 16 Note as well that this 'cross-modal' Theseus-style case also poses a challenge for the necessitarian who opts for a world-indexed but not time-indexed grounding relation, regardless of whether temporal indices are embedded in the relevant facts (see fn. 5). Against Grounding Necessitarianism 723 123 rearrangement involving sandwiches, then there will also be scenarios that involve trees, dolphins, or human bodies. Another less extreme way to deny (P1) by appeal to compositional nihilism is to claim that although composites do not exist, propositions expressed by ordinary statements about the existence of composites are nonetheless strictly and literally true.17 However, let p be the proposition ordinary expressed by the sentence ''o exists''. Presumably, the fact that p is true is grounded in some arrangement of the as.18 If so, then rather than considering scenarios of rearrangement at the end of which o does not exist, one can consider instead scenarios of rearrangement at the end of which p is not true. The rearrangement argument may then proceed exactly as before. A more subtle way to deny (P1) is to claim that even though o exists, there is no such fact as [o exists]. For instance, one might deny that there are 'haecceistic facts' about particular individuals such as this one. Audi (2012b, pp. 700–701) adopts a different tactic, and argues that there are no facts about existence in general to be grounded, since there is no such property as being an existent thing to be a constituent of such facts. I have two replies. The first is to note that I do not (or at least need not) assume that being an existent thing is a genuine property that is a constituent of the fact [o exists]. I need only assume that for o to exist is for there to be something that is o; I need not also assume that for something to be o involves the instantiation of a distinctive property of some kind by o. The second reply is to again note that even if there is no such fact as [o exists], presumably there is such a proposition as the one expressed by ordinary utterances of ''o exists'' that the argument may be run with instead, in just the manner I described before.19 Yet another way to deny (P1) is to claim that the existence of an ordinary composite is grounded not in the arrangement of its parts, but rather in facts of some other sort. One extreme extrinsic way to deny this is to claim that every fact (and thus every fact about the existence of an ordinary composite) either is or is ultimately grounded in features of the entire universe as a whole. That is, one may 17 For discussion of the motivations of 'reconciliatory' compositional nihilism and their varieties, see van Inwagen (1990, ch. 10–11), Cameron (2008), Bennett (2009), Williams (2012), and Sider (2013). 18 An alternative view would take the fact that p is true to be grounded in some arrangement of the as plus various facts about the representational properties of p. Since these latter facts will (presumably) remain fixed throughout the scenario of rearrangement, adopting this view will make no substantive difference to the case at hand. 19 Elsewhere, Audi argues that although there are facts about the truth of particular propositions, these facts are not grounded. If Audi is correct, then one cannot reformulate the rearrangement argument in terms of propositions, as I have claimed. According to Audi, the fact that p is true just is the conjunctive fact that (i) p corresponds to a worldly state-of-affairs and (ii) this state-of-affairs obtains, and ''where there is identity, there is no grounding'' (2012a, pp. 16–17). However, Audi's argument is not valid. At best, it follows that the fact that p is true is not grounded in the conjunctive fact that these two conditions hold. It does not follow that the fact that p is true is not grounded in anything at all. In particular, presumably if Audi is correct that this is a conjunctive fact, it is grounded in its conjuncts, as conjunctive facts are grounded in general (recall our discussion in §2; also cf. Audi 2012b, fn. 23). If so, then the arguments in the past two paragraphs apply. 724 A. Skiles 123 reject (P1) by endorsing a view similar to a much-discussed one that Schaffer (2010a, b) calls priority monism. Rather than attempting to appraise the truth of priority monism, I wish to take a different approach. I instead argue that even if priority monism were true, there is no non-objectionable way to appeal to priority monism in order to evade the rearrangement argument. Although priority monism is an exotic thesis to consider, it will be instructive: less extrinsic strategies for resisting (P1), it turns out, are subject to similar difficulties. The priority monist claims there to be but one ontologically independent (actual, concrete) entity: the unique composite that has every other (actual, concrete) entity as a part. Call this entity ''u''. In order to reject (P1), the priority monist has one option available. The priority monist must claim that there is at least one obtaining fact with the following two features: (i) it specifies some relation that u bears to that particular ontologically dependent individual, and (ii) is fundamental (i.e., not itself grounded in further facts). Why? The remaining two options-to either take [o exists] to be grounded only in derivative (i.e., non-fundamental) facts, or else grounded in facts that do not specify how u relates to o in particular-fail to evade Theseus-style scenarios. Suppose first that C contains only facts that do not involve o. Since one can construct the scenario so that these are the same at end of the rearrangement as they are at the beginning (e.g., by taking care to locate oR in the later epoch exactly where o once was in the earlier epoch), a difference in whether o exists at the beginning and end of the rearrangement cannot be accounted for by a difference in facts such as these. But these o-involving facts must also be fundamental. Suppose one were to account for the difference in whether o exists at the beginning and end of the rearrangement by noting that o is composed of the as at the beginning of the rearrangement but not at the end. If this compositional fact were derivative, it would be as much in need of a necessitating ground, one that (by reasoning as above) must include facts that involve o. Since the o-involving fact must be fundamental, and if priority monism is true only if every fundamental fact is a fact about the features of u, then this fundamental fact in particular must concern how u relates to o in particular. However, at least two difficulties emerge if the monistic necessitarian is forced to reject (P1) in this manner. The first is that it opens her up to all manner of objections for positing a massive amount of antecedently undiscovered fundamental facts concerning every tree, rock, bridge, lizard, or other ordinary composite subject to a scenario of rearrangement. Some would reject such posits by appealing to the principle that no ontologically dependent entity be involved in any fundamental fact; though controversial, the principle is widely held.20 Less controversially, rejecting (P1) may be consistent with priority monism, but seems to undermine one of its main motivations: namely, that it requires only a relatively sparse inventory of entities in order to characterize what reality is like at the fundamental level. Finally, even if there is nothing intrinsically objectionable with rejecting (P1) in this 20 Bennett (2011), Sider (2012), deRosset (2013a), and Cameron (forthcoming) all endorse principles that entail that there are no fundamental facts about non-fundamental entities (which, presumably, would extend to ontologically dependent entities). Against Grounding Necessitarianism 725 123 manner, it is a count against the monistic necessitarianism relative to the contingentist, who need not posit this immense array of fundamental facts. The second difficulty is this. Suppose the monistic necessitarian grounds the existence of o in the fact that o is part of u. Then the monist necessitarian is committed to saying that o plays a role in grounding its own existence. But this I find incoherent. It seems no more plausible to say that o plays a role in causing its own existence in virtue of how I interacted with o prior to pushing the bread, tuna, and tomatoes together, than it is to say that o plays a role in grounding its own existence in virtue of how u relates to o at lower levels of metaphysical fundamentality. (If anything, it is the reverse: what makes o capable of bearing relationships to other entities is at least partly the fact that o exists, not vice versa.) Just as o can only be caused to exist by temporally prior entities, o can only be grounded in facts about more fundamental entities. But no entity is more fundamental than itself. Thus the monistic necessitarian cannot evade (P1) by asserting that the existence of o is grounded in facts involving o itself. So far I have only raised difficulties for the monistic necessitarian's response to (P1). Yet essentially the same problems afflict other necessitarian attempts to deny (P1). First, one might take the existence of o to be at least partially grounded in fundamental facts involving o. There are a number of options available: perhaps the partial ground is the fact that the as compose o, or the fact that the as are exactly colocated with o, or the fact that the as instantiate the 'individual form' of o. But all these options are subject to the same two objections the monistic necessitarian faced: they posit an immense array of fundamental facts that the contingentist can do without, and entail that a particular could play a role in grounding its own existence. Second, one might take the existence of o to be at least partially grounded in derivative facts involving o. However, this maneuver not only fails to avoid o 'bootstrapping into being', but has the additional problem that this new derivative fact about o is as in want for necessitating grounds as the fact that o exists, while merely forestalling the very same unattractive options when faced with Theseusstyle scenarios. For instance, a difference in whether the as compose o at the beginning and end of the rearrangement cannot be accounted for by a difference in fundamental facts about how o is related to the as (since this involves illicit 'bootstrapping into being''), nor in fundamental facts that do not involve o at all (since these facts are preserved throughout the scenario). Third, and building on the previous observation, taking the sought-after partial ground to be any facts not involving o will be a wash. For example, if the existence of o is taken to be grounded in the arrangement of the as plus the fact the as compose a tuna sandwich, this supplemented ground for the existence of o faces scenarios of rearrangement no less than one gets from taking its existence to be grounded in the arrangement of the as alone. What about facts about how o originated in the relevant scenario? Although there has been extensive discussion of what Thomas McKay (1986) calls ''constitutional sufficiency principles'', which aim to specify what is sufficient for a particular composite to exist by appeal to facts regarding its material origin, a growing 726 A. Skiles 123 consensus has emerged that they succumb variations on Theseus-style reasoning.21 Facts that specify the time and place at which o happens to originate do not necessitate its existence. (Suppose it originates at time t. Then consider a scenario of rearrangement that begins with an earlier time than t, but then concludes at t. Of course, one might respond that o's exact time and place of origin is essential to it, but this is prima facie implausible.) Nor do facts that specify the manner in which o originated necessitate its existence. (Suppose o originates due to the creative intentions and recipe of a particular chef. Then consider a scenario of rearrangement in which the chef prepares oR from the same recipe and with the same creative intentions.) Nor do facts that specify how many sandwiches originated before o did. (Suppose that o was preceded by an infinite number of similarly constructed sandwiches-or, if this is impossible for sandwiches, for ordinary composites of another sort. Then oR would have been preceded by the same number of sandwiches as o.) Even if there is no general argument against all conceivable principles of constitutional sufficiency, the continual failure to devise a true one has led Guy Rohrbaugh and Louis deRosset, among many others, to conclude that the project is ''deeply problematic'' (2006, p. 458). It would likewise be deeply problematic for the necessitarian were she to commit herself to supplying such a principle. This completes my defense of (P1). I have not attempted to argue that the existence of an ordinary composite must be grounded in the arrangement of its parts, nor that there is no plausible strategy for rejecting this claim while maintaining necessitarianism. However, what I have shown is that the prospects of responding to the rearrangement argument on this basis look grim. 3.2 In Defense of (P2) What about (P2), which entails that o does not exist at the end of a scenario of rearrangement? An argument in defense of this claim can be constructed as follows. (Recall from the previous subsection that o is composed of a1, a2, ... at the start of the scenario, that on is composed of b1, b1, ... after the gradual replacement of a1, a2, ... and before its annihilation, and that oR is composed of a1, a2, ... as they are reassembled.) The assured destruction argument in defense of (P2): (P2a) o, o1, o2, ..., on, and oR all exist. (P2b) o, o1, o2, ..., on are pairwise identical. (P2c) on is distinct from oR. (P2d) If o is identical to on, and on is distinct from oR, then o is distinct from oR. (P2e) If o exists at the end of the sandwich of Theseus scenario, then o is distinct from oR. Thus: o does not exist at the end of the sandwich of Theseus scenario. Call this the assured destruction argument. The necessitarian who rejects its conclusion must commit to at least one extremely implausible claim about the 21 See Hawthorne (2006), Damnjanovic (2010), and the long list of references in Rohrbaugh and deRosset (2006). Against Grounding Necessitarianism 727 123 metaphysics of ordinary composites. One who denies (P2a) must claim either that none of o, o1, o2, ..., on, and oR exist, or claim that the loss of just one individual as a part (even if replaced with a qualitative duplicate that retains all internal causal and spatial relations) would make the difference as to whether any given ordinary composite exists. One who denies (P2b) yet rejects counterpart theory-which does not help escape (P2) anyway, or so I argue below-must claim either that at least one of o, o1, o2, ..., on, goes out of existence when a qualitatively duplicate part is replaced, or claim that they all exactly coincide with on, or claim that it is impossible for ordinary composites to persist through the exchange of a single part for a qualitative duplicate. One who denies (P2c) must claim that on is not only wholly located at one sandwich-shaped region, but also wholly located at the sandwich-shaped region that oR is wholly located at. One who denies (P2d) must claim that the relation of identity fails to be both symmetric and transitive.22 And finally, one who denies (P2e) must claim, regardless of whether o is identical to on or coincident with it, that even if one vaporizes everything in the sandwich-filled region o occupies, o would survive and come to be exactly coincident with oR. I take it that it would be a serious cost for necessitarianism if it were forced into any of these claims, which are either ad hoc or intrinsically implausible (or both), and at any rate are not commitments that the contingentist is forced to take. An initially promising alternative strategy for the necessitarian is to instead appeal to temporal counterpart theory.23 On this view, ordinary composites are 'stages' bound to a single instant, yet exist and have properties at different times in virtue of having counterparts at earlier or later instants with those properties. The counterparts of o at a time t, if it has any, are those stages that exemplify the highest degree of comparative overall similarity to o at t, where the respects of similarity and how they are weighted depends on how o is referred to or described in contexts in which the relevant de re ascriptions are evaluated.24 Appealing to temporal counterpart theory can help one evade the assured destruction argument in at least two ways. First, one may reject (P2b) by noting that even though o has o1 as a counterpart, o1 has o2 as a counterpart, ..., it does not follow that o has on as a counterpart. Second, one may reject (P2d) by claiming that o has both on and oR as counterparts during the penultimate epoch, and that oR is the counterpart of o in the last epoch. However, there is a serious difficulty with the necessitarian appealing to this response. Recall that necessitarianism is itself a temporal de re statement; if so, the thesis must be reformulated to fit the counterpart-theoretic framework, and the reformulation itself must be true across every relevant context. Say that [...x...], a fact that obtains at t, has [...y...] as a counterpart fact at time t* relative to context 22 Suppose for reductio that o = on, that on = oR, and yet that o = oR. Since identity is symmetric, o = on entails on = o. But since identity is transitive, on = o and o = oR jointly entail on = oR (contradiction). 23 See Sider (2001) for defense. 24 Or at least, according to the version of the view I will consider here. Variants that postulate other semantic or pragmatic mechanisms for selecting from the multiplicity of relevant counterpart relations, face variants of the problem I raise for the version I discuss in the text, so I set them aside here. Thanks to Ghislain Guigon for discussion about this point. 728 A. Skiles 123 C iff (i) x has y as a counterpart at t* relative to C, (ii) for any open formula 'u', [...x...] is identical to the fact that u(x) iff [...y...] is identical to the fact that u(y), and (iii) [...y...] obtains at t*. Then necessitarianism is true relative to C only if the following thesis is true at C as well: Grounding necessitarianism (counterpart-theoretic) For any time t, if [p] is grounded in C at t, then for any time t*, if the facts in C have counterpart facts at t*, then [p] has a counterpart fact at t*. Now, the necessitarian cannot say that this thesis is true with respect to all contexts, no matter how disjunctive and gerrymandered the kind of comparative overall similarity selected as relevant by that context. It is too easy to generate contexts in which the arrangement of the as have counterpart facts at a later time, yet [o exists] does not. (For instance, just allow C to be the highly unselective context that takes the xs to have the ys as counterparts at a later time t* iff there are no tuna sandwiches and the ys are any arbitrary group of things that exist at t* we please.) Yet if counterpart-theoretic necessitarianism is only required to be true relative to some contexts, presumably the restricted class at least includes ordinarily salient contexts. But here again, it is not hard to find contexts in which the thesis is false. (For instance, suppose that o, on, and oR are human bodies rather than tuna sandwiches, and let C be a context that requires there to be a high degree of psychological continuity and connectedness between o and its later counterparts. Then even though on counts as a counterpart of o in the penultimate epoch of the scenario of rearrangement relative toC, oRdoes not count as a counterpart of o in the last epoch of the scenario relative to C, since oR lacks the relevant psychological continuity and connectedness with o.) But if counterparttheoretic necessitarianism cannot even be required to be true in all ordinarily salient contexts, then it is unclear how the class of contexts can be delineated in a manner that is neither ad hoc nor falsifies the view. It is a challenge, at any rate, that the contingentist completely evades. This completes my defense of (P1) and (P2). Since (P1) and (P2) entail that necessitarianism is false, I conclude that necessitarianism is false. In the following section, I consider another case of grounding without necessitarianism. 4 Against Grounding Necessitarianism: Restricted Accidental Generalizations A longstanding philosophical puzzle is to identify which facts could serve to ground the countless general facts about the world. (By a general fact, I include 'positive' facts with the logical form [Vxu], as well as 'negative' facts that take the logical form [:Axu], with ''u'' an open formula in which ''x'' occurs unbound; however, I will focus on positive general facts throughout.) The primary source of this puzzlement is that any general fact that only contingently obtains is neither logically entailed, nor metaphysically necessitated, by any collection of non-general facts about the particular individuals that happen to fall under it. Let F be the property being less than 30 billion years old, and let a, b, ... exhaustively list everything there is in w@ (i.e., the actual world). Then even the unfathomably large collection of facts [Fa], [Fb], ... fails to necessitate that there is nothing besides a, b, ..., and Against Grounding Necessitarianism 729 123 thus fails to necessitate that there is nothing besides a, b, ... that does not have F.25 (To convince yourself, consider a world just like w@, yet that contains a single particle older than 30 billion years.) But it would be bizarre to say that [VxFx] is not grounded at all. Yet if every fact is necessitated by the facts that ground it, what could serve as its ground? Thus the puzzle.26 In this section, I argue that the grounding of a specific class of general facts poses a problem for necessitarianism. Before delving into the details, I should note that I am not the first to argue that general facts pose this trouble. What is novel about my approach is which class of general facts it focuses upon. Anti-necessitarians, reflecting on instances of the puzzle above, have typically focused solely upon what I call unrestrictedly general facts-facts with the form [VxFx], which intuitively concern absolutely everything-and argue that at least some are grounded in, but not necessitated by, the collection of their factual instances.27 Although I am sympathetic to this spin on argument, these critics overlook a stronger argument that instead concentrates upon what I call restrictedly general facts-facts with the form [Vx(Fx ? Gx)] which intuitively concern only the restricted domain of things that have F.28 In what follows I argue that restrictedly general facts pose a tougher difficulty for necessitarians than unrestrictedly general facts because the former are resistant to the standard countermeasures that necessitarians use to deal with the latter. 4.1 The w-Instance Proposal The restrictedly general facts I focus upon are more colloquially known by philosophers as accidental generalizations. For our purposes, let us say that [Vx(Fx ? Gx)] is an accidental generalization iff it obtains in w@, yet fails to obtain in a world that both has the same laws of nature as w@ and contains an F. 29 There is an immense number of such facts regarding myriad kinds of things. Here are just three: (3E) [Vx(x is a swan in Switzerland ? x is white)] (4E) [Vx(x is a tree on Notre Dame's campus ? x is less than 105 feet tall)] 25 I will assume the falsity of necessitism: the view that it is necessarily the case that everything necessarily exists, pace Williamson (1998) and Linsky and Zalta (1994). 26 For proto-instances of this puzzle, see Russell (1985) and Wittgenstein (1990). 27 For example, see Bricker (2006) and Leuenberger (2013). 28 An alternative take on the logical form of restrictedly general facts is that they are expressed with sentences generated by prefixing an open formula with a restricted quantifier expression, i.e. sentences like ''[Vx: Fx]Gx'' (the brackets are standard for restricted quantifier notation, not meant here to refer to facts). One may work with this alternative view instead without affecting the arguments to come. 29 The second clause corrects a problem with how 'accidental generalization' is defined by Chudnoff (manuscript), who independently offers these as counterexamples. If F, and thus any fact that has F as a constituent, does not exist at worlds in which F is not instantiated, then if this second clause is not included, non-accidental generalizations such as [Vx(Fx ? ::Fx)] do not obtain, since they do not exist, at nomologically possible worlds in which nothing is F. I explain why I find Chudnoff's use of accidental generalizations against necessitarianism unconvincing in fn. 33. Heil (2003) and Mellor (2003) argue that accidental generalizations undermine truthmaker necessitarianism; however, neither author considers the full range of responses nor do they extend their arguments to grounding necessitarianism. 730 A. Skiles 123 (5E) [Vx(x is a solid gold sphere ? x is less than a kilometer in diameter)] The necessitarian's difficulty is the following. Suppose [Vx(Fx ? Gx)] is an accidental generalization that obtains at w@. If a, b,... are exactly the things that are F at w@, then say that the collection of facts [Ga], [Gb] ... comprise the instances of [Vx(Fx ? Gx)] at w@. Now, assume momentarily that this accidental generalization exists and is grounded at w@. Then a natural proposal is to take it to be grounded in the collection of all its instances at w@. Call this the w-instance proposal.30 (Note that this leaves open whether this fact is also grounded in other collections of facts.) If this proposal is true, then necessitarianism is false. Take (3E): although this accidental generalization is grounded in its instances at w@, its instances also all obtain at a world, w, that is just like w@ except that I have smuggled a bevy of black swans from Australia into Geneva, and thus they all obtain at a world in which not every swan in Switzerland is white. Why believe that the w-instance proposal is true? My defense proceeds in two steps. First, I will motivate the w-instance proposal against several initial objections. Second, I will argue against rival proposals designed to be necessitarian-friendly, and against those who reject my presupposition that accidental generalizations not only exist but are also grounded. Since these exhaust the options, I conclude that the w-instance proposal is true and necessitarianism is false. Initial support for the w-instance proposal derives from what may be called the metaphysical primacy of the particular to the general. Happenstance patterns of regularity seem neither brute nor inexplicable; rather, they seem to derive from particular facts about the individual swans, trees, and chunks of gold they concern. Assuming these facts are ultimately grounded in particular facts about fundamental entities, the w-instance proposal preserves this natural thought about what anchors reality at rock bottom.31 A helpful way to test this intuition is to imagine which facts would be minimally sufficient for a God to decree in order to create the rest of reality from the ground up. In order to thwart the temptation of His creatures towards false idolatry and excessive greed, suppose the God decides to make it the case that every solid gold sphere (call this property ''F'') be less than a kilometer in diameter (call this property ''G''). The God considers the following two divine directives: (1D) God first decrees that a, b, ... be F Then for every x that is F, God decrees that x also be G 30 For reasons I get into later in fn. 38, I actually endorse what could be called the augmented winstance proposal, which adds as a partial ground the second-order fact that [Ga], [Gb], ... are instances of [Vx(Fx ? Gx)]. However, the difference between the two will not matter for what follows. 31 The intuition is expressed most audaciously in Lewis's classic statement of Humean supervenience: ''It is the doctrine that all there is to the world is a vast mosaic of local matters of particular fact, just one little thing and then another [...] we have an arrangement of qualities. And that is all. There is no difference without a difference in qualities'' (1986, pp. ix–x). However, I wish to remain neutral about whether it extends beyond accidental generalizations, which kinds of properties appear in the fundamental facts (for Lewis, these ''need nothing bigger than a point at which to be instantiated''; ibid., p. xi), and which kinds of individuals these properties are ascribed to. Against Grounding Necessitarianism 731 123 (2D) God first decrees that a, b, ... be F. Then God decrees that a, b, ... be the only things that are F. Then, finally, for every x that is F, God decrees that x also be G To make [Vx(Fx ? Gx)] obtain, all the God has to do is decree that a be F, that b be F, and so forth-and then just stop-and to then decree that a be G, that b be G, and so forth-and again, then just stop. It is of course true that if the God acts in this manner, this will also be the case that every F is G. Given the pattern in the God's decrees creating particular matters of fact, the God does not need to issue a special additional decree to this effect. The second decree listed in (2D) thus seems to be entirely superfluous to guaranteeing a minimally complete base. Since every fact is grounded in a collection of facts from the minimally complete base, the second decree listed in (2D) therefore also seems to be entirely superfluous to grounding [Vx(Fx ? Gx)]. It is tempting to infer that the God's acting in accordance with (1D) somehow implicitly relies on its also acting in accordance with (2D). The temptation begins with a correct observation: that [Ga], [Gb], ... do not ground [Vx(Fx ? Gx)] unless a, b, ... exhaust the things that are F. The temptation is to then infer that [Ga], [Gb], ... therefore must be supplemented by the fact that a, b, and so forth do exhaust all the things that are F in order to yield the full ground for [Vx(Fx ? Gx)]. So even though the God's acting in accordance with (1D) necessitates that this holds (so the thought goes), the God must act in accordance with (2D) in order to genuinely make it the case. Tempting as it is, this inference should be resisted. First, it fails in corresponding cases in which a collection of events causally makes an accidental generalization the case. Suppose that there are two lamps in my office. I can causally make it the case-all by myself-that every lamp in my office is on by flicking on one lamp and then the other-and then just stop-without also making it the case that they are the only lamps in my office. (My officemate was causally responsible for this.) But if the inference fails when a collection of events causally makes some accidental generalization the case, it is hard to see why it would be valid when a collection of facts non-causally makes an accidental generalization the case without substantive further argument. Second, it does not follow in general that if C does not ground [p] unless the facts in C have a certain feature, then they must be supplemented by the fact that these facts have that feature to yield a ground for [p]. For instance, since grounding is factive, a trivial necessary condition for [p] and [q] to partially ground [p ^ q] is that [:p] and [:q] not obtain. But it does not follow that [p] and [q] must be supplemented with a further fact, i.e., [[:p] and [:q] do not obtain], to yield a ground for [p ^ q]: [p] and [q] suffice. So far I have only argued that the w-instance proposal is intuitively motivated and defensible. But are there alternatives to the w-instance proposal that are not only equally attractive but also compatible with necessitarianism? In the next section, I will argue that the answer is no. 732 A. Skiles 123 4.2 Alternatives to the w-Instance Proposal Rosen (2010, §8) suggests three strategies that the necessitarian can pick and choose between when grappling with general facts. The first two strategies certainly will not help deal with accidental generalizations. The first is to claim that [Vx(Fx ? Gx)] is grounded in relationships that hold between F and G in virtue of the essential nature of the two properties, such as when the nature of triangularity is plausibly said to ground the fact that triangles all have three angles (ibid., p. 120). Call this the essentialist proposal. The second is to claim that [Vx(Fx ? Gx)] is grounded in facts about the laws of nature linking F with G, such as when Newton's law of gravitation is plausibly said to (or at least would plausibly be said to, had it obtained) ground the fact that massive bodies attract each with a force inversely proportional to the square of their distance (ibid., pp. 119–120). Call this the nomic proposal. Even ignoring the implausibility of saying that there are essential or nomological relationships between the properties described in (3E)–(5E), the problem with both of the proposals is that the postulated grounds would obtain at all nomologically possible worlds at which the relevant properties are instantiated. So if necessitarianism were true, the accidental generalizations these facts ground would obtain at all nomologically possible worlds as well. But then (3E)–(5E) would not be accidental generalizations. Both proposals are therefore non-starters. The third strategyRosenproposes is themorepromisingoneofpositing as fundamental what Armstrong (1997) famously calls a totality fact. Philosophers have called many different kinds of facts ''totality facts''; for themoment, by ''totality fact'' I simplymean a specific kind of general fact. Just as one should distinguish between restricted and unrestricted general facts, one should also distinguish between restricted and unrestricted totality facts. An unrestricted totality fact is one that takes the logical form [Vx(x = a_ x = b_...)], where a, b,... are everything there is at a givenworldw, while a restricted totality fact takes the logical form [Vx(Fx ? (x = a _ x = b _...)], where a, b,... are everything that is F at w. To make the discussion more compact, some terminology: let ''[X(w)]'' and ''[XF(w)]'' pick out unrestricted and restricted totality facts, respectively. As Rosen notes, unrestricted general facts pose no difficulty for necessitarianism if each is grounded in its instances at a world w plus an unrestricted totality fact, [X(w)]. If a, b, ... are all F, and a, b, ... are everything, then this collection of facts necessitates that everything is F.32 However, this proposal-call it the unrestricted totality fact proposal-fails to work with accidental generalizations. Let F be the property being a tree on Notre Dame's campus, and let G be the property being less than 105 feet tall. Suppose [Ga], [Gb], ... obtain for everything that is F. And finally, suppose that [Ga], [Gb], ..., along with [X(w@)], together ground [Vx(Fx ? Gx)] at w@. Then [Vx(Fx ? Gx)] still fails to be necessitated by its grounds. For let w be a world just like w@, except that Notre Dame has annexed the Sequoia National Forest. Since everything that is F and G at w@ is also F and G at w, it follows that [Ga], [Gb], ..., all obtain at w. Furthermore, [X(w@)] obtains at w as well. For the exact same inventory of things exist at w@ and w. The only difference is that there are things that are F at w but not in w@ (namely, the trees in 32 Rosen (2010, pp. 120–121); cf. Trogdon (2013a, §4). Against Grounding Necessitarianism 733 123 the Sequoia National Forest), and facts that are obtain at w@ but do not at w (namely, the fact that every F is G). So it follows that [Ga], [Gb], ..., along with [X(w@)], all obtain at w but not [Vx(Fx ? Gx)]. Thus supplementing the instances of [Vx(Fx ? Gx)] with an unrestricted totality fact does not bridge the gap between grounding and necessitation. A natural proposal is to claim that an accidental generalization is grounded in its instances plus a restricted totality fact, [XF(w@)]. This is the restricted totality fact proposal. There are many implementations of this proposal, each differentiated by which property F is taken to be. I will focus on perhaps the most natural implementation: namely, to take F to be the property the accidental generalization requiring a necessitating ground is restricted by. Consider (3E); let F be the property being a swan in Switzerland and let G be the property being white. Then if a, b, ... are only the things that are F, one may take the ground of [Vx(Fx ? Gx)] to be the collection of facts consisting of [Ga], [Gb], ... plus the fact that a, b, ... are, in fact, the only Fs. However, there is an immediate problem with this implementation: the fact that these are the only things that are F is itself an accidental generalization, one in need of a necessitating ground. (I take it to be undesirable in the extreme to say that it is a fundamental fact that these particular individuals are the only swans in Switzerland, and even more so-if the proposal is generalized-to say the same for accidental generalizations about trees, tables, cats, etc.) This proposal thus needs a necessitating ground for [XF(w@)] in order to provide a necessitating ground for [Vx(Fx ? Gx)]. However, the one obvious way to do so-that does not simply press the need another step back-problematically reverts back to the unrestricted totality fact proposal. That is, one may say that [XF(w@)] is grounded in the immense collection of facts specifying which things are F, which things are not F, and which things there are altogether. Although this collection necessitates [Vx(Fx ? Gx)], it does so only by virtue of introducing facts that seem entirely irrelevant to making it the case. Facts about the Eiffel Tower, about each particular zebra in Zaire, and about pieces of rock buried deep within the Moon's surface intuitively play no role at all in making it the case that every swan in Switzerland is white. (Here I assume that partial grounding is transitive-i.e., that what partially grounds what partially grounds an accidental generalization also partially grounds that accidental generalization. More on this claim momentarily.) Moreover, the fact that the Eiffel Tower is not a swan in Switzerland itself requires a necessitating ground. (I take it that there are no fundamental facts about the Eiffel Tower, let alone about which properties it lacks.) Presumably, the necessitating grounds of this fact have to do with facts about the essential nature of iron statues; but again, these facts intuitively play no role whatsoever-let alone an essential role-in making it the case that every Swiss swan is white. The only facts that seem to play an essential role in making this accidental generalization the case are facts about swans.33 33 My criticism of the restricted totality fact proposal thus differs from that in Chudnoff (2013, manuscript). First, Chudnoff argues that a restricted totality fact is explanatorily irrelevant to what makes an accidental generalization the case, and concludes from this that the former fact is not a partial ground for the latter fact. However, as I will argue in §5.4, even if the restricted totality fact were explanatorily relevant, it would not follow that it partially grounds the fact at issue. Second, Chudnoff's tests for 734 A. Skiles 123 What should the proponent of the restricted totality fact say in response? First, consider the property being either white or not a swan in Switzerland. One response available is to note that the unrestricted general fact that everything has this property is logically equivalent to the fact that every swan in Switzerland is white. Since it is reasonable to say that facts about the Eiffel Tower partially ground this unrestricted general fact-so the response goes-it is also reasonable to say that facts about the Eiffel Tower partially ground the accidental generalization it is logically equivalent to. The problem with this response is that the inference is invalid. Even if every accidental generalization is logically equivalent to an unrestrictedly general fact that is grounded in C, it does not follow that the accidental generalization is grounded in C too. Logically equivalent facts may differ with respect to their grounds. For instance, [p] seems to at least partially ground logically complex facts such as [::p] and [p ^ [p _ :p]] that it is logically equivalent to, but [p] does not even partially ground itself. There might be some other reason to that accidental generalization has the same grounds as its unrestricted correspondents, but to claim that logically equivalent facts have the same ground will not do. A second response is to reject my assumption that partial grounding is transitive. However, this assumption, although it makes the objection more vivid, is inessential for at least two reasons. First, it seems just as implausible to say that facts about the Eiffel Tower are essential to partially grounding the fact that a, b, ... exhaust the swans in Switzerland as it is to say that that facts about the Eiffel Tower are essential to partially grounding the fact that every swan in Switzerland is white. Second, the proposal fails even if one grants the only extant framework capable of explaining failures of partial grounding, due to Jonathan Schaffer (2012a). In Schaffer's framework, the relation of grounding is doubly contrastive: it relates not just [p] and [q], but rather takes the following form: [p] rather than [p*] is grounded in [q] rather than [q*], where [p*] and [q*] are non-obtaining alternatives to [p] and [q] respectively. However, as Schaffer argues, even though failures of transitivity occur when the contrast facts (usually left implicit) are shifted when grounding relations are chained together, partial grounding remains transitive when the contrast facts are held fixed. So, suppose a and b are white Swiss swans, and that c is a white polar bear. And suppose one said [Vx(Fx ? Gx)] rather than [:Vx(Fx ? Gx)] is partially grounded in [Vx(Fx ? (x = a _ x = b))] rather than [:Vx(Fx ? (x = a _ x = b))]. Granted, it does seem that [Vx(Fx ? (x = a _ x = b))] rather than [:Vx(Fx ? (x = a _ Footnote 33 continued explanatorily irrelevance leave some implementations of the restricted totality fact proposal unscathed. Consider [#(F) = n], i.e. the restricted totality fact that there are exactly n things that are F. This fact is not vacuous in Chudnoff's sense: [Vx(Fx ? Gx)] does not contain information about how many things are F, nor vice versa. Moreover, [#(F) = n] is no more unnatural than [Vx(Fx ? Gx)] is: that the collection of Swiss swans has n members seems no more heterogeneous and disjunctive that that every member of the collection is white. My objection to the restricted totality proposal outperforms Chudnoff's because it applies to this implementation of the proposal as well: presumably, [#(F) = n] itself needs a necessitating ground, but the only obvious candidates either require necessitating grounds as well, or introduce facts that seem entirely irrelevant to grounding the accidental generalization we began with. Against Grounding Necessitarianism 735 123 x = b))] is partially grounded in the fact that c is a polar bear rather than a Swiss swan. But it seems false to say that [Vx(Fx ? Gx)] rather than [:Vx(Fx ? Gx)] is partially grounded in the fact that c is a polar bear rather than a Swiss swan. c is, recall,white. So c's being a polar bear rather than not makes no difference to whether every swan in Switzerland is white. Regardless of whether cwas a polar bear or a Swiss swan, every swan in Switzerland would still have been white. Thus even within Schaffer's doubly contrastive framework, which retains the transitivity of partial grounding under fixed contrasts, my objection stands. A final response is to claim that even though restricted totality facts necessarily co-obtain with general facts of the form [Vx(Fx ? (x = a _ x = b _ ...)], they are distinct. That is, one may posit a new fundamental atomic fact, [TOTF(...)], for each accidental generalization, where ''TOT'' picks out a primitive property expressible by saying that the named entities 'total' the things that are F. This is an extension of a thought due to David Armstrong (1997, ch. 13) and Kit Fine (2012, §7), who both argue that a single such fact, where F is the property being everything there is, should be posited to help ground the truth of unrestricted totality facts. This final response is problematic as well. The first problem has to do with its motivation. Do we have any reason to believe that there are such fundamental facts? As both of Armstrong's and Fine's arguments for positing this sui generis fundamental fact both take the truth of necessitarianism as a premise, one cannot claim any antecedent justification for doing so. The second problem is that in order to constitute a comprehensive response, one must extend the proposal to every accidental generalization. This results in an absolutely immense increase in primitive ideology-one reductively unanalyzable TOT-property for accidental generalizations concerning swans in Switzerland, another for accidental generalizations concerning gold spheres, and so forth-as well as an immense increase in fundamental facts about the holding of each of these patterns. The contingentist easily avoids such profligacy by opting for the w-instance proposal instead. 5 In Defense of Grounding Contingentism In §3 and §4, I considered a number of prima facie implausible ways to escape the purported cases of grounding without necessitation (e.g., claim that ordinary composites cannot survive replacement of a single part). Of course, the dogged necessitarian may respond simply by claiming that the case for necessitarianism is strong enough that one has no other choice but to pick which bullet to bite. In this section, I will show that the best arguments for necessitarian do not succeed. 5.1 The Supplementation Argument Like grounding necessitarianism, the doctrine of truthmaker necessitarianism- that a collection of entities makes a proposition true only if their existence necessitates its truth-has become orthodoxy (more about their relationship later: 736 A. Skiles 123 §6). In a widely cited passage, Armstrong (1997, p. 116, my emphasis) presents the following argument for this thesis: If [a] truthmaker for a truth could have failed to make the truth true, then we will surely think that the alleged truthmaker was insufficient by itself and requires to be supplemented in some way. A contingently sufficient truthmaker will [make it] true only in circumstances that obtain in this world. But then these circumstances, whatever they are, must be added to give the full truthmaker. One might similarly argue for grounding necessitarianism in the following way. Suppose that [p] is grounded in, yet not necessitated by, the facts inC at someworldw. Then there is a class of worlds in which the facts inC obtain yet [p] does not; call these the U-worlds (''U'' for unsupplemented). Intuitively, the facts inC are insufficient by themselves to ground [p] at w, for one must also include as partial grounds of [p] whatever facts necessitate that w is not a U-world. But these facts, along with the facts in C, necessitate [p]. And so it goes for every other putative counterexample to grounding necessitarianism. Thus, grounding necessitarianism is true. This argument-call it the supplementation argument-trades on an equivocation in the phrase ''the facts in C are insufficient by themselves to ground [p]''; once resolved, the argument dissolves. First, ''insufficient by itself'' could be readmodally. On this disambiguation, what is said is that the obtaining of all the facts in C does not constitute a metaphysically sufficient condition for the obtaining of [p]. But that is just another way of saying that [p] is not necessitated by C. But to infer that C must therefore be supplemented with further facts in order to ground [p] is to assume the truth of grounding necessitarianism. A second way to read ''insufficient by itself'' is explanatorily. On this reading, the facts in C are sufficient by themselves, by supposition and contrary to what Armstrong asserts. Absent independent reason to believe that they are not, the supplementation argument cannot get off the ground. 5.2 The Divine Decree Argument Ross Cameron (forthcoming, p. 7, my emphasis) claims that although the following reasoning does not ''prove'' truthmaker necessitarianism, it suggests that it is ''a pretty attractive doctrine'': The truthmaker thought is that explanation only bottoms out at existence facts: for God to give a complete plan of the world He needs only make an inventory of what is to exist. But if necessitarianism is denied this doesn't seem to be the case; I can list everything there is and it still be an open question what is true. [...] That goes against the whole spirit of truthmaker theory; explanation stops at what there is-the ontological inventory as it is should not leave the truthvalue of any proposition undecided. One might similarly argue for grounding necessitarianism in the following way. Suppose for reductio that it is false. Then to ground every fact, God would have had to do more than command His angels to specify the fundamental facts. Yet this goes against their being the fundamental facts-that ''explanation stops'' only at these. For if there is a derivative fact left undecided by them, there would be something further Against Grounding Necessitarianism 737 123 requiring explanation that is left unsettled by the fundamental facts, which are supposed to settle every fact. Thus by reductio, grounding necessitarianism follows. Call this the divine decree argument. The problem with this argument is that it invalidly infers grounding necessitarianism from another thesis linking grounding with necessitation that is compatible with grounding contingentism. By speaking of God's angels specifying ''an ontological inventory'' to ''give a complete plan of the world'' that settles every fact, the argument seems to be putting forth the claim that every fact globally supervenes upon the totality of fundamental facts: The global supervenience of every fact on the fundamental facts If w and w* are any two worlds that are duplicates with respect to which fundamental facts obtain, then w and w* are duplicates with respect to which facts obtain simpliciter. The argument above (insofar as I can understand it) is sound only if (i) every fact globally supervenes on the fundamental facts and (ii) this wouldn't be so were contingentism true. But even if we waive worries that onemight well have with (i), the argument still falters at (ii), which can be seen by reflecting on the cases of grounding without necessitation I offered earlier. For instance, take cases with accidental generalizations: any world differing from our ownwith respect to whether every swan in Switzerland is white presumably will also differ in whatever fundamental facts are ultimately responsible for this otherworldly swan's being another color. Thus even if contingentismwere true, anyworld differing fromour ownwith respect towhether this accidental generalization holds will differ from our own with respect to some fundamental facts, just as the global supervenience principle requires. Since grounding contingentism is therefore compatible with the global supervenience of every fact on the fundamental facts, there is no direct link from the truth of the second thesis to falsity of the first. 5.3 The Differentiation Argument An argument often hinted at in literature on the metaphysics of fundamentality is that the truth of grounding necessitarianism is at least part of what differentiates grounding from other relationships of production such as causation or nomological entailment. For instance, here is Gideon Rosen (2010, p. 118): [That grounds necessitate] is one respect in which the grounding relation, which is a relation of metaphysical determination, differs from causal and other merely nomic forms of determination. There is a difference between the materialist who holds that facts about phenomenal consciousness are grounded in (hence necessitated by) the neurophysiological facts directly, and the dualist who think that facts about the brain cause or generate conscious states according to contingent causal laws. Thus one might argue that if [p] were not necessitated by C, one cannot say what differentiates materialism from emergent dualism. Since part of the utility of the grounding idiom is that it should allow one to articulate such distinctions, one might conclude that necessitarianism is true. 738 A. Skiles 123 Call this the differentiation argument. There are several responses to Rosen's version of the argument; here are two. First, even if it is correct that facts about necessitation distinguish grounding from causation, necessitarianism need not follow. For the distinction between the two might simply be that in at least some cases a fact is necessitated by its ground, while an effect is never necessitated by its causes, given that the metaphysically contingent laws of nature governing causal interaction could have differed. Since the contingentist merely denies that all facts are necessitated by their grounds, distinguishing the two in terms of facts about necessitation is compatible with contingentism. Second, grounding and causation differ in various other ways that the contingentist may point to. However, one must take care to point to the correct differentia. In response to the differentiation argument, it is sometimes said that grounding is a synchronic relation yet causation is not.34 However, emergent dualists typically claim that mental facts are synchronically caused by their physical grounds; moreover, arguably it is possible for a fact to be partially grounded in facts that obtain at other times.35 Rather, what contingentism should point to are the different implications of grounding and causation for relative metaphysical fundamentality. If a fact is grounded, then it must also be metaphysically less fundamental than each of the facts that partially ground it; yet an effect may be more, less, or equal in relative fundamentality with respect to its causes. If there is a way of arguing from differentiation to necessitarianism, then it ought to proceed by showing that there is another difference-maker between grounding and causation that entails the view. An interesting argument along these lines starts from a common suggestion throughout the literature on grounding: that a derivative fact is in some sense 'nothing over and above' the facts that ground it-to borrow Armstrong's famous expression, a 'free lunch' (1997, §2.12). For instance, Fine (2012, pp. 6–7) gestures at this argument in the following passage: The history of analytic philosophy is littered with attempts to explain the special way in which one might attempt to 'reduce' the reality of one thing to another. But I believe that it is only by embracing the concept of a ground as a metaphysical form of explanation in its own right that one can adequately explain how such a reduction should be understood. For we need a connection as strong as that of metaphysical necessity to exclude the possibility of a 'gap' between the one thing and the other; and we need to impose a form of determination upon the modal connection if we are to have any general assurance that the reduction should go in one direction rather than another. Elsewhere, Fine refers to grounding as the ''tightest'' and ''ultimate'' explanatory relation, and that ''it is perhaps for this reason that we are not inclined to think of the truth of a grounded proposition as a further fact over and above its grounds, even though it may be distinct from its grounds and even though it may itself be a real fact'' (2001, pp. 15–16, his emphasis), even if we are inclined to think this about the relata of relationships of causal production. Perhaps, then, necessitarianism could be 34 For example, see Leuenberger (2013, pp. 6–7). 35 For instance, see Hazlett (2006, 2011). Against Grounding Necessitarianism 739 123 established by claiming that if [p] were not necessitated by C, it would follow, incorrectly, that the obtaining of [p] is a ''further fact'' over and above the obtaining of the facts in C. Is this variation on the differentiation argument successful? Although it is common, many take Fine's suggestion as an optional commitment, while others explicitly reject it for reasons such as the following.36 If 'nothing over and above' means identical to, necessitarianism would follow directly from the necessity of identity-but then this would violate the widely held view that no fact grounds itself.37 Even if some facts could be identical to their grounds, in cases in which one fact is grounded in many (e.g., when an accidental generalization is grounded in many instances), the result would be an instance of the kind of 'one-many identity' many find suspicious at best and incoherent at worst. But if 'nothing over and above' does not mean identical to, it is unclear at best why it would be incompatible with a contingent link between a derivative fact and its grounds. Although one may therefore reject the differentiation argument by rejecting its premise that a fact is 'nothing over and above' its grounds, my own view is that there is a way to interpret this elusive phrase that is compatible with contingentism. Indeed, Fine himself comes tantalizingly close to stating it in ''The Question of Realism'', which was largely responsible for inspiring recent interest in grounding. When first glossing what grounding is, Fine writes: I recommend that a statement of ground be cast in the following 'canonical' form: ''Its being the case that S consists in nothing more than its being the case that T, U, ...'', where ''S, T, U, ... are particular sentences. [...] As [a] particular example of such statements, we have: ''Its being the case that Britain and Germany were at war in 1940 consists in nothing more than ...'', where ''...'' is a compendious description of the warring activity of various individuals. (Fine 2001, p. 15) Read literally, and in light of the fact-based grounding framework under consideration in this paper, similar problems emerge as before. Presumably, the obtaining of [p] 'consists in nothing more than' the obtaining of [q1], [q2],... only if [p] itself 'consists in nothing more than' [q1], [q2], ... themselves; yet this would preclude the contingentists from treating the elusive phrase 'consists in nothing more than' as ascribing the unmysterious relation of identity. A way out of this predicament is to recall that [p] is grounded in C not simpliciter, but rather on a particular occasion. This temporal and modal relativity must in some way be encoded into these 'consists in nothing more than' statements. The obvious way to do this is instead to say that if [p] is grounded in C on a particular occasion, then the obtaining of [p] on this occasion 'consists in nothing more than' the obtaining of the facts in C on this occasion. Saying as much is 36 See Jenkins (2011), Raven (2013), and Wilson (forthcoming) for discussion of the irreflexivity of grounding. 37 For instance, Chudnoff (manuscript) suggests that it may only in some cases; Audi (forthcoming) rejects it entirely. 740 A. Skiles 123 completely compatible with contingentism, since what it is for [p] to obtain on one particular occasion may differ from what it is for [p] to obtain on another particular occasion. To evade the other problem-which was that 'consists in nothing more than' talk identifies a fact with its grounds-one must take care to distinguish the proposal I intend to offer from a subtly different one that I think is false. On the unintended non-distributive reading, one takes statements like ''[p] is grounded in [q1], [q2], ... at t and w'' to entail identities of the following form: [[p] obtains at t and w] = [[q1 ^ q2 ^ ...] obtains at t and w] This reading is problematic: given the previously mentioned principle of fact identity, this reading of the proposal entails that [p] is identical to the conjunction of its grounds. Rather, I have in mind the distributive reading, which instead takes grounding statements to entail identities of the following form: [[p] obtains at t and w] = [[q1] obtains at t and w ^ [q2] obtains at t and w ^ ...] Unlike the non-distributive reading, the distributive reading does not imply that [p] is identical to (the conjunction of facts) in C, yet does so while faithfully capturing the elusive sense in which [p] 'consists in nothing more than' the facts in C. In other work, I argue that the presence of identities of this form is what it is for a fact to be grounded.38 But even if one resists this account of what grounding is, the contingentist may still believe that there are such identities in instances of grounding, and note (as I have above) that their presence is compatible with contingentism. 5.4 The Confounding Case Argument Anotherway to argue for necessitarianism is to first draw a link between grounding and explanation, and to then show that the link breaks if a fact fails to be necessitated by its 38 See Skiles (2012). Two additional wrinkles with the account are worth briefly canvassing. First, those who wish to evade ontological commitment to facts may paraphrase by employing the 'just is' operator for expressing generalized identities discussed by Agustın Rayo (2013) and Øystein Linnebo (2014), supplemented with a sentential operator 'for it to be the case at t and w that __'' capable of discriminating claims like ''... just is for it to be the case at t and w that q1 ^ q2 ^__'' from claims like ''... just is for it to be the case at t and w that q1 ^ for it the case at t and w that q2 ^ __''. To avoid trivialization, though, one would need to reject Rayo's assumption that modal covariation is sufficient for the holding of 'just is' statements of the relevant kind. Second, one might object that the account cannot be generalized to all grounding: for instance, if [p] is only grounded in [q], then the proposal leads to the identification of [p] with [q] that it was supposed to evade. One response is to note the presence of various linking principles between a derivative fact and its grounds. For instance, my own view is that [Vx(Fx ? Gx)] is grounded in [a is G] together with the fact that this fact is an instance of [Vx(Fx ? Gx)], that [p _ q] is grounded in [p] together with the fact that [p] is a disjunct of [p _ q], and so on. Rather than adding linking principles into the derivative fact's grounds, another response instead includes them in the identifications that instances of grounding give rise to. For instance, one might say that even though [p _ q] is not partially grounded in the fact that [p] is a disjunct of [p _ q], nonetheless this disjunctive fact's being the case partially consists in this linking principle's being the case. For a fuller discussion of these and other putative difficulties, see Skiles (2012, ch. 5). Against Grounding Necessitarianism 741 123 grounds. Louis deRosset (2010) offers a sophisticated version of this style of argument.39 Say that a confounding case for an explanatory proposal of the form ''p because q1, q2,...'' is any possible scenario in which ''p'' is false yet ''q1'', ''q2'',... are all true. Say that an explanatory proposal is good only if it is true and complete. According to deRosset, no explanatory proposal is good unless it has no confounding cases: to say that a given atom has a stable nucleus because it is an oxygen atom, for instance, is to fail to offer a good explanatory proposal, given the existence of shortlived radio-active oxygen isotopes (ibid., p. 80). But if contingentism were true, explanatory proposals entailed by true grounding statements would have confounding cases. More precisely, deRosset's argument is this: The confounding case argument: (P1) If [p] fails to be necessitated by [q1], [q2], ..., then there is a confounding case for the explanatory proposal ''p because q1, q2, ...''. (P2) If there is a confounding case for the explanatory proposal ''p because q1, q2, ...'', then it is not good. (P3) If [p] is grounded in [q1], [q2], ..., then the explanatory proposal ''p because q1, q2, ...'' is good. Thus: Grounding necessitarianism is true. Call this the confounding case argument. It is clearly valid, and (P1) follows from two plausible claims: that [p] is obtains at a world w iff the proposition p is true at w, and an explanatory proposal is good only if the propositions expressed by the explanans and explanandum clauses are all true. The key premises, then, are (P2) and (P3).What I will do now is pose a dilemma for the conjunction of (P2) and (P3). The dilemma hinges upon what it takes for an explanatory proposal to be complete. Although deRosset does not say what it is for an explanatory proposal to be complete, one may begin by asking whether explanatory proposals entailed by causation are complete. Take an effect (say, the eight-ball ricocheting off the pool table) caused by a collection of some other events (say, involving the momentum and trajectory imparted on it with a cue stick). And say that the explanatory proposal ''p because q1, q2,...'' associatedwith this occurrence isbare iff ''q1'', ''q2,''... solely and exhaustively describe the collection of events that jointly cause the event reported by ''p''. Suppose first that this bare causal explanatory proposal is complete. If so, then (P2) is clearly false for familiar reasons. If there had been a sufficiency large differences in the laws governing the system or in the surrounding circumstances, then the eight-ball would have stuck to the cue stick, or quantum tunneled through the table, or ... even if the momentum and trajectory I imparted on the eight-ball with my cue stick had been precisely the same. The occurrence of causes need not necessitate the occurrence of their effect; bare causal 39 The argument I will discuss is slightly different than deRosset's, but not in any way that matters for what follows. DeRosset's argument serves as a step in a broader case against the view that the ontological commitments of a theory are determined not by what the theory's quantifiers must range over for it to be true (cf. Quine 1948), but rather by which entities appear in facts it takes as fundamental. If my case against deRosset's argument for necessitarianism is successful, then it also undermines his argument against this view about how to calculate ontological commitments. For a defense of this view against deRosset that is compatible with necessitarianism, see von Solodkoff (2012). 742 A. Skiles 123 explanatory proposals can have confounding cases. But if it possible for bare causal explanatory proposals to be complete while having confounding cases, then (P2), which states that no complete explanatory proposal has confounding cases, is false. The obvious response available to the proponent of the confounding case argument would be to say that (P2) only applies to non-causal explanatory proposals. One problem with this response is to motivate the alleged distinction between causal and non-causal explanation-which, as we saw from our discussion of the differentiation argument in §5.3, is a tall order. But set this problem aside, and let us grant that to turn a causal statement into a complete explanatory proposal, further supplemental information regarding the antecedent surrounding circumstances and the relevant laws of nature governing the system must also be added to the explanans. That is, let us grant that a bare causal explanatory proposal is not complete. The problem now with the confounding case argument is that there appears to be no compelling reason to accept (P3). Recall that (P3) claims, in effect, that every bare explanatory proposal about grounding must be complete. But if this constraint does not hold for relationships of production such as causation, why believe that it is true for relationships of production such as grounding? Just as with causation, the contingentist may well hold that to bridge the gap between grounding and a complete explanatory proposal, supplemental information about the antecedent surrounding circumstances (e.g., that a, b,... are everything that is F, when noncausally explaining why every F is G), or about the relationships between the entities involved (e.g., that the tuna sandwich is composed of a1, a2, ..., when noncausally explaining why the tuna sandwich exists) must be added to the explanans in order to complete it. To hold that additional information is required in order to link grounding with explanation seems no more problematic than to hold the same for the link between causation and explanation.40 What, exactly, is the explanatory role of this supplemental information, such that some bare grounding statements need not themselves be complete grounding explanations? A full discussion of the relationship between grounding and grounding explanation is beyond the scope of the paper, but one can see the explanatory role that this supplemental information might play by analogy with requirements on causal explanation. For instance, consider the explanatory proposal: ''Every F is G because a isG, b isG,...'', where a, b,... are the only things that are F. Then the supplemental information that a, b,... are the things that are F can help yield a complete grounding explanation by virtue of a combination of the following: 1. The supplement helps to display how the explanatory proposal has stability under a relatively fixed range of counterfactual interventions. The range might 40 One might claim that it is objectionable to non-causally explain why the sandwich exists partly in terms of the fact that it is composed of a1, a2, ... (recall our discussion in §3.1). But this is no more objectionable than causally explaining why the sandwich exists partly in virtue of the fact that it was the outcome of placing together the bread, tomatoes, and so forth that are its ingredients. There is only an objectionable circularity if one claims that the tuna sandwich played a role in causing itself to exist (since entities are caused to exist only by temporally prior entities). And similarly, there is only an objectionable circularity if it plays a role in grounding its own existence (since entities ontologically depend only upon metaphysically more fundamental entities). Against Grounding Necessitarianism 743 123 be highly robust (if. for instance, it is impossible for an F to be a non-G). Or it might be very fragile (if, for instance, even the slightest variation in the world's history undercuts the generalization). Either way, its bounds may be further illuminated by providing further information about the connection between the instances of the generalization and the properties themselves. 2. The supplement helps to display why these facts about a, b, ... are relevant to addressing the explanatory demand. This may be unneeded if the audience possesses enough background knowledge about the distribution of F, or if the audience is only concerned with identifying how general facts are ultimately grounded in particular facts (as opposed to possessing a fully satisfying explanation, which will itself bring in yet more non-fundamental general facts). 3. The supplement helps to differentiate how this accidental generalization was brought about, in contrast to counterfactual alternatives. Along with further supplemental information, one can see that the fact that a certain mutation preventing the birth of swan a would have led the fact that every swan in Switzerland is white to have been grounded in a subcollection of the facts that actually ground it, while a certain other mutation would have led to a being black, undercutting the generalization altogether. 4. Finally, the supplement helps display that the explanatory proposal is systematic by indicating underlying ''laws of metaphysics'' or (a bit less grandiosely) by indicating that the explanatory proposal is an instance of an interesting pattern of dependence. It might be a 'topic-neutral' pattern such as the one encapsulated by the w-instance proposal in §4, or be a more specific (yet still not nomologically necessary) pattern involving the properties at issue. Stability under a fixed range of circumstances, relevance of explanans to explanandum, difference-making, and systematicity are widely and quite plausibly taken to be reliable indicators that a given causal explanatory proposal is complete. If these indicators can be extended to explanatory proposals undergirded by relationships of grounding-I have only briefly sketched how that extension might be effected, although the project looks promising-then (P3) would be mistaken for the same reason that drawing too close a link between causation and causal explanation is mistaken. However, one may worry that distinguishing between grounding and grounding explanation plays into the hands of the necessitarian in the following way.41 Suppose that we introduce a new relational predicate ''...is grounded1 in...'', that is satisfied by [p] and C iff a subcollection of facts in C brings about [p] by virtue of the relation I have been calling ''grounding'' while the remaining facts in C provide supplemental information that (at least in the case I considered above) bridges the gap between grounding and necessitation. The worry is that even if the contingentist is correct that what I have called ''grounding'' does not entail necessitation, the broader philosophical literature seems all along to have meant ''grounding'' to refer to grounding1, which arguably does. One might reasonably believe this because ''grounding'' talk is frequently introduced, as Fine famously does, by designating it 41 Thanks to Fabrice Correia and Louis deRosset for pressing me to address the following worry. 744 A. Skiles 123 as ''a form of explanation; in providing the ground for a given proposition, one is explaining, in the most metaphysically satisfying manner, what it is that makes it true'' (2001, p. 22). Since it is allegedly only after citing the grounds1 of a fact that one explains it in the ''most metaphysically satisfying manner'', the necessitarian may therefore claim that the relation that philosophers meant to pick out by ''grounding'' talk is one that requires necessitation. There are two points that the contingentist should make in response. The first is to note that the tight connection Fine and others draw between grounding and explanation in second-order discussions (which concern the nature of grounding in abstraction from first-order discussions about which facts are grounded in which) is far from uniform or uncontroversial. Many follow Schaffer and explicitly ''distinguish the worldly relation of grounding from the metaphysical explanations between facts that it backs, just as one should distinguish the worldly relation of causation from the causal explanations between facts that it backs'' (2012a, p. 124). The second point is to note that in first-order discussions, usage tends to go against taking ''grounding'' discourse to refer to grounding1. One piece of evidence is that grounding is standardly taken to be relation of relative metaphysical fundamentality: if [p] is grounded in C, then [p] is metaphysically less fundamental than the facts in C. But as we have seen before, grounding1 does not satisfy this constraint: if one cites the fact that an ordinary composite is grounded in such-and-such parts in the course of explaining why o exists, one does not 'drop down' a level of fundamentality (and if anything, it is the reverse). Given that the grounds1 need not play a role in bringing about the target fact, it seems more natural to say that their role in a grounding explanation is not as partial grounds (in the standard sense of ''grounds'') but rather as ancillary material useful for illuminating why the facts in C brought about [p] to the explanatory proposal's audience-useful, that is, to the extent that the connection is not obvious or irrelevant given the audience's background knowledge and interests.42 I thus conclude that the confounding case argument for necessitarianism does not succeed. It is no more problematic to believe that the grounds of a fact help explain it without necessitating it than it is to believe that the causes of an event can help explain it without necessitating it. 5.5 The Open Question Argument The last argument I will consider is due to Kelly Trogdon, who argues that necessitarianism follows from a ''broadly epistemic feature [...] characteristic of grounding in general'' (2013a, p. 10). To understand this argument, it is best to begin with a concrete example. Following Trogdon, suppose the fragility of a particular Fabergé egg is grounded in facts about the crystalline bonding between its molecules. According to Trogdon, the question ''Why should this Fabergé egg be fragile, given the crystalline bonding between its molecules?'' lacks cognitive significance: ''it's possible that being fully informed about the natures of the relevant entities suffices for the question to lack substantive content for some rational individual'' (ibid., p. 7). 42 See deRosset (2013a, §3) for an application of this distinction to other instances of grounding. Against Grounding Necessitarianism 745 123 Such a question lacks substantive content for a rational individual in Trogdon's sense just in case different answers to this question are epistemically possible for this individual (ibid., p. 5). According to Trogdon, the reason that this question about the Fabergé egg and its molecules lacks substantive content for some possible rational individual, and therefore the reason that it lacks cognitive significance, is that it is part of the nature of the relevant entities that anything made of molecules with weak crystalline bonds is fragile (ibid. p. 15). Given Trogdon's assumption that every truth about the nature of the relevant entities holdswithmetaphysical necessity (ibid., §3), it follows that it is metaphysically necessary that anythingmade ofmolecules with weak crystalline bonding is fragile, and a fortiori anything made of these particular molecules. Thus it follows that these facts about the Fabergé egg's molecules not only ground but also necessitate that it is fragile. According to Trogdon, what holds true of the Fabergé egg is inductively generalizable to every possible instance of grounding. Terminology: if [p] is grounded in C, say that these facts satisfy the epistemic constraint iff the question ''Why should [p] obtain, given that the facts in C obtain?'' lacks cognitive significance, and say that that they satisfy the essence constraint iff it is part of the nature of one or more of these facts, or the entities these facts have as constituents, that [p] obtains if the facts in C all obtain. Terminology in tow, Trogdon's argument can be formulated as follows: The open question argument for grounding necessitarianism: (P1) If [p] is grounded in C, then [p] and C satisfy the epistemic constraint. (P2) If [p] and C satisfy the epistemic constraint, then they satisfy the essence constraint. (P3) If [p] and C satisfy the essence constraint, then [p] is necessitated by C. Thus: If [p] is grounded in C, then [p] is necessitated by C, i.e. grounding necessitarianism is true. Call this the open question argument. The argument is clearly valid; is it sound? Although it is an interesting question whether (P1) and (P3) are true, I will grant them for sake of argument. The problem with the open question argument is that even if we grant that (P1) and (P3) are true, instances of grounding without necessitation easily satisfy the epistemic constraint without also satisfying the essence constraint. For instance, suppose that the w-instance proposal for grounding accidental generalizations is true (as I argued in §4). And suppose that Bob is a possible rational individual who, in addition to being fully informed of the natures of the facts [Ga], [Gb], ..., [Vx(Fx ? Gx)] and their constituents, also knows that a, b, ... are the only things that are F. (The claim here is not that every possible individual such as Bob possesses this last bit of knowledge-I only require the wholly plausible claim that some does.) Then clearly, it follows that the question ''Why should every thing that is F also be G, given that a, b, ... are all G?'' lacks cognitive significance for Bob. It is not epistemically possible for Bob that some F fail to be G, if Bob knows that a is G, knows that b is G, ... and knows that these are the only things that are F. Since this suffices for the question to lack cognitive significance, it follows that [Ga], 746 A. Skiles 123 [Gb],..., [Vx(Fx ? Gx)] satisfy the epistemic constraint. Yet this collection of facts fails to satisfy the essence constraint: it is no part of the essence of any one or more of these facts or their constituents that each one of a, b, ... is F. Thus, even if Trogdon is correct that there is a broadly epistemic constraint upon grounding, that is consistent with the falsity of (P2) and-for all the open question argument shows-consistent with contingentism. The proponent of the open question argument might respond by ratcheting up the threshold for satisfying the epistemic constraint. But it is difficult to see how one could do so without ruling out illustrative cases of grounding along with cases of grounding without necessitation. For instance, one might ratchet up the threshold by claiming that the question ''Why should [p] obtain, given that the facts in C obtain?'' lacks cognitive significance only if it is necessary-and not merely possible, as Trogdon would have it-that being fully informed of the nature of the relevant entities suffices for the question to lack substantive content for a rational individual. First problem: any such question would fail to lack cognitive significance, and thus no fact would be grounded, since is it possible for such a question to have substantive content for rational individuals fully informed about the nature of relevant entities, due to any number of kinds of epistemic misfortune. (Perhaps this individual has undefeated evidence that the relevant entities do not have these natures; perhaps she has mistaken beliefs about the modal status of truths about natures; perhaps she forgets some information about the natures of the relevant entities, or does not draw out all the implications of this information, as she considers the question; etc.) Second problem: even if the first problem is waived, even the case that Trogdon uses to motivate the epistemic constraint would fail to satisfy it. It is not enough for a rational individual to be fully informed about the facts about the nature of the Fabergé egg, its molecules, and their properties in order for the question ''Why is the Fabergé egg fragile, given the crystalline bonding between its molecules?'' to lack cognitive significance. She must also have a basic understanding of the underlying chemistry and how molecules bonded in this manner interact with other kinds of molecules given the relevant chemical laws (as Trogdon seems to grant: cf. ibid., p. 5). Since it is possible for a rational individual to lack this information, it is possible for this question to have substantive content for such an individual, and thus even this illustrative case of grounding would fail to satisfy the epistemic constraint. I thus conclude that the open question argument does not succeed. Even if instances of grounding all exemplify the broadly epistemic features that Trogdon ascribes to them, that is fully compatible with the grounds of a fact failing to necessitate it. 6 Conclusions Over the course of this paper, I have argued that not only is there no good reason to believe that a fact must be metaphysically necessitated by the facts that ground it (as the grounding necessitarian claims), there is good reason to believe that there can be Against Grounding Necessitarianism 747 123 grounding without necessitation (as the grounding contingentist claims). What follows if this is correct? Contingentism bears broad implications first of all for a number of first-order disputes about grounding. First-order disputes about grounding concernwhether every fact about mentality, morality, modality, or some other aspect of reality is grounded at all, and which kinds of facts do the grounding if so. Yet the falsity of contingentism is often a crucial suppressed premise in arguments that bear on specific first-order grounding hypotheses, both for and against. Arguments against such hypotheses typically proceed by attempting to establish that facts of one kind are not necessitated by facts of another kind, then inferring that the former facts are not grounded in the latter facts. This inference is good, of course, only if a fact is always necessitated by facts that ground it.43 Arguments for specific first-order hypotheses instead typically proceed by attempting to establish that each fact of one kind is necessitated by the facts of another kind, then inferring that the best explanation for this truth is that the former facts are also grounded in the latter facts. Although this style of argument need not essentially rely upon the falsity of contingentism as a premise, presumably the putative explanation would not be as good if contingentism were true.44 Contingentism bears important consequences for second-order disputes about grounding-which concern the essential features of grounding itself, and whether it can be characterized in more basic terms-as well. For instance, the falsity of contingentism has been deployed in arguments for surprising and controversial views about the logical form of grounding statements,45 about the relationship between full and partial grounding,46 about what grounds facts about grounding,47 and about how grounding relates to ontological commitment.48 One way to undermine such arguments, of course, would be to reject the premise that contingentism is false. The truth of contingentism would also be relevant to those who take there to be a constitutive relationship between grounding and truthmaking, or who take there to be necessary connections between them, who now must either devise strategies for resisting arguments against truthmaker necessitarianism analogous to those I raised against grounding necessitarianism, or accept that a truth need not be necessitated by the existence of its truthmakers.49 And finally, reductive theories of grounding- 43 Cf. Leuenberger (2013) and Trogdon (forthcoming) for discussion. 44 Cf. Kim (1998, ch. 1) and Wilson (2011) for relevant discussion regarding the grounding of 'higherlevel' special science facts, and McPherson (2012) for relevant discussion regarding the grounding of moral facts. 45 Dasgupta (2014) appeals to the falsity of contingentism in order to argue that a collection of facts can be grounded without any one of the facts in that collection being grounded. 46 Perkins (manuscript) appeals to the falsity of contingentism in order to argue that full grounding should be characterized in terms of partial grounding rather than vice versa. 47 Bennett (2012) and deRosset (2013a) appeal to principles that entail the falsity of contingentism in order to argue that if [p] is grounded in C, then the fact that [p] is grounded in C is itself grounded in C. 48 As we saw in §5.4, deRosset (2010) appeals to the falsity of contingentism to argue that a theory's ontological commitments are not determined by what that theory says are the fundamental (i.e., ungrounded) facts. 49 Such proponents of truthmaker necessitarianism are Armstrong (1997), Rodriguez-Pereyra (2005), and Cameron (forthcoming) inter alia. 748 A. Skiles 123 which have been underexplored in recent literature on the metaphysics of fundamentality-may secure support from contingentism if they help to illuminate how grounding without necessitation is possible, or predict the extent to which grounding without necessitation occurs.50 One final, lingering worry with contingentism is that stable theorizing both about, and with, grounding would become completely unconstrained, and thus little progress could be made while investigating the notion, unless one could 'test' claims about grounding by checking to see whether the putative grounds of a fact necessitate it. Much to the contrary. Breaking the link between causation and necessitation was not the end of philosophical inquiry into causation, but rather just the beginning. Precisely the same is true for grounding as well. There are interesting questions about when grounds necessitate, and when they do not. There are interesting questions about why citing the grounds of a fact along with pieces of supplemental information can in certain contexts suffice to explain it as well. There are interesting questions about what makes for better explanations of this kind. These are just a few of the interesting questions that the metaphysics of fundamentality must eventually face up to if there is grounding without necessitation, and that are capable of anchoring theorizing about grounding. Appreciating the truth of grounding contingentism helps one see these questions directly, and emboldens one to begin to approach them vigorously.51 References Armstrong, D. (1997). A world of states of affairs. Cambridge: Cambridge University Press. Audi, P. (2012a) A clarification and defense of the notion of grounding. In Correia and Schneider (2012). pp. 101–121. Audi, P. (2012b). Grounding: Toward a theory of the in-virtue-of relation. The Journal of Philosophy, 112, 685–711. Barker, S. (2012). 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