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.
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Notes
I adopt formalism from Rosen (2010). Brackets indicate facts: for any true sentence “p”, let “[p]” rigidly denote the fact that p. If “Γ” is a plural term rigidly denoting one or more facts, then a fact is in Γ iff it is identical to one of the facts that “Γ” 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.
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).
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).
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 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 Γ t,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 Γ t,w , then for any t* and any w*, if all the fixed facts in Γ t*,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.
See Trogdon (2013) for a discussion of different varieties of grounding pluralism.
Cf. Correia (2010, §1.1).
Schaffer (2010a, §4) constructs such an argument.
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.
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.
Another scenario of rearrangement is the recycling scenario (cf. McKay 1986). Suppose that in an earlier epoch the existence of o is grounded in Γ. 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 Γ obtain during this later epoch, [o exists] does not.
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 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).
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).
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.
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.
Suppose for reductio that o = o n , that o n ≠ o R, and yet that o = o R. Since identity is symmetric, o = o n entails o n = o. But since identity is transitive, o n = o and o = o R jointly entail o n = o R (contradiction).
See Sider (2001) for defense.
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.
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 “[∀x: 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.
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 [∀x(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.
For reasons I get into later in fn. 38, I actually endorse what could be called the augmented w -instance proposal, which adds as a partial ground the second-order fact that [Ga], [Gb], … are instances of [∀x(Fx → Gx)]. However, the difference between the two will not matter for what follows.
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.
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 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: [∀x(Fx → Gx)] does not contain information about how many things are F, nor vice versa. Moreover, [#(F) = n] is no more unnatural than [∀x(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.
For example, see Leuenberger (2013, pp. 6–7).
For instance, Chudnoff (manuscript) suggests that it may only in some cases; Audi (forthcoming) rejects it entirely.
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 Agustín 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 q 1 ∧ q 2 ∧__” from claims like “… just is for it to be the case at t and w that q 1 ∧ for it the case at t and w that q 2 ∧ __”. 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 [∀x(Fx → Gx)] is grounded in [a is G] together with the fact that this fact is an instance of [∀x(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).
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).
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 a 1, a 2, … (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).
Thanks to Fabrice Correia and Louis deRosset for pressing me to address the following worry.
See deRosset (2013a, §3) for an application of this distinction to other instances of grounding.
Cf. Leuenberger (2013) and Trogdon (forthcoming) for discussion.
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.
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.
Bennett (2012) and deRosset (2013a) appeal to principles that entail the falsity of contingentism in order to argue that if [p] is grounded in Γ, then the fact that [p] is grounded in Γ is itself grounded in Γ.
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.
This paper and its many ancestors (which date back to 2008) have improved tremendously thanks to comments and encouragement from many friends and colleagues, including Paul Audi, Ralf Bader, Andrew Bailey, Mark Barber, Einar Bohn, Pablo Carnino, Fabrice Correia, Sam Cowling, Troy Cross, Marco Dees, Louis deRosset, Thomas Donaldson, Kenny Easwaran, Martin Glazier, Dana Goswick, Ghislain Guigon, Dan Korman, Kathrin Koslicki, Graham Leach-Krouse, Stephan Leuenberger, Dustin Locke, Dan López de Sa, Dan Marshall, Eugene Mills, Kevin Mulligan, Adam Murray, Paul Nedelisky, Samuel Newlands, Bryan Pickel, Jan Plate, Joshua Rasmussen, Bradley Rettler, Michael Rea, Henrik Rydéhn, Noël Saenz, Thomas Sattig, Raúl Saucedo, Jonathan Schaffer, Theodore Sider, Jeff Speaks, Joshua Spencer, Catherine Sutton, Kelly Trogdon, Achille Varzi, Tobias Wilsch, anonymous referees for Erkenntnis, and audiences at the CUNY Graduate Center, Rutgers University, the State University of New York at Fredonia, UMass-Amherst, the University of Geneva, the 2013 Central APA, the 2012 PERSP Metaphysics Workshop, and the 2013 Society for Exact Philosophy. This article was completed while funded by the Swiss National Science Foundation as a member of the research projects “Intentionality as the Mark of the Mental” (CRSI11-127488) and “The Nature of Existence: Neglected Questions at the Foundations of Ontology (10012_150289), and I am grateful for its generous support.
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Skiles, A. Against Grounding Necessitarianism. Erkenn 80, 717–751 (2015). https://doi.org/10.1007/s10670-014-9669-y
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DOI: https://doi.org/10.1007/s10670-014-9669-y