Abstract
Most facts of grounding involve nonfundamental concepts, and thus must themselves be grounded. But how? The leading approaches—due to Bennett, deRosset, and Dagupta—are subject to objections. The way forward is to deny a presupposition common to the leading approaches, that there must be some simple formula governing how grounding facts are grounded. Everyone agrees that facts about cities might be grounded in some complex way about which we know little; we should say the same about the facts of grounding themselves. The kinds of facts that might enter into the grounds of the facts of grounding are explored at length.
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Notes
I do have some concerns. (1) Enthusiasm for ground sometimes leads to its application in places where it doesn’t belong (Sider 2018). (2) Ground’s “conditional” nature encourages positing too little at the fundamental level (Sider 2013a, pp. 741–746). (3) A linguistic variant on ground is more appropriate for accommodating nonfactual discourse (Sider 2011, pp. 125–127).
Fans of Fine (2001) might say instead “...in an ungrounded fact that holds in reality”, and make corresponding adjustments to what follows.
See Sider (2011, Sections 7.2, 7.3, 8.2.1). There I used the term “structural” instead of “fundamental concept”, and spoke of metaphysical semantics rather than ground. Note that ‘fundamental concept’ cannot just mean ‘concept that can appear in ungrounded facts’, since that would trivialize the principle of Purity. For me, the notion of a fundamental concept is undefined (Sider 2011, Sections 7.5, 7.13; Chapter 2). But note: the argument here does not really require a general notion of a fundamental concept, or the general principle of Purity, since the argument needn’t be generalized: most of this paper could be recast using one-off principles banning any ungrounded facts that involve, say, the concept of being a city, or the concept of an economy.
Rabin and Rabern (2016) also make this point. They then go on to provide much-needed clarification of the notion of grounding being “well-founded” (as does Dixon (2016)). They argue that lacking infinite descending chains is an overly strong formulation of the intuitive constraint of well-foundedness, but that is not a concern here since I am arguing that not even this constraint is violated.
Consider the Bennett regress for partial ground (“
”): for some \(X_1, X_2, \ldots \),
Suppose we accepted the following principle: whenever A is a partial ground of B, the fact that A partially grounds B is also a partial ground of B. There would then result an infinite chain of partial ground, running down the right-hand-side of the above series. As applied to the second claim in the series, the principle tells us that
. Thus the consequent of the third member of the series partially grounds the consequent of the second member. Similarly, applying the principle to the third member of the series yields 
, and so the consequent of the fourth member of the series partially grounds the consequent of the third member of the series; and so on. But, in the spirit of Lewis Carroll (1895), we should reject the principle. For it implies, as Bolzano (2014, Section 199) noted, that whenever A partially grounds B, the following facts also partially ground B: 
. Moreover it seems based on the thought that “A cannot, on its own, fully ground B; it is only the combination of A and 
that fully grounds B”, whose first half implies, if the variables A and B are universally quantified and if A encompasses pluralities, that no fact has a full ground; also, the first half, thus understood, contradicts the second half.p. 197. Building is the central concept of Bennett’s book, which is distinct from (though related to) grounding.
Dasgupta (2014a, pp. 572–573) makes a similar objection. He also makes the further objection that
and 
would, according to Bennett and deRosset, have the same ground, whereas “the grounds are surely different and involve something about disjunction in the first case and negation in the second” (Dasgupta 2014a, p. 573). I agree, though I suspect the underlying thought is the same as the original objection.It might seem that a similar objection could be made to Litland (2017), who defends a view similar to that of Bennett and deRosset, namely that nonfactive grounding claims are zero-grounded (in Fine’s (2012) sense). But Litland adds that although grounding claims all have the same (zero) ground, different grounding claims are grounded in different ways, and he goes on to explore the idea of ways of grounds further in subsequent work. This seems to be a fruitful idea, but our concerns about what grounds the facts of grounding would seem to reappear as concerns about what grounds the ways of grounding.
A variant of Dasgupta’s view would say that nonfactive grounding claims are autonomous.
One might instead take the definition to be an act of stipulation. Since acts of stipulations aren’t sentences of the object language, the definition could not be a theorem. Or, one might take the definition to be “\({\forall }x{\forall }y ( x\subseteq y \leftrightarrow {\forall }z(z\in x\rightarrow z\in y))\)”. This is an abbreviation for “\({\forall }x{\forall }y ({\forall }z(z\in x\rightarrow z\in y) \leftrightarrow {\forall }z(z\in x\rightarrow z\in y))\)”, which is a theorem (since it’s a logical truth).
See Sider (2011, Section 7.6) for a discussion of this issue.
I take this martial terminology from Kovacs (2017).
For instance Wilson’s (2014) “little-g” grounding relations.
I actually have in mind nonfactive grounds of (1) and thus am ignoring Ta.
But see Sider (2018, Section 2.5.2).
To be sure, some elements cited in the preceding paragraphs are not unique to the right-hand-side of (1). Some partial grounds of (1) will, as a result, also partially ground other grounding claims. For instance, one partial ground of (1) might be a pure ground of \(Ta_{17}\) (since such a fact grounds \(Ta_{17}\), which grounds \(Ta_{17}{\vee }Ca_{17}\), which grounds \(\mathord {\sim }Ta_{17} \vee (Ta_{17}{\vee }Ca_{17})\), which partially grounds (2), which (I say) partially grounds (1)); but this same fact would also partially ground any other fact of the form
. Nevertheless, appropriate sensitivity to the consequent of (1) is present in the totality of partial grounds of (1).This might be in tension with the suggestion made at the beginning of the paper that some grounding facts ground the corresponding modal statement, depending on which modal claims are said to partially ground the facts of grounding.
Or in \({\Box }(Ta\rightarrow (Ta\vee Ca))\).
Actually I think a more likely view is that \(\tau \) is a functional definition of ‘table’.
This is enabled by the fact that ground is “conditional”, not “biconditional” (see note 3).
Compare Dasgupta’s (2014b) argument against grounding Obama’s existence in a description of an overly large region of space.
There are other plausible candidate grounds of (6) in the neighborhood:
- (7a)
\({\Box }{\forall }x((T_1x\rightarrow (T_1x\vee (C_1x{\vee }C_2x{\vee }\cdots ))) \wedge (T_2x\rightarrow (T_2x\vee (C_1x{\vee }C_2x{\vee }\cdots ))) \wedge \cdots )\)
- (7b)
\({\Box }{\forall }x((T_1x{\rightarrow }(T_1x{\vee }C_1x)) \wedge (T_1x{\rightarrow }(T_1x{\vee }C_2x)) \wedge \cdots \wedge (T_2x{\rightarrow }(T_2x{\vee }C_1x)) \wedge (T_2x{\rightarrow }(T_2x{\vee }C_2x)) \wedge \cdots )\)
In (7), it is only the entire disjunction of the realizers of ‘a is a table’ that is said to suffice for something (namely, the disjunction of the disjunction of realizers of ‘a is a table’ with the disjunction of realizers for ‘a is a chair’). Whereas in (7a) and (7b), each individual realizer of ‘a is a table’ is said to be sufficient for something—for the disjunction of itself with the disjunction of all realizers of ‘a is a chair’, in the case of (7a), and for the disjunction of itself with, in turn, each realizer of ‘a is a chair’ in (7b).
- (7a)
I have in mind Schiffer’s (2003) approach.
Kovacs (2017a) defends a “lightweight” conception of ontological dependence (a close cousin of ground) in which mereological relations play a central role. Also meshing with the spirit of the present paper is Kovacs’s insistence that a lightweight account need not give necessary and sufficient conditions for ontological dependence. (His defense of the propriety of this stance is different from mine.)
This idea could take different forms. Metalinguistic facts might be said to directly ground
, the idea being that there is a direct realization relation between \(T_1\) and T that is partly metalinguistic in nature. Alternatively, it might be said that \(T_1\) realizes, in an entirely nonmetalinguistic sense, a certain functional property F, so that 
is grounded by facts having nothing to do with language; but nevertheless, metalinguistic facts help ground 
, the idea being that they attach F to ‘table’ and hence to tablehood. 
and 
would then ground 
(the latter would be a case of mediate ground in Fine’s (2012) sense).Here I assume that ground is a relation between facts, which is in harmony with the view under discussion.
These propositions would be nonfactive full grounds of A’s grounding B.
In Sider (2011, 7.13) I argue that the concept of a fundamental concept is a fundamental concept. There are subtle issues about what concepts the claim involves; see Sider, (2011, Section 6.3). For a similar view to that of this section, see Wilson (2014, Section IV.i.), who argues that a certain sort of fundamentality is primitive, and that this helps to fix the direction of metaphysical priority.
Similarly, a believer in fundamental laws of metaphysics like Schaffer (2017, Section 4.2) could, consistently with Purity, invoke fundamental laws of metaphysics that involve only fundamental concepts, such as, perhaps, a second-order law to the effect that for all P, Q, if P then \(P\vee Q\).
See Rosen (2010, Section 2), for example.
”): for some 
. Thus the consequent of the third member of the series partially grounds the consequent of the second member. Similarly, applying the principle to the third member of the series yields 
, and so the consequent of the fourth member of the series partially grounds the consequent of the third member of the series; and so on. But, in the spirit of Lewis Carroll (
. Moreover it seems based on the thought that “A cannot, on its own, fully ground B; it is only the combination of A and 
that fully grounds B”, whose first half implies, if the variables A and B are universally quantified and if A encompasses pluralities, that no fact has a full ground; also, the first half, thus understood, contradicts the second half.
and 
would, according to Bennett and deRosset, have the same ground, whereas “the grounds are surely different and involve something about disjunction in the first case and negation in the second” (Dasgupta 
. Nevertheless, appropriate sensitivity to the consequent of (1) is present in the totality of partial grounds of (1).
, the idea being that there is a direct realization relation between 
is grounded by facts having nothing to do with language; but nevertheless, metalinguistic facts help ground 
, the idea being that they attach F to ‘table’ and hence to tablehood. 
and 
would then ground 
(the latter would be a case of mediate ground in Fine’s (References
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Acknowledgements
Thanks to Karen Bennett, Shamik Dasgupta, David Kovacs, Jon Litland, Kris McDaniel, Jonathan Schaffer, and referees.
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Sider, T. Ground grounded. Philos Stud 177, 747–767 (2020). https://doi.org/10.1007/s11098-018-1204-6
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DOI: https://doi.org/10.1007/s11098-018-1204-6