Abstract
The article introduces and defends the Nomological Account of ground, a reductive account of the notion of metaphysical explanation in terms of the laws of metaphysics. The paper presents three desiderata that a theory of ground should meet: it should explain the modal force of ground, the generality of ground, and the interplay between ground and certain mereological notions. The bulk of the paper develops the Nomological Account and argues that it meets the three desiderata. The Nomological Account relies on two central notions: the notion of a ‘law of metaphysics’ and the notion of ‘determination via the laws’. The paper offers the constructional conception of the laws of metaphysics, on which the metaphysical laws are general principles that characterize construction–operations such as composition, constitution, or set-formation. The role of determination in the account is explained and some reductive approaches to the notion are sketched. The case for the Nomological Account presented in this article is also a case for the laws of metaphysics. Since the Nomological Account offers a promising approach to metaphysical explanation we should take the laws of metaphysics seriously.
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Notes
The restriction to qualitative properties rules out counterexamples of the following sort: The fact that Peter has the relational property ‘loves-Peter’ grounds the fact that Peter is narcissistic. But Carla may have the property ‘loves-Peter’ and fail to be narcissistic. Thanks to Shamik Dasgupta here.
deRosset (2010) presents other versions of Generalization and the motivation in the text.
Constituent to Ground is compatible with views on which some wholes are involved in the grounds of facts involving their parts. See especially Schaffer (2010) on Priority Monism. Parts could be ‘constructed’ from wholes and would then count as constituents of parts.
‘F’ is a genuine property term, where this notion is partly characterized by the following necessary condition: if ‘F’ is the result of lambda-abstraction as applied to a logically molecular sentence, then ‘F’ is not a genuine property term. In particular, λx(G1(a) v G2(x)) is not a genuine property term. Consequently, G 1 (a) grounds λx(G 1 (a) v G 2 (x))(b) is not a counterexample to Ground to Constituent. Thanks to an anonymous referee for raising the issue.
Thanks to an anonymous referee for these examples.
Lewis (1983) takes simplicity to be constitutive of the nature of law-hood. But even if we disagree with this, relative simplicity is required to uphold the analogy between the metaphysical laws and the laws of nature.
This idea can be developed further as follows: certain axioms of metaphysical necessity hold in virtue of the nature of metaphysical law-hood. These axioms include the ‘detachment-principle’ □(LM(p) ⊃ p) and the ‘uniformity-principle’ LM(p) ⊃ □M(LM(p)), where ‘□M’ means ‘it is metaphysically necessary that’. Since the notion of metaphysical necessity enters the essence of metaphysical law-hood, the laws are the source of metaphysical necessity. Similarly, detachment- and uniformity-principles of natural necessity may be encoded in the essence of the laws of nature. I argue in ‘The circularity puzzle in the metaphysics of the laws of nature’, (unpublished) that the Anti-Humean about laws of nature should use this maneuver to solve the inference problem articulated in Lewis (1983).
This view faces the challenge of distinguishing arbitrary restrictors from genuine kinds of necessity [cf. Rosen (2006, p. 33), Fine (2002, pp. 265–266)]. A common response to this problem which, to my knowledge, has not been discussed adequately in print (although see Sider 2012, ch. 12), relies on the context-sensitivity of modals: Speakers determine different restrictors on the space of possibilities in different contexts; what counts as necessary in each context is a purely conventional matter. According to this response, the feeling that certain restrictors are ‘genuine necessities’ is misleading.
Note that my notion of ‘ground’ differs from Schaffer’s notion of ‘grounding,’ which Sider (2012) refers to as ‘entity-grounding’.
This characterization of construction is not a definition. Relative fundamentality among individual entities is to be defined in terms of construction. And the claim that constructed entities exist in virtue of the constructing entities is just a gloss of the notion of construction, which I am treating as conceptually and metaphysically primitive. However, there is an interesting view on which construction is defined in terms of ground. On that view, constructional relationships between entities can somehow be read off from the grounding-structure defined over truths. This view would render the Nomological Account presented below non-reductive. A non-reductive proposal might still provide illuminating interconnections between important notions. Thanks to an anonymous referee for suggesting this option.
See Schaffer (2012) for discussion of the ontological innocence of derivative entities.
Operation assumes that construction–operations are ‘functional’ in the sense that an expression of the form ‘O(A1, …, An)’ picks out a unique referent. I think that functionality is plausible if we accept ‘O(…)’ as a context that is both order-sensitive and repetition-sensitive. Thus, O(A, B) need not be identical with O(B, A), and O(A) need not be identical with O(A, A). See Bader (2013) for some discussion of this extended notion of functionality. However, if functionality is rejected, the formulation ‘A = O(B1, …, Bn)’ can be consistently replaced with the relational expression ‘O(B1, …, Bn; A)’. I’ll stick to the formulation that assumes functionality for simplicity.
Fine (2010) argues that construction–operations are more fundamental than construction-relations. I am neutral on this issue.
There may be exceptions. If some operation has no application–condition, then the existence of the entity constructed in this way has no sufficient ground. These entities would be emergent in a sense similar to the one captured by Barnes (2012).
We can also use O in Ontological Principle as a relational expression: ∀xx(CO(xx) ⊃ ∃y(O(xx; y))). Analogous substitutions are possible in the principles below.
See Armstrong (1997) for an account of quantities along these lines.
See Loewer (2012) for a version of this reasoning.
How does the Nomological Account handle the fact that ~CO(aa) grounds ~∃y(y = O(aa))? We could appeal to negative ontological principles of the form ∀xx(~CO(xx) ⊃ ~∃y(y = O(xx))). I prefer an approach on which some negative truths are explained by the absence of possible grounds. Assuming, for instance, that CO(xx) is the only possible ground for ∃y(y = O(xx)), the absence of the former counts as (absence-)ground of the latter. Possible ground is the non-factive version of the notion of ground as defined by the Nomological Account.
As mentioned in the previous section, the necessity of the laws can be explained by the nature of laws or the nature of metaphysical necessity. An anonymous referee suggests that the metaphysical laws might be necessary because they hold in virtue of the nature of the construction–operations. For instance, it might lie in the nature of set-formation that each suitable plurality of entities forms a set. I do not take a stance on this proposal here. But note that these essences would then be generative in the sense that they entail the existence of additional derivative entities on the basis of more fundamental entities. For discussions of such ‘Anselmian’ Essences, see Dasgupta (2014) and Rosen (2006).
Note that this claim about the word “chess” is not linguistic but metaphysical. Claims such as ‘The game of chess exists’ and ‘“chess” is a referring expression in English’ are true. The strategy I suggest, however, denies that chess is ‘in the ontology’ or that chess really exists. This can perhaps be understood in terms of fact-identifications: every chess-fact is identical to some fact that doesn’t feature chess. The notion of fact-identity used here is akin to ‘grounding-theoretic equivalence’ in Fine (2012).
I realize that the appeal to an unfamiliar construction–operation of abstraction is somewhat unsatisfying. But the characterization of the logic and nature of the various construction–operations goes beyond the scope of this paper.
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Acknowledgments
I would like to thank Shamik Dasgupta, Marco Dees, Tom Donaldson, Stephanie Leary, Laurie Paul, Raul Saucedo, Alex Skiles, a referee from this journal, the participants of the Bellingham Summer Philosophy Conference 2014, and especially Jonathan Schaffer for incredibly thoughtful feedback.
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Wilsch, T. The Nomological Account of Ground. Philos Stud 172, 3293–3312 (2015). https://doi.org/10.1007/s11098-015-0470-9
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DOI: https://doi.org/10.1007/s11098-015-0470-9