Abstract
According to Humeanism about the laws, the laws of nature are nothing over and above certain kinds of regularities about particular facts (the “Humean mosaic”). Humeanism has often been accused of circularity: according to scientific practice laws often explain their instances, but on the Humean view they also reduce to the mosaic, which includes those instances. In this paper I formulate the circularity problem in a way that avoids a number of controversial assumptions routinely taken for granted in the literature, and against which many extant responses are therefore ineffective. I then propose a solution that denies the alleged Humean commitment that laws are explained by their instances. The solution satisfies three desiderata that other solutions don’t: it provides independent motivation against the idea that Humean laws are explained by their instances; it specifies the sense in which Humean laws are nonetheless “nothing over and above” their instances; and it gives an alternative account of what does explain the laws, if not their instances. This solution, I will argue, is not only the simplest but also the oldest one: it appeals only to tools and theses whose first appearance predates the earliest statements of the circularity problem itself.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
The standard Humean view today is that laws are metaphysically explained by their instances (Loewer 2012: p. 131). Variants of this view classify these explanations as involving truthmaking (Hicks and van Elswyk 2015: p. 439) and constitution (Bhogal 2017: p. 448). See also Lange (2013, 2018) for chaining metaphysical and scientific explanations.
See Schaffer (2016).
Both Hicks and van Elswyk (2015) and Bhogal (forthcoming) go back and forth between saying that there are two kinds of explanation, metaphysical and scientific (or for Bhogal, ‘nomothetic’), and the different claim that the word ‘explanation’ is ambiguous between metaphysical and scientific senses. But as Marshall (2015: p. 3149) notes, the mere fact that there are two kinds of explanation and that the laws bear the one to their instances, which in turn bear the other one to the laws, doesn’t make the result of widespread mutual (or self-) explanation any more acceptable. Roski (2018: p. 1987) is also explicit that in order to deny P3 (or a premise playing a similar role in his version of the argument), the Humean has to say that ‘explanation’ is ambiguous; it’s not enough to distinguish different kinds of explanation.
See also Marshall (2015: p. 3150) for this point.
See Schaffer (2012).
This is, at least, how I understand the metaphysical circularity problem, which is the main topic of the paper. Some authors have recently argued that Humeans also face a problem with semantic circularity (Roski 2018; Shumener 2019). In other work (Kovacs ms), I argue that this problem ultimately collapses into the metaphysical problem discussed here.
In fairness to Miller, she does offer such reasons when presenting an alternative solution to the circularity problem, which she calls “Contrarian Humeanism”. In the present paper I focus only on Groundless Humeanism, which is closer to the account I will offer.
A referee suggests that a genuinely observer-relative view of explanation would make P4 less plausible. I think that depends on how we understand P4 in an observer-relative framework. Suppose explanation is relativized to observers. Then it may indeed often be the case that A explains B relative to observer O1 and B explains A relative to observer O2. However, what an observer-relativized version of P4 should deny is only that it’s a common and systematic phenomenon that a law of nature and its instance explain each other relative to the same observer. (To keep the argument valid, the remaining premises should likewise be relativized to the same observer. The scope of the argument might need to be restricted to those who accept and understand the Humean view and grasp the explanations it offers, but the conclusion would still be damaging enough for Humeans.).
As I earlier said ‘reduction’ is a weasel word, so in some specific contexts it might even be understood to mean reduction—viz. Lewis’s claim that a “supervenience thesis is […] a stripped-down form of reductionism” (1983: p. 358). Nonetheless, I don’t think that (even asymmetric) supervenience is sufficiently fine-grained to capture the notion of reduction Humeans should care about.
In this, I follow Nolan (2005: p. 83).
Lewis himself presents strength as just one theoretical virtue, which could potentially be traded off against simplicity. This would allow systematizations in which some propositions are neither axioms nor derived from axioms; they are, as it were, casualties suffered by strength in exchange for a gain in simplicity. My impression is that later interpretations of the BSA tacitly assume that any admissible systematization is maximally strong in the sense of being complete: any proposition that is not an axiom in the systematization is derivable from the axioms. However, some authors explicitly reject this requirement. For example, Braddon-Mitchell (2001) recommends an interpretation of laws that admit exceptions as “lossy laws”: laws that allow us to derive some false propositions (their negation is simply an exception to the law in question) but figure in the best systematization. The argument that follows doesn’t hang on the choice between these interpretations, for the following reasons: I will mainly be interested in cases where a proposition is both explained by and derived from certain Humean axioms, and I assume that the conservative and the “lossy” BSA theorist agree on these cases. If there are propositions that are neither axioms nor derived from axioms, they are not explained by anyone’s light. (Thanks to an anonymous referee for requesting clarification on this.).
An incomplete list includes the questions of how the account deals with probabilistic laws (Lewis 1994; Hall 2012), how it can distinguish between laws and background conditions (Hicks 2018), the proper understanding of the simplicity and strength criteria (Hicks 2018; Dorst 2017, 2019; Jaag and Loew 2018), whether the BSA can accommodate special science laws (Cohen and Callendar 2009), and problems about the notion of naturalness at work (Loewer 2007; Cohen and Callendar 2009; Hildebrand 2019).
Lewis (1983: p. 358).
Lewis (1986d).
Though Beebee (2000) argues that it is at least not a conceptual truth that the laws govern.
Bhogal (forthcoming: sec. 2.1) is particularly explicit about this.
See Rosen (2010: p. 131) for a similar justification.
A referee suggests that a more deflationary understanding of ‘essence’-talk might reduce the tension. For example, it might be just a matter of convention that it belongs to the essence of conjunction that if P and Q are true then so is P&Q. My response is that if this notion of essence is to underlie the relevant explanation claim, the notion of explanation in ‘P and Q explain P&Q’ would need to be similarly conventional. However, it strikes me as false that that there is a standing convention according to which conjunctions are explained by their conjuncts. As a response to the question, ‘Why is it dark and rainy?’, most ordinary speakers would not accept as a satisfactory answer ‘Because (1) it is dark; (2) it is rainy’ (cf. Kovacs 2019b). The principle of conjunctive grounding is very much a philosophers’ invention, and I suspect that so is the entire “impure logic of ground” (see Kovacs 2019b; McSweeney forthcoming).
The same goes for the status of particular facts, some of which the BSA theorist derives from universal generalizations. The explained (and so non-fundamental) status of these facts is likewise consistent with the BSA account of laws because the BSA has no commitment to any particular thesis about explanation, given that it’s not a thesis about explanation at all. (Thanks to an anonymous reviewer for pressing me on these questions.).
I’m assuming that the instance of a restricted universal generalization is an instance of the consequent of its embedded conditional, rather than a negation of an instance of its antecedent. This shouldn’t make much difference to the discussion that follows.
Skiles focuses on accidental generalizations, which he thinks pose a tougher problem; certain necessary generalizations (including law-like ones) may be grounded in laws or facts about essences. But of course, these options aren’t available to a Humean anyway, which in the present context makes the restriction unnecessary.
The same problem arises with the proposal that uses the same maximal totality fact, a complete description of the mosaic followed by a ‘that’s all’ clause, to explain all universal generalizations. While this strategy would appeal to only one totality fact instead of many, most of the information involved by this totality fact is completely irrelevant to the universal generalzations it was invoked to explain. (Thanks to an anonymous referee for this suggestion.).
Skiles (2015: pp. 733–734). Similar problems arise with a close cousin of this view, which operates with atomic rather than quantified totality facts, and which Skiles models on similar views defended by Armstrong (1997: p. 199) and Fine (2012: p. 62) about unrestricted totality facts. The idea is that for each generalization ∀x (Fx ⊃ Gx) with certain instances, Fa1…Fan, there is a primitive property of being such that a1…an are the only F-s that there are, such that a1…an plurally instantiate this property (alternatively, perhaps there is a primitive “totaling” relation that a1…an bear to the property of being F). I don’t think that the switch to atomic facts changes much of substance for the present discussion: because of how much is built into the primitive property or relation in question, such facts still look explanatorily irrelevant to the restricted universal generalizations they are invoked to explain, and since they aren’t parts of the Humean mosaic, using them to explain the laws is still anti-Humean in spirit.
I thank an anonymous referee for offering this modified version of the argument.
See Kovacs (2019a: n1) for a long list of recent works focused on the distinction between grounding and ontological dependence.
In fact, I already improved on the formulation that would be strictly required for a formulation in terms of ontological dependence. For keep in mind that the BSA theorist’s laws are propositions. When the first relatum of dependence is a proposition, questions of ontological dependence will concern not that proposition’s truth but its existence. But it’s clear enough that whether laws depend on the mosaic in this sense turns on general questions about the metaphysics of propositions that have nothing to do with laws per se. Thus, I assume that if there’s any question in the vicinity that Humeans have a reason to be interested in, it concerns the dependence of a law’s truth (rather than existence) on the mosaic.
The main difference between Marshall’s view and mine is that while according to him at least some universal generalizations (non-laws) are explained by their instances, on my view this never happens. So how are non-fundamental universal generalizations explained? There is no general answer to this question. For example, universal generalizations about composite material objects are plausibly explained by universal generalizations about their parts: that every coin in my pocket is a 20c coin is explained by the fact that every set of particles arranged coin-wise within the spatial region bounded by my simples arranged pocket-wise are also arranged 20c-coin-wise. (I owe this example to an anonymous referee.) Other cases will have to be treated differently.
References
Armstrong, D. M. (1983). What is a law of nature?. Cambridge: Cambridge University Press.
Armstrong, D. M. (1997). A world of states of affairs. Cambridge: Cambridge University Press.
Beebee, H. (2000). The non-governing conception of laws of nature. Philosophy and Phenomenological Research, 61, 571–594.
Bhogal, H. (2017). Minimal anti-humeanism. Australasian Journal of Philosophy, 95, 447–460.
Bhogal, H. (forthcoming). Nomothetic explanation and humeanism about the laws of nature. Oxford Studies in Metaphysics.
Bird, A. (2007). Nature’s metaphysics: Laws and properties. Oxford: Oxford University Press.
Bliss, R. (2014). Viciousness and circles of ground. Metaphilosophy, 45, 245–256.
Braddon-Mitchell, D. (2001). Lossy laws. Nous, 35, 260–277.
Cohen, J., & Callendar, C. (2009). A better best system account of lawhood. Philosophical Studies, 145, 1–34.
Correia, F. (2014). Logical grounds. Review of Symbolic Logic, 7(1), 1–29.
Dasgupta, S. (2017). Constitutive explanation. Philosophical Issues, 27, 74–97.
Dorst, C. (2017). Towards a best predictive system account of laws of nature. British Journal for the Philosophy of Science, 70, 877–900.
Dorst, C. (2019). Humean laws, circularity, and the aims of scientific explanation. Philosophical Studies, 176, 2657–2679.
Drestske, F. (1977). Laws of nature. Philosophy of Science, 44, 248–268.
Emery, N. (2019). Laws and their instances. Philosophical Studies, 176, 1535–1561.
Fine, K. (2010). Some puzzles of ground. Notre Dame Journal of Formal Logic, 51, 97–118.
Fine, K. (2012). Guide to ground. In F. Correia & B. Schnieder (Eds.), Metaphysical grounding (pp. 37–80). Cambridge: Cambridge University Press.
Friedman, M. (1974). Explanation and scientific understanding. Journal of Philosophy, 71, 5–19.
Guigon, G. (2015). A universe of explanations. Oxford Studies in Metaphysics, 9, 345–375.
Hall, N. (2012). Humean reductionism about laws of nature (manuscript).
Hanley, R. (2004). No end in sight: Causal loops in philosophy, physics and fiction. Synthese, 141, 123–152.
Hicks, M. T. (2018). Dynamic humeanism. British Journal for the Philosophy of Science, 69, 983–1007.
Hicks, M. T., & van Elswyk, P. (2015). Humean laws and circular explanation. Philosophical Studies, 172, 433–443.
Hildebrand, T. (2019). Naturalness constraints on best systems accounts of laws. Ratio, 32, 163–172.
Jaag, S., & Loew, C. (2018). Making best systems best for us. Synthese. https://doi.org/10.1007/s11229-018-1829-1.
Jenkins, C. (2011). Is metaphysical dependence irreflexive? Monist, 94, 267–276.
Kitcher, P. (1981). Explanatory unification. Philosophy of Science, 48, 507–531.
Kitcher, P. (1989). Explanatory unification and the causal structure of the world. In P. Kitcher & W. Salmon (Eds.), Scientific explanation (pp. 410–505). Minneapolis: University of Minnesota Press.
Kovacs, D. M. (2018). What is wrong with self-grounding? Erkenntnis, 83, 1157–1180.
Kovacs, D. M. (2019a). Review of reality and its structure: Essays in fundamentality. In R. Bliss, & G. Priest (Eds.), Notre dame philosophical reviews. Retrieved February 28, 2020 from https://ndpr.nd.edu/news/reality-and-its-structure-essays-in-fundamentality/.
Kovacs, D. M. (2019b). Metaphysically explanatory unification. Philosophical Studies. https://doi.org/10.1007/s11098-019-01279-z.
Kovacs, D. M. (ms). Humean laws and semantic circularity.
Lange, M. (2013). Grounding, scientific explanation, and Humean laws. Philosophical Studies, 164, 255–261.
Lange, M. (2018). Transitivity, self-explanation, and the explanatory circularity argument against Humean accounts of natural law. Synthese, 195, 1337–1353.
Lewis, D. K. (1976). The paradoxes of time travel. American Philosophical Quarterly, 13, 145–152.
Lewis, D. K. (1983). New work for a theory of universals. Australasian Journal of Philosophy, 61, 343–377.
Lewis, D. K. (1986a). Philosophical papers (Vol. 2). Oxford: Oxford University Press.
Lewis, D. K. (1986b). A subjectivist’s guide to objective chance, in Lewis 1986a (pp. 83–132).
Lewis, D. K. (1986c). The plurality of worlds. Oxford: Blackwell.
Lewis, D. K. (Ed.). (1986d). Causal explanation. In Philosophical papers (Vol. Ii, pp. 214–240). Oxford University Press.
Lewis, D. K. (1994). Humean supervenience debugged. Mind, 103, 473–490.
Loewer, B. (1996). Humean supervenience. Philosophical Topics, 24, 101–127.
Loewer, B. (2007). Laws and natural properties. Philosophical Topics, 35, 313–328.
Loewer, B. (2012). Two accounts of laws and time. Philosophical Studies, 160, 115–137.
Marshall, D. (2015). Humean laws and explanation. Philosophical Studies, 172, 3145–3165.
Maudlin, T. (2007). The metaphysics within physics. Oxford: Oxford University Press.
McSweeney, M. (forthcoming). Debunking logical ground: distinguishing metaphysics from semantics. Journal of the American Philosophical Association.
Meyer, U. (2012). Explaining causal loops. Analysis, 72, 259–264.
Miller, E. (2015). Humean scientific explanation. Philosophical Studies, 172, 1311–1332.
Miller, K., & Norton, J. (2017). Grounding: it’s (probably) all in the head. Philosophical Studies, 174, 3059–3081.
Miller, K., & Norton, J. (2019). A psychologistic theory of metaphysical explanation. Synthese, 196, 2777–2802.
Nickel, B. (2010). How general do theories of explanation need to be? Nous, 44, 305–328.
Nolan, D. (2005). David Lewis. Stocksfield: Acumen Publishing.
Rodriguez-Pereyra, G. (2015). Grounding is not a strict order. Journal of the American Philosophical Association, 1, 517–534.
Rosen, G. (2010). Metaphysical dependence: Grounding and reduction. In B. Hale & A. Hoffman (Eds.), Modality: Metaphysics, logic, and epistemology (pp. 109–135). Oxford: Oxford University Press.
Roski, S. (2018). Grounding and the explanatory role of generalizations. Philosophical Studies, 175, 1985–2003.
Schaffer, J. (2008). Causation and the laws of nature: Reductionism. In T. Sider, J. Hawthorne, & D. W. Zimmerman (Eds.), Contemporary debates in metaphysics (pp. 82–107). Oxford: Blackwell.
Schaffer, J. (2012). Grounding, transitivity, and contrastivity. In F. Correia & B. Schnieder (Eds.), Metaphysical grounding (pp. 122–138). Cambridge: Cambridge University Press.
Schaffer, J. (2016). Grounding in the image of causation. Philosophical Studies, 173, 49–100.
Schnieder, B. (2015). The asymmetry of ‘Because’. Grazer Philosophische Studien, 91, 131–164.
Shaheen, J. (2017). The causal metaphor account of metaphysical explanation. Philosophical Studies, 174, 553–578.
Shumener, E. (2019). Laws of nature, explanation, and semantic circularity. British Journal for the Philosophy of Science, 70, 787–815.
Sider, T. (2020). The tools of metaphysics and the metaphysics of science. Oxford: Oxford University Press.
Skiles, A. (2015). Against grounding necessitarianism. Erkenntnis, 80, 717–751.
Thompson, N. (2019). Questions and answers: Metaphysical explanation and the structure of reality. Journal of the American Philosophical Association, 5, 98–116.
Tooley, M. (1977). The nature of laws. Canadian Journal of Philosophy, 7, 667–698.
Turner, J. (2016). Curbing enthusiasm about grounding. Philosophical Perspectives, 30, 366–396.
Acknowledgements
For many helpful comments on and conversations about this paper, I thank Nina Emery, Simon Goldstein, Derek Hardlie, Laci Kocsis, Dan Marshall, Alex Skiles, two anonymous referees of this journal, and audiences at Tel Aviv University, Lingnan University, and the 2nd Bucharest-Budapest Workshop in Philosophy (entitled “Humeanisms”) at the RCH-HAS of the Institute of Philosophy in Budapest. I also thank the Israel Science Foundation for support (Grant No. 2035/19, “The Idealist Program of Metaphysical Explanation”).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Kovacs, D.M. The oldest solution to the circularity problem for Humeanism about the laws of nature. Synthese 198, 8933–8953 (2021). https://doi.org/10.1007/s11229-020-02608-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-020-02608-0