Abstract
A common objection to Humeanism about natural laws is that, given Humeanism, laws cannot help explain their instances, since, given the best Humean account of laws, facts about laws are explained by facts about their instances rather than vice versa. After rejecting a recent influential reply to this objection that appeals to the distinction between scientific and metaphysical explanation, I will argue that the objection fails by failing to distinguish between two types of facts, only one of which Humeans should regard as laws. I will then conclude by rebutting a variant of this objection that appeals to a principle of metaphysical explanation recently put forward by Kit Fine.
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Notes
Humeanism about natural laws and the more general thesis of Humeanism about all broadly explanatory notions are therefore reductive theses similar to reductionism about modality, tense and morality. See Sider (2003) for an analogous formulation of reductionism about modality.
An eligible deductive system is a deductive system all of whose axioms are true and whose non-logical vocabulary consists of predicates expressing sparse properties. The more possibilities ruled out by a theory’s axioms, the stronger the theory is; while the fewer axioms a theory has, and the more syntactically simple those axioms are, the simpler the theory is. For simplicity, a regularity can be taken to be a fact that is expressed by a sentence of the form ‘\(\forall x_1\,\ldots\,\forall\,x_n(Fx_1\,\ldots\,x_n \supset Gx_1\,\ldots\,x_m)\)’, where \(m\le n\), and F and G express sparse properties or relations. This notion of a regularity needs to be extended in order to count the laws that appear in our best scientific theories that involve differential equations as regularities, but this complication can be ignored here. Different versions of BSA can be obtained by employing different notions of a sparse property. For definiteness, I will take a sparse property or relation to be a property or relation that is positive, qualitative, intrinsic and non-disjunctive. This notion of a sparse property at least roughly corresponds to the notion of a perfectly natural property employed in Lewis (1983). For discussion of the different notions of perfect naturalness Lewis employed, see Marshall (2012, pp. 533–535).
A state of affairs is a way things are or a way things fail to be. A fact is an obtaining state of affairs: that is, it is a way things are.
BSA as formulated above has the undesirable consequence that there might be a non-fundamental law that cannot be derived from fundamental laws (and other facts that are expressed by axioms in all best systems). (Fact f can be derived from fact g iff f is expressed by a sentence that can be derived from a sentence expressing g.) Suppose, for example, there are exactly two best systems, one whose only axiom expresses \(\underline{\hbox {All}\, F\hbox {s} \hbox { are } H\hbox {s}}\) and one whose only axiom expresses \(\underline{\hbox {All}\, G\hbox {s } \hbox {are } H\hbox {s}}\) (where \(\underline{\hbox {All}\, F\hbox {s } \hbox {are } H\hbox {s}}\) is not necessarily equivalent to \(\underline{\hbox {All } G\hbox {s are } H\hbox {s}}\)). Then, according to BSA, \(\underline{\hbox {Anything that is both } F \hbox { and } G \hbox { is } H}\) would be a non-fundamental law that cannot be derived from any fundamental laws or from any other facts that are expressed by axioms in all best systems. To avoid this consequence, we might modify BSA by either replacing its account of a law with (a) or replacing its account of a fundamental law with (b):
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(a)
p is a law iff it is a regularity and it is deductively entailed by states of affairs that are expressed by axioms in every best system.
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(b)
p is a fundamental law iff it is a law and either (a) it is expressed by an axiom in every best system, or (b) it is not deductively entailed by any facts that are axioms in every best system.
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(a)
I will also suppose that the predicates F and G express sparse properties (see fn. 3).
I will take a particular matter of fact to be a fact expressed by a sentence of the form \(\ulcorner Ra_1\ldots\,a_n\urcorner\), where R expresses a sparse property or relation, and \(a_1,\,\ldots\,a_n\) are names for concrete objects.
One way a Humean might respond to the objection from explanation is to simply hold that laws don’t help explain their instances. I will assume that this response is unsatisfactory, or at least that it would be better for Humeans if they weren’t forced to hold this view.
Loewer’s response to the objection from explanation is endorsed, for example, by Hicks and van Elswyk (2015).
Given the simplification, if f metaphysically explains g, then f and g are either co-temporal or both non-temporal, and hence g is not temporally prior to f, and so does not scientifically explain it. Hicks and van Elswyk (2015, Sect. 2.2) claim that there are a number of different kinds of explanation, and that each of these different kinds of explanation is supported by a different ‘backing relation’. They further claim that some of these backing relations fail to be asymmetric (indeed, they claim that some are symmetric), and that, as a result of this, the kinds of explanation that are supported by these backing relations also fail to be asymmetric. If these claims are true, then (A) is invalid. However Hicks and van Elswyk give no reason to think that there are any such backing relations, and the fact that their existence would conflict with (A) provides a good reason to think that there aren’t any. The only relation they mention that they claim to be a backing relation and that fails to be asymmetric (at least on a standard understanding of the relation) is the supervenience relation. However, this relation is widely thought not to back explanation, precisely because it fails to be asymmetric, and Hicks and van Elswyk provide no reason to overturn this common judgement.
Ironically, the strongest challenge to (A) doesn’t involve the interaction of scientific explanation and metaphysical explanation, but instead concerns purely scientific explanation. If time travel is possible, as a number of philosophers believe, it might be possible to have causal loops where, for example, an older time traveller, travels back in time to give the blueprint of his time machine to his younger self, who then uses it to build his time machine (see Lewis 1979; Wilson MS.) If such a causal loop is possible, then (A) is invalid, since, given the causal loop, the construction of the time machine is explained by the appearance of the blueprint, which is in turn explained by the construction of the time machine. Since time travel cases are so different from the case involving Humean laws and their instances, however, if (A) fails due to such causal loops, and there are no other independently plausible counterexamples to (A), there is no reason to think that (A) cannot be restricted so that its restriction can be validly applied in the objection from explanation. The existence of causal loops, by itself, therefore, isn’t sufficient to vanquish the objection from explanation.
See Lange (2013, p. 256).
As Miller (2014, Sect. 4) points out, Lange’s reformulation of the objection from explanation can be modified so that it doesn’t rely on the claim that nothing can scientifically explain itself. This can be done by noting that, given (T*), and given the law \(\underline{\hbox {All } F\hbox {s are } G\hbox {s}}\) partly scientifically explains, and is partly metaphysically explained by, its instances, it follows from a and b both being F that \(\underline{a \hbox { is } G}\) partly scientifically explains \(\underline{b \hbox { is } G}\), which is not generally true.
Despite Hicks and van Elswyk’s claim to the contrary, their example above does not have the same “short-circuit” structure as the well known problematic cases for the transitivity of causation (see Hall 2000). As Lange (2013, Fn. 1) in effect points out, if there are examples having this structure that are counterexamples to (T*), then a restricted version of (T*) might still be able to be validly applied in Lange’s version of the objection from explanation. Given the existence of such counterexamples, then, a proponent of Loewer’s response would still have to make it plausible that no such restriction exists.
Miller also proposes a counterexample to (T*) involving statistical mechanics. Like the case of probabilistic explanation described in Sect. 2.1, a defender of (T*) might respond to this example by either denying that it is a genuine case of explanation or by restricting (T*) to cases of deterministic explanation.
If it is denied that the conjunction of the fact that Suzy breaks a window at \(t_1\) with a number of other facts explains the fact that the window breaks at \(t_2\), but it is agreed that the fact that Suzy breaks a window at \(t_1\), together with these other facts, jointly explain the fact that the window breaks at \(t_2\), then this result can instead be obtained from the generalisation of (Sp) given by (Sp*).
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Sp*.
If the conjunction of \(f_1,\ldots f_n\) necessitates the conjunction of \(g_1,\ldots g_m\), but not vice versa, and \(g_1,\ldots g_m\) jointly explain h, then \(f_1,\ldots f_n\) do not jointly explain h.
(Sp*) can similarly be used in place of (Sp) in the arguments below that (Sp) entails that (T*) fails in the James the snail example and Lange’s balloon example, and that the fact that Suzy threw the rock at \(t_1\) does not help explain why the window broke at \(t_2\).
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Sp*.
A Humean might instead respond by denying that the purely existential fact that someone throws a rock at \(t_1\) helps to explain why the window broke. Even if this denial is credible, however, in order to be consistent a Humean who adopts this response should presumably also deny that the relatively general fact that James has B at \(t_1\) scientifically explains the fact that q has E at \(t_2\), and instead claim that it is the fact that p has l at \(t_1\), together with other particular facts about the parts of James, that scientifically explain this fact. Such a Humean would therefore not be able to claim that (T*) fails in the James the snail example.
As a result, Lange’s examples also provide support for the original version of the objection from explanation, since (T) entails (A) given the fact that no fact can explain itself.
As noted in fn. 11, Hicks and van Elswyk claim that there are a number of different kinds of explanation, that these different kinds of explanation have different backing relations, and that these backing relations have radically different features, so that, for example, some are asymmetric while others are symmetric. They claim that this provides a “simple recipe” for constructing counterexamples to (T*). Unfortunately, at least in my case, Hicks and van Elswyk fail to enumerate enough examples of relations they take to be backing relations for me to know how to apply their recipe, and, as noted in fn. 11, some of the examples they do give are commonly not thought to back explanation. The two products of the recipe they describe—the immanent causation case described above, and the case of explanation involved in the objection from explanation—do not help in this regard. Hicks and van Elswyk also argue that (T*) is incompatible with Kim’s (1993) principle of causal exclusion and the anti-reductionism of Fodor (1974). Even if this is the case, however, it would be better if Humeans could respond to the objection from explanation without being committed to these controversial theses.
Beebee (2000, Sect. 4) has argued that it is not a conceptual truth that laws “govern” their instances. Beebee’s argument can be adapted to produce an argument in the vicinity of the argument given here that (2) is not a conceptual truth. If Beebee is right, Humeans need to endorse this argument in order to respond to anti-supervenience arguments against Humeanism put forward, for example, by Tooley (1977), Carroll (1994) and Menzies (1993). It is not entirely clear what Beebee means by “laws governing their instances”. On one interpretation that is suggested by some, but not all, of what Beebee says, a law L governs an instance q iff the fact that L is a law partly explains q. (This interpretation of ‘governing’ is adopted, for example, by Sider (2011, p. 270).) Given this interpretation, Beebee’s denial that laws govern their instances entails the denial of (2).
See Beebee (2000, pp. 576–577), for example, for an explanation of how BSA can account for the fact that laws support counterfactuals and constrain physical possibility.
An anti-Humean might claim that the concept of lawhood we should adopt is one according to which laws are those things that satisfy (2) as well as satisfying the most important roles laws are meant to play in science. A Humean, however, can claim that, on this concept, there are no laws, and that this is a good reason not to adopt this concept. An anti-Humean might instead claim that we have a primitive concept of lawhood that cannot be elucidated in terms of God’s commandments or the roles laws are meant to play in science, that (2) is true on this concept, and that we have good reasons to think that, given this concept, there are laws. The claim that our concept of lawhood is primitive in this way, however, is much less credible than corresponding claims about other concepts such as the concept of causation, and a Humean can simply reject it.
I am indebted to Alex Skiles for suggesting an explanation along these lines in personal correspondence.
Miller (2014, Sect. 5) suggests a response to the objection from explanation that is in some respects similar to the response urged here, but which also differs from it in important respects. Simplifying slightly, according to what Miller calls the contrarian Humean response, a Humean should deny that laws are metaphysically explained by their instances, and should instead claim that particular matters of fact are metaphysically explained at least partly by the conjunction \(C\) of all particular matters of fact (plus perhaps a totality fact), and possibly also partly metaphysically explained by the laws. On this response, Humeans should also deny that particular matters of fact metaphysically explain \(C\), and claim that facts that ascribe lawhood to laws do partly explain the instances of those laws, although they do not partly explain the laws themselves. There are two serious problems with Millers’ contrarian Humeanism. First, it conflicts with the principle that a highly complex fact cannot metaphysically explain a much simpler fact, since it holds, for example, that the highly complex \(C\) can explain simple particular matters of fact, where this explanation is presumably metaphysical since it involves a conjunction explaining one of its conjuncts. Secondly, it doesn’t resolve the objection from explanation, since it doesn’t resolve the clash with (A): Given BSA, facts that ascribe lawhood to laws are plausibly explained by the instances of those laws. But according to contrarian Humeanism, the former facts explain those instances.
See Armstrong (1983).
Hicks and van Elswyk (2015, p. 435) also argue that anti-Humeans face a conflict with (A) given a principle like (FP). Their argument, however, relies on the premise that laws are regularities, which many anti-Humeans will reject.
A fact is explanatorily trivial iff it is explained but is not explained either singly or collectively by any facts. An explanatorily trivial fact is analogous to a theorem in a logical system that is not an axiom and that can be derived using the system’s inference rules without applying those inference rules to any of the axioms. Cf. Fine (2012, p. 47).
This anti-Humean account is in effect that given by Rosen (2010, Sect. 8). As Rosen notes in the anti-Humean case, if one believes in Finian essences, one might wish to add to these accounts by allowing that some universal facts are explained by essences. On some ways of drawing the distinction between scientific and metaphysical explanation, ‘metaphysically explains’ in these accounts might have to be replaced with just ‘explains’.
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Acknowledgments
Thanks goes to Alex Skiles, Shyam Nair, a referee for Philosophical Studies and an audience at the 2014 Australasian Association of Philosophy conference for helpful comments and discussion.
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Marshall, D. Humean laws and explanation. Philos Stud 172, 3145–3165 (2015). https://doi.org/10.1007/s11098-015-0462-9
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DOI: https://doi.org/10.1007/s11098-015-0462-9