Humean Laws and Circular Explanation

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ArticleTitle Humean laws and circular explanation

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Abstract Humeans are often accused of accounting for natural laws in such a way that the fundamental entities thatare supposed to explain the laws circle back and explain themselves. Loewer (Philos Stud 160(1):115–137,2012) contends this is only the appearance of circularity. When it comes to the laws of nature, the Humeanposits two kinds of explanation: metaphysical and scientific. The circle is then cut because the kind ofexplanation the laws provide for the fundamental entities is distinct from the kind of explanation the entitiesprovide for the laws. Lange (Philos Stud 164(1):255–261, 2013) has replied that Loewer’s defense is adistinction without a difference. As Lange sees it, Humeanism still produces a circular explanation becausescientific explanations are transmitted across metaphysical explanations. We disagree that metaphysicalexplanation is such a ready conduit of scientific explanation. In what follows, we clear Humeanism of allcharges of circularity by exploring how different kinds of explanation can and cannot interact. Our defenseof Humeanism begins by presenting the circularity objection and detailing how it relies on an implausibleprinciple about the transitivity of explanation. Then, we turn to Lange’s (Philos Stud 164(1):255–261, 2013)transitivity principle for explanation to argue that it fairs no better. With objections neutral to the debatebetween Humeanism and anti-Humeanism, we will show that his principle is not able to make the circularityobjection sound.

Keywords (separated by '-') Laws - Humeanism - Explanation - Transitivity

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12

3 Humean laws and circular explanation

4 Michael Townsen Hicks • Peter van Elswyk

56 � Springer Science+Business Media Dordrecht 2014

7 Abstract Humeans are often accused of accounting for natural laws in such a way

8 that the fundamental entities that are supposed to explain the laws circle back and

9 explain themselves. Loewer (Philos Stud 160(1):115–137, 2012) contends this is

10 only the appearance of circularity. When it comes to the laws of nature, the Humean

11 posits two kinds of explanation: metaphysical and scientific. The circle is then cut

12 because the kind of explanation the laws provide for the fundamental entities is

13 distinct from the kind of explanation the entities provide for the laws. Lange (Philos

14 Stud 164(1):255–261, 2013) has replied that Loewer’s defense is a distinction

15 without a difference. As Lange sees it, Humeanism still produces a circular

16 explanation because scientific explanations are transmitted across metaphysical

17 explanations. We disagree that metaphysical explanation is such a ready conduit of

18 scientific explanation. In what follows, we clear Humeanism of all charges of cir-

19 cularity by exploring how different kinds of explanation can and cannot interact.

20 Our defense of Humeanism begins by presenting the circularity objection and

21 detailing how it relies on an implausible principle about the transitivity of expla-

22 nation. Then, we turn to Lange’s (Philos Stud 164(1):255–261, 2013) transitivity

23 principle for explanation to argue that it fairs no better. With objections neutral to

24 the debate between Humeanism and anti-Humeanism, we will show that his prin-

25 ciple is not able to make the circularity objection sound.

26

27 Keywords Laws � Humeanism � Explanation � Transitivity

28

A1 Authors are listed alphabetically.

A2 M. T. Hicks (&) � P. van Elswyk

A3 Philosophy Department, Rutgers University, 106 Somerset St, New Brunswick, NJ 08901, USA

A4 e-mail: [email protected]

A5 P. van Elswyk

A6 e-mail: [email protected]

123Journal : Small-ext 11098 Dispatch : 18-3-2014 Pages : 11

Article No. : 310 * LE * TYPESET

MS Code : PHIL-D-13-00783 R CP R DISK

Philos Stud

DOI 10.1007/s11098-014-0310-3

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29 1 Humean explanation

30 Humeanism is the view that all contingent truths about a world supervene on the

31 spatiotemporal distribution of fundamental properties, relations, and quantities had

32 by fundamental entities (c.f. Lewis 1986). Call this distribution the mosaic. The

33 truth of natural laws is not outside the explanatory reach of the mosaic. According to

34 the Humean, laws are generalizations whose truth depends on the mosaic. Two

35 worlds then have different laws only when the way the mosaic is distributed differs.

36 What kind of generalizations are laws? It cannot be that any generalization is a

37 law. There are some that are only accidentally true. The Humean therefore needs to

38 distinguish laws from law-like accidents. The usual way this is done is with the Best

39 Systems Account (BSA). According to the BSA, P is a law if and only if P features

40 in the simplest, most informative axiomatization of the facts about the world (c.f.

41 Lewis 1983). It is only generalizations included in the best system for a world that

42 qualify as that world’s laws.1 The other generalizations do not make the cut.

43 And that’s all there is to the Humean view of natural laws. Inevitably, there are

44 dissenters. Although Humeanism in conjunction with the BSA can distinguish

45 between laws and accidental generalizations, Humeanism still entails that laws are

46 generalizations. As a result, laws and accidental generalizations are made true the

47 same way: by their instances. Their truth still supervenes on the mosaic. It is due to

48 such supervenience that many charge Humeanism with circular explanation. Bird

49 (2007, p. 86) puts his worry this way2:

50 Laws have an explanatory capacity. They explain their instances, indeed they

51 explain the regularities we find in nature. Could the laws fulfill this

52 explanatory role if they themselves were regularities? Anti-Humeans allege

53 they cannot. Facts may explain other facts but they cannot explain themselves.

54 Maudlin (2007, p. 172) voices a similar objection:

55 If the laws are nothing but generic features of the Humean Mosaic, then there

56 is a sense in which one cannot appeal to those very laws to explain the

57 particular features of the Mosaic itself: the laws are what they are in virtue of

58 the Mosaic rather than vice versa.

59 The objection in one form or another has been advanced by many other anti-

60 Humeans like Armstrong (1983) and, most recently, Lange (2013). The argument is

61 also simple. Humeans maintain that the mosaic explains the laws and the laws

62 explain the mosaic. Since explanation is plausibly transitive, the mosaic appears to

63 circle back and explains itself.

1FL01 1 We are papering over unrelated complications. For example, the Humean will have to account for

1FL02 chancy laws, which requires adding a third virtue like fit to measure how well a probabilistic system

1FL03 connects to a world (Lewis 1980, 1994).

2FL01 2 Bird presents a more detailed version of the argument after this passage that relies on a notion of ‘‘the

2FL02 ontological content of a fact or a set of facts’’ (Bird 2007, p. 87). We take the relation being the

2FL03 ontological content of to be a relationship of metaphysical explanation, and so we believe that our later

2FL04 discussion extends to Bird’s argument too.

M. T. Hicks, P. van Elswyk




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64 Let’s call this the circularity objection. We think the objection rests on a

65 misunderstanding about the nature of explanation and how different kinds of

66 explanation interact. To defend this diagnosis, it will help to get the argument out in

67 the open. The objection can be regimented in the following fashion:

68 THE CIRCULARITY OBJECTION

69

70 The argument is valid and the conclusion is not something with which a Humean

71 should want to be saddled. Which premise should be rejected? There are not many

72 qualms to be had with GENERALIZATION or LAWS, and any worries are probably not

73 going to be of use defending Humeanism in a substantive way. That leaves

74 HUMEANISM and TRANSITIVITY. Now, TRANSITIVITY is not usually stated outright in

75 presentations of the objection. It is often just assumed due to its initial

76 plausibility.3 It is not a surprise then that HUMEANISM is ditched by the anti-

77 Humeans.

78 This objection strikes us as far too quick. Humeans and anti-Humeans should

79 agree that law statements are universal generalizations.4 As we see it, the sides

80 disagree over what makes generalizations true and what makes them laws. So

81 perhaps our first premise is misnamed. HUMEANISM (the premise) may follow from

82 Humeanism (the view), but it by no means follows only from Humeanism. If we’re

83 right about this much, anti-Humeans are vulnerable to a tu quoque. When laws are

84 statements taking the form of universal generalizations, even if the statements are

85 rendered laws by something else (e.g. essential natures, relations to other laws), the

86 statements are made true by instances of whatever the law is about. It is here that the

87 specter of circularity appears. How can a law explain its instances if it is also made

88 true by those instances?

(P1) The natural laws are generalizations. (HUMEANISM)

(P2) The truth of generalizations is (partially) explained

by their positive instances.

(GENERALIZATION)

(P3) The natural laws explain their instances. (LAWS)

(P4) If A (partially) explains B and B (partially)

explains C, then A (partially) explains C.

(TRANSITIVITY)

(C1) The natural laws are (partially) explained by their

positive instances.

(P1 & P2)

(C2) The instances of laws explain themselves. (P3, P4, & C1)

3FL01 3 For passages where TRANSITIVITY appears to be assumed, see Armstrong (1983, p. 40), Bird (2007, pp.

3FL02 86–87), and Maudlin (2007, pp. 171–175).

4FL01 4 Not everyone agrees that science is concerned with laws, with Van Bas (1989) being a notable

4FL02 dissenter. Other deny that laws have structure that is at all like that of law statements. Maudlin (2007)

4FL03 takes laws to be fundamental sui generis entities. But among those who agree that there are laws, it is still

4FL04 true that scientific explanation is done with sets of statements that answer why-questions. Accordingly, it

4FL05 is the law statements that feature in explanation and those statements take the form of universal

4FL06 generalizations. Because we are concerned with explanation, and because explanations are made up of

4FL07 statements, we will use ’law’ to refer to law statements throughout.

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89 Luckily, the anti-Humean does not need to look any further than these pages to

90 find a strategy for cutting their own explanatory circles. Our own qualms with the

91 circularity objection are completely bipartisan. We follow Loewer (2012) and

92 maintain that the blame rests with TRANSITIVITY. Loewer notes there is a difference in

93 the kinds of explanation at work in the Humean view of laws. There are scientific

94 and metaphysical explanations. The explanation at work in GENERALIZATION is

95 metaphysical: generalizations are true in virtue of their instances. And the type of

96 explanation at work in LAWS is scientific: the laws explain their instances by showing

97 their natural unity and similarity. TRANSITIVITY is then false because it traffics in

98 ambiguity between the kinds of explanation in GENERALIZATION and LAWS. The

99 mosaic metaphysically explains the truth of laws and laws help to scientifically

100 explain the mosaic, but the mosaic does not explain itself.

101 Lange (2013) finds Loewer’s rejoinder inadequate. He agrees that there are two

102 kinds of explanation, but maintains that the metaphysical explanans scientifically

103 explain whatever their explananda scientifically explain. So despite the different

104 kinds of explanation being posited by the Humean, the mosaic still ends up

105 explaining itself. To motivate this defense of the circularity objection, Lange

106 presents and defends a revised version of TRANSITIVITY. For expository ease, we will

107 use explainm to denote metaphysical explanation and explains to denote scientific

108 explanation. His principle is as follows:

109 TRANSITIVITY*: If A explainsm (or helps to explainm) B and B explainss (or helps

110 to explains) C, then A explainss (or helps to explains) C.5

111 When this principle is swapped in for TRANSITIVITY, a valid argument is produced

112 that accommodates the distinction between kinds of explanation. It appears as if the

113 Humean is saddled with circularity again.

114 What reason do we have to accept TRANSITIVITY*? Two reasons are briefly

115 furnished by Lange (2013, p. 257). First, he argues that the principle is implicit in

116 scientific practice and he gives a few examples to this effect. Second, he maintains

117 that it is assumed by various philosophical arguments, especially those concerning

118 the nature of genetic drift. We are not compelled much by either reason. What of the

119 case against the principle?

120 2 Intransitivity

121 Our case against TRANSITIVITY* has three parts. As an opening salvo, we argue that

122 the principle is ambiguous and so runs the risk of not motivating the circularity

123 objection after disambiguation. Then, we present two problems with what

124 TRANSITIVITY* requires of the interaction between metaphysical and scientific

125 explanation. The first of these concerns cases where the two kinds of explanation are

126 incompatible. The second problem concerns how TRANSITIVITY* requires an

5FL01 5 Our presentation of the principle differs slightly from Lange’s (2013, p. 256). We have reversed the

5FL02 order of the conjuncts in the antecedent, and replaced talk of grounding with more general talk of

5FL03 metaphysical explanation.





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127 untoward reductionism by dealing with the delicate issues of scientific reduction

128 like a bull in a china shop.

129 2.1 The ambiguity problem

130 TRANSITIVITY* can be given eight distinct disambiguations depending on whether

131 explains or helps to explain is most salient. And therein lies a problem. The

132 disambiguations that are most likely to be true are not the disambiguations required

133 to underwrite the circularity objection.

134 We will save the reader time by only discussing three disambiguations of

135 TRANSITIVITY* because only three are relevant to the circularity objection. Keeping

136 our earlier convention of using subscripts to denote the kind of explanation, these

137 disambiguations are as follows:

138 FULL TRANSITIVITY: If A fully explainsm B and B fully explainss C, then A fully

139 explainss C.

140 PARTIAL TRANSITIVITY 1: If A fully explainsm B and B helps to explains C, then

141 A helps to explainss C.

142 PARTIAL TRANSITIVITY 2: If A helps to explainm B and B fully explainss C, then

143 A helps to explains C.

144 Among these options, FULL TRANSITIVITY and PARTIAL TRANSITIVITY 1 and strike us as

145 the most initially plausible. Unlike PARTIAL TRANSITIVITY 2, these disambiguations

146 both start with full explanations in their antecedents. This is relevant to transitivity

147 since far more is required for something to fully explain than for it to partially

148 explain. By our lights, if something fully explains something else, then it seems like

149 it could partially or fully explain the consequences of that other thing.

150 The circularity objection, however, rests upon PARTIAL TRANSITIVITY 2. According

151 to the Humean, each instance of a law helps to metaphysically explain the law just

152 as instances of a generalization help to metaphysically explain that generalization.

153 But each instance does not fully explain the law. The lawhood of the law is fully

154 explained by a complex fact involving all of its instances and some corresponding

155 negative universal fact. We should also not forget the details added by adopting the

156 BSA. The fact that P is a law is explained by all (or nearly all) of the world’s

157 fundamental facts, which are what determine whether some P is a part of the best

158 system. Finally an instance of a law P partially explains that law metaphysically, the

159 law partially explains its instances scientifically in conjunction with boundary

160 conditions, but the instance does not explain the law scientifically.

161 PARTIAL TRANSITIVITY 2 could take us to explanatory circularity were it an

162 acceptable principle. It is not, however, a principle that should be accepted. This is

163 brought out by the the following vignette:

164 LION

165 The position of electron e partially metaphysically explains the position of lion

166 L. The position of L scientifically explains the number of prey animals in

167 region R. But the position of electron e does not explain the number of prey





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168 animals in region R. For if the electron were elsewhere, L would still be

169 warding prey animals out of R.

170 Counterexamples such as this—which are easily replicated—reveal that partial

171 metaphysical explanation is not transitive in the way required to get the circularity

172 objection up and running. This is not too surprising. The transitivity of most

173 varieties of explanation have been vulnerable to counterexamples for awhile. For

174 example, Paul (2000) argues that causal explanation is intransitive and Schaffer

175 (2012) provides counterexamples to the transitivity of grounding explanations. So

176 we suspect this problem with PARTIAL TRANSITIVITY 2 falls out of a more general

177 problem with the transitivity of explanation. As such, when other forms of full

178 explanation cannot be taken as transitive across the same flavor of explanation, we

179 think there is even less reason to believe that a partial explanation will be transitive

180 in conjunction with a different kind of explanation.6

181 We have not yet shown that either FULL TRANSITIVITY or PARTIAL TRANSITIVITY 1 are

182 false. A reader sympathetic to the circularity objection may still hold out hope that it

183 can be rebuilt on a foundation made from one of these other principles. In what

184 remains, we’ll lump these disambiguations back together as TRANSITIVITY* and argue

185 that no such transitivity principle can be true.

186 2.2 The interaction problem

187 Here’s a story we like. Explanations are set of statements that answer questions

188 about why something is such and so. What makes an explanation true is a relation in

189 the world that links the explanandum and the explanans in the way described by the

190 explanation. Not all explanations are alike, however. There are varieties of

191 explanation. Differences between kinds of explanations correspond to the different

192 kinds of relations that back them. Call such relations backing relations (c.f. Ruben

193 1990). The formal features of explanations vary according to their backing relation.

194 An explanation is asymmetric when its backing relation is asymmetric. A different

195 explanation could be symmetric were it to be backed by a symmetric relation. In this

196 way, explanations mirror the relevant relation in the world.

197 Admittedly, this story about explanation is incomplete. It needs a flashy sequel

198 where the missing details are filled in by a complete account of explanation. This is

199 not a task taken up here.7 Our aim is to show that TRANSITIVITY* is implausible in its

200 general form. The likely story about explanation therefore provides what we think is

201 an acceptable starting point from which to think about how kinds of explanation

202 interact.

6FL01 6 Schaffer (2005, 2012) argues that counterexamples to the transitivity of causal and grounding

6FL02 explanations are evidence that these relations are contrastive, and so the relevant transitivity principles

6FL03 are contrastive as well. Perhaps a dedicated anti-Humean could revive the circularity objection with a

6FL04 contrastive principle. Having not seen such an argument, we are agnostic of its cogency. For reasons that

6FL05 will come in Sects. 2.2 and 2.3, we don’t believe that even a contrastive principle can be formulated for

6FL06 linking scientific and metaphysical explanation.

7FL01 7 See Strevens (2008), Woodward (2003), and Ruben (1990) for accounts we think have something going

7FL02 for them.





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203 On our story, the difference between scientific and metaphysical explanation is

204 easy to exposit. They have different backing relations. Metaphysical explanations

205 are backed by a variety of non-causal relations. Many are something like what

206 Bennett (2011) calls building relations. These relations start with parts,

207 properties, or individuals and then, from there, build up more parts, properties,

208 or individuals. What individuates such relations is that the building materials are

209 in some way prior to what’s built, and what’s built cannot typically build itself.

210 There are many differences amongst building relations. They can differ according

211 to arity, what they take as relata, the conditions needed for their obtaining, and so

212 on.

213 Scientific explanations are similarly individuated by their backing relations.

214 Unlike metaphysical explanation, there is not a wide plurality of scientific relations

215 that can underwrite scientific explanation. Scientific explanations are typically

216 understood to be backed either by causation, nomic connection, or some

217 combination of these two relations. This does not mean that there is a consensus

218 about the nature of scientific explanation. There is still disagreement over the exact

219 details of the backing relations and the structure these relations back.

220 Two interrelated problems with TRANSITIVITY* now immediately arise. The first is

221 that the principle is unmotivated. When one backing relation connects A and B, and

222 a distinct backing relation connects B and C, there is no reason to think that either

223 backing relation somehow connects A to C. As a result, TRANSITIVITY* predicts that

224 backing relations obtain even when we lack reason to think they are present. The

225 second problem is more serious. If the relation that backs A and B has features

226 incompatible with the features had by the relation that backs B and C, A cannot

227 explain C in the same way it explains B. This provides a simple recipe for

228 constructing counterexamples. Pick a particular backing relation for a scientific

229 explanation, pick an incompatible backing relation for the metaphysical explana-

230 tion, and TRANSITIVITY* will be invalidated.

231 We suggested earlier that the anti-Humean is vulnerable to her own circularity

232 problem. Here’s a counterexample to TRANSITIVITY* she can get on board with.

233 Suppose there is immanent causation. Causation is immanent when it proceeds from

234 an object not by way of the object’s parts, but from the object as a whole. Not

235 everyone thinks there is immanent causation, but many anti-Humeans accept it

236 because of the explanatory work they think it can accomplish (c.f. Armstrong 1997).

237 Now suppose a view of composition on which the building materials are not

238 identical to what they build. In other words, composition is not identity. The result is

239 a situation in which parts compose a whole, but the parts do not scientifically

240 explain everything caused by the whole because the whole can cause things

241 immanently. TRANSITIVITY* is therefore false. Importantly, it is problematic for

242 reasons that even some anti-Humeans accepts.

243 More counterexamples to TRANSITIVITY* can easily be provided by following our

244 earlier recipe. We’ll give one more, which will come as no surprise. We think the

245 Humean account of laws is a counterexample. The metaphysical explanation that

246 the mosaic provides for the laws is not backed by just any relation. The type of

247 underwriting relation is a truthmaking relation. Lewis (1994, p. 474) thus remarks

248 that ‘‘Humean Supervenience is yet another speculative addition to the thesis that





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249 truth supervenes on being.’’8 The explanation offered by laws for the mosaic,

250 however, is backed by a very different relation. Laws explain why the mosaic

251 behaves with uniformity and regularity. Whatever the exact nature of this backing

252 relation, it is not a truthmaking relation. Yet, this is what TRANSITIVITY* predicts.

253 That is a category error if there ever was such a thing. The explanation the laws help

254 give of the mosaic is not an explanation of the mosaic’s truth. The mosaic is a

255 scattered arrangement of fundamentalia; it is not the kind of thing that can be true or

256 false.

257 We conclude that TRANSITIVITY* is too coarse to be correct. Not only do

258 explanations come in enough variety that there is no good reason to think that

259 explanation is transitive in the way required, but such variety ensures that

260 explanation cannot be transferred because the backing relations had by each

261 explanation can behave very differently.

262 2.3 The levels problem

263 Let’s move on to another problem. A natural picture of the world is that it has

264 multiple levels. At bottom is physics, on physics rests chemistry, and on chemistry

265 rests—in some way or another—biology, psychology, economics, and the other

266 special sciences, with each scientific discipline and/or subdiscipline mapping out a

267 structure of explanations within a level. An important explanatory task that requires

268 both metaphysical and scientific explanation is spelling out how the world is

269 constructed with various levels. Scientific explanations tend to be limited to the

270 level of the discipline that’s offering the explanation, and metaphysical explanations

271 tend to focus on how the levels are built out of each other.

272 Within this picture, it is often worth asking which scientific explanations are

273 reducible to those at a lower level. Some clearly are reducible. For example,

274 explanations in thermodynamics are reducible to those of physics, and there is a

275 general schema in statistical mechanics that details this reduction. Other scientific

276 explanations seem to resist reduction. The explanations offered by macroeconomics

277 do not appear to be reducible to the explanations of physics, nor do the explanations

278 given by Darwinian evolutionary theory. This is true despite the fact that these facts

279 supervene, and so are grounded in, facts about microphysics. In a slogan, the

280 grounding of facts does not imply grounding of their explanatory relations.9

281 In other words, not every case of metaphysical dependence amounts to a

282 scientific reduction. Two macro-level facts can both be grounded in microphysics

283 without the laws that connect the macro-level facts being grounded in microphysics.

284 Reducing the laws of a science to microphysics requires more than just reducing the

285 facts of that science to microphysics. An example helpfully illustrates. For each

286 white swan, there is a microphysical fact grounding that swan’s being white. But

8FL01 8 The Humean has a few different ways they can understand this truthmaking relation. Typically, the

8FL02 relation is thought to be supervenience. But the Humean could think of the relation differently. For

8FL03 example, it could be a grounding relation in the style of Schaffer (2010) where grounding is contingent.

9FL01 9 We use grounding here and throughout loosely to denote something more intimate than supervenience.

9FL02 No commitments are made to a particular metaphysics of ground.





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287 these facts—even taken together—do not ground the generalization or law that all

288 swans are white. And so they don’t ground explanations which appeal to that law.

289 TRANSITIVITY*, however, completely ignores the subtleties involved with answer-

290 ing this question about intra-level reduction. It insists that wherever there is

291 metaphysical explanation, this automatically moves upward from the explanans to

292 also explain whatever the explananda explain. Right away, this predicts widespread

293 overdetermination. Causal explanations provide an easy illustration. When a

294 baseball smashes a window, TRANSITIVITY* maintains that both the baseball and what

295 metaphysically constitutes the baseball explain the shattering. This prediction takes

296 us deep into controversial territory. Not everyone accepts overdetermination.

297 Although some embrace it as a peculiarity of the world, others altogether eliminate

298 objects or properties from their ontology on pain of avoiding overdetermination. As

299 a result, TRANSITIVITY* flatly contradicts principles like Kim’s (1989) principle of

300 causal exclusion, which denies outright that there can be two complete causal

301 explanations of the same event.

302 But the cost TRANSITIVITY* incurs is not merely that it predicts overdetermination.

303 This prediction is just a symptom. The problem is that TRANSITIVITY* cannot

304 distinguish between cases when explanations from one science can be reduced to

305 another, and cases in which they cannot. Even those of us comfortable with

306 overdetermination should require that intra-level explanation tread the safer roads of

307 principled reduction.

308 As another case of TRANSITIVITY*’s trouble, TRANSITIVITY* summarily dismisses the

309 anti-reductionism of Fodor (1974). For Fodor, there can be reductive explanations

310 only so long as they are accompanied by general bridge laws, or bridge definitions,

311 between the differently leveled phenomena. When there are no such laws, the lack

312 of systematic dependence on the higher-level science on the lower-level science

313 makes the lower-level activity non-explanatory. TRANSITIVITY* insists this is all

314 wrong: Lower-level activity is explanatory even in the absence of bridge laws

315 because whatever metaphysically builds scientifically explains that which it builds.

316 Finally, here’s an example to show why Humeans should abandon TRANSITIVITY*.

317 Callender and Cohen (2009) defend a version of the BSA tailored specifically for

318 the special sciences. On their view, each special science autonomously constructs a

319 best system for the natural kinds within its domain, but these natural kinds are

320 different, and incomparable, ways of carving up the same underlying reality.

321 Though the facts of a special science supervene on those of a lower-level science,

322 they hold that there is no fact about which science is fundamental. So there is no

323 systematic connection between the laws of the special science and the laws of

324 physics, and explanations featuring these autonomous special science laws do not

325 reduce to explanations featuring the laws of physics Again, TRANSITIVITY*, does not

326 carry itself carefully. It maintains that the supervenience of the special science facts

327 on the facts of physics implies that a reductive explanation exists.

328 We conclude again that TRANSITIVITY* is far too coarse to be correct. When it

329 comes to explaining the layered nature of the world, TRANSITIVITY* both permits

330 controversial overdetermination and licenses reductive explanations where no

331 reduction can be found.





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332 3 Conclusion

333 Natural laws are generalizations that explain their instances. According to

334 Humeanism, the mosaic of instances makes the generalizations true and makes

335 them laws. At a cursory glance, this appear as though the mosaic ends up

336 explaining itself. But the charge of circularity is unfounded for the same reason

337 supplied by Loewer (2012). The circularity objection relies on a principle about

338 the transitivity of explanation that equivocates between kinds of explanation. As

339 we have now shown, attempts to restitute the argument with a non-equivocating

340 principle are prone to problems. A revised principle like Lange’s (2013) was

341 ambiguous in problematic ways, failed to attend to what distinguishes kinds of

342 explanation, and did not accommodate subtleties in how the world’s levels relate

343 to each other. We suspect these and other problem will plague all similar

344 principles.

345 The reader might see these problems as an invitation to go back to the drawing

346 board. But a revised principle will unavoidably rely on a number of assumptions

347 about the nature of explanation, overdetermination, and other issues of controversy.

348 Each of these assumptions will then afford the Humean another opportunity to

349 contest the circularity objection. Whatever indictments Humeanism may still need

350 to answer to, we think we have given the Humean and the anti-Humean alike ample

351 resources for seeing that a circularity problem is not among them.

352 Acknowledgments For helpful comments and/or conversation, we thank Thomas Blanchard, Marco353 Dees, Erik Hoversten, Barry Loewer, Jonathan Schaffer, Alex Skiles, Christopher Weaver, Tobias354 Wilsch, and participants in the philosophy of science and metaphysics reading groups at Rutgers355 University.356

357 References

358 Armstrong, D. (1983). What is a law of nature? Cambridge, MA: Cambridge University Press.359 Armstrong, D. (1997). A world of states of affairs. Cambridge, MA: Cambridge University Press.360 Bennett, K. (2011). Construction area: No hard hat required. Philosophical Studies, 154, 79–104.361 Bird, A. (2007). Nature’s metaphysics: Laws and properties. Oxford: Oxford University Press.362 Callender, C., & Cohen, J. (2009). The better best system account of lawhood. Philosophical Studies,363 45(1), 1–34.364 Kim, J. (1989). Mechanism, purpose, and explanatory exclusion. Philosophical Perspectives, 3,365 77–108.366 Lange, M. (2013). Grounding, scientific explanation, and humean laws. Philosophical Studies, 164(1),367 255–261.368 Lewis, D. (1980). A subjectivist’s guide to objective chance. In R. C. Jeffrey (Ed.), Studies in inductive369 logic and probability. Berkeley, CA: University of California Press.370 Lewis, D. (1986). On the plurality of worlds. Oxford: Blackwell Publisher.371 Lewis, D. (1994). Humean supervenience debugged. Mind, 103(412), 473–490.372 Loewer, B. (2012). Two accounts of laws and time. Philosophical Studies, 160(1), 115–137.373 Maudlin, T. (2007). The metaphysics within physics. Oxford: Oxford University Press.374 Paul, L. A. (2000). Aspect causation. Journal of Philosophy, 97(4), 235–256.375 Ruben, D.-H. (1990). Explaining explanation. London: Routledge.376 Schaffer, J. (2005). Contrastive causation. Philosophical Review, 114(3), 327–358.377 Schaffer, J. (2010). The least discerning and most promiscuous truthmaker. Philosophical Quarterly,378 60(239), 307–324.





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379 Schaffer, J. (2012). Grounding, transitivity, and contrastivity. In F. Correia & B. Schnieder (Eds.),380 Grounding and explanation (pp. 122–138). Cambridge, MA: Cambridge University Press.381 Strevens, M. (2008). Depth: An account of scientific explanation. Cambridge, MA: Harvard University382 Press.383 Van Bas, F. (1989). Laws and symmetry. Oxford: Clarendon Press.384 Woodward, J. (2003). Making things happen: A theory of causal explanation. Oxford: Oxford University385 Press.

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