Studies in History and Philosophy of Modern Physics 43 (2012) 155–158

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Book review

Marc Lange (2009). Laws and lawmakers: science, metaphysics,and the laws of nature, (pp. xvi þ 257). New York: OxfordUniversity Press. (US$ 99.00 HB), ISBN: 978-0195328134.Roberts, John T. (2007). The Law-governed universe, (pp. 407).New York: Oxford University Press. (US$ 110.00), ISBN: 978-0199557707.

In Laws and Lawmakers Marc Lange climbs off the fenceregarding the metaphysics of laws, landing squarely on the non-Humean side. However, his position is interestingly distinct fromthe standard options: facts about the laws are not metaphysicallyprior to facts about subjunctives, nor are they analyzed in termsof causal powers or dispositions. Instead, the law facts areanalyzed in terms of subjunctive facts. In The Law-Governed

Universe John Roberts reconciles the governing intuition withHumean supervenience, a feat so remarkable it suggests we aredealing not with metaphysics, but metaphysical poetry, charac-terized by Dr. Johnson as that in which ‘‘the most heterogeneousideas are yoked by violence together.’’ These are two highlyoriginal works that stake out sophisticated and genuinely novelpositions in the debate. They provide essential reading for anyoneinterested in laws.

Lange’s main target is a substantive account of nomic neces-sity. Some philosophers, notably Brian Ellis, have found paradoxin the contingency of nomic necessity, and Lange would dissolvethe putative paradox. He also thinks we can improve on explana-tions that brutely take the laws to be the things that support thisspecies of necessity. His solution is a unified analysis of neces-sities in terms of stability under counterfactual variation. Thelaws constitute one particular stable set. Hence, they are neces-sary. However, they are not stable under as broad a range ofcounterfactual variations as, for instance, metaphysical necessi-ties. Hence, contingent.

More precisely, defining a claim as ‘‘sub-nomic’’ exactly if, in anypossible world, what makes it true or false does not include the lawfacts at that world, Lange identifies the set of laws, L, as the largestnon-maximal, logically closed, set of truths that is sub-nomicallystable (pp. 29–30, 43). Roughly, a set of truths is sub-nomicallystable if, and only if, whatever the conversational context, the set’smembers would all still have held under every sub-nomic counter-factual (or subjunctive) supposition logically consistent with theset.1 A set is non-maximal if it does not include all the sub-nomictruths. In broad strokes, the idea is as follows. If G is maximal, thereare no sub-nomic counterfactual variations consistent with G. If G isnon-maximal, then only if it consists entirely of laws would itsmembers be generally preserved under counterfactual twiddlingwith initial conditions or boundary conditions consistent with G. By

016/j.shpsb.2011.11.008

ere is a more precise version of sub-nomic stability in terms of might-

nals (p. 29) that does not permit cases where both A&-M, and A&-�M

t as cases where M is preserved under A, since such cases clearly cheapen

on of stability (p. 21), but these details do not affect our discussion.

contrast, if G consists of the accidental generalization ‘‘all goldspheres are of diameter less than or equal to 1 km’’, R, and its logicalconsequences, it is not preserved under the counterfactual supposi-tion that Bill Gates, or perhaps someone wealthier, desires such agold sphere (pp. 32–33).

How do we know that sets that include non-laws cannot beboth non-maximal and stable? Lange argues (p. 33) that if anyaccidental truth is included in a set of putative laws, stabilityrequires all sub-nomic truths are included. Take an accident like‘‘all the apples on my tree are ripe’’, P, and suppose it is notincluded in a stable set, G, that includes R. ‘‘Either there is a goldsphere of greater than 1 km diameter or an apple on my tree isnot ripe’’, �R v –P, will then be consistent with G, and there willbe some conversational context in which the former disjunct ispreserved, i.e. for which (�R v –P)&-�R. So, stability demandsP is also included in G. Since we can make the argument for anyaccidental truth, a stable G must be maximal.

Lange contrasts his account with Lewis’s and Armstrong’sanalyses, taken as exemplars of Humean or ‘‘bottom-up’’ and non-Humean or ‘‘top-down’’ explanations of necessity. For Lewis, beingthe right kind of regularity underwrites lawhood and nomicnecessity; for Armstrong, nomic necessitation relations betweenuniversals impose necessity on the non-nomic. Some of the pro-blems Lange discerns here are familiar: the Lewisian analysis doesnot fit with our intuitions regarding lawhood, and by extensionnomic necessity; merely dubbing a relation ‘‘nomic necessitation’’should not strong-arm us into accepting we have something thatentails the corresponding law regularity, never mind the corre-sponding necessity. However, more fundamentally, Lange objects totheir demotion of nomic necessity to the status of a relativenecessity, one that derives merely from being the logical conse-quences of some class of facts, in this case the laws. For him, thelaws should not be necessary merely because they arelaws, they should be laws because the lawmakers supply something‘‘pretheoretically recognizable as a species of necessity’’ (p. 58). Heoffers the following general characterization of necessity (p. 66):

M: In any context: &q iff –(pB-�q) for any p where Bp

Lange then argues that relative necessities can only satisfy M ifall relevant facts in a given context are also necessary. By contrast,genuine necessities satisfy M without this explosion of necessarytruths. Sets of genuine necessities, as instanced by his earliercharacterization of nomological necessities, are stable eventhough they are non-maximal. Ultimately, this way of makingthe distinction is justified by an argument (pp. 71–72) analogousto the earlier argument that a stable set that includes anyaccidental truth must include all. So, Lange has his account ofhow the laws combine contingency with necessity, one thatunifies all important species of necessity.

Lange’s discussion of necessity in general, and its relation to lawsin particular, is masterful, and will amply repay the reader’s time.

Book review / Studies in History and Philosophy of Modern Physics 43 (2012) 155–158156

Laws and Lawmakers includes much more besides. In common withhis other work in the area, it provides sophisticated metaphysics ofscience informed by knowledgeable and insightful engagement withparticular sciences, including discussions of instantaneous velocities,symmetry principles in physics, the immutability of laws, andobjective chances. However, I conclude with one concern.

One might think there are straightforward counterexamples tothis type of account. Consider a set of putative laws, G, that includesthe genuine laws and the merely accidental generalization, R, andassume the genuine laws are deterministic. Let A be a completelyspecified possible, but non-actual, initial state that is nomicallysufficient for the existence of a gold sphere of diameter 2 km andconsider the accidental truth –A. For this case, the DisjunctiveAntecedent argument fails to apply. It rests on the claim that, forany accidental truth, P, not in G, �R v –P is consistent with G. But ifP is –A, �R v –P is inconsistent with G, since – –A is truth-functionally equivalent to A, and conjoined with the genuine laws,which are all in G, entails –R. So, it would seem there is no reason for–A to be included in G, and it need not be maximal. However, this isno counterexample. For Lange, sets of putative laws must belogically closed. Given that the conjunction of A and the genuinelaws entails –R, the conjunction of R and the genuine laws entails –A. Thus, �A is a member of G, in virtue of logical closure.

So, logical closure plays an essential role here. It insulates theaccount from counterexamples involving cases where the Dis-junctive Antecedent argument does not apply. Now, intuitively, alaw has consequences that are not themselves laws. Were it a lawthat all pendulums have period T¼kOl, it would not be alaw that all blue pendulums have period T¼kOl. Moreover, thedistinction is plausibly important. The former is fit to play a role inexplanation, because it does not cite explanatorily irrelevantproperties such as blueness, but the latter is not. Lange is awarethat counting the logical consequences of laws as laws is poten-tially problematic (p. 16) but deliberately elects to consider abroad notion of law that includes them all. His account is therebyincomplete, but that is no criticism of his project in Laws and

Lawmakers.However, it does raise a concern about a central feature of

his account: the primacy of subjunctive facts. For worlds whereAs are necessarily B1 or B2 oryor Bn, the law that All As are Cs,and the set of laws {All (A & B1)s are Cs, All (A & B2)s are Cs, y,All (A & Bn)s are Cs} support the same set of subjunctives. So,just as, intuitively, the laws do not supervene on the non-nomicfacts, they also, intuitively, do not supervene on the subjunctivefacts.2 And this point is intimately related to the explanatoryrole of laws. For a world that has the former law, the Bi

quantities are explanatorily irrelevant to whether any particu-lar A is a C, but for a world that includes the latter set of laws,some Bi is relevant. So, my concern is that if Lange’s account iscompleted so that explanatory laws are distinguished frommere nomological necessities, the ontological picture on whichthe subjunctive facts are prior to the law facts may not survive.Ontological economy may counsel that we give priority to thelaw facts, since subjunctive facts alone will not individuatethe laws.

John Roberts holds that an adequate account of scientificpractice should do justice to the idea that laws govern. Thus, herejects the contemporary Humean reduction of laws to merecosmic regularities. However, he also rejects non-Humeanism.Both are species of what he calls ‘‘first-order accounts’’, they takethe laws as part of the subject matter of scientific theories, muchlike electrons or electromagnetic fields, and such accounts, he

2 See Maudlin (2004), for an elegant elaboration of this point.

contends, cannot jointly satisfy the following four constraints:

Lawhood:

There is a distinct class of facts, or truepropositions, fittingly called the laws ofnature.

Discoverability:

Science is in principle capable of discoveringwhich propositions are the laws of nature.

Governing:

The laws of nature govern the universe insome robust, non-figurative sense of ‘govern’.

Science-Says-

So:

We can be justified in believing that the lawsof nature govern the universe withoutappealing to extra-scientific sources ofjustification.

The alternative he offers is the Meta-Theoretic approach(p. 91):

MT: P is a law of a theory T in virtue of playing an appropriaterole, R, in that theory.

On pain of trivializing the distinction with first-order accounts,R must not invoke the nomic, broadly construed: it cannot involvecausal powers or logically contingent counterfactuals, never mindbeing designated a law by T. Meta-theoretic accounts, as Robertsdevelops the idea, must hold that whether a proposition is a lawof theory T supervenes on T’s non-nomic content (p. 125). Whatcounts as a law of nature is then determined by this theory-relative notion of law and contextual factors (p. 113):

MT2: ‘P is a law of nature’ is true at world w in context k iffthere is a theory T such that T is salient in k, T is true at w, andP is a law of T.

The default salient theory in a context is the one thatcomprises all the true theoretical commitments of the extendedepistemic community of the speakers, but salience can shift forvarious reasons, e.g. if we are considering a non-actual possibilitywith different laws from the actual (p. 117).

Roberts’s primary motivation for the meta-theoretic view isan underdetermination argument from the first three con-straints, provided in chapter 4. Let T and T n be two theoriesthat differ only in that T declares L a law, whereas T n holds ittrue, but not a law. Given Governing we cannot determinewhich is true by determining whether L fits into the appro-priate pattern of cosmic regularities. So, if one of T and T n istrue, there is another world in which the other is true and allthe empirical evidence is the same as at the actual world.Hence, Roberts concludes, first-order governing theories violateDiscoverability. However, on the meta-theoretical view thenon-nomic content of T (or T n) is associated with a unique setof laws, those that play role R. Hence, Discoverability demandswe adopt the meta-theoretic view.

In chapter 5, Roberts analyses governing, equating it withinevitability. This is cashed in terms of a notion of counterfactualstability that, as he acknowledges (p. 184), is closely related toLange’s. He ultimately settles on the following formulation(p. 191):

NP: 8Q8P (If Q is consistent with the lawhood of all and onlythe @-LAWs, and the lawhood of all and only the @-LAWSlogically entails P, then Q&-P

A proposition is an @-LAW if, and only if, it is a law of nature atthe actual world, with ‘actual world’ read as a rigid indexical.

For the laws to satisfy both Governing and Science-Says-So,there must be a scientific justification for believing NP. In

3 Incidentally, the Actual-Factualists would be guilty of the former, since they

don’t confirm non-trivial counterfactuals, and are also thereby completely blind to

explanations that invoke counterfactual dependencies.

Book review / Studies in History and Philosophy of Modern Physics 43 (2012) 155–158 157

chapter 7, Roberts argues that NP cannot be non-circularlyconfirmed. Thus, commitment to NP must be a precondition ofanything worth calling scientific activity. In section 7.7, heintroduces as a foil the Actual-Factualists, putative scientistswho hold counterfactuals true only if their antecedents logicallynecessitate their consequents. They reject as false all contingentcounterfactuals, even those supported by the laws of nature.What, Roberts asks, disqualifies them from being scientists? Hisanswer is developed in chapter 8: recognizing something as ameasurement procedure demands we hold it counterfactuallyreliable; we must, granted the truth of the procedure’s setupconditions, hold the Outcome/Pointer variable as a counterfac-tually reliable indicator of the quantity measured. Otherwise ourepistemic success can only be a matter of luck. So, the Actual-Factualists’ wholesale rejection of non-trivial counterfactualsprecludes them from doing science.

To vindicate both Governing and Science-Says-So, NP must beintimately tied to the counterfactuals that figure in the reliabilityconditions of our measurements. Thus, in chapter 9 we arrive atthe meta-theoretic account Roberts favors, the MeasurementAnalysis of Laws (MAL) on which (p. 324):

P is a law of theory T just in case P is a logically contingentlogical consequence of the reliability conditions, entailed by thetheoretical part of T, of all the legitimate measurement methodsrelative to T.

There is much to recommend in this book. Reconciling thelaws’ objectivity with an account rooted in the practices ofscientific communities, and contextualist to boot, looks like a tallorder. However, Roberts addresses such concerns in detail. Healso engages with the character of scientific practice and theepistemology of science in a way that accounts of laws seldom do,and much of the book’s pleasure lies in the nuanced andintrinsically interesting discussion of such matters throughout.However, I conclude with a couple of concerns.

First, NP equates governing with inevitability. But governinginvolves something else: salience. Surely no-one thinks that merenomological necessities govern? If they did, then were it a lawthat all pendulums have period T¼kOl, blue pendulums would begoverned not merely by that law, but also by ‘‘all blue pendulumshave period T¼kOl’’, as would all blue pendulums constructed ona Thursday be governed by an associated Thursday-Blue-Pendu-lum law. Intuitively, this introduces a spurious, all-pervasive,governing overdetermination. Nor should this concern be dis-missed by offering NP as a ‘‘cleaned-up’’ version of governing,purged of non-Humean metaphysical dross. ‘‘Governing’’ in thestandard sense is tied to explanatory salience. Not only does theBlue-Pendulum law not govern a blue pendulum’s period,but as noted earlier, a pendulum’s blueness does not explainits period. Thus, whether we want the non-Humean metaphysicsor not, some relevant notion of salience must plausiblyfeature in any account of laws that does justice to scientificpractice.

My other chief concern is with the underdeterminationargument. The rejection of non-Humean views—in Roberts’sterminology, first-order governing views—because they renderthe laws unknowable even granted knowledge of the entirenon-nomic history, is a venerable Humean theme. Robertsultimately rests his argument on the following principle(p. 169):

RUP: For any pair of mutually inconsistent theories T1 andT2, if every possible body of evidence that is consistentwith T1 is also consistent with T2 and vice-versa, then nobody of empirical evidence can provide any epistemicjustification for believing one of them rather than theother.

However, there is a good reason to deny RUP, one thatclosely relates to the centerpiece of Roberts’s analysis of

governing: laws support subjunctives. Suppose we send aparticle of some charge q into an electric field E and find thatits path deviates in accord with F¼qE. Other things being equal,is it reasonable to take such data as confirming the subjunctive,‘‘were a particle of that particular charge to enter a fieldcharacterized by that field vector, it would be accelerated bythe specified force’’? Yes. If we confirm the equation’s predic-tions for a large variety of values of q and E, should theconfirmation ultimately extend across the family of subjunc-tives supported by ‘‘F¼qE is a law’’, strongly confirming theclaim that it is indeed a law and correspondingly disconfirmingthat it is merely true but not a law? On pain of something thatgreatly resembles inductive skepticism and is certainly atvariance with paradigmatically rational scientific inference,again, yes; if you don’t confirm those subjunctives, you don’thave inductively rational expectations. Yet, is the non-lawhoodof F¼qE consistent with such data? Of course. For howevermany values of q and E we test, there remains at least thelogical possibility that some of the subjunctives supported bythe putative law—whether their antecedents are counterfactualor actual but unobserved—are false. Moreover, the consistencywith such data of the denial of those subjunctives, and hencethe law, is not something we should philosophically negotiateaway. The above example is essentially the flip-side of classiccounterexamples to Humean supervenience, such as JohnCarroll’s (1994) Mirror Worlds. For such worlds, intuitivelywe do not know the laws, because the impoverished non-nomichistory fails to significantly confirm or disconfirm any of thefamilies of subjunctives supported by the competitors. As suchthought experiments make manifest, it is intuitively compel-ling that a subjunctive is consistent with a non-nomic history,unless the history includes a counterexample—a case wherethe antecedent obtains but the consequent does not. And this isnot mere philosophical intuition-mongering in the pejorativesense: consistency of a non-nomic history or data-set with thesubjunctives goes with the consistency of that history or data-set with the explanations that invoke counterfactual depen-dencies supported by the competing laws. Thus, no tendentiousphilosophical presuppositions are required to mobilize theseintuitions, since they are intimately related to a core feature ofscientific practice: explanation (Ward, 2007). Correspondingly,the consistency of subjunctives that contradict ones supportedby ‘‘F¼qE is a law’’ with data that strongly confirms that law,and hence the consistency of some T n that denies it is a lawwith such data, is an intuition to be taken seriously. So, RUPdemands we either, preposterously, deny the rationality ofconfirming ‘‘F¼qE is a law’’ in the manner specified above, ordeny intuitive violations of Humean supervenience that areintimately related to the explanatory role of laws.3 Either way,it is a philosophically motivated epistemological principle thatis radically at odds with paradigm rational scientific practice. Inthis kind of weighting game, scientific practice should surelytrump mere philosophical intuition-mongering.

Notwithstanding its manifest originality and many interestingfeatures, what we have here in the sheep’s clothing of a Governingaccount is recognizably that bad old Humean wolf, with itsidiosyncratic epistemological scruples and associated failure toproperly accommodate the explanatory role of laws.

Book review / Studies in History and Philosophy of Modern Physics 43 (2012) 155–158158

References

Carroll, J. (1994). Laws of nature. New York: Cambridge University Press.Maudlin, T. (2004). Causation, counterfactuals, and the third factor. In: J. Collins,

N. Hall, & L. A. Paul (Eds.), Causation and counterfactuals (pp. 419–443).

Cambridge, MA: MIT PressIn: J. Collins, N. Hall, & L. A. Paul (Eds.), Causation

and counterfactuals (pp. 419–443). Cambridge, MA: MIT Press.Ward, B. (2007). Laws, explanation, governing, and generation. Australasian Journal

of Philosophy, 85, 537–552.