Laws of Nature

First published Tue Apr 29, 2003; substantive revision Mon Nov 16, 2020

Science includes many principles at least once thought to be laws ofnature: Newton’s law of gravitation, his three laws of motion,the ideal gas laws, Mendel’s laws, the laws of supply anddemand, and so on. Other regularities important to science were notthought to have this status. These include regularities that, unlikelaws, were (or still are) thought by scientists to stand in need ofstronger ground. These include the regularity of the ocean tides, theperihelion of Mercury’s orbit, the photoelectric effect, thatthe universe is expanding, and so on. Scientists also use laws but notother regularities to sort out what is possible: It is based on theirconsistency with Einstein’s laws of gravity that cosmologistsrecognize the possibility that our universe is closed and thepossibility that it is open (Maudlin 2007, 7–8). In statisticalmechanics, the laws of an underlying physical theory are used todetermine the dynamically possible trajectories through the statespace of the system (Roberts 2008, 12–16).

Philosophers of science and metaphysicians address various issuesabout laws, but the basic question is: What is it tobe alaw? Two influential answers are the systems approach (Lewis, 1973,1983, 1986, 1994) and the universals approach (Armstrong, 1978, 1983,1991, 1993). Other treatments include antirealist views (van Fraassen1989, Giere 1999, Ward 2002, Mumford 2004) and antireductionist views(Carroll 1994 and 2008, Lange 2000 and 2009, Maudlin 2007). Beside thebasic question, the recent literature has also focused on (i) whetherlaws are determined by matters of fact, (ii) the role laws play in theproblem of induction, (iii) whether laws involve a strong form ofnecessity, and (iv) the role of laws in physics and how that contrastswith the role of laws in the special sciences.

1. The Basic Question: What is it to be a Law?

Here are four reasons philosophers examine what it is to be a law ofnature: First, as indicated above, laws at least appear to have acentral role in scientific practice. Second, laws are important tomany other philosophical issues. For example, sparked by the accountof counterfactuals defended by Chisholm (1946, 1955) and Goodman(1947), and also prompted by Hempel and Oppenheim’s (1948)deductive-nomological model of explanation, philosophers have wonderedwhat makes counterfactual and explanatory claims true, have thoughtthat laws play some part, and so also have wondered what distinguisheslaws from nonlaws. Third, Goodman famously suggested that there is aconnection between lawhood and confirmability by an inductiveinference. So, some sympathetic to Goodman’s idea come to theproblem of laws as a result of their interest in the problem ofinduction. Fourth, philosophers love a good puzzle. Suppose thateveryone here is seated (cf., Langford 1941, 67). Then, trivially,that everyone here is seated is true. Though true, this generalizationdoes not seem to be a law. It is just too accidental. Einstein’sprinciple that no signals travel faster than light is also a truegeneralization but, in contrast, it is thought to be a law; it is notnearly so accidental. What makes the difference?

This may not seem like much of a puzzle. That everyone here is seatedis spatially restricted in that it is about a specific place; theprinciple of relativity is not similarly restricted. So, it is easy tothink that, unlike laws, accidentally true generalizations are aboutspecific places. But that is not what makes the difference. There aretrue nonlaws that are not spatially restricted. Consider theunrestricted generalization that all gold spheres are less than onemile in diameter. There are no gold spheres that size and in alllikelihood there never will be, but this is still not a law. Therealso appear to be generalizations that could express laws that arerestricted. Galileo’s law of free fall is the generalizationthat,on Earth, free-falling bodies accelerate at a rate of9.8 meters per second squared. The perplexing nature of the puzzle isclearly revealed when the gold-sphere generalization is paired with aremarkably similar generalization about uranium spheres:

All gold spheres are less than a mile in diameter.
All uranium spheres are less than a mile in diameter.

Though the former is not a law, the latter arguably is. The latter isnot nearly so accidental as the first, since uranium’s criticalmass is such as to guarantee that such a large sphere will never exist(van Fraassen 1989, 27). What makes the difference? What makes theformer an accidental generalization and the latter a law?

2. Systems

One popular answer ties being a law to deductive systems. The ideadates back to Mill (1843, 384), but has been defended in one form oranother by Ramsey (1978 [f.p. 1928]), Lewis (1973, 1983, 1986,1994), Earman (1984) and Loewer (1996). Deductive systemsare individuated by their axioms. The logical consequences of theaxioms are the theorems. Some true deductive systems will be strongerthan others; some will be simpler than others. These two virtues,strength and simplicity, compete. (It is easy to make a systemstronger by sacrificing simplicity: include all the truths asaxioms. It is easy to make a system simple by sacrificing strength:have just the axiom that 2 + 2 = 4.) According to Lewis (1973, 73),the laws of nature belong to all the true deductive systems with abest combination of simplicity and strength. So, for example,the thought is that it is a law that all uranium spheres are less thana mile in diameter because it is, arguably, part of the best deductivesystems; quantum theory is an excellent theory of our universe andmight be part of the best systems, and it is plausible to think thatquantum theory plus truths describing the nature of uranium wouldlogically entail that there are no uranium spheres of that size(Loewer 1996, 112). It is doubtful that the generalization that allgold spheres are less than a mile in diameter would be part of thebest systems. It could be added as an axiom to any system, but itwould bring little or nothing of interest in terms of strength andadding it would sacrifice something in terms of simplicity. (Lewislater made significant revisions to his account in order to addressproblems involving physical probability (Lewis 1986, 1994).

Many features of the systems approach are appealing. For one thing,it deals with a challenge posed by vacuous laws. Some laws arevacuously true: Newton’s first law of motion — that allinertial bodies have no acceleration — is a law, even thoughthere are no inertial bodies. But there are also lots of vacuouslytrue nonlaws: all plaid pandas weigh 5 lbs., all unicorns areunmarried, etc. With the systems approach, there is no exclusion ofvacuous generalizations from the realm of laws, and yet only thosevacuous generalizations that belong to the best systems qualify (cf.,Lewis 1986, 123). Furthermore, one goal of scientific theorizingis the formulation of true theories that are well balanced in terms oftheir simplicity and strength. So, the systems approach seems tounderwrite the truism that an aim of science is the discovery of laws(Earman 1978, 180; Loewer 1996, 112). One last aspect of the systemsview that is appealing to many (though not all) is that it is inkeeping with broadly Humean constraints on a sensible metaphysics.There is no overt appeal to closely related modal concepts (e.g., thecounterfactual conditional, causation, dispositions) and no overtappeal to modality-supplying entities (e.g., universals or God; forthe supposed need to appeal to God, see Foster 2004). Indeed, thesystems approach is the centerpiece of Lewis’s defense ofHumean supervenience, “the doctrine that all there isin the world is a vast mosaic of local matters of particular fact,just one little thing and then another” (1986, ix).

Other aspects of the systems approach make philosophers wary. (See,especially, Armstrong 1983, 66–73; van Fraassen 1989,40–64; Carroll 1990, 197–206.) Some argue that thisapproach will have the untoward consequence that laws areinappropriately mind-dependent in virtue of the account’s appealto the concepts of simplicity, strength and best balance, conceptswhose instantiation seems to depend on cognitive abilities, interests,and purposes. The appeal to simplicity raises further questionsstemming from the apparent need for a regimented language to permitreasonable comparisons of the systems (Lewis 1983, 367.) Morerecently, Roberts questions the systems approach at a point sometimesthought to be a strength of the view: “We have no practice ofweighing competing virtues of simplicity and information content forthe purpose of choosing one deductive system over others, where allare presumed to be true” (2008, 10). There is the practice ofcurve-fitting, which involves weighing the competing virtues ofsimplicity and closeness of fit, but this is a practice that is partof the process of discoveringwhat is true. Also, the systemsapproach is ill-suited to rule out widespread and strikingregularities as laws, even those that are clearly determined by theinitial conditions. That the universe is closed, that entropygenerally increases, that the planets of our solar system areco-planar, and others (if true) could be added to any true deductivesystem, greatly increasing the strength of the system, with only asmall cost in terms of simplicity (Maudlin 2007, 16; Roberts 2008,23). Interestingly, sometimes the systems view is abandonedbecause it satisfies the broadly Humean constraintson laws of nature; some argue that what generalizations are lawsis not determined by local matters of particular fact. (See Section 4below.) Though Humeans like Lewis generally favor realism to any formof anti-realism (Section 5 below), Berenstain and Ladyman (2012)have argued that scientific realism is incompatible with Humeanismbecause realism requires a notion of natural necessity not susceptibleto Humean analysis.

3. Universals

In the late 1970s, there emerged a competitor for the systems approachand all other Humean attempts to say what it is to be a law. Led byArmstrong (1978, 1983, 1991, 1993), Dretske (1977), and Tooley (1977,1987), the rival approach appeals to universals (i.e., certain kindsof properties and relations) to distinguish laws from nonlaws.

Focusing on Armstrong’s development of the view, here is aconcise statement of the framework characteristic of theuniversals approach:

Suppose it to be a law thatFs areGs.F-ness andG-ness are taken to be universals. Acertain relation, a relation of non-logical or contingentnecessitation, holds betweenF-ness andG-ness. Thisstate of affairs may be symbolized as‘N(F,G)’ (1983, 85).

This framework promises to address familiar puzzles and problems:Maybe the difference between the uranium-spheres generalization andthe gold-spheres generalization is that being uranium does necessitatebeing less than one mile in diameter, but being gold does not. Worriesabout the subjective nature of simplicity, strength and best balancedo not emerge; there is no threat of lawhood being mind-dependent solong as necessitation is not mind-dependent. Some think that theframework supports the idea that laws play a special explanatory rolein inductive inferences, since a law is not just a universalgeneralization, but is an entirely different creature — arelation holding between two other universals (Armstrong 1991, Dretske1977). The framework is also consistent with lawhood not superveningon local matters of particular fact; the denial of Humeansupervenience often accompanies acceptance of the universalsapproach.

For there truly to be this payoff, however, more has to be said aboutwhatN is. This is a problem van Fraassen callstheidentification problem,which he couples this with a secondproblem, what he callsthe inference problem (1989, 96). Theessence of this pair of problems was captured early on by Lewis withhis usual flair:

WhateverN may be, I cannot see how it could be absolutelyimpossible to haveN(F,G) andFawithoutGa. (UnlessN just is constant conjunction,or constant conjunction plus something else, in which caseArmstrong’s theory turns into a form of the regularity theory herejects.) The mystery is somewhat hidden by Armstrong’sterminology. He uses ‘necessitates’ as a name for thelawmaking universalN; and who would be surprised to hearthat ifF ‘necessitates’G anda hasF, thena must haveG? But Isay thatN deserves the name of ‘necessitation’only if, somehow, it really can enter into the requisite necessaryconnections. It can’t enter into them just by bearing a name,any more than one can have mighty biceps just by being called‘Armstrong’ (1983, 366).

Basically, there needs to be a specification of what the lawmakingrelation is (the identification problem). Then, there needs to be adetermination of whether it is suited to the task (the inferenceproblem): DoesN’s holding betweenF andG entail thatFs areGs? Does its holdingsupport corresponding counterfactuals? Do laws really turn out not tosupervene, to be mind-independent, to be explanatory? Armstrong doessay more about what his lawmaking relation is. He states in reply tovan Fraassen:

It is at this point that, I claim, the Identification problem has beensolved. The required relation is the causal relation, … nowhypothesized to relate types not tokens (1993, 422).

Questions remain about the nature of this causal relation understoodas a relation that relates both token events and universals. (See vanFraassen 1993, 435–437, and Carroll 1994, 170–174.)

4. Humean Supervenience

Rather than detailing all the critical issues that divide the systemsapproach and the universals approach, attention has been on thedivisive issue of supervenience (i.e., determination). It concernswhether Humean considerations really determine what the laws are.There are some important examples that appear to show that they donot:

Imagine a world containing ten different types of fundamentalparticles. Suppose further that the behavior of particles ininteractions depends upon the types of the interactingparticles. Considering only interactions involving two particles,there are 55 possibilities with respect to the types of the twoparticles. Suppose that 54 of these possible interactions have beencarefully studied, with the result that 54 laws have been discovered,one for each case, which are not interrelated in any way. Supposefinally that the world is sufficiently deterministic that, given theway particles of typesX andY are currentlydistributed, it is impossible for them ever to interact at any time,past, present, or future. In such a situation it would seem veryreasonable to believe that there is some underived law dealing withthe interaction of particles of typesXandY. … In the universe in which particles oftypesX andY never interact, it might be a law thatwhen they do, an event of typeP occurs. But equally, itmight be a law that an event of typeQ occurs. These twogeneralizations will not be without instances, but none of them willbe of the positive variety. And in the absence of positive instances,there is no basis for holding that one generalization is a law, andthe other not. (Tooley 1977, 669 & 671)

The failure of supervenience arises in other cases. Consider thepossibility that there is a lone particle traveling through otherwiseempty space at a constant velocity of, say, one meter per second. Itseems that this might just be a nearly empty Newtonian universe inwhich it is accidentally true that all bodies have a velocity of onemeter per second; it just so happens that there is nothing to alterthe particle’s motion. But, it might also be the case that thisworld is not Newtonian and that it is a law that all bodies havevelocity at one meter per second; it could be that this generalizationis not accidental and would have held true even if there were otherbodies slamming into the lone particle. (Earman 1986, 100; Lange 2000,85–90.)

Maudlin presses the case against the Humeans by focusing on the commonpractice among physicists of considering models of a theory’slaws.

Minkowski space-time, the space-time of Special Relativity, is a modelof the field equations of General Relativity (in particular, it is avacuum solution). So an empty Minkowski space-time is one way theworld could be if it is governed by the laws of General Relativity.But is Minkowski space-time a modelonly of the GeneralRelativistic laws? Of course not! One could, for example, postulatethat Special Relativity is the complete and accurate account ofspace-time structure, and produce another theory of gravitation, whichwould still have the vacuum Minkowski space-time as a model. So underthe assumption that no possible world can be governed by the laws ofGeneral Relativity and by a rival theory of gravity, the totalphysical state of the world cannot always determine the laws (2007,67).

The suggestion here is that there is the possibility of a matter-lessuniverse with the laws of General Relativity and another with laws ofa conflicting theory of gravitation. (For additional examples, seeCarroll 1994, 60–80). What Maudlin sees as a consequence ofstandard scientific reasoning, Humeans will see as an example exposingthe absurdity of nonsupervenience.

Humeans contend that the various pairs of so-called possible worldsare not really possible. Sometimes this contention turns on the issueof whether laws govern, sometimes on epistemological or ontologicalconcerns, and sometimes on concerns about about how our languageworks. One objection to the nonsupervenience arguments from the Humeancamp is that, if one comes to the debate with the governing conceptionin mind, one is likely to find the antisupervenience examplesconvincing, but using this conception to reject Humean analyses oflawhood is somehow to beg the question or to otherwise be unconvincingbecause it is a conception Humeans reject (Beebee, 2000). (Also seeLoewer 1996 and Roberts 1998.) In contrast, some are sympathetic toHumeanism and aspects of the governing conception (Schneider 2007,Ward 2007, Roberts 2008). In particular, when we consider lawsgoverning the nation, the laws don’t do anything to thegoverned. What governs is the government that creates andenforces the laws. “The proposition that we call the law is notthe agent of the governing, but the content of the governing”(Roberts 2008, 46).

Some argue based on skeptical considerations that their brand ofHumean supervenience is true (Earman and Roberts 2005ab). Othersreject skeptical concerns (Schaffer 2008, 94–99, Carroll2008, 75–79). Schaffer presses an ontological concernto the effect that nonsupervening laws are ungrounded entities(Schaffer 2008, 84–85).

An original manner of responding to apparent counterexamples tosupervenience takes a semantic turn. In the lone-particle examplereported above, there is a world with the lone particle traveling atone meter per second, though it is not a law that all particles travelat that speed. There is also a world with the lone particle travelingat one meter per second, though it is a law that all particles aretraveling at that speed. This reasoning does not contradictsupervenience because of the context sensitivity of the predicate,‘is a law’. Though the sentence, ‘It is a law thatall particles travel at one meter per second’ is (i) truerelative to one context/world pair and (ii) false relative to adifferent context/world pair. This difference in truth-value couldmerely be the result of a difference between two contexts (Roberts2008, 357–61).

For Roberts, a possible worldw in which there exists only asingle particle traveling at constant velocity throughout all ofhistory and relative to a context in which the salient theory is, say,Newtonian Mechanics, ‘It is a law that all particles have aconstant velocity of one meter per second’ is true just in casethe reference of the ‘that’ clause plays the law role inthe salient theory, which it doesn’t in this case. It mightplay the law role relative to some other theory, but this wouldbe a different context. A single generalization cannotboth play the law role and also not play the law role relative to asingle theory, and so a different salient theory and so a differentcontext is required for ‘It is a law that all bodies travel atone meter per second’ to be true (Roberts 2008, 357–61). What is enticing about this reply is that it does not reject anyintuitive claim about the laws in the various possible worlds. Theantisupervenience judgments about what are the laws are reasonableclaims given the contexts. It is just that there is a failure torecognize the influence of context. So, for example, Maudlin’sso-called two possibilities would be seen by Roberts as descriptionsof a single possibility that are made relative to two contexts withdifferent salient theories: General Relativity and some rival theoryof gravity. (Parallel points could be made about Tooley’sexamples involving the 10 different kinds of fundamental particles.)The key is the context sensitivity that is built into the truthconditions of lawhood sentences. Other views that take lawhoodsentences to be context sensitive might also be able to availthemselves of Roberts’ challenge to the antisupervenienceexamples. What is not compelling about Roberts’ position,though, is his view on the context dependence of lawhood ascriptions.His view is devised for one particular phrase of English:‘law of nature’, but it would be better if thecontextual treatment of ‘law of nature’ melded neatlywith the context dependence of other natural language words andphrases. We should try to understand the context dependence of our‘law of nature’ talk by appeal to linguistic principles,and the investigation should be driven by considerations ofconversational practice (Carroll 2018, 131–32). ‘Law ofnature’ should not be an isolated freak of our language(cf., Unger 1971, 202) on the verb ‘to know’.

5. Antirealism

The majority of contemporary philosophers arerealists aboutlaws; they believe that some reports of what the laws are succeed indescribing reality. There are, however, someantirealists whodisagree.

For example, van Fraassen, Giere, and also Mumford believe thatthere are no laws. Van Fraassen finds support for his view in theproblems facing accounts like Lewis’s and Armstrong’s, andthe perceived failure of Armstrong and others to describe an adequateepistemology that permits rational belief in laws (1989,130, 180–181). Giere appeals to the origins of the use ofthe concept of law in the history of science (1999 [f.p. 1995],86–90) and contends that the generalizations often described aslaws are not in fact true (90–91). Mumford’s reasons aremore metaphysical; he maintains that, in order to govern, laws must beexternal to the properties they govern, but, to be external in thisway, the governed properties must lack proper identity conditions(2004, 144–145). Others adopt a subtly different sort ofantirealism. Though they will utter sentences like ‘It is a lawthat no signals travel faster than light’, they are antirealistsin virtue of thinking that such sentences are not (purely)fact-stating. Whether this Einsteinian generalization is a law is nota fact about the universe; it is not something out there waiting to bediscovered. Reports of what are laws only project a certain attitude(in addition to belief) about the contained generalizations (Blackburn1984, 1986, Ward 2002, 197). Ward takes the attitude to be oneregarding the suitability of the generalization for prediction andexplanation.

The challenge for antirealism is to minimize the havoc lawless realitywould play with our folk and scientific practices. Regarding science,the examples and uses of laws described at the start of this entryattest to ‘law’ having a visible role in science thatscientists seem prepared to take as factive. Regarding our folkpractices, though ‘law’ is not often part ofrun-of-the-mill conversations, an antirealism about lawhood wouldstill have wide-ranging consequences. This is due to lawhood’sties to other concepts, especially thenomic ones, conceptslike the counterfactual conditional, dispositions, and causation. Forexample, it seems that, for there to be any interesting counterfactualtruths, there must be at least one law of nature. Would an ordinarymatch in ordinary conditions light if struck? It seems it would, butonly because we presume nature to be regular in certain ways. We thinkthis counterfactual is true because we believe there are laws. Werethere no laws, it would not be the case that, if the match werestruck, it would light. As a result, it would also not be the casethat the match wasdisposed to ignite, nor the case thatstriking the match wouldcause it to light.

Could an antirealist deflect this challenge by denying the connectionsbetween lawhood and other concepts? Would this allow one to be anantirealist about laws and still be a realist about, say,counterfactuals? The danger lurking here is that the resultingposition seems bound to bead hoc. Concepts like thecounterfactual conditional, dispositions, and causation exhibit manyof the same puzzling features that lawhood does; there are parallelphilosophical questions and puzzles about these concepts. It is hardto see what would warrant antirealism about lawhood, but not the othernomic concepts.

6. Antireductionism

Some advocate antireductionist, antisupervenience views (Carroll 1994,2008, Ismael 2015, Lange 2000, 2009, Maudlin 2007, Woodward1992). Regarding the question of what it is to be a law, theyreject the answers given by Humeans; they often deny Humeansupervenience, and they see no advantage in an appeal to universals.They reject all attempts to say what it is to be a law that do notappeal to nomic concepts. Yet they still believe that there really arelaws of nature; they are not antirealists. Maudlin takeslawhood to be a primitive status and laws to be ontological primitives— fundamental entities in our ontology. His project is to showwhat work laws can do, defining physical possibility in terms of lawsand sketching law-based accounts of the counterfactual conditional andof explanation. Carroll’s analysis of lawhood is interms of causal/explanatory concepts. The starting point is theintuition that laws are not accidental, that they are notcoincidences. Not being a coincidence, however, is not all there is tobeing a law. For example, it might be true that there are no goldspheres greater than 1000 miles in diameter because there is so littlegold in the universe. In that case, strictly speaking, thatgeneralization would be true, suitably general, and not a coincidence.Nevertheless, that would not be a law. Arguably, what blocks thisgeneralization from being a law is that somethingin nature— really, an initial condition of the universe, the limitedamount of gold — accounts for the generalization. Contrast thiswith the law that inertial bodies have no acceleration. With this andother laws, it seems that it holds because of nature (itself). Lange’s (2000, 2009) treatment includes an account of what it isto be a law in terms of a counterfactual notion of stability. Theoverall account is intricate, but the basic idea is this: Call alogically closed set of true propositions stable if and only if themembers of the set would remain true given any antecedent that isconsistent with the set itself. So, for example, the set of logicaltruths is trivially stable, because logical truths would be true nomatter what. A set that included the accidental generalization thatall the people in the room are sitting, but is consistent with theproposition that someone in the room shouts ‘Fire!’ wouldnot be a stable set; if someone were to shout ‘Fire’, thensomeone in the room would not be sitting. Lange argues that nostable set of sub-nomic facts — except maybe the set of alltruths — contains an accidental truth. “By identifying thelaws as the members of at least one non-maximal stable set, wediscover how a sub-nomic fact’s lawhood is fixed by thesub-nomic facts and the subjunctive facts about them” (2009,43).

Attempts to undermine antireductionism often include challenges toantisupervenience like those mentioned at the end of Section 4. Hildebrand challenges Carroll’s and Maudlin’santireductionisms based on the failure of primitive laws to explainthe uniformity of nature (Hildebrand, 2013). A symposium onLange’s (2009) Laws and Lawmakers includes, along withLange’s replies, a variety of criticisms from Carroll, Loewer,and Woodward. (See Langeet al., 2011.) Demerest (2012)raises three challenges to Lange’s antireductionism all centeredon whether subjunctives are suited to play the role of lawmakers.

7. Induction

Goodman thought that the difference between laws of nature andaccidental truths was linked inextricably with the problem ofinduction. In his “The New Riddle of Induction” (1983,[f.p. 1954], 73), Goodman says,

Only a statement that islawlike — regardless of itstruth or falsity or its scientific importance — is capable ofreceiving confirmation from an instance of it; accidental statementsare not.

(Terminology:P is lawlike only ifP is a law iftrue.) Goodman claims that, if a generalization is accidental (and sonot lawlike), then it is not capable of receiving confirmation fromone of its instances.

This has prompted much discussion, including some challenges. Forexample, suppose there are ten flips of a fair coin, and that thefirst nine land heads (Dretske 1977, 256–257). The first nineinstances — at least in a sense — confirm thegeneralization that all the flips will land heads; the probability ofthat generalization is raised from (.5)¹⁰up to .5. But this generalization is notlawlike; if true, it is not a law. It is standard to respond to suchan example by arguing that this is not the pertinent notion ofconfirmation (that it is mere “content-cutting”) and bysuggesting that what does require lawlikeness is confirmation of thegeneralization’s unexamined instances. Notice that, in the coincase, the probability that the tenth flip will land heads does notchange after the first nine flips land heads. There are, however,examples that generate problems for this idea too.

Suppose the room contains one hundred men and suppose you ask fifty ofthem whether they are third sons and they reply that they are; surelyit would be reasonable to at least increase somewhat your expectationthat the next one you ask will also be a third son (Jackson andPargetter 1980, 423)

It does no good to revise the claim to say that no generalizationbelieved to be accidental is capable of confirmation. Aboutthe third-son case, one would know that the generalization, even iftrue, would not be a law. The discussion continues. Frank Jackson andRobert Pargetter have proposed an alternative connection betweenconfirmation and laws on which certain counterfactual truths musthold: observation ofAs that areF-and-Bconfirms that all non-FAs areBs only iftheAs would still have been bothA andBif they had not beenF. (This suggestion is criticized byElliott Sober 1988, 97–98.) Lange (2000, 111–142) uses adifferent strategy. He tries to refine further the relevant notion ofconfirmation, characterizing what he takes to be an intuitive notionof inductive confirmation, and then contends that only generalizationsthat are not believed not to be lawlike can be (in his sense)inductively confirmed.

Sometimes the idea that laws have a special role to play in inductionserves as the starting point for a criticism of Humean analyses.Dretske (1977, 261–262) and Armstrong (1983, 52–59, and1991) adopt a model of inductive inference that involves an inferenceto the best explanation. (Also see Foster 1983 and 2004.) On itssimplest construal, the model describes a pattern that begins with anobservation of instances of a generalization, includes an inference tothe corresponding law (this is the inference to the best explanation),and concludes with an inference to the generalization itself or to itsunobserved instances. The complaint lodged against Humeans is that, ontheir view of what laws are, laws are not suited to explain theirinstances and so cannot sustain the required inference to the bestexplanation.

This is an area where work on laws needs to be done. Armstrong andDretske make substantive claims on what can and can’t beinstance confirmed: roughly, Humean laws can’t,laws-as-universals can. But, at the very least, these claims cannot bequite right. Humean laws can’t? As the discussion aboveillustrates, Sober, Lange and others have argued that evengeneralizations known to be accidental can be confirmed by theirinstances. Dretske and Armstrong need some plausible and suitablystrong premise connecting lawhood to confirmability and it is notclear that there is one to be had. Here is the basic problem: As manyauthors have noticed (e.g., Sober 1988, 98; van Fraassen 1987, 255),the confirmation of a hypothesis or its unexamined instances willalways be sensitive to what background beliefs are in place. So muchso that, with background beliefs of the right sort, just aboutanything can be confirmed irrespective of its status as a law orwhether it is lawlike. Thus, stating a plausible principle describingthe connection between laws and the problem of induction will bedifficult.

8. Necessity

Philosophers have generally held that some contingent truths are (orcould be) laws of nature. Furthermore, they have thought that, if itis a law that allFs areGs, then there need not beany (metaphysically) necessary connection betweenF-ness andG-ness, that it is (metaphysically) possible that somethingbeF without beingG. For example, any possibleworld that, as a matter of law, obeys the general principles ofNewtonian physics is a world in which Newton’s first law istrue, and a world containing accelerating inertial bodies is a worldin which Newton’s first law is false. The latter world is also aworld where inertia is instantiated but does not necessitate zeroacceleration. Somenecessitarians, however, hold that alllaws are necessary truths. (See Shoemaker 1980 and 1998, Swoyer 1982,Fales 1990, Bird 2005. See Vetter 2012 for criticism of Bird 2005 fromwithin the dispositional essentialist camp.) Others have heldsomething that is only slightly different. Maintaining that some lawsare singular statements about universals, they allow that some lawsare contingently true. So, on this view, anF-ness/G-ness law could be false ifF-nessdoes not exist. Still, this difference is minor. These authors thinkthat, for there to be anF-ness/G-ness law, it mustbe necessarily true that allFs areGs. (SeeTweedale 1984, Bigelow, Ellis, and Lierse 1992, Ellis and Lierse 1994,and Ellis 2001, 203–228; 2009, 51–72.)

Two reasons can be given for believing that being a law does notdepend on any necessary connection between properties. The firstreason is the conceivability of it being a law in one possible worldthat allFs areGs even though there is anotherworld with anF that is notG. The second is thatthere are laws that can only be discovered in ana posteriorimanner. If necessity is always associated with laws of nature, then itis not clear why scientists cannot always get by withapriori methods. Naturally, these two reasons are oftenchallenged. The necessitarians argue that conceivability is not aguide to possibility. They also appeal to Saul Kripke’s (1972)arguments meant to reveal certaina posteriori necessarytruths in order to argue that thea posteriori nature of somelaws does not prevent their lawhood from requiring a necessaryconnection between properties. In further support of their own view,the necessitarians argue that their position is a consequence of theirfavored theory of dispositions, according to which dispositions havetheir causal powers essentially. So, for example, on this theory,charge has as part of its essence the power to repel like charges.Laws, then, are entailed by the essences of dispositions (cf., Bird2005, 356). As necessitarians see it, it is also a virtue of theirposition that they can explain why laws are counterfactual-supporting;they support counterfactuals in the same way that other necessarytruths do (Swoyer 1982, 209; Fales 1990, 85–87).

The primary worry for necessitarians concerns their ability to sustaintheir dismissals of the traditional reasons for thinking that somelaws are contingent. The problem (cf., Sidelle 2002, 311) is that theytoo make distinctions between necessary truths and contingent ones,and even seem to rely on considerations of conceivability to do so.Prima facie, there is nothing especially suspicious about the judgmentthat it is possible that an object travel faster than light. How is itany worse than the judgment that it is possible that it is raining inParis? Another issue for necessitarians is whether their essentialismregarding dispositions can sustain all the counterfactuals that areapparently supported by laws of nature (Lange 2004).

9. Laws, Circularity and Prospects for Explanation

Going back to Armstrong (1983, 40), there have beenchallenges to those who hold a Humean account of laws, and aboutwhether Humean laws are explanatory. More recently, Maudlin hasput the challenge in a perspicuous way:

If one is a Humean, then the Humean Mosaic itself appears to admit ofno further explanation. Since it is the ontological bedrock in termsof which all other existent things are to be explicated, none of thesefurther things can really account for the structure of the Mosaicitself. This complaint has been long voiced, commonly as an objectionto any Humean account of laws. If the laws are nothing but genericfeatures of the Humean Mosaic, then there is a sense in which onecannot appeal to those very laws to explain the particular features ofthe Mosaic itself: the laws are what they are in virtue of the Mosaicrather than vice versa (Maudlin 2007, 172).

Loewer (2012, 131) offers a response to the issuethat Maudlin highlights. Loewer’s response is that thegreat Humean mosaic makes the laws of nature true. The move he makesto avoid the circularity is that Humean laws do notmetaphysically explain elements of the mosaic, but they doscientifically explain aspects of the mosaic, suggesting thatthere are two notions of explanation and so no circularity. Thismove has spawned a recent slew of excellent journal articles regardingthe viability of Loewer’s move (see especially Lange 2013,Miller 2015, Roski 2018, and Shumener 2017).

An increasingly popular way to look at the relation between laws andtheir instances is taking instances as grounding laws. No individualinstance of a law can fully ground the law, but a conjunction ofinstances does more fully ground the law. Another plausible way ofviewing the relation between laws and their instances is to see lawsas grounding their instances (Emery 2019). Because the groundingrelation is non-symmetric, both of these views cannot be true. The wayout of this dilemma is one that illuminates the debate aboutexplanation in an interesting way. Consider that while (P&Q) is a full ground forQ, it seems wrong toclaim that (P &Q) explains whyQ(Roski 2018). This is because the content of the explanandum (what isto be explained) is embedded in the content of the explanans (what isintended to do the explaining), and something cannot explain itself(or be an essential part of an explanation of itself). Notice thatthis formulation exposes the problem: if the explanans includes theexplanandum as part of its content, it makes the explanation devoid ofunderstanding. Ones audience would have to already have had anunderstanding of the explanandum. Successful explanations are notcircular, so anyone taking laws as grounds for their instances oughtnot to think that the grounding relation is explanatory. The pointhere is not to show that grounding is not an explanatory relation, butrather to show thatlaws of nature are not suited to explaintheir instances. Circularity also infects the DN model ofexplanations. As the authors of the DN model pointed out:

… the content of the explanandum is contained in theexplanans. That is correct since the explanandum is a semanticconsequence of the explanans (Hempel and Oppenheim, cf. 1948, 162;also see Shumener 2017, 793).

The issue here undermines the importance of the role for explanationsto provide understanding. The required validity brings semanticcircularity, because the content of the explanans would then besufficient for the truth of the explanandum. In line with the regularpresentations of the DN model, at least one law of nature is requiredto be a premise in an “explanatory argument”. Indeed, atleast one law needs to be essential to the validity of the argument,and the laws being part of the explanans are clearly a factorregarding the circularity. To add to these challenges, it is goodto remember what Dretske pointed out regarding laws andexplanation.

To say that a law is a universal truth having explanatory power islike saying a chair is a breath of air used to seat people. You cannotmake a silk purse out of a sow’s ear, not even a very goodsow’s ear; and you cannot make a generalization, not even apurely universal generalization, explain its instances. The fact thatevery F is G fails to explain why any F is G, and it fails to explainit, not because its explanatory efforts are too feeble to haveattracted our attention, but because the explanatory attempt is nevereven made … Subsuming an instance under a universalgeneralization has exactly as much explanatory power as deriving Qfrom P & Q. None (1977, 26).

Dretske’s reaction to this quotation was to conclude thatlaws of nature are not universally quantified conditionals; that theyare not mere generalizations. Instead, it was thought that lawshad to be a different kind of thing: a relation between universals,physically necessary generalizations, or a true axiom or theorem of anideal system, or even a metaphysically necessary generalization. Another approach needs to be considered, maybe, just maybe, laws ofnature are generalizations and just aren’t explanatory in anyvery significant way. This is an approach that identifies what sort ofentity a law of nature is.

10. Physics and the Special Sciences

Two separate (but related) questions have received much recentattention in the philosophical literature surrounding laws. Neitherhas much to do with what it is to be a law. Instead, they have to dowith the nature of the generalizations scientists try to discover.First: Does any science try to discover exceptionless regularities inits attempt to discover laws? Second: Even if one science —fundamental physics — does, do others?

10.1 Do Physicists try to discover Exceptionless Regularities?

Philosophers draw a distinction betweenstrictgeneralizations andceteris-paribus generalizations. Thecontrast is supposed to be between universal generalizations of thesort discussed above (e.g., that all inertial bodies have noacceleration) and seemingly less formal generalizations like that,other things being equal, smoking causes cancer. The idea is that theformer would be contradicted by a single counterinstance, say, oneaccelerating inertial body, though the latter is consistent with therebeing one smoker who never gets cancer. Though in theory thisdistinction is easy enough to understand, in practice it is oftendifficult to distinguish strict fromceteris-paribusgeneralizations. This is because many philosophers think that manyutterances which include no explicitceteris-paribus clauseimplicitly do include such a clause.

For the most part, philosophers have thought that if scientists havediscovered any exceptionless regularities that are laws, they havedone so at the level of fundamental physics. A few philosophers,however, are doubtful that there are exceptionless regularities ateven this basic level. For example, Cartwright has argued thatthe descriptive and the explanatory aspects of laws conflict.“Rendered as descriptions of fact, they are false; amended to betrue, they lose their fundamental explanatory force” (1980, 75).Consider Newton’s gravitational principle,F =Gmm′/r².Properly understood, according to Cartwright, it says that for any twobodies the force between them isGmm′/r². Butif that is what the law says then the law is not an exceptionlessregularity. This is because the force between two bodies is influencedby other properties than just their mass and the distance betweenthem, by properties like the charge of the two bodies as described byCoulomb’s law. The statement of the gravitational principle canbe amended to make it true, but that, according to Cartwright, atleast on certain standard ways of doing so, would strip it of itsexplanatory power. For example, if the principle is taken to hold onlythatF = Gmm′/r²if there are no forces other thangravitational forces at work, then though it would be true it wouldnot apply except in idealized circumstances. Lange (1993) uses adifferent example to make a similar point. Consider a standardexpression of the law of thermal expansion: ‘Whenever thetemperature of a metal bar of lengthL₀changes byT, the length of the barchanges byL =kL₀T,’wherek is aconstant, the thermal expansion coefficient of the metal. If thisexpression were used to express the strict generalizationstraightforwardly suggested by its grammar, then such an utterancewould be false since the length of a bar does not change in the waydescribed in cases where someone is hammering on the ends of the bar.It looks like the law will require provisos, but so many that the onlyapparent way of taking into consideration all the required provisoswould be with something like aceteris-paribus clause. Thenthe concern becomes that the statement would be empty. Because of thedifficulty of stating plausible truth conditions forceteris-paribussentences, it is feared that ‘Other things being equal,L =kL₀T’could only mean‘L =kL₀Tprovided thatL =kL₀T.’

Even those who agree with the arguments of Cartwright and Langesometimes disagree about what ultimately the arguments say about laws.Cartwright believes that the true laws are not exceptionlessregularities, but instead are statements that describe causal powers.So construed, they turn out to be both true and explanatory. Langeends up holding that there are propositions properly adopted as laws,though in doing so one need not also believe any exceptionlessregularity; there need not be one. Giere (1999) can usefully beinterpreted as agreeing with Cartwright’s basic arguments butinsisting that law-statements don’t have implicit provisos orimplicitceteris-paribus clauses. So, he concludes that thereare no laws.

Earman and Roberts hold that there are exceptionless and lawfulregularities. More precisely, they argue that scientists doingfundamental physics do attempt to state strict generalizations thatare such that they would be strict laws if they were true:

Our claim is only that … typical theories from fundamentalphysics are such thatif they were true, there would beprecise proviso free laws. For example, Einstein’s gravitationalfield law asserts — without equivocation, qualification,proviso,ceteris paribus clause — that the Riccicurvature tensor of spacetime is proportional to the totalstress-energy tensor for matter-energy; the relativistic version ofMaxwell’s laws of electromagnetism for charge-free flatspacetime asserts — without qualification or proviso —that the curl of theE field is proportional to thepartial time derivative, etc. (1999, 446).

About Cartwright’s gravitational example, they think (473, fn.14) that a plausible understanding of the gravitational principle isas describing only thegravitational force between the twomassive bodies. (Cartwright argues that there is no such componentforce and so thinks such an interpretation would be false. Earman andRoberts disagree.) About Lange’s example, they think the lawshould be understood as having the single proviso that there be noexternal stresses on the metal bar (461). In any case, much more wouldneed to be said to establish thatall the apparently strictand explanatory generalizations that have been or will be stated byphysicists have turned or will turn out to be false. (Earman,etal., 2003 includes more recent papers by both Cartwright andLange, and also many other papers onceteris-paribuslaws.)

10.2 Could there be any Special-Science Laws?

Supposing that physicists do try to discover exceptionlessregularities, and even supposing that our physicists will sometimes besuccessful, there is a further question of whether it is a goal of anyscience other than fundamental physics — any so-called specialscience — to discover exceptionless regularities and whetherthese scientists have any hope of succeeding. Consider an economic lawof supply and demand that says that, when demand increases and supplyis held fixed, price increases. Notice that, in some places, the priceof gasoline has sometimes remained the same despite an increase indemand and a fixed supply, because the price of gasoline wasgovernment regulated. It appears that the law has to be understood ashaving aceteris-paribus clause in order for it to be true. Thisproblem is a very general one. As Jerry Fodor (1989, 78) has pointedout, in virtue of being stated in a vocabulary of a special science,it is very likely that there will be limiting conditions —especially underlying physical conditions — that will undermineany interesting strict generalization of the special sciences,conditions that themselves could not be described in thespecial-science vocabulary. Donald Davidson prompted much of therecent interest in special-science laws with his “MentalEvents” (1980 [f.p. 1970], 207–225). He gave an argumentspecifically directed against the possibility of strictpsycho-physical laws. More importantly, he made the suggestion thatthe absence of such laws may be relevant to whether mental events evercause physical events. This prompted a slew of papers dealing with theproblem of reconciling the absence of strict special-science laws withthe reality of mental causation (e.g., Loewer and Lepore 1987 and1989, Fodor 1989, Schiffer 1991, Pietroski and Rey 1995).

Progress on the problem of provisos depends on three basic issuesbeing distinguished. First, there is the question of what it is to bea law, which in essence is the search for a necessarily truecompletion of: “P is a law if and only if…”. Obviously, to be a true completion, it must hold forallP, whetherP is a strict generalization or aceteris-paribus one. Second, there is also a need todetermine the truth conditions of the generalization sentences used byscientists. Third, there is thea posteriori and scientificquestion of which generalizations expressed by the sentences used bythe scientists are true. The second of these issues is the one wherethe action needs to be.

On this score, it is striking how little attention is given to thepossible effects of context. Mightn’t it be that, when theeconomist utters a certain strict generalization sentence in an“economic setting” (say, in an economics textbook or at aneconomics conference), context-sensitive considerations affecting itstruth conditions will have it turn out that the utterance is true?This might be the case despite the fact that the same sentence utteredin a different context (say, in a discussion among fundamentalphysicists or better yet in a philosophical discussion of laws) wouldresult in a clearly false utterance. These changing truth conditionsmight be the result of something as plain as a contextual shift in thedomain of quantification or perhaps something less obvious. Whateverit is, the important point is that this shift could be a function ofnothing more than the linguistic meaning of the sentence and familiarrules of interpretation (e.g., the rule of accommodation).

Consider a situation where an engineering professor utters,“When a metal bar is heated, the change in its length isproportional to the change in its temperature” and suppose astudent offers, “Not when someone is hammering on both ends ofthe bar.” Has the student shown that the teacher’sutterance was false? Maybe not. Notice that the student comes offsounding a bit insolent. In all likelihood, such an unusual situationas someone hammering on both ends of a heated bar would not have beenin play when the professor said what he did. In fact, the reason thestudent comes off sounding insolent is because it seems that he shouldhave known that his example was irrelevant. Notice that theprofessor’s sentence needn’t include some implicitceteris-paribus clause in order for his utterance to be true;as this example illustrates, in ordinary conversations, plain oldstrict generalization sentences are not always used to cover the fullrange of actual cases. Indeed, they are rarely used in this way. Ifspecial scientists do make true utterances of generalization sentences(sometimesceteris-paribus generalization sentences,sometimes not), then apparently nothing stands in the way of themuttering true special-science lawhood sentences. The issue here hasbeen the truth of special-science generalizations, not any otherrequirements of lawhood.

11. Concluding Remarks: What is Next?

How will matters progress? How can philosophy advance beyond thecurrent disputes about laws of nature? Three issues areespecially interesting and important ones. The first concernswhether lawhood is a part of the content of scientific theories. Thisis a question often asked about causation, but less frequentlyaddressed about lawhood. Roberts offers an analogy in support of thethought that it is not: It is a postulate of Euclidean geometry thattwo points determine a line. But it is not part of the content ofEuclidean geometry that this proposition is a postulate. Euclideangeometry is not a theory about postulates; it is a theory aboutpoints, lines, and planes … (2008, 92). This may be aplausible first step toward understanding the absence of somenomic terms from formal statements of scientific theories. Thesecond issue is whether there are any contingent laws of nature.Necessitarians continue to work on filling in their view, whileHumeans and others pay relatively little attention to what they are upto; new work needs to explain the source of the underlying commitmentsthat divide these camps. Finally, more attention needs to bepaid to the language used to report what are the laws and the languageused to express the laws themselves and whether the lawsexplain. It is clear that recent disputes about generalizationsin physics and the special sciences turn on precisely these matters,but exploring them may also pay dividends on central matters regardingontology, realism vs. antirealism, and supervenience.

Bibliography

Armstrong, D., 1978,A Theory of Universals, Cambridge:Cambridge University Press.
–––, 1983,What Is a Law of Nature?,Cambridge: Cambridge University Press.
–––, 1991, “What Makes InductionRational?,”Dialogue, 30: 503–511.
–––, 1993, “The Identification Problem andthe Inference Problem,”Philosophy and PhenomenologicalResearch, 53: 421–422.
Beebee, H., 2000, “The Nongoverning Conception of Laws ofNature,”Philosophy and Phenomenological Research, 61:571–594.
Berenstain, N. and Ladyman, J., 2012, “Ontic StructuralRealism and Modality,” in E. Landry and D. Rickles (eds.),Structural Realism: Structure, Object, and Causality.Dordrecht: Springer.
Bigelow, J., Ellis, B., and Lierse, C., 1992, “The World asOne of a Kind: Natural Necessity and Laws of Nature,”British Journal for the Philosophy of Science, 43:371–388.
Bird, A., 2005, “The Dispositionalist Conception ofLaws,”Foundations of Science, 10: 353–370.
Blackburn, S., 1984,Spreading the Word, Oxford:Clarendon Press.
–––, 1986, “Morals and Modals,” inFact, Science and Morality, G. Macdonald and C. Wright(eds.), Oxford: Basil Blackwell.
Carroll, J., 1990, “The Humean Tradition,”ThePhilosophical Review, 99: 185–219.
–––, 1994,Laws of Nature, Cambridge:Cambridge University Press.
–––, (ed.), 2004,Readings on Laws ofNature, Pittsburgh: Pittsburgh University Press.
–––, 2008, “Nailed to Hume’sCross?,” inContemporary Debates in Metaphysics, J.Hawthorne, T. Sider and D. Zimmerman, (eds.), Oxford: BasilBlackwell.
___, 2018, “Becoming Humean,” inLaws ofNature, W. Ott and L. Patton (eds.), Oxford: Oxford UniversityPress.
Cartwright, N., 1980, “Do the Laws of Physics state theFacts,”Pacific Philosophical Quarterly, 61:75–84.
Chisholm, R., 1946, “The Contrary-to-FactConditional,”Mind, 55: 289–307.
–––, 1955, “Law Statements andCounterfactual Inference,”Analysis, 15:97–105.
Cross, T., 2012, “Goodbye, Humean Supervenience,”Oxford Studies in Metaphysics 7: 129–153.
Davidson, D., 1980,Essays on Actions and Events, Oxford:Clarendon Press.
Demerest, H., 2012, “Do Counterfactuals Ground the Laws ofNature? A Critique of Lange,”Philosophy of Science,79: 333–344.
–––, 2015, “Fundamental Propertiesand the Laws of Nature”Philosophy Compass, 10:334–344.
Dretske, F., 1977, “Laws of Nature,”Philosophy ofScience, 44: 248–268.
Earman, J., 1978, “The Universality of Laws,”Philosophy of Science, 45: 173–181.
–––, 1984, “Laws of Nature: The EmpiricistChallenge,” inD. M. Armstrong, R. Bogdan (ed.),Dordrecht: D. Reidel Publishing Company.
–––, 1986,A Primer on Determinism,Dordrecht: D. Reidel Publishing Company.
Earman, J., Glymour, C., and Mitchell, S., (eds.), 2003,Ceteris Paribus Laws, Berlin: Springer.
Earman, J. and Roberts, J., 1999, “Ceteris Paribus,There is No Problem of Provisos,”Synthese, 118:439–478.
–––, 2005a, “Contact with the Nomic: AChallenge for Deniers of Humean Supervenience about Laws of Nature(Part I),”Philosophy and Phenomenological Research,71: 1–22.
–––, 2005b, “Contact with the Nomic: AChallenge for Deniers of Humean Supervenience about Laws of Nature(Part II),”Philosophy and Phenomenological Research,71: 253–286.
Ellis, B., 2001,Scientific Essentialism, Cambridge:Cambridge University Press.
–––, 2009Metaphysics of ScientificEssentialism, Montreal and Kingston: McGill-Queen’sUniversity Press.
Ellis, B. and Lierse, C., 1994, “DispositionalEssentialism,”Australasian Journal of Philosophy, 72:27–45.
Emery, N., 2019, “Laws and Their Instances”Philosophical Studies, 176: 1535–1561.
Fales, E., 1990,Causation and Universals, London:Routledge.
Fodor, J., 1989, “Making Mind Matter More,”Philosophical Topics, 17: 59–79.
Foster, J., 1983, “Induction, Explanation and NaturalNecessity,”Proceedings of the Aristotelian Society,83: 87–101.
–––, 2004,The Divine Lawmaker, Oxford:Clarendon Press.
Friend, T., 2016, “Laws are Conditionals,”European Journal for the Philosophy of Science, 6:123–144.
Giere, R., 1999,Science Without Laws, Chicago:University of Chicago Press.
Goodman, N., 1947, “The Problem of CounterfactualConditionals,”Journal of Philosophy, 44:113–128.
–––, 1983,Fact, Fiction, and Forecast,Cambridge: Harvard University Press.
Hall, N, 2015, “Humean Reductionism about Laws,” inA Companion to David Lewis, B. Loewer and J. Schaffer (eds.),Oxford: John Wiley and Sons.
Hempel, C. and Oppenheim, P., 1948, “Studies in the Logic ofExplanation,”Philosophy of Science, 15:135–175.
Hildebrand, T., 2013, “Can Primitive Laws Explain?”Philosophers’ Imprint 13(5) (July) [Available online].
–––, 2014, “Can Bare Dispositions ExplainCategorical Regularities?,”Philosophical Studies, 167(3): 569–584
Ismael, J., 2015, “How to be Humean,” inACompanion to David Lewis, B. Loewer and J. Schaffer (eds.).Oxford: John Wiley and Sons.
Jackson, F. and Pargetter, R., 1980, “Confirmation and theNomological,”Canadian Journal of Philosophy, 10:415–428.
Kripke, S., 1972,Naming and Necessity, Cambridge:Harvard University Press.
Lange, M., 1993, “Natural Laws and the Problem ofProvisos,”Erkenntnis, 38: 233–248.
–––, 2000,Natural Laws in ScientificPractice, Oxford: Oxford University Press.
–––, 2004, “A Note on ScientificEssentialism, Laws of Nature, and Counterfactual Conditionals,”Australasian Journal of Philosophy, 82: 227–41.
–––, 2009,Laws and Lawmakers, NewYork: Oxford University Press.
–––, 2013, “Grounding, ScientificExplanation, and Humean Laws,”Philosophical Studies,164: 255–61.
Lange, M.,et al., 2011, “Counterfactuals All theWay Down? Marc Lange:Laws and Lawmakers,”Metascience, 20: 27–52.
Langford, C., 1941, Review of “An Interpretation of CausalLaws,”Journal of Symbolic Logic, 6: 67–68.
Lewis, D., 1973,Counterfactuals, Cambridge: HarvardUniversity Press.
–––, 1983, “New Work for a Theory ofUniversals,”Australasian Journal of Philosophy, 61:343–377.
–––, 1986,Philosophical Papers, VolumeII, New York: Oxford University Press.
–––, 1994, “Humean SupervenienceDebugged,”Mind, 103: 473–390.
Loewer, B., 1996, “Humean Supervenience,”Philosophical Topics, 24: 101–126.
–––, 2012, “Two Accounts of Laws and Time,”Philosophical Studies, 160: 115–137.
Loewer, B. and Lepore, E., 1987, “Mind Matters,”Journal of Philosophy, 84: 630–642.
–––, 1989, “More on Making MindMatter,”Philosophical Topics, 17: 175–191.
Lyon, A., 1976–1977, “The Immutable Laws ofNature,”Proceedings of the Aristotelian Society, 77:107–126
Marshall, D., 2015, “Humean Laws and Explanations,”Philosophical Studies, 172: 3145–3165.
Maudlin, T., 2007,The Metaphysics Within Physics, NewYork: Oxford University Press.
Mill, J.S., 1843,A System of Logic, London: Longmans,Green and Co.
Miller, E., 2015, “Humean Scientific Explanation,”Philosophical Studies, 172: 1311–1332.
Mumford, S., 2004,Laws in Nature, London:Routledge.
Pietroski, P. and Rey, G., 1995, “When Other ThingsAren’t Equal: SavingCeteris Paribus Laws fromVacuity,”British Journal for the Philosophy ofScience, 46: 81–110.
Ramsey, F., 1978,Foundations, London: Routledge andKegan Paul.
Roberts, J., 1998, “Lewis, Carroll, and Seeing through theLooking Glass,”Australasian Journal of Philosophy, 76:426–438.
–––, 2008,The Law-Governed Universe,New York: Oxford University Press.
Roski, S., 2018, “Grounding and the explanatory role ofgeneralizations,”Philosophical Studies,175,1985–2003.
Schaffer, J., 2008, “Causation and Laws of Nature:Reductionism,” inContemporary Debates in Metaphysics,J. Hawthorne, T. Sider, and D. Zimmerman, (eds.), Oxford: BasilBlackwell.
Schiffer, S., 1991, “Ceteris Paribus Laws,”Mind, 100: 1–17.
Schneider, S., 2007, “What is the Significance of theIntuition that Laws of Nature Govern?,”Australasian Journalof Philosophy, 85: 307–324.
Shoemaker, S., 1980, “Causality and Properties,” inTime and Cause, P. van Inwagen, (ed.), Dordrecht: D. ReidelPublishing Company.
–––, 1998, “Causal and MetaphysicalNecessity,”Pacific Philosophical Quarterly, 79:59–77.
Shumener, E., 2017, “Laws of Nature, Explanation, andSemantic Circularity,”The British Journal for thePhilosophy of Science, 70: 787–815.
Sidelle, A., 2002, “On the Metaphysical Contingency of Lawsof Nature,” inConceivability and Possibility, T.Szabó Gendler and J. Hawthorne, (eds.), Oxford: ClarendonPress.
Sober, E., 1988, “Confirmation and Lawlikeness,”Philosophical Review, 97: 93–98.
Swoyer, C., 1982, “The Nature of Natural Laws,”Australasian Journal of Philosophy, 60: 203–223.
Tooley, M., 1977, “The Nature of Laws,”CanadianJournal of Philosophy, 7: 667–698.
–––, 1987,Causation, Oxford: ClarendonPress.
Tweedale, M., 1984, “Armstrong on Determinable andSubstantival Universals,” inD.M. Armstrong, R. Bogdan(ed.), Dordrecht: D. Reidel Publishing Company.
Unger, P., 1971, “A Defense of Skepticism”The Philosophical Review80, 198–219.
Vetter, B., 2012, “Dispositional Essentialism and the Lawsof Nature,”Properties, Powers and Structures, A. Bird,B. Ellis, and H. Sankey (eds.), New York: Routledge.
van Fraassen, B., 1987, “Armstrong on Laws andProbabilities,”Australasian Journal of Philosophy, 65:243–259.
–––, 1989,Laws and Symmetry, Oxford:Clarendon Press.
–––, 1993, “Armstrong, Cartwright, andEarman on Laws and Symmetry,”Philosophy andPhenomenological Research, 53: 431–444.
Ward, B., 2002, “Humeanism without Humean supervenience: Aprojectivist account of laws and possibilities,”Philosophical Studies, 107: 191–218.
–––, 2007, “Laws, Explanation, Governing,and Generation,”Australasian Journal of Philosophy,85: 537–552.
Woodward, J., 1992, “Realism about Laws,”Erkenntnis, 36: 181–218.

Academic Tools

How to cite this entry.
Preview the PDF version of this entry at theFriends of the SEP Society.
Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO).
Enhanced bibliography for this entryatPhilPapers, with links to its database.

Other Internet Resources

Laws of Nature, by Norman Swartz (Simon Fraser University), inThe InternetEncyclopedia of Philosophy.

Acknowledgments

Portions of the 2006 update to this entry were drawn directly from theintroduction to Carroll (2004). The original version of this entry(2003) served as a basis for that introduction. Thanks to ArnoldKoslow for a helpful correction. Thank you to my student researchassistant, Chase Dill, for searching out sources and providing goodphilosophical insight. Ann Rives provided excellent proofreading.

Open access to the SEP is made possible by a world-wide funding initiative.
The Encyclopedia Now Needs Your Support
Please Read How You Can Help Keep the Encyclopedia Free

Browse

About

Support SEP

Mirror Sites

View this site from another server:

USA (Main Site)Philosophy, Stanford University

Info about mirror sites

Library of Congress Catalog Data: ISSN 1095-5054

Movatterモバイル変換