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H This Element provides an opinionated introduction to the il d metaphysics of laws of nature. The first section distinguishes e between scientific and philosophical questions about laws and b r describes some criteria for a philosophical account of laws. a n Subsequent sections explore the leading philosophical theories d in detail, reviewing the most influential arguments in the Metaphysics literature. The final few sections assess the state of the field and suggest avenues for future research. l laws of nature a w s o f n a t u r e about the Series Series editor This highly accessible series of Elements Tuomas E. Tahko provides brief but comprehensive University of Bristol introductions to the most central topics Tyler Hildebrand in metaphysics. Many of the Elements also go into considerable depth, so the series will appeal to both students and sse rP agcaapds ebmeticwse. eSno mmee tEalpehmyesinctss, bprhidilogeso tphhey ytisrev in U of science, and epistemology. e g d irb m a C y b e n iln o d e h silb u P 9 4 9 9 0 1 9 0 0 1 8 7 9 /7 1 0 1 .0 1 /g ro .io d Cover image: peterkai / iStock / Getty Images Plus //:sp IISSSSNN 22663333--99886524 ((opnrilnint)e) tth sse rP y tisre v in U e g d irb m a C y b e n iln o d e h silb u P 9 4 9 9 0 1 9 0 0 1 8 7 9 /7 1 0 1 .0 1 /g ro .io d //:sp tth Elements in Metaphysics editedby TuomasE. Tahko UniversityofBristol LAWS OF NATURE Tyler Hildebrand Dalhousie University sse rP y tisre v in U e g d irb m a C y b e n iln o d e h silb u P 9 4 9 9 0 1 9 0 0 1 8 7 9 /7 1 0 1 .0 1 /g ro .io d //:sp tth ShaftesburyRoad,CambridgeCB28EA,UnitedKingdom OneLibertyPlaza,20thFloor,NewYork,NY10006,USA 477WilliamstownRoad,PortMelbourne,VIC3207,Australia 314–321,3rdFloor,Plot3,SplendorForum,JasolaDistrictCentre, NewDelhi–110025,India 103PenangRoad,#05–06/07,VisioncrestCommercial,Singapore238467 CambridgeUniversityPressispartofCambridgeUniversityPress&Assessment, adepartmentoftheUniversityofCambridge. WesharetheUniversity’smissiontocontributetosocietythroughthepursuitof education,learningandresearchatthehighestinternationallevelsofexcellence. www.cambridge.org Informationonthistitle:www.cambridge.org/9781009111126 DOI:10.1017/9781009109949 ©TylerHildebrand2023 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress&Assessment. Firstpublished2023 AcataloguerecordforthispublicationisavailablefromtheBritishLibrary. ISBN978-1-009-11112-6Paperback ISSN2633-9862(online) sse ISSN2633-9854(print) rP ytisre CoarmacbcruidrgaceyUonfivUeRrLsistyfoPrreexsste&rnAalsoserstshmiredn-ptahratsyninoterrenseptownseibbsiliitteysforerfethrreepdetrosiisntetnhcise v in publicationanddoesnotguaranteethatanycontentonsuchwebsitesis,orwill U eg remain,accurateorappropriate. d irb m a C y b e n iln o d e h silb u P 9 4 9 9 0 1 9 0 0 1 8 7 9 /7 1 0 1 .0 1 /g ro .io d //:sp tth Laws of Nature Elements in Metaphysics DOI:10.1017/9781009109949 Firstpublishedonline:February2023 TylerHildebrand DalhousieUniversity Authorforcorrespondence:TylerHildebrand,[email protected] Abstract:ThisElementprovidesanopinionatedintroductiontothe metaphysicsoflawsofnature.Thefirstsectiondistinguishesbetween scientificandphilosophicalquestionsaboutlawsanddescribessome criteriaforaphilosophicalaccountoflaws.Subsequentsectionsexplore theleadingphilosophicaltheoriesindetail,reviewingthemostinfluential argumentsintheliterature.Thefinalfewsectionsassessthestateofthe fieldandsuggestavenuesforfutureresearch. Keywords:lawsofnature,Humeanism,Non-Humeanism/Anti-Humeanism, metaphysics,philosophyofscience ©TylerHildebrand2023 ISBNs:9781009111126(PB),9781009109949(OC) ISSNs:2633-9862(online),2633-9854(print) sse rP y tisre v in U e g d irb m a C y b e n iln o d e h silb u P 9 4 9 9 0 1 9 0 0 1 8 7 9 /7 1 0 1 .0 1 /g ro .io d //:sp tth Contents 1 Introduction 1 2 Humeanism 5 3 Objections to Humeanism 19 4 Non-Humean Theories of Laws 29 5 Conceptual Objections to Non-Humeanism 39 6 Further Problems for Non-Humean Theories 47 7 The Explanatory Argument for Non-Humeanism 55 8 Epistemological and Methodological Issues 63 9 An Alternative to Humeanism and Non-Humeanism 70 References 77 sse rP y tisre v in U e g d irb m a C y b e n iln o d e h silb u P 9 4 9 9 0 1 9 0 0 1 8 7 9 /7 1 0 1 .0 1 /g ro .io d //:sp tth LawsofNature 1 1 Introduction 1.1 Scientificvs. Metaphysical Questions about Laws Nature is full of regularities. Some are obvious: that bread nourishes, that heavyobjectsareattractedtotheearth,andsoon.Others,suchasthepatterns described by Schrödinger’s equation or Einstein’s field equations, are much hardertodiscoverbutmoreresilient.Indeed,wetakethemtobenecessary:it’s noaccidentthatoppositelychargedparticlesattract;undernormalconditions, theymustattract.Suchregularitiesareassociatedwithlawsofnature. Laws of nature are a subject of interest for both science and philosophy. However, scientists and philosophers focus on different aspects of laws. Sci- entistsareprimarilyinterestedinwhichlawsofnaturethereare.Forexample, physicistsaskquestionssuchas:Whatarethevaluesofvariousphysicalcon- stants? Is gravity Newtonian or relativistic? Should we accept classical or quantummechanics?Toclarify,let’stakeacloserlookatthethirdquestion. ClassicalMechanics: The behavior of fundamental things is described by Newton’slawsofmotion. QuantumMechanics: Thebehavioroffundamentalthingsisdescribedbythe lawsofquantummechanics,suchastheSchrödingerequation. Thesetheoriesagreethatlawsdescribethemotionsofobjects.However,their lawsdiffer,sotheypositdifferentregularitiesatthemorefundamentallevels ofnature. Incontrast,philosophersareinterestedinmetaphysicalquestionsaboutthe sse rP nature of laws. They ask questions such as: What kind of thing is a law? y tisre Whatmakessomeregularitieslawlikeandothersaccidental?Whydoesnature v in containregularitiesinthefirstplace?1 U e gd Athoughtexperimentwillhelptomotivatesomedifferentanswerstothese irb m metaphysicalquestions. a C y b e n VirtualPhysicists: The departments of Physics and Computer Science have iln o d collaboratedtoproduceavideogame,VirtualPhysicists.Theobjectiveisto e h silb exploreasimulatedenvironment,makeobservations,collaboratewithother u P 9 players,andtogetherformulateascientifictheorythatexplainsandpredicts 4 9 9 eventsinthevirtualworld.Thegameendswhentheplayersdiscoverthetrue 0 1 9 0 finaltheory:thesetoflawlikegeneralizationsandboundaryconditionsinthe 0 1 8 79 programrunningthesimulation. /7 1 0 1 .01/g 1 We’ll see later (especially in Section 9) that philosophers are interested in other sorts of ro questionsaboutlaws,too. .io d //:sp tth 2 Metaphysics Your task in the game is to answer scientific questions about laws. (It’s not called “Virtual Philosophers”!) But suppose we ask why the virtual world containsregularitiesasopposed toirregularities. Theansweris obvious:The regularities–namely,patternsonyourscreen–arenot simplyarock-bottom stoppingpointforexplanation,nordotheyoccurpurelybychance;rather,they areimposed onthevirtualenvironmentbytheprogramandultimatelybythe programmers/developers. Thenatureoflawsinourworldmightbeanalogousoritmightnotbe.Eve- ryone agrees that laws and regularities are intimately related. However, the centralmetaphysicaldisputeaboutlawsconcernsthenatureofthisrelationship. Compare: Humeanism: The world is like a grand mosaic whose tiles could have been arrangedanywhichway.Nothingisultimatelyresponsibleforitsregularities. Theyarejustabasic,fundamentalfeatureofourworld.Statementsoflaws, then,aremerelydescriptionsofthemostsignificantregularitiesthathappen tooccur.Thus,ourworldisnotanalogoustotheworldsinVirtualPhysicists.2 Non-Humeanism: Theworldislikeagrandmosaic,butit’snotthecasethat itstilescouldhavebeenarrangedanywhichway.Somethingimposesstruc- ture on it, analogously to the way in which the computer program Virtual Physicistsimposesstructureonitsvirtualenvironments.Forexample,some Non-Humeanspositagodastheenforcerofnaturallaws,sometreatlawsas primitives, and there are other options besides. But whatever the details, all Non-Humeans accept some sort of basic, fundamental necessity: something thatgoverns,produces,orsomehowconstrainspatternsofeventsinnature.3 sse rP y tisre Thisphilosophicaldisputeconcernsthenatureoflaws(ornaturalnecessities) vin andtheorderofmetaphysicalexplanation:Humeansholdthatregularitiesare U eg prior to laws (or any other sort of natural necessity), whereas Non-Humeans d irb holdthatlaws(orsomenaturalnecessities)arepriortoregularities.Generally m a C y speaking, Humeans and Non-Humeans can agree about which sentences are b en statementsoflaws–amatterlefttoscientists–whiledisagreeingaboutwhat iln o d makesthemlawlike. e h silb Of course, there are also disputes internal to Humeanism and Non- u P Humeanism.Forexample,IsaidinthissectionthatHumeanismtakesthemost 9 4 9 9 0 1 9 00 2 ThisviewissocalledbecauseDavidHume(1748/2000)famouslyarguedthattheconceptof 1 87 naturalnecessityhadtobeanalyzedintermsofobservedpatterns.However,it’scontroversial 9 /7 whetherHumeendorsedHumeanismasI’vedefinedit(Strawson,2015). 1 01 3 Theterms‘Non-Humean’and‘Anti-Humean’areusedinterchangeablyintheliterature.Ipre- .0 1/g fer‘Non-Humean’.AsI’vesaidelsewhere(Hildebrand,2020b),althoughI’mnotaHumean, ro I’mnotanti-Humean! .io d //:sp tth LawsofNature 3 significant regularities to be laws, but the notion of significance is open to interpretation.ThisleadstodifferentversionsofHumeanism.Similarly,there aremanyversionsofNon-Humeanism,differingwithrespecttotheprimitive necessitiestheyposit.SomeappealtoGod,sometreatlawsthemselvesasprim- itive,someinvokespecialsortsofproperties,andsoon.We’llexplorenarrower versionsofboththeoriesinlatersections. 1.2 PhilosophicalMethod As noted, Humeanism and Non-Humeanism are typically formulated in an efforttoaccommodateourbestscientifictheoriesoflaws.Thatseemstosug- gestthatourmetaphysicaltheorieswillbeempiricallyequivalent.How,then, arewetochooseone? In comparison, it might seem easy to settle scientific disputes about laws. Preciselybecausescientificdisputesaboutlawsaredisputesaboutwhichlaws (andthuswhichregularities)thereare,wecansettlethembycarefulobserva- tion.However,eventhequestion“Howdowechooseascientifictheory?”is difficulttoanswer.Considertheapparentpositionofstarsduringthefamous Eddingtonexperimentin1919.Newtoniantheoriesofgravity(oftheday)and Einstein’stheoryofgravitymadedifferentpredictionsaboutwherestarswould appearduringasolareclipse.Eddington’steamlookedatthestarsandfound thepredictionsofEinstein’stheorytobemoreaccurate.Dideveryoneimme- diatelyacceptEinstein’stheoryoverNewton’s?No.Newtoniantheoriescould bemodifiedtomakepredictionsmatchingtheobservationsoftheexperiment. Thus,NewtoniantheoriescouldbemadeempiricallyequivalenttoEinstein’s sserP theory, at least for known observations of the day. How, then, can scientists y tisre justifyachoiceamongempiricallyequivalenttheories? vin Theanswer,inshort,isthatscientistscananddoappealtononempiricalthe- U eg oreticalvirtues.Forexample,Einstein’stheoryseemssimplerandmoreelegant d irbm than its empirically equivalent Newtonian competitors. Generally speaking, a C y nonempirical criteria for theory choice are required to solve problems of b en empiricalunderdetermination. iln o d Analogously,philosophersappealtosimilarcriteriafortheorychoicewhen e hsilb doingmetaphysics.4 I’llprovideabriefsketchofsomeimportantcriteria,but u P 9 itincludesastrongdisclaimer.Inthissection,Iwon’ttrytojustifythemorsay 4 9 9 howtheyfittogethertoformabig-picturemethodformetaphysics.I’llsaya 0 1 9 0 bitmoreaboutthisinSections8and9,afterwe’veseenhowthecriteriaare 0 1 8 7 employedinphilosophicalpractice. 9 /7 1 0 1 .01/g 4 Fordefensesofmetaphysicsthatproceedalongthesesortsoflines,seePaul(2012),Sider ro (2011,11–15),andTahko(2015). .io d //:sp tth 4 Metaphysics Forstarters,atheoryoflawsshouldbeintelligible;itshouldn’tinvolveprim- itiveconceptsthatwecannotunderstand.Forexample,Non-Humeansneedto explainhowwecometopossesstheconceptofprimitivenecessitythatfeatures intheirtheories. Theories should be simple and/or parsimonious. They shouldn’t posit too many(kindsof)entitieswhenfewer(kindsof)entitieswilldo. Theoriesoflawsshouldcoherewithscientificpracticeconcerninglawsand alignwiththeordinaryconceptoflaws.Everyphilosophicalanalysismuststart somewhere. If our account of laws is to be an account of laws – the things scientiststalkaboutwhentheyusetheterm–theaccountshouldclassifythe things we call “laws” as laws, and it should accommodate at least some of our normal intuitions about the work laws are supposed to do. For example, a metaphysical account of laws should make sense of the fact that scientists appealtolawstoexplainobservationsandmakepredictions. Relatedly, it would be nice if a theory of laws could explainwhy there are regularitiesinnature.Butprovidingsuchexplanationscanbedifficult,inpart becausesomeexplanationsmerelypushtheproblembackalevel.Ifweposit anewentitytoexplainaregularity,wecanaskwhythatnewentityistheway thatitis.Wedon’twanttoposit“turtlesallthewaydown.” Finally,anaccountoflawhoodshouldfitwithinourbroadermetaphysics.A metaphysicalnaturalist–onewhothinksthatnothingexistsbeyondtheworld of spacetime – would find it costly to endorse a theory of laws that posits a god. But if your metaphysics of laws fits seamlessly within your broader metaphysicalcommitments,thatwouldbeamarkinitsfavor. sse Insum,therearemanycriteriarelevanttotheselectionofaphilosophicalthe- rP y oryoflaws.We’llexaminethemmorecarefullyinduecourse,butthisoverview tisrev shouldprovideasufficientfoundationtogetstarted. in U e g d irb m 1.3 WhyCare? a C y b e Toconcludethissection,I’llbrieflymentionsomewaysinwhichphilosophical n ilno reflectiononthenatureoflawsmightbevaluable. d e h First,scienceisoneofthebestthingshumanshavecreated.Thatmakesit silb u worthy of philosophical reflection, if only for our own curiosity and enjoy- P 9 49 ment.Moreimportantly,becausescienceisvaluabletous,it’sworthtryingto 9 0 19 understandhowscientifictheoriesaretobeinterpreted;it’sworthaskingwhy 0 0 18 sciencehasthevirtuesithasandwhyit’spossibleforbeingslikeus.Answers 7 9 /7 tosuchquestionsrequireustosayatleastsomethingaboutthenatureoflaws. 1 0 1 .0 Second,themetaphysicsoflawsintersectswithotherphilosophicalissues. 1 /g ro Generallyspeaking,anaccountofthenatureoftheworldisrelevanttoaccounts .io d //:sp tth