Laws of Nature (Stanford Encyclopedia of Philosophy)

18/07/2015 LawsofNature(StanfordEncyclopediaofPhilosophy)

http://plato.stanford.edu/entries/lawsofnature/ 1/15

Stanford Encyclopedia of PhilosophyLawsofNatureFirstpublishedTueApr29,2003substantiverevisionSunDec26,2010

Scienceincludesmanyprinciplesatleastoncethoughttobelawsofnature:Newton'slawofgravitation,histhreelawsofmotion,theidealgaslaws,Mendel'slaws,thelawsofsupplyanddemand,andsoon.Otherregularitiesimportanttosciencewerenotthoughttohavethisstatus.Theseincluderegularitiesthat,unlikelaws,were(orstillare)thoughtbyscientiststostandinneedofexplanation.Theseincludetheregularityoftheoceantides,theperihelionofMercury'sorbit,thephotoelectriceffect,thattheuniverseisexpanding,andsoon.Scientistsalsouselawsbutnototherregularitiestosortoutwhatispossible:ItisbasedontheirconsistencywithEinstein'slawsofgravitythatcosmologistsrecognizethepossibilitythatouruniverseisclosedandthepossibilitythatitisopen(Maudlin2007,78).Instatisticalmechanics,thelawsofanunderlyingphysicaltheoryareusedtodeterminethedynamicallypossibletrajectoriesthroughthestatespaceofthesystem(Roberts2008,1216).

Philosophersofscienceandmetaphysiciansaddressvariousissuesaboutlaws,butthebasicquestionis:Whatisittobealaw?TwoinfluentialanswersareDavidLewis'ssystemsapproach(1973,1983,1986,1994)andDavidArmstrong'suniversalsapproach(1978,1983,1991,1993).Morerecenttreatmentsincludeantirealistviews(vanFraassen1989,Giere1999,Ward2002,Mumford2004)andantireductionistviews(Carroll1994,Lange2000and2009,Maudlin2007).Besidesthebasicquestion,therecentliteraturehasalsofocusedon(i)whetherlawssuperveneonmattersoffact,(ii)therolelawsplayintheproblemofinduction,(iii)whetherlawsinvolvemetaphysicalnecessity,and(iv)theroleoflawsinphysicsandhowthatcontrastswiththeroleoflawsinthespecialsciences.

1.TheBasicQuestion:WhatisittobeaLaw?2.Systems3.Universals4.HumeanSupervenience5.Antirealism6.Antireductionism7.Induction8.Necessity9.PhysicsandtheSpecialSciences

9.1DoPhysiciststrytodiscoverExceptionlessRegularities?9.2CouldtherebeanySpecialScienceLaws?

10.ConcludingRemarks:WhatisNext?BibliographyAcademicToolsOtherInternetResourcesRelatedEntries

1.TheBasicQuestion:WhatisittobeaLaw?

Herearefourreasonsphilosophersexaminewhatitistobealawofnature:First,asindicatedabove,lawsatleastappeartohaveacentralroleinscientificpractice.Second,lawsareimportanttomanyotherphilosophicalissues.Forexample,sparkedbytheaccountofcounterfactualsdefendedby



RoderickChisholm(1946,1955)andNelsonGoodman(1947),andalsopromptedbyCarlHempelandPaulOppenheim's(1948)deductivenomologicalmodelofexplanation,philosophershavewonderedwhatmakescounterfactualandexplanatoryclaimstrue,havethoughtthatlawsmustplaysomepart,andsoalsohavewonderedwhatdistinguisheslawsfromnonlaws.Third,Goodmanfamouslysuggestedthatthereisaconnectionbetweenlawhoodandconfirmabilitybyaninductiveinference.So,somesympathetictoGoodman'sideacometotheproblemoflawsasaresultoftheirinterestintheproblemofinduction.Fourth,philosophersloveagoodpuzzle.Supposethateveryonehereisseated(cf.,Langford1941,67).Then,trivially,thateveryonehereisseatedistrue.Thoughtrue,thisgeneralizationdoesnotseemtobealaw.Itisjusttooaccidental.Einstein'sprinciplethatnosignalstravelfasterthanlightisalsoatruegeneralizationbut,incontrast,itisthoughttobealawitisnotnearlysoaccidental.Whatmakesthedifference?

Thismaynotseemlikemuchofapuzzle.Thateveryonehereisseatedisspatiallyrestrictedinthatitisaboutaspecificplacetheprincipleofrelativityisnotsimilarlyrestricted.So,itiseasytothinkthat,unlikelaws,accidentallytruegeneralizationsareaboutspecificplaces.Butthatisnotwhatmakesthedifference.Therearetruenonlawsthatarenotspatiallyrestricted.Considertheunrestrictedgeneralizationthatallgoldspheresarelessthanonemileindiameter.Therearenogoldspheresthatsizeandinalllikelihoodthereneverwillbe,butthisisstillnotalaw.Therealsoappeartobegeneralizationsthatcouldexpresslawsthatarerestricted.Galileo'slawoffreefallisthegeneralizationthat,onEarth,freefallingbodiesaccelerateatarateof9.8meterspersecondsquared.Theperplexingnatureofthepuzzleisclearlyrevealedwhenthegoldspheregeneralizationispairedwitharemarkablysimilargeneralizationabouturaniumspheres:

Allgoldspheresarelessthanamileindiameter.

Alluraniumspheresarelessthanamileindiameter.

Thoughtheformerisnotalaw,thelatterarguablyis.Thelatterisnotnearlysoaccidentalasthefirst,sinceuranium'scriticalmassissuchastoguaranteethatsuchalargespherewillneverexist(vanFraassen1989,27).Whatmakesthedifference?Whatmakestheformeranaccidentalgeneralizationandthelatteralaw?

2.Systems

Onepopularanswertiesbeingalawtodeductivesystems.TheideadatesbacktoJohnStuartMill(1947[f.p.1843]),buthasbeendefendedinoneformoranotherbyFrankRamsey(1978[f.p.1928]),Lewis(1973,1983,1986,1994),JohnEarman(1984)andBarryLoewer(1996).Deductivesystemsareindividuatedbytheiraxioms.Thelogicalconsequencesoftheaxiomsarethetheorems.Sometruedeductivesystemswillbestrongerthanotherssomewillbesimplerthanothers.Thesetwovirtues,strengthandsimplicity,compete.(Itiseasytomakeasystemstrongerbysacrificingsimplicity:includeallthetruthsasaxioms.Itiseasytomakeasystemsimplebysacrificingstrength:havejusttheaxiomthat2+2=4.)AccordingtoLewis(1973,73),thelawsofnaturebelongtoallthetruedeductivesystemswithabestcombinationofsimplicityandstrength.So,forexample,thethoughtisthatitisalawthatalluraniumspheresarelessthanamileindiameterbecauseitis,arguably,partofthebestdeductivesystemsquantumtheoryisanexcellenttheoryofouruniverseandmightbepartofthebestsystems,anditisplausibletothinkthatquantumtheoryplustruthsdescribingthenatureofuraniumwouldlogicallyentailthattherearenouraniumspheresofthatsize(Loewer1996,112).Itisdoubtfulthatthegeneralizationthatallgoldspheresarelessthanamileindiameterwouldbepartofthebestsystems.Itcouldbeaddedasanaxiomtoanysystem,butitwouldbringlittleornothingofinterestintermsofstrengthandaddingitwouldsacrificesomethingintermsofsimplicity.(Lewislatermadesignificantrevisionstohisaccountinordertoaddressproblemsinvolvingphysicalprobability.Seehis1986andhis1994.)

Manyfeaturesofthesystemsapproachareappealing.Foronething,itappearstodealwitha



challengeposedbyvacuouslaws.Somelawsarevacuouslytrue:Newton'sfirstlawofmotionthatallinertialbodieshavenoaccelerationisalaw,eventhoughtherearenoinertialbodies.Buttherearealsolotsofvacuouslytruenonlaws:allplaidpandasweigh5lbs.,allunicornsareunmarried,etc.Withthesystemsapproach,thereisnoexclusionofvacuousgeneralizationsfromtherealmoflaws,andyetonlythosevacuousgeneralizationsthatbelongtothebestsystemsqualify(cf.,Lewis1986,123).Furthermore,itisreasonabletothinkthatonegoalofscientifictheorizingistheformulationoftruetheoriesthatarewellbalancedintermsoftheirsimplicityandstrength.So,thesystemsapproachseemstounderwritethetruismthatanaimofscienceisthediscoveryoflaws(Earman1978,180Loewer1996,112).Onelastaspectofthesystemsviewthatisappealingtomany(thoughnotall)isthatitisinkeepingwithbroadlyHumeanconstraintsonasensiblemetaphysics.Thereisnoovertappealtocloselyrelatedmodalconcepts(e.g.,thecounterfactualconditional)andnoovertappealtomodalitysupplyingentities(e.g.,universalsorGodforthesupposedneedtoappealtoGod,seeFoster2004).Indeed,thesystemsapproachisthecenterpieceofLewis'sdefenseofHumeansupervenience,thedoctrinethatallthereisintheworldisavastmosaicoflocalmattersofparticularfact,justonelittlethingandthenanother(1986,ix).

Otheraspectsofthesystemsapproachhavemadephilosopherswary.(See,especially,Armstrong1983,6673vanFraassen1989,4064Carroll1990,197206.)Somearguethatthisapproachwillhavetheuntowardconsequencethatlawsareinappropriatelyminddependentinvirtueoftheaccount'sappealtotheconceptsofsimplicity,strengthandbestbalance,conceptswhoseinstantiationseemstodependoncognitiveabilities,interests,andpurposes.Theappealtosimplicityraisesfurtherquestionsstemmingfromtheapparentneedforaregimentedlanguagetopermitreasonablecomparisonsofthesystems.(SeeLewis1983,367.)Morerecently,JohnRobertsquestionsthesystemsapproachatapointsometimesthoughttobeastrengthoftheview:Wehavenopracticeofweighingcompetingvirtuesofsimplicityandinformationcontentforthepurposeofchoosingonedeductivesystemoverothers,whereallarepresumedtobetrue(2008,10).Thereisthepracticeofcurvefitting,whichinvolvesweighingthecompetingvirtuesofsimplicityandclosenessoffit,butthisisapracticethatispartoftheprocessofdiscoveringwhatistrue.TimMaudlin(2007,16)andRoberts(2008,23)alsochargethatthesystemsapproachisillsuitedtoruleoutwidespreadandstrikingregularitiesaslaws,eventhosethatareclearlydeterminedbytheinitialconditions.Thattheuniverseisclosed,thatentropygenerallyincreases,thattheplanetsofoursolarsystemarecoplanar,andothers(iftrue)couldbeaddedtoanytruedeductivesystem,greatlyincreasingthestrengthofthesystem,withonlyasmallcostintermsofsimplicity.Interestingly,sometimesthesystemsviewisabandonedbecauseitsatisfiesthebroadlyHumeanconstraintsonanaccountoflawsofnaturesomearguethatwhatgeneralizationsarelawsisnotdeterminedbylocalmattersofparticularfact.SeeSection4below.

3.Universals

Inthelate1970s,thereemergedacompetitorforthesystemsapproachandallotherHumeanattemptstosaywhatitistobealaw.LedbyArmstrong(1978,1983,1991,1993),FredDretske(1977),andMichaelTooley(1977,1987),therivalapproachappealstouniversalstodistinguishlawsfromnonlaws.

FocusingonArmstrong'sdevelopmentoftheview,hereisoneofhisconcisestatementsoftheframeworkcharacteristicoftheuniversalsapproach:

SupposeittobealawthatFsareGs.FnessandGnessaretakentobeuniversals.Acertainrelation,arelationofnonlogicalorcontingentnecessitation,holdsbetweenFnessandGness.ThisstateofaffairsmaybesymbolizedasN(F,G)(1983,85).

Thisframeworkpromisestoaddressfamiliarpuzzlesandproblems:Maybethedifferencebetweentheuraniumspheresgeneralizationandthegoldspheresgeneralizationisthatbeinguraniumdoesnecessitatebeinglessthanonemileindiameter,butbeinggolddoesnot.Worriesaboutthesubjective



natureofsimplicity,strengthandbestbalancedonotemergethereisnothreatoflawhoodbeingminddependentsolongasnecessitationisnotminddependent.Some(Armstrong1991,Dretske1977)thinkthattheframeworksupportstheideathatlawsplayaspecialexplanatoryroleininductiveinferences,sincealawisnotjustauniversalgeneralization,butisanentirelydifferentcreaturearelationholdingbetweentwootheruniversals.TheframeworkisalsoconsistentwithlawhoodnotsuperveningonlocalmattersofparticularfactthedenialofHumeansupervenienceoftenaccompaniesacceptanceoftheuniversalsapproach.

Fortheretrulytobethispayoff,however,morehastobesaidaboutwhatNis.ThisistheproblemBasvanFraassencallstheidentificationproblem.Hecouplesthiswithasecondproblem,whathecallstheinferenceproblem(1989,96).TheessenceofthispairofproblemswascapturedearlyonbyLewiswithhisusualflair:

WhateverNmaybe,IcannotseehowitcouldbeabsolutelyimpossibletohaveN(F,G)andFawithoutGa.(UnlessNjustisconstantconjunction,orconstantconjunctionplussomethingelse,inwhichcaseArmstrong'stheoryturnsintoaformoftheregularitytheoryherejects.)ThemysteryissomewhathiddenbyArmstrong'sterminology.HeusesnecessitatesasanameforthelawmakinguniversalNandwhowouldbesurprisedtohearthatifFnecessitatesGandahasF,thenamusthaveG?ButIsaythatNdeservesthenameofnecessitationonlyif,somehow,itreallycanenterintotherequisitenecessaryconnections.Itcan'tenterintothemjustbybearinganame,anymorethanonecanhavemightybicepsjustbybeingcalledArmstrong(1983,366).

Basically,thereneedstobeaspecificationofwhatthelawmakingrelationis(theidentificationproblem).Then,thereneedstobeadeterminationofwhetheritissuitedtothetask(theinferenceproblem):DoesN'sholdingbetweenFandGentailthatFsareGs?Doesitsholdingsupportcorrespondingcounterfactuals?Dolawsreallyturnoutnottosupervene,tobemindindependent,tobeexplanatory?Armstrongdoessaymoreaboutwhathislawmakingrelationis.HestatesinreplytovanFraassen:

Itisatthispointthat,Iclaim,theIdentificationproblemhasbeensolved.Therequiredrelationisthecausalrelation,nowhypothesizedtorelatetypesnottokens(1993,422).

Questionsremainaboutthenatureofthiscausalrelationunderstoodasarelationthatrelatesbothtokeneventsanduniversals.(SeevanFraassen1993,435437,andCarroll1994,170174.)

4.HumeanSupervenience

Ratherthantryingtodetailallthecriticalissuesthatdividethesystemsapproachandtheuniversalsapproach,wewilldobettertofocusourattentionontheespeciallydivisiveissueofsupervenience.ItconcernswhetherHumeanconsiderationsreallydeterminewhatthelawsare.Therearesomeimportantexamplesthatappeartoshowthattheydonot.

Tooley(1977,669)asksustosupposethattherearetendifferentkindsoffundamentalparticles.So,therearefiftyfivepossiblekindsoftwoparticleinteractions.Supposethatfiftyfourofthesekindshavebeenstudiedandfiftyfourlawshavebeendiscovered.TheinteractionofXandYparticleshavenotbeenstudiedbecauseconditionsaresuchthattheyneverwillinteract.Nevertheless,itseemsthatitmightbealawthat,whenXparticlesandYparticlesinteract,Poccurs.SimilarlyitmightbealawthatwhenXandYparticlesinteract,Qoccurs.Thereseemstobenothingaboutthelocalmattersofparticularfactinthisworldthatfixeswhichofthesegeneralizationsisalaw.

ThenonsuperveniencesuggestedbyTooley'sexamplearisesinmoreextremecases.Considerthepossibilitythatthereisasinglematerialobjecttravelingthroughotherwiseemptyspaceataconstantvelocityof,say,onemeterpersecond.ItseemsthatthismightjustbeanearlyemptyNewtonian



universeinwhichitistruethatallbodieshaveavelocityofonemeterpersecond,butwherethatisnotalawitjustsohappensthatthereisnothingtoalteritsmotion.But,onehastoadmitthatitmightalsobethecasethatthisworldisnotNewtonianandthatitisalawthatallbodiestravelatonemeterperseconditcouldbethatthisgeneralizationisnotaccidentalandwouldhaveheldtrueeveniftherewereotherbodiesslammingintothemovingobject.(SeeespeciallyEarman1986,100Lange2000,8590.)Somewilltakeitfurther.MaudlinpressesthecaseagainsttheHumeansbyfocusingonthecommonpracticeamongphysicistsofconsideringmodelsofatheory'slaws.

Minkowskispacetime,thespacetimeofSpecialRelativity,isamodelofthefieldequationsofGeneralRelativity(inparticular,itisavacuumsolution).SoanemptyMinkowskispacetimeisonewaytheworldcouldbeifitisgovernedbythelawsofGeneralRelativity.ButisMinkowskispacetimeamodelonlyoftheGeneralRelativisticlaws?Ofcoursenot!Onecould,forexample,postulatethatSpecialRelativityisthecompleteandaccurateaccountofspacetimestructure,andproduceanothertheoryofgravitation,whichwouldstillhavethevacuumMinkowskispacetimeasamodel.SoundertheassumptionthatnopossibleworldcanbegovernedbythelawsofGeneralRelativityandbyarivaltheoryofgravity,thetotalphysicalstateoftheworldcannotalwaysdeterminethelaws(2007,67).

ThesuggestionhereisthatthereisthepossibilityofamatterlessuniversewiththelawsofGeneralRelativityandanotherwithlawsofaconflictingtheoryofgravitation.(Foradditionalexamples,seeCarroll1994,6080).

WhatMaudlinseesasaconsequenceofstandardscientificreasoning,Humeanswillseeasanexampleexposingtheabsurdityofnonsupervenience.Theymustcontendthatthesepairsofsocalledpossibleworldsarenotreallypossible.OneobjectiontothenonsupervenienceargumentsfromtheHumeancampcomesfromHelenBeebee(2000).SheaccusesTooley,JohnCarroll(1990,1994)andothersofbeggingthequestioninvirtueofassumingagoverningconceptionoflaws.(AlsoseeLoewer1996,Roberts1998,andSchaffer2008.)Inapairofpapers,EarmanandRoberts(2005aandb)firstaddresshowtobestformulatethethesisofHumeansupervenience,thentheyarguebasedonskepticalconsiderationsthattheirbrandofHumeansupervenienceistrue.JonathanSchaffer(2008)pressesanontologicalconcerntotheeffectthatnonsuperveninglawsareungroundedentities.Inadditiontoembracingagoverningconceptionoflaw,Roberts(2008,358361)offersanewmannerofchallengingcounterexamplestoHumeanSupervenience.Noticethatthelinguisticcoreofanyapparentcounterexampleisalwaysapairofpossibilitysentences.Forinstance,aboutaloneparticleexampleliketheonereportedabove,thecoremightbesentenceslike:

Itispossiblethatthereexistonlyasingleparticletravelingatconstantvelocitythroughoutallofhistoryanditnotbealawthatallbodieshaveavelocityofonemeterpersecond.

Itispossiblethatthereexistonlyasingleparticletravelingatconstantvelocitythroughoutallofhistoryanditbealawthatallbodieshaveavelocityofonemeterpersecond.

ForRoberts,thesecounterexamplesareboundtobeonlyapparentonesbecause,thougheachsentencemaybetruerelativetoacontext,thatisnotenoughtoraisethechallenge.Thesesentencesneedtobetruerelativetoasinglecontextorelsethechallengewouldbeguiltyofakindofequivocation.ForRoberts,thetruthofisalawsentencesisalwaysrelativetoacontextuallysalienttheory.Asheseesit,theonemeterpersecondvelocitygeneralizationcannotbealawandnotbealawrelativetoasingletheory,andsothecoresentencescannotbetruerelativetoasinglecontext.ThekeyhereisthecontextsensitivitythatRobertsbuildsintothetruthconditionsoflawhoodsentences.Otherviewsthattakelawhoodsentencestobecontextsensitivemightalsogivethisconclusion.Ofcourse,muchdependsonexactlywhatcontextsensitivetruthconditionsareputforward.



5.Antirealism

Themajorityofcontemporaryphilosophersarerealistsaboutlawstheybelievethatsomereportsofwhatthelawsaresucceedindescribingreality.Thereare,however,someantirealistswhodisagree.

Forexample,vanFraassen,RonaldGiere,andalsoStephenMumfordbelievethattherearenolaws.VanFraassenfindssupportforhisviewintheproblemsfacingaccountslikeLewis'sandArmstrong's,andtheperceivedfailureofArmstrongandotherstodescribeanadequateepistemologythatpermitsrationalbeliefinlaws(1989,130and180181).Giereappealstotheoriginsoftheuseoftheconceptoflawinthehistoryofscience(1999[f.p.1995],8690)andcontendsthatthegeneralizationsoftendescribedaslawsarenotinfacttrue(9091).Mumford'sreasonsaremoremetaphysicalhemaintainsthat,inordertogovern,lawsmustbeexternaltothepropertiestheygovern,but,tobeexternalinthisway,thegovernedpropertiesmustlackproperidentityconditions(2004,144145).Othersadoptasubtlydifferentsortofantirealism.ThoughtheywilluttersentenceslikeItisalawthatnosignalstravelfasterthanlight,theyareantirealistsinvirtueofthinkingthatsuchsentencesarenot(purely)factstating.WhetherthisEinsteiniangeneralizationisalawisnotafactabouttheuniverseitisnotsomethingouttherewaitingtobediscovered.Reportsofwhatarelawsonlyprojectacertainattitude(inadditiontobelief)aboutthecontainedgeneralizations.Forexample,BarryWard(2002,197)takestheattitudetobeoneregardingthesuitabilityofthegeneralizationforpredictionandexplanation.(AlsoseeBlackburn1984and1986.)

Thechallengeforantirealismistominimizethehavoclawlessrealitywouldplaywithourfolkandscientificpractices.Regardingscience,theexamplesandusesoflawsdescribedatthestartofthisentryattesttolawhavingavisibleroleinsciencethatscientistsseempreparedtotakeasfactive.Regardingourfolkpractices,thoughlawisnotoftenpartofrunofthemillconversations,anantirealismaboutlawhoodwouldstillhavewiderangingconsequences.Thisisduetolawhood'stiestootherconcepts,especiallythenomicones,conceptslikethecounterfactualconditional,dispositions,andcausation.Forexample,itseemsthat,fortheretobeanyinterestingcounterfactualtruths,theremustbeatleastonelawofnature.Wouldanordinarymatchinordinaryconditionslightifstruck?Itseemsitwould,butonlybecausewepresumenaturetoberegularincertainways.Wethinkthiscounterfactualistruebecausewebelievetherearelaws.Weretherenolaws,itwouldnotbethecasethat,ifthematchwerestruck,itwouldlight.Asaresult,itwouldalsonotbethecasethatthematchwasdisposedtoignite,northecasethatstrikingthematchwouldcauseittolight.

Couldanantirealistdeflectthischallengebydenyingtheconnectionsbetweenlawhoodandotherconcepts?Wouldthisallowonetobeanantirealistaboutlawsandstillbearealistabout,say,counterfactuals?Thedangerlurkinghereisthattheresultingpositionseemsboundtobeadhoc.Conceptslikethecounterfactualconditional,dispositions,andcausationexhibitmanyofthesamepuzzlingfeaturesthatlawhooddoesthereareparallelphilosophicalquestionsandpuzzlesabouttheseconcepts.Itishardtoseewhatwouldwarrantantirealismaboutlawhood,butnottheothernomicconcepts.

6.Antireductionism

Carroll(1994,2008),MarcLange(2000,2009),andMaudlin(2007)advocateantireductionist,antisupervenienceviews.(AlsoseeWoodward1992.)Regardingthequestionofwhatitistobealaw,theyrejecttheanswersgivenbyHumeanslikeLewis,theydenyHumeansupervenience,andtheyseenoadvantageinanappealtouniversals.Theyrejectallattemptstosaywhatitistobealawthatdonotappealtonomicconcepts.Yettheystillbelievethattherereallyarelawsofnaturetheyarenotantirealists.

Maudlin(2007,1718)takeslawhoodtobeaprimitivestatusandlawstobeontologicalprimitives,tobefundamentalentitiesinourontology.Thenhisprojectistoshowwhatworklawscando,defining



phyicalpossibilityintermsoflawsandsketchinglawbasedaccountsofthecounterfactualconditionalandofexplanation.

Carroll(2008)sketchesananalysisoflawhoodintermsofcausal/explanatoryconcepts.Thestartingpointistheintuitionthatlawsarenotaccidental,thattheyarenotcoincidences.Notbeingacoincidence,however,isnotallthereistobeingalaw.Forexample,itmightbetruethattherearenogoldspheresgreaterthat1000milesindiameterbecausethereissolittlegoldintheuniverse.Inthatcase,strictlyspeaking,thatgeneralizationwouldbetrue,suitablygeneral,andnotacoincidence.Nevertheless,thatwouldnotbealaw.Arguably,whatblocksthisgeneralizationfrombeingalawisthatsomethinginnaturereally,aninitialconditionoftheuniverse,thelimitedamountofgoldaccountsforthegeneralization.Contrastthiswiththelawthatinertialbodieshavenoacceleration.Withthisandotherlaws,itseemsthatitholdsbecauseofnature(itself).

Lange's(2000,2009)treatmentincludesanaccountofwhatitistobealawintermsofacounterfactualnotionofstability.Theoverallaccountisintricate,butthebasicideaisthis:Callalogicallyclosedsetoftruepropositionsstableifandonlyifthemembersofthesetwouldremaintruegivenanyantecedentthatisconsistentwiththesetitself.So,forexample,thesetoflogicaltruthsistriviallystable,becauselogicaltruthswouldbetruenomatterwhat.AsetthatincludedtheaccidentalgeneralizationthatallthepeopleintheroomaresittingbutisconsistentwiththepropositionthatsomeoneintheroomshoutsFire!wouldnotbeastablesetifsomeoneweretoshoutFire,thensomeoneintheroomwouldnotbesitting.Langeargues(2009,34)thatnostablesetofsubnomicfactsexceptmaybethesetofalltruthscontainsanaccidentaltruth.Todoso,hemakescleveruseofdisjunctiveantecedents.IfthesetdidincludeanaccidentaltruthPandnottheaccidentaltruthQ,then~P~Qwouldbeconsistentwiththesetandsoforthesettobestable,thecounterfactualconditional(~P~Q)Pwouldhavetobetrue.SinceneitherPnorQisalaw,itwouldnotbethecasethatPtakesprecedenceoverQ(atleastnotineveryconversationalcontext).SoLangeclaimsthat(~P~Q)Pwouldnotbetrue(atleastnotineveryconversationalcontext).Byidentifyingthelawsasthemembersofatleastonenonmaximalstableset,wediscoverhowasubnomicfact'slawhoodisfixedbythesubnomicfactsandthesubjunctivefactsaboutthem(2009,43).

Todate,challengestoantireductionismhaveprimarilybeenlimitedtothechallengestoantisuperveniencementionedattheendofSection4.(So,onceagain,seeLoewer1996,Roberts1998and2008,Beebee2000,EarmanandRoberts2005aandb,andSchaffer2008.)

7.Induction

Goodmanthoughtthatthedifferencebetweenlawsofnatureandaccidentaltruthswaslinkedinextricablywiththeproblemofinduction.InhisTheNewRiddleofInduction(1983,[f.p.1954],73),Goodmansays,

Onlyastatementthatislawlikeregardlessofitstruthorfalsityoritsscientificimportanceiscapableofreceivingconfirmationfromaninstanceofitaccidentalstatementsarenot.

(Terminology:PislawlikeonlyifPisalawiftrue.)Goodmanclaimsthat,ifageneralizationisaccidental(andsonotlawlike),thenitisnotcapableofreceivingconfirmationfromoneofitsinstances.

Thishaspromptedmuchdiscussion,includingsomechallenges.Forexample,supposetherearetenflipsofafaircoin,andthatthefirstninelandheads(Dretske1977,256257).Thefirstnineinstancesatleastinasenseconfirmthegeneralizationthatalltheflipswilllandheadstheprobabilityofthatgeneralizationisraisedfrom(.5)10upto.5.Butthisgeneralizationisnotlawlikeiftrue,itisnotalaw.Itisstandardtorespondtosuchanexamplebyarguingthatthisisnotthepertinentnotionof



confirmation(thatitismerecontentcutting)andbysuggestingthatwhatdoesrequirelawlikenessisconfirmationofthegeneralization'sunexaminedinstances.Noticethat,inthecoincase,theprobabilitythatthetenthflipwilllandheadsdoesnotchangeafterthefirstnineflipslandheads.Thereare,however,examplesthatgenerateproblemsforthisideatoo.

Supposetheroomcontainsonehundredmenandsupposeyouaskfiftyofthemwhethertheyarethirdsonsandtheyreplythattheyaresurelyitwouldbereasonabletoatleastincreasesomewhatyourexpectationthatthenextoneyouaskwillalsobeathirdson(JacksonandPargetter1980,423)

Itdoesnogoodtorevisetheclaimtosaythatnogeneralizationbelievedtobeaccidentaliscapableofconfirmation.Aboutthethirdsoncase,onewouldknowthatthegeneralization,eveniftrue,wouldnotbealaw.Thediscussioncontinues.FrankJacksonandRobertPargetterhaveproposedanalternativeconnectionbetweenconfirmationandlawsonwhichcertaincounterfactualtruthsmusthold:observationofAsthatareFandBconfirmsthatallnonFAsareBsonlyiftheAswouldstillhavebeenbothAandBiftheyhadnotbeenF.(ThissuggestioniscriticizedbyElliottSober1988,9798.)Lange(2000,111142)usesadifferentstrategy.Hetriestorefinefurthertherelevantnotionofconfirmation,characterizingwhathetakestobeanintuitivenotionofinductiveconfirmation,andthencontendsthatonlygeneralizationsthatarenotbelievednottobelawlikecanbe(inhissense)inductivelyconfirmed.

SometimestheideathatlawshaveaspecialroletoplayininductionservesasthestartingpointforacriticismofHumeananalyses.Dretske(1977,261262)andArmstrong(1983,5259,and1991)adoptamodelofinductiveinferencethatinvolvesaninferencetothebestexplanation.(AlsoseeFoster1983and2004.)Onitssimplestconstrual,themodeldescribesapatternthatbeginswithanobservationofinstancesofageneralization,includesaninferencetothecorrespondinglaw(thisistheinferencetothebestexplanation),andconcludeswithaninferencetothegeneralizationitselfortoitsunobservedinstances.ThecomplaintlodgedagainstHumeansisthat,ontheirviewofwhatlawsare,lawsarenotsuitedtoexplaintheirinstancesandsocannotsustaintherequiredinferencetothebestexplanation.

Thisisanareawhereworkonlawsneedstobedone.ArmstrongandDretskemakesubstantiveclaimsonwhatcanandcan'tbeinstanceconfirmed:roughly,Humeanlawscan't,lawsasuniversalscan.But,attheveryleast,theseclaimscannotbequiteright.Humeanlawscan't?Asthediscussionaboveillustrates,Sober,Langeandothershavearguedthatevengeneralizationsknowntobeaccidentalcanbeconfirmedbytheirinstances.DretskeandArmstrongneedsomeplausibleandsuitablystrongpremiseconnectinglawhoodtoconfirmabilityanditisnotclearthatthereisonetobehad.Hereisthebasicproblem:Asmanyauthorshavenoticed(e.g.,Sober1988,98vanFraassen1987,255),theconfirmationofahypothesisoritsunexaminedinstanceswillalwaysbesensitivetowhatbackgroundbeliefsareinplace.Somuchsothat,withbackgroundbeliefsoftherightsort,justaboutanythingcanbeconfirmedirrespectiveofitsstatusasalaworwhetheritislawlike.Thus,statingaplausibleprincipledescribingtheconnectionbetweenlawsandtheproblemofinductionwillbedifficult.Inordertouncoveranomologicalconstraintoninduction,somethingneedstobesaidabouttheroleofbackgroundbeliefs.

8.Necessity

Philosophershavegenerallyheldthatsomecontingenttruthsare(orcouldbe)lawsofnature.Furthermore,theyhavethoughtthat,ifitisalawthatallFsareGs,thenthereneednotbeany(metaphysically)necessaryconnectionbetweenFnessandGness,thatitis(metaphysically)possiblethatsomethingbeFwithoutbeingG.Forexample,anypossibleworldthat,asamatteroflaw,obeysthegeneralprinciplesofNewtonianphysicsisaworldinwhichNewton'sfirstistrue,andaworldcontainingacceleratinginertialbodiesisaworldinwhichNewton'sfirstisfalse.Thelatterworldisalsoaworldwhereinertiaisinstantiatedbutdoesnotnecessitatezeroacceleration.Some



necessitarians,however,holdthatalllawsarenecessarytruths.(SeeShoemaker1980and1998,Swoyer1982,Fales1990,Bird2005.)Othershaveheldsomethingthatisonlyslightlydifferent.Maintainingthatsomelawsaresingularstatementsaboutuniversals,theyallowthatsomelawsarecontingentlytrue.So,onthisview,anFness/GnesslawcouldbefalseifFnessdoesnotexist.Still,thisdifferenceisminor.Theseauthorsthinkthat,fortheretobeanFness/Gnesslaw,itmustbenecessarilytruethatallFsareGs.(SeeTweedale1984,Bigelow,Ellis,andLierse1992,EllisandLierse1994,andEllis2001.)

Tworeasonscanbegivenforbelievingthatbeingalawdoesnotdependonanynecessaryconnectionbetweenproperties.ThefirstreasonistheconceivabilityofitbeingalawinonepossibleworldthatallFsareGseventhoughthereisanotherworldwithanFthatisnotG.Thesecondisthattherearelawsthatcanonlybediscoveredinanaposteriorimanner.Ifnecessityisalwaysassociatedwithlawsofnature,thenitisnotclearwhyscientistscannotalwaysgetbywithapriorimethods.Naturally,thesetworeasonsareoftenchallenged.Thenecessitariansarguethatconceivabilityisnotaguidetopossibility.TheyalsoappealtoSaulKripke's(1972)argumentsmeanttorevealcertainaposteriorinecessarytruthsinordertoarguethattheaposteriorinatureofsomelawsdoesnotpreventtheirlawhoodfromrequiringanecessaryconnectionbetweenproperties.Infurthersupportoftheirownview,thenecessitariansarguethattheirpositionisaconsequenceoftheirfavoredtheoryofdispositions,accordingtowhichdispositionshavetheircausalpowersessentially.So,forexample,onthistheory,chargehasaspartofitsessencethepowertorepellikecharges.Laws,then,areentailedbytheessencesofdispositions(cf.,Bird2005,356).Asnecessitariansseeit,itisalsoavirtueoftheirpositionthattheycanexplainwhylawsarecounterfactualsupportingtheysupportcounterfactualsinthesamewaythatothernecessarytruthsdo(Swoyer1982,209Fales1990,8587).

Theprimaryworryfornecessitariansconcernstheirabilitytosustaintheirdismissalsofthetraditionalreasonsforthinkingthatsomelawsarecontingent.Theproblem(cf.,Sidelle2002,311)isthattheytoomakedistinctionsbetweennecessarytruthsandcontingentones,andevenseemtorelyonconsiderationsofconceivabilitytodoso.Primafacie,thereisnothingespeciallysuspiciousaboutthejudgmentthatitispossiblethatanobjecttravelfasterthanlight.HowisitanyworsethanthejudgmentthatitispossiblethatitisraininginParis?Anotherissuefornecessitariansiswhethertheiressentialismregardingdispositionscansustainallthecounterfactualsthatareapparentlysupportedbylawsofnature(Lange2004).

9.PhysicsandtheSpecialSciences

Twoseparate(butrelated)questionshavereceivedmuchrecentattentioninthephilosophicalliteraturesurroundinglaws.Neitherhasmuchtodowithwhatitistobealaw.Instead,theyhavetodowiththenatureofthegeneralizationsscientiststrytodiscover.First:Doesanysciencetrytodiscoverexceptionlessregularitiesinitsattempttodiscoverlaws?Second:Evenifonesciencefundamentalphysicsdoes,doothers?

9.1DoPhysiciststrytodiscoverExceptionlessRegularities?

Philosophersdrawadistinctionbetweenstrictgeneralizationsandceterisparibusgeneralizations.Thecontrastissupposedtobebetweenuniversalgeneralizationsofthesortdiscussedabove(e.g.,thatallinertialbodieshavenoacceleration)andseeminglylessformalgeneralizationslikethat,otherthingsbeingequal,smokingcausescancer.Theideaisthattheformerwouldbecontradictedbyasinglecounterinstance,say,oneacceleratinginertialbody,thoughthelatterisconsistentwiththerebeingonesmokerwhonevergetscancer.Thoughintheorythisdistinctioniseasyenoughtounderstand,inpracticeitisoftendifficulttodistinguishstrictfromceterisparibusgeneralizations.Thisisbecausemanyphilosophersthinkthatmanyutteranceswhichincludenoexplicitceterisparibusclauseimplicitlydoincludesuchaclause.



Forthemostpart,philosophershavethoughtthatifscientistshavediscoveredanyexceptionlessregularitiesthatarelaws,theyhavedonesoattheleveloffundamentalphysics.Afewphilosophers,however,aredoubtfulthatthereareexceptionlessregularitiesateventhisbasiclevel.Forexample,NancyCartwrighthasarguedthatthedescriptiveandtheexplanatoryaspectsoflawsconflict.Renderedasdescriptionsoffact,theyarefalseamendedtobetrue,theylosetheirfundamentalexplanatoryforce(1980,75).ConsiderNewton'sgravitationalprinciple,F=Gmm/r2.Properlyunderstood,accordingtoCartwright,itsaysthatforanytwobodiestheforcebetweenthemisGmm/r2.Butifthatiswhatthelawsaysthenthelawisnotanexceptionlessregularity.Thisisbecausetheforcebetweentwobodiesisinfluencedbyotherpropertiesthanjusttheirmassandthedistancebetweenthem,bypropertieslikethechargeofthetwobodiesasdescribedbyCoulomb'slaw.Thestatementofthegravitationalprinciplecanbeamendedtomakeittrue,butthat,accordingtoCartwright,atleastoncertainstandardwaysofdoingso,wouldstripitofitsexplanatorypower.Forexample,iftheprincipleistakentoholdonlythatF=Gmm/r2iftherearenoforcesotherthangravitationalforcesatwork,thenthoughitwouldbetrueitwouldnotapplyexceptinidealizedcircumstances.Lange(1993)usesadifferentexampletomakeasimilarpoint.Considerastandardexpressionofthelawofthermalexpansion:WheneverthetemperatureofametalbaroflengthL0changesbyT,thelengthofthebarchangesbyL=kL0T,wherekisa,constant,thethermalexpansioncoefficientofthemetal.Ifthisexpressionwereusedtoexpressthestrictgeneralizationstraightforwardlysuggestedbyitsgrammar,thensuchanutterancewouldbefalsesincethelengthofabardoesnotchangeinthewaydescribedincaseswheresomeoneishammeringontheendsofthebar.Itlookslikethelawwillrequireprovisos,butsomanythattheonlyapparentwayoftakingintoconsiderationalltherequiredprovisoswouldbewithsomethinglikeaceterisparibusclause.Thentheconcernbecomesthatthestatementwouldbeempty.Becauseofthedifficultyofstatingplausibletruthconditionsforceterisparibussentences,itisfearedthatOtherthingsbeingequal,L=kL0TcouldonlymeanL=kL0TprovidedthatL=kL0T.

EventhosewhoagreewiththeargumentsofCartwrightandLangesometimesdisagreeaboutwhatultimatelytheargumentssayaboutlaws.Cartwrightbelievesthatthetruelawsarenotexceptionlessregularities,butinsteadarestatementsthatdescribecausalpowers.Soconstrued,theyturnouttobebothtrueandexplanatory.Langeendsupholdingthattherearepropositionsproperlyadoptedaslaws,thoughindoingsooneneednotalsobelieveanyexceptionlessregularitythereneednotbeone.Giere(1999)canusefullybeinterpretedasagreeingwithCartwright'sbasicargumentsbutinsistingthatlawstatementsdon'thaveimplicitprovisosorimplicitceterisparibusclauses.So,heconcludesthattherearenolaws.

EarmanandRobertsholdthatthereareexceptionlessandlawfulregularities.Moreprecisely,theyarguethatscientistsdoingfundamentalphysicsdoattempttostatestrictgeneralizationsthataresuchthattheywouldbestrictlawsiftheyweretrue:

Ourclaimisonlythattypicaltheoriesfromfundamentalphysicsaresuchthatiftheyweretrue,therewouldbepreciseprovisofreelaws.Forexample,Einstein'sgravitationalfieldlawassertswithoutequivocation,qualification,proviso,ceterisparibusclausethattheRiccicurvaturetensorofspacetimeisproportionaltothetotalstressenergytensorformatterenergytherelativisticversionofMaxwell'slawsofelectromagnetismforchargefreeflatspacetimeassertswithoutqualificationorprovisothatthecurloftheEfieldisproportionaltothepartialtimederivative,etc.(1999,446).

AboutCartwright'sgravitationalexample,theythink(473,fn.14)thataplausibleunderstandingofthegravitationalprincipleisasdescribingonlythegravitationalforcebetweenthetwomassivebodies.(Cartwrightarguesthatthereisnosuchcomponentforceandsothinkssuchaninterpretationwouldbefalse.EarmanandRobertsdisagree.)AboutLange'sexample,theythinkthelawshouldbeunderstoodashavingthesingleprovisothattherebenoexternalstressesonthemetalbar(461).Inanycase,muchmorewouldneedtobesaidtoestablishthatalltheapparentlystrictandexplanatory



generalizationsthathavebeenorwillbestatedbyphysicistshaveturnedorwillturnouttobefalse.(Earman,etal.,2003includesmorerecentpapersbybothCartwrightandLange,andalsomanyotherpapersonceterisparibuslaws.)

9.2CouldtherebeanySpecialScienceLaws?

Supposingthatphysicistsdotrytodiscoverexceptionlessregularities,andevensupposingthatourphysicistswillsometimesbesuccessful,thereisafurtherquestionofwhetheritisagoalofanyscienceotherthanfundamentalphysicsanysocalledspecialsciencetodiscoverexceptionlessregularitiesandwhetherthesescientistshaveanyhopeofsucceeding.Consideraneconomiclawofsupplyanddemandthatsaysthat,whendemandincreasesandsupplyisheldfixed,priceincreases.Noticethat,insomeplaces,thepriceofgasolinehassometimesremainedthesamedespiteanincreaseindemandandafixedsupply,becausethepriceofgasolinewasgovernmentregulated.Itappearsthatthelawhastobeunderstoodashavingaceterisparibusclauseinorderforittobetrue.Thisproblemisaverygeneralone.AsJerryFodor(1989,78)haspointedout,invirtueofbeingstatedinavocabularyofaspecialscience,itisverylikelythattherewillbelimitingconditionsespeciallyunderlyingphysicalconditionsthatwillundermineanyinterestingstrictgeneralizationofthespecialsciences,conditionsthatthemselvescouldnotbedescribedinthespecialsciencevocabulary.DonaldDavidsonpromptedmuchoftherecentinterestinspecialsciencelawswithhisMentalEvents(1980[f.p.1970],207225).Hegaveanargumentspecificallydirectedagainstthepossibilityofstrictpsychophysicallaws.Moreimportantly,hemadethesuggestionthattheabsenceofsuchlawsmayberelevanttowhethermentaleventsevercausephysicalevents.Thispromptedaslewofpapersdealingwiththeproblemofreconcilingtheabsenceofstrictspecialsciencelawswiththerealityofmentalcausation(e.g.,LoewerandLepore1987and1989,Fodor1989,Schiffer1991,PietroskiandRey1995).

Progressontheproblemofprovisosdependsonthreebasicissuesbeingdistinguished.First,thereisthequestionofwhatitistobealaw,whichinessenceisthesearchforanecessarilytruecompletionof:Pisalawifandonlyif.Obviously,tobeatruecompletion,itmustholdforallP,whetherPisastrictgeneralizationoraceterisparibusone.Second,thereisalsoaneedtodeterminethetruthconditionsofthegeneralizationsentencesusedbyscientists.Third,thereistheaposterioriandscientificquestionofwhichgeneralizationsexpressedbythesentencesusedbythescientistsaretrue.Thesecondoftheseissuesistheonewheretheactionneedstobe.

Onthisscore,itisstrikinghowlittleattentionisgiventothepossibleeffectsofcontext.Mightn'titbethat,whentheeconomistuttersacertainstrictgeneralizationsentenceinaneconomicsetting(say,inaneconomicstextbookorataneconomicsconference),contextsensitiveconsiderationsaffectingitstruthconditionswillhaveitturnoutthattheutteranceistrue?Thismightbethecasedespitethefactthatthesamesentenceutteredinadifferentcontext(say,inadiscussionamongfundamentalphysicistsorbetteryetinaphilosophicaldiscussionoflaws)wouldresultinaclearlyfalseutterance.Thesechangingtruthconditionsmightbetheresultofsomethingasplainasacontextualshiftinthedomainofquantificationorperhapssomethinglessobvious.Whateveritis,theimportantpointisthatthisshiftcouldbeafunctionofnothingmorethanthelinguisticmeaningofthesentenceandfamiliarrulesofinterpretation(e.g.,theruleofaccommodation).

Considerasituationwhereanengineeringprofessorutters,Whenametalbarisheated,thechangeinitslengthisproportionaltothechangeinitstemperatureandsupposeastudentoffers,Notwhensomeoneishammeringonbothendsofthebar.Hasthestudentshownthattheteacher'sutterancewasfalse?Maybenot.Noticethatthestudentcomesoffsoundingabitinsolent.Inalllikelihood,suchanunusualsituationassomeonehammeringonbothendsofaheatedbarwouldnothavebeeninplaywhentheprofessorsaidwhathedid.Infact,thereasonthestudentcomesoffsoundinginsolentisbecauseitseemsthatheshouldhaveknownthathisexamplewasirrelevant.Noticethattheprofessor'ssentenceneedn'tincludesomeimplicitceterisparibusclauseinorderforhisutterancetobetrueasthisexampleillustrates,inordinaryconversations,plainoldstrictgeneralizationsentences



arenotalwaysusedtocoverthefullrangeofactualcases.Indeed,theyarerarelyusedinthisway.

Ifspecialscientistsdomaketrueutterancesofgeneralizationsentences(sometimesceterisparibusgeneralizationsentences,sometimesnot),thenapparentlynothingstandsinthewayofthemutteringtruespecialsciencelawhoodsentences.Theissueherehasbeenthetruthofspecialsciencegeneralizations,notanyotherrequirementsoflawhood.

10.ConcludingRemarks:WhatisNext?

Howwillmattersprogress?Howcanphilosophyadvancebeyondthecurrentdisputesaboutlawsofnature?Fourissuesareespeciallyinterestingandimportantones.Thefirstconcernswhetherlawsgoverntheuniverse,exactlywhatitmeanstosaythattheydo,andhowthataffectsourunderstandingoflawhood.Thesecondconcernswhetherlawhoodisapartofthecontentofscientifictheories.Thisisaquestionoftenaskedaboutcausation,butlessfrequentlyaddressedaboutlawhood.Robertsoffersananalogyinsupportofthethoughtthatitisnot:

ItisapostulateofEuclideangeometrythattwopointsdeterminealine.ButitisnotpartofthecontentofEuclideangeometrythatthispropositionisapostulate.Euclideangeometryisnotatheoryaboutpostulatesitisatheoryaboutpoints,lines,andplanes(2008,p.92).

Robertsdrawstheconclusionthatlawhoodisnotpartofscientifictheoriesandgoesontodescribewhathethinkstheroleoflawhoodinscienceis.Thismaybeaplausiblefirststeptowardunderstandingtheabsenceoflawandsomeothernomictermsfromtheformalstatementsofscientifictheories.Thethirdistheissueofwhetherthereareanycontingentlawsofnature.Necessitarianscontinuetoworkfeverishlyonfillingintheirview,whileHumeansandotherspayrelativelylittleattentiontowhattheyareuptonewworkneedstoexplainthesourceoftheunderlyingcommitmentsthatdividethesecampsandtofigurewhateachgroupisdoingright.Finally,moreattentionneedstobepaidtothelanguageusedtoreportwhatarethelawsandthelanguageusedtoexpressthelawsthemselves.Itisclearthatrecentdisputesaboutgeneralizationsinphysicsandthespecialsciencesturnonpreciselythesematters,butexploringthemmayalsopaydividendsoncentralmattersregardingontology,realismvs.antirealism,andsupervenience.

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