【布莱克威尔哲学指南系列】科学哲学 358页

TheBlackwellGuidetothePhilosophyofScience\nBlackwellPhilosophyGuidesSeriesEditor:StevenM.Cahn,CityUniversityofNewYorkGraduateSchoolWrittenbyaninternationalassemblyofdistinguishedphilosophers,theBlackwellPhilosophyGuidescreateagroundbreakingstudentresource–acompletecriticalsurveyofthecentralthemesandissuesofphilosophytoday.Focusingandadvanc-ingkeyargumentsthroughout,eachessayincorporatesessentialbackgroundmaterialservingtoclarifythehistoryandlogicoftherelevanttopic.Accordingly,thesevolumeswillbeavaluableresourceforabroadrangeofstudentsandreaders,includingprofessionalphilosophers.1TheBlackwellGuidetoEpistemologyEditedbyJohnGrecoandErnestSosa2TheBlackwellGuidetoEthicalTheoryEditedbyHughLaFollette3TheBlackwellGuidetotheModernPhilosophersEditedbyStevenM.Emmanuel4TheBlackwellGuidetoPhilosophicalLogicEditedbyLouGoble5TheBlackwellGuidetoSocialandPoliticalPhilosophyEditedbyRobertL.Simon6TheBlackwellGuidetoBusinessEthicsEditedbyNormanE.Bowie7TheBlackwellGuidetothePhilosophyofScienceEditedbyPeterMachamerandMichaelSilberstein8TheBlackwellGuidetoMetaphysicsEditedbyRichardM.Gale\nTheBlackwellGuidetothePhilosophyofScienceEditedbyPeterMachamerandMichaelSilberstein\nCopyright©BlackwellPublishersLtd2002Firstpublished200224681097531BlackwellPublishersInc.350MainStreetMalden,Massachusetts02148USABlackwellPublishersLtd108CowleyRoadOxfordOX41JFUKAllrightsreserved.Exceptforthequotationofshortpassagesforthepurposesofcriticismandreview,nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,withoutthepriorpermissionofthepublisher.ExceptintheUnitedStatesofAmerica,thisbookissoldsubjecttotheconditionthatitshallnot,bywayoftradeorotherwise,belent,resold,hiredout,orotherwisecirculatedwithoutthepublisher’spriorconsentinanyformofbindingorcoverotherthanthatinwhichitispublishedandwithoutasimilarconditionincludingthisconditionbeingimposedonthesubsequentpurchaser.LibraryofCongressCataloging-in-PublicationDatahasbeenappliedfor.ISBN0-631-22107-7(hardback);0-631-22108-5(paperback)BritishLibraryCataloguinginPublicationDataACIPcataloguerecordforthisbookisavailablefromtheBritishLibrary.Typesetin10on13ptGalliardbyBest-setTypesetterLtd.,HongKongPrintedinGreatBritainbyT.J.International,Padstow,CornwallThisbookisprintedonacid-freepaper.\nContentsNotesonContributorsviiPrefacex1ABriefHistoricalIntroductiontothePhilosophyofScience1PeterMachamer2PhilosophyofScience:ClassicDebates,StandardProblems,FutureProspects18JohnWorrall3Explanation37JimWoodward4StructuresofScientificTheories55CarlF.Craver5Reduction,EmergenceandExplanation80MichaelSilberstein6Models,MetaphorsandAnalogies108DanielaM.Bailer-Jones7ExperimentandObservation128JamesBogen8InductionandProbability149AlanHájekandNedHall9PhilosophyofSpace–TimePhysics173CraigCallenderandCarlHoefer10InterpretingQuantumTheories199LauraRuetschev\nContents11Evolution227RobertaL.Millstein12MolecularandDevelopmentalBiology252PaulGriffiths13CognitiveScience272RickGrush14SocialSciences290HaroldKincaid15FeministPhilosophyofScience312LynnHankinsonNelsonIndex332vi\nNotesonContributorsDanielaM.Bailer-JonesstudiedPhilosophyandPhysicsattheUniversitiesofFreiburg,OxfordandCambridge,receivinganM.Phil.inPhysics(1993)andaPh.D.inPhilosophyofScience(1998)fromtheUniversityofCambridge.ShetaughtattheUniversityofPaderborn(1998–2000),andwasattheUniversityofBonnuntilbecomingaFellowattheCenterofPhilosophyofScienceoftheUniversityofPittsburghinthesummerof2001.Hermainresearchinterestisscientificmodels.JamesBogen,havingretiredaftermanyyearsatPitzerCollege,isnowanadjunctprofessorintheUniversityofPittsburghHPSDepartment.Hispublicationsincludepapersontopicsinthetheoryofknowledge,includingmethodologyintheneurosciences.CraigCallenderisanAssistantProfessorofPhilosophyattheUniversityofCaliforniaatSanDiego.HewasformerlyaSeniorLecturerattheLondonSchoolofEconomics,wherehealsoworkedattimeswiththeBritishJournalforthePhilosophyofScienceandMind.WithNickHuggett,herecentlyeditedabookentitledPhysicsmeetsPhilosophyatthePlanckScale(2001).Hehaspublishedandlecturedextensivelyontopicsinthephilosophicalfoundationsofmodernphysics.CarlF.CraverwasAssistantProfessorofPhilosophy,FloridaInternationalUni-versity,andmovedlastFall,toWashingtonUniversity,SaintLouis.HehasaPh.D.fromTheUniversityofPittsburgh,DepartmentofHistoryandPhilosophyofScience,andanM.S.fromUniversityofPittsburgh,DepartmentofNeuroscience.Hisprimaryresearchareasarephilosophyofneuroscience,withparticularempha-sisonmechanisms,mechanicalexplanation,andtheoryconstruction.PaulGriffithswaseducatedatCambridgeandtheAustralianNationalUniver-sity,andtaughtatOtagoUniversityinNewZealandandtheUniversityofSydney,vii\nNotesonContributorsAustraliabeforemovingtotheDepartmentofHistoryandPhilosophyofScienceattheUniversityofPittsburgh.Heisauthor,withKimSterelny,ofSexandDeath:AnIntroductiontoPhilosophyofBiology(1997)andeditor,withSusanOyamaandRussellGray,ofCyclesofContingency:DevelopmentalSystemsandEvolution(2001).RickGrushreceivedhisjointdoctorateinCognitiveScienceandPhilosophyfromUCSanDiegoin1995.From1995to1998,heheldpositionsatthePNPProgramatWashingtonUniversityonSt.Louis,andtheCenterforSemioticResearchattheUniversityofAarhus,Denmark.From1998to2000,hewasattheUniversityofPittsburgh,wherehealsoservedasAssociateDirectoroftheCenterforPhilosophyofScienceforthe1999–2000academicyear.Heiscur-rentlyinthePhilosophyDepartmentatUCSanDiego.Hisworkinvolvesunder-standingthephysicalbasisofthemind.AlanHájekisanAssociateProfessorofPhilosophyattheCaliforniaInstituteofTechnology,Pasadena,California.Heworksmainlyinthefoundationsofproba-bilityanddecisiontheory,epistemology,philosophyofscienceandphilosophyofreligion.Hispublicationshavedealtwithsuchtopicsas:probabilitiesofcondi-tionals;theinterpretationofprobability;therelationshipbetweenconditionalandunconditionalprobability;Bayesianepistemologyandphilosophyofscience;infi-nitedecisiontheoryandPascal’sWager;Hume’smiraclesargument;andMoore’sparadox.NedHall,AssociateProfessorofphilosophyatMIT,worksmainlyonmeta-physics,philosophyofscience,and,morespecifically,philosophyofquantumphysics.Hiscurrentresearchonquantumphysicsfocusesonthemeasurementproblem,andonimplicationsofandproblemsfortheusualquantummechanicaltreatmentofidenticalparticles.Inmetaphysicsandphilosophyofscience,hisworkhasincludedinvestigationsintotheconnectionsbetweenprobabilitytheoryandthelogicofconditionals,theepistemologyandmetaphysicsofobjectiveproba-bility,andtheanalysisofcausation.CarlHoeferisLecturerintheDepartmentofPhilosophy,LogicandScientificMethodattheLSE,andCo-DirectoroftheCentreforPhilosophyofNaturalandSocialScience.Heworksintheareasofphilosophyofspaceandtime(especiallygeneralrelativity)andmetaphysics.HaroldKincaidisProfessorofPhilosophyandDirector,CenterforEthicsandValuesintheSciencesattheUniversityofAlabamaatBirmingham.HeistheauthorofPhilosophicalFoundationsoftheSocialSciences(1996),IndividualismandtheUnityofScience(RowmanandLittlefield,1997),andnumerousarticlesontopicsinthephilosophyofsocialscience.viii\nNotesonContributorsPeterMachamerisProfessorofHistoryandPhilosophyofScienceattheUni-versityofPittsburghandAssociateDirectorofTheCenterforPhilosophyofScience.HeeditedtheCambridgeCompaniontoGalileo(1998),andwasco-editorofScientificControversies(2000)andTheoryandMethodinNeuroscience(2001).Heiscurrentlyworkingonabookaboutinterpretationinscienceandartandmaybepublishingacollectionofhisessaysontheseventeenthcentury.RobertaL.MillsteinisanAssistantProfessorintheDepartmentofPhilosophyatCaliforniaStateUniversity,Hayward.ShereceivedherA.B.fromDartmouthCollegewithadoublemajorinComputerScienceandPhilosophy.SheearnedherPh.D.inPhilosophy,withaminorintheHistoryofScienceandTechnology,attheUniversityofMinnesota.Sheteachescoursesinthehistoryandphilosophyofscience(includingcoursesinscienceandethics),andpublishesarticlesinthephilosophyofbiology.LynnHankinsonNelsonisProfessorofPhilosophyattheUniversityofMissouri-St.Louis.Sheisco-authorwithJackNelsonofOnQuine(2000),co-editorwithJackNelsonofFeminism,Science,andthePhilosophyofScience(1996and1997),guesteditorofaspecialissueofSynthesedevotedtofeminismandscience(1995),andtheauthorofWhoKnows:FromQuinetoFeministEmpiricism(1990).LauraRuetscheisAssistantProfessorofPhilosophyattheUniversityofPitts-burgh.Herinterestsincludethefoundationsofphysicaltheories,theepistemol-ogyofscience(includingfeministapproaches),andPlato.MichaelSilbersteinisAssociateProfessorofPhilosophyatElizabethtownCollege.HehaspublishedanddeliveredpapersinbothPhilosophyofScienceandPhilosophyofMind.Hisprimaryareasofresearchandinterestarephilosophyofphysicsandthephilosophyofcognitive-neurosciencerespectively.JimWoodwardisProfessorofPhilosophyandExecutiveOfficerfortheHumanitiesattheCaliforniaInstituteofTechnology.Heiscompletingabookonexplanation.JohnWorrallisProfessorofPhilosophyofScienceandCo-DirectoroftheCentreforPhilosophyofNaturalandSocialScienceattheLondonSchoolofEco-nomics.HewaseditoroftheBritishJournalforthePhilosophyofSciencefrom1974to1982,andeditorofthecollectedworksofImreLakatos.Hehaspublishedwidelyontopicsingeneralphilosophyofscienceandhistoryandphilosophyofnineteenthcenturyphysics.Heiscurrentlyfinishingabookontheory-changeinscienceanddevelopinganinterestinissuesinthemethodologyofmedicine.ix\nPrefaceThisvolumewasconceivedbyMichaelSilberstein,whothencontactedBlackwellabouttheidea.PeterMachamerjoinedtheprojectbeforethefinalpresentationwasmadetoBlackwell.Ithasbeenacollaborativeeffortthereafter.Theconceptionforthechaptersinthisvolumeweredrawnupalonganumberofparameters.First,wewishedagoodmixofauthors,peopleestablishedinthefieldaswellassomeyoungerscholarswhowouldbringafreshperspectivetotheirchapters.Second,eachauthorwaschargedwithwritingathree-partessay:thefirstparttoreviewtheproblem;thesecondtoassaythecurrentstateofthedisciplinewithrespecttothetopic;andfinallytoprognosticateonthefutureanddiscusswherethefieldshouldbemoving.Allthiswastobedonewithin8500words!Mostchaptersstayednearlywithintheirlimitsandhaveaccomplishedthesettaskwithgreataplomb.Athirdparameterwasthatthechaptersshouldbewrittentobeofusetothosewhoarenotspecialistsinthefieldoronthetopic,butwhowishedasinglesourcetheycouldreadthatwouldbringthem“uptospeed.”However,thechaptersalsoweretobeofinteresttothespecialists,andthusnotmerelyintroductoryinnature.Obviously,differenttopicsrequiredifferentlevelsofexpertiseonthepartofthereader,butwefeelallofthechaptersareaccessible.Thisiscompatiblewiththefactthatsomechaptersaremoretechnicalandrequireaspecializedknowledgeonthepartofthereader.Forexample,wefeltnogoodusecouldcomeofhavingachapteronquantummechanicsthateschewedthemathematics,achapteronspace–timethathadtoexplainthebasisofthegeneraltheoryofrelativityoraprobabilitychapterthatignoredtheprobabilitycalculus.Suchabookcouldhavebeenputtogetherbutitwouldnotbeaguide,itwouldhavebeenapopulariz-ingintroduction.Suchwasnotouraim.Finally,wesoughttocoverthebasictopicswhereresearchinphilosophyofsciencewas,inoureyes,progressing.Duetospacelimitations,wehavenotcoveredeverythingwemighthave,northatwewouldhaveliked.Somethingshouldhavebeensaidabouttherelationbetweensciencesstudiesandphilosophyx\nPrefaceofscienceandagainabouthistoryofscienceandphilosophyofscience.Weshouldhavespentmoretimeonthe“continental”traditionanditsrelationstophiloso-phyofscience.Manyofthespecialsciencesareignored.Wehadonlysomanychapterswecouldchose.Othersmighthavechosendifferently.Wethinkthisbookisgood.Eachchapteriswrittenwithcare,andhassub-stantiveimport.Thisisourjudgment.Thefinalevaluationwillrestwithyou,thereader.Acknowledgmentsandreferencesaregivenineachchapter.Inaddition,MichaelSilbersteinwouldliketothankhisloveandbestfriendElizabethNewellforherkindnessandpatienceandhisassistantMichaelCifoneforhisinvaluablehelp.HewouldalsoliketogiveaspecialthankstoPeterMachamerforhispatience,thoughtfulsuggestions,hardwork,longhoursandwithoutwhomthisbookwouldnotexist.HededicatesthisvolumetoElizabethNewellandhissonChristopherRobinSilberstein.PeterMachamerwouldliketothankBarbaraDivenMachamer,andMichaelandTaraGainfortfortheirsupportandpatiencewithmanylatedinners.HiseffortsarededicatedtoRachel,CourtneyandNico–grandchildrenwhomakelifespecial.xi\nChapter1ABriefHistoricalIntroductiontothePhilosophyofScience*PeterMachamerPhilosophyofscienceisanoldandpracticeddiscipline.BothPlatoandAristotlewroteonthesubject,and,arguably,someofthepre-Socraticsdidalso.TheMiddleAges,bothinitsArabicandhighLatinperiods,mademanycommentariesanddisputationstouchingontopicsinphilosophyofscience.Ofcourse,thenewscienceoftheseventeenthcenturybroughtalongwidespreadruminationsandmanifoldtreatisesonthenatureofscience,scientificknowledgeandmethod.TheEnlightenmentpushedthisprojectfurthertryingtomakescienceanditshallmarkmethoddefinitiveoftherationallife.Withtheindustrialrevolution,“science”becameasynonymforprogress.InmanyplacesintheWesternworld,sciencewasveneratedasbeingthepeculiarlymodernwayofthinking.Thenine-teenthcenturysawanotherresurgenceofinterestwhenideasofevolutionmeldedwiththoseofindustrialprogressandphysicsachievedamaturitythatledsometobelievethatsciencewascomplete.Bytheendofthecentury,mathematicshadfoundalternativestoEuclideangeometryandlogichadbecomeanewlyre-admireddiscipline.Butjustbeforetheturntothetwentiethcentury,andinthosedecadesthatfol-lowed,itwasphysicsthatledtheintellectualway.Freudwastheretoo,heandBreuerhavingpublishedStudiesinHysteriain1895,butitwasphysicsthatgar-neredtheattentionofthephilosophers.MechanicsbecamemoreandmoreunifiedinformwiththeworkofMaxwell,HertzanddiscussionsbyPoincaré.Plankderivedtheblackbodylawin1899,in1902LorenzprovedMaxwell’sequationswereinvariantundertransformation,andin1905Einsteinpublishedhispaperonspecialrelativityandthebasisofthequantum.Concomitantly,Hilbertin1899publishedhisfoundationsofgeometry,andBertrandRussellin1903gaveforthhisprinciplesofmathematics.Thedevelopmentofunifiedclassicalmechanicsandalternativegeometries,nowaugmentedandchallengedbythenewrelativityandquantumtheoriesmadeforperiodofunprecedentedexcitementinscience.Whatfollowsprovidesabriefhistoricaloverviewoftheproblemsandconceptsthathavecharacterizedphilosophyofsciencefromtheturnofthetwentiethcentury1\nPeterMachameruntilthepresentday.Thisispresentedintheformofconceptualandproblem-orientedhistorybecauseIbelievethattherealinterestinphilosophyofscienceandthelessonstobelearnedfromitshistoryarefoundinthetopicsitaddressedandthemethodsitusedtoaddressthem.Further,thecastofcharacters,andthespecificarticlesandbookscanbeeasilyresearchedbyanyonewhoisinterested.Thereis,appendedaselectivechronologicalbibliographyof“classical”sources.Afewcaveatsneedtobestatedfromthestart.First,IdealalmostexclusivelywithcertainaspectsofoneAustro-Germanic-Anglo-Americantradition.ThisisnotbecausetherewasnotinterestingandimportantworkinphilosophyofsciencegoingoninFranceandelsewhere.Idothis,first,becausethistraditionistheonethatisformativeforanddominantincontemporaryAmericanphilosophy(forgoodorill),and,second,becauseitisthetraditioninwhichIwasraisedandaboutwhichIknowthemost.Anothercaveatisthatspacelimitationsandigno-ranceoftenrequiretheomissionofmanyinterestingnuances,qualificationsandevenoutrightimportantfacetsofthehistoryofphilosophyofscience.WhatItrytodoisrunasemi-coherentthreadthroughthetwentiethcentury,insuchwaysthatadevelopmentalnarrativecanbefollowedbythosewhohavenotlivedwithintheconfinesofthediscipline.Manyscholarswouldhavedonethingsdifferently.C’estlavie!Toprovidesomestructurefortheexposition,Ishallbreakthistextintothreeimportantperiods:•1918–50s:LogicalPositivismtoLogicalEmpiricism•1950sthrough1970s:NewParadigmsandScientificChange•ContemporaryFoci:What’s“hot”todayLogicalPositivismtoLogicalEmpiricism:1918–55Aswasnotedabove,theformingspiritoftwentiethcenturyphilosophyofsciencewerethegrandsynthesesandbreakthroughs(orrevolutions)inphysics.Relativityand,later,quantumtheorycausedscientistsandphilosophersaliketoreflectonthenatureofthephysicalworld,andespeciallyonthenatureofhumanknowledgeofthephysicalworld.Inmanyways,theprojectofthisnewphilosophyofsciencewasanepistemologicalone.Ifonetookphysicsasthepar-adigmaticscience,andifsciencewastheparadigmaticmethodbywhichonecametoobtainreliableknowledgeoftheworld,thentheprojectforphilosophyofsciencewastodescribethestructureofsciencesuchthatitsepistemologicalunder-pinningswereclear.Thetwoantecedents,thatphysicswastheparadigmaticscienceandthatsciencewasthebestmethodforknowingtheworld,weretakentobeobvious.Oncethestructureofsciencewasmadeprecise,onecouldthenseehowfartheselessonsfromscientificepistemologycouldbeappliedtoothersareasofhumanendeavor.2\nABriefHistoricalIntroductiontothePhilosophyofScienceAnotherimportantbackgroundtraditionneedstobedescribed.Propositionalandpredicatelogicbecamethemodelforclearreasoningandexplicitstatement.FirstintheworkofFrege(inthe1880s–90s),andlaterwithRussellandWhite-head(inthe19-teens),logiccametoberegardedasthewaytounderstandandclarifythefoundationsofmathematics.Itbecametheideallanguageformodel-inganycognitiveenterprise.Simultaneously,Hilbertre-introducedtotheworldtheidealofaxiomatization.Againthiswasaclarifyingmovetoensurethattherewerenohiddenassumptions,andeverythinginasystemwasmadeexplicit.Thislogico-mathematicallanguagebecamethepreferredform,becauseofitsprecision,intowhichphilosophyofsciencehadtobecast.Theepistemologicalprojectofthepositivistswastoexplicatehowsciencewasgroundedinourobservationsandexperiments.Simultaneously,thegoalwastoprovideanalternativetotheneo-Kantianismthatwasthecontemporaneouslyconcurrentformofphilosophy.TakingfromthetraditionofBritishempiricism,empiricalgrounding,orbeingbasedonthefacts,wasseenasthemajordifferencebetweenscienceandtheothertheoreticalandphilosophicalpretenderstoknowl-edge.Thisinsightledthepositiviststoattempttoformulateandsolvetheproblemofthenatureofmeaning,ormorespecifically,empiricalmeaning.Whatwasit,theyasked,thatmadestatementsabouttheworldmeaningful?Thisattempttoexplicatethetheoryofmeaninghadtwoimportantparts:First,claimsabouttheworldwouldhavetobemadeclear,avoidingambiguityandtheotherconfusionsinherentinnaturallanguage.Tothisend,thepositiviststriedtorestrictthem-selvestotalkingaboutthelanguageofscienceasexpressedinthesentencesofsci-entifictheories,andattemptedtoreformulatethesesentencesintotheclearandunequivocallanguageoffirst-orderpredicatelogic.Second,theytriedtodevelopacriterionthatwouldshowhowthesesentencesinascientifictheoryrelatedtotheworld,i.e.intheirlinguisticmodethisbecametheproblemofhowtheoreti-calsentencesrelatedtoobservationsentences.Forthisoneneededtodevelopaprocedurefordeterminingwhichsentencesweretrue.Thismethodcametobecodifiedintheverificationprinciple,whichheldthatthemeaningofanempiricalsentencewasgivenbytheproceduresthatonewouldusetoshowwhetherthesentencewastrueorfalse.Iftherewerenosuchproceduresthenthesentencewassaidtobeempiricallymeaningless.Theclassofempiricallymeaninglesssentencesweresaidtobenon-cognitive,andtheyincludedthesentencescomprisingsystemsofmetaphysics,ethicalclaimsand,mostimportantly,thosesentencesthatmadeuptheoriesofthepseudo-sciences.Thislatterproblem,distinguishingscientificsentencesfromthoseonlypurportingtobescientific,cametoknown(followingKarlPopper’swork)asthedemarcationproblem.Theverificationprinciplewasthoughttobeawayofmakingprecisetheempiricalobservational,orexperimentalcomponentofscience.Obviously,thepositivists,followingintheempiricisttradition,thought,thebasisofsciencelayinobservationandinexperiment.Theseweretheteststhatmadesciencereliable,thefoundationthatdifferentiatedsciencefromothertypesofknowledgeclaims.3\nPeterMachamerSo,formally,whatwasneededwasasetofsentencesthatbridgedthegapfromscientifictheorytoscientificexperimentandobservation.Thesesentencesthattiedtheorytotheworldwerecalledbridgesentencesorreductionsentences.Thesetofsentencesthatdescribedtheworldtowhichtheoreticalsentenceswerereducedorrelatedwascalledtheobservationlanguage.Sentencesintheobservationlanguageweretakentobeeasilyverifiableordecidableastotheirtruthorfalsity.Sothatthesebridgesentencesmightbemadeveryexplicit,theorieswerethem-selvesidealizedassetsofsentencesthatcouldbeputintoanaxiomaticstructure,inwhichalltheirlogicalrelationsanddeductionsfromthemcouldbemadeexplicit.Themostimportantsentencesinascientifictheorywerethelawsofscience.Lawscameintwotypes:universalandstatistical.UniversalLawsweresentencesofthetheorythathadunrestrictedapplicationinspaceandtime(sometimestheywereexplicitlysaidtobecausal,and,later,theywereheldtobeabletosupportcounterfactualclaims.)Idealizeduniversallawshadthelogicalform:()xFxGx()…Sincesuchaformcouldbeusedtoclearlyestablishtheirlogicalimplications.Obviously,thiswasanidealizedform,sincemostofthelawsofinterestwerefromphysicsandhadamuchmorecomplexmathematicalform.Statisticallawsonlymadetheirconclusionsmoreorlessprobable.Scientificexplanationwasconceivedasdeducingaparticularsentence(usuallyanobservationorbasicsentence)fromauniversallaw(givensomeparticularinitialconditionsaboutthestateoftheworldatatime).Theparticularfact,expressedbythesentence,wassaidtobeexplainedifitcouldbesodeduced.Thiswascalledthedeductive-nomologicalmodelofexplanation.“Nomos”istheGreekwordforlaw.If,aparticularsentencewasdeducedbeforethefactwasobserved,itwasaprediction,andthenlaterifitwasverified,thetheoryfromwhichitwasdeducedwassaidtobeconfirmed.Thiswasthehypothetico-deductivemodelbecausethelawwasconsideredanhypothesistobetestedbyitsdeductiveconsequences.ThenamesofsomeofthemajorplayersinthisperiodofphilosophyofsciencewereMoritzSchlick,RudolfCarnap,OttoNeurath,HansReichenbach,andCarlHempel.Thereweretwomaingroups,onecenteredinVienna(Schlick,CarnapandNeurath),calledtheViennaCirclethatwasestablishedlateinthe1920s,andtheother,comingabitlater,inBerlin(ReichenbachandHempel).TherewasaimportantthirdgroupinWarsaw,doingmostlylogicandconsistingofAlfredTarski,StanislauLesnewskiandTadeuszKotarbinski.Thisviewofscience,asanidealizedlogicallypreciselanguagewhichcouldhaveallitsmajorfacetscodified,neverworked.Throughoutthehistoryoflogicalpos-itivismthereweredebatesandre-formulationsamongitspractitionersabouttheidealizedlanguageofscience,therelationsofexplanationandconfirmation,theadequateformulationoftheverificationprinciple,theindependentnatureofobservations,andtheadequacyofthesemantictruthpredicate.Thestatic,uni-4\nABriefHistoricalIntroductiontothePhilosophyofScienceversalistnatureofsciencethatwasidealizedbypositivismprovedtobewrong.Theattempttofixproceduresandclaimsinalogicallysimplifiedlanguageprovedtobeimpossible.Theneat,clearattemptsatexplicatingexplanation,confirma-tion,theoryandtestability,allprovedtohavebothinternaldifficultieswiththeirlogicalstructuresandexternalproblemsinthattheydidnotseemtofitscienceasitwasactuallypracticed.Thepositiviststhemselveswerethefirsttoseetheproblemswiththeirprogram,and,astheyattemptedtoworkoutthephilosophicaldifficulties,thepositionschangedshiftedintowhatbecamecalledlogicalempiricism.Thishappenedinthemid-tolate1930s,thesametimethatmanyofthegroupleftGermanyandAustriabecauseofWorldWarIIandtheriseofAdolphHitler.ReichenbachleftGermanyimmediatelyafterHitlertookpowerin1933andwentfirsttoIstanbul,Turkey,RichardvonMiseswentalso.Reichenbachthenin1938wenttoUCLAintheUSA.NeurathandPopperbothendedupinEngland.Carnap,fromPrague,andHempel,fromBerlin,cametotheUSA.Hereisbitmoresociologyofthehowphilosophyofsciencedeveloped.Thefirstmodernprograminhistoryandphilosophyofscience(HPS)wassetupatUniversityCollege,London.A.WolffirstofferedahistoryofsciencecourseincollaborationwithSirWilliamBraggandothersin1919–20.Thena“BoardofStudiesinPrinciples,MethodsandHistoryofScience”wasestablishedin1922,andanM.Sc.wasfirstofferedin1924.Wolfwasthefirstholderofthechairin“HistoryandMethodofScience.”In1946,theChairbecamefulltimewiththeappointmentofHerbertDingle.TheLondonSchoolofEconomics’DepartmentevolvedaftertheappointmentofKarlPoppertotheReadershipinLogicandSci-entificMethodin1945.ThesameWolfwhowasassociatedwithU.C.,LondonalsoheldtheChairinLogicandtaughtcoursesatLSE,priortoPopper.TheUni-versityofMelbournein1946beganteachingcoursesinHPS.Erkenntnis,thejournaloftheViennaCircle,orrathertheMaxPlankSociety,wasfirstpublishedin1930.ThisfollowedonthefirstcongressontheEpiste-mologyoftheExactSciencesheldinPragueinSeptemberof1929.In1934thejournal,PhilosophyofScience,publisheditsfirstissue.WilliamM.Malisoff,aRussianbiochemist,wasitsfirsteditor.Malisoffdiedunexpectedlyin1947,andC.WestChurchmanbecameeditor.ThePhilosophyofScienceAssociationwasinexistencein1934.In1948thePSAhad153members,andPhilippFrankwasitsPresident.Inthedisciplineofhistoryofscience,theAmericanHistoryofScienceSocietywasfoundedin1924.TheHSSjournalIsis,hadbeenstartedearlierin1912byGeorgeSartonwhenhewasstillinBelgium.Logicalempiricismneverhadthecoherenceasaschoolthatlogicalpositivismhad.Variousinfluencesbegantomakethemselvesfeltafterthelate1930s.OnemostimportantconceptualadditioncamefromAmericanbornpragmatism.Itsspecificinfluencescanbeseenclearlyinthepost-1940workofHempel,andevenCarnap;alsointheworkofAmericanborn,ErnestNagelandW.V.OQuine.But,untilthelate1950s,philosophersofscience,despitesignificantchangesintheprogramsandallowablemethods,philosophersofsciencewerestilltryingto5\nPeterMachamerworkoutandchangethingstofitintothegoalsandaspirationsleftbytheposi-tivists.Moreover,itoughttobenotedclearlythatvirtuallyallthemajormovesthatweretocomelaterandsochangethecharacterofphilosophyofsciencewerefirstinitiatedbytheoriginalpositiviststhemselves.Thiscontinuitywasnotnotedbythosewhobecamefamousduringthenextdecades;theysawthemselvesasrevolutionaryandstridentlyanti-positivistic.Bythelate1950s,philosophyofscienceincludedever-increasingcomplexmodels,muchlooserclaims,manynewphilosophicalmethodsandincreasinglyvaguephilosophicalgoals.NewParadigmsandScientificChange:Late1950sthroughthe1970sWhilethelogicalpositivists,andlaterthelogicalempiricists,wereattemptingtoexplicateandclarifythestructureofscience,anothergroupofscholarshadbeguntotransformanoldactivityintothemodernacademicdisciplineofhistoryofscience.Thegoalofmuchhistoryofsciencewastoexaminehistoricallysignifi-cantintellectualepisodesinscienceandtoarticulatetheseanalyticallyinawaythatexhibitedthecharacterofscienceatthatparticularhistoricalmomentandalsoshowedthatmomentfitintothedevelopmentandprogressofscience.Questionsforwhichanswersweresoughtwere,e.g.aboutthenatureofGalileo’sphysics,andwhatmadeitbothcontinuouswithandyetdifferentfromhismedievalpre-decessors.WasGalileothelastoftheMedievalsorthefirstofthemoderns?WhatwasthenatureofGalileo’smethodology,andhowdidheframeexplanations?WasGalileo’suseofmathematicsinphysicsreallyrevolutionary?DidGalileoreallyuseexperimentsinsomemodernsense?Ofcourse,itwasnotjustGalileowhowasofinterest,historiansofsciencestudiedalltheheroesofmodernscience,andreachedbackwardsintotheGreek,RomanandMedievalperiods.Theattemptwastodescribetheactualpracticeofscienceofthesethinkersandtodiscernwhatwaspeculiartothesehistoricalperiods.Whilehistoryofsciencecourseshadbeentaughtinanumberofplaces,bythemid-1960shistoryofsciencewasanestab-lishedenterprisewithprogramsanddepartmentsinUniversitiesthattrainedgrad-uatestudentsinthediscipline.Actually,theUniversityofWisconsinstarteditsdepartmentin1942,butWorldWarIIkeptitfrombeingstaffeduntil1947.HarvardoffereddegreesinHistoryofScience,buttheirdepartmentwasstartedonlyin1966.Inthelate1950s,philosopherstoobegantopaymoreattentiontoactualepisodesinscience,andbegantouseactualhistoricalandcontemporarycasestudiesasdatafortheirphilosophizing.Often,theyusedthesecasestopointtoflawsintheidealizedpositivisticmodels.Thesemodels,theysaid,didnotcapturetherealnatureofscience,initsever-changingcomplexity.Theobservationlan-guage,theyargued,couldnotbemeaningfullyindependentofthetheoreticallan-guagesincethetermsoftheobservationlanguageweretakenfromthescientific6\nABriefHistoricalIntroductiontothePhilosophyofSciencetheorytheywereusedtotest.Allobservationwastheory-laden.Yet,again,tryingtomodelallscientifictheoriesasaxiomaticsystemswasnotaworthwhilegoal.Obviously,scientifictheories,eveninphysics,didtheirjobofexplaininglongbeforetheseaxiomatizationsexisted.Infact,classicalmechanicswasnotaxioma-tizeduntil1949,butsurelyitwasaviabletheoryforcenturiesbeforethat.Further,itwasnotclearthatexplanationreliedondeduction,orevenonstatisticalinduc-tiveinferences.Thevariousattemptstoformulatethedeductive-nomologicalmodelintermsofnecessaryandsufficientconditionsfailednotonlybecausecounter-exampleswerefound,butalsobecauseexplanationseemedtobemorecomplexphenomenawhenonelookedatexamplesfromactualsciences.Eventheprincipleofverificationitselffailedtofindaprecise,orevenminimallyadequate,formulation.Allthemajorthesesofpositivismcameundercriticalattack.Butthestorywasalwaysthesame–sciencewasmuchmorecomplexthanthesketchesdrawnbythepositivists,andsotheconceptsofscience–explanation,confirmation,discovery–wereequallycomplexandneededtoberethoughtinwaysthatdidjusticetorealscience,bothhistoricalandcontemporary.Philosophersofsciencebegantoborrowmuchfrom,ortopracticethemselves,thehistoryofscienceinordertogainanunderstandingofscienceandtotrytoshowthedifferentformsofexplanationthatoccurredindifferenttimeperiodsandindifferentdisciplines.Debatesbegantospringupaboutthetheoryladenessofobservation,aboutthecontinuityofscientificchange,aboutshiftsinmeaningofkeyscientificcon-cepts,andaboutthechangingnatureofscientificmethod.Thesewerebothfedbyandfedintophilosophicallynewareasofinterest,areasthathadexistedbeforebutwhichhadbeenlittleattendedtobyphilosophers.Thesocialsciences,espe-ciallysociology,becameofconsiderableinterest,asdidevolutionarybiology.Thesefieldsprovidednotonlynewsciencestostudyandtobecontrastedwithphysics,butalsonewmodelsandmethodswhichwerethenborrowedtostudyscienceitself.Bytheearly1960s,astheresultoftheworkofThomasKuhn–andconcur-rentlyNorwoodRussellHansonandPaulFeyerabend–thebigphilosophicalquestionhadbecome:Werethererevolutionsinscience?Theproblemofscien-tificchange,asitwascalled,dealtwithissuesofcontinuityandchange.Kuhnhadarguedthatscienceinoneperiodischaracterizedbyasetofideasandpracticesthatconstituteaparadigm,andwhenproblemsoranomaliesbegintoaccumulateinagivenparadigm,thereoftenwasintroducedanewparadigmwhich,infactandinlogic,repudiatedtheoldandsupplantedit.(ThismodelwasnotunlikeGastonBachelard’sviewaboutcrisesinscienceleadingtorupture.)Thisconceptofarevolutionaryparadigmshiftimpliedthatscientificchangewasdiscontinuous,andthattheverymeaningofthesameterms,e.g.“mass”,changedfromtheiruseinoneparadigm(Newtonian)totheiruseinthenewparadigm(Einsteinian).Thiswascalledmeaningvariance.Onemethodologicalimplicationforphilosophersofscience,clearly,wasthattostudyscience,onehadtoconfineoneselftoahistoricallydominantparadigmandonecouldnotlookformore7\nPeterMachamergeneral,trans-paradigmaticmodelsthatcoveredallscience,exceptmaybefortheprocessofparadigmchangeitself.ManyphilosophersmadeajobofcriticizingKuhn’sparadigmsandhisprogram.Theybegantosearchforalternative,generalmodelsofscientificchangethatweremoreaccurateindescribingepisodesinscience,moresensitiveinanalyzingthepartsofsciencethatactuallyunderwentchange,andthatavoidedtheambiguitiesandunclaritiesofKuhn.So,talkofparadigmsgavewaytoresearchprogrammes(Lakatos)andthentoresearchtraditions(Laudan).Anothergroupofphiloso-phersbegantolookatexplanationsindifferentperiodsanddisciplinestofindoutiftherecouldbegeneralprinciplesthatcouldbesaidtoapplytoallexplana-tions,andthusundercutthemeaningvariancethesis.Yet,otherthinkers,includ-ingsomephilosophers,begantotakeKuhn’sclaimsaboutpracticesseriously,argued,ashadsomehistoriansofscienceearlier,thatsciencecouldnotbeexplainedsolelyintermsofitsconceptsandinternalstructure.Oneneeded,itwasheld,tounderstandthesocialandpoliticalsettingsinwhichsuchconceptsweredevelopedtounderstandhowtheybecameacceptableandwhytheywerethoughttobeexplanatory.Itshouldbenotedalsothatmanyofthemorepurelyphilosophicalmoves(includingthoseofHanson,KuhnandFeyerabend)hadbeeninfluencedbythenewdominanceofthemorecentralphilosophicalpracticesofordinarylanguagephilosophy,inspiredtoalargeextentbytheworkofthelaterWittgenstein.Thiswasstillphilosophywhichdealtwithanalyzinglanguage,butthelanguagewasnolongerjusttheformalalanguageoflogic,butthevariouslanguagegamesthecomprisedthevariousdisciplinesofhumanendeavor.Newdirectionsinlinguis-tics,spurredonbyChomskyandhisfollowers,hadalsochangedthewaypeople,includingphilosophers,lookedtheproblemofsyntax,semantics,andmeaning.Evenbasicepistemologyitselfbegantobequestioned.W.V.O.Quine(1969)announcedtoworldthatphilosophyofsciencewasphilosophyenough,andepis-temologyhadtobenaturalizedandwaspartofnaturalscience.Bythemid1960s,logicalpositivismandlogicalempiricismwasquiteoutoffashioninAnglo-Americanphilosophy.Atthistime,philosophicalanalysiswasthekeymodeofoperation,andthelogicismthathadprovidedtheguidingmodelfortheearlierphilosophicalwork,wassupersededbythestudyofrealscientificlanguageandbythecomplexitiesuncoveredinstudyingthehistoryofscience.DuringthisperiodIndianaUniversityfoundeditsDepartmentofHistoryandPhilosophyofScience(1960),whichwasfollowedadecadelaterbytheinstitutionofHPSattheUniversityofPittsburgh(1971).AdolphGrünbaumwaspresidentofthePhilosophyofScienceAssociationin1968.(TheprecedingPresidentwasErnestNagel.)ThePSAseemstohavewanedsomewhatduringthepostwaryears,butGrunbaumbeganthetraditionofbiennialmeetingsthatcontinuestothisday.Theresultforphilosophyofsciencewasinvigorating,exciting,anddevastat-ing.Generalcharacterizationsofscientificchangeprovedtobejustasintractableasearliergeneralmodelsofscientificexplanation.Thelaudabletendencytoexplorethenatureofsciencesotherthanphysicsandtoexamineindetailcasesfromthe8\nABriefHistoricalIntroductiontothePhilosophyofSciencehistoryofmanysciencesleftphilosopherswithouta“paradigm.”Therewaslittleconsensusaboutthenatureofexplanation,confirmation,theorytestingor,even,scientificchange.Yetscienceitself,morethanever,wasrecognizedbythepopu-laceatlarge,asa(ifnotthe)majorforceinhumanlife,andphilosophyofsciencehadbecomeadisciplinetostandalongsideofethics,epistemologyandmeta-physics.Buttherewasintellectualdisarrayoveritsnatureinthephilosophicalcommunityatlarge.Infact,somephilosophers,followingPaulFeyerabendtooktheintellectualconfusionasevidencethatsciencehadnoidentifiablestructure,andprofferedtheviewthatinscience,asinart,“anythinggoes.”Allevidenceandproofisjustrhetorical,andthosewiththebestrhetoric,orthemostpower(Foucault),becomethewinners,i.e.theirtheoriesbecametheonesaccepted.Luckily,thisepistemologicalrelativismwasnotfollowedbymanyphilosophers,though,asweshallseebelowinsomecontemporarycommunitiesthisideastillflourishes.Aconsensusdidemergeamongphilosophersofscience.Itwasnotaconsen-susthatdealtwiththeconceptsofscience,butratheraconsensusaboutthe“new”wayinwhichphilosophyofsciencemustbedone.Philosophersofsciencecouldnolongergetalongwithoutknowingscienceand/oritshistoryinconsiderabledepth.They,hereafter,wouldhavetoworkwithinscienceasactuallypracticed,andbeabletodiscoursewithpracticingscientistsaboutwhatwasgoingon.Thiswasamajorshiftinthenatureofphilosophy.Itistruethatmostoftheearlypositivistsweretrainedinscience,usuallyphysics.Butthisscientifictraininghadledthemtotrytomakephilosophyscientificaftertheimageoftheirownphilosophical–logicalmodelofscience.Incontrast,fromthe1950son,moreandmorephilosophershadbeentrainedbytheOxbridgeinspiredanalyticphiloso-phers,whoadheredtoWittgenstein’sdictumthatphilosophywasasuigenerisenterpriseandsohadnothingtodowith,andnothingtolearnfrom,science.Itisnowonderthatstudentsofphilosophysotrainedfoundithardtofigureoutwhatphilosophersofscienceshouldbedoing,andasaresultturnedeithertoscienceitselfortovariousformsofsociologyofscience,whichwastakentobelegitimatebecauseitwasasub-disciplineofanactualscience(sociology).Ironi-cally,despitethisconfusionaboutgoals,thereweremorephilosophersofsciencethaneverbefore.ContemporaryFociandFutureDirectionsTheturntoscienceitselfmeantthatphilosophersnotonlyhadtolearnscienceatafairlyhighlevel,butactuallyhadtobecapableofthinkingabout(atleastsome)scienceinallitsintricatedetail.Insomecasesphilosophersactuallyprac-ticedscience,usuallytheoreticalormathematical.Thisemphasisonthedetailsofscienceledvariouspractitionersintodoingthephilosophyofthespecialsciences.Currently,therearephilosophersofspace-time,whovariouslyspecializeinspecial9\nPeterMachamerorgeneralrelativitytheory,andphilosophersofquantumtheoryandquantumelectro-dynamics.Theredonotseemtobeanyphilosophersofplasmaphysics.Fairlyrecently,philosophyofchemistryhasbecomesomewhatofa“hot”researcharea.Philosophersofbiologycontinuetoworkonproblemsinevolutionarytheory,andfinallysomestudymolecularbiology,whichistheareainwhichalmostallbiologistswork.Workongeneticshasbeenaroundforsometime,butusuallyconnectedtoevolutionarybiology.Workonbiologicaldevelopmentisjuststart-ingandisseentobeincreasinglyimportant.Withtheexplosionofhealthcare,philosophyofmedicinealsobecameanewlyemergentandimportantfieldofresearch.Philosophyofthesocialsciencesstillcontinuestobeworkedupon,butsociologyastheparadigmaticsocialsciencehasbeenreplacedbyanthropology,exceptforthosepeoplewhoworkinsciencestudieswhichstilltreatssociologywithsomerespect.Philosophyofeconomics,especiallygametheoreticmodeling,isasomewhatpopularfieldtoday.Thisisinter-estingsincethegametheorymodelhadbeenstartedinthe1940s(vonNeumannandMorgenstern),andthenmostlydroppedin1960s,onlytoberevivedbybiol-ogistsusinggametheorytomodelevolutionandbyexperimentaleconomiststryingtofindanempiricalmodelforstudyingeconomicbehavior;thesetheninflu-encedphilosophersofeconomicswhorevivedgametheoryastoolforeconomicanalysis.Oneofthemostinnovativeandbiggestchangeshascomeintheareathatusedtobeknownasphilosophyofpsychology.Philosophyofpsychologyusedtobetiedtophilosophicalpsychology,tophilosophyofmind,andtobehaviorismandcognitivepsychology,especiallytoquestionsaboutthenatureofthemental.Inawayitstillis,butthe“cognitiverevolution”hitphilosophyquitehard.Cognitivestudiesnowincludesmanyofthoseworkinginexperimentalpsychology,neuro-science,linguistics,artificialintelligence,andphilosophers.Therearemanyaspectstothisre-definedfield,includingworkonproblemsofrepresentation,explana-toryreduction(usuallytoneuroscience),andevenconfirmation.Confirmationtheoryhasusedtechniquesfromartificialintelligencetore-establishamodernformofolderconfirmationfunctionsasdevelopedoriginallybyCarlHempel.Cognitiveproblemsolvinghasevenbeenusedbysometomodelthenatureofscienceitself.Anewdirectiontobeexploredaretherelationsofneurosciencetotraditionalphilosophicalproblems,sucharepresentationandknowledge.Historically,itisofnotethatcognitivesciencebegantoemergeinthemid-1950s,closetothetimethattheshiftawayfromlogicalpositivismbegan.Manyoftheintellectualforcesthatcausedthephilosophicalchangewerealsothecausesoftheemergingnewcognitiveparadigm,but,evenmoreimportantly,oneneedstonotetheimpactofthecomputeranditsrelatedwaysofactingandthinking.Thecomputerwasnotonlyatoolforcalculation,reasoningandprocessing,butalsobecamealsoamodelforthinkingabouthumanbeings,and,even,forthink-ingaboutscience.Oneinterestingimplicationofthisworkinthespecializedsciencesisthatmanyphilosophershaveclearlyrejectedanyformofascience/philosophydichotomy,10\nABriefHistoricalIntroductiontothePhilosophyofScienceandfinditquitecongenialtoconceiveofthemselvesas,atleastinpartoftheirwork,“theoretical”scientists.Theirgoalistoactuallymakeclarifyingand,sometimes,substantivechangesinthetheoriesandpracticesofthesciencestheystudy.Averydifferentcurrenttrendisexhibitedbythosephilosophersofsciencewhohavebecomepartofthesciencestudiesmovement,whichisdominatedbyhis-toriansandsociologists.Thismovementfocusesonthesocialdimensionsofscience(asopposedtothe“outmoded”intellectualaspects.)Inonesensethesocialstudyofsciencegrewoutofthedisputebetweeninternalistandexternalisthistoriansofscience,whichwasresolvedinfavoroftheexternalistswhenthedis-ciplineofhistoryitselfshiftedtoquantitativesocialhistoryandawayfromintel-lectualhistory.Fromanotherdirectiontheworkoftheepistemologicalrelativists,whomIreferredtoearlier,fitsnicelywiththerelativismthoughttocharacterizehistoricalperiodsandwithcultural(andethical)relativismthatisrampantinmuchofculturalanthropology.Essentiallytheviewhereisthatscienceisahumansocialactivitynotunlikeanyotherandsoissubjecttohistoricalandculturalcontin-gencies.Inordertostudysuchactivitieswemustlookatthesocio-culturalmilieuinwhichscientistsareraised,trained,andinwhichtheirworkoccurs.So,forexample,weshouldstudythelaboratoriesinwhichscientistsworkanddescribehowthesefunctiontoself-validateknowledgeclaimsissuedfromthelaboratory.Moreover,weshouldstudytheconventionsofdiscoursethatcomprisethe“rules”bywhichscientists’influenceandexertpoweroveroneanother.Forexample,intheseventeenthcenturytherewerecodesofconductthatEnglishgentleman“had”toadhereto,andtheseprovided(somehow)thestructureofthedebatesandexperimentalpracticesforthemembersoftheRoyalSociety.Aconcomitantbeliefheldbymostofthesciencestudiesgroup,thoughitisnotnecessarilyimpliedbytheirposition,istherelativismofdifferentorcompetingclaims.Thatis,itisahistorical,culturaland/orepistemicpeculiaritythatagivengroupofscientistsholdstheviewsthattheydo.Fromthis,itispresumedtofollowthatnooneviewisanybetterthananyother.Youarewhatyourtimeandculturehavemadeyou,andthat’sanendtoit.Suchclaimsforrelativismoftenleadpeopletoworryaboutvaluesandtheirstatus,forculturalrelativismiscloselytiedwithethicalrelativism.Butquestionsabouttherelationsbetweenvaluesandsciencealsoarosefromevenmorepressingsources.Perhapsthemostimportantandinfluentialquestionsaboutvaluesarosefrommedicine.Thepracticalproblemsofmedicalethicsbegantomakethemselvesfeltduetochangesinthepracticeofmedicineandinmedicaltechnology.Allofasudden,therewereurgentquestionsconcerninglifeanddeath,physician-patientrelations,andinformedconsentthathadtobeansweredinpragmaticallyexpeditiousways.Thiscoincidedwith,andwasinpartresponsi-blefor,ashiftinphilosophicalethicsawayfromthetheoretical,frommeta-ethics,towardsthepractical.Philosophers,ofethicsandofscience,becameinvolvedinconsultingaboutthedaytodaydecisionsinhospitalsandaboutthere-writingofhealthcarepolicies.Philosophersofscienceareespeciallyusefulherebecausethey11\nPeterMachameractuallyknowsomeofthesciencethatisinvolvedinmakinginformeddecisions,andtheyhaveoftenstudiedvariousaspectsofdecisionmakingandtheuseofevidence.Thispracticalsideofethicsinthescienceshasotherdimensionstoo.Codesofethicsforthevariousprofessions,e.g.engineers,havebecome“hot”topicsforphilosophicalresearch.Oneofthemoreinterestingandimportantnewfieldsthatphilosophersofsciencedealingwithvaluesareinvolvedinhavetodowithissuesconcerninghowscienceisusedtobaseregulatorydecisions,e.g.concerningleadordioxinsorglobalwarming.Also,thereisworkbeingdoneofthevaluesthatareimplicitlyorexplicitlyinvolvedintheactualdoingofscientificresearch.Forexample,whatvaluesareassumedinchoosingacertaintypeofexperimentalpar-adigm,or,moregenerally,whatvaluesareassumedingivingmoremoneytoAIDSresearchratherthanmalaria(whichisbackwithusinabigway.)Thefeministmovementofthelate1960s,alsobroughtmanyvaluequestionstothefore,andsomeexcellentworkhasbeendoneonhowgenderassumptionshaveinfluencedscientificpractice.Thispracticalsideofthe“new”philosophyofscience,Ibelieve,derivesfromthesameneedforrelevancethatpushedotherthinkersintodealingwiththespecialsciences.Thereisan,oftenunacknowledged,awarenessthatphilosophymustbecomeimportantinwaysthatgobeyondthehallowedhallsofacademe.Thelogicalpositivists,thoughsomeofthemhadstudiedphysics,hadlittleinfluenceonthepracticeofphysics,thoughtheircriteriaforanidealscienceandtheirmodelsforexplanationsdidhavesubstantialinfluenceonthesocialsciencesastheytriedtomodelthemselvesonphysics,i.e.on“hard”science.Theanalyticphilosophersofthemid-1950sonwardshadlittleinfluenceoutsideoftheUniversitiesinwhichtheytaught.Theywerecontenttodefendtheirprofessionalturfasbeingathinguntoitselfandinsomewayswerequiteproudtobe“irrelevant”totheconcernsofordinarylife,despitetheironicemphasisonordinarylanguage.Bythe1980s,thisintellectualisolationismhadbeguntobreakdown,philosophers,andespe-ciallyphilosophersofscience,hadtogetinvolvedintherealworld,theworldofscience.Iendthislittleessaybynotingthattheoldquestionsandtopicsthathadbeenraisedbythelogicalpositivists,andeveninprevious2000years,havenotdisap-peared.Philosophersofsciencestillpuzzleoverwhatmakesagoodexplanation,whatkindofevidenceprovideswhatkindofconfirmationfortheory,andwhatisthedifferencebetweenscienceandpseudo-science.Thesearetheperennialques-tionsofphilosophyofscience.Today,westilltrytoanswertheminspecificwaysthatwillhaveeffectsonscienceandthelargerworld.Philosophersofsciencehavebeeninstrumentalinshowingthenon-scientificstatusofcreationismandsomeversionsofsociobiologyand,now,evolutionarypsychology.Theyhavediscussedfruitfullytheroleofscientificevidenceinmakingdecisionsaboutnuclearenergyplantsoraboutlevelsoftoxicityinourenvironment.Theyhaveaskedhardques-tionsabouthowtodiscovermechanismssuchthatfindingthemallowsustounderstandhowsystemsofmolecularbiologyorneurosciencework.Andthey12\nABriefHistoricalIntroductiontothePhilosophyofSciencehavecontinuedtoelucidateandelaboratetheunclaritiesandconfusionsinthespecialsciences.Ofcourse,thereismuchlefttodo.Therearealwaysmorepuzzlesthanpeople,moreproblemsthansolutions.Thetwentiethcenturysawmanychangesinwhataretakentobetheimportantpuzzlesandproblems,butevenmoreimportantly,thesesameyearshaveseenchangesinhowpeopleneedtobetrainedtoapproachproblemsandinwhatsolutionstoproblemsmustlooklike.Maybethispastcenturyhasonlytaughtusthattherearenosimpleanswerstotrulycomplexques-tions.Yet,withthisrealizationcomestheawarenessthattheremustbepragmaticanswersprovidedinatimelyandefficaciousmanner.Decisionsmustbemade,and,hopefully,philosophyofsciencecanhelpustoseehowtheymaybemadeinbetterways.Note*ThankstoAdolphGrünbaum,NorettaKoertge,DavidLindberg,NickMaxwell,WesleySalmonandJohnWorrallforinformationregardingthehistoryofphilosophyofscienceandfoundingofinstitutionsanddepartments.ManythankstoMerrileeSalmon,PaoloParrini,TedMcGuireandAristidesBaltasfortheirhelpandcommentsonanearlierdraftofthisessay.AnevenearlierdraftwasgivenasalectureatTheCatholicUniver-sityofAmerica,andIthankthosepresentwhogavemegoodfeedback,especiallyBillWallace.Appendix:SelectedRelevantPhilosophicalandScientificPublications(1895–1969),theirdates,andafewevents1895JosefBreuerandSigmundFreud,StudiesinHysteria1897LeonBrunschvig,LaModalitéduJudgment1899DavidHilbert,DieGrundlagenderGeometrieMaxPlankderivesblackbodylawSigmundFreud,TheInterpretationofDreams1901ErnstMach,DieMechanikinihrerEntwicklung,4thedn.1902LorentzprovesMaxwell’sequationswereinvariantundertransformationsHenriPoincaré,LaScienceetl’Hypothèse1903BertrandRussell,PrinciplesofMathematics1905ErnstMach,ErkenntnisundIrrtum,BertrandRussell,“OnDenoting”MindAlbertEinstein,“ZurElektrodynamikbewegterKoeper”AnnalenderPhysik13\nPeterMachamerGeneralstrikeandrevolutioninRussiaSigmundFreud,“ThreeessaysontheTheoryofSexuality”1906PierreDuhem,LaTheoriePhysique.SonObjet.SaStructureAlbertEinsteinandPaulEhrenfest,hvindivisibleunitofenergy1907HansHahn,OttoNeurathandPhilippFrankinVienna1908ErnstZermelo,“UntersuchungenuberdieGrundlagenderMengenlehreI”MathematischeAnnalenEmileMeyerson,IdentiteetRealite1910–13RussellandA.N.Whitehead,PrincipiaMathematica1911ArthurSommerfeldintroducesphase-integralformofquantumlawEinstein,“UberdenEinflussderSchwerkraftaufdieAusbreitungdesLichtes”AnnalenderPhysikSolvayCongress,Brussels1913EdmundHusserl,IdeenzuEinerreinenPhanomenologieundPhanomenologischenPhilosophie,vol.1J.B.Watson,“PsychologyastheBehavioristseesit”Psych.Rev.NielsBohr,publishesontheatom(Phil.Mag.)1914Russell,OurKnowledgeoftheExternalWorldasaFieldforScientificMethodinPhilosophyWWI(till1918):FranzFerdinandassassinatedEasterRisinginIrelandRussianRevolution1915SommerfeldexplainsfinestructureofspectrallinesMaxPlankestimatesvalueforh(Phys.Rev.)1916Einstein“DieGrundlagederallgemeinenRelativitatstheorie”AnnalenderPhysik1917RobertMillikan,TheElectron1918–19BertrandRussell,“PhilosophyofLogicalAtomism”,MonistMoritzSchlick,AllgemeineErkenntnislehreArthurEddingtonobserveseclipseconfirminggeneralrelativityNielsBohr’s“PrincipleofCorrespondence”1920N.R.Campbell,Physics,theElements1921LudwigWittgenstein,TractatusLogico-Philosophicus[Logische-PhilosophischeAbhandlung]Englishversion1922J.M.Keynes,ATreatiseonProbability1922MoritzSchlicktoViennaasprofessorofinductivesciencesLeonBrunschvig,L’ExpérienceHumaineelaCausalitéPhysique1923DavidHilbert,“DieLogischeGrundlagenderMathematik”MathematischeAnnalenHeleneMetzger.LesDoctrinesChimiquesDébutduXVIIèmeàlaFinduXVIIIèmeSiècle1925ErwinSchrödingerdevelopswavemechanics1926RudolfCarnaptoViennaasinstructorinphilosophyNielsBohrshowsequivalenceofmatrixandwavemechanics14\nABriefHistoricalIntroductiontothePhilosophyofScience1927WernerHeisenbergformulatesindeterminacyprinciple1928VereinErnstMach(ErnstMachsociety)foundedRudolfCarnap,DerLogischeAufbauderWeltDavidHilbert,GrundzugederTheoretischeLogik(3rdedn.1949byHilbertandAckermann)1927P.W.Bridgman,TheLogicofModernPhysicsCharlesLindbergmakesfirstsolotransatlanticflight1929Carnap,HahnandNeurath,WissenschaftlicheWeltauffassung,DerWienerKrisErnstMachSocietyCongressheldinPragueWallStreetCrash1930Erkenntnisfounded(till1940)Gödel’sCompletenessTheorem1931CarnaptoPrague,FeigltoIowaGödel’sIncompletenessTheorem1932E.A.Burtt,TheMetaphysicalFoundationsofModernScience(revisededn.)1933HitlerappointedChancellor1934Carnap,LogischeSyntaxderSpracheM.R.CohenandE.Nagel,IntroductiontoLogicandScientificMethodGastonBachelard,LeNouvelEspritScientifiquePhilosophyofSciencefirstpublishedHitlerbecomesFührerofGermany(till1945)1935KarlPopper,LogikderForschung(English,1959)KurtKoffka,PrinciplesofGestaltPsychology1936CarnapappointedatChicagoAlfredTarski“DerWahrheitsbegriffindenFormalisiertenSprachen”StudiaPhilosophicaCarnap,“TestabilityandMeaning”PhilosophyofScience(and1937)A.J.Ayer,Language,TruthandLogicSpanishCivilWar(to1939)1938ErnstMachSocietyformallydissolved(publicationsofthesocietyforbiddeninGermany)WaismannandNeurathtoEnglandZilselandKaufmanntoUSA(MengerandGödelalreadytheretoo)ErkenntnismovedtoTheHague,andrenamedJournalofUnifiedScienceClaudeShannon,“ASymbolicAnalysisofRelayandSwitchingCircuits”Trans.ofAm.Inst.ofElectricalEngineersAlexandreKoyre,EtudesGalileennesB.F.Skinner,TheBehaviorofOrganismsHansReichenbach,ExperienceandPredictionWWII(to1945)15\nPeterMachamer1940JournalofUnifiedSciencediscontinuedCarlG.Hempel“StudiesintheLogicofConfirmationI&II”,MindClarkL.Hull,ThePrinciplesofBehavior1947Carnap,MeaningandNecessityJ.vonNeumannandO.Morgenstern,TheoryofGamesandEco-nomicBehavior1948C.G.HempelandPaulOppenheim,“StudiesintheLogicofExplanation”,PhilosophyofScienceJ.H.Woodger,BiologicalPrinciplesNorbertWiener,Cybernetics1949H.FeiglandW.Sellars(eds.),ReadingsinPhilosophicalAnalysisHerbertButterfield,TheOriginsofModernScience,1300–1800AnnelieseMaier,DieVorlauferGalileisim14JahrhundertHansReichenbach,TheTheoryofProbability1951Reichenbach,TheRiseofScientificPhilosophy1952Carnap,LogicalFoundationsofProbabilityGeorgesCanguilhem,LaConnaissancedelaVie1953Wittgenstein,PhilosophicalInvestigations(PhilosophischeUnter-suchungen)H.FeiglandM.Brodbeck(eds.),ReadingsinPhilosophyofScienceW.V.O.Quine,FromaLogicalPointofViewStephenToulmin,PhilosophyofScienceR.B.Braithwaite,ScientificExplanation1954GustavBergmann,TheMetaphysicsofLogicalPositivismA.R.Hall,TheScientificRevolution,1500–1800NelsonGoodman,Fact,Fiction,andForecastLeonardJ.Savage,TheFoundationsofStatistics1955CanguilhemsucceedsGastonBachelardasProfessorofPhilosophyattheSorbonneandDirecteurofInstitutd’HistoiredesSciencesetdesTechniques1956ErnestNagel,LogicwithoutMetaphysicsJ.O.Urmson,PhilosophicalAnalysisHerbertFeiglandMichaelScriven,MinnesotaStudiesinthePhilosophyofScience,Vol.11958NorwoodRussellHanson,PatternsofDiscoveryMarshallClagett,TheScienceofMechanicsintheMiddleAgesE.H.Gombrich,ArtandIllusion:AStudyinthePsychologyofPic-torialRepresentationM.Clagett(ed.),CriticalProblemsintheHistoryofSciencePaulFeyerabend,“AnAttemptataRealisticInterpretationofExperience”Proc.AristotelianSociety1959MortonBeckner,TheBiologicalWayofThought16\nABriefHistoricalIntroductiontothePhilosophyofScience1960W.V.O.Quine,WordandObject1961ErnestNagel,TheStructureofScience1962ThomasKuhn,TheStructureofScientificRevolutionsMaryHesse,ModelsandAnalogiesinScienceIsraelScheffler,TheAnatomyofScientificInquiryRobertG.Colodny,FrontiersofScienceandPhilosophy(firstvolumeofthePittsburghseries)1965Hempel,AspectsofScientificExplanationPaulFeyerabend,“ProblemsofEmpiricism”inR.G.Colodny(ed.),BeyondtheEdgeofCertaintyMichelFoucault,LesMotsetlesChoses1968ImreLakatos,“CriticismandtheMethodologyofScientificResearchProgrammes”W.V.O.Quine,“EpistemologyNaturalized”lecturedelivered(published1969)1969Foucault,L’ArcheolgieduSavoirFurtherreadingContemporarypresentationsofthebasicissuesinphilosophyofscienceMerrileeSalmon,etal.,PhilosophyofScience,(bytheDepartmentofHistory&PhilosophyofScience,UniversityofPittsburgh),Prentice-Hall,1991AcollectionofreadingswhichcoverthefieldofphilosophyofscienceBaruchBrodyandRichardGrandy(eds.),ReadingsinthePhilosophyofScience,2ndedn,PrenticeHall,1989HistoricaloverviewsofthehistoryofpositivismJ.AlbertoCoffa,TheSemanticTraditionfromKanttoCarnap,Cambridge:CUP,1991MichaelFriedman,ReconsideringLogicalPositivism,CambridgeCUP,1999FrederickSuppe,CriticalIntroduction,toTheStructureofScientificTheories,2ndedn,Urbane,Ill.:UniversityofIllinoisPress,1977Asystematictreatmentofthemainpartsofthelogicalpositivist/empiricistprogram:QuitedifficultinpartsIsraelScheffler,TheAnatomyofInquiry,NewYork:BorzoiBooks,1964Areviewofthecriticsofpositivist/empricistprogram.IsraelScheffler,ScienceandSubjectivity,Indianapolis.BobbsMerrill,196717\nChapter2PhilosophyofScience:ClassicDebates,StandardProblems,FutureProspectsJohnWorrallTheBackgroundImmanuelKant’scelebratedinvestigationofhumanknowledgestartedfromtheassumptionthatwehaveachievedrock-solid,indubitableknowledge–ingeometrythroughEuclidandinphysicsthroughNewton–andfromtheques-tionofhowthiswaspossible(especiallyinviewofHume’sdemonstrationoftheinvalidityofinductiveinference).Contemporaryphilosophyofscienceisarichandmulti-facetedenterpriseandsoanyonewayofviewingitwillinevitablyleaveoutmuchofimportanceandinterest.Nonetheless,manyoftheclassicdebatesandareasofcurrentconcerncanbeintroducedbyinvestigatinghowKant’squestionsrequiremodificationinthelightofthedevelopmentofsciencesincehistimeandbyinvestigatingtheattemptsmadetoanswerthosemodifiedquestions.Tworadical–apparently“revolutionary”–changesoffundamentaltheoryoccurredintheearlytwentiethcentury,thoseassociatedwiththetheoryofrela-tivityandwithquantumtheory.TheformerhadthemoredirecteffectonKant’spresuppositionsandquestions.If,atanyrate,wethinkofgeometryasasyntheticdescriptionofthefundamentalstructureofspace,thenEinstein’srevolutioninvolvedtherejectionofEuclideangeometryinfavoroftheRiemannianversionofnon-Euclideangeometry.Instead,forexample,oftwostraightlinesthatareparallelbeingextendableindefinitelywithoutintersecting,thenewgeometrystatesthatanytwostraightlines(geodesics)eventuallyintersect.Farfrombeingcer-tainlytrue,Euclideangeometry(atleastasa“physicalgeometry”)is–itseems–noteventrue.Similarly,althoughNewton’stheory(ofmechanicsplusuniversalgravitation)continuestobeempiricallyadequateoverawiderangeofphenom-ena(basicallymotionsinvolvingvelocitiessmallcomparedtothatoflight),itsfun-damentalclaimsaboutthestructureoftheuniverse–thatspaceisinfinite,thatgravitationactsat-a-distance,thattimeisabsolutesothattwoeventssimulta-neousinonereferenceframearesimultaneousinall–areentirelyrejectedby18\nClassicDebates,StandardProblems,FutureProspectsrelativitytheory.Again,farfrombeingcertainlytrue,Newtonianphysicsis,itseems,noteventrue.Indeed,giventhatrelativitytheorydeniesactionatadis-tance,suggeststhatspaceisfinite(thoughunbounded),andentailsthattwoeventsthataresimultaneousinoneframeofreferencewillnotbesimultaneousinanotherframethatmovesrelativelytothefirst,itisdifficultformanytoseeintuitivelyhowNewton’stheorycouldcountaseven“closetothetruth”(supposingforsakeofargumentthatEinstein’stheorywerethetruth).ThesedevelopmentstransformKant’squestionintoadilemma.Istheresomewayofinterpreting(orreinterpreting?)scientifictheoriessothattheapparentlyradicalnatureoftherevolutionaryshiftfromclassicaltorelativisticphysicsbecomesjustthat–merelyapparent?Ifso,thenitmightstillbepossibletoarguethatsciencewhenproperlyunderstood,delivers,ifnotoutrightcertainty,thensomecloseapproximationtoit.Ifnot,ifwesimplyhavetoacceptthatscientificdevel-opmenthasinvolvedrevolutionarychangeatthemostfundamentaltheoreticallevel,thenwepresumablycannotreasonablyruleoutthepossibilityofstillfurtherrevolutionsinthelightofwhichourcurrenttheorieswillseemjustasfalseasNew-toniantheorynowseemstous.Andinthatcase,thequestionbecomeswhatmakessciencespecialatallfromtheepistemicpointofview?WhyisScienceSpecialfromtheEpistemicPointofView?Let’sbeginonthesecondhornofthisdilemma–concedingforthesakeofargumentthattheapparentlyrevolutionaryshiftsarereal.Inthatcase,thereisnoprospectofcontinuingtoholdthatscientifictheoriesareprovedorestablishedbyunquestionedempiricaldata.Whatisit,then,thatmakesscienceandthemethodsofsciencespecialfromanepistemicpointofview?(Thereareofcoursesomethinkers–mostlysociologistsofscience–whowouldrejectthisquestion,andinsistthattheconclusionweoughttodrawfromtheexistenceofscientificrevo-lutionsisthatscienceisjustonehumansystemofbeliefsamongstothers(suchastheAzandesystemofmagic)withnojustifiedclaimtoanyspecialepistemicstatus.Butthestaggeringpredictivesuccessofourtheoriesin“mature”scienceissostronglyatoddswiththisviewthatitisdifficulttotakeseriously.)DemarcationandfalsifiabilityThequestionofwhatmakessciencespecialisoftencalled“thedemarcationproblem.”Onecelebratedanswer–directlymotivatedbytheEinsteinianrevolu-tion–isKarlPopper’sfalsifiabilitycriterion:scienceisspecialbecause,eventhoughitstheoriesarenotprovablefromevidentialstatements,theyarerefutablebysuchstatements.TheEinsteinianrevolutionis–Popper(1959)suggested–adirectvindicationofthisview(andindeedthatrevolutionwasamajormotivationfor19\nJohnWorralltheview):the“revolution”wasagreatstepforwardbecauseitinvolvedtherefu-tationofahighlyfalsifiable,buthithertounfalsifiedtheory(Newton’s),anditsreplacementbyastillmorefalsifiable–butnotyetfalsified–theory(Einstein’s).Incontrast,non-scientificclaims–metaphysicalclaims,suchasthatGodexists,orclaimsthatPoppercategorizedaspseudoscientific,suchastheclaimsofastrologyorofFreudianpsychoanalysis,are(allegedly)entirelyunfalsifiable:nopossibleevidentialstatementcouldcontradictanysuchclaimandhenceestablishitsfalsity.Scienceisspecialbecauseatleastwecanknowwhenwearewrong.Itisnow(almost)universallyacceptedthatPopper’saccountfails.Oneissue–raisedrightatthebeginningbyReichenbach,forexample–waswhethertheproblemofinduction,and,inparticular,theso-called“pragmaticproblem,”caneverbesolvedinapurelyfalsificationistway.Itseemspositivelyirrationalnottobaseourtechnologicalinterventions–inbuildingsaybridgesoraeroplanes–onthebestavailablescientifictheories.Butwouldthisjudgmentbeunderwrittensimplybythereportthatthosebestavailabletheoriesaresofarunrefuted–thatis,unrefutedintestsalreadyperformed?Wesurelyalsoneedsomesortofreasontothinkthatthepasttest-recordofthosetheoriesreflectstheiroveralltruth-likenessandthereforeatleasttheirlikelyperformanceinfuturetests.(Itis,afterall,perfectlypossiblegivensimplydeductiveconsiderationsthattheoriesthathaveperformedrelativelybadlyinthepastwill,inthefuture,performbetterthanonesthathaveperformedrelativelywellsofar.)Itseemsthatweneed,then,somesortoflinkbetweenpastperformanceintestsandoveralltruth(oratleastoverallempiricaladequacy).ButthisisexactlythesortofinductiveassumptionthatwasanathematoPopper.Difficultieswithfalsifiability–theDuhemproblemMoreover,fundamentalissuesalsoariseabouttheassumedfalsifiabilityofscien-tifictheories.ThemostdirectproblemherehadalreadyinfactbeenexplainedinimpressivedetailsomethirtyyearsbeforePopper’sworkbyPierreDuhem(1906).Scientistsoftentalkabouttestingscientifictheories,suchasNewton’stheory(ofmechanicsandgravitation)bycomparingthattheory’spredictions–about,say,planetarypositions–withthe“data.”ButDuhempointedoutthatifthedeductivestructureofanysuchtestisanalysedcarefullythenfurtherpremises–oftencalled“auxiliaryassumptions”–alwaysturnouttobenecessaryifthedeductionoftheobservationstatementsatissueisreallytobevalid.Nothingthatwearelikelytocharacterizeasa“singletheory”inscience–Newton’stheoryorMaxwell’stheoryofelectromagnetismorquantumtheoryorwhatever–hasanyempiricalconsequencewhenconsidered“inisolation,”furtherauxiliaryassumptionsarealwaysneeded.Forexample,noconsequencesaboutplanetarypositionsatsomegiventimetfollowfromNewton’stheory(ofmechanicsplusuniversalgravitation)andnordotheyfollowfromNewton’stheoryplus“initial20\nClassicDebates,StandardProblems,FutureProspectsconditions”aboutthepositionsofthoseplanetsatsomeearliertimet¢.Whatisneeded,inaddition,isawholesetofotherassumptionsthatareclearlythemselvestheoreticalratherthaninanysense“directlygiven”byobservation–thissetincludesassumptions,forexample,aboutthemassoftheplanetconcernedandthenumberandmassesoftheotherbodiesinthesolarsystem,nottomentionassumptionsabouthowlighttravelsbetweentheplanetconcernedandourtele-scope.(So,inparticular,a–clearlytheoretical–assumptionisneededabouttheextenttowhichlightisrefractedinpassingfrom“emptyspace”intotheearth’satmosphere.)Thisapparentlyminorlogicalpointhasmajorconsequences.SupposewehavesomeobservationsentenceOandarehappytosaythatwecandecidethetruthvalueofOonthebasisofobservationorexperiment.IfcontrarytoDuhem,wecouldinvariablytakeany“single”scientifictheoryTanddeducearangeofsuchresultsOfromit,then,justasPopperemphasized,ifsomesuchOwereestablishedasfalseonthebasisofobservation,thenitwouldfollowthatTmustbefalseaswell.(Theso-called“principleofretransmissionoffalsity”saysthatifsomepremise,inthiscasethetheoryT,entailsdeductivelysomeconclu-sion,inthiscasetheobservationsentenceO,thenifthatconclusionisfalse,soalsomustbethepremise.)Infact,however,asDuhem’sanalysisshowed,thedeductivestructureofanyrealtestofanyrealscientifictheoryalwaysinvolvesauxiliaryassumptions–oftenquitealargesetofthem.ButifwecaninferOonlyfromaconjunctionofsentencesT&A1&...&An,thenshouldwedecide,onthebasisofobservationorexperiment,thatOisfalse,allthatwecaninferisthatatleastoneofthesetoftheoreticalclaimsT,A1,...,Anisalsofalse.(Theprincipleofretransmissionoffalsitywhenappliedtodeductiveinferenceswithmorethanonepremisedoesnot,ofcourse,saythatifthevalidlydeducedcon-clusionisfalse,thensoareallthepremises,butonlythatnotallthepremisescanbetrue–atleastonemustbefalse.)Inparticular,wecannotinferthatitisTitselfthatisfalse.Duhem’sanalysisdoesnotshowthatobservationresultsneversupplygoodgroundsforholdingthatsome“central”theoryTisfalse;butitdoesshowthattheseareneverconclusiveandthatsomethingmorethanfalsificationmustbeinvolved.Theremight,forexample,beindependentgroundsforthinkingthattheauxiliariesA1,...,AnaremorelikelytobetruethanisT.Ifso,thenthefactthatthefalsityofOshowsthatnotallofT,A1,...,AncanbetruewouldsupplygoodgroundsforrejectingT.Or,andthisiswhatgenerallyinfacthappensincasesofscientifictheory-change,whileatheoreticalsystembuiltaroundtheoryTcanbemadetoyieldOonlybyadjustingsomeoftheauxiliariesAiexactlywiththerequirementinmindthatObeentailed,analternativesystembuiltaroundsomealternativetheoryT¢involvingnonadhocauxiliariesisindependentlyempiricallyconfirmed(thatisturnsouttopredictsomefurtherempiricalresultO¢whichisthenconfirmed).Eithersuggestion,however,bringsinideasofconfirmationthatareforeigntoPopper’sscheme.21\nJohnWorrallConfirmation–theattemptatan“objective”accountWhynotthengostraightforconfirmationasthesolutiontotheproblemofwhatmakessciencespecial?TheEinsteinianrevolutionwasaconstructiveproofofthefact–whichinanyeventoughtinretrospecttohavebeenobvious–thatwecanneverconclusivelyprovegeneralexplanatoryscientifictheoriesonthebasisofobservationorexperiment;Duhem’sanalysisshowedthatwecanneverconclu-sivelyfalsifythemeither.Butperhapswecannonethelessconfirmscientifictheo-riesonthebasisofempiricalresults.Perhapswhatdistinguishesabetterscientifictheoryfromagoodoneisthattheformerisbetterconfirmedbytheevidence;perhapswhatexplains“revolutionary”shiftsinscientifictheory–forexample,thatfromNewtontoEinstein–isexactlythat,giventheevidencethathadaccumu-lated,Einstein’stheorywasthebetterconfirmedtheory;andfinallyperhapswhatdistinguishesscientifictheoriesfromnon-scientificones(whethermetaphysicalorpseudoscientific)isthatthelatterarenotevencapableofempiricalconfirmation.Theclaimthat“Godexists”failstobescientific,notbecauseitcannotbeprovedfromevidence,notbecauseitcanneverbefalsifiedbyevidence,butbecauseitcanneverbeconfirmed(andthereforecanneverbedisconfirmedeither)byanypossible–intersubjectivelyagreed–evidence.Asageneralframeworksuggestion,thisanswerstillseemstomeviable(indeedperhapswhenconsideredinaverygeneralway,itistheonlyviableanswer).Theproblemhasbeenthatofgivingamorepreciseaccountofthenotionof“confir-mation”–amorepreciseaccountthatdeliversalltheabovejudgmentsandthatseemsbothcoherentandphilosophicallydefensible.Anumberof“non-standard”approacheshavebeentried(perhapsmostnotablyClarkGlymour’s(1980,1987)“bootstrapping”approach),whichhaverunintotheirowndifficulties.Butmostattemptstoputfleshontotheskeletonoftheconfirmationapproachhave,unsurprisingly,involvedthenotionofprobability.Whatconfirmationdelivers,itissuggested,isgreaterprobabilityofbeingtrue:thechangefromNewtontoEinsteinwasthechangefromonereasonablyprob-abletheory(ofcourseprobableinthelightoftheevidence)toanotherthatisstillmoreprobableinthelightoftheevidence;theory-changeinsciencecanbeexplainedasrationalbecauseinthelightofaccumulatingevidencetherelativeprobabilitiesofrivaltheoriesnaturallychange;andfinally,non-scientifictheoriesarethosewhoseprobabilitycannotbeaffectedonewayortheotherbytheevidence.Althoughthereareintimationsoftheapproachmuchearlierinthehistoryofthought,recentdiscussionsofthisideareallystemfromCarnap’s(1950)ground-breakingwork.Hisinitialideawastoproduceanentirelyobjectiveversionoftheaccountbydevelopingaprobabilistic“inductivelogic”asageneralizationofdeductivelogic.Thecrucialnotioninallaccountsistheprobabilityofsometheorygiven(orconditionalon)someevidence.Carnap’soriginalideawasthatsuchconditionalprobabilitiesmeasuredegreesofpartialentailment–toclaimthatthe22\nClassicDebates,StandardProblems,FutureProspectsprobabilitythatEinstein’stheoryistrue,giventheevidenceis,say,0.8meansthattheevidenceentailsEinstein’stheorytodegree0.8.(Herefull–deductive–entailmentwouldofcoursebedegree1,thatis,theprobabilityofAgivenBis1wheneverBdeductivelyentailsA.)Thisideamightthenbeusedtosupplytherationaleforscientificrevolutionsifitcouldbeshownthatthenewertheory–sayEinstein’stheory–hashigherprobabilityinthelightoftheevidenceavailableatthetimeofthe“revolution”thanhadtheearliertheory–inthiscaseNewton’s.Intuitively,althoughtheevidenceofcourseentailsneithertheory,itcomesclosertoentailingEinstein’stheorythantoentailingNewton’s.Thisidea,forallitssimplicityandappeal,fails.Thebasicproblemisessentiallythesameastheonethatafflictstheso-calledclassicalaccountofprobability–whichdefinestheprobabilityofsomeeventAastheratioofthenumberof“equallypossible”casesinwhichAholdstothenumberofalltheequallypossi-blecases.(Intuitivelytheprobabilitythatafairdicewhenrolledwillfinishwith1“6”upis/6becausetherearesixequallypossiblecasesandjustoneinwhichtheevent“6up”occurs;theprobabilitythatanevennumberedfacewillbeupper-31mostinthesamesituationis/6,i.e./2sincethereareagainsixequallypossibleoutcomesandinthreeofthemtheevent“evennumberuppermost”isinstanti-ated.)Thedifficultyconcernsthenotionofpartitioningthesetofallthepossibleeventsinsomeexperimentintothe“equallypossible”ones.Ingeneral,therearedifferentwaysofdoingthisanditseemsimpossibletoarguethatonlyonesuchwayis“correct.”Andyetwithadifferentpartitionoftheeventsintoequallypossiblecaseswearriveatdifferentprobabilities.Althoughthisapproachandthisdifficultyforitwereoriginallydevelopedinthecontextofprobabilitiesofvariousevents,anentirelyanalogousapproach,andanentirelyanalogousdifficulty,canbedevelopedwhenthinking,asCarnapdid,oftheprobabilitythataparticularsentenceistrue.Suppose,forexample,weareinterestedinhypothesesaboutthecontentsofanurnknowntocontain,say,50balls,eachofwhichiseitherblackorwhitebutinanunknownproportion;supposefurtherthatweare(forsomereason)unabletobreakopentheurnandourevi-denceisrestrictedtodrawingsomenumberofballsfromtheurn,withreplace-ment,andnotingtheircolours.Whatconstitutetheequallylikelycaseshere?Allpossibleproportionsofblacktowhiteballs–all50black,49black1white,48black2white,etc.?Oraretheequallylikelycasesspecifiedbyassumingthateachindividualballhasthesamechanceofbeingwhiteasofbeingblack?Itseemsdifficultindeedtoarguethatoneofthesenotionsisthe“correct”one.Butitisnosurprisethatthetwoyieldquitedifferentprobabilitiesforvarioushypotheses.Supposeweareinterestedinthehypothesisthatexactlyhalfoftheballsarewhiteandourevidenceisthatwehavedrawn10balls,6ofwhicharewhite.Theinduc-tivesupportgiventothathypothesisbythatevidence,thedegreetowhichtheevidencepartiallyentailsthehypothesis,willbequitedifferentdependingonwhichofthesetwowayswesliceupthe“equalpossibilities”;andthismakesitverydifficulttoclaimthatthereisoneobjectiveprobabilityforthehypothesisinthelightoftheevidence.23\nJohnWorrallConfirmation–theBayesianaccountThisandarangeofotherproblemsledthosepursuingtheideathat“confirma-tionisprobability”–includingeventuallyCarnaphimself–toabandonthis“objec-tivist”partialentailmentapproach.Thecurrentlymostpopularversionofthisgeneralideatakestheprobabilitiesatissueinconfirmationtheoryinfacttomeasuresimplyaperson’sdegreeofbeliefinthepropositionatissue.Anagentisconsideredtohavedegreesofbeliefineverypropositionavailabletoherandineverylogicalcombinationofsuchpropositions.Suchanagentis“rational”if(i)atanygiventime,thosedegreesofbeliefcanberepresentedasprobabilities(thatissatisfytheprobabilitycalculus)and(ii)changesinherdegreesofbelieffromonetimetothenextsatisfysomethingcalledthe“principleofconditionalization.”Althoughathoroughlysubject-(oragent-)basedapproach,thisaccountdoeshaveclearobjectiveelements.Forexample,condition(i)requiresthatifanagent’sdegreeofbeliefinthetheorythattheinitialescapevelocityofmatterfromthebigbangwasv1isd1,whileherdegreeofbeliefinthetheorythattheinitialescapevelocityofmatterfromthebigbangwasv2isd2,then(assumingthatshe–properly–believesthatitisnotpossiblefortheescapevelocitytohavebothvalues!),shemustbelievethatthetheorythattheescapevelocitywaseitherv1orv2todegreed1+d2.Also,ifanagenthasdegreeofbeliefdinsomepropositionPthenshemusthaveadegreeofbeliefd¢atleastashighasdinanypropositionQthatisalogicalconsequenceofP.Defendersofthisviewhaveproducedvariousargumentsforwhycondition(i)shouldbeconsideredanabsoluterequirementonrationality.Themostoften-citedargumentproceedsbyidentifyinganagent’sdegreesofbeliefwithfairbettingodds(theworstoddsatwhichtheagentwouldbereadytobetontheproposi-tion’sbeingtrue)andshowingthatifthosedegreesofbeliefwerenotprobabili-ties,didnotsatisfytheprobabilitycalculus,thentheagentwouldbecommittedtoacceptingasfairasystemofbetssuchthatshewouldbeboundtomakeanetloss,whateverwaytheworldturnedouttobe(thatis,whicheversentenceswereeventuallyacceptedastrue).Thisistheso-called“DutchBookArgument.”Acrucialnotioninthisapproachistheconditionalprobabilityp(a|b)–theprob-abilitythataholdsontheassumptionthatbdoes.Theseare,ofcourse,inter-pretedasmeasuringwhatyourdegreeofbeliefinawouldbeifyoucametoacceptb.Themostimportantsuchconditionalsforatheoryofconfirmationwillofcoursebeoftheformp(T|e)whereTissometheoryandesomestatementthatcanbecheckedonthebasisofobservationorexperiment.Principle(ii)inthisimpres-sivelyaustereapproachthensayssomethinglikethefollowing.SupposethatallthathappensofanyepistemicrelevanceconcerningsomeparticulartheoryTbetweentwosuccessivestagesinsciencet1andt2isthatsomeempiricalstatement24\nClassicDebates,StandardProblems,FutureProspectsethatissimplypotentialevidenceatt1hasbeencheckedandactuallyfoundtohold(thatis,hasbecomerealevidence,anacceptedpartof“backgroundknowl-edge”)bytimet2.Howshouldtheagent’sdegreesofbeliefinTattimest1andt2berelated?Giventheunderstandingofp(T|e)asmeasuringthedegreeofbeliefinTthatyouwouldhaveifyouweretocometoknowe,advocatesofthisapproachhavesuggestedthatitisobviousthattheagent’s“new”degreeofbeliefinTatt2shouldbeher“old”degreeofbeliefinTconditionalone.Thatis,introduc-ingsubscriptsontheprobabilitiesforclarity;pTpTett21()=()Andthisisthe“principleofconditionalization.”Conditionalprobabilitieslikep(T|e)arecalculatedusingBayes’theorem,which,initssimplestform,sayspp()()TeTp()Te=p()eBecauseofthefrequentuseofBayes’theorem,theapproachwehavebeendiscussingiscalledtheBayesianapproachtotheory-confirmation,or–forreasonsmadeclearershortly–thepersonalistBayesianapproach.Bayesianismhasanumberofpleasingfeatures.First,asalreadymentioned,itisimpressivelyaustere,appearingatanyratetodefine“inductiverationality”viaonlytwoassumptions.Second,itgivesagratifyinglysimpleaccountofwhatittakesforatheorytobeconfirmedbyevidence:econfirmsTjustincaseeraisesT’sproba-bility,i.e.justincasep(T|e)>p(T).Andthird,itiseasytoseethatthissimpleaccountcapturesanumberoffirmlyentrenchedintuitivejudgmentsaboutconfir-mation.Itis,forexample,partofscientificfolklorethatifatheorypassesa“severetest”(inPopper’sterminology)thenthisconfirmsthetheorymorehighlythanwouldalessseveretest–whereatestisseveretotheextentthatitsoutcomeishighlyimprobableinthelightofbackgroundknowledge.OnefrequentlycitedexamplehereisthepredictionbyFresnel’swavetheoryoflightthatifthe“shadow”ofasmallopaquediskheldinthelightemergingfromapointsourceiscarefullyexaminedthenthecentreofthe“shadow”willbeseentobeilluminated,andillu-minatedindeedtopreciselythesameextentasitwouldhavebeenhadnoopaqueobjectbeeninterposed.Theusualstoryisthattheideathatthereshouldbesucha“whitespot”wassoimprobableinthelightofbackgroundknowledge,that,oncePoissonhadshownthatFresnel’stheoryimplieditsexistence,thescientificestablishmentwasfullyconfidentthatFresnel’sgoosehadbeencooked.Theaccountofconfirmationunderconsideration,usingBayes’stheorem,straight-forwardlycapturesthisintuition.AccordingtotheBayesianformula,theextenttowhicheconfirmsT(i.e.thedifferencebetweenp(T)andp(T|e))isgreaterthesmallerisp(e)–i.e.thelesslikelyeisaccordingtobackgroundknowledge.(Rememberthatanyprobabilityliesintheinterval(0,1).)25\nJohnWorrallVirtueslikethese,combinedwithmajordifficultiesinalternativeapproaches,haveconvincedmanycontemporarycommentatorsthatBayesianismisessentially“theonlygameintown”whenitcomestoprovidingaclear-cut,formaltheoryofconfirmation(asopposedtosimplysomeunsystematiclistofintuitivejudg-mentsabouttheory-evidencerelations).Ifso,thentheonlygameinConfirma-tionTownleavesphilosophersofsciencewithalotofworktodoinaddingtoitsrules.ProblemswithBayesianismOfthedifficultiesfacingthepersonalistBayesianapproach,Ioutlinehereonerel-ativelyspecific“internal”problemandoneissuethatseemstomeamajor,generaldifficultyforthewholeapproach.Themorespecificdifficultyhascometobeknownasthe“problemofoldevidence.”Therehasbeenmuchdiscussioninphi-losophyofsciencegoingbacktodebatesbetweenJohnStuartMillandWilliamWhewell(andbeyond)abouttherelativeconfirmationalvalueofatheory’spredictinghithertounknown“new”evidenceandofitssimplyexplainingalreadyknown“old”evidence.Certainly,manyofthegreatconfirmationalsuccessesfortheoriesthataremuchheraldedinthescientificfolklorewerepredictions:thewavetheoryoflightandthe“whitespot”atthecentreofthe“shadow”ofanopaquedisk(alreadymentioned)isonesuchexample,andthepredictionbythetheoryofgeneralrelativityofstarshift(thatstarswouldseemtobedifferentdistancesapartduringthedaybecauseofthegravitationaleffectofthesun)confirmedbyEddington’sEclipseExpeditionisanother.However,althoughtheremaywellbesomesortofspecialpsychologicaleffectofpredictivesuccess,itisdifficulttoseeanyprincipledreasonwhythetime-orderoftheoryandevidenceshouldcountinitself.Moreover,therearedefinitelycaseswhere“oldevidence”strikinglycon-firmedatheory–indeedconfirmedit,intheeyesofthescientificcognoscenti,justasstronglyasanypieceofpredicted“new”evidencecould.Funnilyenough,twosuchcasesmatchthepredictivesuccessesjustmentioned:Fresnel’sexplana-tionofstraightedgediffraction(aphenomenonknownforaround150yearswhenFresnelproposedhistheory)seemstohaveplayedjustasstrongaroleasthe“whitespot”evidenceintheacceptanceofhistheory;and,certainly,generalrelativity’ssuccessinaccountingforthelong-known“anomalous”precessionofMercury’sperihelioncountedforatleastasmuchasitssuccesswiththe“starshift.”Itseemsclearthat,whateverthetruthaboutthe“predictionversusaccom-modation”issue,itcannotbeablanket“oldevidencealwayscountsless.”Yet,theBayesianaccountofconfirmationseemstoyieldtheevenstrongerresultthatoldevidencecannevercountatall.ThiscanbeseenveryeasilyfromtheBayesformulaandthefactthatallprob-abilitiesinthisapproacharealwaysimplicitlyrelativetobackgroundknowledge–thatis,towhatwealreadytakeourselvestoknow,atwhateverstageofscienceweareconsidering.Butifsomepieceofevidenceeis“old”–alreadyknown,inback-26\nClassicDebates,StandardProblems,FutureProspectsgroundknowledgeatsometimet–thenitsprobabilityatt,relativetothatback-groundknowledge,mustofcoursebeone.Itfollows,however,fromBayesformulaandassumingthatTdeductivelyentailsesothatp(e|T)=1,thatifp(e)=1,thenp(T|e)=p(T).AndthatpreciselymeansontheBayesianaccountthatefailstoconfirmT.Therehavebeensuggestionsfromitsdefendersforhowthis“oldevidenceproblem”mightbesolvedwithintheBayesianframework,thoughnonehaswonwidespreadassent.Themoregeneralproblemseemstome,however,tohavenopossiblesolutionwithinthepurelypersonalistframework,buttorequire–atleast–amajorextensionofit.TheproblemisthattheBayesianapproachseemsclearlytooweak,toallowtoowidearoletosubjectiveopinion,tohaveanychanceofcapturingfullywhatisspecialaboutscience.ConsultagainthecrucialBayesianformula.TheBayesianagentistakentobeaperfectdeductivelogician,sothatifTdeductivelyentailse(usuallymoduloback-groundknowledge)thenshemustassignavalueof1tothetermp(e|T)–andsimilarlyifTisawell-definedprobabilistichypothesisthenshemustassignwhat-everprobabilityT–objectively–assignstoe.Theothertermsintheformulaarehowevertakentobeagent-relative.Inparticular,theso-calledpriorprobabilityofT,p(T),measuringthedegreeofbeliefthatanagenthasinthetheoryTaheadofwhateverevidencewearenowproposingtotakeintoaccountissubjective–thereisnotruthofthematterastowhatthispriorprobabilityis,theBayesiansimplytakesitasafactaboutaparticularagentthatshehasacertaindegreeofbelief.Itistrue,ofcourse,that,inapplyingthisapparatustosomeparticulartheoryasitandtheevidenceforitdevelopovertime,theBayesianwillusuallytellastoryofhowthecurrentpriorforTistheendresultofaseriesofapplicationsoftheprincipleofconditionalizationonearlierpiecesofevidence.But,eventhen,thisserieswill,ofcourse,havestartedwithsomeinitialpriorwhichwillthen,bydef-inition,be“purelysubjective.”Bayesianscitevariousinterestingtheoremsaboutthe“washingout”ofpriorswhichshowthat,incertaincircumstances,twoagentswithradicallydifferentpriorsonsometheoryTwillnonethelessconvergetothesameprobabilityforTasevidenceofcertainkindscomesin.Thefacthoweverthatinsuchcircumstances(whichmaynotinanyeventmatchrealcases)anytwoagentswill,inthe–ofcourseneveractuallyattained–limit,agreehardlyseemssufficienttocapturewhatwegenerallythinkofasscientificrationality.Itwillsurelybegenerallyagreedthat,givenalltheevidencethatwecurrentlyhavefromthefossilrecord,homologies,andvariousexperiments,nottomentiontheresultsofvariousdatingtechniques,thattheDarwiniantheoryofevolutiontogetherwithitsviewoftheearthasextremelyancientisaltogethermoreratio-nallybelievablenowthanthe“scientific”creationistviewthattheearthwascreatedessentiallyasitnowis,stockedwithessentiallythe“kinds”thatitcurrentlyhas,in4004BC.Ifevertherewasanon-defeasibledesideratumonanadequateaccountoftherelationshipbetweenscientifictheoriesandevidencethisissurelyit.Yet,itistrivialtoshowthatgivenanyrelativedegreesofbeliefinDarwinism(D)and27\nJohnWorrallCreationism(C)–sayp(D)=0.000001andp(C)=0.999999–itisentirelypossibleforan“agent”tohavearrivedatthosedegreesinfullaccordancewithBayesianprinciples.Shecouldhaveconditionalizedawayonalltheevidenceandstillhavearrivedatdegreesofbeliefthatanysatisfactoryaccountoughtsurelytobrandasabsurd.Ofcourse,thiswillrequirethesuppositionthattheagentstartedtheprocess–aheadoftheconsiderationofanyevidence–withevenmoreextremepriors.ButthepersonalistBayesianexplicitlyeschewsanyrestrictionsonthesepriors.Anyproofthatsucha“scientific”CreationistisboundtoagreewithusDarwiniansintheindefinitelongrunisnoconsolation–itseemsclearthatthecreationistholdsaviewnowthatiscountertogoodscientificreasoning,andtheBayesianjustcannotdeliverthatjudgment.Thewayforward?Here,then,isaproblemthat,inmyview,remainsverymuchopentofutureresearch.PersonalistBayesianismseemsatbesttocaptureonlyapartofscientificrationality.Itneedstodevelopandtodefendfurtherrequirements–placingatleastrestrictionsonacceptablepriors.Itisbynomeansclearhowthisistobedone,however,withinagenuinelyBayesiancontext.Thealternativeofcoursewouldbetodevelopanother“gameintown”–anotherdifferentsystematicattempttocapturegoodscientificconfirmationalpracticeinaprecise,andphilo-sophicallydefensible,way.One–altogethermoreradical–suggestionthathasbeentakenupbymanyrecentphilosophersisthatthesortofapproachembodiedinBayesianismandsimilarenterprisesinvolvesanentirelymistakensetofaimsandpriorities.Accord-ingtothecurrently(andincreasingly)strongmovementtowardsa“naturalized”philosophyofscience,philosophershavefortoolongbeenobsessedwithtradi-tionalissuesbequeathedtoustobythelikesofDescartesandHume.Weshouldnotbelookingforanythinglikealogicofscienceorofscientificconfirmation.Anysuchsystemwould,inanyevent,itselfrestonassumptions(assumptionswhichmoreovermustcertainlygobeyonddeductivelogic);and,ascenturiesofphilosophyoughttohavetaughtus,weshouldbepowerlessagainstthescepticwhothenasksforjustificationofthoseprinciplesthemselves.Wecannotaskfor,andsoshouldnotseek,anyfirmergroundthanscienceitselfonwhichtobuildourepistemologicalclaims.Philosophyofscienceshouldbepursuedinanatural-ized,scientificway,simplyrecordingthemethodsofscience.Thenaturalizingmovementwithitsgreateremphasisonphilosophersknow-ingaboutthedetailsofsciencehasundoubtedlyledtomanysignificantimprove-ments.(Thoughithastobesaidthatitiseasytogetthe–ofcourse,absurd–impressionfromrecenttreatmentsthatearlierphilosophers(thelikesofReichen-bach,HempelandPopper,nottomentionstillearlierfigureslikePoincaréandDuhem)knewnothingofthedetailsofscience!)FollowingKuhn(1962),Lakatos(1970)andothers,wenowhaveamuchmorenuancedviewofscientifictheory-28\nClassicDebates,StandardProblems,FutureProspectsconstruction;wehaveamuchrichersetofdescriptivetoolsforanalysingscienceanditsdevelopmentinvolvingmodels,idealizationsandthelikeandabetterunderstandingoftheintricaciesofscientific“observation.”But,asforthegeneralideathatafullynaturalizedviewcansomehowestablishthespecialnessofscience,withoutanyrateviciouscircularity,byitselfadoptingascientificapproach–thisseemstomeaverydifficultlinetoargue.Theproblemagainremainsanopenoneforfutureinvestigation.AccumulationinScience,Despite“Revolutions”?IexplainedatthebeginninghowtheEinsteinianrevolutionturnedKant’sproblemintoadilemma.Sofar,wehavebeeninvestigatingtheprospectsforaprogramthatadmitstherevolutionarynatureofscientificchangeandtries,nonetheless,torescuetheepistemicspecialnessofscience.Attemptstoescapetheotherhornofthedilemmainvolveconcedingthattheideaofscientificrationalitywouldindeedbeindeeptroubleifscientificdevelopmentwereas“revolutionary”asitmightatfirstappeartobeandthereforeacceptingthechallengeofarguingthatoncescience,andinparticularscientifictheories,areproperlyunderstood,therevolutionarynatureofscientifictheory-changedisappears(orperhaps“largely”disappears).Weshouldnowinvestigatethissecondpossibility.Revolutioninpermanence?The“pessimisticmeta-induction”First,let’sbeclearabouttheextentoftheapparentdifficulty.Asmanycommen-tatorswouldseeit,therelativisticandquantumrevolutionsaresimplythetipoftheicebergandtheirchiefeffectoughttohavebeentotakeofftheblinkerssothatphilosopherscouldseethat“revolutions”(ofvaryingdegreesofmagnitude)are,infact,ubiquitousinscience.Longbeforetheturnofthecentury,andevenallowingforthesakeofargumentthatscienceonlyreallystartedwith“the”Sci-entificRevolution,therehadbeenplentyoflesswell-publicizedbutnonethelessdefinitecasesofseeminglyradicaltheory-changeinscience.Consider,forexample,thehistoryofoptics–evenwhenrestrictedtothemodernera.Intheeighteenthcentury,thetheorythatlightconsistsofmaterialcorpuscleshadbeenwidelyacceptedonlytobereplacedintheearlynineteenthcenturybythetheorythatlightsourcesdonotemitmatterbutratherenergy–matterwithinthelightsourcevibratesandcausestheneighboringparticlesoftheall-pervading“luminif-erousether”tovibrateandhencethesevibrationsspreadthroughtheetheruntilabsorbedbysomereceptororother(suchasthehumaneye).Thistheory,inturn,wasreplacedbywhatmightbecalledthematureversionoftheMaxwellelectro-magnetictheoryoflightthatdeniestheexistenceofthemechanicaletherandattributeslightinsteadtothe“vibrations”ofelectricandmagneticfieldvectors.29\nJohnWorrallThen,ofcourse,aspartandparcelofthequantumrevolutioncamethephotontheorywithitsprobabilitywaves.Fromparticlestovibrationsinanelasticsolid,tochangingstrengthsofasuigeneriselectromagneticfield,tophotonsgovernedbyprobabilitywaves–theseseemradicalshiftsindeed.And,ofcourse,accordingspeciallytoKuhn(1962),similarrevolutionstookplaceinallotherbranchesofsciencetoo.Instancesofrevolutionarychangesupplythepremisesforthe“pessimisticmeta-induction”thathasreceivedagooddealofattentioninphilosophyofscienceinthepastfewdecades.ThisargumentissimplyanelaborationoftheproblemfromwhichIbegan.Itissurelyacharacteristicofrevolutionarytheory-changethatthenewtheorycontradictstheoldsothat,ifweassumedforthesakeofargumentthatthenewtheoryweretrue,wewouldbeforcedtotheconclusionthattheoldertheorywasfalse.Butwhatpossiblegroundscouldwehaveforthinkingthatscientificrevolutionsarenowatanend–thatwenowhavethefinaltheoriesinallscientificfields?Newtoniansintheeighteenthandnineteenthcenturiesbelieved–onthebasisofverystrongevidence–thatthefundamentaltruthabouttheuniversehadbeendiscovered;andtheyturnedouttobewrong.Nophysicistinthenineteenthcentury,againongoodevidentialgrounds,dreamedthatthefundamentalprocessesinnaturemightbeinherentlyprobabilisticandyetthat,accordingtomostviews,ispreciselywhatpresentlyacceptedtheoriesaretellingusistrue.Aswesaw,theoriesofthebasicconstitutionoflighthaveundergoneradicalshifts.Fromthestandpointofthecurrentphotontheory,thetheorythatlightconsistsofvibrationstransmittedthroughanall-pervadingelasticsolidetherlooksaboutasfalseasanytheorycouldbe–afterall,foronecrucialthing,thenewertheorydeniesentirelytheexistenceofsuchanall-pervadingmechanicalether.How,then,canwehaveanyfaiththatthatcurrentlyacceptedphotontheorywillnot,initsturn,eventuallybereplacedbyatheoryinwhoselightitwillappearjustasfalseasititselfmakestheclassicalwavetheoryappear?And,ifthefindingsofscienceare,atthisfundamentallevel,astransientasthisaccountmakesthemseem,howcanwehaveanyconfidenceintheprocess?Evenifwecouldproducepersuasiveargumentsforthemethodsofscienceascharacterizingarationalprocess–thatis,evenifwecouldsolvetheproblemssketchedearlierwith,say,somedeluxetheoryofconfirmation–thenevenso,ifthat“rational”processproducesconclusionsthataresubjecttoperiodicradical,chalk-and-cheesechange,itseemsdifficulttoseewhyweshouldregardscienceassospecial.Noticethatnooneisassertingherethatthe“pessimisticmeta-induction”isbyanymeansacompellingargument–itisafterallinductiveandnotdeductive.Itisperfectlypossiblethatourscientificpredecessorswereunlucky(ormisguided)andthatwehavenowhitonthetruth.Andindeedtheintuitionunderwritingthepro-gramsdiscussedearlierisexactlythatscience,andscientifictheories,haveimprovedovertime.Butitisdifficulttoseethatimprovementasinanysensequalitative–nineteenthcenturyphysicistshadagooddealofevidencefortheirtheories.Wenowhaveagooddealmoreevidenceinthelightofwhichverydifferenttheoriesseem30\nClassicDebates,StandardProblems,FutureProspectstrue.But,then,sincesciencewillpresumablycontinueto“improve”andevidencecontinuetoaccumulate,whatgroundscouldbegivenforholdingthatourcurrenttheorieswillresistradicalchangeinthelightofthataccumulatingevidence?Thepessimisticmeta-inductiondoesnotneedtoestablishthatwehavegoodgroundsforthinkingthatourcurrenttheorieswilleventuallybe“radically”replaced;theweakerconclusionthatwehavenogoodgroundsforthinkingthattheywillnotbesoreplacedissufficienttoposetheproblem.Resisting“pessimism”byrestoringanessentiallycumulativeviewInstrumentalismSohow,then,couldphilosophersofsciencebefore1962havebeenblindtowhatoughttohavestaredthemintheface?Theansweristhatmanyofthematleastwerenotatallblindtothisphenomenon.Althoughwetendtothinkofthe“pessimisticmeta-induction”asanewphilosophicalargument,start-ingwithHilaryPutnamorLarryLaudan(1981),infactitcanbefoundfullyformedinPoincaré’s(1905)ScienceandHypothesis:Theephemeralnatureofscientifictheoriestakesbysurprisethemanoftheworld.Theirbriefperiodofprosperityended,heseesthemabandonedoneaftertheother;heseesruinspileduponruins;hepredictsthatthetheoriesinfashiontodaywillinashorttimesuccumbintheirturn,andheconcludesthattheyareabsolutelyinvain.Thisiswhathecallsthebankruptcyofscience.Asthewayheintroducesitsuggests,Poincaréwasnotonlyawareoftheproblemhewasconfidentthathehadananswertoit:[The“manoftheworld’s”]scepticismissuperficial;hedoesnottakeaccountoftheobjectofscientifictheoriesandtheparttheyplay,orhewouldunderstandthattheruinsmaystillbegoodforsomething.NotheoryseemedestablishedonfirmergroundthanFresnel’swhichattributedlighttothemovementsoftheether.ThenifMaxwell’stheoryispreferredtoday,doesitmeanthatFresnel’sworkwasinvain?No,forFresnel’sobjectwasnottoknowwhethertherereallyisanether,ifitisorisnotformedofatoms,iftheseatomsreallymovethiswayorthat;hisobjectwastopredictopticalphenomena.Underneaththeapparentlyradicaltheory-changes(producingtheseeming“ruins”)thereis,Poincarésuggests,asteadyaccumulationof“real”knowledgeinscience.Therearetwoimportantlydifferentversionsofthisclaim–versionswhichPoin-caréhimselfdidnotalwaysclearlydifferentiate(thoughIthinkthereis,intheend,nodoubtinghispreferredposition).Asitstands,thelastpartofthisquota-tionsuggestsan“instrumentalist”viewofscience.Scientifictheories,likeFresnel’stheoryoflight,mayseemtomaketrue-or-falseassertionsabouttheunderlyingstructureofreality,aboutmaterialetherealatomsheldinplacebyelasticforces31\nJohnWorrallandaboutthevibrationsofthoseatoms,whichwecannotofcoursedirectlyobserve,butwhichallegedlyconstitutelightandhenceexplaintheopticalphe-nomenathatwecanobserve.However,therealroleofscientifictheoriesisnoteventoattempttodescribeareality“underlying”thephenomena,butinsteadmerelytocodifythosephenomenainacoherent,efficientand“simple”way,andhencetoenabletheirprediction.Andatthelevelof“phenomena”–theresultsofexperiments,suchasvariousinterference,diffractionandpolarizationexperi-ments–Maxwell’stheory,whileattributingthosephenomenatoaradicallydif-ferentprocess,nonethelessagrees(exactly)withFresnel’stheory.Maxwell’stheory,ofcourse,goesontomakefurtherpredictions–about,forexample,radiowaves;butwherethetwotheoriesbothmakeempiricalpredictionstheyalwaysexactlyagree.Therehasbeensomediscussionintheliteratureofso-called“Kuhnloss”ofempiricalcontent–(alleged)caseswheresomeobservationalorexperimentalresultcorrectlyaccountedforbythedeposedtheoryinsome“revolution”isnotcorrectlyaccountedforbythenewertheory.Kuhn’sownexamplesofthisallegedmethodologicalphenomenonareentirelyunconvincing.Thereareundoubtedlycasesinthehistoryofsciencewhereanewtheoryisaccepteddespitethefactthatitcannotatthatstageaccountforsomealreadyknownphenomenonandwheretheoldertheory(whichhas,ofcourse,atthatstagetheadvantageoflongevity)gaveatleastsomesortofaccountofthatsamephenomenon.Agoodexamplefromopticsisprismaticdispersion–accordingtothesimplestmodelsoftheelasticsolid(orindeedelasticfluid)ether,allwaves,nomatterwhattheirfrequency,wouldtravelthroughitatthesamevelocityandyetthephenomenonofprismaticdispersion(exhaustivelystudied,ofcourse,longbeforeFresnel’swavetheorybyNewtonandothers)establishesthatthedifferentmonochromaticcomponentsofsolarlighttravelthroughthematerialoftheprism(usuallyglass)atdifferentveloc-ities.Thecorpusculartheoryoflight,deposedintheearlynineteenthcentury“waverevolution,”giveshintsofanexplanation–forexamplea“fixedforceofrefraction”withthedifferentmonochromaticrayscorrespondingtoparticleswithdifferentmasses.Butthisexplanationwasknowntorunintoenormousdifficulties.Ifthereareanygenuinecasesof“Kuhnloss”inwhichsomephenom-enonwassatisfactorilyexplainedbythepre-revolutionarybutnotbythepost-revolutionarytheory,thentheyarefewandfarbetween.Moreover,itisofthenatureofsciencethatany“losses”wouldbehighontheagendaforworkaimedatmakingthemgood.Thisistrueevenwheretheolder“explanation”ishighlyflawed–intheexamplejustdiscussed,forinstance,acentralthrustofthewaveopticsresearchprogramafterFresnelwaspreciselytodevelopadetailedmechanicalaccountoftheetherthatyieldeddispersion.Itseemsdifficulttodeny,Isuggest,thatthedevelopmentofsciencehasbeen,atleasttoaverygoodapproximation,cumulativeattheobservationalorexperi-mentallevel.Thisneednotmeanthatthe“post-revolutionary”theoryhasexactlythesameempiricalconsequencesasthepre-revolutionaryone(thoughinarestricteddomain).ThathappenstobetrueintheFresnel–Maxwellcasecitedby32\nClassicDebates,StandardProblems,FutureProspectsPoincaré,butthemoreusualpatternistheoneexemplifiedintheshiftfromNewtonianclassicaltoEinsteinianrelativisticphysics.Everypreciseobservationalconsequenceofspecialrelativitytheoryisstrictlyinconsistentwiththecorre-spondingobservationalconsequenceofclassicaltheory.Thoseconflictingobser-vationalconsequences,nonetheless,explainthesamedataacrossawiderange,becausetheyare,withinthatrange,observationallyindistinguishable.Itfollowsthenthattheapparentlyradicaltheorychangesbroughtaboutby“scientificrevolutions”posenoproblemfortheinstrumentalist–asconcernswhatthataccountseesastherealpurposesofscience,thereisessentialcontinuityacrossscientificchange.Scienceisspecialbecauseitdeliversmoreandmoreoftheepistemic“goods”–itisjustthatthosegoodsdonotconsistofeverdeeper,ever“truer”explanatorytheoriesbutratherofeverwidercodificationsofevermorephenomena.AninterestingmorerecentslantonthisoldpositionisprovidedbyBasvanFraassen’s(1980)“constructiveempiricism.”VanFraassencountenancesnopositivistreductionofthetheoreticalclaimsofscience–ifatheoryassertsthatelectronsexist,itassertstheyexist:theclaimcannotberegardedasmerelyshort-handforsomecomplicatedsetofobservationalsentencesorassomesortofnon-assertive“inferencelicence”;andsuchatheoryiseithertrueorfalse(intheregularTarskicorrespondencesense)dependingonhowtheworldreallyis.However,toexplaintherationalityofwhatgoesoninscience,thereisnoneedtoinvolvecon-siderationsofwhethersuchatheoreticalclaimistrue(indeedaswehavebeenseeingsuchinvolvementposesmajorproblemsforideasaboutrationality).Scien-tistsshouldbeseenas“accepting”theories,notastrue,butonlyasempiricallyadequate.AlthoughvanFraassendoesnotdirectlyaddresstheissueof(appar-ently)radicaltheory-change,hispositionprovidesthebasisforaresponseidenti-caltotheonejustconsidered–theprogressofsciencethroughtheory-changecanbeseenasthedevelopmentofevermoreempiricallyadequatetheories,eachnewtheoryrevealingthatitspredecessorwasindeedhighlyempiricallyadequatebutoverarestrictedrange.AlthoughIshallnotdiscussthemhere,thereare,ofcourse,manyproblemswiththisinstrumentalistview–allofthemassociatedinonewayoranotherwiththefactthattheviewdoesnotseemtogiveproperweighttotheroleoftheory,especiallyinthedevelopmentofscience.Resisting“pessimism”byrestoringanessentiallycumulativeviewPositivismandstructuralrealismInstrumentalism,atleastinthewayIaminter-pretingithere,allowsthatsuccessivetheoriesinsciencecontradictoneanother,andhenceallowsthattheory-changeleaves“ruins”(tousePoincaré’sterm)initswake.Theinstrumentalistinsists,however,thatthereisnonethelessaccumula-tionatthelevelthatscienceisreallyallabout–thecodificationofphenomena.Thereareruinsbuttheyareinsignificant.33\nJohnWorrallAdifferentview–aversionofwhichPoincaréhimselfinfactadopted–isthat,whenproperlyviewed,therearenoruins.Oncethecognitivecontentofscientifictheoriesiscorrectlyanalyzed,weseethattheapparentruinsarejustthat–(merely)apparent.ItmayseemasthoughFresnel’stheory,forexample,makesontologi-calclaimsaboutamediumwiththeconstitutionofanelasticsolidpervadingthewholeofspaceandabouttheparticlesofthatmediumvibratingincertainways.Infact,however,whenweunderstandproperlywhatthetheorysaysweseethatthisisnotreallythecase.Oneextremeversionofthisgenerallineis,ofcourse,anoutrightempiricismorpositivism.Thisseestherealcognitivecontentofa“theoretical”claimassomehow“reducingto”some(infinite)setofobservationsentences.InthecaseofFresnel’stheory,forexample,alltheapparenttheoreticaltalkaboutetherparticles,infact,“reducesto”assertionsaboutinterferenceanddiffractionpat-ternsandthelike.Thelogicalempiricistsdidnot,infact,paymuchdirectatten-tiontotheory-change,anddevelopedtheiraccountoftheoriestosolvedifferentproblems.Butiftheiraccountcouldhavebeenmadetowork,thenclearlythephenomenonoftheory-changewouldpresentitwithnoproblem,assumingthat,asIhaveclaimed,thedevelopmentofscienceisessentiallycumulativeattheempiricallevel.Ithasforalongtimenowbeenverywidelyacceptedthatanysuchempiricistaccountisuntenable.Certainly,variousparticularattemptedreductiveanalysesdidnotwork;andthegeneralview,asinthecaseofinstrumentalism,isthatnosuchaccountcandorealjusticetotheroleoftheory,particularitsheuristicroleinthedevelopmentofscience.TheaccountthatPoincaréhimselfendorsedisdifferent(atleastpre-analytically)frombothinstrumentalismandempiricismorpositivism.HavingsaidtheFresnel’stheorywasnotinvaindespiteitsdisplacementbyMaxwell’s,becauseitstillallowsustopredictopticalphenomenaasbefore,heelaboratesasfollows:Thedifferentialequations[inFresnel’stheory]arealwaystrue[thatis,theyarecarriedoverintoMaxwell’stheory],theymayalwaysbeintegratedbythesamemethodsandtheresultsofthisintegrationstillpreservetheirvalue.Itcannotbesaidthatthisisreducingphysicaltheoriestopracticalrecipes;theseequationsexpressrelations,andiftheequationsremaintrue,itisbecausetherela-tionspreservetheirreality.Theyteachusnow,astheydidthen,thatthereissuchandsucharelationbetweenthisthingandthat;onlythesomethingwhichwethencalledmotion,wenowcallelectric[displacement]current.ButthesearemerelythenamesoftheimageswesubstitutedfortherealobjectswhichNaturewillhideforeverfromoureyes.Thetruerelationsbetweentheserealobjectsaretheonlyrealitywecanattain...(Poincaré,1905).Hence,Poincaréclaimsacontinuityacrosstheory-changeinsciencethatextendsnotmerelytotheobservational,butalsotothestructurallevel–asisevinced,atanyrateinthecasehediscusses,bytheretentionofthemathematical34\nClassicDebates,StandardProblems,FutureProspectsequations(andhenceoftheobservationalconsequences).Allthatis“lost”arepreferred“namesofimages.”Therealcognitivecontentispreservedentirelyintact.AnotherproblemthatseemstomestillverymuchanopenoneforcurrentphilosophyofscienceiswhethersomeversionofPoincaré’sstructuralrealismcanbeelaborated,extendedtoallcasesoftheory-changeandbeshowntoavoidcol-lapseintooutrightempiricism.Ifnot,isthereanyserioushopeforanyformofscientificrealism?TheideathatonecanretaintheviewthatNewton’stheorymaybe“approximatelytrue”despitetheEinsteinianrevolutionseemstomeimplicitytopresupposesomesuch(apparently)reducedformofrealism.Otherwise,atthe“ontological”level,wedoseemtohavenotapproximationbutoutrightrejection(ofabsolutespace,absolutesimultaneity,action-at-a-distanceandsoon).OtherIssuesIhavetriedtobuildmyintroductoryaccountofsomecentralissuesinphiloso-phyofsciencearoundatheme.But,justasIsaiditwouldfromtheoutset,anysuchthematictreatmentisboundtoleaveoutmuchofvalue.Ihavenottouchedonsomecentralissues–suchasscientificexplanation,thenotionofcausalityandothers.Manyofthesewillbedealtwithinwhatfollows.Ihavealsonotbeenabletodiscussthoseveryimportantareasofphilosophyofsciencewhichoverlapwiththeoreticalworkinthesciencesthemselves.Analysesofconceptualissuesinthetheoryofgeneralrelativity,quantummechanicsandstatisticalmechanicshaveallbeenattheforefront–andhave,inturn,raisedinespeciallysharpwaysgeneralphilosophicalissuesaboutdeterminism,localityandthelike.Morerecentworkhasseenanextensionintothefoundationsofbiology–particularlythestructureofDarwiniantheoryandofgenetics;and,especiallyviainterestincausalmodels,intothefoundationsofthesocialsciences.ReferencesCarnap,R.(1950):LogicalFoundationsofProbability.Chicago:UniversityofChicagoPress.Duhem,P.(1906):TheAimandStructureofPhysicalTheory,Englishtranslation,Prince-ton:PrincetonUniversityPress,1954.Glymour,C.(1980):TheoryandEvidence.Princeton:PrincetonUniversityPress.Glymour,C.,Scheines,R.,Sprites,P.andKelly,K.(1987):DiscoveringCausalStructure:ArtificialIntelligence,PhilosophyofScienceandStatisticalModeling.NewYork:Aca-demicPress.Kuhn,T.S.(1962):TheStructureofScientificRevolutions.Chicago:UniversityofChicagoPress.35\nJohnWorrallLakatos,I.(1970):“FalsificationandtheMethodologyofScientificResearchPro-grammes,”inI.LakatosandA.Musgrave(eds.),CriticismandtheGrowthofKnowledge,Cambridge:CambridgeUniversityPress,91–196.Laudan,L.(1981):“AConfutationofConvergentRealism,”PhilosophyofScience,48,19–49.Poincaré,H.(1905):ScienceandHypothesis,Englishtranslation,NewYork:DoverBooks.Popper,K.R.(1959):TheLogicofScientificDiscovery.London:Hutchison.VanFraassen,B.(1980):TheScientificImage.Oxford:OxfordUniversityPress.FurtherreadingBoyd,R.(1973):“Realism,UnderdeterminationandtheCausalTheoryofEvidence,”Nous,7,1–12.Cartwright,N.(1989):Nature’sCapacitiesandtheirMeasurement.NewYork:OxfordUni-versityPress.Earman,J.(1989):WorldEnoughandSpace-Time.Cambridge:MITPress.Earman,J.(1992):BayesorBust?ACriticalExaminationofBayesianConfirmationTheory.Cambridge:MITPress.Earman,J.andGlymour,C.(1980):“RelativityandEclipses:TheBritishEclipseExpedi-tionsof1919andtheirPredecessors,”HistoricalStudiesinthePhysicalSciences,11,49–85.Howson,C.andUrbach,P.(1993):ScientificReasoning:TheBayesianApproach,secondedition.Chicago:OpenCourt.Kitcher,P.(1985):VaultingAmbition:SociobiologyandtheQuestforHumanNature.Cam-bridge:MITPress.Mayo,D.G.(1996):ErrorandtheGrowthofExperimentalKnowledge.Chicago:Univer-sityofChicagoPress.Popper,K.R.(1963):“Science:ConjecturesandRefutations,”inConjecturesandRefutations,London:RoutledgeandKeganPaul,33–57.Redhead,M.L.(1987):Incompleteness,NonlocalityandRealism:AProlegomenontothePhilosophyofQuantumMechanics.Cambridge:CambridgeUniversityPress.Sklar,L.(1993):PhysicsandChance:PhilosophicalIssuesintheFoundationsofStatisticalMechanics.Cambridge:CambridgeUniversityPress.Sober,E.(1984):TheNatureofSelection:EvolutionaryTheoryinPhilosophicalFocus.Cam-bridge,MA:MITPress.Worrall,J.(1989):“Fresnel,Poissonandthe‘WhiteSpot’:TheRoleofSuccessfulPre-dictioninTheory-acceptance”inD.Gooding,T.PinchandS.Schaffer(eds.)TheUsesofExperiment,Cambridge:CambridgeUniversityPress,135–57.Worrall,J.(1999):“TwoCheersforNaturalisedPhilosophyofScience,”ScienceandEducation,8(4),July,SpecialEdition.36\nChapter3ExplanationJimWoodwardAlthoughthesubjectofexplanationhasbeenamajorconcernofphilosophysincePlatoandAristotle,modernphilosophicaldiscussionofthistopic,atleastasitper-tainstoscience,beginswiththeso-calleddeductive-nomological(DN)modelofexplanationinthemiddleofthetwentiethcentury.Thismodelhasmanyadvo-catesbutunquestionablythemostdetailedandinfluentialstatementisduetoCarlHempel(1965).TheDNModelThebasicideaoftheDNmodelisthatexplanationshavethestructureofsounddeductiveargumentsinwhichalawofnatureoccursasanessentialpremise.Onededucestheexplanandum,whichdescribesthephenomenontobeexplained,fromanexplanans,consistingofoneormorelaws,typicallysupplementedbytruesentencesaboutinitialconditions.Themodelisintendedtoapplybothtotheexplanationof“generalregularities”byotherlawsandtheexplanationofpar-ticularevents,althoughsubsequentdevelopmentshavelargelyfocusedonthelatter.Thederivationoffactsaboutplanetarytrajectories(e.g.Kepler’slaws)fromthelawsofNewtonianmechanics,thegravitationalinversesquarelawandappro-priateinformationaboutinitialconditionsisaparadigmaticillustrationofthepatternofexplanationthattheDNmodelattemptstocapture.TheDNmodelismeanttocaptureexplanationviadeductionfromdeter-ministiclawsandthisraisestheobviousquestionoftheexplanatorystatusofstatisticallaws.Hempelclaimsthatthereisadistinctivesortofstatisticalexpla-nation,whichhecallsinductive-statisticalorISexplanation,involvingthesub-sumptionofindividualevents(liketherecoveryofaparticularpersonfromstreptococcusinfection)understatisticallaws(suchasalawspecifyingtheprob-abilityofrecovery,giventhatpenicillinhasbeentaken).ThedetailsofHempel’s37\nJimWoodwardaccountarecomplex,buttheunderlyingideaisroughlythis:anISexplanationwillbegoodtotheextentthatitsexplanansconfershighprobabilityonitsexplanandum.Althoughonceaflourishingareaofresearch,thestructureofsta-1tisticalexplanationhasreceivedrelativelylittleattentionrecently.Inwhatfollows,Iwilllargelyignoreit.MuchoftheappealoftheDNmodelliesintheundeniablefactthatinsomeareasofscience,suchasphysics,manyexplanationsdoseemtoinvolvederivationsfromlaws.However,theDNmodel(oratleasttheversionofthemodelIwilldiscuss)iscommittedtoagooddealmorethanthiscommonplaceobservation.Itclaimsthatallexplanationsconformtotherequirementsofthemodel,andthateverythingconformingtothoserequirementsisanexplana-tion.Weneedtoaskwhethertheseclaimsarecorrectandwhetherthekeycomponentsofthemodelsuchasthenotionofalaw,aresufficientlyclearandwell-understoodtoplaytherolethemodelassignstothem.IbeginwiththissecondissueandthenturntowhethertheDNrequirementsarenecessaryandsufficientforexplanation.LawsThereisgeneralagreementamongdefendersoftheDNapproachthatlawsare(atleast)regularitiesoruniformities–theytellusthatifasystemexhibitscertainproperties,itwillalwaysorwithacertainprobabilityexhibitothers.However,notallregularities–evenexceptionlessregularities–arelaws.Totakeastock5example,while“allspheresofuraniumhaveamassoflessthan10kg”isregardedasalaw(sincethecriticalmassforuraniumisonlyafewkilograms),thesyn-tacticallysimilargeneralization,“allspheresofgoldhaveamassoflessthan510kg,”althoughpresumablytrueisnolawandhencecannotplaytheroleofnomologicalpremiseinaDNexplanation.Theproblemofdistinguishinggenuinelawsfromsuch“accidentalregularities”isthuscentraltoadefenseoftheDNmodel.Mostphilosophers,includingbothdefendersandcriticsoftheDNmodel,haveassumedthatanadequateaccountoflawsmustsatisfycertain“empiricist”stric-tures.Thesearerarelyexplainedwithanyprecision,butamountinpracticetotherequirementthattheaccountbe“reductive”:notionslike“law,”“cause,”and“explanation”areseenasbelongingtoafamilyofcloselyinterrelatedconceptsthatmust,onpainof“circularity,”beexplicatedintermsofconceptsthatlieoutsideofthisfamilylike“regularity.”Anumberofcriteriaforlawfulnessthatarethoughttomeetthesestrictureshavebeenproposed:lawsaresaid1tobeexceptionlessgeneralizations2tocontainonlypurelyqualitativepredicatesandmakenoreferencetopar-ticularobjectsorspatio-temporallocations3tosupportcounterfactuals38\nExplanation4tobeconfirmablebyalimitednumberofinstancesinawaythataccidentalgeneralizationsarenot,and5tobeintegratedintosomebodyofsystematictheoryandplayaunifyingroleininquiryinawaythataccidentalgeneralizationsdonot.Whileeachsetofcriteriahasitsdefenders,Ithinkthatafairsummaryofcurrentdiscussionisthatnone,eithersinglyorincombination,isgenerallyaccepted.Many,perhapsmost,paradigmaticlawsviolatecertainofthecriteriasuchas(1).Others,suchas(2)seembothunclearandoverlyrestrictiveandhavebeenaban-donedinmostrecentdiscussions.Criteria(3)and(5)are,asformulated,both2vagueandarguablysatisfiedbyaccidentalaswellaslawfulgeneralizations.Cri-terion(4)looksfundamentallyconfusedfromtheperspectiveofanymoderntreat-3mentofconfirmation.Giventheabsenceofasatisfactoryaccountoflawhood,itisnaturaltowonderwhetherthecontrastbetweenlawsandnon-lawscanplaythecentralroleitisassignedintheDNmodel.Ifwecannotsaywhatlawsare,whyshouldweaccepttheDNclaimthattheyarerequiredforsuccessfulexplanation?Onepossibleresponseisthatalthoughtheremaybenogenerallyacceptedaccountoflaws,thereisatleastgeneralagreementaboutwhichgeneralizationscountaslawsandthisisalltheDNmodelrequires.Infact,however,thereseemstobenosuchagreement.Theso-calledspecialsciences–biology,psychology,economicsandsoon–arefullofgeneralizationsthatappeartoplayanexplanatoryroleand/ortodescribecausalrelationshipsandyetfailtosatisfymanyofthestandardcriteriaforlawfulness.Forexample,althoughMendel’slawofsegregation(M)iswidelyusedinevolutionarymodels,ithasanumberofexceptions,suchasmeioticdrive.Otherwidelyusedgeneralizationsinthespecialscienceshaveverynarrowscopeincom-parisonwithparadigmaticlaws,holdonlyoverrestrictedspatio-temporalregions,andlackexplicittheoreticalintegration.Thereisconsiderabledisagreementoverwhethersuchgeneralizationsarelaws.Somephilosopherssuggestthatsuchgeneralizationssatisfytoofewofthestandardcriteriatocountaslawsbutcanneverthelessfigureinexplanations;henceweshouldabandontheDNrequire-mentthatallexplanationsmustappealtolaws.Others–e.g.Mitchell(1997)–emphasizingdifferentcriteriaforlawfulness,concludeinsteadthatgeneralizationslike(M)arelawsandhencenothreattotherequirementthatexplanationsinvokelaws.Intheabsenceofanadequateaccountoflaws,itishardtoevaluatethesecompetingclaims.MotivationPuttingasidetheseunclaritiessurroundingthenotionoflaw,whysupposethatall(orevensome)explanationshaveaDNorISstructure?Hempelappealstotwocentralmotivatingideas.ThefirstconnectstheinformationprovidedbyaDNargumentwithacertainconceptionofwhatitistoachieveunderstanding:39\nJimWoodwardaDNexplanationanswersthequestion“Whydidtheexplanandum-phenomenonoccur?”byshowingthatthephenomenonresultedfromcertainparticularcircum-stances,specifiedinC1,C2,...,Ck,inaccordancewiththelawsL1,L2,...,Lr.Bypointingthisout,theargumentshowsthat,giventheparticularcircumstancesandthelawsinquestion,theoccurrenceofthephenomenonwastobeexpected;anditisinthissensethattheexplanationenablesustounderstandwhythephenomenonoccurred(Hempel,1965,p.337).ISexplanationinvolvesanaturalgeneralizationofthisidea:itshowsthattheexplanandum-phenomenonwastobeexpected,onthebasisofalaw,withhighprobability.ThesecondmainmotivationfortheDN/IS(hereafterDN)modelhastodowiththeroleofcausationinexplanation.Whetherornotallexplanationsarecausal–itselfadisputedquestioninthetheoryofexplanation–thereisgeneralagree-mentamongphilosophersthatmanyexplanationsciteinformationaboutcauses.However,mostphilosophers,includingadvocatesoftheDNmodellikeHempel,havebeenunwillingtotakethenotionofcausationasprimitiveinthetheoryofexplanation.Instead,theyhaveregardedthenotionofcausationasatleastasmuchinneedofexplicationasthenotionofexplanationandhavesoughtanaccountofcausationmeetingthereductionistorempiricistrequirementsdescribedaboveinconnectionwithnotionoflaw.Whiletherearemanyformsthatatheoryofcau-sationmighttake,advocatesoftheDNmodelhavegenerallyacceptedabroadlyHumeanorregularitytheoryofcausation,accordingtowhich(veryroughly)allcausalclaimsimplytheexistenceofsomecorrespondinglaworregularitylinkingcausetoeffect.Thisisthentakentoshowthatallcausalexplanations“imply,”perhapsonly“implicitly,”theexistenceofsomelawandhencethatlawsare“involved”inallsuchexplanations,justastheDNmodelclaims.Toillustrateofthislineofargument,consider(Ex1)Theimpactofmykneeonthedeskcausedthetippingoveroftheinkwell.(Ex1)isaso-calledsingularcausalexplanation,advancedbyMichaelScriven(1962)asacounterexampletotheclaimthattheDNmodeldescribesnecessaryconditionsforsuccessfulexplanation.AccordingtoScriven,(Ex1)explainsthetippingoveroftheinkwelleventhoughnolaworgeneralizationfiguresexplicitlyin(Ex1)and(Ex1)appearstoconsistofasinglesentence,ratherthanadeduc-tiveargument.Hempel’sresponse(1965,p.360)wasthat(Ex1)shouldbeunder-stoodclaimingthereisa“law”orregularitylinkingkneeimpactstotippingoverofinkwells.Itistheclaimthatsomesuchlawholdsthat“distinguishes”(Ex1)from“ameresequentialnarrative”inwhichthespillingissaidtofollowtheimpactbutwithoutanyclaimofcausalconnection.WeshouldthinkofthislawasthenomologicalpremiseintheDNargumentthat,accordingtoHempel,is“implicitly”assertedby(Ex1).Criticshaveinturnrespondedthattheclaimthat(Ex1)implies,invirtueofitsmeaning,theexistenceofanunderlyingDNargu-40\nExplanationmentlooksimplausible,giventhefactthatpeopleuseandunderstandsuchexpla-nationseveniftheylacktheconceptslike“deductivelyvalidargument”and“lawofnature.”CounterexamplesWhile(Ex1)isapotentialcounterexampletotheclaimthattheDNmodelpro-videsnecessaryconditionsforexplanation,severalotherexampleschallengetheclaimthattheDNmodelprovidessufficientconditions.ManyexplanationsexhibitdirectionalorasymmetricfeaturestowhichtheDNmodelappearstobeinsensitive.Frominformationabouttheheight(h)ofaflagpole,theanglefitmakeswiththesun,andlawsdescribingtherectilinearprop-agationoflightonecandeducethelength(s)ofitsshadow–suchaderivationisarguablyanexplanation(callit(Ex2))ofs.Itisequallytruethatfroms,thesesamelaws,andf,onecandeduceh.Suchaderivation(Ex3)althoughitappar-entlymeetsallofthecriteriaforanacceptableDNargument,isnoexplanationofwhytheflagpolehasthisheight(Bromberger,1966).Thereareotherkindsofexplanatoryirrelevanciesbesidesthoseassociatedwiththedirectionalfeaturesofexplanation.Considerawell-knownexampleduetoWesleySalmon(1971).(Ex4)(L)Allmaleswhotakebirthcontrolpillsregularlyfailtogetpregnant.JohnJonesisamalewhohasbeentakingbirthcontrolpillsregularly.JohnJonesfailstogetpregnant.(L)appearstomeetthecriteriaforlawfulnessacceptedbyHempelandmanyother4writers.Despitethis,(Ex4)isnoexplanationofwhyJonesfailstogetpregnant.Sincebothofthesederivationsshowthattheirputativeexplanandawere“nom-icallyexpectable,”theyseemtocastdoubtonthewholeideathatexplaininganoutcomeis(just)amatterofshowingthatitwastobeexpectedonthebasisofalaw.Oneobviousdiagnosisofbothexamplesisthattheyneglecttherolethatcausationplaysinexplanation.Theheightoftheflagpolecausesthelengthofitsshadowandthisiswhywefindaderivationoftheformerfromthelatterexplana-tory.Bycontrast,thelengthoftheshadowisaneffect,notacauseoftheheightoftheflagpoleandthisiswhywedon’tregardaderivationofhfromsasexplana-tory.Similarly,takingbirthcontrolpillsdoesnotcauseJones’failuretogetpreg-nantandthisiswhy(Ex4)isnotanacceptableexplanation.Asexplainedabove,advocatesoftheDNmodelwouldnotregardthisdiag-nosisasveryilluminating,unlessaccompaniedbysomepositiveaccountofcau-sation.Weshouldnote,however,thatanapparentlessonof(Ex3)and(Ex4)isthattheregularityaccountofcausationfavoredbyDNtheoristsisatbestincom-41\nJimWoodwardplete:theoccurrenceofc,eandtheexistenceofsomelawlinkingthem(orx’shavingpropertyPandx’shavingpropertyQandsomelawlinkingthese)isatbestanecessaryandnotasufficientconditionforthetruthoftheclaimthatccausedeorx’shavingPiscausallyorexplanatorilyrelevanttox’shavingQ.Contrarytowhatisoftenclaimed–see,forexampleKim(1999,p.17)–wecannotarguethatexplanationslike(Ex1)haveanimplicitDNstructureonthegroundsthatinstaniationsofsuchastructure“guarantee”thatciscausallyorexplanatorilyrelevanttoe.TheSRModelToasignificantextent,subsequentdevelopmentsinthetheoryofexplanationrepresentattemptstocapturethefeaturesofcausalorexplanatoryrelevancethatappeartobeleftoutofexampleslike(Ex3)and(Ex4),usuallywithintheempiricistconstraintsdescribedabove.WesleySalmon’sstatisticalrelevance(orSR)model(Salmon,1971)attemptstocapturethesefeaturesintermsofthenotionofstatisticalrelevance(conditionaldependencerelationships).OntheSRmodel,arequestforexplanationwilltakethefollowingcanonicalform:WhydoesthismemberxoftheclasscharacterizedbyattributeAhaveattributeB?DefineahomogenouspartitionofAasasetofsubclassesorcellsCiofAthataremutuallyexclusiveandexhaustive,whereP(B|A.Ci)πP(B|A.Cj)forallCiπCjandwherenofurtherstatisticallyrelevantpartitionofanyofthecellsA.CicanbemadewithrespecttoB–thatis,therearenoadditionalattributesDkinAsuchthatP(B|A.Ci)πP(B|A.Ci.Dk).ThenanSRexplanationofwhyAisBconsistsof(i)thepriorprobabilityofBwithinA:P(B|A)=p(ii)ahomogeneouspartitionofAwithrespecttoB,(A.C1,...A.Cn),togetherwiththeprobabilityofBwithineachcellofthepartition:P(B|A.Ci)=pi,and(iii)Thecellofthepartitiontowhichxbelongs.ToemployoneofSalmon’sexamples,supposewewanttoconstructanSRexplanationofwhyxwhoisateenager(=A)isdelinquent(=B).SupposefurtherthattherejusttwoattributesandnoothersthatarestatisticallyrelevanttoBinA–gender(MorF)andwhetherresidenceisurban(U)orrural(R),withtheprob-abilityofBconditionalonAandeachthefourpossibleconjunctionsoftheseattributesbeingdifferent.Then{A.M.U,A.M.R,A.F.U,A.F.R}isahomogenouspartitionofAwithrespecttoBandtheSRexplanationwillconsistof(i)astatementoftheprobabilityofbeingadelinquentwithintheclassofteenagers42\nExplanation(ii)astatementoftheprobabilityofdelinquencywithinthisclassaswecondi-tiononeachofthefourpossiblecombinationsofattributes,and(iii)thecelltowhichxbelongs.Intuitively,theideaisthatthisinformationtellsusabouttherelevanceofeachofthesecombinationsofattributestobeingdelinquentamongteenagersandhasexplanatoryimportforjustthisreason.Asanadditionalillustration,supposethatinthebirthcontrolpillsexample(Ex4)theoriginalpopulationTincludesbothgenders.ThenPP()PregnancyTMaleTakesbirthcontrolpills..=()PregnancyTMale.whileP()PregnancyTMaleTakesbirthcontrolpills..πP()PregnancyTTakesbirthcontrolpills.assumingthatbirthcontrolpillsarenotalwayseffectiveforwomen.Inthisway,wecancapturetheideathatamongmales,takingbirthcontrolpillsisexplanato-rilyirrelevanttopregnancy,whilebeingmaleisrelevant.TheSRmodelhasanumberoffeaturesthathavegeneratedsubstantialdis-cussion,butIwanttofocusonwhatItaketobethecentralmotivatingideasofthemodel:(i)explanationscitecausalrelationshipsand(ii)causalrelationshipsarecapturedbystatisticalrelevancerelationships.ThefundamentalproblemwiththeSRmodelisthat(ii)isfalse–asasubstantial5bodyofworkhasmadeclear,casualrelationshipsaregreatlyunderdeterminedbystatisticalrelevancerelationships.ConsiderSalmon’sexampleofasysteminwhichatmosphericpressureAisacommoncauseoftheoccurrenceofastormSandthereadingofabarometerBwithnocausalrelationshipbetweenBandS.SalmonclaimsthatBisstatisticallyirrelevanttoSgivenA–i.e.P(S|A.B)=P(S|A)butAremainsrelevanttoSgivenB–i.e.P(S|A.B)πP(S|B)andthusthatAisexplana-torily(causally)relevanttoSwhileBisnot.However,manyothercausalstruc-turesarecompatiblewiththesestatisticalrelevancerelationships.StructuresinwhichBcausesAwhichinturncausesSwill,ifwemakeassumptionslikeSalmon’sconnectingcausationandprobability,leadtoexactlythesamestatisticalrelevancerelationships.Inthesestructures,unlikeSalmon’sexample,Biscausally(andpre-sumablyexplanatorily)relevanttoS.Similarly,thestatisticalrelevancerelationshipsamongA,BandS,willnottelluswhetherwearedealingwithasysteminwhich,say,AcausesBwhichcausesSandinwhichAalsodirectlycausesS,indepen-dentlyofB,oroneinwhichthedirectionofthecausalarrowfromAtoBisreversed,sothatBcausesA.Amerelistofstatisticalrelevancerelationships,whichiswhattheSRmodelprovides,doesnottellsuswhichcausalorexplanatoryrela-tionshipsareoperative.43\nJimWoodwardTheCausalMechanicalModelInmorerecentwork,Salmon(1984)acknowledgesthisandabandonstheattempttocharacterizeexplanationorcausalrelationshipsinpurelystatisticalterms.Hisnewaccount,whichhecallstheCausalMechanical(CM),attemptstocapturethe“somethingmore”involvedincausal/explanatoryrelationshipsoverandabovefactsaboutstatisticalrelevance.TheCMmodelemploysseveralcentralideas.Acausalprocessisaphysicalprocess,likethemovementofaparticlethroughspace,thatischaracterizedbytheabilitytotransmititsownstructureinacontinuousway.Adistinguishingfeatureofcausalprocessesistheirabilitytotransmitmarks.Intuitivelyamarkissomelocalmodificationtothestructureofaprocess,aswhenonescuffsthesurfaceofabaseball.Abaseballisacausalprocessandoneexpectsthescuffmarktopersistasthebaseballmovesfromonespatio-temporallocationtoanother,evenintheabsenceoffurtherinterventionsorinteractions.Causalprocessescontrastwithpseudo-processeswhichlacktheabilitytotransmitmarks.Anexampleistheshadowofamovingphysicalobject.Intuitively,Salmon’sideaisthat,ifwetrytomarktheshadowbymodifyingitsshapeatonepoint(forexample,byalteringalightsourceorintroducingasecondoccludingobject),thismodificationwillnotpersistunlesswecontinuallyintervenetomaintainitastheshadowoccupiessuccessivespatio-temporalpositions.Causalinteractionsoccurwhenonecausalprocessspatio-temporallyintersectsanotherandproducesamodificationofitstructure.Anexamplewouldbeacollisionbetweentwopar-ticleswhichaltersthedirectionandkineticenergyofboth.AccordingtotheCMmodel,anexplanationofsomeeventEwilltracethecausalprocessesandinteractionsleadinguptoE(Salmoncallsthistheetiologicalaspectoftheexplanation),oratleastsomeportionofthese,aswellasdescribingtheprocessesandinteractionsthatmakeuptheeventitself(theconstitutiveaspectofexplanation).Inthisway,theexplanationshowshowE“fit[s]intoacausalnexus”(1984,p.9).Thesuggestionthatexplanationinvolves“fitting”anexplanandumintoacausalnexusdoesnotofcoursegiveusanyveryprecisecharacterizationofjustwhattherelationshipbetweenEandothercausalprocessesandinteractionsmustbeifinfor-mationaboutthelatteristoexplainE.Butratherthanbelaboringthispoint,Iwillfocusontheintuitiveideabehindthissuggestionandexaminewhatimpliesforsomespecificexamples.Supposethatacueball,setinmotionbytheimpactofacuestick,strikesasta-tionaryeightballwiththeresultthattheeightballisputinmotionandthecueballchangesdirection.Theimpactofthestickalsotransmitssomebluechalktothecueballwhichisthentransferredtotheeightballonimpact.Thecuestick,thecueballandtheeightballarecausalprocessesandthecollisionofthecuestickwiththecueballandthecollisionofthecueandeightballsarecausalinter-actions.Salmon’sintuitiveideaisthatcitingsuchfactsaboutprocessesandinter-actionsexplainsthemotionoftheballsafterthecollision;bycontrast,ifone44\nExplanationoftheseballscastsashadowthatmovesacrosstheother,thiswillbecausallyandexplanatorilyirrelevanttoitssubsequentmotionsincetheshadowisapseudo-process.However,asChristopherHitchcockshowsinanilluminatingpaper(Hitchcock,1995)theinformationaboutcausalprocessesandinteractionsjustdescribedleavesoutsomethingimportant.Theusualelementarytextbook“scientificexplanation”ofthemotionoftheballsfollowingcollisionproceedsbyderivingthatmotionfrominformationabouttheirmassesandvelocitybeforethecollision,theassump-tionthatthecollisionisperfectlyelastic,andthelawoftheconservationoflinearmomentum.Wethinkoftheinformationconveyedbythisderivationasshowingthatitisthemassandvelocityoftheballs,ratherthan,say,theircolororthepres-enceofthebluechalkmark,thatisexplanatorilyrelevanttotheirsubsequentmotion.However,itishardtoseewhatintheCMmodelallowsustopickoutthelinearmomentumoftheballs,asopposedtovariousotherfeatures,asexplana-torilyrelevant.Partofthedifficultyisthattoexpresssuchrelativelyfine-grainedjudgmentsofexplanatoryrelevance(thatitislinearmomentumratherthanchalkmarksthatmatter)weneedtotalkaboutrelationshipsbetweenpropertiesormagnitudesanditisnotclearhowexpresssuchjudgmentsintermsoffactsaboutcausalprocessesandinteractions.Boththelinearmomentumandthebluechalkmarkcommunicatedtothecueballbythecuestickaremarksthataretransmittedbythespatio-temporallycontinuouscausalprocessconsistingofthemotionofthecueball,andwhichthenaretransmittedviaaninteractiontotheeightball.Ironically,asHitchcockgoesontonote,asimilarobservationmaybemadeabout(Ex4).SpatiotemporallycontinuouscausalprocessesthattransmitmarksaswellascausalinteractionsareatworkwhenmaleMr.Jonesingestsbirthcontrolpills–thepillsdissolve,componentsenterhisbloodstream,aremetabolizedorprocessedinsomewayandsoon.Similarly,causalprocesses(albeitdifferentprocesses)andspatio-temporallycontinuouspathsareatworkwhenfemaleMs.Jonestakesbirthcontrolpills.Intuitively,itlooksasthoughtherelevanceorirrelevanceofthebirthcontrolpillsdoesnotjusthavetodowithwhethertheactualprocessesthatleaduptoMr.Jonesnon-pregnancyarecapableofmarktransmissionbutrather(roughly)withthecontrastbetweenwhathappensinactualsituationinwhichJonestakesthepillsandanalternativesituationinwhichJonesdoesnottakethepills.Itisbecausetheoutcome(non-pregnancy)wouldbethesameinbothcasesifJonesismalethatthepillsareexplanatorilyirrelevant.Thislinksexplanatoryrelevancetocounterfactuals–apointtowhichIwillreturn.Asecond,notunrelatedsetofworrieshastodowithhowwearetoapplytheCMmodeltomorecomplexsystemswhichinvolvealargenumberofinteractionsamongwhatfromafinegrainedlevelofanalysisaredistinctcausalprocesses.Supposethatwehaveamoleofgas,confinedtoacontainer,withvolumeV1,atpressureP1,andtemperatureT1.ThegasisthenallowedtoexpandisothermallyintoalargercontainerofvolumeV2.Onestandardwayofexplainingthebehav-iorofthegas–itsrateofdiffusionanditssubsequentequilibriumpressureP2–45\nJimWoodwardappealstothegeneralizationsofphenomenologicalthermodynamics–e.g.,theidealgaslaw,Graham’slawofdiffusion,etc.Salmonappearstoregardputativeexplanationsbasedonatleastthefirstofthesegeneralizationsasnotreallyexplana-torybecausetheydonottracecontinuouscausalprocesses–theindividualmol-eculesarecausalprocessesbutnotthegasasawhole.However,itisobviouslyimpossibletotracethecausalprocessesandinteractionsrepresentedbyeachof23the6¥10moleculesmakingupthegasandthesuccessiveinteractions(colli-sions)itundergoeswitheveryothermolecule.Theusualstatisticalmechanicaltreatment,whichSalmonpresumablywouldregardasexplanatory,doesnotattempttodothis.Instead,itmakescertaingeneralassumptionsaboutthedis-tributionofmolecularvelocitiesandtheforcesinvolvedinmolecularcollisionsandthenusesthese,inconjunctionwiththelawsofmechanics,toderiveandsolveadifferentialequation(theBoltzmanntransportequation)describingtheoverallbehaviorofthegas.Thistreatmentabstractsradicallyfromthedetailsofthecausalprocessesinvolvingparticularindividualmoleculesandinsteadfocusesonidenti-fyinghigherlevelvariablesthataggregateovermanyindividualcausalprocessesandthatfigureingeneralpatternsthatgovernthebehaviorofthegas.Aplausi-bleversionofthecausalmechanicalmodelwillneedtoavoidtheconclusionthatanexplanationofthebehaviorofthegasmusttracethetrajectoriesofindividualmoleculesandprovideanalternativeaccountofwhattracingcausalprocessesandinteractionsmeansforsuchasystem.SuchanextensionoftheCMmodelhasnot6yetbeendeveloped.Asimilarpointholdsforothercomplexsystems.Thereisanotheraspectofthisexamplethatisworthyofcomment.Evenif,perimpossible,anaccountthattracedindividualmoleculartrajectoriesweretobeproduced,thereareimportantrespectsinwhichitwouldnotprovidetheexpla-nationofthemacroscopicbehaviorofthegasthatwearelookingfor.Thisisbecausethereareaverylargenumberofdifferentpossibletrajectoriesoftheindividualmoleculesinadditiontothetrajectoriesactuallytakenthatwouldproducethemacroscopicoutcomethatwewanttoexplain.Veryroughly,giventhelawsgoverningmolecularcollisionsonecanshowthatalmostall(i.e.,allexceptasetofmeasurezero)ofthepossibleinitialpositionsandmomentaconsistentwiththeinitialmacroscopicstateofthegas,ascharacterizedbyP1,T1,andV1,willleadtomoleculartrajectoriessuchthatthegaswillevolvetothemacroscopicoutcomeinwhichthegasdiffusestoanequilibriumstateofuniformdensitythroughthechamberatpressureP2.Similarly,thereisalargerangeofdifferentmicrostatesofthegascompatiblewitheachofthevariousotherpossiblevaluesforthetemperatureofthegasandeachofthesestateswillleadtoadifferentfinalpressureP2*.Itisanimportantlimitationofthestrategyoftracingactualindi-vidualmoleculartrajectoriesthatitdoesnot,atleastasitstands,captureorrep-resentthisinformation.ExplainingthefinalpressureP2ofthegasseemstorequireidentifyingboththefullrangeof(counterfactualandnotjustactualobtaining)conditionsunderwhichP2wouldhaveoccurredandthe(counterfactual)condi-tionsunderwhichitwouldhavebeendifferent.Justtracingthecausalprocesses(intheformofactualmoleculartrajectories)thatleadtoP2,astheCMmodel46\nExplanationrequires,omitsthisinformationaboutwhatwouldhappenunderthesecounter-factualconditions.UnificationistModelsThefinalaccountofexplanationthatwewillexamineistheunificationistaccount.ThebasicideawasintroducedbyMichaelFriedman(1974)butitssubsequentdevelopmenthasbeenmostassociatedcloselywithPhilipKitcher(1989).OnepossibleassessmentoftheDNmodelisthatit(orsomethingbroadlylikeit)iscorrectasfarasitgoes–itstatesplausiblenecessaryconditionsonexplanation–butthatitneedstobesupplementedbysomeadditionalconditionXwhichavoidsthecounterexamplestothesufficiencyofthemodeldescribedabove.ThisisroughlyKitcher’sview.Explanationsarederivationsfrompremisesthatincludegeneralizationsofconsiderablescope(whetherornotweregardtheseaslaws)butsuchderivationsmustalsomeetanadditionalcondition=Xhavingtodowithunification.Theunderlyingideaisthatexplanatorytheoriesarethosethatunifyarangeofdifferentphenomena.Suchunificationsclearlyhaveplayedanimpor-tantroleinscience;paradigmaticexamplesincludeNewton’sunificationofter-restrialandcelestialtheoriesofmotionandMaxwell’sunificationofelectricityandmagnetism.Kitcherattemptstomakethisideamoreprecisebysuggestingthatexplanationisamatterofderivingasmanydescriptionsaspossibleofdifferentphenomenabyusingthesame“argumentpatterns”overandoveragain–thefewerthepatternsused,themore“stringent”theyareinthesenseofimposingrestrictionsonthederivationsthatinstaniatethem,andthegreatertherangeofdifferentconclusionsderived,themoreunifiedourexplanations.Kitcherdoesnotproposeacompletelygeneraltheoryofhowtheseconsiderations–numberofconclusions,numberofpatterns,andstringencyofpatterns–aretobetradedoffagainstoneanother,buthedoessuggestthat,inmanyspecificcases,itwillbeclearenoughwhattheseconsiderationsimplyabouttheevaluationofparticularcandidateexplanations.Hisbasicstrategyistoarguethatthederivationsweregardasgoodexplanationsareinstancesofpatternsthattakentogetherscorebetteraccordingtothecriteriajustdescribedthanthepatternsinstantiatedbythederivationsweregardasdefectiveexplanations.FollowingKitcher,letusdefinetheexplanatorystoreE(K)asthesetofargumentpatternsthatmaximallyunifiesK,thesetofbeliefsacceptedataparticulartimeinscience.Showingthataparticularderivationisanacceptableexplanationisthenamatterofshowingthatitbelongstotheexplanatorystore.Asanillustration,considerKitcher’streatmentoftheproblemofexplanatoryasymmetries.Ourpresentexplanatorypractices–calltheseP–arecommittedtotheideathatderivationsofaflagpole’sheightfromthelengthofitsshadowarenotexplanatory.KitchercontrastsPwithanalternativesystemizationinwhichsuchderivationsareregardedasexplanatory.AccordingtoKitcher,Pincludesthe47\nJimWoodwarduseofasingleoriginanddevelopment(OD)patternofexplanation,accordingtowhichthedimensionsofobjects–artifacts,mountains,stars,organismsetc.–aretracedto“theconditionsunderwhichtheobjectoriginatedandthemodificationsithassubsequentlyundergone”(1989,p.485).NowconsidertheconsequencesofaddingtoP,anadditionalpatternS(theshadowpattern)whichpermitsthederivationofthedimensionsofobjectsfromfactsabouttheirshadows.SincetheODpatternalreadypermitsthederivationofallfactsaboutthedimensionsofobjects,theadditionofStoPwillincreasethenumberofargumentpatternsinPandwillnotallowustoderiveanynewconclusions.Ontheotherhand,ifweweretodropODfromPandreplaceitwiththeshadowpattern,wewouldhavenonetchangeinthenumberofpatternsinPbutwouldbeabletoderivefarfewerconclusionsthanwewouldwithOD,sincemanyobjectsdonothaveshadowsfromwhichtoderivetheirdimensions.ThusODbelongstotheexplanatorystore,andtheshadowpatterndoesnot.Kitcher’streatmentofotherproblemcasesinthetheoryofexplanationissimilar–forexample,derivationslike(Ex4)aboveareclaimedtoinstantiatepatternsthatbelongtoatotalityofpatternsthatarelessunifyingthanthetotalitytowhichthepatterninstantiatedbyaderivationthatjustappealstoageneralizationaboutallmalesfailingtobecomepregnant.Whatistheroleofcausationonthisaccount?Kitcherclaimsthat“the‘because’ofcausationisalwaysderivativefromthe‘because’ofexplanation”(1989,p.477).Thatis,ourcausaljudgmentssimplyreflecttheexplanatoryrelationshipsthatfalloutofour(orourintellectualancestors’)attemptstoconstructunifiedtheoriesofnature.Thereisnoindependentcausalorderoverandabovethiswhichourexplanationsmustcapture.Althoughtheideathatexplanationhassomethingtodowithunificationisintu-itivelyappealing,Kitcher’sparticularwayofcashingouttheideaseemsproblem-atic.Histreatmentoftheflagpoleexampleobviouslydependsheavilyonthecontingenttruththatsomeobjectsdonotcastshadows.Butwouldn’titstillbeinappropriatetoappealtofactsabouttheshadowscastbyobjectstoexplaintheirdimensionsinaworldinwhichallobjectscastenoughshadows(theyareillumi-natedfromavarietyofdifferentdirectionsetc.)sothatalloftheirdimensionscan7berecovered?Thematterbecomesclearerifweturnourattentiontoavariantexampleinwhich,unliketheshadowexample,thereareclearlyjustasmanybackwardsderivationsfromeffectstocausesastherearederivationsfromcausestoeffects.Consider,followingBarnes(1992),atime-symmetrictheorylikeNewtonianmechanics,asappliedtoaclosedsystemlikethesolarsystem.Callderivationsofthestateofmotionoftheparticlesatsomefuturetimetfrominformationabouttheirpresentpositions(attimet0),masses,andvelocities,theforcesincidentonthembetweent0,andthelawsofmechanicspredictive.Nowcontrastsuchderiva-tionswithretrodictivederivationsinwhichthepresentmotionsoftheparticlesarederivedfrominformationabouttheirfuturevelocitiesandpositionsatt,theforcesoperativebetweent0andtandsoon.Itlooksasthoughtherewillbejustasmanyretrodictivederivationsaspredictivederivationsandeachwillrequirepremisesof48\nExplanationexactlythesamegeneralsort–informationaboutpositions,velocities,massesetc.andthesamelaws.Thus,thepatternorpatternsinstantiatedbytheretrodictivederivationslooksexactlyasunifiedasthepatternorpatternsassociatedwiththepredictivederivations.However,wethinkofthepredictivederivationsandnottheretrodictivederivationsasexplanatoryandthepresentstateoftheparticlesasthecauseoftheirfuturestateandnotvice-versa.Itisfarfromobvioushowcon-siderationshavingtodowithunificationcouldgeneratesuchanexplanatoryasymmetry.ExamplesofthissortcastdoubtonKitcher’sclaimthatonecanbeginwiththenotionofexplanatoryunification,understoodinawaythatdoesnotpresupposecausalnotions,anduseittoderivethecontentofcausaljudgments.Thisconclu-sionisreinforcedbyamoregeneralconsideration:TheconceptionofunificationunderlyingKitcher’saccountis,atbottom,oneofdescriptiveeconomyorinfor-mationcompression–derivingasmuchfromasfewassumptionsorviaasfewpat-ternsofinferenceaspossible.However,therearemanyschemesandproceduresinsciencethatinvolveinformationcompressionandunifieddescriptionbutdon’tseemtoprovideinformationaboutcausalrelationships.Thisistrueofmanyclas-sificatoryschemesincludingschemesforbiologicalclassification,andschemesfortheclassificationofgeologicalandastronomicalobjectslikerocksandstars.IfIknowthatindividualsbelongtoacertainclassificatorycategory(e.g.Xsaremammals),Icanusethisinformationtoderiveagreatmanyoftheirotherprop-erties(Xshavebackbones,hearts,theiryoungarebornalive,etc.)andthisisapatternofinferencethatcanbeusedrepeatedlyformanydifferentsortsofXs.Nonetheless,anddespitethewillingnessofsomephilosopherstoregardsuchderivationsasexplanatory(XiswhitebecauseXisapolarbearandallpolarbearsarewhite),mostscientiststhinkofsuchschemesas“merelydescriptive”andastellinguslittleornothingaboutthecausesormechanismsthatexplainwhyXshaveheartsorarewhite.Similarly,therearenumerousstatisticalprocedures(factoranalysis,clusteranalysis,multi-dimensionalscalingtechniques)thatallowonetosummarizeorrepresentlargebodiesofstatisticalinformationinaneconomical,unifiedwayandtoderivemorespecificstatisticalfactsfromamuchsmallersetofassumptionsbyrepeateduseofthesamepatternofargument.Forexample,knowingthe“loading”ofeachofnintelligencetestsonasinglecommonfactorg,onecanderiven(n-1)/2conclusionsaboutpairwisecorrelationsamongthesetests.Again,however,itisdoubtfulthatthis“unification”tellsusanythingaboutcausalrelationships.ConclusionandDirectionsforFutureWorkWhatconclusions/moralsmaywedrawfromthishistoricalsketch?Whatarethemostpromisingdirectionsforfuturework?Anyproposalsaboutthesematterswillbetendentious,butwiththiscaveatinmind,Isuggestthefollowing.First,many49\nJimWoodwardofthelimitationsofthetheoriesreviewedabovemaybetracedtotheirfailuretosatisfactorilycapturecausalnotions.Amoreadequateaccountofcausationisthusoneofthemostimportantitemsontheagendaforfutureworkonexplanation.TheapproachIregardasmostpromisingdiffersfromthosedescribedabove–ittakescounterfactualdependencetobethekeytounderstandingcausationandhenceexplanation.Tomotivatethisapproach,notethatanobviousdiagnosisofthedifferencebetweentheacceptableanddefectiveexplanationsdescribedaboveisthattheformerbutnotthelatterexhibitapatternofcounterfactualdependencebetweenexplanansandexplananduminthefollowingsense:inthegoodexpla-nationsbutnotthebadones,changingtheexplanansvariableswillbeassociatedwithacorrespondingchangeintheexplanandum.Thus,thebirthcontrolpillsarecausallyandexplanatorilyirrelevanttoMr.Jones’pregnancybecausewhetherhebecomespregnantdoesnotdependcounterfactuallyonwhetherhetakespills.Wemightestablishthisabsenceofcounterfactualdependencebydoinganexperimentinwhichweobservethatmanipulatingwhethermalestakebirthcontrolpillsisassociatedwithnochangeinwhethertheybecomepregnant.Similarly,ifwechangethelengthofaflagpolewhileleavingothercausallyrelevantfactorsundis-turbed,thelengthofitsshadowwillchange,butchangingtheshadow’slengthbychangingtheelevationofalightsourceortheanglethepolemakeswiththegroundorinanyotherwaythatdoesnotinvolvedirectlychangingtheflagpole’slengthwillnotresultinachangeinthepole’slength.Inthissense,thelengthoftheshadowiscounterfactuallydependenton(andisexplainedby)thelengthofthepoleandnotviceversa.Again,changingwhetherthereisabluespotonthecueballwillchangenotchangethesubsequentmotionoftheballsbutchangingtheirlinearmomentumwill.Inthissense,thesubsequentmotioncounterfactu-allydependson(andisexplainedby)themomentumbutnotthespot.Thisviewoftheconnectionbetweenexplanationandcounterfactualdepen-denceallowsustodealwithapuzzlethatwillhaveoccurredtothealertreader.Ontheonehand,derivationsfromlawsorothergeneralprinciplesseemtoplayanexplanatoryroleinmanyareasofscience.Ontheotherhand,(Ex3)and(Ex4)seemtoshowthatnotallsuchderivationsareexplanatoryand(Ex1)seemstoshowthatnotallexplanationstaketheformofderivations.Wemayresolvethispuzzlebyrethinkingtheroleofderivationalstructureinexplanation.AccordingtotheDNmodel,theroleofderivationfromalawistoshowthattheexplanan-dumphenomenonwastobeexpected.Isuggestinsteadthatexplanationsexplaininvirtueofconveyinginformationaboutpatternsofcounterfactualdependence.Derivationfromalawissometimesaveryeffectivewayofconveyingsuchinfor-mation,aswhenaderivationofthesubsequentmotionofthecueballsfromtheconservationoflinearmomentumandtheirpriormomentashowsusinaverydetailedandfinegrainedwayexactlyhowthesubsequentmotionoftheballswouldhavebeendifferentinvariouswaysiftheirpriormomentumhadbeendif-ferentinvariousways.However,notallderivationsfromlawsconveysuchinfor-mationaboutcounterfactualdependenceandwhentheydonot,asinthecaseof(Ex3),thereisnoexplanation.Moreover,thereareotherwaysofconveyingsuch50\nExplanationcounterfactualinformationbesidesexplicitderivationandaslongasinforma-tionisconveyed,onehasanexplanation.Thus,(Ex1)tellsusaboutthecounter-factualdependenceoftheinktippingonthekneeimpactandisexplanatoryforjustthisreason–weneednotseeitasexplanatoryinvirtueofinstaniatinganimplicitDNstructure,whichinanyeventisnotsufficientforexplanatorinessintheabsenceofcounterfactualdependence.Otherrepresentationaldevicessuchasdiagramsandgraphssimilarlyconveyinformationaboutcounterfactualdepen-dencewithoutconsistingofexplicitderivations.Therearemanycounterfactualtheoriesofcausationinthephilosophicalliter-8ature–DavidLewis’theory(1973)isprobablythebestknown.Forthemostpart,however,philosophersofsciencehavebeenunwillingtomakeextensiveuseofcounterfactualnotionsindevelopingtheoriesofexplanation.Thisattitudeispartlyduetosuspicionthatcounterfactualsfailtomeettheempiriciststricturesdescribedatthestartofthischapter,butithasbeenexacerbatedbyfeaturesoftheveryinfluentialsemanticsforcounterfactualsdevelopedbyLewis.Althoughthesemanticsisawonderfulachievement,itsappealtotrade-offsalongdifferentdimensionsof“similarity”across“possibleworlds”andto“miracles”thatviolatelawsofnatureleavesitopaquehowcounterfactualclaimscanbetestedbyordi-naryempiricalevidenceandseemstohavelittlecontactwithscientificpractice.Theresulthasbeentomakecounterfactualslookscientificallydisreputable.Recently,however,thissituationhaschanged.JudeaPearlandothers–seeespe-ciallyPearl(2000)–drawingonasubstantialpreexistingtraditionsindisciplineslikestatistics,experimentaldesign,andeconometricshaveprovidedrigorousformalframeworksforexploringtheconnectionbetweencausationandcounter-factuals.Theyhavealsoemphasizedtheverycloseconnection(gesturedatabove)betweencounterfactualsandexperimentation,andhaveexploredthewaysinwhichevenwhenexperimentationisnotpossible,statisticalevidencemaybebroughttobearoncausalclaims;inthelatterconnection,seeespecially,Spirtesetal.(1993).AlthoughIlackthespacetodefendthisjudgment,Ithinkthisworkgoesalongwaytowardmakingcounterfactualsandaccountsofexplanationandcausationbasedoncounterfactualsscientificallyrespectable.Thetaskthenbecomesoneofworkingoutindetailhowvariouscausalandexplanatorynotionscanbecapturedwithinthiscounterfactual/experimentalistframework–workof9thissortisalreadyunderwayand,inmyjudgment,representsoneofthemostpromisingfuturedirectionsinthetheoryofexplanation.Iwillalsoaddthepre-dictionthatthebestworkinthisareawillmakeuseofformalmachinerylikesystemsofequationsanddirectedgraphs–machinerythatisbothricherthanrepresentationaldevicesstandardlyemployedbyphilosophers(logic,probabilitytheoryunsupplementedbyanythingelse)andclosertothemachineryemployedbyscienceitself.Neitherlogicnorprobabilitytheorybythemselvescancapturethemodalandcounterfactualelementsthatarecentraltoexplanation.“Lawsofnature”isalsoatopiconwhichmuchworkremainstobedone.Therearemanyquestionsthatneedtobeanswered.Whichifanyofthetraditionalcri-teriaforlawfulnesscanbereformulatedinadefensibleway?Isitpossibletodraw51\nJimWoodwardarelativelysharpdistinctionbetweenlawsandnon-lawsatalland,ifso,doesthisdistinctioncoincidewiththedistinctionbetweenthosegeneralizationsthatcanfigureinexplanationsandthosethatcannot,asDNtheoristsclaim?Ifthereisnocleardistinction,whatfollowsforthetheoryofexplanation?Whataretheadvan-tagesanddisadvantagesofthinkingofthegeneralizationsofthespecialsciencesaslawseventhoughtheylackmanyofthefeaturestraditionallyassignedtolaws?Mysuspicionisthatprogressontheseissueswillrequireabandoningthe“allAsareBs”frameworkforrepresentinglawstraditionallyfavoredbyphilosophersinfavorofafocusonexamplesofreallaws,whicharerepresentedbyequationsofvarioussortswhichhaveamuchricherstructure.Theissueofreductionismalsomeritsrethinking.Agreatdealofworkonexpla-nation,includingtheaccountsdescribedabove,seemsanimatedbytheassumptionthat,withoutafullreduction,nointerestingprogresshasbeenmade.Thisattitudeisnotself-evidentlycorrect.Somenon-reductionisttheoriesofcausation/explana-tion(e.g.,cexplainseifcproducese,withnofurtheraccountof“production”)doseemcompletelyunilluminating.Butnotallnon-reductivetheoriesaretrivialinthewayjustillustrated.Non-reductivetheoriescanbeinterestingandcontroversialinvirtueofconflictingwithotherreductiveornon-reductivetheoriesandsuggestingdifferentassessmentsofparticularexplanations.Forexample,eveniftheCMmodelfailstofullymeetempiriciststrictures,itwillstilldisagreewithcounterfactualtheories(includingnon-reductiveversionsofsuchtheories)initsassessmentofexplanationsthatappealtoactionatadistanceorotherwisefailtotracecontinuouscausalprocesses,sincecounterfactualtheoriespresumablywillregardsuchexplana-tionsaslegitimate.Relatedly,evenifweoptforanon-reductiveaccountofsomenotionwithinthecircleofconceptsthatincludes“cause,”“counterfactual,”etc.,westillfacemanynon-trivialchoicesaboutexactlyhowthisnotionshouldbecon-nectedupwithorusedtoelucidateothernotionsofinterest–choicesthatcanbemadeinmoreorlessdefensibleways.Finally,evenintheabsenceofafullyreduc-tiveaccountofexplanation,itmaybepossibletoshowhowparticularexplana-tory/causalclaimscanbetestedbymakinguseofotherparticularcausalclaimsandcorrelationalinformation.Myownviewisthat,intheirenthusiasmforreductiveaccounts,philosophershaveoftenmisdescribedthestructureoftheexplanatoryclaimstheyhavehopedtoreduce.Ialsothinkthatmanyoftheempiricistcon-straintsimposedonaccountsofexplanationhavebeenabandonedelsewhereinphi-losophyandhavelittlejustification.Regardlessofwhetherthisiscorrect,theentiresubjectwouldbenefitfromamoreexplicitdiscussionoftherationaleforthecon-straintsthatarestandardlyimposed.Notes1Woodward(1989)arguesitisamisconceptionthatstatisticaltheoriesexplainindivid-ualoutcomes.Instead,theyexplainfeaturesofprobabilitydistributionssuchasexpec-tationvalues.52\nExplanation2Forexample,theparadigmaticallyaccidentalgeneralization“Alltheballsinthisurnarered”arguablysupportsthecounterfactual“Ifaballweredrawnfromthisurn,itwouldbered.”Ifwewanttousesupportforcounterfactualstodistinguishlaws,weneedtobemorepreciseaboutwhichcounterfactualsaresupportedbylawsbutnotbyacci-dentalgeneralizations.Criterion(5)isarguablysatisfiedbyaccidentalcosmologicaluni-formitiessuchasthegeneralizationthatatasufficientlylargescalethemassdistributionoftheuniverseisuniform,sincetheseplayaunifyingroleincosmologicalinvestiga-tion.Severaloftheobjectionstounificationisttheoriesofexplanationdiscussedbelowalsoappeartotellagainstthiscriterion.3Virtuallyallrecenttreatmentsofconfirmation,whetherBayesianornon-Bayesian,agreethat“positiveinstances”bythemselvesneverconfirmgeneralizations,whetherlawfuloraccidental.Instead,itisonlyinconjunctionwithbackgroundassumptionsthatpositiveinstancesoranyotherformofevidencecanbeconfirming.Oncethisisrec-ognized,itbecomesclearthatinconjunctionwiththerightbackgroundassumptions,accidentalgeneralizationsarejustasconfirmablebyalimitednumberofinstancesaslawfulgeneralizations.Forexample,inconjunctionwiththeinformationthatanappro-priatesmallsamplehasbeendrawnrandomlyfromtheUSpopulation,thesamplecanaccidentalgeneralizationsaboutpoliticalattitudesinthatpopulation.4Somereadersmayrespondthat(L)isnotabona-fidelawbutthisjustillustratesagainthatdefenseoftheDNmodelrequiresamoreadequateaccountoflaws.5SeeespeciallyCartwright(1979)andSpirtesetal.(1993).6Formoreonthistheme,seeWoodward(1989).7Kitcher’simplausibleassumptionthatthereisasingleODpatternofexplanationalsoinvitesfurthercomment.Whiletheassumptionmaymakelittledifferencetothepar-ticularexampleunderdiscussion,forreasonsdescribedinBarnes(1992),itraisestheimportantissueofwhethertherearenon-arbitrarycriteriaforcountingorindividuat-ingpatternsofargument.8MyowndefenseofacounterfactualtheoryofexplanationcanbefoundinWoodward(1984)andWoodward(2000).9InadditiontoPearl(2000)see,forexample,Hitchcock(2001).ReferencesBarnes,E.(1992):“ExplanatoryUnificationandtheProblemofAsymmetry,”PhilosophyofScience,59,558–71.Bromberger,S.(1966):“WhyQuestions,”inR.Colodny(ed.),MindandCosmos:EssaysinContemporaryScienceandPhilosophy,Pittsburgh:UniversityofPittsburghPress,86–111.Cartwright,N.(1979):“CausalLawsandEffectiveStrategies,”Nous,13,419–37.Friedman,M.(1974):“ExplanationandScientificUnderstanding,”JournalofPhilosophy,71,5–19.Hempel,C.(1965):AspectsofScientificExplanationandOtherEssaysinPhilosophyofScience.NewYork:FreePress.Hitchcock,C.(1995):“Discussion:SalmononExplanatoryRelevance,”PhilosophyofScience,62,304–20.53\nJimWoodwardHitchcock,C.(2001):“TheIntransitivityofCausationRevealedinEquationsandGraphs,”TheJournalofPhilosophy,xcviii(6),273–99.Kim,J.(1999):“Hempel,Explanation,Metaphysics,”PhilosophicalStudies,94,1–20.Kitcher,P.(1989):“ExplanatoryUnificationandtheCausalStructureoftheWorld,”inW.SalmonandP.Kitcher(eds.),410–505.Lewis,D.(1973):“Causation,”JournalofPhilosophy,70,556–67.Mitchell,S.(1997):“PragmaticLaws,”PSA96,SupplementtoPhilosophyofScience64(4),S468–S479.Pearl,J.(2000):Causality:Models,ReasoningandInference.Cambridge:CambridgeUniversity.Salmon,W.(1971):“StatisticalExplanationandStatisticalRelevance,”inW.Salmon(ed.),StatisticalExplanationandStatisticalRelevance,Pittsburgh:UniversityofPittsburghPress,29–87.Salmon,W.(1984):ScientificExplanationandtheCausalStructureoftheWorld.Prince-ton:PrincetonUniversityPress.Salmon,W.andKitcher,P.(eds.)(1989):MinnesotaStudiesinthePhilosophyofScience,Vol13:ScientificExplanation.Minneapolis:UniversityofMinnesotaPress.Scriven,M.(1962):“Explanations,PredictionsandLaws,”inH.FeiglandG.Maxwell(eds.),MinnesotaStudiesinthePhilosophyofScience,volumeIII,Minneapolis:UniversityofMinnesotaPress,170–230.Spirtes,P.Glymour,C.andScheines,R.(1993):Causation,PredictionandSearch.NewYork:Springer-Verlag.Woodward,J.(1984):“ATheoryofSingularCausalExplanation,”Erkenntnis,21,231–62.Woodward,J.(1989):“TheCausalMechanicalModelofExplanation,”inW.SalmonandP.Kitcher(eds.),357–83.Woodward,J.(2000):“ExplanationandInvarianceintheSpecialSciences,”BritishJournalforthePhilosophyofScience,51,197–254.54\nChapter4Structuresof1ScientificTheoriesCarlF.CraverIntroductionAcentralaimofscienceistodeveloptheoriesthatexhibitpatternsinadomain2ofphenomena.Scientistsusetheoriestocontrol,describe,design,explain,explore,organize,andpredicttheitemsinthatdomain.Masteringafieldofsciencerequiresunderstandingitstheories,andmanycontributionstoscienceareevalu-atedbytheirimplicationsforconstructing,testing,andrevisingtheories.Under-standingscientifictheoriesisprerequisiteforunderstandingscience.Thetwodominantphilosophicalanalysesoftheorieshavesoughtanabstractformalstructurecommontoallscientifictheories.Whiletheseanalyseshaveadvancedourunderstandingofsomeformalaspectsoftheoriesandtheiruses,theyhaveneglectedorobscuredthoseaspectsdependentuponnonformalpat-ternsintheories.Progresscanbemadeinunderstandingscientifictheoriesbyattendingtotheirdiversenonformalpatternsandbyidentifyingtheaxesalongwhichsuchpatternsmightdifferfromoneanother.Aftercriticallyreviewingthetwodominantapproaches(pp.55–64),Iusemechanistictheoriestoillustratetheimportanceofnonformalpatternsforunderstandingscientifictheoriesandtheiruses(p.67).TheOnceReceivedView(ORV)Centraltologicalpositivistphilosophyofscienceisananalysisoftheoriesasempir-34icallyinterpreteddeductiveaxiomaticsystems.Thisformalapproach,theORV,emphasizesinferentialpatternsintheories.TheprimaryvirtueoftheORV(andsomeofitsvice)liesinitsassociationandfitwithargument-centeredanalysesof,forexample,explanation,prediction,reduction,andtesting.Themaincommit-mentsoftheORVareasfollows.55\nCarlF.CraverLogicalandextralogicalvocabularyAccordingtotheORV,theoriesarelinguisticstructurescomposedofalogicalandanextralogicalvocabulary.Thelogicalvocabularycontainstheoperatorsoffirst-orderpredicatecalculuswithquantifiers,variouslysupplementedwithrelationsof5identity,modality,andprobability.Theextralogicalvocabulary(V)containsthepredicatesthatconstitutethetheory’sdescriptiveterms.Theoriessystematizephe-nomenabyexhibitingdeductiveandinductiveinferentialrelationsamongtheirdescriptiveterms;thissystematizationprovidesa“logicalskeleton”forthetheoryand“implicitlydefines”thepredicatesinV(Nagel,1961,p.90).Correspondencerulesandthetheory/observationdistinctionThepredicatesofV,ontheORV,canbesortedintoanobservationalvocabulary(VO)andatheoreticalvocabulary(VT).PredicatesinVOaredefineddirectlyintermsoftheobservableentitiesandattributestowhichtheyrefer.ThepredicatesinVTrefertoentitiesandattributesthatcannotdirectlybeobserved;thesepredicatesaredefinedindirectlyviacorrespondencerulestetheringthemtopredicatesinVO.Correspondencerulesgivetheoriestheirempiricalcontentandtheirexplana-toryandpredictivepower.Correspondenceruleshavebeencharacterizedasexplicitdefinitions(includingoperationaldefinitions),asreductionsentences(par-tiallyorconditionallydefiningthetermwithinthecontextofagivenexperimen-talarrangement),orintermsofamoreholisticrequirementthatthetheoryformaninterpretivesystemwithnopartfailingtomakeadifferencetotheobservableconsequencesofthetheory(Hempel,1965,chs4and8).LawsofnatureOntheORV,theexplanatorypoweroftheoriesspringsultimatelyfromthelawsthataretheiraxioms.Explaininganeventorregularity(theexplanandum),onthe“coveringlaw”account,isamatterofinductivelyand/ordeductivelysystematiz-ing(fitting)theexplanandumintotheaxiomaticstructureofthetheoryandtherebydemonstratingthattheexplanandumwastobeexpectedgiventhelawsofnatureandtherelevantconditions.WithintheORV,lawstatements(descriptionsoflaws)arecanonicallyrepre-sentedasuniversallyquantifiedmaterialconditionals(e.g.,“Forallx,ifxisFthenxisG”).Minimally,lawstatementsare(i)logicallycontingent(ii)true(withoutexception)(iii)universalgeneralizations,thatare(iv)unlimitedinscope.56\nStructuresofScientificTheoriesRequirement(iv)isgenerallyunderstoodtoprecludethelaw’srestrictiontopar-ticulartimesandplaces.Manyrecommendtheadditionalrequirementthattheregularitydescribedbythelawstatement(v)holdbyphysicalnecessity.Thisrequirementmightbeusedtodistinguishstatementsoflawfrommerelyaccidentalgeneralizations(Hempel,1966,ch.5),ortopickoutthosegeneralizationsthatsupportcounterfactualsfromthosethatdonot(Goodman,1983).Theoryconstruction,theorychange,andderivationalreductionTheORViscommonlyassociatedwithageneralization/abstractionaccountoftheoryconstruction,asuccessionalaccountoftheorychange,andaderivationalaccountofintertheoreticreduction.ThestricturesoftheORVrestrictitsflexibil-ityforanalyzingtheoryconstructionandtheorychange.Thegeneralization/abstractionaccountdepictstheoryconstructionasa“layercake”inferencefirstfromparticularobservations(viainductivegeneralization)toempiricalgeneralizationsconstructedfromVO,andthenfromtheseempiricalgen-eralizations(viae.g.,hypothetico-deductiveinference)tolawsofnature(con-structedfromVT).ThisaccountisnotmandatedbytheORV,butitslogicalframingofthetheoryconstructionprocess(withitsdichotomiesoftypeandtoken,generalandparticular,observableandtheoretical)naturallysuggestssuchapic-ture;see,forexample,Nagel(1961,ch.5).TheORV’sanalysisofmeaningenforcesasuccessionalaccountoftheorychange.First,theORVindividuatestheoriestoofinelytoilluminatethegradualandextendedprocessoftheorybuilding.Theweakeningofcorrespondencerulestoan“interpretivesystems”requirementineffecttiesthemeaningofanyterminVtoitsinferentialrelationshipstoalloftheothers.Evenrelativelyinsignificantchanges,suchasthedevelopmentofanewexperimentaltechnique,produceanentirelydifferenttheory(Suppe,1977).Understandinggradualtheoryconstruc-tionrequiresadiachronicnotionoftheorythatpersiststhroughsuchchanges(Schaffner,1993a,chs3and9).TheORVanalyzessuccessionaltheorychangeasintertheoreticreductionorreplacement.Onthemostsophisticatedaccount–Schaffner’sgeneralizedreduc-tion/replacement(GRR)model(1993a,ch.9)–reductionisthedeductivesub-sumptionofone(corrected)theorybyanother(restricted)theory.Thereducedtheoryoftenhastobecorrectedbecauseitisliterallyfalse,andthereducingtheoryoftenhastoberestrictedbecausethereducedtheoryisaspecialcaseofthereduc-ingtheory.Asmorerevisionandrestrictionarerequired,itbecomesmoreap-propriatetodescribethesuccessortheoryasreplacing,ratherthanreducing,itspredecessor.Somereductionsareinterlevel;theoriesaboutoneintuitiveonticlevelaredeductivelysubsumedbytheoriesatanotherintuitiveonticlevel(asintheputa-tivereductionoftheidealgaslawstostatisticalmechanics).Thisderivationalviewofinterlevelrelationstendstoenforceastratigraphicpictureofscienceandofthe57\nCarlF.Craverworld–apictureinwhichontologicallevelsmapontolevelsoftheorywhichinturnmapontofieldsofscience(OppenheimandPutnam,1968).Onthiscarica-ture,theoriesateachleveldevelopinrelativeisolationuntilitispossibletoderivethehigherleveltheoryfromthelower.Schaffner’sinclusionofcorrectionandrevisionintheGRRmodelaccommodatesthefactthattheoriesatdifferentlevelsmayco-evolveundermutualcorrectionandrevision(Churchland,1986;Bechtel,1988).CriticismsoftheORVVirtuallyeveryaspectoftheORVhasbeenattackedandrejected,butthereisnoconsensusastowhereitwentwrong.Thereareasmanydifferentdiagnosesas6thereareperspectivesonscienceanditsphilosophy.Here,Ifocusonthelimita-tionsoftheORVfordescribingtheories“inthewild”(i.e.,astheyareconstructed,conveyed,learned,remembered,presented,taughtandtestedbyscientists).Thechargesarethat•theORVmisdescribestheorystructure(s)inthewild(p.58)•theORVdistortstheorydynamicsinthewild(p.60),andthat•theORV’semphasisonlawsofnaturemakesitinapplicabletomanyacceptedtheories(p.62).TheorystructureinthewildTheORVisnottypicallydefendedasanaccuratedescriptionoftheoriesinthewild;rather,itisaregimentedreconstructionoftheirsharedinferentialstructure.AdescriptivegulfbetweentheORVandtheoriesinthewildcannonethelesssuggest(i)thatthereareimportantstructuresofscientifictheoriesthatareneglected,de-emphasized,oratbestawkwardlyaccommodatedbytheORV,and(ii)thattherearesignificantaspectsoftheORVthatareperipheraltotheusesoftheoriesinthewild.Attentiontoinferentialstructurepaysdividendsforregimentingarguments,butinferentialpatternsdonotexhausttheusefulpatternsinscientifictheories.Multiple,partial,andincompletetheoryformulationsareneglectedorhomogenizedTheoriesinthewildaresometimeswritteninanaturallanguage;theyarealsocharted,graphed,diagrammed,expressedinequations,explicatedbyexemplars,and(increasingly)animatedinthestreamingimagesofwebpages.Onlyrarelyare58\nStructuresofScientificTheoriestheoriesrepresentedinfirst-orderpredicatecalculus.EventhetheoriesmostamenabletotidytreatmentontheORVcanbegivendifferentequivalentlogicalformulationsandcanbescriptedwithdifferentformalisms,andthesedifferencesoftensignificantlyinfluencehowthetheoriesareusedandhowtheyrepresentthepatternsinadomain.RegimentingtheoriesintotheORVstructureobscuresthediverserepresentationaltacticsusedbyscientistswhentheydeploy,express,andteachtheirtheories;see,forexample,Nersessian(1992).Representationsoftheoriesinthewildarealsooftenpartialorincomplete.Trumpler’s(1997)historicalstudyofthedevelopmentandrefinementofdiffer-2+entvisualrepresentationsoftheNachannelisanexcellentexample.Thetheory,inthiscase,ispartiallyrepresentedbyahostofrepresentations(e.g.,imagesofprimary,secondary,andtertiaryproteinstructure,circuitdiagrams,current-to-voltagegraphs,cartoonsofpossiblemechanismslikethatshowninFigure4.1),+nonewhichrepresentsthetheoryofhowtheNachannelworksinitsentirety.Learningthistheoryinvolvesinternalizingtheserepresentationsandmasteringthereticulateconnectionsamongthem.Theoriesinthewildarealsofrequentlyincompleteastheyarecobbledtogetherovertime.Suchincompletenessblocksderivationalarguments,butistreatedasaninnocuousfactoflifeinscienceaspracticed.Nomologicalpatternsemphasizedovercausal/mechanicalpatternsManycriticismsofthe“coveringlaw”accountofexplanationturnontheimportanceofcausal/mechanicalratherthanmerelynomologicalpatternsinourexamplesofintu-itivelygoodexplanations.Therearemanynowfamiliarexamples–propagatedinpartbyW.Salmon(1984;1989):theelevationofthesunandtheheightoftheflagpoleexplainthelengthofthepole’sshadowandnotviceversa;fallingbaro-metricpressure,andnotthefallingmercuryinthebarometer,explainstheensuingstorm;andthecurrentpositionsoftheplanetscanbeexplainedonthebasisoftheirpositionsyesterdaybutnotonthebasisoftheirfuturewandering.Examplesofthissort(andsimilarcounter-examplestoinductiveexplanations)canbeusedtoarguefortheexplanatoryimportanceofexplicitlycausal/mechanicalpatternsratherthanmerelyinferentialornomologicalpatterns;seeSalmon(1989)butalsoseeKitcher(1989).SuchcriticismsapplyequallytothedescriptiveadequacyoftheORVforaccommodatingandhighlightingcausal/mechanicalpatternsinthe-ories;seepage67.MathematicalstructuresareawkwardlyaccommodatedFinally,therestrictionoftheORVtothefirst-orderpredicatecalculusawkwardlyaccommodatesthemath-ematics,statistics,andprobabilitiesrequiredforexpressingthetheoriesof,forexample,quantummechanics,relativity,andpopulationgenetics.Asproponentsofamodel-basedviewoftheorieshaveemphasized(p.64),set-theoretic(Suppes,1967)andstate-spaceapproaches(Suppe,1989)torepresentingtheoriesnatu-rallyaccommodatethesemathematicalrelationsand,inmanycases,are,infact,59\nCarlF.CraverNa+Na+Na+HairpinturnNa+Na+Na+MEMBRANENa+Spreadingdepolarization-helixNa+3.HairpinsbendNa+Na+Na+4.Na+ionsdiffuseintoporethroughpore,furtherdepolarizingmembraneNa+Na+MEMBRANE2.-helicesrotatetocreatepore1.SpreadingRepeldepolarizationRepelNa+repels-helicesNa+Na+Na+Na+Na+Na+Na+Figure4.1therepresentationalconventionsfavoredbythescientists(McKinseyandSuppes,1953a,1953b;Suppe,1989).TheorydynamicsinthewildAsecondmajorcriticismoftheORV’sdescriptiveadequacyisthatitneglectsordistortsthedynamicsofscientifictheories–theprotractedprocessofgenerating,evaluating,revising,andreplacingtheoriesovertime.Forexample,Darden(1991,60\nStructuresofScientificTheoriesch.2)arguesthatdiscoveryhasbeenneglectedbytraditionalORV-basedapproaches;Lloyd(1988)developsheralternativeaccountofscientifictheoriestohighlightaspectsoftheorytestingthatareneglectedontheORV;andSchaffner(1993a)emphasizestheimportanceofdevelopingadiachronicaccountoftheo-ries.Closeattentiontoscienceanditshistoryhaverevealedaspectsoftheorydynamicsthatareneglected,orawkwardlyaccommodatedwithintheORV’sstrictures.Thegeneralization/abstractionaccountoftheorybuildingtreatstheorybuild-ingasthejointapplicationofinductivegeneralizationandhypothetico-deduction.Thesestrategiesareincomplete,andleaveunansweredquestionsaboutwhichinductivegeneralizationstodraw(Goodman,1983)andabouthowscientistsgen-eratethehypothesesfromwhichtodeducepredictions.Successionalaccountsoftheorychangeneglectordistortthegradualandpiece-mealcharacteroftheorybuilding.Inthewild,grandclashesbetweenrivalhypothesesareinfrequentandisolatedcomparedtothemorecommonprocessofarticulating,refining,andelaboratingasingletheoryovertime.However,makingsenseofthisgradualandpiecemealprocessofcobblingatheorytogetherrequiresadiachronicnotionoftheorieswithcriteriaofindividuationthataccommodatesuchgradualchanges.Argumentsforthetheory-ladennessofobservationstate-mentsglosssuccessionaltheorychangeasaparadoxicalchoiceamongincom-mensurabletheories(Kuhn,1962;Feyerabend,1965),obfuscatingthereasoninginvolvedintheorychangeovertime.Furthermore,theORVobscuresthetargetednatureoftheoryconstructionbecausethetheory’sramifiedmeaningstructuremakesitdifficulttotargetpraiseorblameatpartsofthetheory.Forthesereasons,theORVdivertsattentionfromgradualandpiecemealconstruction,evaluation,andrevisionoftheoriesovertime;seeDarden(1991,ch.2)andcomparewithWimsatt(1976).Finally,theORV’sderivationalaccountofreductionhasbeenthesubjectofavarietyofattacksdiscussedinChapter5ofthisvolume.Onecriticismworthemphasizinghereisthatderivationalreductionsarelargelyperipheraltomanycasesofreductionandtheorysuccessioninthewild(Schaffner,1974;1993a)andareaccomplished,ifever,longaftertheinterestingscienceiscompleted(P.S.Churchland,1986,ch.9).Thederivationalaccountofintertheoreticreductionisalsounforgivingofgapsinthedeductiveargument,although,inthewild(therearemanygoodexamplesinmolecularandevolutionarybiology,neuroscience,andmedicine),boththepredecessorandthesuccessortheoryarepartialandincom-pletetothepointthatderivationisoutofthequestion.Additionally,therela-tionshipbetweenlevels,scientificfieldsandtheorieshasprovedsignificantlymorecomplicatedthantheOppenheim–Putnamstratigraphywouldsuggest;boththeoriesandfieldsinthebiologicalsciences,forexample,arecharacteristicallymultilevel.TherigidstricturesoftheORVleaveitill-suitedfordealingwithgradualandpiecemealtheorychangeandalsoforhighlightingthenonformalpatternsthatsci-entistsusetoconstruct,evaluate,andrevisetheirtheories.61\nCarlF.CraverTheoriesandlawsAthirdobjectiontotheORVisthattherearelegitimatetheoriesinthewild(ine.g.,molecularandevolutionarybiology,neuroscience,andmedicine)thatlackORV-stylelaws.Manyhavedeniedtheimportanceoflawsinphysicsaswell(Cartwright,1983;Giere,1999).Itwouldbedogmaticandunmotivatedtoinsistthatthesescientificproductsarenottheories.Itismoreplausibleeither(a)toinsistthatthesetheoriesdocontainORV-stylelaws,or(b)togiveupthelawrequirementaltogether.Mosthavechosensomevariantof(b).Opponentsof(a)arguethatthecentralgeneralizationsinsuchtheoriesarenonuniversalorrestrictedinscope(seenextsubsection),thattheyarephysicallycontingent(p.62),orthatlawstatementsinthewildaretypicallyeitherfalseorvacuous(p.63).Mostadvocatesof(b)havechoseneithertoreplace(orredefine)thenotionofalawwithsomethinglessstringent(p.63)ortosidesteptheissueentirely(p.64).Laws,universality,andscopeORV-stylelawsareuniversal,unrestrictedandexceptionless.Rosenberg(1985),Schaffner(1993a),andSmart(1963)haveeachsuggestedthat(most)biologicaltheoriesfailtosatisfytheserequirements.Theo-riesinthesedomainsholdonlyonearth(theyare,atbest,“terrestriallyuniver-sal”),theyoftenholdonlyforparticularspecies,andtheyhaveexceptionsevenwithinspecies.Eventhebestcandidatesforuniversalbiologicallaws,suchasthetheoriesofthegeneticcodeandproteinsynthesis,areunlikelytoholdforexoticlifeforms(e.g.,indistantsolarsystems),andareknowntohaveearthboundexcep-tions.VirusesuseRNAastheirgeneticmaterial,andproteinscanbesynthesizedwithoutaDNAtemplate(Darden,1996,p.410);seealsoBeatty(1981,1995).Thusbiologicallawsareoftenrestrictedtoparticularspecies,strains,andindivid-uals.Thisfeatureisnotuniquetothelawsofbiology;seeLange(1995)andGiere7(1988,ch.3;1999,ch.6).LawsandnecessityAseconddifficultyforORV-stylelawsinbiologicaltheoriesisthatmanyofthegeneralizationsinsuchtheoriesholdonlybythegraceofevo-lutionbynaturalselection,andsoareevolutionarilycontingent(Beatty,1995).Suchgeneralizationsmightnothavecometoholdandmay,someday,nolongerhold.Butlawsaresupposedtoexpresswhatmustnecessarilybethecaseratherthanwhatisaccidentally(orcontingently)thecase.Beattythusraisesarathermorespecificformofquitegeneralworriesaboutthekindofnecessitybyvirtueofwhichstatementsoflawcansortaccidentalgeneralizationsfromnonaccidentallawsorgeneralizationsthatsupportcounterfactualsfromthosethatdonot.Oneimportantchallenge,ifoneistomaintainthesedistinctions,todosowithoutrunningafoulofwhatEarman(1986)callsan“empiricistloyaltytest”62\nStructuresofScientificTheoriesandLewis(1986)callsthedoctrineof“HumeanSupervenience”(HS).HSistherequirementtherebenodifferenceinthelawsofnaturewithouttherebeingadifferenceinpast,present,orfutureoccurrentfacts(i.e.,particulars,theirmani-festproperties,andtheirspatiotemporalrelations).AsRoberts(1999)argues,denyingHS(i)amountstoacommitmentthatknowledgeofthelawsofnatureisinprin-cipleforeverbeyondourgrasp(the“epistemologicalproblem”)and(ii)leavesoneunabletospecifywhichsetoftruepropositionsistheextensionoftheterm“lawofnature”(the“semanticproblem”).TheimportanceandtenabilityofHShavebeenchallengedbyCarroll(1994).YetreconcilingnomologicalnecessitywithHSremainsamajorchallengeforthephilosophyofscience.SomearedrivenbytheseempiricistintuitionsinHSintodenyingthatthereisanyformofphysicalornaturalnecessity;thiscementorglueistobefoundonlyinmodelsandnotinthephenomenaintheirdomains.Stillothershavesoughtthisnaturalnecessityincausalrelationsamongobjects,processes,orevents.Thesesuggestionsarewellbeyondthescopeofthepresentdiscussion.LawsinthewildaretypicallyinaccurateorvacuousAthirdchallengefortheORV’semphasisonlawsisthatthebestexamplesoflawsholdonlyunderarangeofconditionsthattypicallydonotobtain,thatcannotobtainorthatcannotexhaustivelybedescribed(andsoareglossedbyso-called“ceterisparibus”clauses).Manylawsholdonlyunderextremeconditions(e.g.,intheabsenceofairresis-tance,orassumingallothergravitationaleffectsarenegligible),andmanyspecifywhatwillhappenunderidealizedconditions(e.g.,assumingfrictionlessplanesandpointmasses).Inanefforttospelloutthelaw’sceterisparibusconditions,onerisksturninglawsintomeaninglesstruisms,i.e.,thetheoryholdsunlessitdoesnothold(Hempel,1965,pp.166–7).Ontheotherhand,unlessallpossiblycon-foundingconditionsareincludedinthelawstatement,thelawisinaccurate.Crit-icismsofthissorthavebeenmostrigorouslypursuedbyCartwright(1983)andGiere(1999);forcounter-arguments,seeEarmanandRoberts(1999).WeakeningthelawrequirementOneresponsetocriticismsofORV-stylelawsistoreplacethemwithaweakeralternative.However,thereisnoforeseeablecon-sensusastowhatthatalternativeshouldbe.Schaffner(1993a)distinguishesuni-versalgeneralizations1anduniversalgeneralizations2,theformerapplyingto“all(terrestrial)organisms”(p.121),andthelatter“referringtothepropertyillus-tratedbythephrase‘samecause(orsameinitialconditionsandmechanisms),sameeffect’”(p.121).Generalizationsmayhavearestrictedscopeorknownexcep-tions,butthisdoesnotdetractfromthefactthatthesegeneralizationhavethekindofnecessityassociatedwiththesupportforcounterfactuals.Also,focusingontheimportanceofcounterfactualsupport,Woodward(1997)hassuggested63\nCarlF.Craverthattherequiredphysicalnecessitycanbesuppliedby“invariant”generalizations,thosethatholdunderarangeofinterventionsandsocanbeusedtocontrolormanipulate(andhenceunderstand)someeffectunderconditionswithinthatrange(whichmayberatherlimited).Stillmorepluralistically,Mitchell(2000)hassug-gestedthatORV-styleemphasisonuniversality,nonaccidentality,andunrestricted-nessproduces,“animpoverishedconceptualframeworkthatobscuresmuchinterestingvariationinboththetypesofcausalstructuresstudiedbythesciencesandthetypesofrepresentationsusedbyscientists”(p.243).Inasimilarspirit,Lange(1995)arguesthatlawsofnature,asidentifiedinscientificpractice,needbeneitherexceptionlessnorunrestrictedtoparticulartimesandplaces.Instead,hesuggeststhatstatementsoflawsbeidentifiedbytheirfunctionsinthepracticeofscienceandbecharacterizedaswarrantsforreliableinferences(intheserviceofrelevantpurposes).ItisnotnecessarytoabandontheORVtoaccommodatetheorieswithoutORV-stylelawsofnature;oneneedonlyamenditbyremovingthelawrequire-mentorreplacingitwithsomethingelse.Somecharacterizelawsastheaxiomsofthebestsystemfordescribingtheworld,thuseffectivelyremovingtheneedtoprovideaconceptualanalysisoflawtalkintermsofachecklistofpropertiestheyallshare(Lewis,1986).Othershavesoughttodivorcethediscussionoflawsfromdiscussionoftheorystructurebymakingclaimsaboutscope,necessityanduni-versalityextrinsictothetheory(p.64).ConclusionAlthoughtheORVneglectsordistortsawiderangeofinterestingquestionsaboutscience,anunderstandingofthelogicalpatternsinscientificargumentisindis-pensableforanyaccountoftheepistemologyofscience,andsotheORVisreallytheonceandfuturereceivedview,atleastforsomecentralquestionsinphiloso-phyofscience.Yet,theORVisawkwardatbestinitstreatmentoftheorybuild-ing,laws,andthenonformalpatternsexhibitedbytheoriesinthewild.The“ModelModel”ofScientificTheoriesSomecriticsoftheORVhavefounditsfailingssosystematicastowarrantanalter-8nativeformalapproachtotheorystructure.Thisalternative(orclusterofalter-natives)hasbeendubbedthe“semanticconception,”the“nonstatementview,”andthe“modelsapproach”toscientifictheories.Iwillrefertoitasthemodel9model(MM).MMwasdevelopedinpartinresponsetocriticismsofthesortdis-cussedonpage58.MMoffersalessrestrictiveframeworkforrepresentingthenonformalpatternsexhibitedbytheoriesbutultimatelyprovideslittleguidanceincharacterizingandunderstandingthesenonformalpatterns.64\nStructuresofScientificTheoriesTheoriesandmodelsThedifferentversionsofMMshareacorecommitmenttoviewingtheoriesasan10abstractspecificationsofaclassofmodels.Theterm“model”isnotoriouslyambiguous;meaningarepresentationorsimulation(ascalemodel,map,orcom-puterprogram),anabstraction(asinsomemathematicalmodels),ananalogue(Bohr’splanetarymodeloftheatom),anexperimentalorganism(asintheadultmaleSprague–Dawleyrat)oranexperimentalpreparation(suchastheamphet-aminemodelofschizophrenia).AccordingtoMM,amodelisastructurethatsatisfies(i.e.,renderstrue)atheory.Therelationshipbetweentheories,models,andtherealsystemsintheworldcanbeunderstoodasfollows:(i)Theoriesspecifyordefineabstractoridealizedsystems.(ii)Modelsarethestructuresthatsatisfy(orinstantiate)thesespecificationsordefinitions(theabstractandidealizedsystemisitselfamodelofthetheory).(iii)Thesemodelsaremoreorlesssimilarto,orhomomorophic,withrealsystems,andsocouldbeusedtocontrolandpredictrealsystemsifthereal11systemsweresufficientlysimilartothemodel.TheoriesasextralinguisticstructuresCentraltoMMistheideathattheoriesareabstractextralinguisticstructuresquiteremovedfromthephenomenaintheirdomains.Theoriesarenotidentifiedwithanyparticularrepresentation.Inthisway,MMaccommodatesthediverseconventionsforcommunicatingtheoriesinthewild(p.58)aswellasthemath-ematicalstructuresthatoftencomposetheories(p.59).Modelsmaybepartial,as+arethediverserepresentationsoftheNachannel,andtheymayverywellbeincomplete,givingMMaflexibilitynotavailablewithintheinferentialstricturesoftheORV.MMismotivatedinpartbyitsabilitytoaccommodatethevariedstructuresandstatesofcompletionoftheoriesinthewild(Beatty,1981;Beth,1949;Lloyd,1988;Suppe,1977;vanFraassen,1980,pp.64–5).AbstractionandidealizationAccordingtoMM,theoriestypicallyarenotisomorphictoanyrealsystem;instead,theyaremorenaturallythoughtofashomomorphicwith,asreplicasof(Suppe,1989),orassimilarto(Giere,1999),realsystems.Theories(andtheirmodels)aretypicallyabstractand/oridealized.Theoriesareabstracttotheextentthattheydescriberealsystemsintermsofonlyafewoftheirrelevantparameters,assum-ingthatallothersimpactnegligiblyonthebehaviorofthesystem(Suppe,1989,pp.94–5).Theoriesareidealizedifitisphysicallyimpossiblefortherealsystem65\nCarlF.Cravertotakeontheallowablevaluesoftheparameters(e.g.,pointmassesorfriction-lessplanes).OnSuppe’scounterfactualaccountoftherelationshipbetweentheories/modelsandrealsystems,theoriesandmodelsarereplicasofrealsystems(Suppesays“phenomenalsystems”).ReplicasdescribewhatarealsystemRwouldbelikeifitwereisolatedfromthedisturbinginfluenceofparametersnotincludedinthemodelM(Suppe,1989,p.95).Abstractmodelssatisfythisrequirement,sinceitisphysicallypossiblethatRsatisfytheconditionsspecifiedinM(perhapsunderextremeexperimentalconditions).Idealizedmodelssatisfythiscounterfactual12requirementsincetheantecedentisphysicallyimpossible.ThiscounterfactualformulationisonemeansbywhichadvocatesofMMhopetosidesteptheORV’sproblemsconcerninglawsofnature(p.62).MM,theories,andlawsofnatureSuppe(1989)describesthreevarietiesoflawsappearinginscientifictheories:laws13ofcoexistence,lawsofsuccessionandlawsofinteraction.Eachofthesemaybedeterministicorstatistical.Lawsofcoexistence,suchastheBoyle–Charlesgaslaw,specifypossiblepositionsinthestatespacebydescribingequationsfixingpossibleoverallstatesofthesystem.Lawsofsuccession,suchasNewton’slawsofmotion,specifypossibletrajectoriesthroughthestatespaceandsospecifyhowthesystem,lefttoitself,willchangeovertime.Finally,lawsofinteraction,specifytheresultsofinteractionbetweentwoormoresystems,suchastheinteractionofaparticlewithameasuringdevice.Theselawstogetherdefinetheclassofmodelsofthetheory.AdvocatesofMMsplitontheempiricalstatusofbothscientifictheoriesoflaws.Suppe’scounterfactualaccounttreatstheoriesasempiricalcommitmentsastohowsomerealsystemwouldworkiftheabstractedvariablesweretheonlydetermi-nantsofitsbehaviororiftheidealizingconditionsweremet.Others–Beatty(1981),Giere(1999)andvanFraassen(1980)–seetheoriesasdefinitions;the-oriesdefineaclassofmodels,andtheempiricalclaimsofscience,asBeattyputsit,“aremadeonbehalfoftheories”(1981,p.400,emphasisinoriginal),assertingthatsome(typeof)realsystemisaninstance(s)ofthekindofsystemdefinedbythetheory(Giere,1999,ch.5).TheseaccountsareeachmotivatedbydifficultieswithORV-stylelaws(concern-ingscope,abstractionandidealization).Theaccountsdifferastowhethertheoriesexpressempiricalcommitments.Oneachaccount,questionsaboutscopeanduni-versalityareseenasexternalquestionsabouttherelationbetweenatheoryandthephenomenainitsdomain,questionstobeansweredbyexperimentandauxiliaryhypotheses.Thisisausefulsuggestion,sincepreoccupationwithuniversalityandunrestrictedscopedistractsattentionfromthefactthattheoriesoftenhavelimiteddomains.Becausetheoriesareabstractandidealized,theytypicallydonotapplyuniversally.Abstracttheoriesapplyonlytorealsystemsforwhichtheinfluenceofextraneousvariablesisnegligible;idealizedtheoriesliterallyhaveascopeofzero.66\nStructuresofScientificTheoriesEachoftheseMMapproachestolawsprovidestoolstograpplewithissuesofuniversality,scope,abstraction,andidealization.Suppes’approachisprimafacieamoreappealingbecauseitsustainsthereasonableclaimthattheoriesexpressempiricalcommitments.Neitherapproachclarifiesthenecessityoflaws.Giere(1999,p.96)suggeststhatthenecessityoflawsstatementsshould,likeissuesofscope,beconsideredexternaltotheories.Thissuggestionisunattractiveprimar-ilybecausemanyusesoftheories(includingexplanation,control,andexperimen-taldesign)dependcruciallyuponnotionsofnecessity;anaccountoftheoriescannotcavalierlydismissproblemswithlawspreciselybecauselaws(orsomethingelsefillingtheirrole)aresocrucialtothefunctionsoftheoriesinscience.MMandthenonformalstructuresofscientifictheoriesInarecentelaborationofMM,Schaffnerarguesthatmosttheoriesinthebio-medicalsciences(e.g.,theclonalselectiontheoryofimmunology)aretypically“overlappinginterleveltemporalmodels”oflessthanuniversalscope(1993a,ch.3).IndoingsoSchaffneristhefirsttoclearlyrecognizeandexplorethisprevalentnonformalstructureoftheoriesinthebiologicalsciences.Hetermsthesetheories“theoriesofthemiddlerange”(1993a)andshowshowtheycanbeaccommodatedwithinMM;seealsoSuppe(1989,ch.8).Schaffner’s“models”areessentiallythesameasthosedescribedabove.Thesemodelshavenonuniver-saldomains,andtheyaretypicallyconstructedarounddifferent“standardcases”or“experimentalmodels”thatserveasprototypesandareallmoreorlesssimilartooneanother(hence“overlapping”).Schaffneralsorecognizesatemporalcom-ponenttotheorganizationofthesetheories;theydepicttemporalpathwaysofsequentialeventsrelatedbygeneralizations.Finally,thesetheoriesare“interlevel”inthattheyincludeentitiesatdifferentOppenheimandPutnam-stylelevels.Schaffner(1993a)isahair’sbreadthawayfromrecognizingthatmanytheoriesaremultileveldescriptionsofmechanisms;hethentoyswiththisidea(Schaffner,1993b).MMavoidssomeofthecriticismsoftheORV,especiallythoseproblemsrelat-ingtorepresentationalflexibility,theabstractionandidealizationoftheories,andperhapsproblemswithlawsofnature.Yet,theaddedabstractionofMMrendersitevenlessinformativethantheORVaboutnonformalpatternsintheoriesinthewild.Mechanisms:InvestigatingNonformalPatternsinScientificTheoriesWhileMMaccommodatesnonformalpatternsbetterthantheORV,itdoeslittletohighlightormotivatethesearchforthem.Attentiontononformalpatterns67\nCarlF.Craverprovidesimportantresourcesforunderstandinghowtheoriesarebuiltandthediversekindsofexplanationsthatscientifictheoriesprovide.Consideronekindoftheory,theoriesaboutmechanisms,andnoticehowthenonformalpatternsofsuchtheoriesareusedintheconstruction,evaluation,andrevisionoftheoriesovertime.MechanismsandtheirorganizationMechanismsareentitiesandactivitiesorganizedsuchthattheyrealizeofregularchangesfromstartorsetupconditionstofinishorterminationconditions(Wimsatt,1976;BechtelandRichardson,1993;Glennan,1996;Machameretal.,2000,p.2).Entitiesaretheobjectsinmechanisms;theyaretypicallydescribedwithnounsinlinguisticrepresentations.Activitiesarewhattheseentitiesdo;theyaretypicallydescribedwithverbsordepictedwitharrows.Together,thesecom-ponententitiesandactivitiesareorganizedtodosomething–toproducethebehaviorofthemechanismasawhole,tousethetermsuggestedbyGlennan14(1996);behaviorsarethe“regularchanges”thatmechanismsrealize.Typesofmechanismscanbeindividuatedonthebasisoftheiroverallbehavior,theircomponententitiesandactivities,orthewaythecomponentsareorganized.First,mechanismscandifferbehaviorally–bythephenomenathattheyrealize.Inspecifyingthebehaviorofamechanism,oneimmediatelyconstrainstheentities,activities,andorganizationalstructuresthatarerelevanttothatbehavior,andsoplacesaglobalconstraintonthesearchforthemechanism.Mechanismscanalsobeindividuatedbythe(kindsof)entitiesandactivitiesthatconstitutetheircompo-nents.Finally,mechanismscanbeindividuatedbytheiractive,spatial,andtemporalorganization.Amechanism’sactiveorganizationincludesactivitiesandinteractions(excitatoryandinhibitory)ofthemechanism’scomponententities(Wimsatt,1974;Craver,2001).Spatialorganizationincludestherelativelocations,shapes,sizes,orientations,connections,andboundariesofthemechanism’sentities.Finally,amechanism’stemporalorganizationincludestheorders,rates,durations,andfrequenciesofitsactivities(CraverandDarden,2001).+Considerthisexample.ThevoltagesensitiveNachannelsinTrumpler’s(1997)discussionarecrucialcomponentsinthemechanismforproducingactionpoten-tials,theelectricalwavespropagatedassignalsthroughneurons(thisisthebehav-iorofthemechanismasawhole).Neuronsareelectricallypolarizedattheirrestingmembranepotential(approximately-70mV).Theintracellularfluidisnegativelychargedwithrespecttotheextracellularfluidbecauseofdifferencesbetweenintra-cellularandextrecellularionconcentrations.Depolarizationisapositivechangeinthemembranepotential.Neuronsdepolarizeduringanactionpotentialwhen++voltage-sensitiveNachannelsopen,selectivelyallowingNaionstofloodthecell,therebyspikingthemembranepotential(peakingatroughly+50mV).Oneplau-+siblemechanismfortheactivationoftheNachannelisrepresentedinFigure4.1(drawnfromHall’s(1992)verbaldescription).68\nStructuresofScientificTheoriesHereishowthemechanismworks(showninthebottompanel).First,asmallinitialdepolarizationofthemembrane(resultingfromchemicaltransmissionatsynapsesorspreadingfromelsewhereinthecell)repelstheevenlyspacedpositivechargescomposingthea-helix.Second,thealphahelixrotatesineachofthefourproteinsubunitscomposingthechannel.Therotationofthehelixchangestheconformationofthechannel,creatingaporethroughthemembrane.Third,theporeislinedwitha“hairpinturn”structurecontainingchargesthatselectspe-+cificallyNaionstoflowintothecellbydiffusion.Thispaneldepictsthemecha-nism’sactiveandtemporalorganization;itshowsanorderlysequenceofsteps(repelling,rotating,opening,anddiffusing),eachsystematicallydependenton,andproductivelycontinuouswith,itspredecessor.Thetoppanneldepictstheset-upconditionsforthismechanism,includingthe+relevantentities(Naions,a-helices,hairpinturns),theirrelativesizes,shapes,+positions,locations(e.g.,thechannelspansthemembrane,andNaionsfitthroughthepore),andtheconnections,compartments,andboundariesbetweenthem.Notrepresentedinthediagramaresuchfactorsastemperature,pH,andtherelevantionicconcentrations.Suchfactorsarethebackgroundorstandingconditionsuponwhichthebehaviorofthemechanismcruciallydepends.Figure4.1thusnicelyillustratestheactive,spatial,andtemporalorganizationofthecom-+ponentsinthemechanismofNachannelactivation,butitnonethelessabstractsfromseveralcrucialparametersfortheworkingofthemechanism.MechanismschemataMechanistictheoriesaremechanismschemata.LikeMM-theories,mechanismschemataareabstractandidealizeddescriptionsofatypeofmechanism.Theydescribethebehaviorofthemechanism,itscomponententitiesandactivities,theiractive,spatial,andtemporalorganization,andtherelevantbackgroundconditionsaffectingtheapplicationofthetheory.Thescopeofmechanismschematacanvaryconsiderably,fromnoinstances(foridealizeddescriptions)touniversality,andanypointbetween.LevelsMechanismschemataoftendescribehierarchicallyorganizednetworksofmecha-nismsnestedwithinmechanisms.Insuchschemata,higher-levelactivities(y)ofmechanismsasawhole(S)arerealizedbytheorganizedactivities(f)oflower-levelcomponents(Xs),andtheseare,inturn,realizedbytheactivities(s)ofstill+lower-levelcomponents(Ps).Thegating(s)oftheNachannel(P)ispartofthemechanism(X)forgeneratingactionpotentials(f),whichispartofalmosteverybrainmechanisminvolvingelectricalsignals.Therelationshipbetweenlowerandhighermechanisticlevelsisapart-wholerelationshipwiththeadditionalrestric-69\nCarlF.Cravertionthatthelower-levelpartsarecomponentsof(andhenceorganizedwithin)thehigher-levelmechanism.Lowerlevelentities(e.g.Xs)areproperpartsofhigher-levelentities(S),andsotheXsarenolarger,andtypicallysmaller,thanS;theyarewithinS’sspatialboundaries.Likewise,theactivitiesofthelower-levelpartsarestepsorstagesinthehigher-levelactivities.Exactlyhowmanylevelsthereare,andhowtheyaretobeindividuated,areempiricalquestionsthatareanswereddifferentlyfordifferentphenomena(Craver,2001).Mechanistichierarchiesshouldnotbeconfusedwithintuitiveontichierarchies,whichmapoutamonolithicstratigraphyoflevelsacrosstheories,entities,andsci-entificfields.Mechanistichierarchiesaredomainspecific,framedwithrespecttosomehighestsystemSanditsy-ing.Thepartsinmechanistichierarchiesarecom-ponentsorganized(actively,spatially,temporally,andhierarchically)torealizethebehaviorofthemechanismasawhole.Thisdistinguishesmechanisticwholesfrommereaggregates(suchaspilesofsand),merecollectionsofimproperparts(suchasthesetof1-inchcubesthatcomposemydog,Spike),andmereinclusivesets(suchasthealbumsintheClashdiscography).Therearenodoubtmanysensesof“level”thatarenotsufficientlydistinctinthephilosophicalliterature.Sortingthemoutisanimportantandunresolvedprojectinthephilosophyofscience(Simon,1969;Wimsatt,1974;Haugeland,1998).VarietiesofmechanismsBoththeORVandMMarepitchedtooabstractlytocapturerecurrentnon-formalpatternsexhibitedbymechanismschemata:patternsintheorganizationofmechanismsthatarecrucialforunderstandinghowthesetheoriesexplainandhowtheyareconstructedovertime.Consideronebranchinapossible(nonexclusive)taxonomyofmechanisms.Beginwithetiologicalmechanismsandconstitutivemechanisms(Shapere,1977;Salmon,1984,ch.9).Etiologicalmechanisms(suchasnaturalselection)includetheorganizedentitiesandactivitiesantecedenttoandproductiveofthephe-nomenontobeexplained(e.g.,themechanismbywhichatraitcomestobefixed+inapopulation).Constitutivemechanisms(likethemechanismofNachannelgating)realize(ratherthanproduce)higher-levelphenomena;thesehigher-levelphenomenaarecontemporaneouswith(ratherthansubsequentto)andcomposedof(ratherthanproducedoreffectedby)theorganizedactivitiesoflower-levelcomponents.Etiologicalmechanismsincludebothstructuringmechanismsandtriggeringmechanisms.Dretske(1995)hasdistinguished“structuringcauses”from“trig-geringcauses,”onthegroundsthatthetriggeringcauseTcompletesasetofotherwiseinsufficientpreexistingconditionsCthusmaking(T+C)asufficientcauseoftheexplanadumeventorphenomenonE.Forexample,spreadingdepo-+larization(T),giventheNachannelsetup(C),triggerstheopeningofthechannel(E).AstructuringcauseU,incontrast,preparestheconditionsCwithinwhich70\nStructuresofScientificTheoriesTcanbeatriggeringcauseandsoproducesthemechanismlinkingTandC(1995,p.124).Forexample,onemayperhapslooktoevolutionarytheorytoexplainhowthesodiumchannelcametoactivateunderconditionsofslightdepolariza-tion.Intriggeringmechanisms,TinCissufficientforE;instructuringmecha-nisms,UproducesthemechanismbywhichTissufficientforE.Twoetiologicalvarietiesofstructuringmechanismsareselectiveandinstructivemechanisms.Inselectivemechanisms,apopulationofvariantsisproduced(rela-tively)independentlyofenvironmentalinfluencesandthen,byvirtueofsomecriticalenvironmentalfactor,thesetofvariantsischangedsuchthatcertaintraitsareincreasinglyrepresentedinthepopulation.Examplesofselectivemechanismsincludeevolutionbynaturalselection,clonalselectionforantibodiesinimmunol-ogy,andperhapsneuralDarwinism;eachisdiscussedinDardenandCain(1989).Instructivemechanisms(suchasinheritanceofadaptiveacquiredcharacteristicsorpedagogy)aredifferentinthefirststage,sincetheproductionofadaptivevariantsisdirectlyinfluencedbyfeaturesofthepopulation’senvironment.Differenttypesofmechanismscanbedistinguishedonthebasisofrecurrentpatternsintheirorganization.Mechanismsmaybeorganizedinseries,inparallel,orincycles.Theymaycontainbranchesandjoins,andtheyoftenincludefeed-backandfeedforwardsubcomponents.Somemechanismsareredundantlyor-ganized,andsomehaveconsiderablecapacityforreorganizationorplasticityinthefaceofdamage.TheserecurrentpatternsinmechanisticorganizationhavebeeninvestigatedbyWimsatt(1986),butthereremainsconsiderableworktobedoneinsortingouttheaxesalongwhichmechanismsandschematamightdiffer.Scientifictheoriesexhibitavarietyofpatternsindomainsofempiricalphe-nomena,patternsthatareinvisibleifoneabstractstoofarawayfromthedetailsofscientifictheoriesinthewild.Attentiontothesedetailspaysdividendsforunderstandingmechanisticexplanation(nextsection)andtheprocessofbuildingmultilevelmechanismschemata(p.72).MechanisticexplanationMechanismschemataexplainnotbyfittingaphenomenonintoawebofinferen-tialrelationshipsbutbycharacterizingthemechanismbywhichthephenomenonisproducedorrealized.ThissuggestionisconsistentwiththeMM-relatedaccountofexplanationaspatterncompletion,orprototypeactivation(Giere,1999,ch.6;Churchland,1989),butinsists,inaddition,onanexplanatoryroleforthenonformalpatternsinthesetheories.Notallpatternsareexplanatory;onegoalistodistinguishthosethatarefromthosethatarenot.Salmon(1984)hassuggestedthatatleastoneimportantkindofkindofexplanationinvolvestracingpathwaysinacausalnexus;aphenomenonisexplainedbyshowinghowthatphenomenonfitsintoapatternofcausalprocessesandtheirinteractions.Mechanisticpatternsarefurtherdistinguishedbytheiractive,spatial,temporal,andhierarchicalorganization;andthesefeaturesofmechanismschematadrawour71\nCarlF.Craverattentiontosalientfeaturesrelevanttotheintelligibilityprovidedbyadescriptionofamechanism.Scriven(1962)emphasizesthenarrativestructureofmanyexplanations.There+arenogoodstorieswithoutverbs.TheverbstheNachannelschemainclude“repelling,”“rotating,”“opening,”and“diffusing.”Verbsprovidetheproductivecontinuityinthemechanism,intelligiblylinkingearlierstagestolaterstages.Sub-stantivalistsinthephilosophyofsciencehaveemphasizedstaticstructures,occur-rentevents,entitiesandrelationsoverdynamicactivities,extendedprocesses,changesandforces.Substantivalistsnominalizeorneglectactivefeaturesofscien-tificontology,thediversekindsofchangingthatunderlieregularities;theyleaveouttheverbs.Thisneglectcanberedressedwithattentiontotypesofactivities,criteriafortheirindividuation,andthedifferencesbetweenthescientificinvesti-gationofactivitiesandentities(Machameretal.,2000).Emphasizingtheimportanceofactivitiesinmechanismscannotsidesteptheproblemswithlawsofnaturediscussedonpages62and67.Anadequateaccountofmechanismschematamustawaitanaccountofhowactivitiesaredif-ferentfrommereregularities.Someprogressontheseproblemswillbegainedbyexploringtheconnectionsbetweenthemechanisticperspectivesontheorystruc-turesketchedhereandrecentworkonlaws(Lange,1995;Roberts,1999),invari-antgeneralizations(Woodward,1997),physicalcausality(Dowe,1992),capacities(Cartwright,1989;Glennan,1997),andthepragmaticsoflaws(Mitchell,2000).Afreshperspectivemightbeprovidedbyinvestigatingthepracticesofscientistsastheyintroduce,individuate,characterize,anddescribetheactivitiespickedoutbytheverbsinmechanismschemata.ConstructingmechanismschemataAttentiontothenonformalpatternsexhibitedbytheorieshasalreadyyieldeddividendsinthinkingabouttheoryconstruction.Forexample,BechtelandRichardson(1993)discussdecompositionandlocalizationasresearchstrategiesintheconstructionofmechanistictheories.CraverandDarden(2001)haveextendedthiswork,showingthattheconstructionofmechanismschematatypi-callyproceedsgraduallyandpiecemealbyrevealingconstraintsonthemechanism,constraintsfromthebehaviorofthemechanism,theavailableentitiesandactivi-tiesforthemechanism,andfeaturesoftheiractive,spatial,temporal,andhierar-chicalorganization.Findingsuchempiricalconstraintsprunesthespaceofplausiblemechanismsandoftensuggestspotentiallyfruitfulavenuesforfurtherresearch.Onegoalinconstructingadescriptionofamechanismistoestablishaseam-lessproductivecontinuityofthemechanism,withoutgaps,frombeginningtoend.Inpursuitofthisgoal,researchersfrequentlyforwardchain,usingknownstagesearlyinthemechanismtoconjectureorpredictstagesthatarelikelytofollow,andbacktrack,usingknownstageslateinthemechanismtoconjectureorpredict72\nStructuresofScientificTheoriestheentities,activities,ororganizationalfeaturesearlierinthemechanism.Non-formalaspectsoftheorystructureareusedbyscientiststogeneratenewhy-pothesesandtotargetthepraiseandblamefromempiricaltestsatspecificportionsofthetheory(DardenandCraver,2001).Asecondgoalinconstructingspecificallymultilevelmechanismschemataistointegratethedifferentlevelstogetherintoadescriptionofonecoherentmechanism.Interlevelintegrationinvolveselaboratingandaligningthelevelsinahierarchytoshow,forsomeX’sf-ing(i)howitfitsintotheorganizationofahigherlevelmechanismforS’sy-ing,and(ii)howitcanbeexplainedintermsoftheconstitutivemechanism(theorganizeds-ingofps).Theselevelsarelinkedtogetherthroughresearchstrategiesthatexhibitthecon-stitutivecausalrelevanceoflowerlevelorganizedentitiesandactivitiestohigherlevelentitiesandactivities.Inthisway,upwardlookinganddownwardlookingresearchstrategiescombinetoprovideanintegrateddescriptionofthepatternexhibitedbyamultilevelmechanism(Craver,2001).ConclusionScientifictheorieshavemanydifferentstructures,structuresthatexhibitpatternsindiversedomainsofphenomena.Inferentialpatternsarecrucialtounderstand-ingsomeaspectsofscienceandthewaythatitchangesovertime.Butthereisagreatdealmoretobesaidaboutthesepatternsthancanbesaidbyassimilatingthemtoaninferentialpattern.Nonformalpatterns(suchasmechanisticpatterns)arealsoimportantforunderstandinghowtheoriesareusedandconstructed.Closerscrutinyofthediversestructuresofscientifictheories,especiallymechanis-ticpatterns,islikelytopayseriousdividendsforunderstandingscienceandsci-entificpractice.Notes1ThankstoLindleyDarden,PeterMachamer,andKenSchaffnerfortheirtimeandhelp.2Patternscanbeunderstood,followingDennett(1991),eitherintermsoftheirabilitytoberecognizedorintermsoftheirsusceptibilitytoexpressioninsomethinglessthana“bitmap”;seealsoHaugeland(1998);Toulmin’s(1953)discussionofmapsisinmanywayssimilartothisnotionofapattern).A“domain”followingShapere(1977)issomebodyofitemsof“information”variouslyinterrelatedinawaythathelpsonetosolveanimportantproblemthatscienceisreadytotackleatagiventime(Shapere,1977,p.525).73\nCarlF.Craver3ClassicstatementsoftheORVcanbefoundinBraithwaite(1953),Carnap([1939]1989),Duhem(1954),Hempel(1965,chs4and8;1966,ch.6)andNagel(1961,chs5and6).ValuablecriticalexpositionsincludeSuppe(1977,50–1;1979;1989)andThompson(1989,chs2and3).TheORVwasdevelopedprimarilyfortheexpres-sionofphysicaltheories,butithasbeenappliedwithdebatablesuccesstoevolution-arybiologyand/orpopulationgenetics(Braithwaite,1953;Hull,1974;Ruse,1973;Williams,1970),andpsychology(Skinner,1945).4Thisinferentialapproachtoscientifictheorieshasbeendubbedthe“received”(Putnam,1962)or“orthodox”(Feigl,1970)view,the“statementview,”the“syn-tacticconception”(Thompson,1989),the“hypothetico-deductive”account(Lloyd,1988),“theEuclideanideal”(Schaffner,1993a,b),andthe“sentential”or“proposi-tional”account(Churchland,1989).IcallittheORVtoflagitswaningholdonthephilosophyofscienceandtoavoidenshrininginanameasingleinterpretationofeithertheORVorofitsshortcomings.5ThisimageoftheorystructurewasinspiredatleastinpartbyRussellandWhitehead’seffortstoreducemathematicstologic.6Someobjecttotheory-centeredapproachestothephilosophyofsciencegenerally.Amongthese,“Globalists”focusonmoreinclusiveunitsofanalysisthantheories,recommendingsuchalternativesasdisciplinarymatricesorparadigms(Kuhn,1962),fields(DardenandMaull,1977;Darden,1991),practices(Kitcher,1993,p.74),researchprograms(Lakatos,1970),andtraditions(Laudan,1977).Theseglobalunitsofscienceinclude,inadditiontotheories,alsoexperimentaltechniques,institutionalpractices,consensualstandardsandnorms,organizations,andworldviews.“NewExperimentalists,”ontheotherhand,decentertheoriesintheanalysisofscienceandcenterexperimentationinstead(Hacking,1983;Galison,1987;Rheinberger,1997).Stillothers,withprimarilyepistemologicalconcerns,havecriticizedcorrespondencerules,thetheory/observationdistinction,andthetenabilityofscientificrealism(Achinstein,1968;Putnam,1962;Schaffner,1969;vanFraassen,1980).Suppe(1977)isthedefinitivehistoryofthislineofcriticism.7Oneresponsetothislineofcriticism,onepursuedbyWaters(1998),istoarguethatphilosophershavemistakenlyconfuseduniversalcausalregularitieswithdistributions(claimsabouthowatraitorpropertyisdistributedacrossapopulationoforganisms).Onewayofputtingthisisthatthelaw(x)(Fx…Gx)istrueofeverything(auni-versalcausalgeneralization),althoughonlysomethingssatisfytheantecedent(adistribution).8ImportantstatementsandelaborationsofthemodelmodelincludeBeth(1949),Giere(1979;1988),Schaffner(1993a),Suppe(1977;1989),Suppes(1967),andvanFraassen(1980).Beth(1949)appliedthisapproachtoNewtonianandquantummechanics,andithasbeenworkedoutfortheoriesinclassicalmechanics(McKinseyandSuppes,1953),quantummechanics(vanFraassen,1991),evolutionarytheoryandpopulationgenetics(Beatty,1980;1981;Lloyd,1988,ch.2;Thompson1989,ch.5),sociobiology(Thompson,1989),biologicaltaxonomy(Suppe,1989,ch.7)andmostrecently,declarativememoryandsynapticmechanismsinneuroscience(Bickle,1998).9ThereisnoconsensusonhowtodrawthecontrastbetweentheORVandMM.Themostcommonapproachreliesonthedistinctionbetweensyntaxandsemantics,adis-tinctionthathardlyclearinitsownrightandonethathasbeendifficulttoapplyneatly74\nStructuresofScientificTheoriestoORVandMM.AnothercontrastisbetweenORVasa“statementview”oftheo-riesandMMasa“nonstatementview,”butstatementscanbemodelsandthecom-ponentsoftheORVmightbereasonablyinterpretedaspropositionsratherthanstatements.SomehavearguedthatanythingrepresentableintheORVcanberepre-sentedinMMandviceversa,minimizingthemotivationtospelloutthedifferencesindetail.Littleofsignificancehasturnedongettingthisdistinctionright.10TherearetwoclassicformulationsofMM:asettheoreticformulation,recommendedbySneed(1971),Stegmüller(1976),andSuppes(1967),accordingtowhichtheo-riesarestructuresrepresentedbysettheoreticpredicatesthatdefineaclassofmodels;andastate-spaceapproach,favoredbyBeth(1949),Suppe(1989)andvanFraassen(1980),accordingtowhichtheoriesareconstraintsonmultidimensionalstate-spacesorconfigurationsofsetsofsuchspaceswhichdefineaclassofmodels.Debatesovertherelativemeritsoftheseapproachescanbesafelyneglectedforpresentpurposes(vanFraassen,1972;Suppe,1979).11Ineglectafourthelement,a“phenomenalsystem”(Suppe,1989)oran“empiricalmodel”(Lloyd,1988)thatisconstructedonthebasisofdataandintermediatebetweenmodelsandrealsystems.12Thissuggestion,ifIunderstanditcorrectly,hasthestronglycounterintuitiveconse-quenceofrenderingallidealizedstemsmodelsofanygivenrealsystem.13Suppe(1989)alsoincludeslawsofquasi-succession.14Ononereasonableinterpretationofthisrealizingrelationship–modifiedfromKim(1995),discussingLeporeandLoewer(1987)–amechanismMcomposedoftheactively,spatially,andtemporallyorganizedf-ingofXsrealizesS’sy-ingjustincase(i)itisphysicallyimpossibleofS’sy-ingtodifferwithouttherebeingsomediffer-enceinM,and(ii)S’sy-ingisexhaustivelyexplainedbyM(inanonticandnotnecessarilyepi-stemicsense).Thiswayofspellingouttherealizationrelationshipdiffersinthatitspecifiesmorepreciselythecharacteroftheorganizingrelationshipsinvolvedinrealizingahigher-levelphenomenon.ReferencesAchinstein,P.(1968):ConceptsofScience:APhilosophicalAnalysis.Baltimore,MD:JohnsHopkinsUniversityPress.Beatty,J.(1980):“Optimal-DesignModelsandtheStrategyofModelBuildinginEvolu-tionaryBiology,”PhilosophyofScience,47,532–61.Beatty,J.(1981):“What’sWrongWiththeReceivedViewofEvolutionaryTheory?”inP.D.AsquithandR.N.Giere(eds.),PSA1980,vol.2,EastLansing,MI.:PhilosophyofScienceAssociation,397–426.Beatty,J.(1995):“TheEvolutionaryContingencyThesis,”inJ.G.LennoxandG.Wolters(eds.),Concepts,TheoriesandRationalityintheBiologicalSciences,Konstanz,Germany:UniversityofKonstanzPressandPittsburgh,PA:UniversityofPittsburghPress,45–81.Bechtel,W.(1988):PhilosophyofScience:AnOverviewforCognitiveScience.Hillsdale,N.J.:Erlbaum.75\nCarlF.CraverBechtel,W.andRichardson,R.(1993):DiscoveringComplexity:DecompositionandLocal-izationasStrategiesinScientificResearch.Princeton:PrincetonUniversityPress.Beth,E.(1949):“TowardsanUp-to-DatePhilosophyoftheNaturalSciences,”Methodos,1,178–85.Bickle,J.(1998):PsychoneuronalReduction:TheNewWave.Cambridge,MA:MITPress.Braithwaite,R.(1953):ScientificExplanation.Cambridge:CambridgeUniversityPress.Carnap,R.([1939]1989):“TheoriesasPartiallyInterpretedFormalSystems,”inB.A.BrodyandR.E.Grandy,(eds.),ReadingsinthePhilosophyofScience,EnglewoodCliffs,NJ:PrenticeHall,5–11.ReprintedfromCarnap,FoundationsofLogicandMathe-matics,Chicago:UniversityofChicagoPress.Caroll,J.(1994):LawsofNature.Cambridge:CambridgeUniversityPress.Cartwright,N.(1983):HowtheLawsofPhysicsLie.Oxford:ClarendonPress.Cartwright,N.(1989):Nature’sCapacitiesandtheirMeasurement.Oxford:OxfordUni-versityPress.Churchland,P.M.(1989):ANeurocomputationalPerspective.Cambridge,MA:MITPress.Churchland,P.S.(1986):Neurophilosophy.Cambridge,MA:MITPress.Craver,C.F.(2001):“RoleFunctions,Mechanisms,andHierarchy,”PhilosophyofScience,68(1),53–74.Craver,C.F.andDarden,L.(2001):“DiscoveringMechanismsinNeurobiology:TheCaseofSpatialMemory,”inP.K.Machamer,R.GrushandP.McLaughlin(eds.),TheoryandMethodintheNeurosciences,Pittsburgh,PA:UniversityofPittsburghPress,112–37.Darden,L.(1991):TheoryChangeinScience:StrategiesfromMendelianGenetics.NewYork:OxfordUniversityPress.Darden,L.(1996):“GeneralizationsinBiology,”StudiesintheHistoryandPhilosophyofScience,27,409–19.Darden,L.andCain,J.A.(1989):“SelectionTypeTheories,”PhilosophyofScience,56,106–29.Darden,L.andCraver,C.F.(2001):“InterfieldStrategiesintheDiscoveryoftheMech-anismofProteinSynthesis,”StudiesintheHistoryandPhilosophyofBiologyandBio-medicalSciences,forthcoming.Darden,L.andMaull,N.(1977):“InterfieldTheories,”PhilosophyofScience,44,43–64.Dennett,D.(1991):“RealPatterns,”JournalofPhilosophy,88,27–51.Dowe,P.(1992):“WesleySalmon’sProcessTheoryofCausalityandtheConservedQuan-tityTheory,”PhilosophyofScience,59,195–216.Dretske,F.(1995):“MentalEventsasStructuringCauses,”inJ.HeilandA.Mele(eds.),Ment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ightforward.Historically“reductionism”isthe“ism”thatstandsforthewidelyheldbeliefthatbothontologicalandepistemologicalreductionismaremoreorlesstrue.Reductionismistheviewthatthebestunderstandingofacomplexsystemshouldbesoughtatthelevelofthestructure,behaviorandlawsofitscomponentpartsplustheirrelations.However,accordingtomereologicalreductionism,therela-tionsbetweenbasicpartsarethemselvesreducibletotheintrinsicpropertiesoftherelata(seebelow).Theontologicalassumptionimplicitisthatthemostfunda-mentalphysicallevel,whateverthatturnsouttobe,isultimatelythe“real”ontol-ogyoftheworld,andanythingelsethatistokeepthestatusofrealmustsomehowbeabletobe‘mappedonto’or‘builtoutof’thoseelementsofthefundamentalontology.Relatedly,fundamentaltheory,inprinciple,isdeeperandmoreinclu-siveinitstruths,hasgreaterpredictiveandexplanatorypower,andsoprovidesadeeperunderstandingoftheworld.“Emergentism”,historicallyopposedtoreductionism,isthe“ism”accordingtowhichbothontologicalandepistemologicalemergentismaremoreorlesstrue,whereontologicalandepistemologicalemergencearejustthenegationoftheirreductivecounterparts.Emergentismclaimsthatawholeis“somethingmorethanthesumofitsparts”,orhaspropertiesthatcannotbeunderstoodintermsofthepropertiesoftheparts.Thus,emergentismrejectstheideathatthereisanyfun-damentallevelofontology.Itholdsthatthebestunderstandingofcomplexsystemsmustbesoughtatthelevelofthestructure,behaviorandlawsofthewholesystemandthatsciencemayrequireapluralityoftheories(differenttheo-riesfordifferentdomains)toacquirethegreatestpredictive/explanatorypowerandthedeepestunderstanding.Theproblemofreductionandemergenceis(andhasbeen)ofgreatinterestandimportanceinphilosophyandscientificdisciplinesfromphysicstopsychol-ogy;seePhilosophicalStudies,Vol.95,1999andBeckermannetal.,(1992),Blazeretal.,(1984)andSarkar(1998).Itisalwayspossibletodivideclaimsaboutreductionismandemergentism.Onemayacceptontologicalreduction-ismbutrejectepistemologicalreductionism,andvice-versa,likewiseforontologicalemergentismandepistemologicalemergentism.Further,onemayrestrictthequestionofreductionismandemergentismtoparticulardomainsofdiscourse.Forexample,onemightacceptreductionism(epistemicand/orontic)forthecaseofclassicalmechanicsandquantummechanics,butrejectit(epistemicand/orontic)forthecaseoffolkpsychologyandtheoriesfromneuroscience.81\nMichaelSilbersteinTheVarietiesofReductionism:OntologicalandEpistemologicalThebasicideaofreductionisconveyedbythe“nothingmorethan...”cliché.IfXsreducetoYs,thenwewouldseemtobejustifiedinsayingorbelievingthingssuchas“Xsarenothingother(ormore)thanYs,”or“Xsarejustspecialsorts,combinationsorcomplexesofYs.”However,oncebeyondcliches,thenotionofreductionisambiguousalongtwoprincipaldimensions:thetypesofitemsthatarereductivelylinkedandthenatureofthelinkinvolved.Todefineaspecificnotionofreduction,weneedtoanswertwoquestions:•Questionoftherelata:Reductionisarelation,butwhattypesofthingsmayberelated?•Questionofthelink:Inwhatway(s)musttheitemsbelinkedtocountasareduction?Letusfirstconsiderthequestionoftherelata.Thethingsthatmayberelatedhavebeenviewedeitheras:•realworlditems–entities,events,properties,etc.–whichistheOntologicalformofReduction,or•representationalitems–theories,concepts,models,frameworks,schemas,regularities,etc.–whichistheEpistemologicalformofReduction.Thus,thefirststepinourtaxonomysubdividesintotwotypesofreduction.Eachtypefurthersubdividesbasedonthespecifickindsofrelatainquestion.Ontologi-calsubdivisionsinclude:partsandwholes;properties;events/processes;andcausalcapacities.Epistemologicalsubdivisionsinclude:concepts;laws(epistemicallycon-strued);theories;andmodels.(Theselistsarenotintendedtobeexhaustive,butmerelyrepresentative.)Thesecondquestionaboutthelinkwasinwhatway(s)musttheitemsbelinkedtocountasacaseofreduction?Again,thereareavarietyofanswersonboththeontologicalandtheepistemologicalside.Questionoftheontologicallink:Howmustthingsberelatedforonetoonto-logicallyreducetotheother?Atleastfourmajoranswershavebeenchampioned:•Elimination•Identity•Mereologicalsupervenience(includes“composition”,“realization”andotherrelatedweakerversionsofthiskindofdeterminationrelation)•Nomologicalsupervenience/determination82\nReduction,EmergenceandExplanationTherelativemeritsofcompetingclaimshavebeenextensivelydebated,butforpresentpurposesitsufficestosayabriefbitabouteachandgiveageneralsenseoftherangeofoptions.EliminationOneofthethreeformsofreductionlistedbyKemenyandOppenheimintheirclassicpaperonreduction(1956)wasreplacement,i.e.,casesinwhichwecometorecognizethatwhatwethoughtwereXsarereallyjustYs.Xsareeliminatedfromourontology,e.g.,claimsofdemonicpossession(Rorty,1970;Churchland,1981;Dennett,1988;Wilkes,1988,1995).IdentityIdentityinvolvescasesinwhichwecontinuetoaccepttheexistenceofXsbutcometoseethattheyareidenticalwithYs(orwithspecialsortsofYs).XsreducetoYsinthestrictestsenseofbeingthesamethingasYs.ThismayhappenwhenalaterY-theoryrevealsthetruenatureofXtous.Forexample,wehavecometoseethatheatisjustkineticmolecularenergyandthatgenesarejustfunctionallyactiveDNAsequences.However,theidentitydoesnotrequireeliminationordenytheexistenceoftheprioritems,ratherweseethattwodistincttheorieshavedescribedorreferredtothesameentities/properties.MereologicalsupervenienceReductionismpertainingtopartsandwholesgoesbyseveralnames:“mereologi-calsupervenience,”“Humeansupervenience”and“part/wholereductionism.”Mereologicalsuperveniencesaysthatthepropertiesofawholearedeterminedbythepropertiesofitsparts(Lewis,1986,p.320).Morespecifically,mereologicalsupervenienceholdsthatallthepropertiesofthewholearedeterminedbythequalitativeintrinsicpropertiesofthemostfun-damentalparts.Intrinsicpropertiesbeingnon-relationalpropertieshadbythepartswhichthesebearinandofthemselves,withoutregardtorelationshipswithanyotherobjectsorrelationshipswiththewhole.Sometimes,philosopherssaythatintrinsicpropertiesarepropertiesthatanobjectwouldhaveeveninapossi-bleworldinwhichitaloneexists.Paradigmaticexamplesincludemass,charge,andspin.Further,intrinsicpropertiesaremuchliketheolderprimaryqualities.Itisnotoriouslydifficulttodefinethenotionofanintrinsicpropertyorarelationalpropertyinanon-circularandnon-questionbeggingmanner;nonetheless,philosophersandphysicistsrelyheavilyonthisdistinction(Lewis,1986).83\nMichaelSilbersteinNomologicalsupervenience/determinationFundamentalphysicallaws(ontologicallyconstrued),governingthemostbasiclevelofreality,determineornecessitateallthehigher-levellawsintheuniverse.Mere-ologicalsupervenience,ontheonehand,saysthattheintrinsicpropertiesofthemostbasicpartsdetermineallthepropertiesofthewhole–thisisaclaimaboutpart-wholedetermination(purelyphysicalnecessity).Nomologicalsupervenienceisaboutnomicnecessity,themostfundamentallawsofphysicsultimatelynecessi-tateallthespecialsciencelaws,andthereforethesefundamentallawsdetermineeverythingthathappens(inconjunctionwithinitialorboundaryconditions).Thus,iftwoworldsarewhollyalikeintermsoftheirmostfundamentallawsandintermsofinitial/boundaryconditions,thenweshouldexpectthemtobethesameinallotherrespects.Inepistemologicalreductiononesetofrepresentationalitemsisreducedtoanother.Theserepresentationalitemsareallhumanconstructionsandoftentakentobelinguisticorlinguisticsurrogates,thoughthisneednotbethecase.Itwasnotedabovethatreductionrelationsmightholdamongatleastfourdifferentkindsofrepresentationalitems.Concerningtheepistemologicallinks(orrelations)thatdothereducing,adiver-sityofclaimshavebeenmade.Somerelations,suchasderivability,makesenseasarelationbetweentheoriesseenassetsofpropositionsbutnotamongmodelsorconcepts.However,certaincommonalitiesrunthroughthefamilyofepistemological-reductiverelations.Mostofthespecificvariantsofepistemologicalreductionfallintooneoffourgeneralcategories:•Replacement•Theoretical-derivational(logicalempiricist)•Semantic/model-theoretic/structuralistanalysis•PragmaticReplacementTheanalogueofeliminationontheepistemologicalsidewouldbereplacement.Ourpriorwaysofdescribingandconceptualizingtheworldmightdropoutofuseandbesupersededbynewermoreadequatewaysofrepresentingreality.Forexample,manyofourfolkpsychologicalconceptsmightturnoutnottodoagoodjobofcharacterizingtheaspectsoftheworldatwhichtheyweredirected,ashappenedwithsuchconceptsasdemonicpossession(Feyerabend,1962).84\nReduction,EmergenceandExplanationTheoretical-derivationalTheclassicnotionofintertheoreticreductionintermsoftheoreticalderivation,asfoundinKemenyandOppenheim(1956)orinErnestNagel’sclassictreatment(1961),descendsfromthelogicalempiricistviewoftheoriesasinterpretedformalcalculistatableassetsofpropositionsofsymboliclogic.Intertheoreticreductionisthederivationofonetheoryfromanother;andsoconstitutesanexplanationofthereducedtheorybythereducingtheory.Thismodeltreatsintertheoreticreductionasdeductive,andasaspecialcaseofdeductive-nomologicalexplana-tion.ThusifonesuchtheoryT1couldbelogicallyderivedfromanotherT2,theneverythingT1saysabouttheworldwouldbecapturedbyT2.BecausethetheorytobereducedT1normallycontainstermsandpredicatesthatdonotoccurinthereducingtheoryT2,thederivationalsorequiressomebridgelawsorbridgeprin-ciplestoconnectthevocabulariesofthetwotheories.Thesemaytaketheformofstrictbiconditionalslinkingtermsinthetwotheories,andwhentheydosuchbiconditionalsmayunderwriteanontologicalidentityclaim.However,therele-vantbridgeprinciplesneednotbestrictbiconditionals.Allthatisrequiredisenoughofalinkbetweenthevocabulariesofthetwotheoriestosupportthenecessaryderivation.Onecaveatisinorder.Strictlyspeaking,inmostcaseswhatisderivedisnottheoriginalreducedtheorybutanimageofthattheorywithinthereducingtheory,andthatimageistypicallyonlyacloseapproximationoftheoriginalratherthanapreciseanalogue(Feyerabend,1977;Churchland,1985).Nagel’saccount(1961)ofintertheoreticreductionhasbecomeastandardforthistype,andallalternativeaccountsareinonewayoranotheramendmentstoitorreactionsagainstit.So,letuslookatitalittlemoreclosely,andseehowproblemsforthisaccounthavearisen.Nageldistinguishestwotypesofreductionsonthebasisofwhetherornotthevocabularyofthereducedtheoryisasubsetofthereducingtheory.Ifitis–thatis,ifthereducedtheoryT1containsnodescriptivetermsnotcontainedinthereducingtheoryT2,andthetermsofT1areunderstoodtohaveapproximatelythesamemeaningsthattheyhaveinT2,thenNagelcallsthereductionofT1byT2“homogeneous”(Nagel,1961,p.339).Fromahistoricalperspective,thisattitudeissomewhatnaïve(Sklar,1967,pp.110–11).Thenumberofactualcasesinthehistoryofsciencewhereagenuinehomogeneousreductiontakesplacearefewandfarbetween.OneescapefortheproponentofNagel-typereductionsistodistinguishexplainingatheory(orexplainingthelawsofagiventheory)fromexplainingitaway(Sklar,1967,pp.112–13).Thus,wemaystillspeakofreductionifthederivationoftheappro-ximationstothereducedtheory’slawsservestoaccountforwhythereducedtheoryworksaswellasitdoesinits(perhapsmorelimited)domainofapplicability.Thetaskofcharacterizingreductionismoreinvolvedwhenthereductionishet-erogeneous,thatis,whenthereducedtheorycontainstermsorconceptsthatdonotappearinthereducingtheory.Nageltakesasaparadigmexamplethe(appar-ent)reductionofthermodynamics,oratleastsomepartsofthermodynamics,to85\nMichaelSilbersteinstatisticalmechanics.Forinstance,thermodynamicscontainstheconceptoftem-perature(amongothers)thatislackinginthereducingtheoryofstatisticalmechan-ics.Nagelnotesthat“ifthelawsofthesecondaryscience(thereducedtheory)containtermsthatdonotoccurinthetheoreticalassumptionsoftheprimarydisci-pline(thereducingtheory)thelogicalderivationoftheformerfromthelatterisprimafacieimpossible”(Nagel,1961,pp.352–4).Asaconsequence,Nagelintro-ducestwo“necessaryformalconditions”requiredforreductiontotakeplaceknownasconnectabilityandderivability.Connectabilityhastodowiththebridgelawsthatrelatethesetsoftermsfromthetheoriesinquestion.Theconsiderationofcertainexampleslendsplausibilitytotheideathatthebridgelawsshouldbecon-sideredtoexpresssomekindofidentityrelation.Forinstance,Sklarnotesthatthereductionofthe“theory”ofphysicalopticstothetheoryofelectromagneticradia-tionproceedsbyidentifyingoneclassofentities–lightwaves–with(partof)anotherclass–electromagneticradiation(Sklar,1967,p.120).Infact,ifsomethinglikeNagelianreductionisgoingtowork,itisgenerallyacceptedthatthebridgelawsshouldreflecttheexistenceofsomekindofsyntheticidentity.Oneproblemfacingthetheoretical-derivationalaccountofintertheoreticreductionwasforcefullypresentedbyFeyerabendin“Explanation,Reduction,andEmpiricism”(Feyerabend,1962).Considertheterm“temperature”asitfunctionsinclassicalthermodynamics.ThistermisdefinedintermsofCarnotcyclesandisrelatedtothestrict,nonstatisticalzerothlawasitappearsinthattheory.Theso-calledreductionofclassicalthermodynamicstostatisticalmechanics,however,failstoidentifyorassociatenonstatisticalfeaturesinthereducingtheory,statisticalmechanics,withthenonstatisticalconceptoftemperatureasitappearsinthereducedtheory.Howcanonehaveagenuinereduction,iftermswiththeirmean-ingsfixedbytheroletheyplayinthereducedtheoryareidentifiedwithtermshavingentirelydifferentmeanings?Classicalthermodynamicsisnotastatisticaltheory.Theverypossibilityoffindingareductionfunctionorbridgelawthatcap-turestheconceptoftemperatureandthestrict,nonstatisticalroleitplaysinthethermodynamicsseemsimpossible(Takesaki,1970;Primas,1998).Manyphysicists,now,wouldaccepttheideathatourconceptoftemperatureandourconceptionofotherexacttermsthatappearinclassicalthermodynamicssuchas“entropy,”needtobereformulatedinlightoftheallegedreductiontostatisticalmechanics.Textbooks,infact,typicallyspeakofthetheoryof“statisti-calthermodynamics.”Becauseoftheproblemmentionedabove,aswellasothers,manyphilosophersofsciencefeltthatthetheoretical-derivationalmodel(Nagel,1961)didnotreal-isticallycapturetheactualprocessofintertheoreticreduction.AsPrimasputsit,“thereexistsnotasinglephysicallywell-foundedandnontrivialexamplefortheoryreductioninthesenseofNagel(1961).Thelinkbetweenfundamentalandhigher-leveltheoriesisfarmorecomplexthanpresumedbymostphilosophers”(1998,p.83).Therefore,alternativemodelsofintertheoreticreductionabandononeormoreontologicalassumptionsmadebythetheoretical-derivationalaccount(i.e.,thelogicalempiricistaccount):86\nReduction,EmergenceandExplanation1Property/kindcross-theoretic(ontological)identitiesaretobedeterminedsolelybyformalcriteriasuchassuccessfulintertheoreticreduction,e.g.,smoothintertheoreticreductionisbothnecessaryandsufficientforcross-theoreticidentity.2Realism,scientifictheoriesaremorethanmere“computationaldevices.”and/oroneormoreepistemologicalassumptions:1Philosophyofscienceisprescriptiveratherthandescriptive,e.g.,philos-ophyofscienceshouldseekagrand,universalaccountofintertheoreticreduction.2Scientifictheoriesareaxiomaticsystems.3Reduction=logicaldeduction,oratleastdeductionofastructurespecifiedwithinthevocabularyandframeworkofthereducedtheoryorsomecorrectedversionofit.4Necessityofbridgelawsorsomeotherequallystrongcross-theoreticcon-nectingprinciplestoestablishsyntheticidentities.5Symboliclogicistheappropriateformalismforconstructingscientifictheories.6Scientifictheoriesarelinguisticentities.7Hardcoreexplanatoryunification.Reductionisproofofdisplacement(inprin-ciple)showingthatthemorecomprehensivereducingtheorycontainsexplana-toryandpredictiveresourcesequalingorexceedingthoseofthereducedtheory.8Intertheoreticreductionsareanallornothingsynchronicaffairasinthecaseof“microreductions”(OppenheimandPutnam,1958;Causey,1977):thelower-leveltheoryanditsontologyreducethehigher-leveltheoryanditsontology.Ontologicallevelsaremappedone-to-oneontolevelsoftheorywhicharemappedone-to-oneontofieldsofscience.9Thearchitectureofscienceisalayerededificeofanalyticallevels(Wimsatt,1976).AlternativestotheNagel(1961)modelaredeemedmoreorlessradical(bycomparison)dependingonwhichoftheprecedingtenetsareabandoned.Onthemoreconservativeside,manyalternativeaccountsofintertheoreticreductionmerelymodify(3)bymovingtologico-mathematicaldeduction,butreject(4).Forexample,therequirementofbridgelawsgetsreplacedbynotionssuchas:“analogrelation”–anorderedpairoftermsfromeachtheory(Hooker,1981;Bickle,1998),“complexmimicry”(PaulChurchland,1989)or“equipotentimage”(PatriciaChurchland,1986),tonameafew.Manyofthesecomparativelyconservativeaccountsalsoreject(8),preferringtotalkaboutarangeofreduc-tions,fromreplacementononeendofthecontinuumtoidentityontheother.MoreradicalalternativestotheNagelmodelsareasfollows.87\nMichaelSilbersteinSemantic/model-theoretic/structuralistanalysisThisapproach(the“semantic”approachforshort),isregardedbysomeascom-parativelyradicalbecauseitrejectstheconceptionofscientifictheoriesasformalcalculiformalizableinfirst-orderlogicand(partially)interpretablebyconnect-ingprinciplessuchasbridgelaws.Thesemanticapproachmakesthefollowingassumptions:(i)Scientifictheoriesarenotessentiallylinguisticentities(setsofsentences),butaretermsorfamiliesoftheirmathematicalmodelsormathematicalstructures.(ii)Theformalexplicationofthestructureofscientifictheoriesisnotproperlycarriedoutwithfirst-orderlogicandmetamathematics,butwithmathe-matics,thoughthechoiceofmathematicalformalismswilldifferdependingonwhoyouread(Giere,1988;Bickle,1998;Batterman,2000).Thesemanticapproachminimallyrejectsepistemologicalassumptions(2)–(6)and(8),i.e.,rejectsthederivationoflawsandabandonstruthpreservation(everythingthereducedtheoryassertsisalsoassertedbythereducingtheory).Ontheseman-ticapproach,thereductionrelationmightbeconceivedofassomekindof“iso-morphism”or“expressiveequivalence”betweenmodels(Bickle,1998).However,asweshallshortlysee,moreradicalversionsofthesemanticapproachrejectalltheprecedingepistemologicalassumptionsheldbythelogicalempiricistaccountofintertheoreticreduction.PragmaticSuccessinrealworldrepresentationis,inlargepart,apracticalmatterofwhetherandhowfullyone’sattemptedrepresentationprovidespracticalcausalandepi-stemicaccesstotheintendedrepresentationaltarget.Agoodtheoryormodelsuc-ceedsasarepresentationifitaffordsreliableavenuesforpredicting,manipulatingandcausallyinteractingwiththeitemsitaimstorepresent.Itisthepracticalaccessthatthemodelaffordsinitscontextofapplicationthatjustifiesviewingitashavingtherepresentationalcontentthatitdoes(VanFraassen,1989;Kitcher,1989).Ifalower-leveltheoryaboutaspecificdomainprovidessuperiorreal-worldexplana-toryandpredictivevaluecomparedtoahigher-leveltheoryrepresentingthesamedomain,thenthelower-leveltheoryhasmettheultimatetestofsuccessfulintertheoreticreduction.Notethatthiscontextual,pragmaticaccountofinterthe-oreticreductionisalsohighlyparticularist;itadvocatesadjudicatingonacase-by-casebasis;nouniversaltheoryofreductionissought.Thisaccountrejectsatleastassumptions(1)–(6)intheepistemologicalcategory,andassumption(1)in88\nReduction,EmergenceandExplanationtheontologicalcategory(PatriciaChurchland,1986).Moreradicalversionsrejectallnineoftheprecedingepistemologicalassumptions.Whereasthetheoretical-derivationalaccount(i.e.,thelogicalempiricistaccount)ofintertheoreticreduction(anditsvariants)onlymakessenseifyoupre-supposenomologicalandmereologicalsupervenience;inprinciple,boththesemanticandthepragmaticaccountsofintertheoreticreductionarecompatiblewiththefailureofmereologicalsupervenienceandperhapsevennomologicalsupervenience.Weshallencounterspecificversionsofsuchaccountsofreductionshortly.Whiletherearecertainlymutuallyexclusiveandcompetingaccountsofintertheoreticreductionthatrepresenteachofourfourtypes,thereisnoprinci-pledreasonwhythefourtypescouldnotbesynthesizedintoasingleaccount.Schaffner’s“generalizedreplacement-reduction”(GRR)modelofintertheoreticreductionisonesuchattempt(Schaffner,1992,1998,2000).Thoughmuchmorecouldbesaidaboutthemanyvarietiesofontologicalandepistemologicalreductionandtheirrespectivefaultsandmerits,themainversionsmaybegraphicallysummarized(figure5.1):RealworlditemsRepresentationalitemsONT-reductionbetweenEPIST-reductionbetween•entities•concepts•properties•theories•events•models•processes•frameworks······ReductionrelationOntologicalEpistemological•Elimination•Replacement•Identity•Derivation•Mereologicalsupervenience•Semantic•Nomologicalsupervenience•PragmaticFigure5.1TheVarietiesofEmergence:OntologicalandEpistemologicalEmergence,likereduction,isinterpretedindiverseways(SilbersteinandMcGeever,1999).Again,myaimistosurveythemainvariants.Thebasicideaofemergenceisroughlytheconverseofreduction.Thoughthe89\nMichaelSilbersteinemergentfeaturesofawholeorcomplexarenotcompletelyindependentofthoseofitspartssincethey“emergefrom”thoseparts,thenotionofemergencenonethelessimpliesthat,insomesignificantway,theygobeyondthefeaturesofthoseparts.Therearemanysensesinwhichasystem’sfeaturesmightbesaidtoemerge,someofwhicharerelativelymodest(Rueger,2000a,b;Batterman,2000;Bedau,1997)andotherswhicharemorecontroversial(Humphreys,1997;Silberstein,1998).Thevarietiesofemergencecanbedividedintoseveralgroupsalonglinessimilartothosedivisionsbetweenthetypesofreduction(figure5.2).RelataofemergenceRealworlditemsRepresentationalitemsONT-emergencebetweenEPIST-emergencebetween•parts/wholes•concepts•properties•theories•events/processes•models•causalcapacities•frameworks•laws•laws•entities···•statesofadynamicalsystem···Figure5.2Ontologicalrelationsareobjectiveinthesensethattheylinkonticitems,e.g.,properties,independentofanyepistemicconsiderations.Relationsofthesecondsortareepistemic,becausetheydependonourabilitiestocomprehendthenatureofthelinksordependenciesamongrealworlditems.Atleastfourmajorformsofemergencehavebeenchampioned;eachisanelaborationofthefailureofitscorrespondingreductionrelation:•Non-elimination•Non-identity•Mereologicalemergence(holism)•NomologicalemergenceNon-eliminationIfaproperty,entity,causalcapacity,kindortypecannotbeeliminatedfromourontology,thenonemustbearealistaboutsaiditem.Obviously,thisleavesopenthequestionofwhatthecriteriaoughttobefornon-eliminationinanygivencase;buttheywillalmostcertainlybeepistemological/explanatoryinnature.90\nReduction,EmergenceandExplanationNon-identityIfaproperty,typeorakindcannotbeultimatelyidentifiedwithaphysical(orlower-level)property,typeorkindthenonemustacceptthatsaiditemisadis-tinctnon-physical(orhigher-level)property,typeorkind.Again,thisleavesopenthecriteriafornon-identifiabilityandagain,suchcriteriaaregenerallyepistemo-logical/explanatoryinnature.Mereologicalemergence(holism)Thesearecasesinwhichobjectshavepropertiesthatarenotdeterminedbytheintrinsic(non-relational)physicalpropertiesoftheirmostbasicphysicalparts.Or,casesinwhichobjectsarenotevenwhollycomposedofbasic(physical)partsatall.British(classical)emergentismheldthatmereologicalemergenceistrueofchemical,biologicalandmentalphenomena(McLaughlin,1992).NomologicalemergenceThesearecasesinwhichhigher-levelentities,properties,etc.,aregovernedbyhigher-levellawsthatarenotdeterminedbyornecessitatedbythefundamentallawsofphysicsgoverningthestructureandbehavioroftheirmostbasicphysicalparts.Forexample,accordingtoKim(1993),Britishemergentismheldthatwhiletherewerebridgelawslinkingthebiological/mentalwiththephysical,suchbridgelawswereinexplicablebrutefacts.Thatis,onKim’sviewBritishemergentismdidnotdenyglobalsupervenience.ButBritishemergentismdiddenythatthelawsgoverningthementalforexampleweredetermined(orex-plained)bythefundamentallawsofphysics(McLaughlin,1992;Kim,1993).Amoreextremeexampleofnomologicalemergencewouldbewheretherewerenobridgelawswhatsoeverlinkingfundamentalphysicalphenomenawithhigher-levelphenomena.Insuchcases,fundamentalphysicalfactsandlawswouldonlyprovideanecessaryconditionforhigher-levelfactsandlaws.Thiswouldimplypossibleviolationsofglobalsupervenience.BothCartwright(1999)andDupré(1993)seemtodefendsomethinglikethiskindofnomologicalemergence.Anevenmoreextremeexampleisfoundincasesinwhicheitherfundamentalphysicalphenomenaorhigher-levelphenomenaarenotlaw-governedatall.Thiswouldamounttoeliminativismorantirealismregardingnomologicalorphysicalnecessity;seeVanFraassen(1989)foradefenseofthisview.Itisimpor-tanttonotethatinallcasesofnomologicalemergence,itisinprincipleimpossibletoderiveorpredictthehigher-levelphenomenaonthebasisofthelower-levelphenomena.Theepistemologicallinkmustdescribehowthingsarerelatedsuchthatone91\nMichaelSilbersteinepistemologicallyemergesfromanother.Atleasttwomajorviewshavebeenchampioned:•Predictive/explanatoryemergence•Representational/cognitiveemergencePredictive/explanatoryemergenceWholes(systems)havefeaturesthatcannotinpracticebeexplainedorpredictedfromthefeaturesoftheirparts,theirmodeofcombination,andthelawsgoverningtheirbehavior.Inshort,Xbearspredictive/explanatoryemergencewithrespecttoYifYcannot(reductively)predict/explainX.Morespecifically,intermsoftypesofintertheoreticreduction,Xbearspredictive/explanatoryemergencewithrespecttoY:ifYcannotreplaceX,ifXcannotbederivedfromY,orifYcannotbeshowntobeisomorphictoX.Alower-leveltheoryY(description,regularity,model,schema,etc.),forpurelyepistemologicalreasons(conceptual,cognitiveorcomputationallimits),canfailtopredictorexplainahigher-leveltheoryX.IfXispredictive/explanatoryemergentwithrespecttoYforallpossiblecognizersinpractice,thenwemightsaythatXisincommensurablewithrespecttoY.Apara-digmaticandnotoriousexampleofpredictive/explanatoryemergenceischaotic,non-lineardynamicalsystems(SilbersteinandMcGeever,1999).Theemergenceinchaoticsystems(ormodelsofnon-linearsystemsexhibitingchaos)followsfromtheirsensitivitytoinitialconditions,plusthefactthatphysicalpropertiescanonlybespecifiedtofiniteprecision;infiniteprecisionwouldbenecessarytoperformtherequired“reduction”,givensaidsensitivity.Itdoesnotfollow,however,thatchaoticsystemsprovideevidenceofviolationsofmereologicalsupervenienceornomologicalsupervenience(Kellert,1993,pp.62,90),e.g.,dynamicalsystemshaveattractorsashigh-levelemergentfeaturesonlyinthesensethatyoucannotdeducethemfromequationsforthesystem.McGinn(1999)andothermysteri-ansholdthatfolkpsychologyispredictive/explanatoryemergentwithrespecttothetheoriesofneuroscience.Representational/cognitiveemergenceWholes(systems)exhibitfeatures,patternsorregularitiesthatcannotbefullyrep-resented(understood)usingthetheoreticalandrepresentationalresourcesade-quatefordescribingandunderstandingthefeaturesandregularitiesoftheirmorebasicpartsandtherelationsbetweenthosemorebasicparts.Xbearsrepresentational/cognitiveemergencewithrespecttoY,ifXdoesnotbearpredictive/explanatoryemergencewithrespecttoY,butnonethelessXrepresentshigher-levelpatternsornon-analyticallyguaranteedregularitiesthatcannotbe92\nReduction,EmergenceandExplanationfully,properlyoreasilyrepresentedorunderstoodfromtheperspectiveofthelower-levelY.AslongasXretainsasignificantpragmaticadvantageoverYwithrespecttounderstandingthephenomenainquestion,thenXisrepresenta-tional/cognitiveemergentwithrespecttoY.Nonreductivephysicalismholdsthatfolkpsychologyisrepresentational/cognitiveemergentwithrespecttothetheo-riesofneuroscience(Antony,1999).TheReductionandEmergenceDebateToday:SpecificCasesSeemingtoWarranttheLabelofOntologicalorEpistemologicalEmergenceNotsincethefirsthalfofthetwentiethcenturyhaveemergenceandreductionenjoyedsomuchcriticalattention.Claimsinvolvingemergencearenowrifeindiscussionsofphilosophyofmind,philosophyofphysics,variousbranchesofphysicsitselfincludingquantummechanics,condensedmattertheory,non-lineardynamicalsystemstheory(especiallyso-calledchaostheory),cognitive-neuroscience(includingconnectionist/neuralnetworkmodelingandcon-sciousnessstudies)andso-calledcomplexitystudies(SilbersteinandMcGeever,1999).ToquoteKim:wearenowseeinganincreasingandunapologeticuseofexpressionslike“emergent,”“emergentproperty,”and“emergentphenomenon”...notonlyinseriousphilo-sophicalliteraturebutinthewritingsinpsychology,cognitivescience,systemstheory,andthelike(1998,pp.8–9).Kimalsosaysthatthereturnofemergentismisseldomnoticed,andmuchlessopenlycelebrated;itisclear,however,thatthefortunesofreductionismcorrelateinverselywiththoseofemergentism...Itisnoundueexaggerationtosaythatwehavebeenunderthereignofemergentismsincetheearly1970s(1999,p.5).Therearetwoprimaryreasonsforthereturnofemergentism.First,regardingnomologicalemergence,agrowingbodyofliteraturefocusingonactualscientificpracticesuggeststhattherereallyarenotmanycasesofsuccessfulintertheoreticreductionintheempiricisttraditionofdemonstratingnomologicalsupervenience.Ourscientificunderstandingoftheworldisapatchworkofvastscope;itcoverstheintricatechemistryoflife,thesociologyofanimalcommunities,thegiganticwheel-inggalaxies,andthedancesofelusiveelementaryparticles.Butitisapatchworknevertheless,andthedifferentareasdonotfitwelltogether(Berry,2000,p.3).93\nMichaelSilbersteinFocusonactualscientificpracticesuggeststhateithertherereallyarenotmanycasesofsuccessfulepistemological(intertheoretic)reductionorthatmostphilosophicalaccountsofreductionbearlittlerelevancetothewayreductioninscienceactuallyworks.Mostworkingscientistswouldprobablyoptforthelatterclaim.Oftendiscussedcasesoffailedorincompleteintertheoreticreductioninthelit-eratureinclude:1thereductionofthermodynamicstostatisticalmechanics(Primas,1991,1998;Sklar,1999)2thereductionofthermodynamics/statisticalmechanicstoquantummechanics(Hellman,1999)3thereductionofchemistrytoquantummechanics(Cartwright,1997;Primas,1983)4thereductionofclassicalmechanicstoquantummechanics(suchastheworrythatquantummechanicscannotrecoverclassicalchaos)(BelotandEarman,1997).Takethecaseofchemistryanditsallegedreductiontoquantummechanics.Currentlychemistsdonotusefundamentalquantummechanics(HamiltoniansandSchrödinger’sequation)todotheirscience.QuantumchemistrycannotbededuceddirectlyfromSchrödinger’sequationduetomultiplefactorsthatincludethemany-bodyproblem(Hendry,1998).Quantummechanicalwavefunctionsarenotwell-suitedtorepresentchemicalsystemsorsupportkeyinferencesessen-tialtochemistry(Woody,2000).Itisstillanopenquestionastowhetherquantummechanicscandescribeorrepresentamolecule(Berry,2000).Indeed,littleofcurrentchemistrycanberepresentedbypurequantummechanicalcalculations(Primas,1983;Scerri,1994;Ramsey,1997).Chemistryusesidealizedmodelswhoserelationshiptofundamentalquantummechanicsisquestionable(Primas,1983;Hendry,1999).AsCartwright(1997,p.163)putsit:Notoriously,wehavenothinglikearealreductionoftherelevantbitsofphysicalchemistrytophysics–whetherquantumorclassical.Quantummechanicsisimpor-tantforexplainingaspectsofchemicalphenomenabutalwaysquantumconceptsareusedalongsideofsuigeneris–thatis,unreduced-conceptsfromotherfields.Theydonotexplainthephenomenaontheirown.Anotherwell-knownexampleisthecaseofthermodynamicsandstatisticalmechanics.First,thereisavarietyofdistinctconceptsofbothtemperatureandentropythatfigureinbothstatisticalmechanicsandclassicalthermodynamics.Second,thermodynamicscanbeappliedtoanumberofverydifferentlyconsti-tutedmicrophysicalsystems.Thermodynamicscanbeappliedtogases,electro-magneticradiation,magnets,chemicalreactions,starclustersandblackholes.AsSklar(1993,p.334)putsit:94\nReduction,EmergenceandExplanationTheallegedreductionofthermodynamicstostatisticalmechanicsisanotheroneofthosecaseswherethemoreyouexplorethedetailsofwhatactuallygoeson,themoreconvincedyoubecomethatnosimple,generalaccountofreductioncandojusticetoallthespecialcasesinmind.Third,thestatusoftheprobabilityassumptionsthatarerequiredtorecoverther-modynamic’sprincipleswithinstatisticalmechanicsarethemselvesproblematicoradhoc.Forexample,theassumptionthatthemicro-canonicalensembleistobeassignedthestandard,invariant,probabilitydistribution.Fourth,perhapsthethorniestproblemofall,statisticalmechanicsistimesymmetricandthermody-namicspossessestimeasymmetry.Theseareespeciallyimportantexamplesbecausetheyinvolvedifficultiesbetweendifferentlevelsofexplanationwithinphysicalscience.Someofthefour(e.g.,thereductionofthermodynamicstostatisticalmechanics)wereoncethoughtofassuccessesforphilosophicalaccountsofintertheoreticreduction(Sklar,1993).Perhapsthemosthighlyadvertisedcaseoffailedintertheoreticreductionistheattempttoreducefolkpsychologytotheoriesofneuroscience.Presentlyapopularontologicalversionofthemind/bodyproblemgoesbythenameof“thehardproblemofphenomenalconsciousness”:howandwhyarebrainstatesconscious?(Chalmers,1996).AsKim(1998,pp.102–3)putsit:Wearenotcapableofdesigning,throughtheoreticalreasoning,awhollynewkindofstructurethatwecanpredictwillbeconscious;Idon’tthinkweevenknowhowtobegin,orindeedhowtomeasureoursuccess...Inanycaseitseemstomethatifemergentismiscorrectaboutanything,itismorelikelytobecorrectaboutqualiathanaboutanythingelse.FormoreontheproblemsofphenomenalconsciousnessandemergenceseeSilberstein(2001).Inthisspirit,philosophersofscienceandmindhavemadeacottageindustryofcollectingmanyofthecasesofincompleteintertheoreticreduction,callingthemall“emergence”;see,forexample,SpecialIssue:ReductionandEmergence,Philo-sophicalStudies,95(1–2),August1999andBeckermannetal.(1992).Theessaysinbothvolumesspanpsychology,biologyandphysics.Eachoftheessaysisanexaminationofanattemptedintertheoreticreductionthatiscurrentlyhavinggravedifficulties.Takenintoto,thesecasesseemabarometeroftheprospectsforuni-fyingthesciences,andthereforeindicativeoftheprospectsofepistemologicalandontologicalreductionism.Thereisamovementafootdevotedtoarguingthispoint.Themovementisknownasthe“disunityofsciencemovement”orthe“anti-fundamentalismmovement”(Dupré,1993;Cartwright,1999).However,anindicationisnotanargument,soeachcasedeservestobeexaminedinitsownright.Thereisnodoubtdangerinlumpingallthesecasestogether.Itisclear,forexample,thatthermodynamicsispredictive/explanatoryemergentwithrespectto95\nMichaelSilbersteinstatisticalmechanics.Asofyet,fewarereadytoconcludethatthermodynamicalphenomenaare,forexample,nomologicallyormereologicallyemergentwithrespecttostatisticalmechanicalphenomena.Bywayofcontrast,whenKimtalksaboutphenomenalconsciousnessbeingemergent,heseemstobemakingaclaimaboutemergentphenomenalconsciousnesswhichgoesbeyondafunctionofigno-ranceinterpretation(Kim,1998,1999).Itisnotuncommonforsuchequivoca-tionsontheterm“emergence”toappearinthesamevolume.Thisbringsmetothesecondmajorreasonforthereturnofemergence.Therearesomepeoplewhoallegethatquantummechanicsitselfprovidesexamplesofmereologicalemergence:Inquantumtheory,then,thephysicalstateofacomplexwholecannotalwaysbereducedtothoseofitsparts,ortothoseofitspartstogetherwiththeirspatiotem-poralrelations,evenwhenthepartsinhabitdistinctregionsofspace.Modernscience,andmodernphysicsinparticular,canhardlybeaccusedofholdingreductionismasacentralpremise,giventhattheresultofthemostintensivescientificinvestigationsinhistoryisatheorythatcontainsanineliminableholism(Maudlin,1998,p.55).Byandlarge,asysteminclassicalphysicscanbeanalyzedintoparts,whosestatesandpropertiesdeterminethoseofthewholetheycompose.Butthestateofasysteminquantummechanicsresistssuchanalysis.Thequantumstateofasystemgivesaspecificationofitsprobabilisticdispositionstodisplayvariouspropertiesonitsmea-surement.Quantummechanics’mostcompletesuchspecificationisgivenbywhatiscalledapurestate.Evenwhenacompoundsystemhasapurestate,itssubsystemsgenerallydonothavetheirownpurestates.Schrödinger,emphasizingthischarac-teristicofquantummechanics,describedsuchcomponentsubsystemsas“entan-gled.”Suchentanglementofsystemsdemonstratesnonseparability–thestateofthewholeisnotconstitutedbythestatesofitsparts.Stateassignmentsinquantummechanicshavebeentakentoviolatestateseparabilityintwoways:thesubsystemsmaysimplynotbeassignedanypurestatesoftheirown,orelsethestatestheyareassignedmayfailtocompletelydeterminethestateofthesystemtheycompose.Thequantumstateofasystemmaybeeitherpureormixed.Apurestateisrep-resentedbyavectorinthesystem’sHilbertspace.Itiscommonlyunderstoodthatanyentangledquantumsystemsviolatestateseparabilityinsofarasthevectorrep-resentingthestateofthesystemtheycomposedoesnotfactorizeintoavectorintheHilbertspaceofeachindividualsubsystemthatcouldbetakentorepresentitspurestate.Asetofentangledquantumsystemscomposeasystemwhosequantumstateisrepresentedquantummechanicallybyatensor-productstate-vectorwhichdoesnotfactorizeintoavectorintheHilbertspaceofeachindividualsystem:YY12,,,KRRπƒƒƒ1YY2LNowinsuchacaseeachsubsystem1,2,...,nmaybeuniquelyassignedwhatiscalledamixedstate(representedinitsHilbertspacenotbyavectorbutbya96\nReduction,EmergenceandExplanationso-calledvonNeumanndensityoperator).Butthenstateseparabilityfailsforadifferentreason:thesubsystemmixedstatesdonotuniquelydeterminethecom-poundsystem’sstate.Onthebasisofnonseparability,manypeoplehavearguedthatquantummechanicsprovidesuswithexamplesofsystemsthathavepropertiesthatdonotalwaysreducetotheintrinsicpropertiesofthemostbasicparts,i.e.,quantummechanicalsystemsexhibitmereologicalemergence(Healey,1991;HawthorneandSilberstein,1995;Humphreys,1997).Suchentangledsystemsappeartohavenovelpropertiesoftheirown.Quantumsystemsthatareinsuperpositionsofpossiblestatesarebehaviorallydistinctfromsystemsthatareinmixturesofthesestatesandindividualsystemscanbebecomeentangledandthusformanewunifiedsystemwhichisnotthesumofitsintrinsicparts.Fromthis,somefurtherinferthat:“thestateofthecompound[quantum]systemdeterminesthestateoftheconstituents,butnotviceversa.Thislastfactisexactlythereverseofwhat[mereological]superveniencerequires”(Humphreys,1997,p.16).TheopinionofagrowingnumberofphilosophersofphysicsisexpressedbyMaudlin(1998,pp.58–60):Quantumholismoughttogivesomemetaphysicianspause.Ashasalreadybeennoted,onepopular“Humean”thesisholdsthatallglobalmattersoffactsuperveneonlocalmattersoffact,thusallowingacertainontologicalparsimony.Oncethelocalfactshavebeendetermined,alloneneedstodoisdistributethemthroughoutallofspace-timetogenerateacompletephysicaluniverse.Quantumholismsuggeststhatourworldjustdoesn’tworklikethat.Thewholehasphysicalstatesthatarenotdeterminedby,orderivablefrom,thestatesoftheparts.Indeed,inmanycases,thepartsfailtohavephysicalstatesatall.Theworldisnotjustasetofseparatelyexist-inglocalizedobjects,externallyrelatedonlybyspaceandtime.Somethingdeeper,andmoremysterious,knitstogetherthefabricoftheworld.Wehaveonlyjustcometothemomentinthedevelopmentofphysicsthatwecanbegintocontemplatewhatthatmightbe.Atanyrate,quantumnonseparabilityisnotrestrictedtosettingssuchastwin-slitexperimentsandEPR(non-locality)experiments.Superpositionsandentan-gledstatesarerequiredtoexplaincertainchemicalandphysicalphenomenasuchasphasetransitionsthatgiverisetosuperconductivity,superfluidity,paramag-netism,ferromagnetism;seeAnderson(1994),Auyang(1998)andCornellandWieman(1998).SomeinterpretationsofquantummechanicssuchasBohr(1934)andBohmandHiley(1993)implymereologicalemergence(holism)withrespecttoentities:therearephysicalobjectsthatarenotwhollycomposedofbasic(physical)parts.OnBohr’sinterpretationonecanmeaningfullyascribepropertiessuchaspositionormomentumtoaquantumsystemonlyinthecontextofsomewell-definedexperimentalarrangementsuitableformeasuringthecorrespondingproperty.Althoughaquantumsystemispurelyphysicalonthisview,itisnotcomposedofdistincthappeningsinvolvingindependentlycharacterizablephysicalobjectssuch97\nMichaelSilbersteinasthequantumsystemontheonehand,andtheclassicalapparatusontheother.OnBohm’sinterpretation,itisnotjustquantumobjectandapparatusthatareholisticallyconnected,butanycollectionofquantumobjectsbythemselvescon-stituteanindivisiblewhole.Acompletespecificationofthestateofthe“undivideduniverse”requiresnotonlyalistingofallitsconstituentparticlesandtheirposi-tions,butalsoofafieldassociatedwiththewave-functionthatguidestheirtra-jectories.Ifoneassumesthatthebasicphysicalpartsoftheuniversearejusttheparticlesitcontains,thenthisestablishesontologicalholisminthecontextofBohm’sinterpretation.Forthepurposesofthisdiscussion,whatismostimportantisnotwhetherornotquantummechanicsactuallydoesprovidecasesofmereologicalemergence,butthatthebeliefthatitdoes,inpart,fuelsemergentism.Thoughitmustbesaid,therearesomephilosopherswhoarestillskepticalaboutthereality,coherenceorimportanceofquantumholism(Lewis,1986;Dickson,1998).Noteveryoneacknowledgesthatnonseparabilityimpliesmereologicalemergence.Forexample,Healeyarguesthatwhetherornotnonseparabilityimpliesmereologicalemergenceisamatterofinterpretation(1989,pp.142–5).Healey’sownmodalinterpreta-tion(1989)doesimplymereologicalemergence,howeverhestipulatesthattheformalismofquantummechanicsisopentointerpretationsthatdonot.Heargues(Healey,1991)thatnonseparabilityingeneralandso-callednon-localityarebestexplainedbypositingmereologicalemergence.QuestionsforFutureResearchRecallthatthebestreasonforbelievinginreductionismisanacceptanceofmere-ologicaland/ornomologicalsuperveniencebasedinlargepartonsuccessfulintertheoreticreduction(orepistemologicalreduction).Dotheprecedingexam-plesofepistemologicalandontologicalemergenceindicateemergentismistrue?Atthisjuncture,mayweevensaywhetheremergentismorreductionismismoreprobable?Whatdoesthecurrentstateofdisunitywithinanygivenscienceandacrossthevarioussciencesimplyaboutemergence?Regardingtheultimatefateofmereologicalandnomologicalemergencerespectively,therearetwogeneralpos-sibilities.Eithertheserespectiveformsofemergencearemerelyafunctionofourignoranceortheyarerealfactsabouttheworld.Iftheyarerealfactsabouttheworldthentheymaybeeitheruniversallytrueorrestrictedtoaparticulardomainsuchasmicrophysics.Ofcourse,theultimatefateofmereologicalemergencemightbedifferentfromthatofnomologicalemergenceandvice-versa.Forexample,thepossibilitiesfornomologicalemergenceareasfollows:Therearefourreductiveoutcomes:1Anyclaimedemergenceisduetophilosophicalignorance.Abetter,moreappropriatephilosophicaltheoryofintertheoreticreductionneedstobecon-98\nReduction,EmergenceandExplanationstructedthatwillshowthatthelower-leveltheorydoesreductivelyexplainthehigher-leveltheoryinquestion.Itispossible(ifnotprobable)thatdifferentcaseswillrequiredifferentaccountsofintertheoreticreductionfortheirresolution.2Anycaseofemergenceisduetoempiricalorexperimentalignorance.Futurediscoverieswillallowustoseehowthelower-leveltheorydoesinfactreduc-tivelyexplainthehigher-leveltheoryinquestion.3Anyclaimtoemergencereliesonlower-leveltheoriesthatarefalseorincom-plete,andsuchtheorieswillbereplacedorsupplementedbycorrectlower-leveltheoriesinordertoreductivelyexplainthehigher-leveltheory.Outcomes1–3wouldallbeunqualifiedwinsforepistemologicalreductionismifnotontologicalreductionism.4Thehigher-leveltheorywillceasetobepredictive/explanatoryemergentwithrespecttothelower-leveltheory,butforsome(indeterminate)lengthoftimethehigher-leveltheorywillberepresentational/cognitiveemergentwithrespecttothelower-leveltheory.Thisismoreorlessawinforepistemological(ifnotontological)reductionism.Therearethentwoemergentoutcomes:5Thehigher-leveltheoryispredictive/explanatoryemergentwithrespecttothelower-leveltheoryandforwhateverreason,duetowhateverepistemologicallimits,thelower-leveltheoryanditssuccessorswillneverbeabletoreduc-tivelyexplainthehigher-leveltheory.Thisisawinforepistemologicalemer-genceonly.6Thehigher-leveltheoryispredictive/explanatoryemergentwithrespecttothelower-leveltheory(anditssuccessors)becausethephenomena/lawsrepre-sentedbythehigher-leveltheoryarenomologicallyemergentwithrespecttothephenomena/lawsrepresentedbythelower-leveltheory.Thelower-levelphenomenaonlyprovideanecessary(butnotsufficient)conditionfortheemer-genceofthehigher-levelphenomena.Thiswouldbeanunqualifiedlossforbothepistemologicalandontologicalreductionism.Oneimportantquestionforthefutureistodetermine,ineachspecificinstanceofincompleteintertheoreticreduction(suchasthecasesdiscussedearlier),whichofthesesixpossibilitiesactuallyobtains.Howeveritshouldbeclearthatemer-gentismandreductionismmightformacontinuumandnotadichotomy.Thisistrueinseveralrespects.First,evenifmereologicalemergenceisrealitdoesnotnecessarilyimplynomologicalemergence.Evenifthequantumismereologicallyemergent,itcouldstillbethecasethatallhigher-levelphenomenanomologicallysupervenesuponit.Second,bothmereologicalandnomologicalemergencemightberestrictedtocertaindomains.Forexample,mereologicalemergencemightbe99\nMichaelSilbersteinlimitedtothequantumandnomologicalemergencelimitedtothemental.Third,foranygivencasewecanalwaysdividethequestionforontologicalandepiste-mologicalemergence.Ormoregenerally,itcouldturnout,forexample,thatepistemologicalemergenceisinescapablewhileontologicalemergenceisrareornonexistent.Ofcourse,giventheformer,itisanopenquestionhowwewouldeverdiscoverthelatter.Recentaccountsofintertheoreticreduction,themoreradicalversionsofthesemanticandpragmaticmodelsmentionedearlier,suchasGRR(Schaffner,1992,1998)andthemoreexplicitlypragmaticandonticcausalmechanicalmodel(Machameretal.,2000),explicitlyrejectmicroreduction,inpartbecauseoftheproblematiccasesmentionedearlier.Suchalternativeaccountsofintertheoreticreduction,intheirrejectionofmicroreduction,explicitlyacknowledgethecon-tinuumbetweenreductionandemergence.Forexample,thecausalmechanicalmodelofintertheoreticreductionfocusesonexplanationsascharacterizingcomplex(nestedandinter-connected)causalmechanismsandpathways,suchaswefindinmolecularbiologyandneuroscience.Theemphasisinthismodelisoncausal/mechanicalprocessesasopposedtonomologicalpatternsofexplanation.Moreimportantlyforourpurposes,thismodeladmitsofmultileveldescriptionsofcausalmechanismsthatmixdifferentlevelsofaggregationfromcelltoorganbacktomolecule.Takethefollowingexamplefrombehavioralgenetics:thereisnosimple[reductive]explanatorymodelforbehavioreveninsimpleorganisms.WhatC.elegans[asimpleworm]presentsuswithisatanglednetworkofinfluences[causalmechanisms]atgenetic,biochemical,intracellular,neuronal,musclecell,andenvironmentallevels(Schaffner,1998,p.237).Thiskindofreductiveexplanationfocusesoninterlevelcausalprocessesandemphasizesthelimitsandrarityoflogicalempiricistaccountsofintertheoreticreduction.Thisapproachtoreductionisdiachronic,emphasizingthegradual,partialandfragmentarynatureofmanyrealworldcases.Thismodelclearlyviewsintertheoreticreductionasacontinuumandnotadichotomy.Onecanalsofindsimilarweb-likeandbushycasesofintertheoreticreductionwithinphysics.Forexample,casesinwhichtwodomains(suchasquantummechanicsandchemistry)arerelatedbyanasymptoticseriesoftenrequireappealtoanintermediatetheory(Berry,1994;Primas,1998;Batterman,2000,2001).Intheasymptoticborderlandsbetweensuchtheories,phenomenaemergethatarenotfullyexplainableintermsofeitherthelower-levelorthehigher-leveltheory,butrequireboththeoriesoranintermediary(Batterman,2000,2001).Examplesofthisphenomenacanbefoundinthebordersbetween:quantummechanicsandchemistry,aswellasthermodynamicsandstatisticalmechanics(BerryandHowls,1993;Berry,1994;2000;Batterman,2000).Battermanspeaksofthe“asymptoticemergenceoftheupperlevelproperties”insuchcases,andhegoesontosuggestthat“itmaybebest,inthiscontext,togiveuponthevariousphilosophicalmodels100\nReduction,EmergenceandExplanationofreductionwhichrequiretheconnectionofkindpredicatesinthereducedtheorywithkindpredicatesinthereducingtheory.Perhapsamorefruitfulapproachistoinvestigateasymptoticrelationsbetweenthedifferenttheorypairs.Suchasymp-toticmethodsoftenallowfortheunderstandingofemergentstructureswhichdominateobservablyrepeatablebehaviorinthelimitingdomainbetweenthetheorypairs”(2000,pp.136–7).Intertheoreticreductionàlasingularasymptoticexpansionsisnoteasytochar-acterize,thoughitisfairtosaythatitfallswithinthesemanticapproachtointertheoreticreduction.Examplesofintertheoreticrelationsinvolvingsingularasymptoticexpansionsinclude:Maxwell’selectrodynamicsandgeometricaloptics;molecularchemistryandquantummechanicsand;classicalmechanicsandquan-tummechanics(Primas,1998;Berry,2000).Thereareseveralthingsworthnoticingaboutboththeprecedingmodelsofintertheoreticreduction.Suchreductionsarenotuniversallyvalid,theycanonlybeconsideredonacase-by-casebasis.Suchreductionsrequirespecificationofcontext,thenewdescriptionorhigher-leveltheorycannotbederivedfromthelower-leveltheory.Indeed,suchreductionsgenerallystartwiththehigher-leveltheory/contextandworkbacktothemorefundamentaltheory(Berry,1994).Thelower-leveltheory(thereducingtheory)isnot,asarule,morepowerfuloruniversalinitspredictive/explanatoryvaluethanthehigher-leveltheory(thereducedtheory).Indeed,thenewontologyandtopologygeneratedbythehigher-leveldescriptioncannotbereplacedoreliminatedpreciselybecauseofitsmoreuniversalexplanatorypower;andtheintertheoreticreductionsonsuchaccountsshowwhythismustbethecase.Contrarytothestandardview,failureofreduc-tionneednotimplyfailureofexplanation.Amorefundamentaltheorycanexplainahigher-leveltheory(“frombelow”asitwere)withoutprovidingareductionofthattheoryinthestandardsensesoftheterm.Emergentphenomenaneednotbeinexplicablebrutefactscontrarytoclassicalemergentism.Givensuchaccountsofintertheoreticreduction,thereisgoodreasontothinkthatcontrathedreamsoftheunityofsciencemovement,thatunificationofscientifictheorieswillbelocalatbest.Suchalternativeaccountsofintertheoreticreductionsuggestthattherelation-shipbetween“higher-level”and“lower-level”scientifictheoriesisanestedhier-archyasopposedtoapyramidstructure.Andifwethinksuchaccountsofreductionreflecttheactualontologyoftheworld,theysuggestthattherelation-shipbetweenthevarious“levels”(subatomic,atomic,molecular,etc.)isalsoanestedhierarchy.Anevenmoreradicalspeculationalongtheselinesisthattherelationshipbetweenhigher-levelandlower-levelscientifictheoriesaswellasbetweenthevariousontic“levels”themselveslooksmorelikenon-Booleanlat-tices(Primas,1991).Thevariousdomainswillhaveoverlappingareasorunions,buttheywillnotbeco-extensional.Sopropertiesinonedomainmaybeneces-saryforpropertiesinanotherdomaintoemerge,butnotsufficient.Suchalter-nativeaccountsofintertheoreticreductiondonotobviouslyimplyordemandeithermereologicalornomologicalsupervenience.101\nMichaelSilbersteinHumphreyssuggests(1997)iftherewerewidespreadmereologicalemergenceornonseparabilitythenlower-levelpropertyinstanceswouldoften“merge”intheformationofhigher-levelpropertiessuchthattheynolongerexistasseparatesub-veniententities.Widespreadmereologicalemergencecallsintoquestiontheverypictureofrealityasdividedintoa“discretehierarchyoflevels”;ratheritismorelikelythateveniftheorderingonthecomplexityofstructuresrangingfromthoseofelementaryphysicstothoseofastrophysicsandneurophysiologyisdiscrete,theinteractionsbetweensuchstructureswillbesoentangledthatanyseparationintolevelswillbequitearbitrary(Humphreys,1997,p.15).Givenwidespreadmereologicalemergence,thestandarddivisionsandhierarchiesbetweenphenomenathatareconsideredfundamentalandemergent,simpleandaggregate,kinematicanddynamic,andperhapsevenwhatisconsideredphysical,biologicalandmentalareredrawnandredefined.Suchdivisionswillbedependentonwhatquestionisbeingputtonatureandwhatscaleofphenomenaisbeingprobed.Butonthefaceofit,onecanembracethesealternativemodelsofintertheo-reticreductionwhilemaintainingthatallapparentemergenceisjustafunctionofignorance.Forexample,Schaffnerstronglysuggeststhatnothingaboutsuchtangledcausalprocesseswarrantsanyclaimsforeithermereologicalemergenceornomologicalemergence(suchasvitalorconfigurationalforces).Rather,atworst,suchsystemsprovideuswithcasesofpredictive/explanatoryemergenceorrep-resentational/cognitiveemergence(Schaffner,1998,pp.242–5).Atpresent,boththeemergentistandreductionistfeelthat,sofar,thingsaregoingtheirway.Theemergentistpointstofailuresofontologicalandmethod-ologicalreductionism,andthereductionistpointstosuccesses.Regardingtheproblematiccasesofintertheoreticreduction,theperennialreductionistreplyistoclaimthatthefuturewillbringsuccess,justasinthepast;emergentistslike-wisefeelthattheywillberedeemedbythefuturejustastheyarebythepresent.ThismuchistrueIthink,giventheexamplesofbothepistemologicalandonto-logicalemergencecanvassed,thereisnoreasonwhytheburdenofproofshouldcontinuetolieexclusivelywithemergentism.Atthisjuncture,neitherviewisirra-tionalinlightoftheevidenceandneitherviewisconclusive.Ultimately,emer-gentistsandreductionistsaredividedbyadeeplyheldphilosophicaloraestheticpreferencethatneitherwillrelinquisheasily.Forexample,manyphilosopherspersistinassumingthatnomologicalandmereologicalreductionismaretrueinspiteoftheactualstateofunificationwithinscienceandinspiteofthefactthatfundamentalphysicsitselfmightproveacounter-exampletomereologicalsuper-venience.Dothepastsuccessesofreductionismwarrantthoseassumptionsontheirpartoristheassumptionbasedlargelyonfaith?Weknowwhatquestionsneedtobeansweredtoresolvethedebatebetweenemergentismandreductionism,butisitpossibletoeveranswerthem?Howwillweknowwhenwehaveansweredthem?Itisnodoubtprudenttoremainagnostic102\nReduction,EmergenceandExplanationwhilepatientlyawaitingtheoutcomeofeach“crucialquestion”forthedebate.Butunfortunately,notalltheproblemsandquestionsareempirical.Giventhatprogressontheontologicalquestionsofreductionism/emergentismisinextricablyboundwithprogressontheepistemologicalquestionsofreductionism/emergentism,andvice-versa,therestillremainsadeeperconceptualorphilosophicalproblemabouthowtoultimatelyadjudicatetheevidenceatanygivenpointintime.Forexample,theproblemwithreducingchemistrytoquantummechanicsisnotjustacomputa-tionalorcalculationalone.Theexplanatorysuccessofchemistryrequiresbothanewontologyandanewtopology(e.g.,molecules)beyondthatofquantummechan-ics(Primas,1998;Hendry,1999).Canwethereforeconcludethatchemicalphe-nomenaareontologicallyemergentinsomeimportantrespects?ButtryingtoanswerthisseeminglystraightontologicalquestionwillimmediatelyraisethespecteroftryingtocuttheGordianknotofontology(e.g.,cross-theoreticidenti-ties)andepistemology(e.g.,intertheoreticreduction).Anyanswertothequestionwillrequirefallingbackonphilosophicalcriteriathatarenoteasilyjustified.Perhapsthepointhereisthat,inanygivencase,decidingonthemeansofintertheoreticreduction(formalorotherwise)anddecidingwhetherornottheattemptedreduc-tionissuccessful(thecriteriaforsuccessfulreduction),isinescapablynormative.Forexample,isitsmoothintertheoreticreductionthatmotivateandsustainclaimsofcross-theoreticpropertyidentityortheotherwayaround?Likewise,isitthefailureofsmoothintertheoreticreductionthatmotivatesandsustainsclaimsforfailuresofcross-theoreticidentities,ortheotherwayaround?Isthereanyfactofthematterregardingsuchquestionsoraresuchquestionslargelynormative?Whicheverwaywechoose,itseemstoeitherleadincirclesorraisenewandequallyhairyproblems.Ifweholdthatontologicalconcernssuchasthequestionofidentifyingthementalandthephysicalforexampleshouldbecompletelysub-ordinatedtotheepistemologicalquestionofwhetherornotthetheoryoffolkpsychologycanbeintertheoreticallyreducedtosometheoryofneuroscience,thenweneedanacceptableandagreeduponaccountofintertheoreticreduction.AsPatriciaChurchlandputsit,“Bymakingtheoriesthefundamentalrelata[ofthereductionrelation],muchofthemetaphysicalbewildermentanddottinesscon-cerninghowentitiesorpropertiescouldbereducedsimplyvanishes”(asquotedinBickle,1998,p.44).Butthis,ofcourse,bringsusbackfullcircletoourprob-lematiccasesofintertheoreticreduction.Exactlywhatwelackatthemomentisanacceptableandagreeduponaccount,methodorcriteriaofintertheoreticreduc-tioninmanyproblematiccases.Takethecaseofnonreductivephysicalismversusreductivephysicalismforexample.Bothaccountsofthementalacceptmereologicalandnomologicalsuper-venience,yettheformerdeniesthatthementalcanbecross-identifiedwiththephysical.Thisisbecausenonreductivephysicalismdeniesthatsuccessfulintertheo-reticreductionis,inprincipleorinpractice,sufficientforontologicalidentifica-tionofproperties(Antony,1999,pp.37–43).Onthisview,mentalpropertiesareontologicallydistinctwhilebeingexplicableandpredictableinprinciplefromtheirphysicalbasis.Nonreductivephysicalismholdsthattheidentificationofone103\nMichaelSilbersteinpropertywithanotherisnotafunctionofsuccessfulintertheoreticreduction,butwhetherornotthehigher-levelpropertyfiguresinpatternsorcausalrelationsinnon-analytically-guaranteedregularities.Anentity/propertyisontologicallynon-identifiableifitparticipatesessentiallyinregularitiesthatarenovelfromthepointofviewoftheallegedreducingbase–asituationnotprecludedbysuccessfulintertheoreticreduction.Truthsdiscoveredthatarenottruebydefinitionabouthigher-levelpropertiesareirreducibletolower-leveltruths.AsAntony(1999)putsit,nonreductivephysicalismis“anon-ontologically-reductivematerialism,coupledwithaninsistenceonexplanatoryreduction”(p.43).Thus,theonlythingthatreallyseparatesreductivefromnonreductivephysicalismthen,istheirrespectivephilosophicalcriterionforidentifyingonenaturalkind/propertywithanother;thereisnodisagreementhereaboutthebasicontologicalandscientificfacts.Accordingtononreductivephysicalismthefactthatfolkpsychologyisrepresentational/cog-nitiveemergentwithrespecttoneuroscientfictheoriesofmind,issufficienttoblockthecross-theoreticidentityofmentalpropertieswithphysicalproperties.Accord-ingtoreductivephysicalismontheotherhand,iffolkpsychologycaninprinciplebeintertheoreticallyreducedtosometheoryofneurosciencethenthatissufficientforcross-identificationofmentalpropertieswithphysicalproperties.Thequestionisthis:Isthereanyobjectivefactofthematteraboutwhoisrightinsuchadispute?Inthelongrun,itisimportanttotrytoseparateoutthenormativefromthemoreempiricalaspectsofthedebatebetweenemergentismandreductionism.ReferencesAnderson,P.W.(1994):ACareerinTheoreticalPhysics.Singapore:WorldScientificPublishing.Antony,L.(1999):“MakingRoomfortheMental.CommentsonKim’s‘MakingSenseofEmergence,’”PhilosophicalStudies,95(2),37–43.Auyang,S.(1998):FoundationsofComplex-SystemTheories.Cambridge:CambridgeUni-versityPress.Batterman,R.W.(2000):“MultipleRealizabilityandUniversality,”BritishJournalofthePhilosophyofScience,51,115–45.Batterman,R.W.(2001):TheDevilintheDetails:AsymptoticReasoninginExplanation,Reduction,andEmergence.Oxford:OxfordUniversityPress.Beckermann,A.,Flohr,H.andKim,J.(eds.)(1992):EmergenceorReduction?EssaysontheProspectsforNonreductivePhysicalism.Berlin:DeGruyter.Bedau,M.(1997):“WeakEmergence,”inJ.E.Tomberlin(ed.),PhilosophicalPerspectives(11):Mind,Causation,andWorld,Boston:Blackwell,374–99.Belot,G.andEarman,J.(1997):“ChaosoutofOrder:QuantumMechanics,theCorre-spondencePrincipleandChaos,”StudiesinHistoryandPhilosophyofModernPhysics,2,147–82.Berry,M.V.(1991):“Asymptotics,Singularities,andtheReductionofTheories,”inD.Prawiz,B.SkyrmsandD.Westersta°hl(eds.),Logic,Methodology,andPhilosophyofScienceIX:ProceedingsoftheNinthInternationalCongressofLogic,MethodologyandPhilosophy104\nReduction,EmergenceandExplanationofScience,Uppsala,Sweden,August7–14,1991,volume134ofStudiesinLogicandFoun-dationsofMathematics,Amsterdam:ElsevierScienceB.V,597–607.Berry,M.V.(1994):“SingularitiesinWavesandRays,”inR.Balian,M.KlémanandJ.P.Poirier(eds.),PhysicsofDefects(LesHouches,SessionXXXV,1980),Amsterdam:NorthHolland,453–543.Berry,M.V.(2000):“ChaosandtheSemiclassicalLimitofQuantumMechanics(istheMoontherewhensomebodylooks?),”ProceedingsoftheVaticanConferenceonQuantumMechanicsandQuantumFieldTheory,2–26.Berry,M.V.andHowls,C.(1993):“InfinityInterpreted,”PhysicsWorld,12,35–9.Bickle,J.(1998):PsychoneuronalReduction:TheNewWave.Cambridge,MA:MITPress.Blazer,W.,Pearce,D.A.andSchmidt,H.-J.(1984):ReductioninScience:StructureExam-plesandPhilosophicalProblems.Dordrecht:D.ReidelPublishingCompany.Bohm,D.andHiley,B.J.(1993):TheUndividedUniverse.London:Routledge.Bohr,N.(1934):AtomicTheoryandtheDescriptiveofNature.Cambridge:CambridgeUni-versityPress.Cartwright,N.(1997):“WhyPhysics?”inR.Penrose,A.Shimony,N.CartwrightandS.Hawking(eds.),TheLarge,theSmallandtheHumanMind,Cambridge:CambridgeUni-versityPress,161–8.Cartwright,N.(1999):TheDappledWorld:AStudyoftheBoundariesofScience.NewYork:CambridgeUniversityPress.Causey,R.L.(1977):UnityofScience.Dordrecht:Reidel.Chalmers,D.(1996):TheConsciousMind.Oxford:OxfordUniversityPress.Churchland,P.M.(1981):“EliminativeMaterialismandthePropositionalAttitudes,”JournalofPhilosophy,78,67–90.Churchland,P.M.(1985):“Reduction,Qualia,andtheDirectIntrospectionofBrainStates,”JournalofPhilosophy,82,8–28.Churchland,P.M.(1989):ANeurocomputationalPerspective:TheNatureofMindandtheStructureofScience.Cambridge,MA:MITPress.Churchland,P.S.(1986):Neurophilosophy:TowardaUnifiedScienceoftheMind-Brain.Cambridge,MA:MITPress.Cornell,E.A.andWieman,C.E.(1998):“TheBose-EinsteinCondensate,”ScientificAmerican,278(3),40–5.Dennett,D.(1988):“Quiningqualia,”inA.J.MarcelandE.Bisiach(eds.),ConsciousnessinContemporaryScience,Oxford:ClarendonPress,240–78.Dickson,W.M.(1998):QuantumChanceandNon-Locality.Cambridge:CambridgeUni-versityPress.Dupré,J.(1993):TheDisorderofThings:MetaphysicalFoundationsoftheDisunityofScience.Boston:HarvardUniversityPress.Feyerabend,P.K.(1962):“Explanation,ReductionandEmpiricism,”inH.FeiglandG.Maxwell(eds.),MinnesotaStudiesinthePhilosophyofScienceIII.Minnesota:Univer-sityofMinnesotaPress,231–72.Feyerabend,P.K.(1977):“ChangingPatternsofReconstruction,”BritishJournalforthePhilosophyofScience,28,351–82.Giere,R.(1988)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he1960swiththeaimtoshowthatmetaphoricalmodelsandanalogyaremorethanheuristicdevicesthatcanbejettisonedoncea‘proper’theoryisinplace.(Forareviewoftheworkatthattimeandbefore,seeLeatherdale(1974).)Workonmodelsandmetaphorcontinuestobediscussedtothisday(Paton,1992;BhushanandRosenfeld,1995;Miller,1996;Bradie,1998,1999;109\nDanielaM.Bailer-JonesBailer-Jones,2000b),anditusuallyconcurswiththerejectionofthereceivedopinionthattheoriesprevailovermodels–arejectionwhichneednotbelinkedtoametaphorviewofmodels,however(Cartwright,1999;Giere,1999;MorganandMorrison,1999).Metaphor,inthiscontext,isseenasverycloselytiedtoanalogy,justasmodelsarecloselytiedtoanalogy(Achinstein,1968;Harré,1988).Inaddi-tion,model,metaphorandanalogyhavebeenpopularnotionsintheirownrightoverthepastdecades.Thereisagreatdealofworkonanalogycomingfromartifi-cialintelligenceresearch(Falkenhaineretal.,1989;HolyoakandThagard,1989;Hofstadter,1995)andfromcognitivepsychology(GentnerandMarkman,1997;VanLehn,1998).Metaphorhasbeenaddressedinphilosophyoflanguage(Davidson,[1978]1984;Searle,1979)aswellasincognitivelinguistics(Kittay,1987;Langacker,1987;LakoffandJohnson,1980,1999;Lakoff,1993).Today,thestudyofscientificmodelsasmetaphorsoranalogiesinphilosophycannotbeseparatedfromthestudyofthesephenomenainneighboringsubjects,norshouldthey.Ontheotherhand,drawingfromalargenumberoffieldswithdifferentaimsandresearchquestionsdoesnotmakeprogressinresearchonscientificmodelsanyswifter.Todrawinferencesabouttheuseofmetaphorandanalogyinscientificmodeling,oneneedstotreadcarefullywhenassessingwhetherfindingsfromneigh-boringdisciplinescanbeintegrated–whileintegratingthemislikelytobeanimportantsteppingstoneintheanalysisofscientificmodels.Inanycase,theideathatanalogycentrallyoccursinhumaninformationprocessingandknowledgegen-erationiscommontoworkdoneinalltheseareas.AnalogyTheGreekwordanalogy(a
alogia)means‘proportion’,e.g.2isto4as4isto8.TouseanalogyforillustrationisacommonoccurrenceinGreekthought,aswhenthepre-SocraticThalesofMiletusclaimsthattheearthfloatsonwaterlikeapieceofwoodwould(Aristotle,DeCaelo,B13,294a28f.)Analogyisoftenunderstoodaspointingtoaresemblancebetweenrelationsintwodifferentdomains,i.e.AisrelatedtoBlikeCisrelatedtoD.Togiveanexample,theelec-tronsinanatomarerelatedtotheatomicnucleusliketheplanetsarerelatedtothesun.Theterm“formal”analogypointstorelationsbetweencertainindivid-ualsoftwodifferentdomainsthatareidentical,oratleastcomparable.Suchanidentityofstructuredoesnotrequirea“material”analogy,thatis,theindivid-ualsofthedomainsarenotrequiredtoshareattributes(Hesse,1967).Boththemotionofelectronsandplanetsisdeterminedbyanattractiveforcewhichiswhytheyorbitaroundtheatomicnucleusandthesunrespectively,eventhoughthecausesofattractionarenotthesame(gravitationalversuselectrostatic)whichiswhytherelationshipsareperhapsmorecorrectlycalled“comparable”than“iden-tical.”Althoughelectronsandplanetssharetherelationshipofattraction,theydifferhugelyinattributes,suchassizeandphysicalmake-up.110\nModels,MetaphorsandAnalogiesAnalogiescanexistasformalrelationshipsbetweenphenomenaor,rather,betweenthetheoreticaltreatmentofphenomena.Pointingtoexamples,suchaslightandsoundwavesormagnetismanddielectricpolarisation,PierreDuhemstressesthat“itmayhappenthattheequationsinwhichoneofthetheoriesisformulatedisalgebraicallyidenticaltotheequationsexpressingtheother....[A]lgebraestablishesanexactcorrespondencebetween[thetheories]”(Duhem,[1914]1954,p.96).Tofindsuchacorrespondenceserves“intellectualeconomy,”anditcanalso“[constitute]amethodofdiscovery”by“bringingtogethertwoabstractsystems;eitheroneofthemalreadyknownservestohelpusguesstheformoftheothernotyetknown,orbothbeingformulated,theyclarifyeachother”(Duhem,1954,p.97).Thereis“nothingherethatcanastonishthemostrigorouslogician”;itisastrategyinperfectagreementwith“thelogicallycon-ductedunderstandingofabstractnotionsandgeneraljudgements”(1954,p.97),andyet,Duhemjudgesanalogiesinscienceasheuristic,thusasnolongeressen-tialonceatheoryisformulated.NormanCampbell([1920]1957)treatsanalogyinscienceassomewhatmorecrucialforhisnotionoftheory.Inhisaccountatheorycontainsahypothesis,asetofpropositionsofwhichitisnotknownwhethertheyaretrueorfalseaboutacertainsubject(formypurposes,“firstsubject”).Iftheideasexpressedinthesepropositionswerenotconnectedtosomeotherideas(associatedwitha“secondsubject”),theywouldbe,accordingtoCampbell,nobetterthanarbitraryassump-tions.Asthepropositionsconstitutingthehypothesisarenotthemselvestestable,theyrequiresomekindofconfirmationviaatranslationintootherideas,i.e.ideasaboutasecondsubject,wherebythelatterareknowntobetruethroughobser-vationallaws.Campbell’sexampleisthekinetictheoryofgases(firstsubject)beingthehypothesisformulatedintermsofasetofpropositions.Thesecondsubjectwouldthenbe“themotionofalargenumberofinfinitelysmallandhighlyelasticbodiescontainedinacubicalbox”(Campbell,1957,p.128).Forthelatter,lawsareavailablesothatitcanbeknownwhichpropositionsconcerningthesecondsubjectaretrue.Thefirstsubject,Campbellproposes,benefitsfromthisknowledge:Viaa“dictionary,”thetransitionfromfirsttosecondsubjectcanbemade,andtheknowledgeaboutthesmallelasticbodiesilluminatesthecaseofinterest,i.ethefirstsubject,andisemployedtotestthehypothesisindirectly.Campbellasserts:“[i]norderthatatheorymaybevaluable...itmustdisplayananalogy.Thepropositionsofthehypothesismustbeanalogoustosomeknownlaws”(Campbell,1957,p.129).Inmodernterms,thesmallelasticbodiesintheboxwouldbeconsideredasamodel,thoughCampbelldoesnotusethisterm.WhileCampbellgreatlyadvertisestheimportanceofanalogy,heseemslittleconcernedwithitsadvantagesforthepracticeofscience,thatisfordiscoveryor1teaching.BesidesanalogiesbetweenthetheoreticaltreatmentsofphenomenawhichCampbellconsiders,Hesse(1966)alsoproposedthatscientificmodelsaretobe2viewedasanaloguestotheaspectsoftherealworldthataretheirsubject(Hesse,1953,p.201);seealsoHesse(1967)andHarré(1970,p.35).RomHarrécalls111\nDanielaM.Bailer-Jonesthis“[a]behaviouralanalogybetweenthebehaviouroftheanalogueoftherealproductiveprocessandthebehaviouroftherealproductiveprocessitself”(1988,p.127).Incontrasttothis,mostsubsequentdiscussionsabouttheformalrela-tionshipofanalogyconcernanalogiesbetweentheoreticaltreatmentsofdifferentempiricalphenomenaandtheexaminationofthepotentialoftheuseofanalogyforpurposesof“intellectualeconomy”andfor“scientificdiscovery.”Forthis,thestudyofnineteenthcenturyscience,specificallytheworkofKelvin,Faraday,andMaxwell,providesnumerouscasestudies(Duhem,[1914]1954;Campbell,[1920]1957;Hesse,1953).Examplesincludetheanalogybetweenheatandelec-trostatics,wherethesameequationscanbeemployedinbothareas,withtem-peraturecorrespondingtoelectricalpotentialandsourceofheattopositivecharge(North,1980,p.123),orMaxwell’sapproachtoelectromagnetismbyanalyzinganelectromagneticetherintermsofvorticesalonglinesofmagneticforce(Harman,1982,1998).Fromsuchexamples,analogycanberecognizedasacon-stituentofscientificargument(North,1980)andcanbeappreciatedascognitivelyrelevant.Itseemsplausiblethatthedevelopmentofmodelsofnewphenomenabenefits,inmanycases,fromconsideringanalogiestoother,alreadyexistingandmorefamiliarmodels,eveniftheseappeartobelongtoquitedifferentphenom-ena.Thekeypointispreciselythatthetwophenomenaarenotthesame.Pro-claimingonethingtobeanalogoustoanotherisnotsimplyastatementaboutwhatthetwosubjectshaveincommon.Rather,intheinterestingcasesofanalogy,therearedifferencesbetweentherelationsandattributespresentinbothdomains;thesearecalled“disanalogies”or“negativeanalogies.”Electronsandplanetsareattractedbytheatomicnucleusandthesunrespectively,butnotthroughthesamekindofforce.Anypositiveanalogycomeswithnegative,andalsosometimeswithneutral,notyetexploredanalogies(Hesse,1966,1967;Harré,1970,1988).Theeffectiveuseofanalogypresupposesthatitsusersknow,orcanexplore,whatthepositiveandthenegativeanalogiesbetweentwodomainsare.Analogyisoftenthoughttooccurinsciencebecauseitsupportsacentralfunc-tionofmodels:explanation(Harré,1960;Nagel,[1960]1979,p.107;Hesse,1966;Achinstein,1968).Accordingtosomeauthors,modelsbeingexplanatorymostlycoincideswiththembeingdevelopedonthebasisofananalogytosomeotherobjectorsystem(Achinstein,1968,p.216).Explanationisthuslinkedtomakingthetransitionfromsomethingunfamilartosomethingmorefamiliar:“Theanalogieshelptoassimilatethenewtotheold,andpreventnovelexplanatorypremisesfrombeingradicallyunfamiliar”(Nagel,[1960]1979,p.46).Analogycountsasaplausiblecandidateforprovidingexplanationsbecausetheuseofmorefamiliarandalreadyacceptedmodels(modelsthathaveledtounderstandingindifferent,butcomparablesituations)appearsasapromisingstrategyinanewcontext.Correspondingly,PeterAchinsteinstates:Analogiesareemployedinsciencetopromoteunderstandingofconcepts.Theydosobyindicatingsimilaritiesbetweentheseconceptsandothersthatmaybefamiliarormorereadilygrasped.Theymayalsosuggesthowprinciplescanbeformulated112\nModels,MetaphorsandAnalogiesandatheoryextended:ifwehavenotedsimilaritiesbetweentwophenomena(forexample,betweenelectrostaticandgravitationalphenomena),andifprinciplesgov-erningtheoneareknown,then,dependingontheextentofthesimilarity,itmaybereasonabletoproposethatprinciplessimilarincertainwaysgoverntheotheraswell(Achinstein,1968,pp.208–9).Achinsteinquotesasexamples,amongothers,theanalogiesbetweentheatomandthesolarsystem,betweenwavesoflight,soundandwater,betweennuclearfissionandthedivisionofaliquiddrop,betweentheatomicnucleusandextranuclearelectronshells,andbetweenelectrostaticattractionandtheconductionofheat(Achinstein,1968,pp.203–5).Exploringhowpeopleunderstandisthesubjectofcognitivepsychology,whereresearchintoanalogyhasgeneratedconsiderableinterestoverthelasttwentyyears;foroverviews,seeGentnerandMarkman(1997)andHolyoakandThagard(1997).Resultsinvolvethatanalogycanbeanalyzedintermsofsimilarity,simi-laritiesofrelationships(e.g.encounteringinterferenceinwaterwavesandinlight)andsimilaritiesofobjectattributes(e.g.oxygenandheliumbeinggaseousatroomtemperature).Correspondingly,analogycanconsistofattributemappingsaswellasofrelationshipmappings,butGentner(1983)producesempiricalevidenceaccordingtowhichmappingsofrelationstendtobefavoredandconsideredthe“deeper”analogiesbythosewhoareconfrontedwiththeanalogies.Analogiesbecomerelevant,inscienceinparticular,whentheyhighlighta“systemofcon-nectedknowledge,notamereassortmentoffacts”(Gentner,1983,p.162).Fur-thermore,thereisapreferenceforcomparingitemsthataresimilarbecausetheirdifferencesare“alignable.”Itemsthataredissimilarhavelittleincommon,theirdifferencesarenotalignable,andtheythushaveasmallerimpactonpeople’sper-ceptionofsimilarity.GentnerandMarkmanview“theabilitytocarryoutfluent,apparentlyeffortless,structuralalignmentandmapping[as]ahallmarkofhumancognitiveprocessing”(1997,p.53).Acknowledgingtheimportanceofanalogyinscientificreasoning(Hesse,1966;Gentner,1982;Harré,1988)makesittemptingtoidentifyscientificmodelingwithdrawinganalogies.However,whilemanymodelshavetheirrootsinananalogy,suchasThomson’splumpuddingmodeloftheatomorBohr’smodeloftheatombasedonthesolarsystem,fewexistingmodelsinsciencehavenotdevelopedbeyondtheboundariesoftheanalogyfromwhichtheyoriginated,andothersmaysimplynothavetheirorigininananalogyatall(Bailer-Jones,2000b).Moreover,ananalogyisarelationshipbetweenthingsorprocesseswhileamodelisatypeofdescriptionaboutsomethingorprocess.Ifanything,amodelcouldbeananalogue,butthisisnottheissuebecausethewaytoevaluateamodelisnottojudgewhetheritisanalogoustosomething,butwhetherit,asitstands(analogousornot),providesaccesstoaphenomenoninthatitinterpretstheavailableempiricaldataaboutthephenomenon.Ananalogyusedformodelingcanactasacatalysttoaidmodeling,eventhoughtheaimofmodelinghasnothingintrinsicallytodowithanalogy.Itis,ofcourse,morethanreasonabletostressthe113\nDanielaM.Bailer-Jonesimportanceofanalogyinthemodelingprocessgiventhatanalogyisoneofthecognitivestrategiesavailableforcreativediscoveryfromwhichscientificmodelsresult.MetaphorAmetaphorisalinguisticexpressioninwhichatleastonepartoftheexpressionistransferred(metajerei
)fromonedomainofapplication(sourcedomain),whereitiscommon,toanother(targetdomain)inwhichitisunusual,orwasprobablyunusualatanearliertimewhenitmighthavebeennew.Thistransferservesthepurposeofcreatingaspecificallysuitabledescriptionofaspectsofthetargetdomain,wheretherewasnodescriptionbefore(e.g.“blackhole”)ornonewasjudgedsuitable.MartinandHarré(1982,p.96)callthese“crisesofvocab-ulary.”Metaphoricexpressionsareusedfordescriptions,andtheoccasionfortheuseofmetaphorariseswhenthetwodomainsbetweenwhichthetransferoccurscanbeviewedasbeingrelated:bysimilarityofobjectattributes,orbysimilarityofrelationships(Gentner,1983).Thustherelationshipofanalogyisusuallyanimportantfactorinbeingabletounderstandametaphor.However,establishingtheimportanceofanalogyforunderstandingametaphorisnottoclaimthattheanalogynecessarilyprecedesthemetaphor.Onecouldequallyarguethatitisthemetaphorthatpromptstherecognitionofananalogy–itisfeasiblethatbothtypesofcasesoccur;thelatterpossibilitywouldstillwarrantthatthemetaphoriscon-nectedtotheanalogy(oranalogies)suggestedbyit:“everymetaphormaybesaidtomediateananalogyorstructurecorrespondence”Black([1977]1993,p.30).Inastronomicalobservations,onetalksaboutsignal-to-noiseratio.Signalisthelightemittedfromtheobjectonewantstoobserve;noiserepresentstheuncer-taintyinthesignal(andthebackground)duetoquantumfluctuationsofphotonemissionandthusrepresentalimittotheprecisionwithwhichthesignalcanbedetermined.Theanalogyconnectedwiththenoisemetaphoristoasoundsignal,e.g.emittedfromaninterlocutorwhilstnoisefromotherpeopletalkingandperhapsanearbyroadneedstobeseparatedfromthesignalsoastomakeouttheinformationofinterest.Aslistenersdealingwithsoundwaves,wearequitepro-ficientinfilteringoutallthoseunpredictablerandomfrequenciesthatcouldpreventusfrommakingoutthesignalinwhichweareinterested,andacompa-rableskillwouldberequiredforopticalwavesinastronomy.Withoutthisanalogy,themetaphorofnoise,asusedinastronomy,isincomprehensible.Theclaimthatscientificmodelsaremetaphorsistiedtothefactthatoftenananalogyisexploitedtoconstructamodelaboutaphenomenon.Thus,ifscientificmodelsaremetaphors,thenanalogyisanimportantfactorinthis.“Thebrainisthehardwareforwhichachildgraduallydevelopssuitablesoftware”impliesananalogybetweendataprocessinginacomputerandthecognitivedevelopmentofachild,justliketheliquiddropmodeloftheatomicnucleussuggestsananalogy114\nModels,MetaphorsandAnalogiesbetweentheatomicnucleusandaliquiddropinthattheoverallbindingenergyofthenucleusis,inapproximation,proportionaltothemassofthenucleus–likeinaliquiddrop.Theviewthatscientificmodelsaremetaphorsdepends,ofcourse,onwhatmetaphoristakentobe,otherthanmetaphorsbeingconnectedtoanalo-gies.Onlyinviewofthatcanoneassesshowtheanalysisofmetaphortranslatesintoanunderstandingofscientificmodels.Istartbyfocusingonthefirstoftheseissues.Theanalysisofmetaphoristraditionallyconductedbycontrastingliteralwithfigurative(ormetaphorical)language(adistinctiononwhichIshallshedsomedoubtbelow).Thisrequirestherelianceonanintuitiveorcommon-senseunder-standingof“literal,”despitethedifficultyofpinpointingwhatmakesliterallan-guageliteral.Ofcourse,wehaveasenseinwhichtalkabout“littlegreenmen”appearsmetaphoricalincomparisonto“extraterrestrialintelligentlife.”“Literal”implies,bydefault,thatanexpressionisnottransferredfromanotherdomain,i.e.is“moredirectly”aboutsomethingandperhapsmore“typical,”“common,”“usual”or“expected.”Inevitably,suchaclassificationremainsunsatisfactory,partlybecausewedonottendtofindmetaphoricalstatementsmoredifficulttocomprehendthanso-calledliteralstatementsthatcouldstandintheirplace(Rumelhart,[1979]1993).Metaphors,moreover,canbeperfectlyusualandfamiliar.Nobodystumblesoverprocessinginformationordevelopingsoftwaresaidofthemind,oraphylogenetictreemerelybecauseitisnooak,beech,limeorfir.Justasweunderstandthebrain-as-computermetaphor,weunderstandthataphy-logenetictreedisplaysdependencyrelationsofagroupoforganismsderivedfromacommonancestralform,withtheancestorbeingthetrunkandorganismsthatdescendfromitbeingthebranches.Mostmetaphorsareunderstoodwitheasewhichindicatesthattherearenogroundstotreatthemasdeviationsoflanguageuse.Onthecontrary,theyarepervasiveandcentral(Richards,1936).Whiletheremaybenoclear-cutdistinctionbetweenliteralandmetaphorical,onecanstillobservedifferent“degrees”ofmetaphoricity,andtheconditionsunderwhichwearecapableofcomprehendingmetaphorscanbeoutlinedcorrespondingly:AEventhoughametaphorisentirelynoveltous,weareendowedwiththecog-nitiveskilltointerpretitjustaseasilyasifwewerefamiliarwiththatparticu-laruseofterminology.BWhilewerecognizeaphraseasmetaphoricalinprinciple,wearesofamiliarwiththeparticulartypeofmetaphorthatthemetaphorisneitherunusualnorunexpected;thebrain-as-a-computermetaphorisanexampleofthis.Anotheristothinkoftheenergydistributionofasystemasalandscapewithmoun-tainsandvalleys,andagravitationalforcethatisresponsiblefordifferencesinpotentialenergydependingonheight,exemplifiedinphrasessuchaspoten-tialwellortunnellingthroughapotentialbarrier.CWearesofamiliarwithwhatoncewasametaphorthataspecialeffortwouldberequiredtorecognizeitassuch;examplesareelectriccurrent,electricfield,115\nDanielaM.Bailer-Jonesexcitedstateorachemicalbondforming,breaking,bending,twistingorevenvibrating.Suchmetaphorsare“dead”;theyarepervasiveinourlanguageandtheyappeartousjustlikeliteralexpressions(Machamer,2000),especiallyassometimestheyareouronlyexpressionforwhattheydescribe.Historicalpri-oritywouldprobablybetheonlygroundsonwhichacurrentofariverorafieldploughedbyafarmerwouldbejudgedmoreliteralthanelectriccurrentorelectricfield.Thesedegreesofmetaphoricityareonlypartiallyrelatedtothenoveltyofthemetaphors,becausesomemetaphors,(unlikethoseinC,oreveninB),willalwaysremainrecognizableasmetaphorical,nomatterhowfamiliarandwell-knowntheyhavebecome.Anexamplewouldbe“Goddoesnotplaydice”expressingresis-tancetoindeterminacyinphysics.Inthefollowing,Ishallfocusonmetaphorsofthefirstandsecondkind,namelymetaphorsthathavenotbecomeandperhapsneverwillbecomeentirelyordinaryandareconsequentlynotquitesoeasilytakenforliterallanguage.Inthesecases,itisoftenpresumedthatthemetaphoricalphrasehasaspecialqualityinthewayitcommunicatesinformation,sometimesreferredtoas“cognitivecontent”(Black,1954).A“strongcognitivefunction”isassignedtometaphorwhen“ametaphori-calstatementcangeneratenewknowledgeandinsightbychangingrelationshipsbetweenthethingsdesignated(theprincipalandsubsidiarysubjects)”(Black,[1977]1993,p.35).Thisisthoughttohappenbecausemetaphorinspiressomekindofcreativeresponseinitsusersthatcannotberivalledbyliterallanguageuse.Thinkof“littlegreenmen”asametaphorforextraterrestrialintelligentlife,asitisusedinscience,notrestrictedtofantasy.Ofcourse,theoriginaldomainofthatexpressionisfantasy,andthere“littlegreenmen”maymeanexactlythat:smallgreenpeople.Ifthephraseisusedinsciencecontexts,however,theimplicitref-erencetofantasyhighlightsthefactthatwehavenoideaofwhatextraterrestrialintelligentlifemightbelike.Somethingnaivelyandrandomlyspecific–littlegreenmen–ischosentoindicatethatthereisnoscientificwayofbeingspecificaboutthenatureofextraterrestrialintelligentlife.Preciselythatwedonotknowwhatextraterrestrialsarelikeiswhatwecangraspfromthephrase“littlegreenmen.”Noamountofinterpretingtheliteralphrase“littlegreenmen”withoutasystemof“associatedcommonplaces”(Black,1954);“implicativecomplex”inBlack([1977]1993)wouldenableustoachievethis,thusknowledgeofthedomainofapplicationiscrucial.“Littlegreenmen”istransferredfromthedomainoffantasytotheradicallydifferentdomainofsciencewhereonewouldnotusuallyexpectthisexpression.Nonetheless,thereisnoreasontothinkthatthemetaphoroflittlegreenmencanbelessreliablyinterpretedandunderstoodbyitsrecipientsthananyphrasefromthe“right”domainoflanguageuse,suchas“notfurtherspeci-fiableformsofextraterrestrialintelligentlife.”Onthecontrary,accordingtoMaxBlack’sinteractionviewwhichgoesbacktoIvorRichards(1936),weevengaininsightthroughthemetaphorthatnoliteralparaphrasecouldevercapture;ametaphorcannotbesubstitutedbyaliteralexpression.Neitherisitsimplyacom-116\nModels,MetaphorsandAnalogiesparisonbetweenthetworelevantdomains,asinanellipticalsimile(“Extraterres-trialintelligentlifeis(like)littlegreenmen”),because,asBlacksuspects,metaphor3cancreatesimilarity.Ifthisistrue,metaphoricalmeaningcannolongerbeviewedasasheerfunctionoftheliteralmeaningoflinguisticexpressionsbelongingtoadifferentdomain.Instead,theproposaloftheinteractionviewisthatthemean-ingsofthelinguisticexpressionsassociatedwitheitherdomainshift.Themean-ingsoftheexpressionsareextendedduetonewideasthataregeneratedwhenthemeaningsassociatedwithprimaryandsecondarysubjectinteract.Theinteractiontakesplaceonaccountofthemetaphorwhichforcestheaudiencetoconsidertheoldandthenewmeaningtogether.4WhiletheideathatscientificmodelsaremetaphorsappearsinBlack(1962),itwasfurtherexploredinHesse(1966,pp.158–9)whodrawsfromtheinterac-tionview:Inascientifictheorytheprimarysystemisthedomainoftheexplanandum,describ-ableinobservationlanguage;thesecondaryisthesystem,describedeitherinobser-vationlanguageorthelanguageofafamiliartheory,fromwhichthemodelistaken:forexample,“Sound(primarysystem)ispropagatedbywavemotion(takenfromasecondarysystem)”,“Gasesarecollectionsofrandomlymovingparticles.”Hessepostulatesameaningshiftformetaphors.Theirshiftshetakestobeinprag-maticmeaningthatincludesreference,useandarelevantsetofassociatedideas(1966,p.160).Correspondingly,ashiftinmeaningcaninvolvechangeinasso-ciatedideas,changeinreferenceand/orchangeinuse.Onthesegrounds,Hessegetsclosetodissolvingtheliteral/metaphoricaldistinction:“thetwosystemsareseenasmorelikeeachother;theyseemtointeractandadapttooneanother,eventothepointofinvalidatingtheiroriginalliteraldescriptionsiftheseareunder-stoodinthenew,postmetaphoricsense”(1966,p.162);seealsoHesse(1983).Thecrucialpointisthatmetaphorscan(inspiteorbecauseofthis)beusedtocommunicatereliablyandarenotpurelysubjectiveandpsychological.Not“anyscientificmodelcanbeimposedapriorionanyexplanandumandfunctionfruit-fullyinitsexplanation”(1966,p.161).Scientificmodels,incontrasttopoeticmetaphors,havetosubjecttocertainobjectivecriteria,orasHesseputsit,“theirtruthcriteria,althoughnotrigorouslyformalizable,areatleastmuchclearerthaninthecaseofpoeticmetaphor”(1966,p.169).Correspondingly,onemay“[speak]inthecaseofscientificmodelsofthe(perhapsunattainable)aimtofinda‘perfectmetaphor,’whosereferentisthedomainoftheexplanandum”(1966,p.170).Inmyformulation,amodelisevaluatedwithregardtowhetheritpro-videsaccesstoaphenomenonandmatchestheavailableempiricaldataaboutthephenomenonreasonablywell.RomHarréandhisco-authorsalsodiscussmodelsandmetaphortogether.Theyclaimthatbothcouldbeinterpretedsuccessfullywiththesametool,namelytheirtype-hierarchyapproach(Aronsonetal.1995,p.97).Yet,theroleofmetaphorinscienceisdifferent(Harré,1960,1970,p.47;MartinandHarré,1982).AccordingtoMartinandHarré(1982),metaphoricallanguageisusedin117\nDanielaM.Bailer-Jonesthesciencestofillgapsinthescientificordinarylanguagevocabulary.Examplesaremetaphoricalexpressionsthathaveacquiredveryspecificinterpretations,likeelectricfield,electriccurrentorblackhole,whichiswhytheyshouldbeunderstood“withouttheintentionofapoint-by-pointcomparison”(MartinandHarré,1982,p.100).Suchmetaphoricaltermscan,however,beviewedasa“spinoff”ofsci-entificmodels(1982,p.100).MartinandHarré(1982,p.100)explain:Therelationshipofmodelandmetaphoristhis:ifweusetheimageofafluidtoexplicatethesupposedactionoftheelectricalenergy,wesaythatthefluidisfunc-tioningasamodelforourconceptionofthenatureofelectricity.If,however,wethengoontospeakofthe“rateofflow”ofan“electricalcurrent”,weareusingmetaphoricallanguagebasedonthefluidmodel.Itseemsthatmanyexampleslendforcetotheviewthatmetaphoricalscientificterminology,evenifhardlyrecognizableassuchanylonger,canbea“spinoff”ofmodels(withouttheclaimthatmodelsthemselvesaremetaphorical)andIshalldiscussoneexamplebelow.ThatMartinandHarré,differentfrommyself,con-sidermodelssimplyasanalogueshasnobearingonthisspecificpoint.MetaphoricalModelsInowsingleoutthefeaturesofmodelsdiscussedinassociationwiththeclaimthatscientificmodelsaremetaphors.Thelistedpointspresupposethatthemetaphorsinquestionareconnectedtoanalogiesandthatsomethinglikethecognitiveclaimattachedtotheinteractionviewholds.FamiliarityandunderstandingModelsandmetaphorsexploitthestrategyofunderstandingsomethingintermsofsomethingelsethatisbetterunderstoodandmorefamiliar;theyexploittheanalogyrelationshipsuggestedbyametaphororexploredinamodel.Ofcourse,beingfamiliardoesnotequatewithbeingunderstood,butfamiliaritycanbeafactorinunderstanding.Thisisalsonottosuggestthatunderstandingcanbereducedtotheuseofanalogy,buthavingorganizedinformationinonedomain(source)ofexplorationsatisfactorilycanhelptomakeconnectionstoanddothesameinanotherdomain(target).Theaimistoapplythesamepatterninthetargetdomainasinthesourcedomain,withthesameassumptionsofstructuralrela-tionshipsinboththesourceandthetargetdomains.Forinstance,tothinkoftheenergygenerationprocessinquasarsintermsofenergygenerationinbinarystarsishelpfulbecauseitwasbystudyingbinarystarsystemsthattheimportanceof118\nModels,MetaphorsandAnalogiesaccretionofmassasapowersourcewasfirstrecognized.Moreover,turningthegravitationalenergyintothe“internal”energyofasystemisperhapstheonlywaytoaccountfortheenormousenergiesthatmustbepresentinquasars.Thepro-posedconversionprocessofgravitationalenergyis,inturn,inspiredbydisksinplanetorstarformation.Piecingtogethertheseideasbasedonanalogiestoalreadybetter-analyzedempiricalphenomenapavedthewaytotheformulationoftheaccretiondiskmodelthatisconstitutiveinexplainingenergypresentinquasarsandradiogalaxies.Formoreexamples,seeCornelis(2000).MaterialforexplorationModelsandmetaphorscanbehypotheticalandexploratory.Besidesapositiveanalogywhichmayhavegivenrisetotheformulationofamodelormetaphor,therearenegativeandneutralanalogiesthatcanbeexplored.Thisexplorationfurtherscreativeinsight,astheinteractionviewproposes,becausesometimesnegativeandneutralanalogiesofferapoolofideasofwhatcanbetestedaboutthetargetdomain.Metaphoricalmodelsneverthelesshavetostanduptoempir-icalreality,whichiswhyHessetalksabout“clearertruthcriteriathanforpoeticmetaphors”and“the(perhapsunattainable)aimtofinda‘perfectmetaphor’”(1966,p.170),i.e.aperfectdescription,onethatprovidesanempiricallyade-quatedescriptionofaphenomenon.Anexampleformetaphoricalexplorationisartificialneuralnetworksasusedincomputingforpatternrecognition.Digitalcomputersareserialprocessorsandgoodatserialtaskssuchascountingoraddingup.Theyarelessgoodattasksthatrequiretheprocessingofamultitudeofdiverseitemsofinformation,taskssuchasvision(amultitudeofcolorsandshapesetc.)orspeechrecognition(amultitudeofsounds)atwhichthehumanbrainexcels.Theexampleofthebraindemonstrateshowtocopewithsuchtasksthroughmanysimpleprocessingelementsthatworkinparalleland“sharethejob.”Thismakesthesystemtoleranttoerrors;insuchaparalleldistributedprocessingsystem,asingleneurongoingwronghasnogreateffect.Theideaofartificialneuralnetworkswasthereforetotransfertheideaofparallelprocessingtothecomputersoastotakeadvantageoftheprocessingfeaturesofthebrain.Moreover,theassumptionthatlearningoccursinthebrainwhenmodificationsaremadetotheeffectivecouplingbetweenonecellandanotheratasynapticjunctionissimulatedinartificialsystemsthroughpositiveornegativereinforce-mentofconnections.Artificialneuralnetworksproduceimpressiveresultsinpatternrecognition,eventhoughthereremainconsiderablenegativeanalogiesbetweenthemandthehumanbrain.Notonlydothenumberofconnectionsdifferhugelyfromthebrain,butthenodesinartificialneuralnetworksarehighlysimplifiedincomparisontoneuronsinthebrain.Explainingtheneuralnetworkmetaphorinvolvesbecomingawareofitsappropriateapplicationsaswellasitslimits.119\nDanielaM.Bailer-JonesCopingwithnegativeanalogiesMetaphors,analyzedasbeingconnectedtoanalogies,usuallyinvolvethestate-mentofnegativeanalogies;thesedonottendtohindertheuseofthemetaphor,however.Scientificmodels,incontrast,requireattentiontoso-callednegativeanalogies.Eventhoughmodelsclaimnomorethantobepartialdescriptions,tousethemefficiently,theirusersneedtobeawareofthenegativeanalogies,those“things”notdescribedbythemodelandthatdonotstanduptoempiricaltests.Knowingwhatthemodelisnotamodelofispartofthemodel.Asshown,anartificialneuralnetworkdoesnotsimulatethestructureofthehumanbrainineveryrespect,butweneedtoknowinwhatrespectsitdoes.Notspellingoutdis-analogiesexplicitlyinamodelcanhavedetrimentaleffects.Somemetaphors,espe-ciallyifeventhepositiveanalogyisquestionable,canbepositivelymisleading,e.g.thecommoninterpretationofentropyasameasureofdisorder.Considertheexampleofapartitionedboxofwhichonehalfcontainsagasandtheotherisempty.Whenthepartitionisremoved,thegasspreadsoverbothhalvesofthebox.Thisconstitutesanincreaseofentropybecauseitisextremelyunlikelythatallgasmoleculeswilleverreturntoonehalfoftheboxspontaneously.Itisnotintuitivewhythesecondsituationshouldbeviewedasastateofhigherdisorderthanthefirst;amoreprecisewayofmodelingentropyistotalkaboutthenumberofavailablemicrostatespermacrostate.Forsomeexamplesfromchemistry,seeBhushanandRosenfeld(1995).NewterminologyMetaphoricalmodelsare“newvocabulary”intermsofwhichempiricaldatacanbedescribed.This“vocabulary”makespossibleadescriptionintendedtoprovideinterpretationsofdata.Inanarrowersenseofavocabulary,metaphoricaltermi-nologyisemployedtomeettheproblemofcatachresis,i.e.toprovidescientificterminologywherenoneexistedpreviously(Boyd,1993).Sometimes,suchnewterminologyhasitsrootintheanaloguesthatinspiredtheformulationofthemodeltowhichtheterminologybelongs(a“spinoff”ofthemodel);MartinandHarré(1982).Anexampleofthisissimulatedannealing,amethodusedinopti-mizationfordeterminingthebestfitparametersofamodelbasedonsomedata.Thephysicalprocessofannealingisoneinwhichamaterialisheatedtoahightemperatureandthenslowlycooled.Thisprocessincreasesthechancethatthematerialrelaxestoalowenergystateratherthangettingstuckinahigherenergymetastablestate.Annealingisaboutavoiding“localminima”ofenergystatessoastoreachthe“globalminimum.”Havingfoundalocalminimum,itmaybenec-essarytoexpendsomeenergyfirst,i.e.to“climbover”an“energymountain,”tofindamoreglobalminimum,thelowenergystate.Thiscanbeinterpretedtocor-respondtofindingan“optimalfit”inthesearchforthebestfittingparameters120\nModels,MetaphorsandAnalogiesforadatamodel;onewantstoavoidterminatingthesearchearlyatwhatseemsagoodfitinalocalsearcharea.Inthecomputationalmethodofsimulatedanneal-ing,notonlytheequationsfromstatisticalphysics,suchastheBoltzmannequa-tion,areadoptedalmostexactly,butthedescriptiveterminologyisalsotakenover.Termssuchastemperature,specificheatcapacityandentropyareappliedtoopti-mizationinameaningfulway.LiteralversusmetaphoricalFinally,theconverseofthemetaphorclaimneedstobeconsideredbriefly:Whatwould“beingliteral”meaninthecontextofscientificmodeling?Whatwouldbetheconsequencesofaliteral–metaphoricaldistinctionforscientificmodelsiftheyare,astheclaimgoes,metaphors?Inthecontextofscience,thiswouldpresumablymeanthatthereare“proper,”“precise”or“literal”waysofdescribinganempiricalphenomenonandother,metaphoricalandlessdirectways,thelatterbeingexemplifiedbyscientificmodels.Onewouldthenhavetoaskwhat“literal”waysofdescribingempiricalphenomenaare.Ofcourse,theremayjustnotbeanyalternativedescriptionforcertainphenomena,e.g.for“elec-tronspin,”althoughthisiswhattalkaboutliteralandmetaphoricallanguageimplies.Oneanswerthatmaybeputforwardbysomeisthattheoriesaretheliteraldescriptions.However,theoriescannotrangeasanalternativetomodels,if,asmyclaimgoes,theyarenotdescriptionsofphenomena(Cartwright,1999).Instead,theoriesmaybeemployedinmodelsandappliedtoempiricalphenomenaonlythroughscientificmodels.Inthiscasetheycannotbeviewedasanindependentmodeofdescriptionofphenomena,i.e.asliteralincontrasttomodelsthataremetaphorical.CurrentIssuesThereisarangeofgeneralissuesconcerningscientificmodelswhichIhavebarelycovered.Theseincludehowmodelswork,whytheyareneededandtowhatextenttheyareused.Otherissuesare,forinstance,howmodelsrelatetotheoriesorwhethersimulationsaremodels.Yet,inthislastsection,Iwanttofocusonlyonpointsthatarespecificallyraisedinthecontextofcomparingscientificmodelswithmetaphors.CreativityEmployingmetaphorscansometimesbeacreativeuseoflanguage,bothinfor-mulationandinterpretation.Consequently,explaininghumancreativity,inscience121\nDanielaM.Bailer-Jonesandelsewhere,isacommonagendaofthoseseekingtoknowhowmetaphorworks.Metaphorisapopularanswertoanyexplorationofcreativity,butitisalsoafairlyimpenetrablekeeperofitssecretbecauseitisnotsoeasilyanalyseditself.Especiallyinthelightofmetaphoricalmodels,Iwonderwhetheroneoughtnotdispeltheopinionthatmetaphorsareformedbysuddenstrikesofgenius.(Notethatthiswould,inanycase,onlyapplytonewmetaphorsonfirstuse,notonthevastnumberofwornandtritespecimens.)Certainlythemajorityofscientificmodelsaredevelopedbylaboriousandcontinuedeffortsthatstretchoveryearsandrequireenormousenduranceonthesideofthosewhoseektheseresults(Bailer-Jones,2000a).Ingenuitydoesnotequatewitheffortlessness,andprogressoftenoccursinverysmallsteps.Correspondingly,oneshouldexaminethethesisthatmetaphorsalsoonlygraduallybecomewidelyacceptedanduniformlyunder-stood,justlikescientificinsightrarelystrikesscientistsoutoftheblue.Inanycase,itisworthchallengingthemythofsudden,inexplicableinsightsinsciencethatisoftenassociatedwithcreativity-generatingmetaphor(e.g.Kekulé’snotoriousdreamofthesnakebitingitstaleleadinghimtotheconceptionofthesix-carbonbenzenering).Creativityinsciencedeservestobeinvestigatedinitsownright,andnotonlyintheframeworkofmetaphor;seeissues4-3and4-4,1999,ofFoun-dationsofScienceonScientificDiscoveryandCreativity.AcquisitionofnewmeaningFormulatingametaphorisaboutgaininga“newish”expressionconnectedwitha“newish”descriptionofinterpretationofasubjectmatter.“Newish”issupposedtotakeaccount(a)ofagradualdevelopmentofmetaphoricalexpressions,and(b)ofthoseaspectsoftheexpressionthatarefamiliarbywayoftheanaloguewhichthemetaphorexploits.Theinteractionviewproposessomethinglikeasuddendiscoveryofanewmetaphorensuedpossiblybyagradualshiftinmeaningoftheprimaryandthesecondarysubjectinresponsetothatdiscovery.Theimplicationisthatthemetaphoricalexpressionislikelytogiveuponemeaningandslowlytoacquireanother.However,evenifwenowtalkaboutelectriccurrentsorartificialneuralnetworks,wehavenotlostthecapacityofusing“current”todescribeariveror“neuralnetwork”todescribeneuronsconnectedinthebrain.Expansionofthedomainofapplicationcanbeobservedbecausetheexpressionnowoccursmetaphorically,buttheuseoftheexpressioninitssourcedomainneednotdis-appear.Whethertalkisaboutelectricfieldsorploughingafield,bothareunder-stoodequallywell,andthereisnoobviousreasonwhymetaphorshouldfunctiondifferentlyfromliterallanguageuseindescribing(Rothbart,1984;Machamer,2000).Atsomepoint,“field”hasobviouslyacquiredanadditionalmeaningthat122\nModels,MetaphorsandAnalogiespermitsittobeappliedinthecontextofelectromagnetism.Understandingitisamatterofworkingoutwhichmeaningatermhappenstohaveinwhichcontext.Similarly,ideasformodelscanbeemployedindifferentdomains:modelsofsta-tisticalmechanicsdonotdisappearbecausetheyhaveanewapplicationinthetechniqueofsimulatedannealing.Yet,evenifonedeniesafundamentaldifferencebetweenliteralandmetaphoricallanguage,questionsremainabouthowwesucceedinthecomplextaskofinterpretinglinguisticexpressions,pickingamongtherangeofpossibleinterpretationsinviewofcontextandassociations.Forsci-entificmodels,thismeansthatevenwhenwesurmountviewingthemaseitherliteralormetaphorical,westillneedtoexaminehowpreciselytheyprovideinfor-mationabouttheempiricalworld.MetaphoricalmodelsandmetaphoricalterminologyInfuturework,itisessentialtodistinguishcarefullywhetheritisamodelasawholethatisportrayedasmetaphoricalorwhetheritismerelyacaseofmetaphor-icalordinarylanguagebeingusedindescribingamodel(metaphoricalornot),orboth.Severaldifferentcombinationsseempossible,anditremainstobeexaminedwhateffectthesedifferentlevelsofmetaphoricalpenetrationhaveonscientificthinking:•Certainmodelsareconsideredmetaphoricalinthesensethatatransferfromonedomaintoanotherhastakenplace,butwherenospecificmetaphoricalterminologyisusedinthismodel,e.g.Bohr’smodeloftheatom.•Inothercases,astructuralrelationshipismadeoutbetweentwodomainsthatwarrantsatransferleadingtotheformulationofamodelinthetargetdomain.Inaddition,thistransfergivesrisetometaphoricallanguageuseaccompany-ingtheuseofthemodel,e.g.temperatureinsimulatedannealingornoiseinobservationalastronomy.•Thentherearemodelswherethedescriptiveterminologyemployedismetaphorical,butthetwodomainsinvolvedinthismetaphoricalterminologyarenotrelatedinstructure.Anexampleisgravitationallensing.Allagravita-tionallenshasincommonwithanopticallensisthatitbendsalightray.Thebendingofalightrayduetogravitationis,unlikethecaseofanopticallens,notinterpretedintermsoftheopticalphenomenonofrefraction,sothemetaphorisnotconnectedtoanydeeperstructuralanalogybetweengravita-tionalandopticallenses.•Finally,yetotherscientificmetaphorsthatcanbefoundinpopularculturearewithoutimpactonscientificmodelingwhichiswhytheycanbedisregardedforthecurrentpurposes.Examplesarelitmustestsinpolitics,acriticalmassofparticipantsneededbeforeideascanbegenerated,amilitarynervecentre,learningbyosmosis,beingtunedinorturnedoff,somebodybeinganElvisclone,etc.(HutchinsonandWillerton,1988).123\nDanielaM.Bailer-JonesTherelationshipsbetweenmodels,metaphorsandanalogiesIbrieflyrecapitulatetheconnectionsbetweenscientificmodels,metaphorsandanalogiestohighlightthecentralresearchquestionresultingfromtheirconfrontation.Amodelisaninterpretationofanempiricalphenomenon.Assuch,itisadescription,althoughapartialdescriptionnotintendedtocoverallaspectsofthephenomenoninquestion,justlikemetaphorsare,althoughthelatterneednotbeinterpretations.Thetaskofscientificmodelsistofacilitate(perceptualaswellasintellectual)accesstophenomena.Whilemetaphorsmayalsofacilitateaccesstophenomena,theirmaincharacteristicisnotthis,butatransferofatleastonepartofanexpressionfromasourcedomainofapplicationtoatargetdomain.Theimplicationisthattheuseoftheexpressioninthesourcedomainmaybemorefamiliarand/orbetterunderstoodthanitsuseinthetargetdomain.Somescien-tificmodelscanbeanalyzedasmetaphorsbecausetheirformulationsinvolveatransferofconceptionsfromadifferentdomain(artificialneuralnetworks,simu-latedannealing,Bohr’smodeloftheatom).However,suchatransferisonlyofinterestinthecontextofmodelsinsofarasitassiststhepurposeofthemodel,namelytointerpretanempiricalphenomenon.Insightfulmetaphorsarethosethatpointtoananalogybetweenphenomenaoftwodifferentdomains.Thedevelopmentofscientificmodelsalsooftenreliesonanalogies.Boththeinterpretationofmodelsandthatofmetaphorsfrequentlybenefitsfromtheanalogiesassociatedwiththem.Analogydealswithresemblancesofattributes,relationsorprocessesindifferentdomains,exploitedinmodelsandhighlightedbymetaphors.Notethatneithermetaphorsnormodelsareanalogies–theyaredescriptions.Thisraisesthequestionwhether,atthecognitivelevel,thereisanythinginvolvedinthemetaphorclaimconcerningscientificmodelsthatcannotbereducedtoanalogy.Istheresomething,e.g.theimportanceofcontextorassociations,thatliftsthecognitiveforceofmetaphorabovethatofanalogy?Muchofthisquestionseemstorestonnotonlythestudyofanalogy,butalsoonwhetherthereexistalternativestrategiesforknowledgeformation.Tosummarize,neithermetaphorsnormodelsaremysteriouslycreativeorotherwisemysteriousinhowtheycontributetoourthinkingaboutphenomena,althoughthisisnottosuggestthatweunderstandeverythingaboutmetaphororaboutscientificmodeling.Bothcanbe,andneedtobe,however,subjecttoresearch.Manycognitiveandcreativeclaimsaboutmetaphorsandmetaphoricalmodelsappearreliantontherelationshipofanalogy,butwhetheranalogyreallydeservestobeconsideredasthebasecategoryindevelopinginterpretativedescrip-tionsequallyrequiresfurtherinvestigation.Finally,beyondthecommonaltiesofscientificmodelsandmetaphoralreadyhighlighted,thereisoneother:scientificmodelsappeartobe,contrarytopastresearchtraditions,ascentralinscientificpracticefordescribingandcommunicatingaspectsoftheempiricalworldasmetaphorsareinordinarylanguage.124\nModels,MetaphorsandAnalogiesAcknowledgmentsFortheircommentsonaspectsofthisarticleIwouldliketothankPeterMachamer,StephanHartmann,MichaelBradie,AndreasBartelsandCorynBailer-Jones.Notes1Mellor(1968)arguesthatCampbellrequiresanalogylargelytoovercometheabyssbetweentheoryandobservation,andthat,wereitnotforCampbell’sstricttheory–observationdistinction,hisaccountwouldnotdiffersignificantlyfromDuhem’s.2“Analogy”referstotherelationshipbetweentwoobjects;an“analogue”istheobjectitselfthatisseentobeintherelationshipofanalogytosomething.3Thisclaimputforwardverycarefullyislaterreaffirmed:“Istillwishtocontendthatsomemetaphorsenableustoseeaspectsofrealitythatthemetaphor’sproductionhelpstoconstitute”(Black,[1977]1993,p.38).4Black([1977]1993,p.30)latercontends:“Iamnowimpressed,asIwasinsufficientlywhencomposingMetaphor,bythetightconnectionsbetweenthenotionsofmodelsandmetaphors.Everyimplication-complexsupportedbyametaphor’ssecondarysubject,Inowthink,isamodeloftheascriptionsimputedtotheprimarysubject:Everymetaphoristhetipofasubmergedmodel.”ReferencesAchinstein,P.(1968):ConceptsofScience.Baltimore,Maryland:JohnHopkinsPress.Aronson,J.L.,Harré,R.andWay,E.C.(1995):RealismRescued:HowScientificProgressisPossible.Chicago,Illinois:OpenCourt.Bailer-Jones,D.M.(2000a):“ModelingExtendedExtragalacticRadioSources,”StudiesinHistoryandPhilosophyofModernPhysics,31B,49–74.Bailer-Jones,D.M.(2000b):“ScientificModelsasMetaphors,”inF.Hallyn(ed.),MetaphorandAnalogyintheSciences,Dordrecht:KluwerAcademicPublishers,181–98.Bhushan,N.andRosenfeld,S.(1995):“MetaphoricalModelsinChemistry,”JournalofChemicalEducation,72,578–82.Black,M.(1954):“Metaphor,”ProceedingsoftheAristotelianSociety,55,273–94.Black,M.(1962):ModelsandMetaphors.Ithaca,NewYork:CornellUniversityPress.Black,M.([1977]1993):“MoreaboutMetaphor,”inA.Ortony(ed.),MetaphorandThought,Cambridge:CambridgeUniversityPress,19–41.Boyd,R.(1993):“MetaphorandTheoryChange:Whatis‘Metaphor’aMetaphorfor?”inA.Ortony(ed.),MetaphorandThought,Cambridge:CambridgeUniversityPress,481–532.Bradie,M.(1998):“ModelsandMetaphorsinScience:TheMetaphoricalTurn,”Protoso-ciology,12,305–18.125\nDanielaM.Bailer-JonesBradie,M.(1999):“ScienceandMetaphor,”BiologyandPhilosophy,14,159–66.Campbell,N.R.([1920]19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olutionispunctuatedratherthanlinear–markedasmuchbyabandonmentandmodificationofpreviouslyacceptedtoolsandtechniquesasbyconservationandaccumulation.Failingastheydidtotakeintoaccountthediversityandmalleabilityofobser-vationalandexperimentalpractice,twentiethcenturyphilosophersofsciencewhotriedtoderivehighlygeneralaprioriepistemicdirectivesfromtheoriesoflogic,rationality,judgment,andthelike,havebeenunabletoanswerimportantques-tionsaboutthedesignandconductofscientificresearch.Thischapter’smoralisthatbecauseofthisfailure,philosophersofscienceshouldpaymoreattentiontonutsandboltsdetailsofobservationandexperimentation.Althoughexperimentandobservationareundertakentofurtheragreatmanydifferentpurposes(includingdiscoveringneweffectsforscientiststoexplain,fillingin,andcorrectingdetailsoftheories,developing,calibrating,andfiguringoutfruitfulapplicationsofequipment)Iwillbeconcentratingonjustone–theproductionandinterpretationofdataforuseintestingtheoreticalclaimsandprac-3ticalideasabouttheirapplications.I’lluseasingleterm“empirical”inconnectionwithbothobservationandexperiment(alongwiththeirequipment,techniques,epistemics,etc.).William128\nExperimentandObservationHerschel(discovererofUranus)drawsausefuldistinctionbetweenthem.Obser-vation,hesays,isamatterofnoticingfactsastheyoccurwithoutanyattempttoinfluencethefrequencyoftheiroccurrence...(Herschel,1966,p.76)Itcanbelikenedtopassivelylisten[ing]toatale,toldus,perhapsobscurely,piecemeal,andatlongintervalsoftime,withourattention,moreorlessawake(p.77)[whereinmanycasesthe]...taleistoldslowlyandinbrokensentences(p.78).Experiment,bycontrast,isamatterofputtinginactioncausesandagentsoverwhichwehavecontrol,andpurposelyvaryingtheircombinations,andnoticingwhateffectstakeplace(Herschel,p.76)Herschellikensthistocross-examiningawitnessandbycomparingonepartofhisevidencewiththeother,whileheisyetbeforeus...reasoninguponitinhispresence[sothatwecan]...putpointedandsearchingquestions,theanswertowhichmayatonceenableustomakeupourminds(Herschel,1966,pp.66,77).Inexperiments,naturalorartificialsystemsarestudiedinartificialsettingsdesignedtoenabletheinvestigatorstomanipulate,monitor,andrecordtheirworkings,shielded,asmuchaspossiblefromextraneousinfluenceswhichwouldinterferewiththeproductionofepistemicallyusefuldata.Investigatorswhocannotproducethedatatheyneedinthiswaycansometimesrelyon“experi-mentsofnature.”That’sthetermBernardusedinconnectionwithdiseaseswhichprovidedevidenceforthestudyofthephysiologyoftheaffectedorgansandsystems(Bernard,1949,p.10).Likeobservableinstancesofastronomicalregularities,experimentsofnatureareinteractionsinwhichnaturalmechanismsconspire,withoutcontrivancebytheinvestigators,toproduceeffectsofinteresttotheinvestigator.Obtainingandinterpretingdatafromsuchoccurrencessome-timesinvolvesenoughequipmentandelaboratearrangementstoblurHerschel’sdistinction.(Eddington’suseofeclipsephotographstocalculatethedeflectionofstarlightisanexample(Dicke,1964,p.2).)Butevenso,thereareepistemicallysignificantdifferencesbetweenobservingwithoutinterfering,andsettingupanexperiment,alteringitscomponents,andinterveningintheirworkingsasneededtoinvestigatethesignificanceofthedatatheexperimentproduces.Medicalresearchcandramatizethispoint.Supposeahideousdiseaseisobservedmorefrequentlyinpeoplewhoeatcertainfoodsthaninpeoplewhodonot.Itmaynotbeatallobviousfromthestatisticaldistribu-tionoftheseandotherobservedfactorswhetherthedietandthediseasearecon-129\nJamesBogennectedcausallyoronlyaccidentally.Someonemightbeabletofindoutbymanip-ulatingpeople’sdiets,lifestyles,andenvironmentsasrequiredtoeliminateorcontrolforconfoundingfactorswhicharenotapparentinthestatistics,butthiswouldbemorallyimpermissible.Todealwithcaseslikethis(andcaseswheretheexperimentsneededtosettleaquestionwouldbetoocostlyortoodifficulttoperform),philosophersandstatisticianshavebeentryingtodevelopformalmethodsofcausalanalysiswithwhichtoinfercausalrelationsfromstatisticaldis-tributions.Thetechnicaldifficultiestheyconfrontprovideadetailedmathemati-calpictureofcertainfascinatingepistemicdifferencesbetweenexperimentandobservation(Glymour,1997,pp.233–42).RobertBoyle’sdialogue,TheSkepticalChymist,contrastsusingempiricalevi-dencetoevaluate,andusingittoillustrateatheory.OneofthecharactersisThemistius,aperipateticwhobelievestheoriescanbeevaluatedonlybyargumentfromundisputedaprioriprinciples,andaccordinglythattheonlylegitimateuseofexperimentis“toillustrate,ratherthantodemonstrate”afterthemannerofastronomerswhousecardboardspherestoexplaintheirtheoriestolaymenwhodon’thaveenoughmathematicstofollowdemonstrationsoftheirtruth(Boyle,1661,pp.20,21).Forexample,heburnssomegreenwoodandusestheresult-ingashes,moisture,smoke,andfireusedtoillustratetheperipateticdoctrinethatallnon-elementalstuffsarecomposedofearth,water,airandfire.Tomaketheillustrationwork,heusesperipatetictheorytoexplaintotheobserverswhattheyhaveseen.Since(accordingtothetheory)elementalearthisheavyanddrythedrynessandweightoftheashesprovethattheyarecomposedofearth.Sinceallelementstendtomovetowardtheirnaturalplaces,thesmokeprovesitselftobeairby“ascendingtothetopofthechimneyand...vanishingintoair,likeariverlosingitselfinthesea”(Boyle,1661,p.21),andsoon.Carneades,thedialogue’sskepticalchemist,maintainstothecontrarythatscientificclaimsshouldbetestedbyexperimentsinwhichfactorswhichcannotbefruitfullystudied(andmaynot4evenoccur)innaturalsettings,areproduced,isolated,andtortureduntiltheyconfesstruthsaboutnature(Boyle,1661,p.10).AlthoughCarneadesisrightaboutthis,itwouldbehardtoteachscienceifempiricalmethodscouldn’talsobeusedtoprovideillustrations;andshabbyasitis,Themistius’illustrationexemplifiesapointwhoseimportancecannotbeover-stated:Naturalandartificialempiricalresultsaretypicallyverydifferentfromthethingsscientistsusethemtoinvestigate.Thus,whatJeanPerrinwantedtolearnaboutwereunobservableatoms,notthemotionsofresinbeadsheobservedinhopesoflearningaboutthem(Perrin,1990,chsIII,IV).Whatneuro-cognitivepsychologistswanttofindoutaboutarecognitiveprocessesandneuronalmech-anismswhichsupportthem,notthescoresonpsychologicaltests,thefunctionalimagesofthebrain,andtheotherempiricalevidencetheyusetostudythem.Tothinktheirmaingoalistounderstandthescores,andotherempiricalevidence,ratherthanthebrainfunctionsislikethinkingthatchefsmakesaucesforthepurposeofusingwhisksandmixingbowls.AmoraltodrawfromThemistiusandCarneadesisthatwhatempiricalresultscanteachdependsuponwhattheycan130\nExperimentandObservationlegitimatelybeinterpretedasindicating.TheSkepticalChymistisfilledwithexam-plesofwhatcanbeinvolvedindecidingwhetheraproposedinterpretationislegitimate.Themistius’illustrationassumesthatburningdecomposeswoodintoitscomponentelements.Carneadesobjectsthatforalltheyknow,heatingpro-ducesnewstuffs,orthattheashandotherresiduescamefromtheair,thecon-tainerinwhichthesamplewasheated,orimpuritiesinthesample(Boyle,1661,p.27ff).Aswe’llsee,anumberoftwentiethcenturycontroversiesinthephilos-ophyofscienceamounttoversionsofthequestionwhetherreasoningfromexperi-mentalorobservationaloutcomescanrevealmoreaboutwhatgoesoninnaturethanThemistius’questionbeggingillustrations.NeglectingExperiment;DistortingObservation5Thelogicalpositivistsarethegiantswhoseshoulderswestandon.Theymadeinvaluablecontributionstophilosophyofscience,andarelargelyresponsibleforitsestablishmentasanacademicdiscipline.Theirworkwasimportanttothelin-guisticturnwhichfoundedanalyticphilosophy,buttheyarelargelyresponsibleforaneglectofexperimentandobservationwhichblindedtwentiethcenturyphilosophersofsciencetofactsabouttheproductionandinterpretationofem-piricaldatawhichbearimportantlyontheirepistemologicalandmetaphysicalcon-cerns.Thelogicalpositiviststaughttheirfollowerstotreatscientifictheoriesasiftheyweredeductivelyclosedcollectionsofpropositions,includingobservationreportsexpressedinavocabularywhichincludestermswhichsignifyobservables,theoreticalpropositionsexpressedinavocabularywhosetermsdonotsignifyobservables,andcorrespondencerulesofmixedvocabularywhichcanbeusedtoderivepredictionsandexplanationsofobservablesfromtheoreticalpropositions,andtotesttheoreticalpropositionsagainstobservationreports(Nagel,1961,pp.90–117).Thisconceptionmodelsscientificprediction,explanation,andtheorytestingintermsofinferentialrelationsamongsentence-likestructures.Butsocon-ceived,whatdoessciencehavetodowiththenaturalworldofnon-sentential,extra-linguisticthings,features,events,processes,etc.,scientistsinvestigate?Hempel(1935,pp.50–1)respondedtorelatedquestionsbyclaimingthatnotheoristwhosupportsacleavagebetweenstatementsandrealityisabletogiveapreciseaccountofhowacomparisonbetweenstatementsandfactsmaypossiblybeaccomplished.Inkeepingwiththis,andwiththeirappreciationofthepowerofnewlydevelopedlogicaltoolsforthestudyofthesystemsofsentencestheyusedtomodelscientifictheories,analyticphilosophersofsciencedownplayedthecleavageanddevotedthemselvestoinvestigatingthesyntaxandsemanticsofobservationandtheoreticallanguages.Insharpcontrasttonineteenthcenturyfigures–like131\nJamesBogenWhewell(1991)andDuhem(1991)–andearlierempiricallymindedthinkers–likeBacon(1994),Boyle(1661),andHooke(1968)–whoengagedinwhatamountstophilosophyofsciencebeforethesubjectbecameinstitutionalizedinitspresentform,thelogicalpositivistsandtheirsympathizerstreatedobserva-tionandexperimentasblackboxeswhichoutputtedobservationsentencesin6relativelymysteriouswaysofnexttonophilosophicalinterest.Decadeswouldpassbeforephilosophersofsciencebegantoappreciatehowmuchtheepistemicvalueofempiricaldataasevidencefororagainstascientificclaimdependsuponthewayitwasproduced,andthedegreetowhichsomefeaturesofscientificpracticecanbeilluminatedbyconsideringfactsaboutdataproduc-tioninsteadoflogicalrelationsbetweentheoreticalclaimsanddescriptionsofempiricalresults.Butyoudidn’thavetosympathizewiththelogicalpositiviststoignoreempiricalmethods.Inthelate1950s,agroupoftheircriticsincludingKuhn,Hanson,andFeyerabenddevelopednewdistractionsassociatedwithHanson’sslogan,“seeingisatheoryladenenterprise”(Hanson,1958,p.19)todirectphilosophers’attentionawayfromempiricalpractice.Asaresultofallofthis,AlanFranklincouldcomplain30yearslaterthatsomeonewhotoldphiloso-phersofscienceofthedeathofLummerandPrigsheimwould“getthesamereaction–totalunconcern–thattheambassadorfromEnglandgetsattheendofHamletwhenheannouncesthedeathofRosenkrantzandGuildenstern”(Franklin,1989,p.1).(Lummer’sandPrigsheim’sinvestigationsofblackbodyradiationfeatured“someofthemostimportantexperimentsinthehistoryof7physics”(ibid.)).Feyerabend(1985),Kuhn(1970),Hanson,andtheirfollowersunderstoodtheoryloadingindifferentways.ThemostcommonunderstandingsresembledoneormoreofthefollowingsubstantiallydifferentversionsKuhn8developedofhisownideathatparadigmsinfluenceobservationtosuchanextentthatobserverswhoworkindifferentparadigmscannot“see”thesamethings.(Kuhn,1970,pp.111–23.)K1:PerceptualBrunerandPostmanfoundthatonshortexposures,subjectslookingatnormalandanomalousplayingcardsdescribedthemallasiftheywerenormal,failing,e.g.toreportthatablackfourofheartswasblack.Ittookrepeated,longerexpo-sureforthemtolearntodescribetheanomalouscardscorrectly(Kuhn,1970,p.63).Kuhninterpretsthisasindicatingthatsomeonewholackstheconceptofadeckcontainingaredcluborablackdiamondcannothave(ornoticehaving)thesamevisualexperienceasanobserverwhohasit.Hegoesontosuggestthatsci-entificparadigmsdetermineobservers’conceptstosuchanextentthatwheninves-tigatorswithconflictingparadigmslookatthesamething,theirobservationswilldiffer.Inparticular,aninvestigator’sparadigmmaypreventherfromobservingwhatwouldotherwisesupportacompetingparadigm’stheoreticalclaims(Kuhn,1970,pp.111,113–14,115,120–1).132\nExperimentandObservationK2:SemanticalWhetherornotthepartiestoascientificdisagreementcanhavethesameper-ceptualexperiences,thetheoreticalcommitmentsoftheirparadigmsinfluencethemeaningsofcrucialdescriptivetermstosuchanextentthattheywillbeunabletoaccepteachothersobservationreportsunlesstheyunderstandthemtomeandifferentthings(Kuhn,1970,p.127ff).K3:SalienceParadigmsdeterminewhatexperimentsandobservationsinvestigatorswillcarryout,andwhatfeaturesoftheirresultstheywillattendtoortakeseriously.Theparadigmsinvestigatorsworkinmaythuspreventthemfromobtainingsignificantempiricalevidenceorappreciatingitsbearingontheirpositions(Kuhn,1970,pp.64,121–38).Suchideasencouragedphilosopherstoignorethestudyofreal-worldempiri-calmethodsanddirecttheirenergiestodisputesabouttheoryloadinganditsimplicationsfortheoryevaluationandscientificprogress.Somephilosopherswerethusledtoworry,ineffect,whetherempiricalresearchcandeliveranythingmoreepistemicallyrespectablethanThemistianillustrationsoftheinvestigator’stheo-reticalcommitments.Butlet’stakeaquicklookatthemeritsofK1andK2beforeweturntothis.Nowitisnotoriousthatobservers’mentalsetscanleadthemtosincerely9reporthavingseenwhatwasnottheretobeseen.Butasageneralization,K1isbothimplausibleandfalse.PriestleyandLavoisierperformedsimilarexperi-mentsusingsimilarequipment.Theywatchedsuchthingsasburningcandles,levelsofwateringraduatedtubes,andsmallanimalsasphyxiatinginbelljars.Despitetheirconflictingparadigms,thereisnoevidencethatthewaterlevels,thecandlesburningout,theanimalskeelingover,orthechronometerreadingstheyusedtotimethemlookedsignificantlydifferenttothem.Opposedastheirparadigmswere,theyfrequentlyreportedthesameobservations.Whatseparatedthemwasnottheirperceptions,buttheconclusionstheydrewfromtheir10evidence(Conant,1957).CaseslikethisareastroublesomeforK2asforK1.Evenif(asK2supposes)theinvestigatorsunderstoodtheirtheoreticaltermsdifferently,thatisnoreasontothinktheycouldn’tunderstandthenumbersandothersymbolstheyusedtorecordtemperature,pressure,orweightreadings,etc.,inthesameway.FurthermoreK2doesn’tevenapplytothemanydatawhichconsistofdrawings,photographs,tracings,soundrecordings,andothernon-verbalrecords.AmoresophisticatedversionofK2hasitthatdifferentbackgroundbeliefsenableinvestigatorstousedifferenttheoreticaltermstodescribewhattheyobserveinsignificantlydifferentways.Forexample,observerswhoidentifymusicalpitch133\nJamesBogenwithairpressureoscillationscanuseoscillationtalktoreportwhattheyhear.Justasobserverswholackedtherelevanttheoryofpitchwouldn’treporttheirobser-vationsthisway,peoplewhousephraseslike“440Hertz”butnotletters,A–G,toreportpitcheswouldn’treportpitchesthewaywedo(Churchland,1992,p.53).Alternatively,somesaythatanexperimentalistwhobelievesthevisualdisplayshelooksatcontains“informationtransmittedwithoutinterference”fromneu-trinoemittinginteractionsintheinteriorofthesun“totheappropriatereceptor”inherlaboratorycansaythatinlookingatthedisplay,sheseestheinteriorofthesun,whileinvestigatorswholacktherelevantbackgroundbeliefswouldhavetosayinstead,e.g.thattheyseesolarneutrinofluxes,orjustGeigercountersplodges(Shapere,1982,p.492).Thismightseemtohelpexplainhowobservationreportscanbearontheoreticalclaimsaboutthingswealwaysthoughtwereunobservable.Ifyoudon’tunderstandhowthevisualdisplaytheobserverwatchescanhaveany-thingtodowithunobservablesolarneutrinofluxes,justdescribeherasseeingthefluxes!K2mightseemtoexplainhowscientistswithdifferenttheoreticalcom-mitmentscanhavehonestdisagreementsoverthesignificanceofanempiricaloutcome.Ofcourse,theydisagreeiftheirtheoriespreventthemfromacceptingeachothers’observationreports.11Suchstoriestalkpasttheissuesofempiricalepistemology.Mostempiricalworkisaimedatdetectingandansweringquestionsaboutthings,facts,events,processes,andtheirfeatures,allofwhichI’llrefertoaseffects.Someeffectsareinstancesofphenomenawhichoccurinnature(e.g.astronomicalregularities)orinthelaboratory(e.g.Comptonscattering,lasereffects)withsufficientregular-ity,andresultfromuniformenoughoperationsofsufficientlysimplesystemsofcausalinfluencestomakethemsusceptibletothederivationofquantitativepre-dictionsanddetailed,systematicexplanationsbasedfromhighlygeneraltheo-12reticalprinciples.Othereffects,producedlesstidilyandoccurringlessregularly,mayalsobeexplainedorpredicted,butonlybyappealtocausalinteractionswhichdependtooheavilyupon,andvarytoomuchwith,localconditionstobeaccountedforbymodelsassimple,andgenerallyapplicableasthoseusedinconnectionwithphenomena.ExamplesincludeevolutionaryphenomenalikethecolorchangeinmothsinManchesterduringtheindustrialrevolution(Mitchell,1987,p.354).Investigatorsusewhattheycanfindoutabouteffectsofbothkindstotesttheirtheoriesanddevisepracticalapplicationsofthem;todesign,calibrateandassessthereliabilityoftheirequipment;todesignexperimentsanddevisetacticsformakingobservationsandproducingdata.Effectsarestudiedbyreasoningfromdata.Dataaresententialornon-sententialrecordsofthingswhichinvestigatorsperceive,orwhichregisterontheirequipment.Numericalrecordsofmeasurementsandtestsscores,drawings,photographs,EKG,andseismictracingsareexamplesofthelatter.Thecrucialepistemicquestionsofempiricalepistemologyhavetodowithhowconclusionsabouteffectsaresup-portedbyreasoningfromdata.AmongthemostimportantofthesearequestionsI’llcallthethreeRs:134\nExperimentandObservation1Relevance:Whatbearingdoestheeffecttheinvestigatorsbelievetheirdatarevealshaveonthetheoreticalorpracticalissuestheyusethemtopursue?2Reality:Istheeffectwhoseoccurrence,orwhosefeatures,thedataseemtoindicaterealorspurious?and3Reliability:Arethedataimprecise,inaccurate,orotherwiseepistemicallydefectivewithrespecttothefeaturesuponwhichtheinvestigator’sreasoningtoconclusionsabouttheeffectofinterestdepends?Equipmentandmethodsofdataproductionarenotrequiredtobereliable,anddataarenotrequiredtobetrue,approximatelytrue,accurate,precise,etc.,toanydegree,orwithrespecttoanyfeatureswhicharenotessentialtotheevaluationoftherea-soningwhichusesit.Thatiswhy,forexample,thevisuallyobviousdis-paritiesbetweentheshapes,relativesizes,andrelativepositionsoflunarmountainsandcratersastheyare,andasGalileo’sdrawingsdepictthemdonotdiscreditGalileo’suseofthedrawingstoarguethatthesurfaceofthemoonisopaqueandirregular,ratherthansmoothandcrystalline(Galileo,1989,pp.41–7).Theinvestigator’sobservationsofitemswhoserelevantfeaturesareeasilyperceivedandperceptuallydiscriminatedneednotbeatallproblematic.Butevenwhentheyareproblematic,thefactthatonecandescribeaninvestigatorashavingobservedwhatshecanlearnaboutonlybyreasoningfromdatashedsnolightontheepistemiclegitimacyofinferencesfromdata,ortheepistemicsignificanceofthedatatheydependupon.Inshort,Idon’tthinkempiricalepistemologiesneedconcernthemselveswithK1orK2.K3,however,isanothermatteraswe’llsee.TheSocio-TheoreticalTurnWithregardtothesecondR,mostphilosophers,historians,andotherstudentsofsciencewouldnowagreewithPeterGalison,thatunlikesounddeductiveargumentsbywhichmathematiciansandlogicianscanhopetosettletheirdisputesdecisivelyenoughtopermanentlyclosedebate,experimentaliststypicallycannot13demonstrateonceandforall“thereality–orartificiality–ofaneffect”(Galison,1987,p.2).ThesameholdsfordisputesaboutRelevanceandReality.Atthesametime,itisundeniablethatscientistscanoftenenddisputesandachievelonglastingconsensusoverthethreeRs.Anumberofphilosophersbeganattendingtoexperimentandobservationinresponsetotheattemptsofadiverse,multi-disciplinarygroupoftheoristswhomadeittheirprojecttoexplainconsensusastheproductofsocialinteractionsshapedbytheinfluenceofavarietyofsocialandbehavioralfactors.Althoughtheytendtodisagreetoomuchamongthem-selvestowanttobelumpedtogether,andalthoughnooneusesthelabelI’ve135\nJamesBogenchosenforthem,I’llcallthemSocialTheorists.Allofthemarguefortherela-tivelyinnocuousviewthatregardlessofhowwellascientificclaimisconfirmedbytheavailableevidence,theconsensusgeneratingprocessesbywhichtheclaimcomestobeacceptedorrejectedbyanyparticulargroupofscientistsisalwayssignificantlyinfluencedinavarietyofwaysbyavarietyofsocial,political,andculturalfactors.Muchmorecontroversially,manySocialTheoriststhinkthatsocial,political,andculturalvaluesdetermine,notjustwhetheramoreorlesswellconfirmedclaimwillbeaccepted,butalso,thatwhetherortowhatdegreeitis14supportedbytheevidence(Shapin,1994,pp.193–309).Manythinkthatsuchepistemicvirtuesastruth,precision,accuracy,andrationality,canbecompletelyaccountedforbyappealtotheverysamesortsoffactors.Forexample,BloorscoffsatDurkheimforsayingthat[I]ntheearlystagesofculturalevolution...a[scientific]beliefmightbedeemedtruebecauseitissociallyaccepted...forusitisonlysociallyacceptableoncondi-tionthatitistrue(Bloor,1983,p.3).andmaintains,tothecontrary,thattruthitselfistheproductofsocialacceptance.Differentgroupsofinvestigatorsdoinfactdisagreeoverwhetherabodyofempiricalevidenceissufficientlyaccurate,orwhetheraninstrumentoraproce-dureforproducingdataissufficientlyreliable.Forexample,somecognitiveneu-roscientistsarehappytobasetheirconclusionsonfunctionalbrainimageswhoseaccuracywithregardtolevelsandlocationsofneuronalactivityareconsideredinadequatebyothers(SteinmetzandSeitz,1991,Mazziotaetal.,1995).AndNewtonandsomeofhiscontemporarieswerehappytoarguefrommeasurementsandestimatesofspeeds,distancesandtimeswhichseemsignificantlyinaccuratetous(Newton,1999,pp.797–801,803).SocialTheoriststakesuchvariabilitytomeanthatthemeaningandtheauthorityofanepistemicnormdependsupon,andisrelativetothepracticesofthegroupswhoembraceit.Becausedifferentgroupsrelyupondifferentproceduresandstandardsformeasurement,descrip-tion,andmathematicalanalysis,whatitisforagivenresulttomeetagivenstandardofaccuracy,precision,etc.,mayalsovaryfromgrouptogroup.SocialTheoristsconcludefromthisthattruth,degreeofaccuracy,error,andthelikearenotfeatureswhichempiricalresultspossessindependentlyoftheirevaluation.Instead,theyareconstitutedbytheprocessesbywhichinvestigatorsagreetoassignthem.Liketheepistemicnormstheyfigurein,theyarerelativetothepracticesofinvestigators,noneofwhichisintrinsicallyanybetterepistemicallythananyother.SomeSocialTheoriststreattheproductionandmaintenanceofconsensusastheproductsofsocialinteractionsinwhichindividualsfunction(whetherornottheyrealizeit)topromotetheirortheirgroups’interests(Barnes,1997;Collins,1999).SocialTheoristsapplyavarietyofstrategiestothestudyoftherelevantinter-actionsandtheconsensusgeneratingmechanismstheybelongto.Latouremploysthemodelofpoliticalcontestsinwhichcompetitorsemployrhetoricalandother136\nExperimentandObservationdevicestogainandconsolidatesupport,andneutralizeopposition,treatinglabo-ratoryequipment,chemicalreagents,experimentalanimals,books,papers,andothernaturallyoccurringandartificiallyproducedobjectsonanalogytopotentialfriendsandfoes(Latour,1987,pp.30–59,63–94).WithWoolgar,heusedethno-graphicaltechniquestostudythefolkwaysofinvestigatorsatworkinalaboratory(LatourandWoolgar,1986,chs1,2).Shapinexplorestherolestrustandauthor-ityplayinresolvingempiricalcontroversies,andtheinfluenceonthemoftheinvestigators’class,socialpositionandpublicpersona(Shapin,1994,pp.3–125;Lloyd,1993).AnumberofSocialTheoriststhinkofinvestigatorsastechnicianswhoemploytheirmaterialandconceptualresourcestoproducewhattheirintendedaudienceswillacceptascredibleandusefulempiricalresults.Socon-ceived,animportantpartofthescientist’sworkistomanipulatetheoreticalconsiderationsandlaboratoryeffectstoobtainasatisfactoryandsustainablefit.Understandingthetricksofthistraderequiresclose,casebycasestudiesofprob-lemsposed,andopportunitiesaffordedbytheskillsandlimitationsoftheinves-tigators,thepeculiaritiesoftheirmethods,andthebehaviorsoftheirequipmentandtheitemstheyapplyitto.Seeforexample,Pickering(1986),ClarkeandFujimara(1992,chs3,5,6),Gooding(1992),Hacking(1991,pp.186–209)andGalison(1987;1997,chs2–8).TheSocialTheorists’pursuitsofsuchideashelpedredirectphilosophers’attentiontorealworldempiricalpractices.Bothsupporters15andopponentsoftheirpositionscanlearnagreatdealfromthewealthofinfor-mationaboutempiricalpracticetheirworkprovides.SomeIssuesforEmpiricalEpistemologistsThefollowingarebriefillustrationsofissueswhicharenowengaging,andshouldcontinuetoengagephilosophersinterestedinexperimentandobservation.Evaluatingreality,relevance,andreliabilityPhilosophersofsciencehaveproposedanumberofhighlyabstract,general,pur-portedlyexceptionlessepistemicstandardsforuseinconnectionwiththethreeRs.Somearesupposedtodeterminetheacceptabilityofdata.Othersaresupposedtodeterminetheacceptabilityofreasoningfromdata.Althoughmanyexamplesofgood,realworldscientificworkaccordwiththemostplausibleofstandards,theirclaimstouniversalityhavefaredbadly.Herearesomeofthemostinfluentialofthesereceived,butdiscreditedproposals.Contrarytotheassumption(a)thatunreplicatedevidenceisalwaysepistemicallydefective,neuroscientists,evolutionaryandotherbiologists,particlephysicists,cosmologists,engineers,andmanyotherscientistsrelyonunreplicated,poorlyreplicated,andincomecases,unreplicabledataandeffects(Bogen,2001;Galison,137\nJamesBogen1987,pp.180–97).Galileo’smoondrawings,Eddington’scalculationsofstarlightdeflection(EarmanandGlymour,1980),andMillikan’soildropexperiments(seebelow)areafewofmanycounterexamplestothecommonassumptionthat(b)bothdataandclaimsabouteffectsderivedfromdataareunacceptableunlessthereisgoodreasontothinktheyaretrue,orthattheyreachsomehighthresholdofaccuracy,approximationtothetruth,orprobability.Althoughithasseemedobviousthat(c)ininterpretingdataonemustnotassumethecorrectnessofcentralcomponentsofthetheoryitisbeingusedtotest,justsuchassumptionsfigureintheuseofMichelson–MorleydatatoargueagainstFresnel’saethertheory(Laymon,1988,p.250).Contrarytotheassumptionthat(d)descriptionsofeffectscalculatedfromdatamustbelogicallyconsistentwiththeclaimstheyareusedtoarguefor,NewtonappealedtoKepler’slawsinhisdemonstrationofUniversalGravitationeventhoughtheyareincompatiblewithUniversalGravitationwhenappliedtothesolarsystem(Duhem,1991,pp.190–5;Laymon,1983).Thuspurportedlyexcep-tionlessreceivedepistemicstandardstowhichmanyexamplesofgoodscientificresearchaccordareviolatedbyothers.Bayesianconfirmationtheory(BC),isthemostwidelyacceptedrecentalter-nativetoreceivedaccountsoftheorytesting.Butitprovidesnobetterepistemicstandardsfortheevaluationofreasoningfromdatathanthereceivedaccounts.AccordingtoBC,empiricalevidence,e,confirmsaclaim,h,onlyiftheprobabil-ityofhconditionaloneandbackgroundknowledge,k,ishigherthantheprob-abilityofhconditionalonkalone(and,accordingtosomeBayesians,higherthansomethresholdprobabilityabove0.5)(EarmanandSalmon,1992,pp.89–100).Butmanyeffectscalculatedfromdatawhichinvestigatorsacceptasgoodevidencefailtomeetthistest,asdomostofthedatainvestigatorsrelyupon.Oftentheyfailbydefaultbecausetherearenonon-arbitrary,objectivewaystodeterminethepriorprobabilitiesrequiredforthecalculationoftherelevantconditionalprob-abilities.Forexample,considertheoildropexperimentMillikanusedtoargueforhm.Themagnitudesof“allstaticelectricalchargesbothonconductorsandinsu-lators’aremultiplesofthefixedandunvaryingmagnitudeofthechargeontheelectron”(Millikan,1935,pp.72–3,76)isacaseinpoint.Theeffecthecalculatedfromhisdatainsupportofhmwasamathematicalrelationshipamongthemagnitudesofchargesonoildropsmovingorheldinsuspensionbetweenchargedplatesinaclosedchamber,andthechargesonionsproducedbyirradiatingtheairinthechamber:(em).Everysuchchargeisamultipleofthesmallestchargeonanion(Millikan,1935,pp.75,76).Millikan’sdataincluded:D1stopwatchreadingsusedtotimethemotionsofoildropscarryingstaticelectricalchargesastheymovedundertheinfluenceofgravity,theelectricfieldbetweenthechargedplates,andadditionalchargestheypickedup(Millikansupposed)fromionstheycapturedoncollisionD2measurementsofthechargesontheplatesundervariousexperimentalconditions,and138\nExperimentandObservationD3measurementsofairpressure,temperature,andothernon-electricalinflu-encesonthedropsmotion.Toproduce(D1),aninvestigatorwouldalignadropwiththetopcrosshairofalowpowertelescope,stopthefirsthandofastopwatchwhenthedropreachedthemiddlehair,andthesecondwhenthedropreachedthebottomhair.Beforeattemptingtocalculatechargesfromhisdata,Millikaneliminatedanimpressivenumberofstopwatchdatapoints.Somewereoutriders.Some,heassumed,reflectedtheinfluencesontheoildropmotionsofconvectioncurrents,encoun-terswithdustparticlesandotherextraneouscausalinfluenceshecouldnototherwisecorrectfor.AccordingtoFranklin,somecouldnotberetainedwithoutrunningafoulofindependentlyacceptedprinciples(Franklin,1989,p.150).Afewotherdatapointswerethrownoutwithoutexplanation.Next,Millikanesti-matedandcorrectedforerrorduetoidiosyncrasiesoftheobservers’reactiontimesandvisualacuities,andpeculiaritiesoftheequipment,andcalculatedtherangeofrandomerror.Fordetails,seeMillikan(1935,pp.57–124)andFranklin(1989,138–64).Whetherornotitcantellusanythingabouttheevidentialbearingofemonhm,thisexamplebodesillforBCasageneralaccountofreasoningfromdata.Accord-ingtoBayes’theorem,theprobabilityofhm,conditionalonrawdata(ofkindsD1,D2,D3)andbackgroundknowledge,km,mustbecalculatedfromtheprob-abilityofhmconditionalonkm,theprobabilityoftherawdataconditionalonhmandkm,andtheprobabilityoftherawdataconditionalon(kmandhm+kmandhm)!ItshouldbeobviousjustfromthedetailsofMillikan’sdatareductionthatanyattempttowritedownallofthenumbersneededforthecalculationofthoseprobabilitieswouldbewhimsicalatbest.ThusBCcannotexplainwhyMillikan’sdatawasrelevanttotheevaluationofhm.ThesameholdsforMillikan’suseofhisdatainsupportofem.Ifemisarealeffect,andnotanartifactofdataproductionandinterpretationitisaninstanceofhm,andassuch,itclearlycountsinfavorofit.Thecrucialques-tionforanempiricalepistemologisttoaskisnot“howprobableishmoremcon-ditionalonthedata?”,butrather,“isemarealeffect?”.Theanswertothatquestiondependsupontheresultsofdetailedevaluationsoflocalfactorswhichareidio-syncratictotheworkingsoftheequipment,thedesignandconductoftheexper-iment,Millikan’streatmentofhisdata(includinghisdecisionsaboutwhattothrowout)andsoon.ThepointoftheevaluationswouldnotbetodecidewhetherMillikan’scleanedupdataandthequantitieshecalculatedfromittoargueforemwerehighlyaccurate(there’slittlechancetheywere)orwhetherMillikan’spro-ceduresforcleaningupthedataandcalculatingvelocitiesandmagnitudesofchargesweregenerallyreliable(someofthemcertainlywerenot).Thepointistodecide(localreliability)whetherthequantitiesMillikanrecordedandcalculatedaremistakeninwayswhichdiscredittheargumentforem.Thisturnsonconsider-ationsasdifferentfromoneanotherastheerrorgeneratingcharacteristicsofthestopwatches,theinfluencesofconvectioncurrentsanddustparticles,thestatisti-139\nJamesBogencalsignificanceofMillikan’sdatareductionprocedures,andsuchphysicalissuesaswhethercapturebyanoildropchangesthemagnitudeofthechargeonatrappedion.Asthisexampleillustrates,theepistemicworthofanempiricalresultusedtoarguefororagainstascientificclaimtypicallyinvolvestheapplicationofavarietyofdifferentideasandtechniquesfromdifferentareasofmathematics,naturalscience,engineering,etc.toavarietyofdifferentandindependentdetailsofexperi-mentaldesignandexecution.Thesemixesarefartooheterogeneoustobeinfor-mativelymodeledalongthelinesofreceivedconfirmationtheoriesasinstancesoftheuniformapplicationofgeneralprinciplesassimpleandgeneralasBayes’theorem,ortherulesofapredicatecalculus.ThisisbynomeanstodenythatBayesiantechniques,alongwiththedeductiveandinductivetechniquestraditionalphilosophersofsciencehavefavoredareusedinindividualstepsthatmaybetakentowardthedetermination,e.g.,ofwhetheragiveneffectislikelytohavebeenanexperimentalartifact,ortheestimationoftheerrorcharacteristicsofaparticularprocessforproducingdata.ThemoraltodrawfromexperimentslikeMillikan’sisthatratherthanprovidingperfectlygeneralaccountsoftheacceptabilityofdataanditsrelevancetotheoryevaluation,theyareamongthetoolswhichmaybeapplied(indifferentwaysfordifferentpurposes)toparticularinvestigations.Detailedstudiesofrealworldevaluationsofrealityandlocalreliabilityandthemotleyofformalandempiricallybasedstandardsandprinciplestheyemployhavedirectedtheinterestsofepistemologistsofsciencetoaccountsofcausalitywhichcanbeusedtounderstandhowinvestigationsofthecausalinfluencesofcompo-nentsofdatageneratingmechanismsfigureinthedetectionandinvestigationofeffects(Cartwright,1989;Spirtesetal.1993;Woodward,1997,2000;Pearl,2000)andtothestatisticalandprobabilitytechniquesemployedinrealworldscience(Earman,1992;Mayo,1996).Whetherfurtherinvestigationsalongtheselinescanleadtoanythingmoregeneralthanpiecemeal,casebycaseepistemo-logicalaccountsisanopenquestion.LaboratoryeffectsLikethemotionsofMillikan’soildrops,lasereffects,Comptonscattering,theeffectsofknockoutgenesonneuronalinteractions,andtheevolutionandpecu-liaritiesofnewstrainsoffruitfliesstudiedbygeneticists,experimentalistsoftenstudyeffectswhich“seldomornever”occurinapurestatebeforepeoplehavebroughtthemundersurveillance.Hackingthinksitisn’tmuchofanexaggerationtosaytheeffectsstudiedby“sciences...whoseclaimstotruthanswerprimarilytoworkdoneinthelaboratory...arecreatedinthelaboratory”(Hacking,1992,p.33).Exaggerationornot,thisconfrontsphilosopherswiththetaskoffindingouthow,andtowhatextent,dataobtainedfromeffectsproducedorisolatedinthelaboratorycanbeindicativeoffactsaboutnaturalphenomena.140\nExperimentandObservationSalienceK3correctlysuggeststhatthesalienceandavailabilityofempiricalevidencecanbeheavilyinfluencedbytheinvestigator’stheoreticalandideologicalcommit-ments,andbyfactorswhichareidiosyncratictotheeducationandtraining,andresearchpracticeswhichvarywith,andwithindifferentdisciplines.Inanexperimentdesignedtoproducedatabearingontheevolutionarysig-nificanceoffemaleorgasms,femalemacaquesinthecompanyofmaleswereriggedwithbatteryoperatedequipmenttorecordmusclecontractions,temperatures,andotherphysiologicalitemsrelevanttosexualactivity.Theequipmentwasminia-turizedtoallowthemacaquestobehavenormallybutlimitationsofbatterystoragecapacityprecludedcontinuousmonitoring.Tosavepower,theinvestigatorsarrangedthingssothattheequipmentwouldbeturnedonwhenthemalesweresexuallyaroused–anoddchoicebecausefemalemacaqueorgasmstypicallyoccurwithoutmalearousalduringmasturbationandsamesexplay.Whenaskedaboutthis,theprincipalinvestigatorssaidtheyjustwantedtorecordtheimportantorgasms!AsElisabethLloydargues,thisisbestunderstoodasareflectionofgender-basedculturalpreconceptionsaboutfemalesexualitywhichwereacceptedwithoutquestionbyresearchersinprimatologyandevolutionarybiology(Lloyd,1993,pp.139–42,149–50).Inthe1960s,experimentalistswereconfrontedwitha“zoo”ofcompetingrelativistictheoriesofgravitation(Earman,1992,p.174).The“extremeweak--40nessofthegravitationalinteraction,only10ofthestrengthofthestronginter-action”(Dicke,1964,p.2)andthelimitationsofavailableempiricalequipmentandtechniquestofrustrateattemptstoproducelocallyreliablelaboratorydatarel-evanttotheevaluationofGTRanditscompetitors.Tomakethemostofwhatlittleempiricalevidencewasavailable,physicistsdecidedtoreducethenumberofalternativesitwouldberequiredtohelpevaluate.Tothisend,theydrewupalistofvaluestheywantedagravitationaltheorytopossess,andeliminatedtheorieslackingoneormoreofthem.Tomakethecut,atheoryhadtobelogicallycon-sistent,todeliverapproximationsofNewtonianpredictionsforslowspeeds,toaccommodatetheuseofco-variantequationstodescribegravity,andtoallowspace-timetobetreatedasafour-dimensionalmanifold.Althoughtheavailableevidencewasinconclusivewithregardtotheoriginalsetofalternatives,itfavoredGTRoveranumberofalternativeswhichmetthoseconditions(Earman,1992,p.176–81).Thusreducingthefieldofalternativestobejudgedgaveoldevidencenewepistemicsignificance.Thisillustratesonewayinwhichaninvestigators’the-oreticalcommitments(e.g.,toNewtonianpredictionsforslowspeeds,totheuseofco-variantequations)influencethesignificantofempiricalevidence,andtheconclusionstheywillfinditreasonabletodrawfromthem.Themacaqueexperimentisremarkableforshowinghowstronganinfluenceculturalfactorscanhave,notjustonbiologytheorizing(that’snosurprise)but141\nJamesBogenonthetreatmentofalow-levelprobleminexperimentaldesignarisingfromafactorasideologicallyandculturallyneutralasbatterylife.Theepistemicsignificanceofabitofevidencecandependontheentrench-16mentofatechniqueorpieceofequipment,i.e.,theextenttowhichtheinves-tigatorsdependonittoproduceorinterpretdata,andtheextenttowhichtheytreatitasepistemicallyunproblematic.WilliamLabov’scritiqueoftheargumentsbywhicheducationalpsychologiststriedtodemonstrateseverelanguagedeficitsininnercityblackchildrenisanillustration.Inoneexperiment,theinvestigator(awhiteadultmale)showedablackchildatoyairplaneandasked“whatwouldyousaythislookslike?”,“whatcolorisit?”“whatwouldyouuseitfor?”and“wheredoyouthinkwecouldgetanotheroneofthese?”.Thedata(audiotapesoftheinterviews)exhibitedhesitant,monosyllabicrepliesbrokenbypausesofupto20seconds.Thesewerethefeaturesoftheevidenceonwhichtheeducationalpsychologistsbasedtheirarguments.Labovwasimpressedinsteadbythechildren’sintonation–anequallyaudiblefeaturewhichwasnotsalienttothepsychologists.Inaccordancewithstandardsocio-linguisticpractices,hetranscribedtheinterviewsinanotationdesignedtoindicateintonationpatterns.Thusanutteranceof“Idon’tknow”iswritten:3‘o’22aknowLabovarguedthatbecausesuchintonationpatternsaretypicalofblackchil-dren’sresponsesincomparablesituationstheyfindthreateningthedatamaybeindicative,notofverbalincapacity,butofdefensivebehaviorelicitedbyfearoftheinvestigatorandtheapparentpointlessnessofhisquestions(Labov,1972,pp.206–7).Labov’sconsiderationofintonationledalsotothedesignofnewexperimentswhichhadnotoccurredtothepsychologists(Labov,1972,pp.208,214).Becausedifferenttechniqueswereentrenchedintheirresearchpracticesafeatureofthedatawhichwassalienttothesocio-linguistswasignoredbythepsychologists.Asthisexampleillustrates,philosophersshouldconcernthemselveswiththeepistemicimportofentrenchment.TechnologyandideologyRecallthatinLloyd’sprimatologyexample,increasedbatterystoragewouldhaveenabledtheinvestigatorstorecordlongenoughtoproducedataontypical,aswellasatypicalfemaleorgasms.Thissuggestshowimportantarolethenatureoftheequipmentandtechnologyavailabletotheresearchercanplayintheinterac-tionswhichbringculturalbiasestobearondataproduction.Galison’saccountofsymbiosisinthedevelopmentofsparkandbubblechamberexperimentaltech-nologiesandtheconceptualresourcesofparticlephysicsisawell-documented142\nExperimentandObservationexampleoftheepistemicallysignificantinterplaybetweentheoreticalcommitments17anddataproduction(Galison,1997,pp.xvii–63).HiddenpossibilitiesIfanempiricalresultagreeswithatheory,doesthatentitleustoconcludeany-thingmorethanthattheresultagreedwiththetheory?Baconissupposedtohavethoughtsoforcasesofcrucialexperimentsinwhichtheresultalsorulesoutthe18theory’sknowncompetitors.ButDuhemarguesthat,toprovethecorrectnessofatheory,acrucialexperimentwouldhavetotesteverypossiblealternative,andscientistsareneverinapositiontoknowwhatalternativesremaintobediscov-ered(Duhem,1991,pp.180–90).Thus,Duhemwoulddenythatempiricalevi-dencewhichfavoredGTRoverallofitsknowncompetitorsestablishesitscorrectness.ThemostitestablishesisthatGTRdidbetterthanthealternativeswithwhichitwascompared.Thatwouldn’tbesobadiftheevidencetoldtheinvestigatorswhatprobabilitytoassigntoGTR.Butaslongasthepossibilityspaceremainsuncharted,itwouldseemthatprobabilitycouldbeassignedonlyrelativetotheknownpossibilities,orbyassigningapriorprobabilitytothedisjunctionofunknownalternativepossibilities.Thelatteralternativeisunattractivebecauseitisashardtoseehowthepriorscouldbeassignednon-arbitrarily,astoseewhatshouldbemadeofprobabilitieswhichdependonarbitrarilystipulatedpriors.Theformerconjuresupmemoriesofdefectivetheorieswhichwereacceptedonevi-dencewhichwouldhavebeenunimpressiveifalternativetheorieshadbeendevel-oped(Earman,1992,ch.7).Thusapressingquestionforempiricalepistemologyistheissueofhowempiricalresultscancontributetotheexplorationandlimita-tionofpossibilityspaces.ReplacingempiricismOld-fashionedempiriciststhoughtthetestofascientificclaimishowwellitstacksupagainstevidencedeliveredbythesenses–unaided,oraidedbymagnifyingoramplifyingdevices.ButwhataboutevidenceproducedbyequipmentlikeGeigercountersandgalvanometerswhichareattunedtosignalswhichthesensescannotpickup?Itdoesn’ttaketoomuchofastretchforempiriciststoextendtheirnotionofempiricalevidencetoapplytowhatregistersonlyonobservationalequipment.Butsomeoftheevidencescientistsrelyonpresentsamoreseverechallengetoempiricism.Forexample,PETandfMRIimagingaresofarthebest,non-invasivetechniquesforcomparinglevelsofcognitivelysignificantneuronalactivityinanatomicallydifferentregionsofthebrainduringtheperformanceofamentaltask.ThequantitiesexhibitedbyPETimagesareusuallycalculatedfromsignalsemittedbyanoxygenisotopewhichhasbeenintroducedintothecircula-143\nJamesBogentorysystem.fMRIcalculatesitsquantitiesfromweakradiosignalswhichvarywithlevelsofoxygenatedhemoglobininthebloodemittedwhenthebrainissubjectedtoastrongmagneticfield.Bothquantitiesareindicativeofbloodvolumeswhichvarywiththeelectro-chemicalneuronalactivitiesofinteresttotheinvestigator.TheempiricalevidenceproducedbyPETandfMRIconsistsofimagesresultingfromelaboratecomputationsembodyingassumptionsandtechniquesfromphysics,biology,statistics,andelsewhere(Corbetta1998;Haxbyetal.,1998).Theimagesarenotsomuchdataasgraphicrepresentationsofinterpretationsofradiationorradiosignals.Unlikethedistinctionbetweenwhatcanbeperceivedbyhumansandwhatcanregisteronlyonexperimentalequipment,thedistinctionbetweenproducingandinterpretingdataistoocentraltoempiricismforitsadher-entstogiveup.Itwilltakeanalternativetoempiricismtohelpusunderstandevidencelikethiswhichblursthedistinctionbetweendataproductionandinterpretation.Notes1ThankstoPeterMachamerforhelpfulsuggestions,someofwhichIfollowed.2Forsomeearlyhistory,seeEamon(1994)andDear(1995).3ThisisnottoendorsePopper’sideathatexperimentalandobservationalresultsarescientificallysignificantonlyiftheywereproducedforthepurposeoftestingatheory,letalonethehypothetico-deductiveaccountaccordingtowhichtheorytestingisalwaysamatteroftryingtofalsifyitbyproducinganexperimentalorobservationalresultwhichisincompatiblewithapredictionthetheoryentails(Popper,1959,pp.27–48).Forsomeinfluentialalternatives,seeGlymour(1980,pp.33–9,110–75)andHowsonandUrbach(1993,pp.6–11,117–70).4ThetortureimagecomesfromBaconwhohasbeenaccusedinrecentfeministsciencecriticismofsupportingtheviolationofnaturebywhite,malescienceandtechnology;seeMerchantinZimmermanetal.(1993,pp.272–5).5Tosavespace,IusethistermforlogicalempiricistsaswellastheViennaCircle,andvariousoftheirsympathizers.6Forsamplesofissuesthatoccupiedphilosophersofscienceastheyneglectedexperi-ment,seeSchlick(1959,pp.209–27),Neurath(1983,ch.7,8),Russell(1940,pp.124–57)andCarnap(1953).7InadditiontoFranklin(1989),philosophersIanHacking(1991),andDeborahMayo(1996),historiansPeterGalison(1987,1997),andMaryJoNye(1972)andsociol-ogistsandanthropologistsofscienceincludingAndrewPickering(1986),HarryCollins(1999),BrunoLatourandSteveWoolgar(1986)areamongthewriterswhohelpedcorrecttheneglectofexperiment.8By“paradigm”Kuhnsayshesometimesmeansa“constellation”ofshared“beliefs,values,techniques,andsoon,”andsometimes“onesortofelementinthatconstel-lation,theconcretepuzzle-solutionswhich,employedasmodelsorexamples”onwhichscientistsbasetheirinvestigations(Kuhn,1970,p.175).9Forexample,seeStuewer’sstoryofpainfullyconscientiousobserversreportingnon-existentflashesonascintillationscreen(Stuewer,1985,pp.284–9).144\nExperimentandObservation10Surprisingly,PriestleyvLavoisierisoneoftheexamplesKuhnarguesfrom!(Kuhn,1970,pp.56,118).11Forthecaseofneutrinos,seeFranklin(2001,pp.249–318).12ThisandthedistinctionbetweenphenomenaanddataarediscussedinBogenandWoodward(1988,1992)andWoodward(1989).13Galisoncametothispointbypayingcloseattentiontoexperimentalpractice.Sur-prisingly,Popperwasabletoappreciatealinguisticversionofthesameproblem(Popper,1959,PartI,chp.v)eventhoughhethoughtit“maybeoflittleconcerntothepracticalresearchworker”(Popper,1959,p.93,PartI,ch.v).14Onthedistinctionbetweensupportandacceptance,seeHempel(1965,pp.90–3).15ForanexcellentoverviewandsamplesofsomeSocialTheoristpositions,seePickering(1992,ch.1–6).16SeeGriesemeronentrenchmentinClarkeandFujimara(1992,pp.52–60).17Forfurtherexamples,seeMitmanandFausto-Sterling,andHolmesinClarkeandFujimara(1992).18ButseeUrbach(1993,pp.18,168).ReferencesBacon,F.(1994):NovumOrganum,trans.,P.UrbachandJ.Gibson(eds.),Chicago:OpenCourt.Barnes,B.(1997):InterestsandtheGrowthofKnowledge.London:RKP.Bernard,C.(1949):AnIntroductiontotheStudyofExperimentalMedicine,tr.H.C.Greene,USA:HenrySchuman,Inc.Bloor,D.(1983):KnowledgeandSocialImagery.Chicago:UniversityofChicagoPress.thBogen,J.(2001):“TwoasGoodasOneHundred–PoorlyReplicatedEvidencein19CenturyNeuroscience,”StudiesintheHistoryandPhilosophyofBiologyandBiomedicalScience,forthcoming.Bogen,J.andWoodward,J.(1988):“SavingthePhenomena,”PhilosophicalReview,July,303–52.Bogen,J.andWoodward,J.(1992):“Observations,TheoriesandtheEvolutionoftheHumanSpirit,”PhilosophyofScience,59,590–611.Boyle,R.(1661):TheSkepticalChymist,reprintKila,Mt:KessingerPublishingCo.Carnap,R.(1953):“TestabilityandMeaning,”inH.FeiglandM.Brodbeck(eds.),Read-ingsinthePhilosophyofScience,NewYork:Appleton-Century-Crofts,47–92.Cartwright,N.(1989):Nature’sCapacitiesandTheirMeasurement.Oxford:OxfordUni-versityPress.Churchland,P.(1992):ANeurocomputationalPerspective.Cambridge:MITPress.Clarke,A.E.andFujimara,J.H.(eds.),(1992):TheRightToolsfortheJob.Princeton:PrincetonUniversityPress.Collins,H.M.(1999):ChangingOrder.Chicago:UniversityofChicago.Conant,J.B.(1957):“TheOverflowofthePhlogistonTheory:TheChemicalRevolutionof1775–1789,”inJ.BConantandL.K.Nash(eds.),HarvardCaseHistoriesinExperi-mentalScience,vol.1,Cambridge:HarvardUniversityPress,65–116.Corbetta,M.(1998):“FunctionalAnatomyofVisualAttentionintheHumanBrain:StudieswithPositronEmissionTomography,”inParasu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nalAnatomyofLanguageProcessing:NeuroimagingandtheProblemofIndividualVariability,”Neuropsychologia,29(12)1149–61.147\nJamesBogenStuewer,R.H.(1985):“ArtificialDisintegrationandtheCambridge–ViennaControversy,”inP.AchinsteinandO.Hannaway(eds.),Observation,Experiment,andHypothesisinModernPhysicalScience,Cambridge:MITPress,239–308.Urbach,P.(1993):FrancisBacon’sPhilosophyofScience.LaSalle:OpenCourt.Whewell,W.(1991):SelectedWritingsontheHistoryofScience,Y.Elkana(ed.),Chicago:UniversityofChicagoPress.Woodward,J.(1989):“DataandPhenomena,”Synthese,79,393–472.Woodward,J.(1997):“Explanation,Invariance,andIntervention,”PhilosophyofScience,64,S26–S46.Woodward,J.(2000):“Data,Phenomena,andReliability,”inD.Howard(ed.),Proceed-ingsofthe1998MeetingsofthePhilosophyofScienceAssociation,S163–S169.Zimmerman,M.E.,Callicott,J.B.,Sessions,G.,Warren,K.J.andClark,J.(eds.)(1993):EnvironmentalPhilosophyFromAnimalRightstoRadicalEcology.EnglewoodCliffs:PrenticeHall.148\nChapter8InductionandProbabilityAlanHájekandNedHallWewilldiscussinductionandprobabilityinthatorder,aimingtobringoutthedeepinterconnectionsbetweenthetwotopics;wewillclosewithabriefoverviewofcutting-edgeresearchthatcombinesthem.Induction:SomePreliminariesArguably,Hume’sgreatestsinglecontributiontocontemporaryphilosophyofsciencehasbeentheproblemofinduction(Hume,1739).Beforeattemptingitsstatement,weneedtospendafewwordsidentifyingthesubjectmatterofthiscornerofepistemology.Atafirstpass,inductionconcernsampliativeinferencesdrawnonthebasisofevidence(presumably,evidenceacquiredmoreorlessdirectlyfromexperience)–thatis,inferenceswhoseconclusionsarenot(validly)entailedbythepremises.Philosophershavehistoricallydrawnfurtherdistinctions,oftenappropriatingtheterm“induction”tomarkthem;sincewewillnotbeconcernedwiththephilosophicalissuesforwhichthesedistinctionsarerelevant,wewillusetheword“inductive”inacatch-allsensesynonymouswith“ampliative.”Butwewillfollowtheusualpracticeofchoosing,asourparadigmexampleofinductiveinferences,inferencesaboutthefuturebasedonevidencedrawnfromthepastandpresent.Afurtherrefinementismoreimportant.Opiniontypicallycomesindegrees,andthisfactmakesagreatdealofdifferencetohowweunderstandinductiveinfer-ences.For,whileitisoftenharmlesstotalkabouttheconclusionsthatcanberationallybelievedonthebasisofsomeevidence,theforceofanygivenevidenceismoreaccuratelymeasuredbynotingitseffectsontherationalassignmentofdegreesofbelief.Theusualassumption–onethatdirectlyconnectsthetwotopicsofthischapter–isthatrationallywarranteddegreeofbeliefcanbemodeledasaspeciesofprobability,inductiveinferenceitselfbeingmodeledbysomeruleforchangingprobabilitiesinlightofevidence.149\nAlanHájekandNedHallThestrengthofthesupportthatsomeevidencegivessomehypothesisisnotmeasuredbythedegreeofbeliefinthehypothesisthatiswarrantedinlightofthatevidence.Thereiswidespreaddisagreementamongphilosophersofscienceastohowexactlyitshouldbemeasured(Milne,1996);butallpartiesagreethatthenotionisanessentiallycomparativeone,inthatitdependsnotonlyonhowlikelyanhypothesisis,inlightofthegivenevidence,butalsoonhowlikelyitwouldbe,inlightofdifferentevidence.TheFirstProblemofInductionOneseriousproblemthatinductiveinferencespresentuswithisthatofsayingwithanyprecisionwhatdistinguishesthegoodonesfromthebadones.Wewillapproachthatproblemshortly,andbecausewetakeitupsecondwillcallitthe“secondproblemofinduction.”Itshouldbedistinguishedfromthefirstproblem,whichisthatofsayingwhythe“good”onesdeservethislabel.Forvariousreasons(whoseelucidation,spacedoesnotpermit),wethinkitisbesttoformulatethisproblemasaproblemaboutsettlingaconflictbetweentworivalinductivemethods–rivalsetsofrulesforadjustingdegreesofbeliefinlightofevidence.LetuspersonifytwosuchrivalsintheformofBillyandSuzy,twofriends.Suzyisaparagonofcognitivevirtue:shealwaysevaluatestheimpactofevidenceonhypothesesinaccordancewiththe“right”inductiveprinciples.Billyevaluatestheforceofevidenceinaccordancewithdifferentprinciples,afactwhichshowsupinthefollowingbizarrebehavior.Heregularlystickshisfingersinlightsockets,alwaysgettinganastyshockwhenhedoesso.Tobeclear,Billydoesn’tliketheseshocksatall.It’sjustthateachtime,hisinductivemethodsleadhimtotheconclusion,giventheevidenceavailabletohim,thatitisoverwhelminglylikelythatthesensationwillbeexquisitelypleasant.BillyandSuzydisagreeaboutthesepredictions,andsince–letusstipulate–theyhaveexactlythesameevidence,theirdisagreementtracestothedifferentprinciplestheyadheretoinevaluatingtheforceofsuchevidence.IsitpossibletoprovideanycompellingargumentfortheconclusionthattheinductiveprinciplestowhichSuzyadheresarerationallysuperiortoBilly’s?Therearetworelevantpartieshere,andweneedtoconsiderthepossibilitythatthereisanargumentcompellingtoonebutnottheother.Letusstipulatethatsuchanargumentmustmakeuseofacceptablepremisesthatdonotbegtheques-tionagainstthepartytobecompelled.WewilltakeitthatsuchpremiseswillatleastincludeallpropositionsdetailingtheevidenceavailabletoBillyandSuzy.Letusfurtherstipulatethatthepremisesmust,insomesense,supportthegivencon-clusion,andthattheycandosoinoneofonlytwoways:eithertheyentailtheconclusionthatSuzy’sinductiveprinciplesarerationallypreferabletoBilly’s,ortheyprovidesomemeasureofinductivesupportforthisconclusion.150\nInductionandProbabilityItmightseemthatnoargumentofthefirstkindthatwouldbecompellingtoeitherBillyorSuzyispossible,especiallyifwelimitourattentiontoargumentsthatproceedonlyfromtheavailableevidence,andthatattempttoestablishthesuperiorityofSuzy’sinductivemethodsoverBilly’sbywayoftheintermediateconclusionthathermethodswill,inthefuture,yieldcorrectpredictionsmoreoftenthanBilly’s.Here,thepoint,familiarsinceHume,thatthepastplacesnologicalconstraintsonthefuturerenderssuchanintermediateconclusioninaccessible.Butthereisalwaysthepossibilityoffindingadditional,non-question-beggingpremises,oroffindingsomeotherroutetotheconclusion–loopholesthat,aswe’llseebelow,Reichenbach’s“pragmatic”justificationofinductionattemptstoexploit.Moreover,thereisatleastoneclearwayinwhichsuchanargumentcouldbeconstructed:namely,ifBilly’sinductiverulesunderminethemselvesbypredicting,giventheevidence,thattheywillsystematicallyissuefalsepredictionsinthefuture.IfSuzy’sprinciplesdonotunderminethemselvesinthisway,thentheywillclearlyberationallypreferable;what’smore,thisconclusionvalidlyfollowsfrompremisesperfectlyacceptabletoboth.Still,thereislittlepointinhopingforsuchanargu-ment,asitturnsouttobefartooeasy–andcostless–toconstructinductive1methodsthatareimmunefromself-undermining.SowemightaswellbuildintoourdescriptionoftheBilly/SuzyscenariothatBillyisadheringtojustsuchamethod.TheInductiveJustificationofInductionWhatthenofthepossibilityofacompellinginductiveargument?NonecouldsucceedinconvincingBilly.ForeithertheevidenceavailabletoBillyinductivelywarrants,byhislights,theconclusionthatSuzy’sinductivemethodsareprefer-abletohisown,oritdoesn’t.Butiftheevidencewarrantsthisconclusionthenhisprinciplesunderminethemselves,andwehavestipulatedthattheyareimmunefromsuchself-undermining.SoconsiderwhethersomeinductiveargumentcouldbeproducedthatwouldprovideSuzywithcompellinggroundsforholdingherinductivemethodstoberationallypreferabletoBilly’s.Togiveherthebestpossiblecase,letussupposethatSuzy’sowninductiveprinciplesstronglyendorse,inlightoftheevidenceavailabletoher,theconclu-sionthatthoseveryprincipleswillyieldwildlysuccessfulpredictionsinthefuture,whereasBilly’swillyieldanunbrokenstringoffalsehoods.Itseems,then,thatshehasacompellingandpowerfulargumentforthetargetconclusion.Buttherehasbeenabitofsleightofhand.Theproblemisnotthather“induc-tivejustificationofinduction”iscircularorquestion-begging,forgiventhatsheisitstargetitmanifestlyisn’t(vanCleve,1984);anylingeringsensethatitiscanbeexplainedawaybynotingthatnosuchinductiveargumentcouldconvince151\nAlanHájekandNedHallBilly.)Rather,weneedtorememberthatstrengthofinductivesupportisacom-parativenotion.Inthecaseathand,the“trackrecord”ofSuzy’sinductivemethodsprovides,bythelightsofthesemethods,extrareasontohavefaithinthemonlytotheextentthatothertrackrecordswerepossiblethatwouldhaveyieldedamorepessimisticprediction–i.e.,onlyifitwasatleastpossiblefortheevidencetoproduceaself-underminingverdict.Butitisprimafaciequitedesir-abletoadheretoaninductivemethodthatisimmunefromthepossibilityofself-undermining,particularlygiventhatthisisbotheasyandcostlesstodo.AssumingthatSuzyisfollowingsuchamethod,thetrackrecordofitssuccesses,howeverspectacular,contributesnothingatalltothecaseinitsfavor.Inanycase,evenatthebeginningofinquiry–beforeanyevidencehasbeenamassed–thereremainsjustasclearandintuitiveadifferenceintherationalacceptabilityofSuzy’sandBilly’sinductivemethods,onewhichneedwaitonno“supportingevidence”tobecomevisible:Thedifferenceisthathersaresuperior.Not,then,becausetheevidencefavorsthem.ThePragmaticJustificationItseemstransparentthatnovalidargumentcouldbeproducedwhosepremisesareobviouslycorrectandnon-question-beggingandwhoseconclusionisthatourparticularinductivepracticesarerationallywarranted.Famously,Reichenbach(1938,1949)attemptstoproducejustsuchanargument.Themoreformalversionoftheargumentseekstojustifytheuseofthe“straightrule”inmakingpredictionsaboutthelimitingrelativefrequencyofoutcomesinaninfinitelyrepeatedexperiment(therulepredictsthislimittoequalthefrequencyobservedsofar);ithasbeensothoroughlydiscussedintheliteraturethatwewillpassoverit(Salmon,1967).Thelessformalversionismoreclever,andlesstalked-about.Forthesakeofdefiniteness,letususethelabel“thescientificmethod”(SM)asanameforwhatevermethoditisweuse–atleast,whenweareatourcognitivebest–fordrawinginductiveconclusions.Andletussupposethatwehavesomestandardofsuccessforaninductivemethod–say,thatthelong-rangefrequencyofcorrectinferencesdrawnonitsbasismustbesufficientlyhigh.Foranygiveninductivemethod,thereisofcoursenoguaranteethatitwillsucceedinthissense:theworldmustcooperate,anditisacontingentmatterwhetheritwilldoso.ReichenbachthusgrantsthatwecanhavenoaprioriguaranteeofthesuccessofSM.Buthearguesthatweare“pragmatically”justifiedinourcon-tinuedadherencetoSM,sinceifanymethodwillsucceed,itwill.ForsupposetheworldissuchthatsomerivalmethodRMwillsucceed,butSMwillnot.Well,acentralcomponentofSMconsistsinprojectingobservedregularitiesintothefuture,andinaworldwhereRMsucceeds,arelevantsuchregularitysimplyisthepatternofRM’ssuccesses.If,forexample,asuccessfulmethodforpredictingthefutureinworldwistoconsultanoracle,thenSMwilleventuallyestablishthat152\nInductionandProbabilitytheoracleisreliable–andsoSMwillitselfultimatelyyieldtheadvicethatoneshouldconsulttheoraclewhenmakingpredictions.Thekeyclaim–thatiftheworldisniceenoughtoallowforthesuccessofsomeinductivemethod,thenitisniceenoughtoallowforthesuccessofSM–issimplyageneralizationofthisexample.So,wehaveademonstrativeargumentthatSMwillbesuccessfulifanymethodwill;hence,itseems,ademonstrativeargumentthatwearerationallywarrantedinadheringtoSM.Buttheexampleoftheoracleisentirelymisleading.Foralongstringofsuc-cessfulpredictionsbysuchanoraclesurelyconstitutesaverysalientregularity.Supposethesuccessoftherivalinductivemethodisnotnearlysovisible;whyshouldwehaveanyconfidencethatSMwill“latchonto”thisstringofaccuratepredictions?Weshouldhavenosuchconfidenceifthefollowingconditionholds:ForeverypropositionAaboutthefuture,therearerivalinductivemethodsthathavebeenhighlysuccessful,andequallysuccessful,inthepast,butthatdisagreewidelyastothelikelytruthofA(giventheavailableevidence).Ifthatconditionismet,thentheargumentforthecrucialpremisefailsdisastrously–forwhichstringofsuccessesshouldSMlatchonto?Itiseasytoseewhatwentwrong:theargumentinvolvedabitofmisdirectioningettingustoagreeimplicitlythatSMwas,intheimaginedworldw,upagainstjustonerivalRM.Moreplausibleisthatitwouldbeupagainstabatteryofrivalssoextensivethattheyfailasagrouptoagreeonanypredictionofsubstance.ItiswishfulthinkingtosupposethatSMcouldsomehowpickthe“winner”.Hume’s“SkepticalSolution”Hume’sown“skeptical”solutiontohisproblemofinductionforeshadowedanimportantmovementincontemporaryepistemology,whichseeksto“naturalize”thesubject(Kornblith,1985).ForHumetookitthatnorationalbasisforinduc-tionispossible,whileaddingthatperfectlylegitimateempiricalpsychologicalques-tionsremainabouthowexactlyitisthatdeliberatingagentsdrawinductiveconclusionsfromevidence.Hume’sownansweremphasizedthecentralroleoftheapparentlybrutepsychologicaldispositionhecalled“custom”or“habit”;con-temporaryfansofthiskindofnaturalizedapproachtoinductiveepistemologycouldpresumablybeexpectedtodrawonmuchmoresophisticatedtheoriesofhumancognitivepsychology.Aseriousworryisthatitisunclearthatthenaturalizingmoveinepistemologyleavesroomforalegitimate,coherentsub-disciplineofnormativeepistemology,adisciplinethatseekstoarticulatetheprinciplesaccordingtowhichweoughttoformourbeliefs.Thatisunfortunate,sinceournaturalor“untutored”cognitiveabilitiesintheinductivedomainarenotoriouslyandsystematicallyunreliable,par-ticularlywhenwe’reinasituationthatforcesustoattendsensitivelytotheprob-153\nAlanHájekandNedHallabilisticbearingofevidenceonhypotheses(Kahnemanetal.,1982).Itwouldseemtorequirecarefulapriorireflectiontodistinguishrationalinductiveinfer-encesfrommistakes.Attheveryleast,thedefenderofapurelynaturalizedepis-temologyofinductionowesusanaccountofhowelsewemightsystematicallyidentifyandguardagainstinductiveerror.Popper’sFalsificationismPopper(1968)arguesforadifferentwayofdismissingtheproblemofinduction:whileagreeingwithHumethatnorationaljustificationofinductioncanbefound,heinsiststhatthisresultisinnocuous,simplybecauseinductionformsnopartofthepracticeofscience.AccordingtoPopper,scientistspropose“conjectures,”andthensubjecttheseconjecturestosevereobservationaltestsinanefforttofalsifythem.Heclaimsthatweareneverrationallywarrantedinconsideringsuchanhypothesistobeprobable,giventhatithaspassedsuchtests.Andsince,accord-ingtothesimplestversionoffalsificationism,deductiverelationsareallthatweneedattendtoinordertocheckthatanhypothesishasbeenrefutedbysomeevi-dence,theproblemofinductionposesnothreattotherationalityofscientificpractice.Asadescriptiveclaimaboutwhatscientists,quascientists,actuallydo–letaloneaboutwhattheybelieveaboutwhattheydo–Popper’sviewstrikesusasabsurd.Butevenasanormativeclaimitfareslittlebetter.Thesimplestandmostdevas-tatingpointwasnicelyemphasizedbyPutnam(1974):Popperseemswillfullyblindtothefactthatweuseevidencefromthepastandpresentasabasisformakingpracticaldecisions,decisionswhoserationalityishostagetotherationalityoftheinferencesdrawnabouttheirlikelyconsequencesonthebasisofthegivenevidence.WhatwouldPoppersay,forexample,aboutthedisagreementbetweenBillyandSuzy?ThatBilly’sbehaviorissomehowrationallypermissible,eveninlightoftheextensiveandpainfulevidentialrecord?Evenwereitunderstoodmerelyasaclaimabouttherationalityofbelief,falsificationismwouldbeunpalat-able;butbeliefandactionaretooinextricablylinkedtosustainsuchanunder-standing.Theconsequencesofthepositionfortherationalityofdecisionprovideit,ironicallyenough,withadecisiverefutation.TheDogmaticResponseThefinalapproachtothefirstproblemofinductionthatwewillconsiderwecallthe“dogmatic”response–notasaninsult,butbecausethewordnicelysumma-rizesitsmainfeatures.Foraccordingtothedogmaticresponse,inductionisper-154\nInductionandProbabilityfectlyrational–certainwaysofadjustingdegreesofbeliefinthelightofevidencearerationallywarranted,andcertainotherwaysareirrational–butabsolutelynojustificationcanbegivenofthisclaim,notevenajustificationofthekindthatwouldonlybecompellingtothelikesofSuzy(Strawson,1952).Itisratherthatthefactthatcertaininductiveinferencesarerationalandcertainothersirrational(andperhapsstillothersneitherrationalnorirrational)isabruteepistemologicalfact,incapableoffurtherphilosophicalexplanationordefense.Theprincipalmeritsoftheviewareclearenough.Itallowsustomaintain,contraHumeandotherskepticsaboutinduction,avigorousdistinctionbetweenrationalandirrationalinductivemethodsandinferences,anditacquiresatleastsomemeasureofplausibilityfromthedismalfailureofmoreambitiousattemptstogiveajustificationofinduction.Still,theviewshouldonlybeseenasakindofphilosophicallastresort.Fortherearetoomanyinterestingquestionsaboutwhichthedogmaticresponsefallssilent.Notably,whereasanyattempttoprovideasub-stantivejustificationofinductioncanbeexpected,totheextentthatitsucceeds,alsotoprovideinsightsintowhatdistinguishesgoodfrombadinductiveinfer-ences,thedogmaticresponseishopelessinthisregard.And,asnotedabove,theproblemofprovidingaclearexplicationofthedistinctionbetweenrational(“good”)andirrational(“bad”)inductiveinferencesisadeepandcentraloneinitsownright.Weturnnowtoabriefdiscussionofsomeofthemainphilo-sophicalapproachesinthisarea.TheSecondProblemofInduction:SyntacticApproachesTraditionally,logicaimstodistinguishvalidfrominvalidargumentsbyvirtueofthesyntacticformofthepremisesandconclusion(e.g.,anyargumentthathastheformpandq,thereforepisvalidinvirtueofthisform).Butthedistinctionbetweenvalidandinvalidisnotfineenough:afterall,manyinvalidargumentsareperfectlygood,inthesensethatthepremisesprovidestronginductivesupportforthecon-clusion.Carnap(1950)describedthisrelationofsupportasthelogicalprobabil-itythatanargument’sconclusionistrue,giventhatitspremisesaretrue–hopingthatlogic,morebroadlyconceived,couldgiveitasyntacticanalysis.WewilldiscussCarnap’sapproachinmoredetailbelow.Other,lessambitiousapproachestriedtofindsyntacticcriteriafor“qualitativeconfirmation”–criteria,thatis,thatwouldidentifyatleastsomeinstancesinwhichevidenceraisedtheprobabilityofanhypothesis,toatleastsomedegree.(SeeHempel(1945a,b)foranexcellentoverviewofworkinthisarea.)Theseattemptstodesigna“logic”ofinductiononthemodelofformaldeductivelogicdidnotsucceed.Thedecisiveproblemconcernsthelanguage-dependencethatanysuch“logic”wouldhavetoexhibit.Consider,forexample,alanguageusedtorepresenttheoutcomesofrandomdrawsfromanurnfilled155\nAlanHájekandNedHallwithcoloredballs;letthelanguagecontainthecolorpredicates“blue”and“green,”andalso,inthespiritofGoodman(1983),thepredicate“grue,”wherexisgrueatdrawiisequivalenttoxisgreenatdrawiandi£1,000,000orxisblueatdrawiandi>1,000,000Surelythe“logicalstrength”oftheargument,“thefirstmilliondrawsaregreen,1thereforethenextdrawwillbegreen”isgreaterthan–;ifsyntaxisallthatmatters,2thensotooisthelogicalstrengthoftheargument,“thefirstmilliondrawsaregrue,thereforethenextdrawwillbegrue.”Butthetwoconclusionscontradict1eachother,andsocannotbothreceiveprobabilitygreaterthan–.2Onemighttrytospecifyacanonicallanguage,tosentencesofwhichthesyn-tacticrules,whatevertheyare,aremeanttoapply–alanguagefreeofsuchmon-strositiesas“grue”.Butnotonlydoestraditionallogicfindnoneedforsuchaprocedure,itisalsoextraordinarilydifficulttoseehowonecouldcarryitout,atleastifwewanttoanalyzetheinductivestrengthofanyargumentofrealinter-est.Bythemiddleoftheseventeenthcentury,theavailableevidencestronglysup-portedKeplerianoverPtolemaicastronomy;butwhatwouldbethecanonicallanguageinwhichtotranslatethisevidenceandthesehypotheses,soastoanalyzethedifferentialsupportsyntactically?TheSecondProblem:ModestProbabilismOnemightagreewithCarnapthatinductionshouldbemodeledusingthetoolsofprobabilitytheory,whiledenyingthatsyntacticanalysisalonecanprovideorevenconstrainthevaluesoftherelevantprobabilityfunction.Andindeed,whatwewillcall“modestprobabilism”aboutinductionandconfirmationhasbecomeincreasinglypopularsincethedemiseoflogicalempiricism.Wecallthisapproach“probabilism”becauseitseestheinductivesupportordegreeofconfirmationthatevidenceEgiveshypothesisHasmeasuredbysomehowcomparingP(H),theprobabilityofH,withP(H|E),theconditionalprobabilityofH,givenE.(Wewillhavemoretosayaboutthesequantitiesshortly.)PerhapsthisinductivesupportismeasuredbythedifferenceP(H|E)-P(H);perhapsbytheratioP(H|E)/P(H);perhapsinsomeotherway(Good,1985).Buttheapproachismodesttotheextentthatitisagnosticaboutthenatureorsourceofthe“confirmation-probability”inquestion.Itsagnosticismnotwithstanding,modestprobabilismisabletoachievesomeremarkablesuccesses.Forexample,itexplainsstraightawaythesuccess(suchasitis)ofthehypothetico-deductiveaccountofconfirmation.ForifHimpliesE,andifP(E)<1,thenitfollowsatoncethatP(H|E)>P(H)156\nInductionandProbability(forthisconditionisequivalenttoP(E|H)>P(E)).Moreinterestingly,modestprobabilismneatlyexplainsawaytheRaven’sParadox,andcanbeeasilyadaptedtoilluminatetheconfirmationofhypothesesthatarethemselvesprobabilistic;seeEarman(1992)forafullerdiscussion.Partlytofleshouttheresourcesofandproblemsforthisprobabilisticapproach,wewillnowswitchgearsslightly,andtakeupthesecondofourtopics:aninves-tigationofprobabilitytheoryandthemostimportantattemptsatexplicatingitsconceptualfoundations.Webeginwithanoverviewofthewidelyacceptedmath-ematicalfoundations.Kolmogorov’sAxiomatizationProbabilitytheorywasinspiredbygamesofchanceinseventeenthcenturyFranceandinauguratedbytheFermat–Pascalcorrespondence.However,itsaxiomatiza-tionhadtowaituntilKolmogorov’sclassicbook(1933).LetWbeanon-emptyset(“theuniversalset”).Asigma-field(orsigma-algebra)onWisasetFofsubsetsofWthathasWasamember,andthatisclosedundercomplementation(withrespecttoW)andcountableunion.LetPbeafunctionfromFtotherealnumbersobeying:1P(A)≥0forallAŒF.2P(W)=1.3P(A
B)=P(A)+P(B)"A,BŒFsuchthatAB=∆.CallPaprobabilityfunction,and(W,F,P)aprobabilityspace.Wecouldinsteadattachprobabilitiestomembersofacollectionofsentencesofaformallanguage,closedundertruth-functionalcombinations.ItiscontroversialwhetherprobabilitytheoryshouldincludeKolmogorov’sfurtheraxiom:4(Continuity)EnØ∆impliesP(En)Æ0(whereEnŒF"n)Equivalently,wecanreplacetheconjunctionofaxioms3and4withasingleaxiom:3¢(Countableadditivity)If{Ai}isacountablecollectionof(pairwise)disjointsets,eachŒF,then••ÊˆPAÁUn˜=ÂP()An˯n=1n=1TheconditionalprobabilityofXgivenYisstandardlygivenbytheratioofuncon-ditionalprobabilities:157\nAlanHájekandNedHallPXY()PXY()=PY()providedP(Y)>0.WecannowproveversionsofBayes’theorem:PBAPA()().PAB()=PB()PBAPA()().=PBAPAPBAPA()()..+ÿ()()ÿMoregenerally,supposewehaveapartitionofhypotheses{H1,H2,...,Hn},andevidenceE.Thenwehave,foreachi:PEHPH()ii()PHE()i=nÂPEHPH()jj()j=1TheP(E|Hi)termsarecalledlikelihoods,andtheP(Hi)termsarecalledpriors.IfP(X|Y)=P(X)–equivalently,ifP(Y|X)=P(Y);equivalently,ifP(XY)=P(X)P(Y)–thenXandYaresaidtobeindependent.Twocautions:first,thelocution“XisindependentofY”issomewhatcareless,encouragingonetoforgetthatindependenceisarelationthateventsorsentencesbeartoaprobabilityfunction.Second,thistechnicalsenseof“independence”shouldnotbeidentifiedunreflectivelywithcausalindependence,oranyotherpretheoreticalsenseoftheword,eventhoughsuchidentificationsareoftenmadeinpractice.IfP(X|Y)>P(X)–equivalently,ifP(Y|X)>P(Y)–thenXandYarepositivelycorrelated.Acorner-stoneofanyprobabilisticapproachtoinductionistheideathatevidenceabouttheobservedispositivelycorrelatedwithvarioushypothesesabouttheunobserved.Wenowturntotheso-called“interpretations”ofprobability.Thetermismis-leadingtwiceover.Variousquantitiesthatintuitivelyhavenothingtodowith“probability”obeyKolmogorov’saxioms–forexample,length,volume,andmass,eachsuitablynormalized–andarethus“interpretations”ofit,butnotintheintendedsense.Conversely,themajorityofthemostinfluential“interpretations”ofPviolatecountableadditivity,andthusarenotgenuineinterpretationsofKolmogorov’sfullprobabilitycalculusatall.Bethatasitmay,wewilldropthescarequotesofdiscomfortfromnowon.TheClassicalInterpretationTheclassicalinterpretation,whichowesitsnametoitsearlyandaugustpedigree–notablythePort-RoyalLogic,Arnauld(1662)andLaplace(1814)–purportstodetermineprobabilityassignmentsinthefaceofnoevidenceatall,orsymmetri-158\nInductionandProbabilitycallybalancedevidence.Insuchcircumstances,probabilityissharedequallyamongallthepossibleoutcomes,sothattheclassicalprobabilityofaneventissimplythefractionofthetotalnumberofpossibilitiesinwhichtheeventoccurs–aversionoftheso-calledprincipleofindifference.Unlessmoreissaid,itisalsoarguablytheinterpretationfurthestremovedfromconsiderationsofinduction,reflectingasitdoesacertainaprioristicinnocence:intypicalapplications,thenumberofpossi-bilities,andthusthesharethateachgetsofthetotalprobability,remainthesame3(e.g./6)whatevertheoutcomesintheactualworldhappentobe.Unfortu-nately,theclassicalinterpretationcanapparentlyyieldcontradictoryresultswhenthereisnosingleprivilegedsetofpossibilities,asBertrand(1889)broughtoutinhisparadoxes.Classicalprobabilitiesareonlyfinitelyadditive(deFinetti,1974).TheLogicalInterpretationLogicaltheoriesofprobabilityretaintheclassicalinterpretation’sguidingideathatprobabilitiescanbedeterminedaprioribyanexaminationofthespaceofpossi-bilities.However,theygeneralizeitintwoimportantways:thepossibilitiesmaybeassignedunequalweights,andprobabilitiescanbecomputedwhatevertheevi-dencemaybe,symmetricallybalancedornot.Indeed,thelogicalinterpretation,initsvariousguises,seekstocodifyinfullgeneralitythedegreeofsupportorconfirmationthatapieceofevidenceEconfersonagivenhypothesisH,whichwemaywriteasc(H,E).EarlyproponentsoflogicalprobabilityincludeKeynes(1921),W.E.Johnson(1932),andJeffreys(1939).However,byfarthemostsystematicstudyoflogicalprobabilitywasbyCarnap.Hisformulationoflogicalprobabilitybeginswiththeconstructionofaformallanguage.Heconsiders(Carnap,1950)aclassofverysimplelanguagesconsistingofafinitenumberoflogicallyindependentmonadicpredicates(namingproperties)appliedtocountablymanyindividualconstants(namingindividuals)orvariables,andtheusuallogicalconnectives.Thestrongest(consistent)statementsthatcanbemadeinagivenlanguagedescribealloftheindividualsinasmuchdetailastheexpressivepowerofthelanguageallows.Theyareconjunctionsofcompletedescriptionsofeachindividual,eachdescriptionitselfaconjunctioncontainingexactlyoneoccurrence(negatedorunnegated)ofeachpredicateofthelanguage.Callthesestrongeststatementsstatedescriptions.Anyprobabilitymeasurem(-)overthestatedescriptionsautomaticallyextendstoameasureoverallsentences,sinceeachsentenceisequivalenttoadisjunctionofstatedescriptions;minturninducesaconfirmationfunctionc(-,-):mH()&EcHE(),=mE()Thereareobviouslyinfinitelymanycandidatesform,andhencec,evenforverysimplelanguages.Carnaparguesforhisfavoredmeasure“m*”byinsistingthat159\nAlanHájekandNedHalltheonlythingthatsignificantlydistinguishesindividualsfromoneanotherissomequalitativedifference,notjustadifferenceinlabeling.Astructuredescriptionisamaximalsetofstatedescriptions,eachofwhichcanbeobtainedfromanotherbysomepermutationoftheindividualnames.m*assignseachstructuredescriptionequalmeasurewhich,inturn,isdividedequallyamongtheirconstituentstatedescriptions.Itgivesgreaterweighttohomogenousstatedescriptionsthantoheterogeneousones,thus“rewarding”uniformityamongtheindividualsinaccordancewithputativelyreasonableinductivepractice.Itcanbeshownthattheinducedc*allowsinductivelearningfromexperience–as,annoyingly,doinfinitelymanyothercandidateconfirmationfunctions.Carnapclaimsthatc*neverthelessstandsoutforbeingsimpleandnatural.Helatergeneralizeshisconfirmationfunctiontoacontinuumoffunctionscl.Defineafamilyofpredicatestobeasetofpredicatessuchthat,foreachindividual,exactlyonememberofthesetapplies,andconsiderfirst-orderlanguagescontain-ingafinitenumberoffamilies.Carnap(1963)focusesonthespecialcaseofalanguagecontainingonlyone-placepredicates.Helaysdownahostofaxiomsconcerningtheconfirmationfunctionc,includingthoseinducedbytheprobabilitycalculusitself,variousaxiomsofsymmetry(forexample,thatc(H,E)remainsunchangedunderpermutationsofindividuals,andofpredicatesofanyfamily),andaxiomsthatguaranteeundogmaticinductivelearning,andlong-runconvergencetorelativefrequencies.Theyimplythat,forafamily{Pn},n=1,...,k,k>2:skj+lcsl()individual+1,isPjjssofthefirstindividualsarePj=s+lwherelisapositiverealnumber.Thehigherthevalueofl,thelessimpactevidencehas:inductionfromwhatisobservedbecomesprogressivelymoreswampedbyaclassical-styleequalassign-menttoeachofthekpossibilitiesregardingindividuals+1.Significantly,Carnap’svariousaxiomsofsymmetryarehardlylogicaltruths.Moreseriously,wecannotimposefurthersymmetryconstraintsthatareseeminglyjustasplausibleasCarnap’s,onpainofinconsistency(Fine,1973,p.202).Goodmantaughtus:thatthefuturewillresemblethepastinsomerespectistrivial;thatitwillresemblethepastinallrespectsiscontradictory.Andwemaycontinue:thataprobabilityassignmentcanbemadetorespectsomesymmetryistrivial;thatonecanbemadetorespectallsymmetriesiscontradictory.Thisthreatensthewholeprogramoflogicalprobability.FrequencyInterpretationsFrequencyinterpretationscanbethoughtofaselevatingamethodologicalruleforinduction–thestraightrule–tothestatusofadefinitionofprobability.160\nInductionandProbabilityEmpiricistininspiration,andoriginatingwithVenn(1876),theyidentifyanevent’sprobabilitywiththerelativefrequencyofeventsofthattypewithinasuit-ablychosenreferenceclass.Theprobabilitythatagivencoinlands“heads,”forexample,mightbeidentifiedwiththerelativefrequencyof“heads”outcomesintheclassofalltossesofthatcoin.Butthereisanimmediateproblem:observedrelativefrequenciescanapparentlycomeapartfromtrueprobabilities,aswhenafaircointhatistossedtentimeshappenstolandheadseverytime.VonMises(1957)offersamoresophisticatedformulationbasedonthenotionofacollec-tive,renderedprecisebyChurch(1940):ahypotheticalinfinitesequenceof“attributes”(possibleoutcomes)ofaspecifiedexperiment,forwhichthelimitingrelativefrequencyofanyattributeexists,andisthesameinanyrecursivelyspeci-fiedsubsequence.TheprobabilityofanattributeA,relativetoacollectivew,isthendefinedasthelimitingrelativefrequencyofAinw.Limitingrelativefre-quenciesviolatecountableadditivity(deFinetti,1974).Anotoriousproblemforanyversionoffrequentismistheso-calledproblemofthesinglecase:wesometimesattributenon-trivialprobabilitiestoresultsofexperimentsthatoccuronlyonce.Themovetohypotheticalinfinitesequencesoftrialscreatesitsownproblems:Thereisapparentlynofactofthematterastowhatsuchahypo-theticalsequencewouldbe,norevenwhatitslimitingrelativefrequencyforagivenattributewouldbe,norindeedwhetherthatlimitisevendefined;andthelimitingrelativefrequencycanbechangedtoanyvalueonewantsbysuitablypermutingtheorderoftrials.Inanycase,theempiricistintuitionthatfactsaboutprobabilitiesaresimplyfactsaboutpatternsintheactualphenomenahasbeenjettisoned.PropensityInterpretationsAttemptstolocateprobabilities“intheworld”arealsomadebyvariantsofthepropensityinterpretation,championedbysuchauthorsasPopper(1959),Mellor(1971),andGiere(1973).Probabilityisthoughtofasaphysicalpropensity,ordisposition,ortendencyofagiventypeofphysicalsituationtoyieldanoutcomeofacertainkind,ortoyieldalongrunrelativefrequencyofsuchanoutcome.Thisviewisexplicitlyintendedtomakesenseofsingle-caseprobabilities.Accord-ingtoPopper,aprobabilitypofanoutcomeofacertaintypeisapropensityofarepeatableexperimenttoproduceoutcomesofthattypewithlimitingrelativefrequencyp.Giventheirintimateconnectiontolimitingrelativefrequencies,suchpropensitiespresumablylikewiseviolatecountableadditivity.Giereexplicitlyallowssingle-casepropensities,withnomentionoffrequencies:probabilityisjustapropensityofarepeatableexperimentalset-uptoproducesequencesofoutcomes.This,however,createstheproblemofderivingthedesiredconnectionbetweenprobabilitiesandfrequencies.Thisquicklyturnsintoaproblemforinductiveinference:itisunclearhowfrequencyinformationshouldbebroughttobearonhypothesesaboutpropensitiesthatwemightentertain.161\nAlanHájekandNedHallTheSubjectivistInterpretation:OrthodoxBayesianismDegreesofbeliefSubjectivismisthedoctrinethatprobabilitiescanberegardedasdegreesofbelief,sometimescalledcredences.Itisoftencalled“Bayesianism”thankstotheimpor-tantrolethatBayes’theoremtypicallyplaysinthesubjectivist’scalculationsofprobabilities,althoughthisisyetanothermisnomersinceallinterpretationsofprobabilityareequallyanswerabletothetheorem,andsubjectiveprobabilitiescanbedefinedwithoutanyappealtoit.Unlikethelogicalinterpretation(atleastasCarnaporiginallyconceivedit),subjectivismallowsthatdifferentagentswiththeverysameevidencecanrationallygivedifferentprobabilitiestothesamehypothesis.Butwhatisadegreeofbelief?Astandardanalysisinvokesbettingbehavior:anagent’sdegreeofbeliefinXispiffsheispreparedtopayuptopunitsforabetthatpays1unitifX,0otherwise(deFinetti,1937).Itisassumedthatsheisalsopreparedtosellthatbetforpunits.Thus,opinionisconceptuallytiedtocertainbehavior.Criticsarguethatthetwocancomeapart:anagentmayhavereasontomisrepresentheropinion,orshemaynotbemotivatedtoactaccordingtoheropinioninthewayassumed.Bayesiansclaimthatideallyrationaldegreesofbeliefare(atleastfinitelyaddi-tive)probabilities.“DutchBook”argumentsareonelineofdefenseofthisclaim.ADutchBookisaseriesofbets,eachofwhichtheagentregardsasfair,butwhichcollectivelyguaranteeherloss.DeFinetti(1937)provesthatifyourdegreesofbeliefarenotfinitelyadditiveprobabilities,thenyouaresusceptibletoaDutchBook.Equallyimportant,andoftenneglected,isKemeny’s(1955)conversetheorem.ArelateddefenseofBayesianismcomesfromutilitytheory.Ramsey(1926)andSavage(1954)derivebothprobabilitiesandutilities(desirabilities)frompreferencesconstrainedbycertainputative“consistency”assumptions.UpdatingprobabilitySupposethatyourdegreesofbeliefareinitiallyrepresentedbyaprobabilityfunc-tionPinitial(-),andthatyoubecomecertainofE(whereEisthestrongestsuchproposition).WhatshouldbeyournewprobabilityfunctionPnew?ThefavoredupdatingruleamongBayesiansisconditionalization;PnewisrelatedtoPinitialasfollows:(Conditionalization)PXPXnew()=initial()E()providedPEinitial()>0Conditionalizationissupportedbya“diachronic”DutchBookargument(Lewis,1998):ontheassumptionthatyourupdatingisrule-governed,youare162\nInductionandProbabilitysubjecttoaDutchbookifyoudonotconditionalize.Equallyimportantistheconversetheorem(Skyrms,1987).Jeffreyconditionalizationallowsforlessdecisivelearningexperiencesinwhichyourprobabilitiesacrossapartition{E1,E2,...}changeto{Pnew(E1),Pnew(E2),...,},wherenoneofthesevaluesneedbe0or1:PXnew()=ÂPXinitial()(EPEinewi)i(Jeffrey,1965).ItisagainsupportedbyaDutchbookargument(Armendt,1980).SeeDiaconisandZabell(1986)forfurtherprobabilityrevisionrules.OrthodoxBayesianismcannowbecharacterizedbythefollowingmaxims:B1Rationalityrequiresanagent’s‘prior’(initial)probabilitiestoconformtotheprobabilitycalculus.B2Rationalityrequiresanagent’sprobabilitiestoupdatebytheruleof(Jeffrey)conditionalization.B3Rationalitymakesnofurtherrequirementsonanagent’sprobabilities.IforthodoxBayesianismiscorrect,thenthereisasenseinwhichHume’sproblemofinductionisimmediatelysolved.Inductiveinferencesbasedonobser-vationalevidencearejustifiedbytheappropriatepriorsubjectiveprobabilityassign-ments,suitablyupdatedonthatevidence.Forexample,byB3,rationalitypermitsyoutoassign:Pinitial(thesunwillriseonday10001|thesunrisesondays1,2,...,10000)=0.9999Supposeyourevidenceis:thesunrisesondays1,2,...,10000Thenconditionalizingonthatevidence,asrationallyrequiresaccordingtoB2,gives:Pnew(thesunwillriseonday10001)=0.9999Similarly,ifyourpriorisoftherightform,rationalityrequiresyoutoassignextremelyhighprobabilitytoallmarblesbeinggreenafterasuitablecourseofexperiencewithgreenmarbles.And,ingeneral,theproblemofjustifyingourinductivepracticesfactors,accordingtoBayesians,intotheproblemofjustifyingthechoiceofprior,andtheproblemofjustifyingconditionalization;andtheyclaimtohavemadegoodonboth.Sofar,sogood.However,non-BayesianswillfindthisaPyrrhicprobabilisticvictory.FororthodoxBayesianismequallyallowspriorsthatwouldlicensecounterinductiveandgrue-someinferences,basedonthesameevidence.ButBayesianismisathemethatadmitsofmanyvariations.163\nAlanHájekandNedHallUnorthodoxBayesianismEachofB1–B3hasitsopponents.Itwillproveconvenienttorevisittheminreverseorder.ThesuspicionjustraisedisthatorthodoxBayesianismistoopermissive:itimposesnoconstraintsontheassignmentofpriors,besidestheirconformitytotheprobabilitycalculus.Rationality,theobjectiongoes,isnotsoecumenical.Astandarddefence–see,forexampleSavage(1954)orHowsonandUrbach(1993)–appealstofamous“convergence-to-truth,”and“merger-of-opinion”results.Roughly,theircontentisthat,inthelongrun,theeffectofchoosingonepriorratherthananotherisattenuated:successiveconditionalizationsontheevidencewill,withprobabilityone,makeagivenagenteventuallyconvergetothetruth,andthusinitiallydiscrepantagentseventuallycometoagreement.Inanimpor-tantsense,atleastthismuchinductivelogicisimplicitintheprobabilitycalculusitself.Unfortunately,thesetheoremstellusnothingabouthowquicklytheconver-genceoccurs.Inparticular,theydonotexplaintheunanimitythatweinfactoftenreach,andoftenratherrapidly.Wewillapparentlyreachthetruth“inthelongrun”;but,asKeynesquipped,“inthelongrun,weshallallbedead.”AgainstB3,then,therearemorestringentBayesianswhoholdthistruthtobeself-evident:Notallpriorsarecreatedequal.Theythusimposefurtherconstraintsonpriors.Onesuchconstraintisthattheyberegular,orstrictlycoherent:ifP(X)=1,thenX=W(Xisnecessary/alogicaltruth);seeShimony(1955).Itismeanttoguardagainstthesortofdogmatismthatnocourseoflearningby(Jeffrey)con-ditionalizationcouldcure.Wemightalsowanttorecognizetherolethatcertainobjectivefacts,orthatcertain“expert”opinions,mighthaveinconstrainingone’ssubjectiveprobabili-ties.CallprobabilityfunctionQanexpertfunctionforPifthefollowingcondi-tionholds:forallXPXQXxx,()()==(8.1)Forexample,onemightconformone’ssubjectiveprobabilitiestocorrespond-ingrelativefrequencies.WithQbeingthe“relativefrequency”function,(8.1)becomesaversionoftheso-calledprincipleofdirectprobability.Oronemightthinkthatwhateverobjectivechancesmightbe,theyarecharacterizedbytheirroleinconditionallyconstrainingrationalcredence.WithQbeingthe“objectivechance”function,(8.1)becomesaversionofaprinciplethat,suitablyfinessed,becomesLewis’(1980)PrincipalPrinciple.Oronemightargue,asvanFraassen(1995)does,thatepistemicintegrityrequiresoneideallytoregardone’sfutureopinionsasbeingtrustworthy–perhapsbecauseoftheirhavingarisenfromarationalprocessoflearning.WithQbeingone’sprobabilityfunctionatsome164\nInductionandProbabilityfuturetime,(8.1)becomesaversionofvanFraassen’sReflectionPrinciple.Qcouldalsoencapsulatetheopinionsofsimplyanexpert–apersonwhomonetrusts,forwhateverreason.Therehavebeenvariousproposalsforresuscitatingsymmetryconstraintsonpriors,inthespiritoftheclassicalandlogicalinterpretations.MoresophisticatedversionsoftheprincipleofindifferencehavebeenexploredbyJaynes(1968).Theguidingideaistomaximizetheprobabilityfunction’sentropy,whichforanassign-mentofpositiveprobabilitiesp1,...,pntonpossibilitiesequals-Sipilog(pi).Asetofevents(orsentences)isexchangeablewithrespecttoagivenprobabil-ityfunctionifeveryeventhasthesameprobability,everyconjunctionoftwoeventshasthesameprobability,everyconjunctionofthreeeventshasthesameproba-bility,andsoon.SeeSkyrms(1994)foranexcellentdiscussionofgeneralizationsofexchangeability,andtheiruseinformulatingvariousGoodmanianthesesaboutprojectability.Indeed,commonsenseoften(butnotinvariably)seemstorequireone’sprobabilitiestobeexchangeableover“green”-likehypotheses,butnot“grue”-likehypotheses.SotherearemanymotivationsforrejectingB3.Butthesuspicionattheendofthelastsectionmaystillremain:Bayesianism,evenwithvariousofthesebellsandwhistlesadded,isstilltoopermissive.Whatiswantedisajustificationofthe“good”inductiveinferences,andnoparalleljustificationofthe“bad”ones.Theseprinciplesdonotseemtodistinguishthegoodfromthebad.Someofthem,onthecontrary,onlyseemtonurturethebadinferences–forexample,wherewemighthavehopedtokilloffgrue-likehypotheses,regularitykeepsthemallalive.Otherprinciplescanplaybothsideswithequalease:exchangeability,forinstance,ischaracterizedpurelysyntactically,soitcanbedeployedtovindicategrue-likeinferencesaswellasgreen-likeinferences.Stillothers,suchastheReflectionPrin-ciple,seemtobeneutralwithrespecttoissuesofinduction.B2alsohasitsopponents.Someauthorsallow,andeveninsistupon,otherrulesfortheupdatingofprobabilitiesbesidesconditionalization.Jaynesadvocatesrevi-siontotheprobabilityfunctionthatmaximizesentropy,subjecttotherelevantconstraints.AndsomeBayesiansdroptherequirementthatrationalprobabilityupdatingberule-governedaltogether;seevanFraassen(1990a)andEarman(1992).Note,however,thatinasensethisonlymakestheproblemofinductionworse.Giventhatthesuggestedconstraintsonthepriorsdonotsolvetheproblem,onemighthavehopedthattheupdatingrulecouldtakeuptheslack(andaccordingtotheproponentsoftheconvergenceresultsmentionedabove,inthelongrunitdoes).Butiftheveryrequirementofanupdatingruleisabandoned,thenitbeginstolookasifanythinggoes:ifyouwantsuddenlytojumptoaprobabilitydistribu-tionthatassignsoverwhelmingprobabilitytoallmarblesbeinggrue,thenyouareapparentlybeyondreproach.TherejectionofB1isalargetopic,anditmotivatesandcanbemotivatedbysomeofthenon-Kolmogoroviantheoriesofprobability,towhichwenowturn.165\nAlanHájekandNedHallNon-KolmogorovianTheoriesofProbabilityAnumberofauthorswouldabandonthesearchforanadequateinterpreta-tionofKolmogorov’sprobabilitycalculus,sincetheyabandonsomepartofhisaxiomatization.Someauthorsquestionitsset-theoreticunderpinnings.Notethattheusualjus-tificationsoftheprobabilityaxioms–DutchBookargumentsandsoon–takeforgrantedthesigma-fieldsubstructure,ratherthanjustifyingitaswell.Fine(1973)arguesthattherequirementthatthedomainoftheprobabilityfunctionbeasigma-fieldisoverlyrestrictive.Somedisputetherequirementthatprobabilitieshavenumericalvalues.Finesympatheticallycanvassesvarioustheoriesofcompar-ativeprobability,exemplifiedbystatementsoftheform“AisatleastasprobableasB.”Thenthereareadvocatesofindeterminateorofvagueprobabilities,whorepresentprobabilitiesnotassinglenumbers,butasintervals,ormoregenerallysetsofnumbers,e.g.Levi(1980),Jeffrey(1983)andvanFraassen(1990b).Suchvaguenessmightbeindicatedbyasetofconstraintsthatgobeyondthoseoftheprobabilitycalculus,butthatfallshortoftheCarnapianidealoffixingauniqueprobabilityfunction.Somedisputetheusualconstraintsonthenumericalvalues.Kolmogorov’sprobabilityfunctionsarereal-valued.Anumberofphilosophers–e.g.Lewis(1980)andSkyrms(1980)–allowprobabilitiestotakevaluesfromtherealnumbersofanonstandardmodelofanalysis;seeRobinson(1966)orSkyrms(1980)fortheconstructionofsuchamodel.Inparticular,theyallowprobabili-tiestobeinfinitesimal:positive,butsmallerthaneverypositive(standard)realnumber.Thiscanbemotivatedbyadesiretorespectbothregularityandcertainsymmetriesininfiniteprobabilityspaces.Meanwhile,physicistssuchasDirac,Wigner,andFeynmanhavecountenancednegativeprobabilities,andFeynmanandCoxhaveflirtedwithcomplex-valuedprobabilities;seeMückenheim(1986)forreferences.Renyi(1970)allowsprobabilitiestoattainthe“value”•.Wemayalsowanttoallowlogical/necessarytruthstobeassignedprobabilitylessthanone,perhapstoaccountforthefactthatmathematicalconjecturesmaybeconfirmedtovaryingdegrees;see,forexamplePolya(1968).Thus,mathematicstoomightbesusceptibletoinduction(tobedistinguishedfrom“mathematicalinduction,”adeductiveargumentform!).Kolmogorov’smostcontroversialaxiomisundoubtedlycontinuity–thatis,the“infinitepart”ofcountableadditivity.Heregardeditasanidealizationthatfinessedthemathematics,butthathadnoempiricalmeaning.Aswehaveseen,accordingtotheclassical,frequency,andcertainpropensityinterpretations,prob-abilitiesviolatecountableadditivity.DeFinettimarshalsabatteryofargumentsagainstit(inthenameofsubjectivism,buthisargumentsmayberegardedasmoregeneral).Variousnon-additivetheoriesofprobabilitythatgiveupevenfiniteadditivityhavebeenproposed–forexample,Dempster–Shafertheory,whichsomeregard166\nInductionandProbabilityascodifyingthenotionof“weightofevidence”(Shafer,1976).So-called“Baconianprobabilities”representanothernon-additivedeparturefromtheprobabilitycalculus.TheBaconianprobabilityofaconjunctionisequaltotheminimumoftheprobabilitiesoftheconjuncts.L.J.Cohen(1970,1977)regardsthemasappropriateformeasuringinductivesupport.SeeGhirardato(1993)forasurveyofnon-additivemeasuresofuncertainty,andHowson(1995)forfurtherreferences.Lastly,variousauthors,ratherthanaxiomatizingunconditionalprobabilityanddefiningconditionalprobabilitytherefrom,takeconditionalprobabilityasprimi-tiveandaxiomatizeitdirectly;seeSpohn(1986).SomeFutureAvenuesofResearchHavingdiscussedvariouslandmarksofpastworkininductionandprobability,wefindourselvesnowinthecuriouslyreflexivepositionofpredictingwhatfutureworkintheseareaswilllooklike.Suitablycautionedbytheverynatureofoursubject,andwithappropriatedegreesofuncertainty,herearesomeofourbestbets.WethinkthatthereisstillmuchresearchtobedonewithinabroadlyBayesianframework.Therearealreadysignsoftherehabilitationoflogicalprobability,and,inparticular,theprincipleofindifference,byauthorssuchasStove(1986),Festa(1993),Maher(2000,2001),andBarthaandJohns(2001).Thiswillsurelyresonatewithdevelopmentsinthetheoryofinfinitesimals,forexamplewithinthesystemof“surrealnumbers”(Conway,1976;Ehrlich,2001).Relevantherewillalsobeadvancesininformationtheory,randomnessandcomplexitytheory(Fine,1973;LiandVitanyi,1997),andapproachestostatisticalmodelselection,andinparticularthe“curve-fitting”problemthatattempttocodifysimplicity–e.g.theAkaikeInformationCriterion(ForsterandSober,1994),theBayesianInforma-tionCriterion(Kieseppä,2001),MinimumDescriptionLengththeory(Rissanen,1999)andMinimumMessageLengththeory(WallaceandDowe,1999).Thesemayalsoshedlightonthetime-honoredbutall-too-nebulousintuitionthat“green”-likehypothesesaresomehow“simpler”than“grue”-likehypotheses.Probabilitytheorytraditionallypresupposesclassicalsettheory/classicallogic.Thereismoreworktobedoneon“non-classical”probabilitytheory.Bayesiansmaywanttoenrichtheirtheoryofinductiontoencompasslogical/mathematicallearninginresponsetotheso-called“problemofoldevidence”(Zynda,1995),andtoallowfortheformulationofnewconceptsandtheories.Wealsoseefertileconnectionsbetweenprobabilityandlogicthathavebeenexploredundertherubricof“probabilisticsemantics”or“probabilitylogic”–seeHailperin(1996)andAdams(1998).RoeperandLeblanc(1999)developsuchprobabilisticseman-ticsforprimitiveconditionalprobabilityfunctions.Moregenerally,weenvisageincreasedattentiontothetheoryofsuchfunctions;see,forinstance,Festa(1999)167\nAlanHájekandNedHallforatreatmentofBayesianconfirmationtheorywhichtakessuchfunctionsasprimitive,andHájek2001forgeneralargumentsinfavorofsuchfunctions).Furthercriteriaofadequacyforsubjectiveprobabilitieswillbedeveloped–perhapsrefinementsof“scoringrules”(Winkler,1996),andmoregenerally,candidatesforplayingaroleforsubjectiveprobabilityanalogoustotherolethattruthplaysforbelief.Therewillbemoreresearchonthetheoryofexpertfunctions–forexample,intheaggregationofopinionsandpreferencesofmultipleexperts.Thisproblemiswellknowntoaficionadosoftherisk-assessmentliterature,whichhasyettobeminedbyphilosophers(Kaplan,1992).Weexpectthatnon-Bayesianresearchprogramswillalsoflourish.Non-additiveprobabilitiesaregettingimpetusfromconsiderationsof“ambiguityaversion”(Ghirardato,2001)and“plausibilitytheory”(Hild,2001).Formallearningtheory(Kelly,1996)isalsogainingsupport,andmorebroadly,philosopherswillfindmuchinterestingworkoninductionandlearninginthecomputerscienceandartificialintelligenceliterature.Andthereisaneedformorecross-fertilizationbetweenBayesianismandclassicalstatistics,anditsrecentincarnationinthetheoryoferrorstatistics(Mayo,1996).Forexample,hypothesistestingataconstantsignificancelevelhaslongbeenknowntobeinconsistentwithBayesianinferenceanddecisiontheory.RecentworkbySchervishetal.(2002)showsthatsuch“incoherence”isamatterofdegree.Moreover,inlightofworkintheeconomicsliteratureon“boundedrationality,”thestudyofdegreesofincoherenceislikelytobearfruit.Weforeseerelatedattemptsto“humanize”Bayesianism–forexample,thefurtherstudyofvagueprobabilityandvaguedecisiontheory.Andclassicalstatistics,foritspart,withitstacittradeoffsbetweenerrorsandbenefitsofdifferentkinds,needstobeproperlyintegratedintoamoregeneraltheoryofdecision.Decisiontheoryandthetheoryofinductionwillprofitfrominsightsinthecausalmodelingliterature.Forexample,theso-called“referenceclassproblem”arisesbecauseagivenevent-tokencantypicallybeplacedunderindefinitelymanyevent-types;thisiswhatgivesthevariousproblemsofinductiontheirteeth.Butprogresscanbemadewhentherelevantcausesareidentified,andtechniquesalongthelinesofthosedevelopedbyPearl(2000)andSpirtesetal.(1993)canbeappealedto.Thesetechniqueswilldoubtlessbefinessed.Moregenerally,inthisbravenewworldofinter-disciplinarityandrapidcommunication,inferentialmethodsdevelopedwithinonefieldareincreasinglylikelytobeembracedby2practitionersofanother.Notes1Spacepreventsusfromgivingthedetails,butthekeyideaistobuildintoone’sinduc-tiveprinciplesaversionofvanFraassen’sReflectionPrinciple,whichwewilldiscussbelow.2WethankespeciallyBrandenFitelson,MatthiasHild,ChrisHitchcock,JimJoyce,andTimMaudlinforhelpfulcomments.168\nInductionandProbabilityReferencesAdams,E.(1998):ProbabilityLogic.StanfordUniversity:CSLI.Armendt,B.(1980):“IsThereaDutchBookArgumentforProbabilityKinematics?”PhilosophyofScience,47,583–9.Arnauld,A.(1662):Logic,or,TheArtofThinking(“ThePortRoyalLogic”),tr.J.DickoffandP.James,Indianapolis:Bobbs-Merrill,1964.Bartha,P.andJohns,R.(2001):“ProbabilityandSymmetry,”PhilosophyofScience,Supplementalvolume,forthcoming.Availableathttp://hypatia.ss.uci.edu/lps/psa2k/bartha.pdf.Bertrand,J.(1889):CalculdesProbabilités,1stedn.Paris:Gauthier-Villars.Reprintedas3rdedition,NewYork:ChelseaPublishingCompany,1972.Carnap,R.(1950):LogicalFoundationsofProbability.Chicago:UniversityofChicagoPress.Carnap,R.(1963):“RepliesandSystematicExpositions,”inP.A.Schilpp(ed.),ThePhilosophyofRudolfCarnap,LaSalle,Ill:OpenCourt,966–98.Church,A.(1940):“OntheConceptofaRandomSequence,”BulletinoftheAmericanMathematicalSociety,46,130–5.Cohen,L.J.(1970):TheImplicationsofInduction.London:Methuen.Cohen,L.J.(1977):TheProbableandtheProvable.ClarendonPress:Oxford.Conway,J.(1976):OnNumbersandGames.London:AcademicPress.DeFinetti,B.(1937):“Foresight:ItsLogicalLaws,ItsSubjectiveSources,”translatedinKyburgandSmokler(1964,pp.53–118).DeFinetti,B.(1974):TheoryofProbability.NewYork:JohnWiley.Reprinted1990.Diaconis,P.andZabell,S.(1986):“SomeAlternativestoBayes’sRule”,inB.GrofmanandG.Owen(eds.),InformationPoolingandGroupDecisionMaking,ProceedingsoftheSecondUniversityofCalifornia,Irwine,ConferenceonPoliticalEconomy,Greenwich,CT:JaiPressInc,25–38.Earman,J.(1992):BayesorBust?ACriticalExaminationofBayesianConfirmationTheory.Cambridge,MA:MITPress.Ehrlich,P.(2001):“NumberSystemswithSimplicityHierarchies:AGeneralizationofConway’sTheoryofSurrealNumbers,”TheJournalofSymbolicLogic,66(3),September.Festa,R.(1993):OptimumInductiveMethods:AStudyinInductiveProbability,BayesianStatistics,andVerisimilitude.Dordrecht:KluwerAcademicPublishers,SyntheseLibrarySeries,vol.232.Festa,R.(1999):“BayesianConfirmation,”inM.C.GalavottiandA.Pagnini(eds.),Experience,Reality,andScientificExplanation,Dordrecht:Kluwer,55–87.Fine,T.(1973):TheoriesofProbability.NewYork:AcademicPress.Forster,M.andSober,E.(1994):“HowtoTellwhenSimpler,MoreUnified,orLessAdHocTheorieswillProvideMoreAccuratePredictions,”BritishJournalforthePhilosophyofScience,45,1–35.Ghirardato,P.(1993):“Non-additiveMeasuresofUncertainty:ASurveyofSomeRecentDevelopmentsinDecisionTheory,”RivistaInternazionalediScienczeEconomicheeCommerciali,40,253–76.Ghirardato,P.(2001):“CopingwithIgnorance:UnforeseenContingenciesandNon-AdditiveUncertainty,”EconomicTheory,17,247–76.Giere,R.N.(1973):“ObjectiveSingle-CaseProbabilitiesandtheFoundationsof169\nAlanHájekandNedHallStatistics”,inP.Suppes,L.Henkin,G.C.MoisilandA.Joja(eds.),Logic,MethodologyandPhilosophyofScience,IV,Amsterdam:NorthHolland,467–83.Good,I.J.(1985):“WeightofEvidence:ABriefSurvey,”inJ.Bernardo,M.DeGroot,D.LindleyandA.Smith(eds.),BayesianStatist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e?Orisitpartlyrelativeandpartlyabsolute?Noneofthesequestionsreceivesaclear-cutanswerfromGTR,whichiswhyabsolutelyinclinedandrelationallyinclinedthinkerscaneachfindgristfortheirontologicalmillsinthetheory.Thecomplexityandambiguityofthesituationleadssomephilosopherstoarguethatitispointlesstotrytoimposethecategoriesofseventeenthcenturymetaphysicsonatheorythathasoutgrownthem(Rynasiewicz,1996,2000).Below,webrieflysurveysomeofthekeyfeaturesofGTRthatintrigueandfrustratephilosophicalinterpretation,andreturnattheendtothequestionofwhethertheoldcategoriesandquestionsstillhavevalue.NopriorgeometryInallearliertheoriesofmechanicsand/orgravitationthatcontaineddefinitedoctrinesaboutthenatureofspaceandtime(orspace–time),spaceandtimeweretakenas“absolute”structures,fixedandunchanging.AsEarman(1989)shows,eventheviewsofthetraditionalrelationistthinkersinvolvedsomesignificantpriorgeometricand/ortemporalstructures.TheEuclideanstructureofspace,forexample,wasuniversallyassumed,aswellassome1absolutenessoftemporalstructure.NotsoGeneralRelativity.ThebackgroundarenainGTRisjustM,whichcanhaveanyofahugevarietyoftopologies,andwhoseonly“absolute”featuresare4-dimensionalityandcontinuity.Therestofthespatio-temporalproperties,geo-174\nPhilosophyofSpace–TimePhysicsmetricandinertialandtemporal,areallencodedbyg,whichisnotfixedorprior2butrathervariableundertheEFE.Thislooksextraordinarilypromisingfromarelationistviewpoint:absolutespacehasfinallybeenbanished!Orhasit?Althoughabsolutespaceorspace–time,inthesenseofapre-definedandinvariantbackground,isabsent,itisnotclearthatthisamountstosatisfac-tionofarelationist’sdesires.Motionhasnotbecome“purelyrelative”inanyclearsense;rather,motionisdefinedrelativetothemetric,andthemetricisbynomeansdefinableonthebasisofrelationsbetweenmaterialthings.Infact,theEFEturnsmatterstheotherwayaround:giventhemetricg,themotionsofmaterialthings(encodedinT)aredetermined.Ifmaterialprocessesaffectthestructureofspacetime,perhapsthisissomuchthebetterforasubstantivalviewofGTR’sspace–times.ThedifferingrolesofMandgcorrespondtotwodifferentstrandsofargumentforsubstantivalism,whichitwillbeusefultodistinguish.ThefirststrandnotesthatitisindispensabletothemathematicalapparatusofGTRthatitstartfrom3Mandbuildthespatio-temporalstructuregonit.Then,invokingtheQuineandoctrinethattherealisthatoverwhichweineliminablyquantifyinourbestsci-entifictheories,Misclaimedtorepresentareal,existingmanifoldofspace–timepointsintheworld.Thesecondstrandlooksatgitself,arguesthatitrepresentsarealstructureintheworldnotreducibletoorderivablefrommaterialbodiesandtheirrelations,andconcludesthatwehaveadescendentofNewton’sabsolutespaceinGTR.ManifoldandMetricAbovewehaveindicatedthatMistheonly“fixedback-ground”inGTR,andthatonlyinthesenseofdimensionalityandcontinuity,notglobalshape.Butmotions(particularlyacceleration,butalsovelocityandpositioninsomemodels)aredefinedbyg.Whichone,then,representsspace–timeitself?Ormustwesayitisacombinationofboth?Thesequestionsopenanewcanofinterpretiveworms.Amanifoldisacollectionofspace–timepoints,notspacepoints.Inotherwords,thepointsdonothaveduration;eachoneisanidealpoint-event,arep-resentativeofaspatiallocationatasingleinstantoftime.Theydonotexistovertimeandhenceserveasastructureagainstwhichmotionmaybedefined,asNewton’sspacepointsdid.Ifspace–timesubstantivalismisunderstoodastheclaimthatthesepointsaresubstantialentitiesthemselves,thentheso-calledholeproblemarises(EarmanandNorton,1987).ThegeneralcovarianceoftheEFE,interpretedinanactivesense,allowsonetotakeagivenmodelM1=andconstructasecondviaanautomorphismonthemanifold:M2=whichalsosatisfiestheEFE.Intuitively,thinkofM2asobtainedfromM1byslidingboththemetricandmatterfieldsaroundonthepoint-manifold(Figure9.1).IfM2andM1agreeormatchforalleventsbeforeacertaintimet,butdifferforsomeeventsafterward,thenwehaveaformofindeterminism.Relativetoourchosensubstantialentities,space–timepointsconsideredastheelementsofM,whathappensatwhatspace–timelocationsisradicallyundetermined.Thiscanbe175\nCraigCallenderandCarlHoeferOutsidetheHole:InsidetheHole:h*=Identity,nothingh*shiftsmatterandchanged.metricwithrespecttomanifoldpointsTimeSpaceSpaceCauchyhypersurfacet=0:identicaltoeverywhereoutsidetheHole(hence,atalltimesbeforet=0).Figure9.1Aholediffeomorphism’seffectpresentedasanargumentagainstthekindofsubstantivalism(manifoldsubstan-tivalism)westartedfrom.Notehowevertwopoints.First,thisindeterminismisunobservable:M1andM2arequalitativelyindistinguishable.Second,butrelatedly,theholeproblemassumesthattheidentitiesofthemanifoldpointsaregivenorspecified,insomesense,independentlyofthematerial/observableprocessesoccurringinspacetime(representedbygandT).Infact,onewayofthinkingofaholeautomorphismisasa(continuous)permutationofthepointsunderlyingphysicalprocesses,orasare-labelingofthepoints.Notsurprisingly,mostresponsestotheholeargumenthavedepartedfromthesepoints,arguingthatsubstantivalismcanbereinterpretedinwaysthatdonotleadtotheapparentindeterminism.MetricandmatterDerivationofthemetricofspace–timefroma(somehow!)antecedentlygivenspecificationoftherelationaldistributionofmatterisacharacteristicMachianambition.Mach’sScienceofMechanics(1989),atleastasEinsteinreadit,proposedthatinertiashouldbeconsideredaneffectofrelativeaccelerationofabodywithrespecttootherbodies–mostnotably,the“fixedstars.”TransplantingthisideatothecontextofGTRseemstoindicatehavingtheinertialstructure(whichgdetermines)determinedbytherelationalmatterdistribution.GTRdoesnotseemtofulfillthisideaingeneral.Insomemodels(notablyFriedman–Robertson–Walker(FRW)BigBangmodels),thisideaseemsintuitivelyfulfilled.ButmakingtheideabothpreciseandsatisfiableinGTRhasprovendifficultifnotimpossible,despitetheeffortsofoutstandingphysicistssuchasEinstein,Sciama,Wheeler,andDicke.Andaswenotedabove,superfi-ciallyatleastthedeterminationrelationseemstogotheotherway(frommetrictomatter).176\nPhilosophyofSpace–TimePhysicsDespitethesedifficulties,aMachianprogramforextending(orrestricting)GTRhasappealedtomanythinkers.Inadditiontoanti-absolutistprejudices,thereareacoupleofreasonsforthis.First,GTRdoesyieldsomenon-Newtonianiner-tialeffectsofthekindMachspeculatedon:theso-called“frame-dragging”effects.Second,itisdifficulttotakeasamerecoincidencethefactthattheFRWmodels,whichseemmostMachianintuitively,arealsothosethatseemtobestdescribeourcosmos.Andtherearedifficultieswithtakingthemetric“field”asasubstantialentitythateithersubsumesordinarymatterorisincausalinteractionwithit.Theformeridea,whichcanbethoughtofas“super-substantivalism”,wouldinvolveextend-ingournotionofthemetricinanattempttoderivefine-grainedpropertiesofmatterintermsoffine-grainedperturbations(knots,singularities?)oftheformer.AttemptsbyEinsteinandothersalongtheselineshavenotledtonotablesuccesses.Thelessambitiousideaofthemetricand(ordinary)matterasontologicalpeersinmutualinteractionfaceschallengestoo.TheEFEgivearegularity,butinordertoviewtheregularitycausally,wewouldideallyliketobeabletoquantifythestrengthoftheinteraction,intermsofenergyormomentumexchange.Butthemetricfield’senergy,ifitexistsatall,ispoorlyunderstoodandverydifferentfromordinaryenergy(Hoefer,2000).Attemptsthroughtheendofthetwentiethcenturytodetectthemostintuitivelycausal-lookinginteractions–absorptionofgravitationalwaveenergy–wereuniformlynegative.CurrentworkTherelationism/substantivalismissuewasdominatedthroughthelate1980sand1990sbyresponsestotheEarmanandNortonholeargument.Theargumenthaspushedphilosopherswhohavemoresympathywithsubstantivalistviewsthanrelationistviewstomakemoreprecisetheirontologicalclaims(Maudlin,1990;Butterfield,1989;Stachel,1993).Dependingonwhethertheyviewsubstan-tivalismasprimarilyattractiveduetotheQuineanindispensabilityargumentorratherthemetric-basedconsiderations,philosophersre-worktheirviewsindifferentways.Theholeargumentinspiredthosewithrelationistleaningstorevivetheidea,advocatedbyReichenbachearlierinthetwentiethcenturybuteffectivelykilledbyEarman(1970)andFriedman(1983),thatGTRcanbeinterpretedasfullycompatiblewithrelationism.Teller(1991),Belot(1999)andHuggett(1999)areexamplesofthisapproach.Whatmakesthispositionpossibleis(a)focusingonthepoint-manifold-indispensabilityargumentforsubstantival-ismprimarily,and(b)takingaliberalattitudetowardtheideaofrelationsbetweenmaterialthings.177\nCraigCallenderandCarlHoeferIfthemanifoldistakenasonlyrepresentingthecontinuity,dimensionalityandtopologyofspace–time(assomesubstantivalistswouldagreeanyway),thenwhat’sreallyindispensableisthemetric.Canitbeinterpretedrelationally?Thephiloso-pherswhoarguethatitcanarenotclaimingaMachianreductionofmetricalstruc-turetomaterialrelations.Instead,theyclaimthatthemetricitselfcanbeinterpretedasgivingthestructureofactualandpossiblespatiotemporalrelationsbetweenmaterialthings.gisnotathingorsubstance.Wherematterispresent,itiscrucialtothedefinitionoflocalstandardsofaccelerationandnon-acceleration;theEFErecordjustthisrelationship.Inmanyways,thedesiresoftraditionalrela-tionists(especiallyLeibniz,HuygensandMach)are–arguably–metbyGTRwheninterpretedthisway.Currentworkhasservedtoclarifythevarioustypesofsubstantivalistviewthatmaybebroughtforth,andthestrengthsandweaknessesofthem.Toalesserextent,relationistalternativeshavealsobeenclarified.Othersfeelunhappyaboutbothalternatives,andtheirreasonsstemfromaconvictionthattheontologicalcategoriesofabsolutism,substantivalismandrelationismhavenoclearmeaningsinGTRandhavethusoutlivedwhatusefulnesstheyeverhad.Rynasiewiczhaspublishedtwoprovocativepapersonthistopic.His1996paperarguesthatthecategoriesofabsoluteandrelationalsimplydonotapplyinGTR,soitisamug’sgametryingtoseewhichone“wins”inthattheory.Tracingrela-tionalandabsolutistideasfromDescartesthroughtoEinsteinandLorentz,thecoreofhiscaseisthatthemetricfieldofGTRisabitlikeaCartesiansubtlematterandabitlikeNewton’sabsolutespace,butintheendnotenoughlikeeither(thoughitisalotlikeether).Inhis2000paper,hedoesasimilarhistorical/conceptualanalysisofthenotionsofabsoluteandrelativemotion,concludingthatthenotionsareimpossibletodefineinGTR.Whileitispossibletomountcounter-argumentsindefenseofthetraditionalnotions(Hoefer,1998),itisimpossibletodenythatGTRisanawkwardtheorytocomprehendusingtraditionalconceptsofspaceandtime.RobertDisalle(1994,pp.278–9)arguesalongsimilarlines.Heoffersaposi-tivewaytounderstandspace–timeafterwehavefreedourselvesfromtheout-modedcategories.Inhis1995,hearguesthatachiefmistakeofthetraditionisthinkingofspace–timestructureasanentitythatwepostulatetocausallyexplainphenomenaofmotion.Itcan’tdothejobofexplainingmotionsbecauseitissimplyanexpressionofthefactsaboutthosemotions–whencertaincoordinat-ingdefinitionsarechosentorelatespatio-temporalconceptswithphysicalmeasurementsandprocesses.Thepointisnicelymadebyanalogy.Whenpre-nineteenthcenturythinkersassertedtheEuclideannatureofspace,theywereclaimingthatobservationsoflength,angleanddistancewillalwaysconformtotherulesofEuclid’sgeometry.ButsayingspaceisEuclideanisnotgivingacausalexplanationofrulersandcompassesbehavingastheydo,anditisnotthepostu-lationofanew,substantial“thing”inwhichrulersetc.areembedded.Norisit,however,aclaimthatallspatialfactsarereducibletoobservablesormeasurement178\nPhilosophyofSpace–TimePhysicsoutcomes.Onecan,saysDisalle,bearealistaboutspace(orspace–time)’sstruc-ture,withoutmakingthemistakeofinappropriatereification.FutureworkThenotionsofrelationalandsubstantivalspacetimemayhavereachedasortofimpassewhenitcomestotheinterpretationofGTR’soverallstructure,aspre-sentedinentry-leveltextbooks.Thishardlymeansthatwehaveanadequateunder-standingofspace–time’sontology,acomfortablerestingplaceforphilosophicalcuriosity.AsearchoftheabstractsofrecentworkinthefoundationsofGTRandquantumgravitywillshownumerousoccurrencesofwordslikerelationalandabsolute,LeibnizandMach.Thisisbecausephilosophersandphysicistsalikestillwanttodeepentheirunderstandingoftheworld’sontology.Thereisstillimpor-tantworkthatcanbedoneonclassicalGTR.Forexample,whatisthestatusofenergyconservationlaws?Doesmatter–energyreallygetexchangedbetweenordi-narymatterandemptyspace–time?Howmightrelationalistsunderstandparitynonconservation?ArethereMachianreplacementsfororrestrictionsofGTRthatareobservationallyequivalentoverthestandardrangeofcurrenttests?(SeeBarbourandBertotti(1982)andBarbour(1999).)ConventionalismaboutSpace–timeSomeofthemostbasicprinciplesofscience(andperhapsmathematics)seemtobetrueasamatterofdefinitionalchoice.Theyarenotquitepurelyanalyticortrivial;theycannotbedemonstratedtruesimplyonthebasisofpriorstipulativedefinitionsandlogicalrules.Further,incompatible-lookingalternativeprinciplesareconceivable,eventhoughwemaynotbeabletoseehowausefulframeworkcouldbebuiltonthem.Suchprinciplesareoftenheldtobetruebyconvention.OneexampleinmathematicsisthefamousparallelpostulateofEuclideangeometry.Physicalexamplesarelesscommonandtypicallyfraughtwithcontro-versy.PerhapsNewton’sfamous2ndlaw,F=ma,isanexample.Thismaybethoughtapoorchoice,forsurely,asthecenterofhismechanics,the2ndlawisfarfromtruebydefinition.ButintheNewtonianparadigm,the2ndlawservedasultimatearbiterofthequestions(a)whetheraforceexistedonagivenobject;and(b)ifso,whatitsmagnitudewas.Anyfailureoftheaofanobjecttoconformtoexpectationwasgroundsforassum-ingthatanunknownorunexpectedforcewasatwork,notgroundsforques-tioningthe2ndlaw.179\nCraigCallenderandCarlHoeferOfcourse,thereisnoguaranteethatonecanalwaysmaintainanyputativecon-ventionaltruth,comewhatmay.Rather,onecanusuallyimagine(orexperimen-tallyfind,asintheexampleathand)circumstancesinwhichunbearabletensionsariseinourconceptualframeworksfromtheinsistenceonretentionofthecon-ventionalprinciple,andoneiseffectivelyforcedtogiveitup.(Duhem(1954)givesaclassicdiscussionofthesematters.)Ifthisisright,thentheoriginalclaimofconventionalitylookslikesomethingofanexaggeration.Arethereinfactanychoicesinthecreationofadequatephysicaltheorythataregenuinelyfree,con-ventionalchoices(as,e.g.choiceofunitsis),withoutbeingcompletelytrivial(as,again,choiceofunitsis)?Manyphilosophershavethoughtthatspace–timestruc-turesgiveustrueexamplesofsuchconventionality.HistoryBeforetheeighteenthcenturyallphilosophersofnatureassumedtheEuclideanstructureofspace;itwasthoughtthatEuclid’saxiomsweretrueapriori.TheworkofLobachevsky,RiemannandGaussdestroyedthisbelief;theydemon-strated,first,thatconsistentnon-Euclideanconstant-curvaturegeometrieswerepossible,andlaterthatevenvariablycurvedspacewaspossible.Itwasalsoappar-entthatourexperienceoftheworldcouldnotruleoutthesenewgeometries,atleastinthelarge.Butwhat,exactly,doesitmeantosaythatspaceisEuclideanorRiemannian?Anaïve-realistinterpretationcan,ofcourse,begiven:thereexistsathing,space,ithasanintrinsicstructure,andthatstructureconformstoEuclid’saxioms.Butsomephilosophers–especiallyempiricistssuchasReichenbach–worriedabouthowspaceisrelatedtoobservableproperties.Thesephilosophersrealizedthatourphysicaltheoriesalwayscontainassumptionsorpostulatesthatcoordinatephysicalphenomenawithspatialandtemporalstructures.Lightraysinemptyspacetravelinstraightlines,forexample;rigidbodiesmovedthroughemptyspaceoveraclosedpathhavethesametruelengthafterwardasbefore;andsoon.So-calledaxiomsofcoordinationareneededtogivemeaningandtestabil-itytoclaimsaboutthegeometryofspace.Theneedforaxiomsofcoordinationseemstomakespaceforconventionalism.Forsupposethat,underouroldaxiomsofcoordination,evidencestartstoaccu-mulatethatpointstowardanon-Euclideanspace(trianglesmadebylightrayshavinganglessummingtolessthan180°,forexample).Wecouldchangeourviewofthegeometryofspace;butequallywell,sayconventionalists,wecouldchangetheaxiomsofcoordination.Byeliminatingthepostulatethatlightraysinemptyspacetravelinstraightlines(perhapspositingsome“universalforce”thataffectssuchrays),wecouldcontinuetoholdthatthestructureofspaceitselfisEuclid-ean.Accordingtothestrongestsortsofconventionalism,thispreservationofaconventionallychosengeometrycanalwaysbedone,comewhatmay.Poincaré(1952)defendedtheconventionalityofEuclideangeometry;buthealsomadean180\nPhilosophyofSpace–TimePhysicsempiricalconjecture,nowregardedasfalse:thatitwouldalwaysbesimplertocon-structmechanicsonassumptionofEuclideangeometry.DiscussionsofconventionalismtookadramaticturnbecauseoftheworkofEinstein.Withitsvariablycurvedspace–time,GTRposednewchallengesandopportunitiesforbothsidesontheconventionalityofgeometry.Cassirer,Schlick,Reichenbach,andGrünbaumaresomenotablefiguresoftwentiethcenturyphi-losophywhoarguedfortheconventionalityofspace–time’sgeometryinthecontextofGTR.Recentscholarshavetendedtobeskepticalthatanynon-trivialconventionalistthesisistenableinGTR;Friedman(1983)andNerlich(1994)areprominentexampleshere.Butitwasin1905,ratherthan1915,thatEinsteingavethegreatestwindtoconventionalist’ssails.Intheastoundingfirstfewpagesofthepaperthatintroducedthespecialtheoryofrelativity(STR),EinsteinoverthrewtheNewtonianviewofspace–timestructure,andinpassing,notedthatpartofthestructurewithwhichheintendedtoreplaceithadtobechosenbyconvention.Thatpartwassimultaneity.Einsteininvestigatedtheoperationalsignificanceofaclaimthattwoeventsatdif-ferentlocationshappensimultaneously,anddiscoveredthatitmustbedefinedintermsofsomeclocksynchronizationprocedure.Theobviouschoiceforsuchaprocedurewastouselight-signals:sendasignalateventAfromobserver1,haveitbereceivedandreflectedbackbyobserver2(atrestrelativeto1)ateventB,andthenreceivedby1againateventC.TheeventBisthensimultaneouswithaneventE,temporallymid-waybetweenAandC(Figure9.2).Orisit?TosupposesoistoassumethatthevelocityoflightonthetripfromAtoBisthesameasitsvelocityfromBtoC(or,moregenerally,thatlighthasC2ε=—31ε=—EB21ε=—3A12Figure9.2SimultaneityconventionsinSTR181\nCraigCallenderandCarlHoeferthesamevelocityinagivenframeinalldirections).Thisseemslikeaverygoodthingtoassume.Butcanitbeverified?Einsteinthoughtnot.Allwaysofdirectlymeasuringtheone-wayvelocityoflightseemedtorequirefirsthavingsynchro-nizedclocksatseparatedlocations.Butifthisisright,wearegoingincircles:weneedtoknowlight’sone-wayvelocitytoproperlysynchronizedistantclocks,buttoknowthatvelocity,weneedantecedentlysynchronizedclocks.Tobreakthecircle,Einsteinthoughtweneededsimplytoadoptaconventionalchoice:wedecidethateventEissimultaneouswithB(i.e.thatlight’svelocityisuniformanddirection-independent).Otherchoicesareclearlypossible,atleastforthepurposesofdevelopingthedynamicsandkinematicsofSTR.Following1Reichenbach,thesearesynchronizationswitheπ–(ebeingtheproportionofthe2round-triptimetakenontheoutboundlegonly).Adoptingoneofthesechoicesisarecipeforcalculationalmiseryofaverypointlesskind.ButtheEinsteinof1905,andmanyphilosophersofanoperationalist/verificationistbentsincethen,thoughtthatsuchachoicecannotbecriticizedaswrong.Ultimately,theysay,distantsimultaneityisnotonlyframe-relative,butpartlyconventional.Takingupthechallengeofestablishingaone-wayvelocityforlight,EllisandBowman(1967)arguedthatslowclocktransportoffersameansofsynchronizingdistantclocksthatisindependentofthevelocityoflight.InSTR,whenaclockisacceleratedfromrestinagivenframeuptosomeconstantvelocity,thendeceleratedtorestagainatadistantlocation,therearetime-dilationeffectsthatpreventusfromregardingtheclockashavingremainedinsynchwithclocksatitsstartingpoint.Andcalculationofthesizeoftheeffectdependsonhavingestablishedadistant-simultaneityconvention(i.e.achoiceofe).Soitlooksasthoughcarryingaclockfromobserver1toobserver2willnotletusbreakthecircle.ButEllisandBowmannotedthatthetimedilationeffecttendstozeroasclockvelocitygoestozero,andthisisindependentofe-synchronization.Therefore,an“infinitelyslowly”transportedclockallowsustoestablishdistantsynchrony,andmeasurelight’sone-wayvelocity.Conventionalistswerenotpersuaded,andtheoutcomeofthefiercedebateprovokedbyEllisandBowman’spaperwasnotclear.In1977,DavidMalamenttookuptheconventionalistchallengefromadif-ferentperspective.OnewayofinterpretingtheclaimofconventionalistssuchasGrünbaumisthis:theobservablecausalstructureofeventsinanSTR-worlddoesnotsufficetodetermineauniqueframe-dependentsimultaneitychoice.By“causalstructure”wemeanthenetworkofcausalconnectionsbetweenevents;looselyspeaking,anytwoeventsarecausallyconnectableiftheycouldbeconnectedbyamaterialprocessorlight-signal.InSTR,the“conformalstructure”orlight-conestructureatallpointsistheidealizationofthiscausalstructure.Itdetermines,fromagivenevent,whateventscouldbecausallyconnectedtoit(towardthepastortowardthefuture).Grünbaumandothersbelievedthatthecausalstructureofspace–timebynomeanssinglesoutanypreferredwayofcuttingupspace–timeinto“simultaneityslices”.182\nPhilosophyofSpace–TimePhysicsMalamentshowedthat,inanimportantsense,theywerewrong.Thecausal/conformalstructureofMinkowskispace–timedoespickoutauniqueframe-relativefoliationofeventsintosimultaneityslices.Orrather,moreprecisely,theconformalstructuresufficestodetermineauniquerelationoforthogonality.Ifwethinkofane-choiceasthechoiceofhowtomakesimultaneityslicesrelativetoanobserverinagivenframe,thenMalamentshowedthattheconformalstruc-tureissufficienttodefineaunique,orthogonalfoliationthatcorrespondstoEin-1stein’se=–choice.Formanyphilosophers,thisresultmarkedtheendofthe2debateoverconventionalityofsimultaneity.(ButseeJanis,1983andRedhead,1993forconventionalistresponses.)CurrentworkArecentpaperbySarkarandStachel(1999)triestore-opentheissueofconformalstructureandsimultaneityrelations.StachelandSarkarnotethatoneofMalament’sassumptionswasthatthecausalconnectabilityrelationistakenastime-symmetric,i.e.thatitdoesnotdistinguishpast-futurefromfuture-pastdirectionsofconnec-tion.Theyarguethatitispossibletodistinguishthebackwardfromforwardlightconesusingonlythecausal-connectabilityrelationMalamentstartsfrom.Ifthisisgranted,andwedonotimposetheconditionthatanycausally-definablerelationmustbetime-symmetric,thentheuniquenessresultMalamentprovedfails.Manydifferentcone-shapedfoliationsbecomedefinable.StachelandSarkaradvocatethebackward-lightconesurfaceasanalternativesimultaneitysurfacechoicethatcouldbemade.Itremainstrue,however,thatonlythegenuineorthogonalityrelation1(e=–)istransitiveandlocation-independent.Thesearetwoofthecorefeaturesof2classicalsimultaneity.ToputforwardStachelandSarkar’salternativerelationasagenuinecandidateforadistant-synchronyrelationistherefore,atbest,awkwardandoutoflinewithcoreintuitionsaboutsimultaneity.Still,manyphilosophersofphysicsfeeldissatisfiedwitheventhismuchofacon-cessiontoconventionalism.Theysuspectthat,evenifitmayhavebeeninsome1sensepossibletodophysicswitheπ–in1905,morerecentquantumfieldtheory2hassurelyruledthatout.Zangari(1994)arguedthatthemathematicsofspinor1fieldsinMinkowskispace–time–usedindescribingspin-–particles,forexample2–isonlyconsistentinframeswithstandardsynchrony.GunnandVetharaniam(1995)claimedthatZangariwasmistaken,andthatusingadifferentformalism,1theDiracequationcouldbederivedinaframeworkincludingeπ–frames.2Karakostas(1997)hasarguedthatbothoftheprecedingauthors’argumentsareflawed,thoughZangari’smainclaimiscorrect.Andmostrecently,Bain(2000)arguesthatnoneoftheseauthorshasitexactlyright.Thereisalwaysawaytodophysicsusingarbitrarycoordinates(includingthosecorrespondingtonon-standardsimultaneitychoices);butwhetherthatamountstotheconventionalityofsimultaneityinaninterestingsenseremainsatrickyquestion.183\nCraigCallenderandCarlHoeferIntryingtoseeone’swaythroughthedensethicketoftechnicalclaimsandcounter-claimsinthesepapers,ithelpstofallbackonthenotionofgeneralcovari-ance.Kretschmannhypothesizedin1918thatanyphysicaltheorycouldbeexpressedinagenerallycovariantform,i.e.inaformthatisvalidinarbitrarycoordinates.Nonstandard-synchronyframesdocorrespondtocoordinatesystemsallowedundergeneralcovariance.KarakostasdoesnotdenyKretschmann’sclaim.Instead,henotesthatgenerallycovarianttreatmentsofspinorfieldscanbedone,buttheyhavetointroduceageometricstructure(a“frame”or“vierbeinfield”)thateffectivelypicksouttheorthogonal(=standardsimultaneity)directionforagivenobserverinagivenframe.Thisisatypicalsortofmovewhentheorieswithabsolutespace–timestructuresaregiveninagenerallycovariantform.Geometricobjectsorfieldsreplaceprivilegedcoordinatesorframes,butthe“absoluteness”isonlyshifted,notremoved.Inthecaseofspinorfields,itseemsthatsomethingthateffectivelyencodestheEinstein-standardsynchronyrelationismathematicallynecessary.Cantheconventionalistrespondbyclaimingthatthisnecessarystruc-tureis,withal,notasimultaneitystructure?Bainclaimsthatshecan;forspinorfieldshavenothingtodowithrodsandclocks,andthemeasurementoflight’sone-wayvelocity–i.e.withtheoriginalpointconventionalistsmade.Conventionalistclaims–concerningbothgeometryandsimultaneity–seemtobeconstantlyindangerofcollapsingintotriviality:thetrivialclaimthat,ifwearemathematicallycleverandnotafraidofpointlesshardwork,wecanchooseanyperversesortofcoordinatesystemwelike,andthenclaimthatthecoordinatesreflectthegeometric/simultaneityrelationswehave“chosen.”Perhapswecandothis;buttosupposethatthisamountstoagenuinechoiceofspatio-temporalfactsistobesomewhatdisingenuousaboutthecontentofsuchfacts.Tobesure,axiomsofcoordinationareneededtolinkpuregeometricconceptstoobservablephe-nomena.Buttheaxiomswechoosearethemselvesconstrainedinmanywaysbytheneedtocoherewithfurtherpracticesandmetaphysicalassumptions.Inprac-tice,theseconstraintsseemtofullydetermine,orevenover-determineour“choices”regardinggeometry.Whatkeepsthedebateconcerningconventional-ityofsimultaneityaliveisthewayinwhichour“conventionalchoices”playonlyacompletelytrivialrolequaaxiomsofcoordination.Justasonecandophysicswithanychoiceofe,onecanalsodophysicswithoutanychoiceofclocksynchronization.FutureworkRelativitytheory(STRandGTR)providesthenaturalhomeforatleastlimitedformsofconventionalism,thoughitremainsasubjectofdisputejusthowsignif-icanttheconventionalityis.TheworkofKarakostas,Bainandotherspointsinthedirectionfutureworkonthesetopicswilltake:towardnewphysics.Onewouldalsoexpectthatadvancesinthegeneralmethodologyofsciencewillcontinuetobearontheseissues.184\nPhilosophyofSpace–TimePhysicsBlackHolesandSingularitiesOurbesttheoriestellusthatstarseventuallyrunoutofnuclearfuel.Whentheydoso,theyleaveequilibriumandundergogravitationalcollapse,endingaswhitedwarvesifthecollapsingcore’smassM<1.4solarmasses,asneutronstarsif5>M>1.4,orasblackholesifM>5.Blackholesareregionsofspace–timeintowhichmattercanenterbutfromwhichmattercannotescape.Theirendstatesaresingularities,whichfornowwemightassociatewitha“hole”inspace–timeorapointwherethespace–timemetric“blowsup”andisill-defined.Thereissomeastronomicalevidencefortheexistenceofblackholes,andtheyarerelevanttoanumberofquestionsthatinterestphilosophers,suchaswhethertimetravelispossibleandwhetherthepastandfuturearefinite(Weingard,1979).However,weherefocusonsingularities,astheyaremoregeneralsincetheycanexistwithoutblackholes,andtheyalsoposeseveraldifferentphilosophicalquestionsthatarethesubjectofactiveresearch.HistorySingularitiesarehardlynoveltoGTR.TheclassicalCoulombfieldwhencom-binedwithSTRgoestoinfinityatpoints.CollapsingsphericaldustcloudsandotherhighlysymmetricsolutionsprovideexamplesofsingularitiesinNewtoniangravitationaltheory.ButsingularitiesinGTRareespeciallypuzzling,aswewillsee.TheexistenceofsingularitiestoEFEwasknownfromthetheory’sinception.Hilbert,forinstance,wroteaboutthenotorioussingularitiesintheSchwartzchildsolutionasearlyas1917.Thelineelementofthissolutionhassingularitiesatr=0andr=2M.Einsteinin1918worriedaboutthemonlybecausehetookthemasathreattoMachianism.Singularitiesinthesolutionstothefieldequa-tionsdidn’tcausegeneralalarmformanymoredecadesbecausetheywerenotverywellunderstood(Earman,1999;EarmanandEisenstaedt,1999).Theywereviewedasunacceptablepathologies,butitwasassumedthattheyweredefectsofonlycertainmodels.From1918untilthemid-1950s,itwasnotrealizedthatthesingularitiesinthesespace–timeswere“essential”insomesense.Thereweretwootheroptions.First,asingularitymightbemerelya“coordinatesingularity”andnotafeatureofthespace–time.Toillustratethedistinction,considercoordinizingasphere.Itisatheoremthatnosinglecoordinatesystemcancoverthespherewithoutsin-gularity.Thisrepresentsaproblemforthecoordinatesystem,notthesphere.Thesphereisaperfectlywell-definedgeometricobject;moreover,therearewaysofcoveringthespherewithoutsingularityusingtwodifferentcoordinatepatches.TheSchwartzchildsolutioncausedparticularmischiefinthisregardduringthefirsthalfofthetwentiethcentury;itfamouslyemergedthatonlyone(r=0)of185\nCraigCallenderandCarlHoeferitstwoapparentsingularitiesisgenuine–the“Schwartzchildradius”(r=2M)isamereartifactofthecoordinates.Second,likethesingularitiesinclassicalgravitationaltheory,relativisticsingu-laritiesmightbeduetoanartificialsymmetryofthesolution.ThesingularnatureofasolutionofNewton’sequationsrepresentingaperfectlysphericalcollapseofdustisrealenough.Itisnoartifactofthecoordinateschosen.Butthefeelingis,whatchanceistherethatthisisourworld?Ourworlddoesnothaveitsmatterarrangedlikedustformedinaperfectsphere.Changethedistribu-tionsomewhatandthesingularitydisappears.Whyworry?Similarly,whenitbecameclearthat(forexample)theSchwarzchildandFriedmansolutionscon-tainedgenuinesingularities,thehopewasthatthesearosefromtheartificialsymmetriesinvoked;afterall,theSchwartzchildsolutionrepresentsthegeometryexteriortoasphericallysymmetricmassivebodyandtheFriedmansolutionsrep-resentsahomogeneousandisotropicmatterdistribution.Thesingularsolutionswerehopedtobeinsomesense“measurezero”inthespaceofallthesolutionsofEFE.Thesehopesweredashedbysingularitytheoremsinthe1950sbyRaychaud-huriandKomar,andespeciallybytheoremsinthe1960sandearly1970sbyPenrose,GerochandHawking.Thesetheoremsappeartodemonstratethatsin-gularitiesaregenericinspace–timeslikeours.Theyassumewhatseemtobeplau-sibleconditionsonthestress-energyofmattertoforcegeodesicstocross;theythenemployglobalconditionsonthegeometrytoshowthatthesegeodesicster-minateinasingularity.Theseadvancesinthe1960sand1970sweremadepossibleinpartbythenew,minimaldefinitionofasingularity.Withoutgoingintothedetails,aspace–timeissaidtobesingularaccordingtothesetheoremsjustincaseitcontainsamaximallyextendedtimelikegeodesicthatterminatesafterthelapseoffinitepropertime.Brieflyput,aspace–timeissingulariffitistimelikegeodesicallyincomplete.(Thisdefinitioncanbeextendedtocovernullandspacelikecurves,andcanbeextendedinotherwaystoo–toso-called‘b-incompleteness’–butwewillnotgointothishere.)Theideabehindthisdefinitionisthatitmustbeaseriousfaultofthespace–time,oneworthyofthenamesingularity,ifthelifeofafreelyfallingimmor-talobserverneverthelessterminatesinafinitetime.Howeverfruitfulthisdefinition,ithasprovedtobecontroversial,ashavethesignificanceofthesingularitytheorems.Thecurrentworkinphilosophyonthesetopics,largelydrivenbyEarman(1995),focusesonthesetwoquestions.CurrentworkThissectionfocusesontheanalysisofsingularities.Weconcentrateonthistopicnotbecausewefeelthatitisanymoreimportantthanotherquestions–indeed,wefeeltheopposite,that(forinstance)thequestionofthesignificanceofsingu-laritiesforGTRisfarmoreimportant–rather,wesoconcentratebecauseitisa186\nPhilosophyofSpace–TimePhysicsnecessarypointofentryintotheliterature.Onecannotsuccessfullyevaluatethesignificanceofsingularitieswithoutfirstknowingwhattheyare.Naively,onehastheideathatasingularityisaholeinspace–timesurroundedbyincreasingtidalforcesthatdestroyanyapproachingobject.Thispicturecannotbecorrectforgeneralrelativisticspace–times.Thereasonissimple:thesingulari-tiesherearesingularitiesinthemetricspaceitself,sothereisliterallynolocationforahole.GeneralrelativityrequiresamanifoldwithasmoothLorentzmetric,sobydefinitiontherearenolocationswherethemetricissingular.Fieldsonspace–timecanbesingularatpoints;butspace–timeitselfhasnowheretobesingular.FollowingGeroch(1968),commentatorshaveidentifiedseveralquitedistinctmeaningsofsingularity.Tonameafew,andsparingdetails,considerthefollow-ingconditionsproposedformakingaspace–timesingular:(a)curvatureblowup:ascalarcurvatureinvariant,e.g.Ricci,tensorgoesunboundedalongacurveinspace–time(b)geodesicincompleteness:seeabove(c)missingpoints:pointsare“missing”fromalargermanifold,arisingfromtheexcisionofsingularpoints.Allthree,wesuppose,areinvolvedinourintuitiveideaofaspace–timesingu-larity.AndforaRiemannianspace,(b)and(c)areco-extensive.TheHopf–Rinowtheoremstatesthat,forconnectedsurfaces,theconditionsofbeingacompletemetricspaceandbeinggeodesicallycompleteareequivalent.AmetricspaceiscompleteifeveryCauchysequenceofpointsinitconvergestoapointinthatspace.Intuitively,incompletenessisassociatedwithmissingpoints.Forinstance,2theplaneminustheorigin,thesurface
–{(0,0)},isnotcompletebecausetheCauchysequence{(1/n,0)}convergestoapointexcisedfromtheplane.Itisalsonotgeodesicallycompletesincetherearenogeodesicsjoiningpoints(-1,0)and(1,0),sohereweseeaconnectionbetweengeodesicincompletenessandmissingpoints.However,arelativisticspace–timeisnotaRiemannianspace,butapseudo-Riemannianone,andtheHopf–Rinowtheoremdoesnotsurvivethechange.Noneofthethreedefinitionsareco-extensive:theliteratureshowsthatwhile(c)implies(b),(b)doesnotimply(c);(a)implies(b),but(b)doesnotimply(a);and(a)seemstoimply(c),but(c)doesnotimply(a).Theofficialdefinition,(b),thusseemstoactasakindofsymptomoftheothertwopathologies.Evenheretherearecounterexamples.Acurvemightbeincompleteevenifthecurvatureisbehavingnormally,ashappensinCurzonspace–time;andasMisnershows,acurvemightbeincompleteeveninacompact,andhence,completeand“hole-less”,space–time.Itisofinteresttoseehowharditistoevenmakesenseofdefinition(c).Asmentionedabove,arelativisticspace–timehasnoroomforsingularpointsinthemetric.Definition(c)wouldthenhaveuslookforthetracesofanexcisedpoint,187\nCraigCallenderandCarlHoeferi.e.lookforwhatisnotthere.Howdoyoufindpointswhicharenotonthespace–timebutwhichhavebeenremoved?Lookingatthetopologywillnothelpsince,ingeneral,avarietyofnon-singularmetricscanbeputonanygiventopol-22ogy(forinstance,theSchwartzchildtopologyofR¥Siscompatiblewithplentyofnon-singulartopologies).Althoughthiswayofunderstandingsingularitiesisstillactive,itmaybethatthewholeideaofasingularityassomelocalizableobjectismisleading.OncewehaveanunderstandingofsingularitiesinGTR,thenextquestiontoaskisabouttheirsignificance.Dothey“sowtheseedsofGTR’sdemise”asisoftenalleged?Oraretheyharmless,perhapsevensalutary,featuresofthetheory?Earman(1996)providesanargumentfortoleratingsingularities;butmanyphysi-cistsclaimthattheyrepresentagenuinedeficiencyofthetheory.FutureworkThetopicofsingularitiesisreallyanewoneforphilosophersofscience.Wecanscarcelymentionalltheareasopentofutureendeavor.Themajorityofourfocusbelowdepends,perhapsnaturally,onrelativelyrecentideasinphysics.GoodargumentsneededEarman(1996)piecestogetherandcriticizesvariousargumentsforthewidespreadbeliefthatsingularitiessowtheseedsofGTR’sdemise.Asurveyoftheliteratureshowsthatthereisadearthofgoodargumentsupportingthisbelief.Canagoodargumentbearticulatedonbehalfofthisopinionthatdoesnotrelyonmisleadinganalogieswithotherpitfallsinthehistoryofscience?Aretherereallysingularities?Thesingularitytheoremsdonotfalloutasdeduc-tiveconsequencesofthegeometriesofrelativisticspace–times.Tosayanything,thestress-energytensormustbespecified,and,infact,allthetheoremsuseoneoranotherenergycondition.Theso-calledweakenergycondition,forinstance,statesthattheenergydensityasmeasuredbyanyobserverisnon-negative.But,isitreasonabletosupposethesehold?ThephilosopherMattingly(2000)soundsanoteofskepticism,pointingoutthatvariousclassicalscalarfieldsandquantumfieldsviolatealltheconventionalenergyconditions.EvenifMattingly’sskepticismisnotvindicated,abetterunderstandingoftherelationbetweentheenergycon-ditionsandrealphysicalfieldsiscertainlyworthhaving.QuantumsingularitiesPhilosophersmayalsowishtocastcriticaleyesoversomeofthemethodssuggestedforescapingsingularitieswithquantummechanics.Itissometimessaidthatoneshoulddefineaquantumsingularityasthevanishingoftheexpectationvaluesforoperatorsassociatedwiththeclassicalquantitiesthatvanishattheclassicalsingularity.Thenitispointedoutthattheradiusoftheuni-verse,forexample,canvanishinwhatispresumedtobeaninfinitedensityand188\nPhilosophyofSpace–TimePhysicscurvaturesingularity,eventhoughtheexpectationvaluedoesnotvanish(Lemos,1987).Thisissometimestakenasshowingthatquantummechanicssmoothesovertheclassicalsingularity.But,isthisreallyso?CallenderandWeingard(1995),forexample,arguethatthisquantumcriterionforsingularstatusfitspoorlywithsomeinterpretationsofquantummechanics.BlackholethermodynamicsHawking’s(1975)“discovery”thatablackholewillradiatelikeablackbodystrengthenedBeckenstein’sworksupportingananalogybetweenclassicalthermodynamicsandblackholes.Thefieldknownasblackholethermodynamicswasspawned,andtherearenowthoughttobeblackholecoun-terpartstomostoftheconceptsandlawsofclassicalthermodynamics.Forinstance,theblackhole’ssurfacegravitydividedby2pactslikethetemperatureanditsareadividedby4actsliketheentropy.Physicistsenticedbythisanalogyoftenclaimthatitisnoanalogyatall,thatblackholethermodynamicsisther-modynamicsandthat(forinstance)thesurfacegravityreallyisthetemperature.Thesignifianceofthesestartlingclaimsandtheanalogyarecertainlyworthyofinvestigationbyphilosophersofscience.InformationlossArelatedtopicistheblackhole“informationlossparadox”thatarisesfromHawking’s(1975)result.Takeasysteminaquantumpurestateandthrowitintoablackhole.Waitfortheblackholetoevaporatebacktothemassithadwhenyouinjectedthequantumsystem.NowyouhaveasystemofablackholewithmassMplusathermalmixedstate,whereasyoustartedwithablackholewithmassMplusapurestate.Apparently,youhaveaprocessthatconvertspurestatesintomixedstates,whichisanon-unitarytransformationprohibitedbyquantummechanics(suchatransformationallowsthesumoftheprobabilitiesofallpossiblemeasurementoutcomestonotequal1).SeeBelotetal.(1999)andBokulich(2000)forsomephilosophicalcommentaryonthistopic.CosmiccensorshipPerhapsthebiggestopenquestionrelevanttosingularitiesandmanyothertopicsingravitationalphysicsisthestatusofPenrose’scosmiccen-sorshiphypothesis;forarecentassessment,seePenrose(1999).Thishypothesisisoftenglossedastheclaimthatnakedsingularitiescannotexist;thatis,thatsingularitiesareshieldedfromviewbyaneventhorizon,ashappensinsphericallysymmetricgravitationalcollapse.Nakedsingularitiesareunpleasantbecausetheysignalabreakdownindeterminismandpredictability.Ifanakedsingularityoccurstoourfuture,thennoamountofinformationonthespace-likehypersurfaceweinhabitnowwillsufficetoallowadeterminationofwhathappensatallfuturepoints.Singularitiesare,intuitively,holesoutfromwhichanythingmightpop.Asingularitythatwecanseemeanswemightseeanythinginthefuture,sincethecausalpastwillnotsufficientlyconstrainthesingularity.Statedastheclaimthatnakedsingularitiescannotexist,however,thehypoth-esisisclearlyfalse,sincethereareplentyofrelativisticspace–timesthatviolateit.Thoughformulatedinavarietyofnon-equivalentways(Earman,1995,ch.3),it189\nCraigCallenderandCarlHoeferiscommontospeakofweakandstrongversionsoftheclaim.Weakcosmiccen-sorshipholdsthatgravitationalcollapsefromregularinitialconditionsnevercreatesaspace–timesingularityvisibletodistantobservers,i.e.anysingularitythatformsmustbehiddenwithinablackhole.Strongcosmiccensorshipholdsthatanysuchsingularityisnevervisibletoanyobserveratall,evensomeoneclosetoit.By“regularinitialdata”wemeanthatthespace–timesarestablewithrespecttosmallchangesintheinitialdata.Elaboratingthisdefinitionfurtherobviouslyrequiressomecare.Theonlyconsensusonthetopicofcosmiccensorshipisthatthehypothesisisbothimportantandnotyetproventrueorfalse.Regardingthelatter,thereareplentyofcounter-examplestobothformulationsofthehypothesis,thoughespe-ciallytostrongcosmiccensorship;see,forexample,Singh(1998).Currentandfutureworkwilldwellonwhethertheseexamplesreallycount.Inthebackgroundthereis,youmightsay,the“moral”cosmiccensorshiphypothesis,whichclaimsthattheonlynakedsingularitiesthatoccurareGoodones,notBadones.TheexactformulationsofGoodandBaddepend,asonewouldexpect,onthechar-acteroftheparticularinvestigator:prudishinvestigatorshopeGTRdoesn’toffersomuchasahintofnakedness,whereasthemorepermissivewilllowertheirstandards.Itisimportanttoknowwhethersomeversionofthehypothesisistrue.Ifacosmiccensoroperates,thenmanytopicsdeartophilosopherswillbeaffected.Acosmiccensorwillnaturallyaffectwhatkindsofsingularitieswecanexpect,andthereforeinfluencethequestionoftheirsignificanceforGTR(Earman,1996);itwouldmeanthetime-travelpermittingsolutionsofEFEsuchasGödel’swillnotbeallowed;thatthepossibilityofspatialtopologychange(CallenderandWeingard,2000)willnotbepossible,andsoon.Andalackofacosmiccensorwillalsobearonmuchofthephysicsofpotentialinteresttophilosophers,e.g.blackholethermodynamicshangscruciallyontheexistenceofacosmiccensor.Therearealsophilosophicaltopicsaboutcosmiccensorshipthatneedfurtherexploration.Tonametwo,whatismeantby“notbeingallowed”inthestatementofcosmiccensorshipandhowdowhiteholes(thetimereversesofblackholes)squarewiththehypothesisandthetimesymmetryofEFE?HorizonsandUniformityHistoryTheobservedisotropy(ornearisotropy)andpresumedhomogeneityofouruni-versesuggestthatweinhabitaworldwhoselargescalepropertiesaregivenbythewell-knownFriedmanstandardmodel.Inthismodel,theworld“began”inahotdensefireballknownastheBigBang,andmatterhassinceexpandedandcooledeversince.Therateofexpansionandcoolingdependontheequationofstatefor190\nPhilosophyofSpace–TimePhysicsthecosmologicalfluid,andtheultimatefateoftheuniverse(closedoropen)dependsonthecurvature.Partofthecorroborationofthismodelcomesfromtheobserveduniformityofthecosmicmicrowavebackgroundradiation(CMBR).Neglectingsomerecentlydetectedsmallinhomogeneities(whicharethemselvesnotdefectsbutharmonicoscillationsexpectedinsomeBigBangmodels),theseobservationsshowthatthetemperatureofthisradiationisuniformtoatleastonepartin10,000ineverydirectionwelook.WhencoupledwiththeFriedmanmodel,theuniformityoftheCMBRpro-ducesapuzzle.Toseethis,weneedtoresolveanapparentcontradictionbetweenone’snaïveviewoftheBigBangsingularitywiththefactthatintheFriedmanmodelnotallbodiescancommunicatewitheachother,evenmerelyafractionofasecondaftertheBigBang.Considertwonearbyco-movingparticlesatthepresenttime.Thescalingfactor,a,isthedistancebetweentheparticles,sayonelight-second.Becausetheuniverseisexpandingda/dt>0.Nowonewouldexpectthat,sinceaÆ0astÆ0foralltheparticles,anyparticlecouldhavebeenincausalcontactwithanyotherattheBigBang.Sincetheyareall“squashedtogether,”alightpulsefromonecouldalwaysmakeittoanyotherparticleintheuniverse.Thisisnotso.Firstoff,thereisnopointonthemanifoldwheret=0anda=0;thispointisnotwell-definedanditisnotclear,anyway,thatalltheparticlesintheuniverseoccupyingthesamepointreallymakessense.Sothis“point”doesnotcount.Butnowitisaquestionofhowfasttheworldlinesareacceleratingawayfromeachotherandwhetherlightsignalsfromeachcanreachalltheothers.Willlightema-natingfromabody“justafter”theBigBangsingularitybeabletoreachanarbi-trarybodyXbytimet,wheretissomesignificantlylongtime,possibly(inacloseduniverse)theendoftime?Ingeneral,theanswerisNo,fortherearesome(real-istic)valuesoftheexpansionparameterthatdonotallowthelightsignaltocatchuptoXbyt.Thespace–timecurvatureisthekeyhere.Imaginethatyouandafriendaretravelinginoppositedirectionsonaflatplane.Assumingnothingtravelsfaster-than-light,canyouevadealightpulsesentoutinyourdirectionfromyourfriend?No:thoughyoumaygiveitagoodrunforitsmoney,eventuallyitwillcatchyouiftheuniverseisopen.Nowimaginethatyou’removingonaballoonandtheballoonisbeingquicklyinflated.Then,dependingonthespeedofinfla-tionandyourvelocity,youmaywellbeabletoescapethelightsignal,possiblyforalltime.Thecurvatureduetotheexpansionanddecelerationcausestheworldlinesofgalaxiestocurve.Intwospatialdimensions,ourpastlightconebecomespear-shapedratherthantriangular(Figure9.3).Notethatduetothiscurvaturewecannot“see”theentireBigBang.Ausefulpictureofthecausalsituationemergesifwe“straightenout”thecurvature,muchaswedowhenweuseaMercatorprojectionwhenwedrawaflatpictureoftheearth(Figure9.4).Herethetopofthelargetriangleisthepointweareatrightnow,andthetwoshadedtrianglesarethepastnullconesoftwopoints,separatedbyanangleA,191\nCraigCallenderandCarlHoeferFigure9.3OurpastlightconeFigure9.4Straighteningoutthecurvaturethatwecanseeinourpast.IfAissufficientlygreattheshadedregionsdonotintersect.Butsincethepastnullconeofapointrepresentsallthepointswithwhichitmighthavehadcausalcontact,thismeansthatnopointintheshadedregionscouldhavehadcausalcontactwitheachother(ignoringthepossibilityof192\nPhilosophyofSpace–TimePhysicsfaster-than-lighttravel).Aparticlehorizonisdefinedasthemaximumcoordinatedistancethatonecanseefromagivenpointinspace–time.Fromthediagram,onecanseethatthepointsatthetopoftheshadedregionshavehorizonsthatprecludethemfromseeingeachother’spasts.ThepuzzleabouthorizonsarisesfromthefactthataFriedmanmodellikethatpicturedcanbesaidtofairlyrepresentouruniverse,wheretheshadedregionsarepointsinourpastwherematterdecoupledfromradiation.Sincetheysharenocommoncausalpast,thismeansthattheyhavenomechanismincommonthatwillmakethemicrowaveradiation’stemperaturethesame.How,then,didtheyarriveatthesametemperature?Itseemsthat,shortofdenyingthattheearlyuni-versecanbeapproximatelyrepresentedbyaFriedmanmodel,theonlyansweristhattheuniversewas“born”inahighlyisotropicandhomogenousstate.Thisnecessaryspecialinitialstateisthecauseofthehorizonproblem.CurrentworkInphysics,themainresponsetothispuzzleistochangethephysicsofexpansion.Thoughthereareotherresponses,theoneknownasinflationisalmostuniversallymaintained.Ininflationaryscenarios,thestandardFriedmanexpansionisjettisonedinanearlyepochinfavorofaperiodofexponentialexpan-sion;theuniversethenundergoesaphasetransitionthatslowsitdownbacktothemoremoderateFriedmanexpansion.Thedetailsofthisperiodvarywithdif-ferentproposals(therearemorethanfifty).Inflationdoesnotremoveparticlehorizons;instead,itincreasesthesizeofeachpoint’spastnullconesothatpairswilloverlap.Theshadedpastlightconesinthediagramwouldintersectwhileremainingpropersubsetsofeachother.Thehopeisthatthecommoncausalpastbetweentwopointswillbelargeenoughsothatitaccountsfortheiruniformtemperature.WorkbyPenrose(1989),Earman(1995)andEarmanandMosterin(1999)haveseverelycriticizedinflationforfailingtodeliveronitsoriginalpromises.Thetheory,theysay,doesnotridcosmologyoftheneedforspecialinitialconditionstoexplaintheapparentuniformityofthecosmicbackgroundradiation,nordoesitenjoymuchinthewayofempiricalsuccess.FutureworkThehorizonproblemsharessomegeneralfeatureswithotherwell-known“prob-lems”inphysics.Theproblemofthedirectionoftime(well,oneofthem)asksforanexplanationofthethermodynamicarrowoftimeandendsuprequiringthepostulationofaveryspecialinitialconditionoflowentropy(Price,1996).Philo-sophically,itisnon-trivialwhetherrequiring“special”boundaryconditionsisa193\nCraigCallenderandCarlHoefergenuinedefectofatheory.Forthesituationwithentropyandthedirectionoftime,manydonotseethespecialpositasagenuinefailingofthetheorytoprovideascientificexplanation(Callender,1997);inthecosmologicalcasewithhorizons,however,itisorthodoxynowthatitisagenuinefailingofthestandardmodelthatitcannotexplaintheuniformityofthecosmicbackgroundradiation.Butisit?Thefailingiscertainlynotoneofempiricaldisconfirmation,sincegiventhe“special”initialconditionsthemodelisempiricallyadequate–weevengetadeter-ministicexplanationthroughtimeofwhyweseethefeatureswedo.EarmanandMosterindomuchtocriticizeinflationasasolutiontothisproblem,butthelargerissue,commontothistopicandothers–whethertherereallyisaproblemhereatall–isleftopen.Arelatedissueiswhetherthenotionof“specialness”canbesharpened.Inthecosmologicalcaseconsideredhere,itisespeciallyproblematictospecifyinexactlywhatsensetheboundaryconditionsare“special,”asPenrose(1989)emphasizes.Bycontrast,inthethermodynamiccasethisissomewhatclearersinceoneistalkingaboutastatisticaltheory(statisticalmechanics)equippedwithastandardproba-bilitymeasurewithrespecttowhichtheneededinitialconditionsdoindeedoccupysmallmeasure.Tobesure,thereareproblemsinthiscasetooinjustify-ingthis“natural”probabilitymeasure,buttheyappeartopaleincomparisontotheproblemsofdefiningaprobabilityforcosmicinflation.Finally,thequestionofwhethertherewasinflationwillprobablyultimatelybedecidedbyobservationandexperimentratherthanphilosophicalargument.Recentandfutureimprovementsinobservationalcosmology(e.g.CMBmea-surements,measurementsoftype1asupernovaeathighredshifts)haveopenedupthepossibilityofempiricalsupportordisconfirmationofsomeinflationsce-narios.Theepistemologyofthisoptimistic,burgeoningbranchofphysicsisyetanotherfieldripeforphilosophicalanalysis.ConclusionThespecterhangingoverallfutureworkinthisfieldisquantumgravity.Itiswidelybelievedthatgeneralrelativityisinconsistentwithquantumfieldtheory;“quantumgravity”istheresearchprogramthatseeksathirdtheorythatunifies,oratleastmakesconsistent,thesetwotheories.Thoughnosuchtheoryyetexists,therearesomewell-developedapproachessuchasstringtheoryandcanonicalquantumgravityaswellassomelessdevelopedtheoriessuchastopologicalquantumfieldtheoryandtwistertheory;foraphilosophicalslant,seeCallenderandHuggett(2001)andreferencestherein.Webelieveitisfairtosaythatallofthesetheoriesarequiteradicalintheirimplicationsforspaceandtime.Ifanyofthem,orremotelysimilardescendents,succeed,theymaywellhavedramaticcon-sequencesforvirtuallyalloftheissuesdiscussedabove.194\nPhilosophyofSpace–TimePhysicsAcknowledgmentsFigures9.3and9.4arereproduced,withpermission,fromNedWright’sCosmologyTutorial(http://www.astro.ucla.edu/%7Ewright/cosmolog.htm).Notes1Whetherthisreallyspoilstherelationalambitionsofahypotheticalphysicssetinthemisadifficultquestion.Ifspace’sstructureisnothingmorethanwhatisimpliedbyallthedistance/anglerelationsbetweenphysicalthings–asoneformofrelationismholds–thenthegeometryofspacemustbeanempiricalmatter,notsomethingwecanfixapriori.2Actually,thereisafurtherelementofabsolutenessinGTR,namelythedemandthatthemetricfieldhavesignature(1,3)andhencebe“locally”likeMinkowskispace–time.SeeBrown(1997)foranilluminatingdiscussionofthisposit.3Infact,HartryField’s(1980)usesthepoint-manifold,interpretedrealistically,toeliminateplatonicentitiesfromthemathematicsofphysics.So,fromhisperspective,themanifoldisnotjustindispensableinGTR,butinallofphysicalscience.ReferencesArntzenius,F.andMaudlin,T.(2000):“TimeTravelandModernPhysics,”StanfordOnlineEncyclopediaofPhilosophy,http://plato.stanford.edu/entries/time-travel-phys.Bain,J.(2000):“TheCoordinate-Independent2-ComponentSpinorFormalismandtheConventionalityofSimultaneity,”StudiesinHistoryandPhilosophyofModernPhysics,31B,201–26.Barbour,J.(1999):TheEndofTime:TheNextRevolutioninourUnderstandingoftheUni-verse.London:Weidenfeld&Nicolson.Barbour,J.andBertotti,B.(1982):“Mach’sPrincipleandtheStructureofDynamicalTheories,”ProceedingsoftheRoyalSocietyofLondonA382,295–306.Belot,G.(1999):“RehabilitatingRelationalism,”InternationalStudiesinthePhilosophyofScience,13,35–52.Belot,G.Earman,J.andRuetsche,L.(1999):“TheHawkingInformationLossParadox:TheAnatomyofaControversy,”BritishJournalforthePhilosophyofScience,50,189–229.Bokulich,P.(2000):“BlackHoleRemnantsandClassicalvs.QuantumGravity,”availableatthePSA2000programpagehttp://hypatia.ss.uci.edu/lps/psa2k/program.html.Brown,H.(1997):“OntheRoleofSpecialRelativityinGeneralRelativity,”InternationalStudiesinthePhilosophyofScience,11,67–80.Brown,H.andPooley,O.(2001):“TheOriginoftheSpace–TimeMetric:Bell’s‘Lorentz-ianPedagogy’anditsSignificanceinGeneralRelativity,”inC.CallenderandN.Huggett(eds.),PhysicsMeetsPhilosophyatthePlanckScale,CambridgeUniversityPress,256–74.Alsoavailableatgr-qc/9908048.195\nCraigCallenderandCarlHoeferButterfield,J.(1989):“TheHoleTruth,”BritishJournalforthePhilosophyofScience,40,1–28.Callender,C.(1997):“Whatis‘TheProblemoftheDirectionofTime’?”PhilosophyofScience,Supplement,63(2),223–34.Callender,C.andHuggett,N.(eds.)(2001):PhysicsMeetsPhilosophyatthePlanckScale.NewYork:CambridgeUniversityPress.Callender,C.andWeingard,R.(1995):“BohmianCosmologyandtheQuantumSmear-ingoftheInitialSingularity,”PhysicsLetters,A208,59–61.Callender,C.andWeingard,R.(2000):“TopologyChangeandtheUnityofSpace,”StudiesinHistoryandPhilosophyofScience,31B,227–46.Disalle,R.(1994):“OnDynamics,IndiscernibilityandSpaceTimeOntology,”BritishJournalforthePhilosophyofScience,45,265–87.Disalle,R.(1995):“SpaceTimeTheoryasPhysicalGeometry,”Erkenntnis,42,317–37.Duhem,P.(1954):TheAimandStructureofPhysicalTheory,trans.P.Wiener,Princeton,NJ:PrincetonU.P.Earman,J.(1970):“Who’sAfraidofAbsoluteSpace?”AustralasianJournalofPhilosophy,48,287–319.Earman,J.(1989):Worldenoughandspace–time:absoluteversusrelationaltheoriesofspaceandtime.Cambridge,Mass.:MITPress.Earman,J.(1995):Bangs,Crunches,WhimpersandShrieks:SingularitiesandAcausalitiesinRelativisticSpacetimes.NewYork:OxfordUniversityPress.Earman,J.(1996):“ToleranceforSpace–timeSingularities,”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list’sbeliefcontent,tellstheconstructiveempiricistwhathedoesnotbelieve,andmakesavailabletoallpartiestheunderstandingofatheoryconsti-tutedbyagraspofitstruthconditions.Interpretationcanpromotetheorydevel-opment:HowardSteinofferstheexampleofinterpretivequestionsabouttheether’sstateofmotioninMaxwelltheory,questionswhoseanswers“revolution-izedthetheoryanddeepenedourunderstandingofnatureveryconsiderably”(Stein,1972,p.423).Havingissuedthisapologyforinterpretation,thischaptersurveystheinter-pretationofquantumtheories.Itchroniclespasthighlights(pp.200–9);coverscurrentwork(pp.209–17);andpresentsfuturedirections(pp.217–21).Theremainderofthissectionsetsthestage.TheHeisenberg–Born–JordanmatrixmechanicsandSchrödinger’swavemechanicsweretwinformulationsofquantumtheorysofraternalittookvonNeumanntopinpointtheirrelation.Hecalledthestructuretheyshared“Hilbert1Space.”PurequantumstatesarenormedHilbertspacevectors;quantumobserv-ablesareself-adjointHilbertspaceoperators;oncetheHamiltonianoperatorHˆisprovided,Schrödinger’sequationdeterminesdynamicaltrajectoriesthroughstatespace.Becauseclassicalobservablesarefunctionsfromstatespaceelementstothereals,asystem’sclassicalstatefixesthevaluesofallclassicalobservablespertain-199\nLauraRuetscheingtoit.Inquantummechanics(QM),thisisnotso.Astate|yÒdoesnotingeneralfixthevalueofanobservableÂ;rather|yÒ,viatheBornRule,determinesaprobabilitydistributionoverÂ’spossiblevalues.InitsstandardHilbertspaceformulation,QMlackswhatI’llcallasemantics,anaccountofwhichobservableshavedeterminatevaluesonaquantumsystem,andofwhatthosevaluesareormightbe.Thequartet{statespace,observables,dynamics,semantics}characterizeswhatisorcanbetrueforatheoryovertime,andsoconstitutesaninterpretationofatheory.Correlatively,degreesoffreedomavailabletothoseengagedininterpre-tiveprojectsincludefreedomstoproposeandmodifymembersofthequartet.Onewaytoseethevenerabledebateaboutthenatureofspace(time)isasadebateabouthowbesttotuneclassicaltheory’sstatespace,observableset,anddynamicstooneanother.Butinterpretationscanbe–manyinterpretationsofQMare–effortsincreativephysics.BohrandComplementarityInterpretiveeffortscanalsoretardcreativephysics,asEinsteinfearedBohr’sphi-losophyofcomplementaritywould.Thedoctrineistoointricatetoexplicateinashortspace,soIwillsettleforlistingafewofitskeyelements,someofwhichpersistininfluence,byseemingtothoseworkingatpresenteithertodeserveexpli-cation,ortoconstituteexculpation.Bohrdeniesthatpositionandmomentumcanbesimultaneouslydeterminateonaquantumsystem.Positionandmomentumarewhathestylescomplementarymodesofdescription,“complementaryinthesensethatanygivenapplicationofclassicalconceptsprecludesthesimultaneoususeofotherclassicalconceptswhichinadifferentguiseareequallynecessaryfortheelucidationofthephenomenon”(1934,p.10).ForBohr,itisasthoughrealitywereastereoscopicimagewewereconstrainedtoviewoneeyeatatime.Thedoctrineoriginatesinaninsistenceontheuseofclassicalconcepts,whichBohrcouplestoanoperationalismgoverningtheiruse.Heobservesthattheexperimentalcircumstanceswarrantingtheuseofthemomentumconceptareincompatiblewiththosewarrantingtheuseofthepositionconcept.Theupshotisthecomplementarityofpositionandmomentumconcepts,representativesofthecomplementaryclassesofkinematic(thatis,spatio-temporal)anddynamic(thatis,subjecttoconservationlaws)concepts.Bohrtakestheposition-momentumuncertaintyrelationstoexpress–andbeexplainedby–thisdeeperprincipleofcomplementarity(1934,p.57);seealsoMurdoch(1987,2ch.3).Bohrrepeatedlyemphasizesthatthequantumofactioniscentraltothedoctrine.Butthequantumofactionseemstohavegonemissingfromtheforegoingrecon-struction.Oneplaceitmightlurkisaloopholethroughwhichasortofcounter-factualdiscoursemightsneak.Havingboltedourdiaphragmtothetable,wemay200\nInterpretingQuantumTheorieswithBohr’sblessingspeakofthepositionofanelectronpassingthroughourexperi-mentalarrangement.Couldwealso,andindefianceofcomplementarity,speakofitsmomentum,byappealtoexperimentalresultswewouldhaveobtained,hadweinsteaddangledourdiaphragmfromaspringbalance?Notiftheuncontrollableexchangeofthequantumofactionblockssuchextrapolation.Adisturbancetheoryofmeasurementfertilizesyetanotherrootofcomplementarity.ConsiderhowBohr’sphilosophycouldinteractwithlivingphysics.Aphysicscommunityembracingthephilosophyofcomplementaritywouldtherebyabandontheproject,declaredinconceivablebythedoctrineofcomplementarity,of“completing”QMbydevelopingatheorywhichdescribedthesimultaneouslydeterminatepositionsandmomentaofsystems.Einstein(Fine,1986,p.18)fearedthat“theHeisenberg-Bohrtranquilizingphilosophy–orisitreligion?–issodel-icatelycontrivedthat,forthetimebeing,itprovidesagentlepillowforthetruebelieverfromwhichhecannotveryeasilybearoused.”In1935,withPodolskyandRosen,heissuedawakeupcall.TheEinstein-Podolsky-Rosen(EPR)ArgumentBohrdeniesthatcomplementarymagnitudesaresimultaneouslydeterminate.Einstein,PodolskyandRosen(1935)arguethatquantumstatisticsthemselvesimplythatBohriswrong.Crucialtotheirargumentisthe“criterionofreality”:Ifwithoutinanywaydisturbingasystemwecanpredictwithcertainty...thevalueofaphysicalquantity,thenthereexistsanelementofphysicalrealitycorrespondingtothisphysicalquantity(Einsteinetal.,1935,p.777).(Itaketheconsequenttobeequivalentto“thisphysicalquantityhasadetermi-natevalue.”)Theyarguethattherearecircumstancesinwhichcomplementaryobservablessatisfytherealitycriterion.Theirkeymoveistoconsiderquantumstatesofcompositesystemsinstitutingcorrelationsbetweenobservablespertainingtocomponentsubsystems.Bohm(1951)reformulatestheargumentforapairofelectronsinthespinsingletstate:1YÒsinglet=()ÆÒ¨Ò-¨ÒÆÒIIIIII(10.1)2Although(10.1)expresses|yÒsingletintermsofeigenstates|ÆÒand|¨Òofthex-componentofspinsˆx,|yÒsingletassumesbiorthogonalformfor,andinstitutesperfectcorrelationsbetween,sˆneigenstatesofthetwosystemsforalln.Thus,|yÒsingletassignsBornruleprobability1totheexperimentalresultthattheout-comesofsˆnmeasurementsonsystemsIandIIdisagree.EPRconsiderapairofelectronspreparedin|yÒsingletandsenttolaboratoriesremotefromoneanother.201\nLauraRuetscheMeasuringsˆxonsystemIaffordstheprediction,withcertainty,thatansˆxmea-surementperformedonsystemIIwillyieldtheoppositeresult.TheremotenessofthelaboratoriesensuresthatameasurementonsystemIcannotinanywaydisturbsystemII–providedtheuniverseis“local”inawaythatrendersdistanceanassuranceofisolation.Bytherealitycriterion,then,sˆxonsystemIIisanelementofreality.EPRcouldwellhavestoppedhere(Fine,1986,ch.3)mustersevidencethatEinsteinwishestheyhad).Theyhaveshownthat,forthosewhowouldwith-holddeterminatenessfromthequantumrealm,itisasthoughthespinmeasure-mentinfirstlaboratory,instantaneouslyandatadistance,bringsintobeinganelementofrealityinthesecondlaboratory.ButEPRcontinue.WemightratherhavemeasuredsˆyonsystemI.|yÒsingletanti-correlatessˆyeigenstatesjustaswellasitanticorrelatessˆxeigenstates.Byparityofreasoning,inthiscounterfactualsituation,sˆyonsystemIIwouldbeanelementofreality.EPRagainappealtolocalitytoconcludefromthisthatsˆyonsystemIIisanelementofreality–otherwise“therealityof[sˆx]and[sˆy]dependontheprocessofmeasurementcarriedoutonthefirstsystem,whichdoesnotdisturbthesecondsysteminanyway.Noreasonabledefinitionofrealitycouldbeexpectedtopermitthis”(Einsteinetal.,1935,p.780).(Bohr’sreplytoEPRistopermitwhattheydeemimpermissible:thenonlocaldependenceofsystemII’smattersoffactonsystemImanipulations.Thereis“noquestionofamechanicaldistur-bance,”Bohrwrites,butthereis“thequestionofaninfluenceontheverycon-ditionswhichdefinethepossibletypesofpredictionsregardingthefuturebehaviorofthesystem”(Bohr,1935,p.699).)Becausethecorrelations|yÒsingletinstitutesarethoroughgoing,iftheEPRargumentworks,itworksforeveryspinobserv-able.Thoseconvincedbytheargumentshouldundertaketheprojectof“com-pleting”QM,forinstance,bydevisingatheorywhichattributesadeterminatevaluetoeveryelementofrealityestablishedbytheEPRgambit,atheorywhichmoreoverrespectsa“locality”requirementofthesortEPRexploit.(Thosecon-vincedabinitiothattheprojectofcompletingQMisworthundertakingneedn’tbeconstrainedbylocality,orbyreconstitutingrealityEPRelementbyEPRelement.)OneofJohnBell’sgroundbreakingcontributionstothefoundationsofQMwastobring“local”hiddenvariabletheories(HVTs)incontactwithempir-icaldata.Bell’sTheoremandOtherNo-GoResultsBell’stheoremshowsthatlocalHVTsarecommittedtosetsofstatisticalpredic-tionsknownasBellInequalities.InsofarasthereexistquantumstatespredictingtheviolationoftheInequalities,Bell’stheoremsetsupacrucialtestoflocalHVTsvs.standardQM.ExperimentupholdsQM,violatestheInequalities,andfalsifieslocalHVTs.Thefieldissetforthegameofexperimentalmetaphysics.Toplay,showhowtoderiveBellInequalitiesfromasetofpremisesbearingphilosophically202\nInterpretingQuantumTheoriesfraughtnames(“determinism,”“completeness,”“locality”).ObservethattheexperimentalviolationoftheInequalitiesrevealsatleastoneofthesepremisestobefalse.Invokingpriorsofvarioussorts,singleoutleadingsuspects.Thelitera-tureisvast;seeCushingandMcMullin(1989)forasample.Inthissection,I’llreviewafewofitsdefiningmoments,expressaconcernthatlocalityisaredherring,andtouchuponquestionstheviolationoftheBellInequalitiesraisesaboutthenatureofexplanation.TheBellinequalitiesLiketheEPRargument,Bell’s(1964)theoremconcernsdistantcorrelationsestab-lishedby|yÒsinglet.InBell’sversionoftheexperimentalsetup,thedistantdevicesneednotmeasurethesamecomponentofspin.ThusthegenericoutcomeofaBellcorrelationmeasurementis(x,y|a,b)wherex,yŒ{+,-}aretheoutcomesofmeasurementsofspincomponentssˆa,sˆbonparticlesIandIIrespectively.The12Bornruleprobability|yÒsingletassigns(x,y|a,b)is/2sinqab/2,whereqabistheanglebetweenorientationsaandb.ConsiderhowaHVTmighthandlesuchprobabil-ities.Letldenoteacompletesetofparametersbywhichsuchatheorycharac-terizesthestateofaphysicalsystem;letLdenotethefullsetofsuchstates.LetPrl(x,y|a,b)betheprobabilitythehiddenstatelassignstheexperimentalresult(x,y|a,b).So-calleddeterministicHVTscountenanceonlyprobabilitiesof1or0;stochasticHVTscountenancenon-trivialprobabilities.AquantumsystemhasahiddenstatelŒL,weknownotwhich;anormalizedprobabilitydensityr(l)overLencodesourignorance.ToobtaintheempiricalprobabilityforaBell-typemeasurementoutcome,aHVTintegrates,overthesetL,theprobabilitieseachlassignsthisoutcome,weightedbythedensityr(l):Pr()xyab,,=ÚPrl()xyab,,rll()d(10.2)LToderivetheBellInequalities,oneimposesadditionalconstraintsontheHVT’sprobabilityassignment.Appealingbroadlytointuitionsaboutlocality,Bellrequiredthejointprobabilitytofactorizeintoprobabilitiesforoutcomesoneachwing,whichprobabilitiesconditionalizeonlyonsettingspropertothatwing:Prll()xyab,,=Pr()xa¥Prl()yb(10.3)3HVTsobedienttothefactorizationcondition(3)obeytheInequality-£++1Pr(),,,,ab,++Pr()+¢ab,++Pr()+¢¢ab,-+Pr()+¢ab,-+Pr()ab-+Pr()£0(10.4)ThisisaBellInequality.Therearequadruplesoforientations(a,a¢,b,b¢)–forinstance(p/3,p,0,2p/3)–forwhichstandardQMpredictsitsviolation.Uphold-ingstandardQM,experimentfalsifieslocalHVTs.203\nLauraRuetscheForthepurposesofprobinglocality,thefactorizationconditionisblunt.Inhis1983dissertation–Jarrett(1986)providesaprécis–JohnJarrettsharpenedit,bydemonstratingitsequivalencetothepairofconditions:Prll()xab,=Pr()xa(JarrettLocality)Prll()xaby,,,=Pr()xab(JarrettCompleteness)ThefirstexpressesthedesideratumthattheoutcomeofaparticleImeasurementbeindependentofdetectorII’ssetting(ergoShimony’s(1984b)label:“parame-terindependence”).Jarrettequatesittoaprohibitiononsuperluminalsignaling,whichprohibitionhesupposesthespecialtheoryofrelativity(STR)toissue.IfJarrettLocalityfails,bychangingthesettingofherdetector,aphysicistinlabo-ratoryIcansendinstantaneouslytolaboratoryIIasignalintheformofalteredmeasurementstatistics(Shimonycallsthis“controllablenon-locality”oraction-at-a-distance).JarrettCompletenessexpressesthedesideratumthattheoutcomeofaparticleImeasurementbeindependentoftheoutcomeofaparticleIImea-surement(ergoShimony’slabel:“outcomeindependence”).Becausethelabora-toryIphysicisthasnocontroloverlaboratoryIIoutcomes,shecannotexploitbreakdownsinJarrettlocalitytosignal(Shimonycallthis“uncontrollablenon-locality”or“passion-at-a-distance”).TheviolationoftheBellInequalitiesimpliesthatoneoftheassumptionsgen-eratingthemmustbefalse.Havingfurnishedhisfactorizationof(10.3),andsup-posingourcommitmenttothespecialtheoryofrelativitytheorytocommitus,atleastmorally,toJarrettLocality,JarrettfingersCompletenessastheculprit(1986,p.27).Settingl=|yÒ,standardquantummechanicsitselfcanbecastasastochastichiddenvariabletheoryviolatingcompleteness:|yÒsingletmakesparticleIprobabilitiessensitivetoparticleIIoutcomes.Itappearsthatthequantumdomainisruledbypassion-at-a-distance.EnlistingaLewis-stylecounterfactualanalysisofcausation,Butterfield(1992)hasarguedthatthisviolationofJarrettcompletenesssignalsacausalconnectionbetweendistantwingsoftheaparatus.Muchcarehasbeenlavishedonarticulatingrelativisticlocalityconstraintssuitedtothisstochasticsetting,sothatthequestionofwhetherQMandtheSTRcan“peacefullycoexist”(Redhead,1983)mightbesettledonceandforall.No-GoresultswithoutlocalityIwouldadvocatepostponingthequestion.STRdoesnotissuebansonsuperlu-minalcausation.Itdoesnotaddresscausationatall.Itratherrequiresofthatclassofspace–timetheoriesformulatedinMinkowskispace–timethattheybeLorentz-4covariant.Non-relativisticQM,whichisnotaspace–timetheory,isnotsubjecttoSTR’srequirements.SothequestionofwhetherSTRandQMcanpeacefullycoexistisill-posed.Anotherquestion–cantherebeLorentz-covariantquantumtheories?–iswell-posed.Quantumfieldtheory(QFT)associatesobservables204\nInterpretingQuantumTheories5Â(D)withregionsofspace–timeD.TheinhomogeneousLorentzgroupLisrepresentedontheHilbertspacewhichisthecommondomainoftheseobservablesbyagroupofunitaryoperatorsÛ(L).QFTsoformulatedisLorentzcovariantifftheobservablesassociatedwiththeLorentztransformLDofaregionDisthecorrespondingunitarytransformoftheobservablesassociatedwithD:AUˆ()LLDD=ˆ()()Aˆ(LC-QFT)ThatthereareQFTssatisfying(LC-QFT)shouldsettlethepeacefulcoexistencequestion.IntheQFTcontext,bansonsuperluminalsignalpropagationareexpressedbythemicrocausalityrequirementthatoperatorsassociatedwithspace-likeseparatedregionscommute(intuitively,itdoesnotmatterwhatordertheyactin).ThatthismicrocausalityrequirementisindependentoftherequirementofLorentzcovariancesuggeststhatthefolkloricconnectionbetweenSTRandtheprohibitiononsuperluminalsignalpropagationisonlythat.Bell’stheoremmaybeprofitablyanalyzedwithoutrecoursetolocalitynotionstenuouslylinkedtoSTR.Fine(1982a,b)showedthe(Clauser–Horneformof)theBellInequalitiestobeequivalentto1theexistenceofadeterministicHVT2theexistenceofjointdistributionsforallpairsandtriplesofobservables3theexistenceofastochasticHVTsatisfying(10.3).Intuitionsaboutlocalitymightmotivate(3),buttheyarenotdirectlyimplicatedineither(1)or(2),whichsimplyofferambitiouspatternsofdeterminatevalueassignment.Indeed,afamilyofargumentsoriginatingwithBell(1966–whichhewrotebeforethe1964BellInequalitiespaper)butrefinedbyKochenandSpeckerrevealsthattheprojectofassigningdeterminatevaluestosufficientlyrichsetsofobservablesisuntenable,ifthevalueassignmentissubjecttoprimafaciereason-ableconstraints.Here’saninformalsketchofBell’sversionoftheNo-Goresult;seeRedhead(1987,ch.5)formoredetailsandreferences.Consideraprojectofdeterminatevalueassignmentsatisfying(Spectrum)Ô’sdeterminatevalue[Ô]isoneofitseigenvaluesand(FUNC)IfÂ=f(Bˆ),then[Â]=f([Bˆ])InaHilbertspaceofdimensionthree,anytrio{Pˆi}ofmutuallyorthogonalpro-jectionoperatorsfurnishesaresolutionoftheidentityoperatorÎ:IPPPˆˆˆˆ=++123(10.5)205\nLauraRuetscheBytheSpectrumrule[Î]=1and[Pˆi]Œ{0,1}.The{Pˆi}commutepairwise;thereisthereforeanoperatorofwhicheachofthemisafunction.SotheFUNCrulerequires[]IPPPˆˆˆˆ=[]123+[]+[](10.6)Equations(10.5)and(10.6)togetherimplythatforanytrioofmutuallyorthog-onalprojectors,oneofthemwillbeassignedthevalue1whiletheothertwowillbeassignedthevalue0.Thisassignmentinducesalinear,normalizedmapfromthesetofprojectionoperatorsonHilbertspacetotheinterval[0,1]–indeedtotheset{0,1}containingonlytheendpointsofthatinterval.ThismapisalsoaprobabilitymeasureovertheclosedsubspacesofHilbertspace.AccordingtoGleason’stheorem,forHilbertspacesofdimensionthreeorgreater,allsuchprob-abilitymeasuresarecontinuous.Butthemapinducedbytheprojectofcompletedeterminatevalueassignmentisdiscontinuous–intuitively,asitsweepsthroughthesetofprojectors,itisgoingtohavetoleapfromaprojectoritmapsto0toaprojectoritmapsto1,withoutassigningintermediateprojectorsintermediatevalues.AHVTinducingsuchamapfromHilbertspaceoperatorstotheirdeter-minatevaluesisthereforeinconsistent.Bellneedsinfinitelymanyobservables–thefullsetofprojectionoperatorsonathree-dimensionalHilbertspace–togeneratethecontradiction.KochenandSpeckershowedthat117projectorsonafour-dimensionalHilbertspacecouldnotwithoutcontradictionbeassigneddeterminatevaluesobedienttotheFUNCandSpectrumrules;Bell–Kochen–Speckertypecontradictionsforeversmallersets6ofobservableshavebeenemergingeversince.Mermin’sexcellentpresentationofBell–Kochen–Speckerresults(1993)situatesoneversionoftheBellInequali-tiesamongthem.TheNo-GoargumentjustsketchedattributesPˆ1thesamedeterminatevaluewhetherit’sconsideredanelementoftheorthogonaltripleT={Pˆ1,Pˆ2,Pˆ3}oranelementofthedifferentorthogonaltripleT¢={Pˆ1,Pˆ¢2,Pˆ¢3}.Itassignsanon-maximalobservableanon-contextualvalue,thatis,onenotrela-tivizedtoaparticulareigenbasisoftheobservable.(Thequestionofcontextual-izingdoesnotariseformaximalobservables,whoseeigenbasesareunique.)Contextualizingdeterminatevalueassignments,onecanavertNo-Goresults,bywithoutcontradictionassigningPˆ1inthecontextofthebasisTavaluedifferentfromtheoneit’sassignedinthecontextofthebasisT¢.Whilesuchamovemightseemshamefullyadhoc,itispreciselythemoveBellmakesafterpresentinghisversionoftheNo-Goresult.Theargument,hewrites,“tacitlyassumedthatthemeasurementofanobservablemustyieldthesamevalueindependentlyofwhatothermeasurementsmustbemadesimultaneously”(Bell,1966,p.451).ToseewhatthisvaguelyBohrianpronouncementhastodowithcontextualism,andtoanticipateitsconnectionwiththeBellinequalities,considerthedramaticallynon-maximalcompositesystemobservableÎsˆx.Onewaytoselectaneigenbasisfromthemyriadavailableforthisobservableistospecifyaspinobservableforparticleone:forinstancesˆxsˆxhasauniqueeigenbasiswhich206\nInterpretingQuantumTheoriesisalsoaneigenbasisforÎsˆx.ToattributeÎsˆxanon-contextualvalueadmit-tingfaithfulmeasurementistoassumethataÎsˆxmeasurementhasthesameoutcomeregardlessofwhichparticleImeasurementismade.Seeingnoreasontosupposethatmeasurementoutcomesareingeneralinsensitivetomeasuringenvi-ronments,Bellrejectsthenon-contextualityrequirement.Whetherthis“judo-likemaneuver”(Shimony,1984a)ofinvokingBohrtoprotectambitiousplansofvalueassignmentsucceedsornot,itsuggestsaconnectionbetweenBell–Kochen–SpeckerargumentsandtheBellInequalities.ThelocalityassumptionsinvokedinderivingtheInequalitiesareaspeciesofanon-contextualityrequirement.Mermin(1993)showshowtouselocality-as-non-contextualitytoconvertaneight-dimensionalBell–Kochen–SpeckerresultintooneversionoftheBellInequalities.(WhatislostinthetranslationisthestateindependenceoftheBell–Kochen–Speckerresult;contradictionensuesintheconvertedcaseonlyforcertainstates.)Iwouldregardthisconversionasfurtherevidencethattofocusonlocalityistodistortthediscussion.WhatprecipitatesNo-Goresultsareoverambitiousplansofnon-contextualdeterminatevalueassign-ment,whetherthesystemsatissuearecompositeandspatiallyseparated,orsimple.Others(includingBell!)wouldsaythatitisonlyinthecaseswherelocalitymotivatestherequisitenon-contextualitythattheNo-Goresultshaveanybite.CorrelationandexplanationInarticulatinghisprincipleofthecommoncause,HansReichenbachheededtwentieth-centuryrevolutionsinphysics.Takingquantummechanicstoprecludedeterministiccausesandrelativitytoprecludenon-localones,heofferedcommoncausesascauseswhichactbothlocallyandstochastically.Roughly,whereAandBareeventscorrelatedinthesensethatPr()AB&πPr()A¥Pr()BtheircommoncauseCisaneventintheoverlapoftheirbackwardslightconesrenderingAandBprobabilisticallyindependentinthesensethatPr()ABC&=Pr()AC¥Pr()BCTheprincipleofthecommoncauseframesaninfluentialandintuitivelyattractiveaccountofexplanation.Correlations–forinstance,thecorrelationseffectedby|yÒsinglet–arewhatrequireexplanation;explanationproceedsbyspecifyingacommoncauseforthecorrelatedevents.Straightforwardlyappliedtoquantumcorrelations,theprinciplecomestogrief.Articulatedtoregulatedemandsforexplanationinthecontextofstatisticaltheories,theprinciple,appliedtotheperfect(anti)correlationsestablishedby|yÒsinglet,issatisfiedonlybydeterministiccommoncauses,thatis,CssuchthatPr(A|C),Pr(B|C)Œ{0,1}(vanFraassen,207\nLauraRuetsche1989).What’smore,theassumptionthattherearecommoncausesforcorrela-tionsobservedintheBellexperimentsimpliestheBellInequalities(vanFraassen,1989).ThusanytheorysatisfyingReichenbachiandemandsforexplanationwillbeempiricallyfalse.Explanatoryactivityadherestostandards:notalldemandsforexplanationarelegitimate;notallputativeexplanansaresatisfactory.Philosophersofsciencewouldliketotellthedifference.Onewaytotellthedifferenceis,asitwere,aheadoftime,byarticulatingatemplatetowhichscientificexplanationsalwaysandevery-whereconform.Takingthecommoncausalaccountofexplanationasjustsuchatemplate,Fine(1989)andvanFraassen(1989)presentitsquantumtravailsasevi-dencethatessentialismaboutexplanationismisplaced,thatexplanatorystrategiesarisewithinthevarioussciencesvariously.Butformany,thefeelingpersiststhatQM’scapacitytopredictcorrelationsfallsdramaticallyshortofacapacitytoexplainthosecorrelations.TheMeasurementProblemTheseNo-Goresultscanbereadasfableswhosemoralisthatweoughtnotbetooambitiousinascribingquantumobservablesdeterminatevalues.Onewaytomoderateourambitionistoadoptthesemanticstypicallyannouncedbytextbooks:[I]tisstrictlylegitimatetosaythatÔhasavalueinastate|yÒifandonlyifamea-surementofÔonthisstateiscertaintoyieldadefiniteresult–i.e.ifandonlyif|yÒcoincideswithaneigenvectorofÔ(Gillespie,1973,p.61).Althoughthiseigenstate/eigenvaluelinkavertsNo-Goresults,thereisanotherdebacleinstoreforit.AmeasurementisaninteractionbetweenanobjectsystemSandanapparatusRpreparedinitsreadystate|p0Ò,ideallyonethatestablishesaperfectcorrelationbetweeneigenstatesoftheobjectobservableÔandpointerobservablePˆ.Ifmeasurementisaquantummechanicalprocess,thiscorrelation-establishingevolutionshouldbeSchrödingerevolution,andsoimplementedbyaunitaryoperatorÛM:UopˆMi()ÒÒ0=ÒÒopii(10.7)Theright-handsideof(10.7)isthepost-measurementstate,astateinwhichboththeobjectandpointerobservableshavedeterminatevalues,accordingtotextbooksemantics;astateinwhichthepointervaluereflectsthevalueoftheobjectobserv-able.ThisconsolidatesthestatusofevolutiondrivenbyÛMasmeasurementevolution.ButconsiderwhathappenswhenanobjectsysteminitiallyinasuperpositionSici|oiÒofÔeigenstatesissubjecttoameasurementofthesortjust208\nInterpretingQuantumTheoriesdescribed.Toobtainthepost-measurementstateofthecompositesystem,applyÛMtothepremeasurementstate.UˆˆÈÂÂcopÒÒ˘=ÒÂcUop()Ò=ÒcopÒ(10.8)Mii00iMiiiiÎÍi˚˙ii(UseÛM’slinearitytomovefromthefirstexpressiontothesecond,and(10.7)tomovefromthesecondtothethird.)Unitarymeasurementleavestheobject+apparatussystemintheentangledstateSici|oiÒ|piÒwhichisnotaneigenstateofthepointerobservablePˆ.Accordingtotextbooksemantics,then,thepointerobservablehasnodeterminatevalue,andthemeasurementhasnooutcome.(Oneversion)ofthemeasurementproblemisthatifmeasurementprocessesobeythelawsofquantumdynamics,thenmeasurementsrarelyhaveoutcomes.CautiousenoughtoavoidNo-Goresults,textbooksemanticsaretoocautioustoaccommodatethemanifestandempiricallycentralfactthatexperimentshappen.IfQMasinterpretedbytextbooksemanticsweretrue,we’dbeunabletoconfirmit!Recognizingthisproblem,vonNeumann(1955[1932])respondedbyinvok-ingthedeusexmachinaofmeasurementcollapse,asudden,irreversible,discon-tinuouschangeofthestateofthemeasuredsystemtoaneigenstateoftheobservablemeasured.Accordingtothis(quiteorthodox–manytextsaccordthis“CollapsePostulate”axiomaticstatus)wayofthinking,reconcilingtextbooksemanticswiththedatumthatthereareempiricaldatarequiressuspendingunitarydynamicsinmeasurementcontexts,andinterpretingBornRuleprobabilitiesasprobabilitiesforcollapse.CollapseisaHumeanmiracle,aviolationofthelawofnatureexpressedbytheSchrödingerequation.Ifcollapseandunitaryevolutionaretocoexistinasingle,consistenttheory,situationssubjecttounitaryevolutionmustbesharplyandunambiguouslydistinguishedfromsituationssubjecttocol-lapse.Anddespiteevocativeappealstosuchfactorsastheintrusionofconscious-nessorthenecessarilymacroscopicnatureofthemeasuringapparatus,noonehasmanagedtodistinguishthesesituationsclearly.ContemporaryWorkInowhaveonhandmaterialsufficienttoframemuchrecentphilosophicalworkonQM.ThechallengeistoofferaninterpretationofthetheorywhichmakessenseofmeasurementoutcomeswithoutrunningafoulofNoGoresults.Suchaninterpretationwillhavetoreviseoneormoreofthefollowingnaiveidentifica-tions,thesetofwhichprecipitatesthemeasurementproblem:Quantumstatesarenormedvectors|yÒonaHilbertspaceH.Quantumobservablesareself-adjointoperatorsonH.QuantumdynamicsisunitarySchrödingerdynamics.Quantumsemanticsaregivenbytheeigenstate/eigenvaluelink.209\nLauraRuetscheTherevisionsthatrequiretheleastnewphysics,aresemanticrevisions;revisionswhichretainthestandardstatespacebutreconfigureitsdynamicaltrajectoriesaremoreradical;mostradicalofallarerevisionstothefundamentalstatespaceandobservablesetofQM.ArecurrentfeatureofinterpretationsofQMisthattheirconservativeexteriorshideradicalhearts.Changingthedynamics:TheGRWmodelTheGRWmodelofquantumprocesses(Ghirardi,RiminiandWeber,1986)–seealsoPearle(1989)–wouldavoidhavingtoreconcileSchrödingerandnon-SchrödingerevolutionbydispensingwithSchrödingerevolution.GRWoffersinitssteadamoregeneralformofstateevolution,towhichSchrödingerevolutionisnearlyapproximate.TheGRWequationofmotionforanisolatedquantumsystemsupplementstheusualunitarytermwithanon-unitaryterm.Theeffectofthisextratermis,rarelyandatrandom,butwithauniformprobabilitypersecond-15(10),tomultiplythesystem’sconfigurationspacestate|y(x)>byaGaussian-7(bellcurve)ofwidth10meters,thennormalize.TheresultofahitbyaGauss-iancenteredatx=qisawavefunction|yq(x)>localizedaboutq.Giventhataparticleinthestate|y(x)>ishitbyaGaussian,theGRWdynamicssettheprob-abilitythatit’shitbyaGaussiancenteredatx=qequaltotheBornRuleprob-2ability|y(q)|thatapositionmeasurementperformedonasysteminthestate|y(x)>hastheoutcomeq.Generally,whensystemsinteract,theircompositestatebecomesentangled.Forinstance,apurelyunitarysˆxmeasurementcouplingapointersystemcontainingNparticlestoanelectronininitialstatec+|Æ>+c-|¨>generatesthepostmea-surementstatenncx+Æ>ƒcc+-()Ò+icx¨>ƒ-()Òi(10.9)i=11i=thwhere|c±(x)>irepresentstheiparticleinapointerlocalizedaboutx=±L.Asthenumberofparticlesinthepointergrows,sotoodoestheprobabilitythatoneofthemexperiencesaGRWcollapse.Theentanglementof(10.9)ensuresthatmultiplyingthestateofanyparticleinthepointerbyaGaussiancenteredat+Lrendersthesecondtermontheright-handsidenegligible,andsoleavesthecompositesystemlocalizedabout+L.Becauseourmeasuringapparatuses(gener-ally)coupleamacroscopicnumberofsystemstogether,suchareductionisover-whelminglylikelytooccurpracticallyimmediatelyuponthecompletionofmeasurement.Thus,theGRWdynamicsimplythatthequantumstatesofindividualsystemswillalmostalwaysSchrödingerevolve,whilethequantumstatesofmacroscopicmeasuringapparatusesarealmostalwayshighlylocalized.ButthisdoesnotrenderGRWanunqualifiedsuccess.Itaccountsonlyformeasurementoutcomesrecordedinpositions.However,itmaynotbethatallmeasurementoutcomesareso210\nInterpretingQuantumTheoriesrecorded(Albert(1992,ch.5)presentsonewhich,primafacie,isnot).Andinadditiontomodifyingthedynamicsofthenaiveinterpretation,GRWmustmodifyitssemantics,andperhapsevenitsobservableset.ForGRWreductionsarenotreductionstostrictlylocalizedstates(thatis,states|j(x)ÒsuchthatforsomefiniteintervalD,ÚDj*(x)j(x)dx=1–recallthattherearenopoint-valuedpositioneigen-states).Rather,theyarereductionstostateswithinfinitetailsinconfigurationspace.Theproblemoftailsisthatadheringstrictlytotheorthodoxsemanticsmoti-vatingtheirpursuitofreduction,GRWcannotattributeeveninterval-valueddeter-minatepositionstoevensystemsinpost-reductionstatessuchas|yq(x)>.Relievingusofpeculiarmeasurementdynamics,GRWdoesnotsupplyourpointerswithdeterminatepositions.Apossiblerecourseistoliberalizeeigenstate/eigenvaluesemanticssothat“SystemSin|y(x)ÒislocalizedintheintervalD”istrueiffÚyy*()()xxxd1>-eD1where01particles,withwavefunctionsy(x1,...,x3N).Thensurf’sup3notin
butina3N-dimensionalconfigurationspacewhichitisnottemptingtoidentifywithphysicalspace.Naturalornot,theBohmtheoryissignificant.Byrefusingtoconstitutemattersoffactfromdeterminatequantumobservables,BohmnotonlycircumventstheusualNo-Goresults,butshowshowtheystackthedeckagainstthenon-quantumphysicistbyfoistinguponheraquantum-theoreticspaceofpossibilities.Changingthesemantics:ModalinterpretationsModalinterpretations–seeKochen(1985),Healey(1989),Dieks(1989),vanFraassen(1991)and,formorerecentwork,DieksandVermaas(1998)–wouldresolvetheMeasurementProblembymaintainingtheuniversalityofSchrödingerevolutionwhilerevisingtheeigenvector/eigenvaluelink.Astockexampleofamodalinterpretationexploitsthebiorthogonaldecompositiontheorem,accord-SRingtowhichanyvector|yÒinthetensorproductspaceHSHRadmitsadecompositionoftheformSRYÒ=Âcaii>bi>iwhere{ci}arecomplexcoefficients,{|ai>}and{|bi>}aresetsoforthogonalvectorsonHSandHRrespectively,andthesummationindexidoesnotexceedthedimen-2sionalityofthesmallerfactorspace.Iftheset{|ci|}isnon-degenerate,thenthisSRbiorthogonaldecompositionof|yÒisunique.Modalinterpretationsreplacetheorthodoxeigenvector/eigenvaluelinkwiththefollowingsemanticrule:SRIfYSÒ=iiica>biistheuniquebiorthogonaldecompositionofthestateofacompositeS+Rsystem,thensubsystemShasadeterminatevalueforeachHSobservablewitheigenbasis{|ai>},andsubsystemRhasadeterminatevalueforeach2HRobservablewitheigenbasis{|bi>}.|ci|givestheprobabilitythattheseobserv-ables’actualvaluesaretheeigenvaluesassociatedwith|ai>|bi>.Considertheunitarilyevolvedpost-measurementstateSR+Y>=Âcoii>pi>iTheeigenbasisofthepointerobservablePˆconspiresinitsbiorthogonaldecom-position.Bymodalsemantics,then,thepointerobservablePˆisdeterminateon213\nLauraRuetschetheapparatussystemaftermeasurement.Moreover,theprobabilitythatPˆ’sactualvalueispnisjusttheBornRuleprobability.Thuswouldmodalinterpretationsexplainwhattextbookinterpretationscannot:howmeasurementinteractionsobe-dienttothelawsofquantumdynamicsissuedeterminateoutcomescorroborat-ingquantumstatisticalpredictions.Fourproblemsforthisstockmodalinterpretationarelistedhere:(i)WhattosaywhenthebiorthogonaldecompositionisdegenerateIntheextremecasewhereHSandHRareeachofdimensionN>2and1SRYÒ=Âabii>>iNtheeigenbasisofeveryobservableonthecomponentsystemsconspiresinsomebiorthogonaldecomposition,andKochen–Speckercontradictionsthreaten.(ii)WhattosayaboutthedynamicsofpossessedvaluesAviableoption,onepreservingthestatusofthemodalinterpretationasaninterpretationthatsucceedsnotbydevelopingnewphysicsbutbyadjustingsemanticstoexistingphysicsis:nothing.Dickson(1998a)describesmodaldynamicswhicharedramaticallyunderdeterminedbytherequirementthattheyreturnsingletimeprobabilitiesconformingtotheBornRule,anddis-cussesthatunderdetermination.(iii)Whattosayaboutstatepreparation,thelaboratoryprocesseswherebyweassignstatestoquantumsystemsModalinterpretationscannotavailthemselvesofthestandardaccountthatmeasurementcollapseleavesthepreparedsystemintheeigenstateofthemeasuredobservablecorrespondingtotheeigenvalueobtained.Perhapsmodalinterpretationscanaccountforpreparationbyappealtoconditionalprobabilities:the“prepared”stateistheonemimickingthepost-preparationcompositestate’spredictionsforthepreparedsystem,conditionalonthe“outcome”ofthepreparation–Wessels(1997)treatspreparationalongtheselines.Adoptingstandardquantumexpressionsforconditionalprobabilities,modalinterpretationscantakethiswaywithpreparationatthecost,incertainsettings,ofviolatingtheMarkovconsistencyrequirementthatPr()ab=ÂPr()acii¥Pr()cbiwhere{ci}isanexhaustivesetofmutuallyexclusiveeventsintermediatebetweenaandb.Usingnon-standardconditionalprobabilities,modalinter-pretationsembarkonvaluestatedynamics,withtheclassofcandidatedynamicsnarrowedtothosethatmakesenseofpreparation.(iv)Whattomakeofnon-idealmeasurements(Albert,1992,appendix)Thesearemeasurementswhichfailtocorrelateeigenstatesofthedesignatedpointerobservablewithorthogonalstatesoftheobjectsystem,sothatthe214\nInterpretingQuantumTheoriespointereigenbasisfailstofurnishabiorthogonaldecompositionofthepost-measurementcompositestate.Bythebiorthogonaldecompositiontheorem,someapparatuseigenbasiswillfurnishabiorthogonaldecomposition,andobservableswiththiseigenbasis,notthepointerobservable,aredeterminateaftermeasurement,accordingtomodalsemantics.Perfectlyerror-freemea-surementsconfrontmodalintepretationswiththisproblem,andthereisaclassofobservableswhoseonlyerror-freemeasurementsareofthissort(Ruetsche,1995).Responsesto(iv)(andalso(i)and(iii))appealtodecoherenceprocesses–interactionsbetweenthepointeranditsenvironmentthattendtocorrelate11distinctpointereigenstateswithnearlyorthogonalstatesoftheenvironment.Thesuggestionisthatdecoherencecarriespostnon-idealmeasurementsystemsintostatesbiorthogonallydecomposedbyapparatusobservablescloseenoughtothedesignatedpointerobservablesthatoneneedn’tfret(BacciagaluppiandHemmo,1996).Becausedecoherenceisnotperfect,thisresponseleavesthemodalinterpretationwithitsownversionoftheproblemoftails,aproblemwhoseresolutionmightlieinthenow-familiarmaneuverofconstitutingmattersoffactfromsomethingotherthandeterminatequantumobservables.Relativestateformulations“Postulat[ing]thatawavefunctionthatobeysalinearwaveequationeverywhereandatalltimessuppliesacompletemathematicalmodelforeveryisolatedphysi-calsystemwithoutexception”(Everett,1983[1957],p.316),HughEverett’sRelativeStateFormulationpromisesaninterpretationaccordingtowhichthequantumstatedescriptioniscompleteandthequantumdynamicsareuniversal.Althoughtheentangledpost-measurementstateSR+Y>=Âcoii>pi>iassociatesnoÔ(Pˆ)eigenstateswiththeobject(apparatus)simpliciter,itcorrelatesÔandPˆeigenstateswithoneanother.ThisillustratesEverett’smoralthat“thestateofonesubsystemdoesnothaveanindependentexistence,butisfixedonlybythestateoftheremainingsubsystem”(1983[1957],p.316),sothat“itismeaninglesstoasktheabsolutestateofasubsystem–onecanonlyaskthestaterelativetoagivenstateoftheremainderofthesystem”(1983[1957],p.317).(Relativelyspeaking)whensystemShasdeterminateÔvalueon,systemRhasdeterminatePˆvaluepn,and“thiscorrelationiswhatallowsonetomaintaintheinterpretationthatameasurementhasbeenperformed”(1983[1957],p.320).S+RThusEverettpurportstoreconciletheuncollapsedcompositestate|y>withdeterminatemeasurementoutcomes.215\nLauraRuetscheButthetermsofreconciliationarenotoriouslyunclear.Anoptionproposedbyphysicistsbutembracedbythesciencefictioncommunityisthat“theuniverseisconstantlysplittingintoastupendousnumberofbranches,allresultingfromthemeasurement-likeinteractionsbetweenitsmyriadsofcomponents”(DeWitt,1970,p.161);withineachbranch,therelativestateofthepointerregistersadeterminateoutcome.CriticismsofthisversionofEverett(AlbertandLoewer,1988)includethatitsprofligatecreationofnewuniversesviolatestheconserva-tionofmass/energyrequiredbyunitaryevolution,andthatitmakeshashofquantumprobabilitiesbyrenderingeveryoutcomecertaintooccuralongsomebranch.What’smore,todisambiguatethisversionofEverett,itsproponentsmustfurnishanaccountofwhensplittingoccurs,andintowhatbranches.SuchanaccountwouldservealsoonthevonNeumanncollapseinterpretationtodistin-guishsystemssubjecttocollapsefromsystemsevolvingunitarily,renderingthatinterpretationconsistent,unambiguous,andfreeofsuspectmetaphysics.MorerecentEverett-styleinterpretationshaverespondedtothedisambigua-tionprobleminoneoftwobroadways.Themorefancifulnotesthatitis,afterall,onlyourdeterminateexperienceswhichmustbereconciledwithuniversalunitaryevolution,andsopostulates“eigenstatesofmentality”–brainstatestowhichcorrespondmentalstateswhosecontentsaredeterminatebeliefs–asapreferredbasisofrelativestates.PerhapsthemostastonishingvariationofthisapproachistheManyMindsinterpretation,aradicaldualismwhichinvitesustoSupposethateverysentientphysicalsystemthereisisassociatednotwithasinglemindbutratherwithacontinuousinfinityofminds;andsuppose(thisispartoftheproposaltoo)thatthemeasureoftheinfinitesubsetofthosemindswhichhappentobeinsomeparticularmentalstateatanyparticulartimeisequaltothesquareoftheabsolutevalueofthecoefficientofthebrainstateassociatedwiththatmentalstate,inthewavefunctionoftheworldatthatparticulartime.(Albert,1992,p.130)Amoreprosaicresponse(Griffiths,1993;Hartle,1990)tothedisambiguationproblemoffersconsistent(ordecoherent)historiesasthepreferedbasisofrelativestates.Atime-indexedsetofdeterminateobservablesgeneratesafamilyofhisto-riesforasystem;anindividualhistoryinthefamilyassignsobservablesinthetime-indexedsetdeterminatevalues.Giventheinitialstateofthesystemandtheunitaryoperatorgoverningitsevolution,ageneralizedBornRuleassignsprobabilitiestosuchhistories.Afamilyofhistoriesissaidtobeconsistentiftheprobabilitiessoassigneddonot“interfere”–roughly,theyareMarkovconsistent.Thushistoriesinaconsistentfamilyadmitmulti-timeprobabilityassignmentsthatconstituteatractabledynamics.TherubisthatwhiletheinitialstateandthesystemHamiltonianconstrainwhichfamiliesofhistoriesareconsistent,theydon’tdetermineauniquefamilyofconsistenthistories.So,whiletheremaybeaconsistentfamilyofhistoriesdeclar-ingthepointerobservabledeterminateatmeasurement’scompletion,therewill216\nInterpretingQuantumTheoriesalsobeotherconsistentfamilieswhichdonot.Whatassuresthataconsistentfamilycontainingthepointerobservable,andnotoneexcludingit,correspondstowhatactuallyoccursinthelaboratory?Brandingfamiliesofconsistenthistorieswhichfoilmergerintoafamilysatisfyingthenon-interferencecondition“complemen-tary,”GriffithsrejectsthisyenforreassuranceonbroadlyBohriangrounds:“Aquestionoftheform,‘Whichofthesereallytookplace?’askedintermsofcom-paringtwomutuallyincompatiblehistories,makesnosensequantummechani-cally”(Griffiths1993,p.2204).Liketheperspectivalmetaphysicsofthemanyworldsapproach,thisresponseisphilosophicallysuspect.YetEverett-styleapproachesarethepreferredquantumframeworkformanyworkingphysicists.Rovelli(1997)seesin“relationalQM”theseedsofasolutiontotheproblemoftimeinquantumgravity;Hartle(1990)putstheconsistenthistoriesapproach,andthetractable(ifperspectival)dynamicsitunderwrites,tocosmologicaluse.Meanwhile,interpretationsofQMmore12philosophicallyrespectablelanguishrelativelyunloved.Saundersoffersastarkdiagnosis:“ThedisturbingfeatureofboththeBohmandGRWapproachesisthattheyseemtorequirethatweredohighenergyphysics”(Saunders,1996,pp.125–6).Requiringapreferredtimefoliation,bothapproachesfundamentally(ifnotphenomenologically)violateLorentzandgeneralcovariance,andthusdeprivephysicistsofapowerfulcriterionforwinnowingdownthesetofacceptabletheo-ries.Thisshouldremindusatleastthatnon-relativisticQMisnottheonlygameintown–alessonthoseworkingonthefoundationsofquantumtheorieshaveincreasinglytakentoheart.FutureDirections:InterpretingQFTWithapologiestothosewhohavebeenworkinginthefieldforyears–foraveryrecentreview,seeHuggett(2000)–IofferQFT–andquantumgravity,atheoryaboutwhoseeventualshapeQFToncurvedspactimesmightholdaclue–asonefuturedirectionforthephilosophyofquantumtheories.Movingfromtheleasttothemostexoticspace–timesettings,thissectionsketchessomeissuesthatarekickedupbythepursuitofquantumtheoriesinsuchsettings.Minkowskispace–timeThepropersettingforquestionsabout“locality,”QFTisalsoaprovocativeone.AstrikingexampleistheReeh–Schliedertheorem,whichstatesthatwhere{A(O)}isthesetofobservablesthetheoryassociateswithanopenboundedregionofspace–timeOand|0ÒistheMinkowskivacuumstate,{A(O)|0Ò}isdenseinthetheory’sstatespace–thatis,anystatethetheoryrecognizescanbeapproximatedarbitrarilycloselybyactingonthevacuumbypolynomialcombinationsof217\nLauraRuetscheobservablesin{A(O)}.IfitwereappropriatetomodeleventsintheregionOasapplicationsofelementsof{A(O)}totheglobalvacuumstate,thiswouldmeanthatmachinationsinlocalregionscouldproducearbitraryapproximationsofarbitraryglobalstates!Themodelisnotapt,butitswhiffofnon-localityis.TheReeh–Schleidertheoremimpliesthat|0Òisaneigenstateofnoobservableasso-ciatedwithafinitespace–timeregion,whichinturnimpliesthatthevacuumspreadscorrelationsfarandwide.Redhead(1995)illuminatestheReeh–Schleidertheorembyexplicatinganalogiesbetweenhowthevacuumstandstolocalalgebrasofobservablesandhowthespin-singletstatestandstoalgebrasofspinobservablespertainingtothecomponentsystems.Cliftonetal.(1998)showthatstateswith|0Ò’sfeaturethatgivenanypairofspace–timeregions,anyobservablefromoneiscorrelatedwithsomeobservablefromtheother,aredense;Butter-field(1994)discussesthecapacityofsuchcorrelationstoviolateBell-typeinequal-ities(theycan,evenmaximally).Thenatureandextentofsuchnon-localfeaturesofQFT,aswellasthetheory’shospitabilitytocausaltalk,aretopicsofongoingresearch.ToseehowquestionsabouttheontologyofQFT,aswellasitsstatespace,arise,weneedtogointoabitmoredetail.Thecanonicalapproachtoquantiza-tioncastsaclassicaltheoryinHamiltonianform,thenpromotesitscanonicalobservablesqk,pktosymmetricoperatorsqˆk,pˆkobeyingcanonicalcommutationrela-tionsarisingfromthePoissonbracketsoftheclassicaltheory.Aclassicalfieldtheory.assignsafieldconfigurationj(x)andaconjugatemomentumdensityp(x)∫∂L/∂f(whereListhetheory’sLagrangiandensity)toeverypointxofspace–time;itsquantizationproceedsbyfindingoperatorsjˆ(x)andpˆ(x)obeyingtherelevant13canonicalcommutationrelations.Iwillreferinwhatfollowstoamathematicallywell-behavedexponentialformofthesecommutationrelationsknownastheWeylrelations,andcallsetsofoperatorssatisfyingthemrepresentationsoftheWeylrelations.AsimpleclassicalfieldistheKlein–Gordonfieldj(x),whichsatisfiesaba2()gm——-aj()x=0ItssolutionscanbeFourier-decomposedintouncouplednormalmodeswithangularfrequencywk,andsotheclassicalfieldcanbemodeledasaninfinitecollectionofindependentoscillators.Thetextbookroutetoquantizationexploits†thisanalogybyintroducingcreationandannihilationoperatorsâkandâkforfieldmodesobeying†††[]aaˆkk,ˆˆ¢==0[]aaaakk,ˆ¢¢,[]ˆk,ˆk=dkk¢Iˆ(10.10)Formalexpressionsforoperatorsjˆ(x)andpˆ(x)satisfyingthecanonicalcommuta-tionrelationscanbeconstructedfromthese.Theresultingquantizationisthefreebosonfield;imposinganti-commutationrelationsinlieuof(10.10)yieldsthefreefermionfield.218\nInterpretingQuantumTheoriesThestate|0>suchthatâk|0>=0forallkisthelowestenergyeigenstateofthe†nquantumHamiltonianforthefreebosonfield.Thestate(âk)|0>isaneigenstateoftheHamiltonianwiththesameenergyasystemofnparticleseachwithenergyhwkwouldhave–providedthemomentaandrestmassesoftheseparticlesaregivenbystandardrelativisticexpressions.Thus,thetheorytemptsaparticleinterpretation:•thevacuumstate|0>isthenoparticlestate†•thestateâk|0>describesoneparticleofenergyhwk....†•Nˆk=âkâkisthenumberoperatorforparticlesoftypek•Naˆ=ˆˆ†aisthetotalnumberoperatorjjjandsoon.Counteringthistemptationinthefirstinstancearesomedistinctlyunparticulatefeaturesofthetheorysointerpreted(Teller,1995,ch.2).Foronething,thetheoryhostsstateswithindeterminateparticlenumbers.Foranother,evenstateswhichareeigenstatesofthetotalnumberoperatorareconstrainedby(10.10)tobesymmetric–thatistobeunchangedunderpermutationsofpar-ticlelabels.Whetherthis,andtheirensuingobediencetoBose-Einsteinstatistics,deprivesbosonsofthegenidentityonemightexpectfromparticleshasbeenatopicoflivelydebate,well-representedinCastellani(1998).Apriorchallengetotheviabilityofparticleinterpretationshasexcitedsome-whatlessinterestamongphilosophers.Considertwoquantumtheories,eachtakingtheformofaHilbertspaceH,andacollectionofoperators{Ôi}.Whenarethesetheoriesphysicallyequivalent?Anaturalcriterionofequivalenceisthatthetheoriesrecognizethesamesetofstates,thatis,probabilitydistributionsovereigenprojectionsoftheirobservables.AndasufficientconditionforthisisthatthetheoriesbeunitarilyequivalentinthesensethatthereexistsaunitarymapÛ:H-1ÆH¢s.t.ÛÔ¢iÛ=Ôiforallvaluesofi,inwhichcasetheexpectationvaluesassignedobservables{Ôi}byanystate|yÒinthefirsttheoryareduplicatedbythoseassigned{Ô¢i}bythestateÛ|yÒinthesecond.Iftheobservablesetisrichenough,unitaryequivalenceisnecessaryaswell.Ifphysicalequivalenceisunitaryequiva-lence,thequantizationofaclassicaltheoryyieldsauniquequantumtheoryifandonlyifallrepresentationsoftherelevantWeylrelationsareunitarilyequivalent.TheStone–VonNeumanntheoremensuresthatrepresentationsofWeylrelationsexpressingthequantizationofaclassicaltheorywithafinitedimensionalstatespaceareuniqueuptounitaryequivalence.Butclassicalfieldshaveinfinitelymanydegreesoffreedom.TheStone–VonNeumanntheoremdoesnotapply.Indeed,theWeylrelationsencapsulatingthequantizationofclassicalKlein–Gordontheoryadmitcontinuouslymanyinequivalentrepresentations.††Let{âk,âk}beonequantizationofsomeclassicalfieldtheory,and{â¢k,âk¢}beanother,unitarilyinequivalenttothefirst.Ingeneral,theprimedvacuumstatewillnotbeastateintheunprimedrepresentation,norwilltheprimedtotalnumberoperatorbeanoperatorthere,andmutatismutandis.Onemightsaythatassociatedwiththeunitarilyinequivalentquantizationsareincommensurable219\nLauraRuetscheparticlenotions.Evengrantingthatitisappropriatetorunaparticleinterpreta-†tionofaquantization{âk,âk},onecannotrunasensibleparticleinterpretationofQFTunlessonecanprivilegeasphysicalaunitaryequivalenceclassofrepresenta-tionsadmittingparticleinterpretations–asSaunders(1988)discusses,notalldo.ThedefaultsettingforaQFTisMinkowskispace–time.Andthisfurnishesadefactocriterionofprivilege:physicalrepresentationsrespectthesymmetriesofthespace–time,inthesensethattheirvacuaareinvariantunderitsfullisometrygroup.Coupledwiththerequirementthatphysicalrepresentationsadmitonlystatesofnon-negativeenergy,thissinglesoutaunitaryequivalenceclassofrep-resentations.Butthisstrategyforprivilegebreaksdowningenericcurved14space–timesettings,whichdonotsupplythesymmetriesitrequires.Thealgebraicapproachtoquantumtheoriesgroundsanentirelydifferentresponsetounitarilyinequivalentrepresentations.Thealgebraicapproacharticu-latesthephysicalcontentofatheoryintermsofanabstractalgebraA.Observ-ablesareelementsofA,andstatesarenormed,positivelinearfunctionalsw:AÆ.TheexpectationvalueofanobservableAŒAinstatewissimplyw(A).AbstractalgebrascanberealizedinconcreteHilbertspaces.Amappfromele-mentsofthealgebratothesetofboundedlinearoperatorsonaHilbertspaceHfurnishesaHilbertspacerepresentationofthealgebra.Inparticular,allHilbertspacescarryingarepresentationoftheWeylrelationsarealsorepresentationsoftheabstractWeylalgebra.Forthealgebraist,“[t]heimportantthinghereisthattheobservablesformsomealgebra,andnottherepresentationHilbertspaceonwhichtheyact”(Segal,1967,p.128).Inequivalentrepresentationsneednotpuzzlehim,forconceivingthestatespaceofaquantumtheoryasthespaceofalgebraicstates,hehasrenderedunitaryequivalenceaninappropriatecriterionofphysicalequivalence.(Earlyproponentsofthealgebraicapproachconcoctedbaldlyoperationalistmotivationsforalternativeglossesonphysicalequivalence;seeSummers(1998)forareview.)Norneedhetroublewithparticles,forparticlenotionsare(atleastprimafacie)theparochialresiduesofconcreterepresentations.StandardquantumstatesareprobabilitymeasuresoverclosedsubspacesofHilbertspace.Theclassofalgebraicstatesisbroaderthantheclassofsuchprobabil-itymeasures.Thereare,forinstance,algebraicstateswhichcanaccomplishwhatnoHilbertspacestatecan:theassignmentofpreciseandpunctalvaluestocontinuousobservables(Clifton,1999).Somewouldadvocaterestrictingadmissablealgebraicstates.ArestrictionthatlooksdowntheroadtoquantumgravityistheHadamardcondition,whichrequiresadmissablestatetobestatesforwhichaprescriptionassigningthestress-energytensoranexpectationvaluesucceeds.(Provocatively,inclosedspace–timessuchstatesformaunitaryequivalenceclass(Wald,1994,§4.6).Bothmathematicalandphysicalfeaturesofalgebraicstatesmerit,andarereceiving,furtherattention,attentionwhichshouldinformdiscussionaboutthestatespace,andmaybeeventheontology,appropriatetoQFT.220\nInterpretingQuantumTheoriesCurvedspace–timeDifferentnotionsofstatedemanddifferentdynamicalpictures.HilbertspacedynamicsareimplementedbyunitaryHilbertspaceoperators.HavingjettisonedHilbertspacesasessentialtoQFT,thealgebraisthasjettisonedaswellthisaccountofthetheory’sdynamics.Initsstead,heimplementsquantumfielddynamicsbymeansofautomorphismsoftheabstractalgebraAofobservables(thatis,structure-preservingmapsfromAtoitself).Aquestionofequipollencearises:isitthecasethateverydynamicalevolutionimplementablebyanautomorphismontheabstractalgebraisalsoimplementableasaunitaryevolutioninsomefixedHilbertspace?AlgebraicevolutionbetweenCauchyslicesrelatedbyisometriescanbeimplementedunitarily,butmoregeneralalgebraicevolutioncannotbe;seeArageorgisetal.(2001)fordetails.Onemoralwemaydrawfromtheseresultsisthatinexactlythosespace–timeswhosesymmetriesfurnishprinciplesbyappealtowhichaunitaryequivalenceclassofrepresentationsmightbeprivileged,dynami-calautomorphismsareunitarilyimplementable.Inmoregeneralsettings,thealge-braicformulationisbettersuitedtocapturingthetheory’sdynamics.Unitaritybreaksdownevenmoredramaticallyintheexoticspace–timesettingofanevaporatingblackhole.Hawkinghasarguedthatapuretomixedstatetran-sition–thesortoftransitionvonNeumann’scollapsepostulateassertstohappenonmeasurement–occursinthecourseofblackholeevaporation.Notonlyuni-taritybutalsosymmetriesoftimeandpre/retrodictionarelostifHawkingisright.Belotetal.(1999)reviewreactionstotheHawkingInformationLossParadox;nottheleastofthemanyquestionstheHawkingparadoxraisesishowtopursueQFTinnon-globallyhyperbolicspace–times.QuantumgravityTheQFTsdiscussedsofararefreefieldtheories,whereastheQFTsbroughtintocollisionwithdatafromparticleacceleratorsareinteractingfieldtheories,whoseempiricalquantititesarecalculatedbyperturbativeexpansionsofthefreefield.Thedivergenceoftheseexpansionscallsfortheartandcraftofrenormalization,chronicledinTeller(1995,chs6and7).Cushing(1988)arguesthatthis(andeveryother!)featureofQFTraisesnot“foundational”but“methodological”issues.Insofarasmethodologicalpredilectionsareaffectedbyfoundationalcom-mitmentsandaffecttheshapeoffuturetheories,thetwodomainsmightnotbesocleanlyseparableasCushingsuggests;ongoingworkonQuantumGravityisoneplacetolookfortheirentanglement.Notes1SeeHughes(1989,pt.I)foranintroduction.Asspacelimitationsprohibitevenarudimentaryreview,Iattemptinwhatfollowstominimizetechnicalapparatus.2Suchexplanationhasitslimits.Considersˆxandsˆy,perpendicularcomponentsof221\nLauraRuetscheintrinsicangularmomentumorspin.Theyobeyuncertaintyrelations,andtheirmeasurementrequiresincompatibleexperimentalapparatus.Yetspinisexplicitlyandinfamouslyaquantumphenomenon,andsˆxandsˆyareindividuallyconserved.Theyarenotclassicalconceptsprecludingoneanother’sapplication,noroccupantsdiffer-entsidesofthekinematic/dynamicdivide.3Foraderivation,whichissimplyamatterofbringingahometruthaboutsumsof1sand-1stobearuponprobabilitiestheHVTassigns,seeRedhead(1987,pp.97–8).ThisformofBellInequalityappliestobothdeterministicandstochasticHVTs.Apar-ticularlysimplederivationofaBellInequality,duetoWigner,appliestodeterminis-ticHVTsrequiringperfect(anti-)correlation;seeHughes(1989,pp.170–2).OnecanderiveBell-typeinequalitieswithouttheintermediaryofhiddenvariables,pro-videdoneassumesthatjointprobabilitydistributionsfornon-commutingobservablesarewell-defined;seeRedhead(1987,pp.81–3)forthisStapp-Eberhardformoftheinequalities.4Maudlin(1994)discussesSTR’srealandimaginedimplications,andtheconstraintstheyplaceontheinterpretationofQM.5Conventionallydenotedbythesameletteras,butnottobeconfusedwith,thespaceofhiddenvariablestates.6Bub(1997)givesathoroughreview,andpresentsBubandClifton’strend-bucking“Go”theorem,whichcharacterizesthelargestsetofobservablesthatcanwithoutcon-tradictionbeattributeddeterminatevaluesobedienttotheSpectrumandFUNCrules.7Sosettingealsohastherepercussionsthatourdiscourseaboutlocalizationfeaturesodditiesreminiscentofdiscourseinvolvingvaguepredicates.Forinstance,eachofapairofpredicates(“islocalizedinD”and“islocalizedinD¢”)canbetrueofsomesystemSwithouttheirconjunction(“islocalizedinDD¢”)beingtrueofS.Whetherwecanlivewiththisisatopicofongoingdebate;see,forinstance,CliftonandMonton(1999).8TheanalogiespliedinBohm’soriginalpresentationinvokeaquantumpotentialwithdisquietingfeatures;Dürretal.(1996)attempttoeliminatethisinvocationbyshowinghowthevelocityfunctionissuggested(ifnotimplied)bysymmetryconsiderationsalone.9Vink(1993)extendsBohm’sapproachtoassigneveryobservableadeterminatevalue(albeitacontextualone),andofferforthosepossessedvaluesageneralizationofBohmiandynamicswhichisstochasticwhentheobservablesarediscrete.10Valentini(1991)wouldliketounifiytheroleofy(xi)intheBohmtheorybyprovinga“quantumH-theorem”accordingtowhicharbitraryinitialdistributionsevolveunder2theinfluenceoftheBohmianequationsofmotiontothedistribution|y(xi)|.Thiswouldrenderthedistributionpostulateotiose.Dickson(1998b,pp.123–5)offerscriticismsofValentini’sapproach.11Zurek(1982)offerstoymodelsofdecoherenceprocesses,aswellastheclaimthatdecoherencesolvesthemeasurementproblem.Anapparatusentanglednotonlywiththeobjectsystembutalsowithitsenvironmentisstillentangled,andnotasystemtowhicheigenstate/eigenvaluesemanticsattributedeterminatevalues.Torespondtothemeasurementproblem,decoherenceproposalsneedtobeaccompaniedbynon-standardsemantics.Modalsemanticsworkadmirably.12ButseeHuggettandWeingard(1994)forBohmianapproachestoQFTs,andPearle(1992)forLorentz-invariantquantumfieldversionofcontinuousspontaneouslocalization.222\nInterpretingQuantumTheories13Mathematicalnicetydemandsthatthequantumfieldbecastnot(astheforegoingsuggests)asamapfromspace–timepointstooperators,butasoperator-valueddis-tributionsoverspace–timeregions.Wald(1994)isanexcellentintroductiontothisandotherissuesdiscussedinthissection.14Notoriously,itevenbreaksdowninasubsetofMinkowskispace–time.PositiveenergystatescorrespondtosolutionstotheKlein–Gordonequationthatoscillatewithpurelypositivefrequency.StatesinthestandardMinkowskirepresentationarepositivefre-quencywithrespecttotimeasmeasuredbyfamiliesofinertialobservers.Butrestrict-ingourattentiontotherightRindlerwedgeoftwo-dimensionalMinkowskispace–timesettingc=1,thisistheregionwherexispositiveand|x|