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Synthese Library 467 Studies in Epistemology, Logic, Methodology, and Philosophy of Science Ralph Jenkins A Protocol-theoretic Framework for the Logic of Epistemic Norms Synthese Library Studies in Epistemology, Logic, Methodology, and Philosophy of Science Volume 467 Editor-in-Chief OtávioBueno,DepartmentofPhilosophy,UniversityofMiami,CoralGables,USA EditorialBoardMembers BeritBrogaard,UniversityofMiami,CoralGables,USA AnjanChakravartty,DepartmentofPhilosophy,UniversityofMiami,CoralGables, FL,USA StevenFrench,UniversityofLeeds,Leeds,UK CatarinaDutilhNovaes,VUAmsterdam,Amsterdam,TheNetherlands DarrellP. Rowbottom,DepartmentofPhilosophy,LingnanUniversity,TuenMun, HongKong EmmaRuttkamp,DepartmentofPhilosophy,UniversityofSouthAfrica,Pretoria, SouthAfrica Kristie Miller, Departmentof Philosophy,Centre for Time, University of Sydney, Sydney,Australia The aim of Synthese Library is to provide a forum for the best current work in themethodologyandphilosophyofscienceandinepistemology,allbroadlyunder- stood.Awidevarietyofdifferentapproacheshavetraditionallybeenrepresentedin theLibrary,andeveryeffortis madetomaintainthisvariety,notforits ownsake, butbecausewebelievethattherearemanyfruitfulandilluminatingapproachesto thephilosophyofscienceandrelateddisciplines. Specialattentionispaidtomethodologicalstudieswhichillustratetheinterplay of empirical and philosophical viewpoints and to contributions to the formal (logical,set-theoretical,mathematical,information-theoretical,decision-theoretical, etc.) methodology of empirical sciences. Likewise, the applications of logical methodstoepistemologyaswellasphilosophicallyandmethodologicallyrelevant studies in logic are strongly encouraged.The emphasis on logic will be tempered by interest in the psychological,historical, and sociologicalaspects of science. In additiontomonographsSyntheseLibrarypublishesthematicallyunifiedanthologies and edited volumes with a well-defined topical focus inside the aim and scope of the book series. The contributionsin the volumes are expected to be focused and structurally organizedin accordancewith the centraltheme(s), and should be tied togetherbyanextensiveeditorialintroductionorsetofintroductionsifthevolume isdividedintoparts.Anextensivebibliographyandindexaremandatory. Ralph Jenkins A Protocol-theoretic Framework for the Logic of Epistemic Norms RalphJenkins CUNYCityCollegeofNewYork NewYork,NY,USA ISSN0166-6991 ISSN2542-8292 (electronic) SyntheseLibrary ISBN978-3-031-08596-3 ISBN978-3-031-08597-0 (eBook) https://doi.org/10.1007/978-3-031-08597-0 ©SpringerNatureSwitzerlandAG2022 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland ForLouie,whosepurewarmth,attentiveness, andconstantcompanionshiphavebeen intertwinedwiththisprojectfromits inception,and whoseabsenceis an unrecoverableloss. Preface Epistemicrationalityisfundamentallyaregulativeconcept;thepointofitisguiding thedeliberatecontrolofepistemicaction.Thismeansthatepistemicnormssharean underlyingproceduralstructurewithplans,programs,oralgorithms,andthelogical investigation of epistemic norms should reflect this procedural structure. This, in short,isthesetofideasthatmotivatetheprojectofwhichthisbookisapart. This bookdefinesa logicalsystem called the Protocol-theoreticLogicof Epis- temicNorms(PLEN),itdevelopsPLENintoa formalframeworkforrepresenting and reasoning about epistemic norms, and it shows that PLEN is theoretically interesting and useful with regard to the aims of such a framework. In order to motivate the project, I defend an account of epistemic norms called epistemic proceduralism.Thisistheviewthat,invirtueoftheirindispensable,regulativerole incognitivelife,epistemicnormsarecloselyintertwinedwith—ifnotreducibleto— proceduralrulesthatrestrictepistemicactions,procedures,andprocesses.Epistemic proceduralismisanabstract(orformal)andcomprehensivetheory;it’satheoryof thestructure(orcontent),regulativefunction,andlogicofepistemicnorms,without commitmentto any specific list of norms or accountof the structure of epistemic states(i.e.,fullbelief,acceptance,partialbelief,...).Inotherwords,itdoesn’ttry to tell us what the norms for (e.g.) belief change are; it providesa frameworkfor reasoningaboutthekindsofthingsthatnormsforbeliefchangeareandhowthey work. Nonetheless, the defense of the abstract theory does appeal to substantive observationsaboutsuch norms,as well as their roles in cognitivelife, and it does haveconsequencesforthecontentofsubstantivetheoriesofepistemicrationality. ThemaintechnicalprojectofthebookisdevelopingPLEN,whichisessentially a novel variant of propositional dynamic logic (PDL) distinguished by more or less elaborate revisions of PDL’s syntax and semantics. The syntax encodes the procedural content of epistemic norms by means of the well-known protocol or program constructions of dynamic and epistemic logics. It then provides a novel language of operators on protocols, including a range of unique protocol equivalence relations, syntactic operations on protocols, and various procedural relations among protocols in addition to the standard dynamic (modal) operators of PDL. The semantics of the system then interprets protocol expressions and vii viii Preface expressionsembeddingprotocolsoveraclassofdirectedmultigraph-likestructures ratherthanthestandardlabeledtransitionsystemsormodalframes.Theintentofthe systemistobetterrepresentepistemicdynamics,buildalogicofprotocolsatopit, andthenshowthattheresultinglogicofprotocolsisusefulasalogicalframework forepistemicnorms.Theresultingtheoryofepistemicnormscentersonnotionsof norm equivalence derived from theories of process equivalence familiar from the studyofdynamicandmodallogics.Thecanonicalaccountofprotocolequivalence in PLEN turns out to possess a number of interesting formal features, including satisfaction of important conditions on hyperintensional equivalence, a matter of recentlyrecognizedimportanceinthelogicofnorms,generally. Giventhosefoci,thisbookisprimarilyforphilosophersoflogic,philosophical logicians, and epistemologists interested in the formalrepresentationof epistemic dynamics, foundational topics concerning epistemic normativity, or the analysis of normativeand proceduralcomponentsof methodologiesforbelief revisionand theorychange.Moretechnicallyinclinedreadersinterestedinapplicationsofmodal logics(especiallydynamiclogics)andprocesstheoriestotheanalysisofepistemic rationality may find something of interest or use in this book. Such readers may be disappointedwith the levelof technicaldevelopment,however,as I’vefocused ondevelopingthe technicalpropertiesofthe formalframeworkonlywith specific philosophical projects in mind, leaving many of the standard metatheorems as plausibleconjectures,and I’vedeliberatelyset outto doas muchas possible with elementarytools. Thisbookisarevisionandrefinementoftheprojectofmydoctoraldissertation, The PhilosophicalFoundationsof PLEN: a Protocol-theoreticLogic of Epistemic Norms (City University of New York, Graduate Center). As such, some of the materialhereappearsthere,thoughnoneofitappearsunchanged,nordoesanyofit appearelsewhere.Chapters1,2,and3ofthisbookrefineandexpandthearguments and stage-setting of Chaps. 1 and 2 of the dissertation. Chapters 4, 5, 6, and 7 of this book provide a marked refinement of the eponymous system, containing somematerialfromChap.3ofthedissertation.Chapters8,9,and10ofthisbook refine some of the material from Chaps. 4 and 5 of my dissertation, and move past it considerably. There is little direct overlap, but the project here is a direct continuationofthatinauguratedinthedissertation. NewYork,NY,USA RalphJenkins Acknowledgments Iowemuchtomany.TanyaManthey,withoutwhomIwouldhavebeenlostmany times.Mysmallcircleoffamilyandclosefriends,forwhommuchthesameistrue. Thephilosophers,logicians,andcomputerscientistsworkingindynamic,epistemic, deontic,andnon-classicallogics;thesefieldsaredrivenbysharpermindsthanmine, andtheyhousemanyofthesourcesoftechnicalinventionandphilosophicalinsight thathaveinformedthisproject,andtowhichIoweadeepdebtofgratitude. Thisprojectcouldn’thaveseencompletionifnotforthepatienceandguidance ofthefacultyattheGraduateCenter(CUNY),especiallythesupervisorofmydis- sertation:GrahamPriest. Asidefromdirectlyprovidingvirtuallyendlesstechnical guidance,philosophicalinsight, and a continualstream of letters of recommenda- tion,Graham’scontinueddefenseanddevelopmentofdialetheismovertheyearsin ever more diverse and surprising ways is an exemplarof the “hard core” research strategy.It’s an examplethathasfundamentallyre-shapedmyphilosophicalgoals and professionalaspirations. Sergei Artemov and David Papineau deserve special considerationaspatientandsupportivedissertationcommitteemembers. In virtue of this project’s genesis from my dissertation research and my reluc- tance to show work-in-progress, the set of philosophers I owe gratitude to for talking these ideas through are those I associated or worked with closely during grad school—some from my cohort, others from the rotating cast of Graham’s dissertation supervision seminars. Nonetheless, there are too many helpful col- leagues to name, and here is a frankly poor attempt: Daniel Weissglass, David Nagy, Daniel Boyd, Yuval Abrams, Sophie Bishop, Erik Stei, Tommy Kivatinos, Thomas Ferguson, Amanda Bryant, Hitoshi Omori, Filippo Casati, and Federico MatiasPalos,andmorebesides!IfI’veomittedanyone,it’safailureofmemoryon mypartratherthanafailureofimportantcontributionontheirs. Thereareverymanywaysinwhichthisprojectcouldhavefailed,whetherfrom technicalorphilosophicalerrororfromthenumerouswaysinwhichextra-academic factorsgetin the way. Somehow,I haven’tquite runinto them face-first,yet. The explanationliespartlyinthecombinationofguidanceandfreedomfromconstraint provided by Graham and the Graduate Center. Another part of the explanation is Rutgers-Newark. Where the Graduate Center guided the path of the education ix x Acknowledgments and research that lead to this book,it was Rutgers-Newark’ssmall, excellent, and deeplyencouragingphilosophydepartment—andJeffBuechner,inparticular—that groundedtherootstateandtheinitialstepsofthatpath. Specialthanksto:JohnMacFarlaneforgraciouslylettingmeciteanunpublished paper,ananonymousreviewerthatharshly(andrightly)rejectedanearlierversion ofthisbook,andanotheranonymousreviewerthatcheckedmytechnicalworkand providedencouragingandhelpfulsuggestions.