(cid:2) (cid:2) OUPCORRECTEDPROOF–FINAL,//,SPi (cid:2) (cid:2) Foundations of Logical Consequence (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) OUPCORRECTEDPROOF–FINAL,//,SPi (cid:2) (cid:2) MIND ASSOCIATION OCCASIONAL SERIES Thisseriesconsistsofcarefullyselectedvolumesofsignificantoriginalpaperson predefinedthemes,normallygrowingoutofaconferencesupportedbyaMind AssociationMajorConferenceGrant.TheAssociationnominatesaneditoror editorsforeachcollection,andmaycooperatewithotherbodiesinpromoting conferencesorotherscholarlyactivitiesinconnectionwiththepreparationof particularvolumes. Director,MindAssociation:M.Fricker PublicationsOfficer:JulianDodd RecentlyPublishedintheSeries: TheHighestGoodinAristotleandKant EditedbyJoachimAufderheideandRalfM.Bader HowWeFight EthicsinWar EditedbyHelenFroweandGeraldLang TheMoralityofDefensiveWar EditedbyCécileFabreandSethLazar MetaphysicsandScience EditedbyStephenMumfordandMatthewTugby ThickConcepts EditedbySimonKirchin Wittgenstein’sTractatus HistoryandInterpretation EditedbyPeterSullivanandMichaelPotter PhilosophicalPerspectivesonDepiction EditedbyCatharineAbellandKaterinaBantinaki EmergenceinMind EditedbyCynthiaMacdonaldandGrahamMacdonald Empiricism,PerceptualKnowledge,Normativity,andRealism EssaysonWilfridSellars EditedbyWillemA.deVries SpheresofReason NewEssaysinthePhilosophyofNormativity EditedbySimonRobertson (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) OUPCORRECTEDPROOF–FINAL,//,SPi (cid:2) (cid:2) Foundations of Logical Consequence edited by Colin R. Caret Ole T. Hjortland 1 (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) OUPCORRECTEDPROOF–FINAL,//,SPi (cid:2) (cid:2) 3 GreatClarendonStreet,Oxford,OXDP, UnitedKingdom OxfordUniversityPressisadepartmentoftheUniversityofOxford. ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,scholarship, andeducationbypublishingworldwide.Oxfordisaregisteredtrademarkof OxfordUniversityPressintheUKandincertainothercountries ©theseveralcontributors Themoralrightsoftheauthorshavebeenasserted FirstEditionpublishedin Impression: Allrightsreserved.Nopartofthispublicationmaybereproduced,storedin aretrievalsystem,ortransmitted,inanyformorbyanymeans,withoutthe priorpermissioninwritingofOxfordUniversityPress,orasexpresslypermitted bylaw,bylicenceorundertermsagreedwiththeappropriatereprographics rightsorganization.Enquiriesconcerningreproductionoutsidethescopeofthe aboveshouldbesenttotheRightsDepartment,OxfordUniversityPress,atthe addressabove Youmustnotcirculatethisworkinanyotherform andyoumustimposethissameconditiononanyacquirer PublishedintheUnitedStatesofAmericabyOxfordUniversityPress MadisonAvenue,NewYork,NY,UnitedStatesofAmerica BritishLibraryCataloguinginPublicationData Dataavailable LibraryofCongressControlNumber: ISBN –––– Printedandboundby CPIGroup(UK)Ltd,Croydon,CRYY LinkstothirdpartywebsitesareprovidedbyOxfordingoodfaithand forinformationonly.Oxforddisclaimsanyresponsibilityforthematerials containedinanythirdpartywebsitereferencedinthiswork. (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) OUPCORRECTEDPROOF–FINAL,//,SPi (cid:2) (cid:2) Preface This volume is a result of talks given at events organized under the auspices of theAHRC-fundedprojectFoundationsofLogicalConsequence(FLC).Theproject ranfromtoattheUniversityofStAndrews,directedbyStephenRead (PrincipalInvestigator),GrahamPriest,andStewartShapiro(Co-Investigators). WewereincrediblyfortunatetoworkwiththemasPostdoctoralResearchFellows intheArchéResearchCentre,andtoparticipateinthemanagementoftheonly large-scaleprojectonthenatureoflogicalconsequencetodate. Theprojectwasaresoundingsuccess.Ithasproducedhigh-levelresearchonall ofthetopicsthattheprojectsetouttocover.Thepresentvolumeisonlyasmall sample of the many excellent papers presented at FLC events. We are confident thatthesecontributionswillbeofgreatvaluebothtoresearchersandtograduate studentsinthefieldandinphilosophymorebroadly.Inordertomakethebook moreusefultothosewhoarenotfamiliarwithallthedebatesinthephilosophy oflogic,wehavewrittenanintroductiontocurrentresearchtrends,outliningthe majorargumentsinthelastcoupleofdecades.Alongthewaywegiveindications ofhowtheessaysinthevolumecontributetothesedebates. We are immensely grateful to the authors of this volume. Their contributions stand as a testimony to the vibrant and productive workshops during the FLC project. They have all been extremely helpful and patient while the volume has been edited. We also want to thank the many visitors to the FLC project, and especially all the members of Arché who joined us in discussions in seminars andconferences.SpecialthanksalsogotoTobyMeadows,whohelpedusherthe project through its final stages. Finally, we are grateful for wonderful help and advicefromOUP’sAssistantCommissioningEditor,EleanorCollins. (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) OUPCORRECTEDPROOF–FINAL,//,SPi (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) OUPCORRECTEDPROOF–FINAL,//,SPi (cid:2) (cid:2) Contents ListofContributors ix PartI. Introduction . LogicalConsequence:ItsNature,Structure,andApplication  ColinR.CaretandOleT.Hjortland PartII. Consequence:ModelsandProofs . WhatisLogicalValidity?  HartryField . LogicalConsequenceandNaturalLanguage  MichaelGlanzberg . IstheTernaryRDepraved?  GrahamPriest . Proof-TheoreticValidity  StephenRead PartIII. PropertiesandStructureofLogicalConsequence . TheCategoricityofLogic  VannMcGee . TheMeaningofLogicalTerms  StewartShapiro . BreakingtheChains:Following-fromandTransitivity  EliaZardini . Non-detachableValidityandDeflationism  JcBeall PartIV. ApplicationsofLogicalConsequence . EmbeddingDenial  DavidRipley . Assertion,Denial,Accepting,Rejecting,Symmetry,andParadox  GregRestall (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) OUPCORRECTEDPROOF–FINAL,//,SPi (cid:2) (cid:2) viii contents . KnowabilityRemixed  HeinrichWansing . Accuracy,Logic,andDegreeofBelief  J.RobertG.Williams Index  (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) OUPCORRECTEDPROOF–FINAL,//,SPi (cid:2) (cid:2) List of Contributors JcBeall,UniversityofConnecticutandUniversityofTasmania ColinR.Caret,YonseiUniversity HartryField,NewYorkUniversity MichaelGlanzberg,NorthwesternUniversity OleT.Hjortland,UniversityofBergen VannMcGee,MassachusettsInstituteofTechnology GrahamPriest,CityUniversityofNewYork StephenRead,UniversityofStAndrews GregRestall,UniversityofMelbourne DavidRipley,UniversityofConnecticut StewartShapiro,OhioStateUniversity HeinrichWansing,Ruhr-UniversitätBochum J.RobertG.Williams,UniversityofLeeds EliaZardini,UniversityofLisbon (cid:2) (cid:2) (cid:2) (cid:2)