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INTUITIONINKANT

Inthisbook,DanielSmythoffersacomprehensiveoverviewof ImmanuelKant’sconceptionofintuitioninallitsspecies – divine, receptive,sensible,andhuman.Kantconsiderssenseperceptiona paradigmofintuition,yetclaimsthatwecanrepresentinfinitiesin intuition,despitethe finitudeofsenseperception.Smythexamines thisheterodoxcombinationofcommitmentsandarguesthatthe variousfeaturesKantascribestointuitionaremeanttoremedy specificcognitiveshortcomingsthatarisefromthediscursivityof ourintellect,withintuitionactingastheintellect’scognitivepartner tomakeknowledgepossible.HereconstructsKant’sconceptionof intuitionanditsroleinhisphilosophyofmind,epistemology,and philosophyofmathematics,andshowsthatKant’sconceptionof sensibilityisasinnovativeandrevolutionaryashismuch-debated theoryoftheunderstanding.

 isAssistantProfessorofLetters,Philosophy,and GermanStudiesatWesleyanUniversity,Connecticut.Hepublishes onKant,philosophyofmathematics,andaesthetictheoryandhas translatednumerousbooksandarticlesfromGerman.

INTUITIONINKANT

TheBoundlessnessofSense

DANIELSMYTH

WesleyanUniversity,Connecticut

ShaftesburyRoad,Cambridge   ,UnitedKingdom

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, rdFloor,Plot ,SplendorForum,JasolaDistrictCentre,NewDelhi – ,India

 PenangRoad,#–/,VisioncrestCommercial,Singapore 

CambridgeUniversityPressispartofCambridgeUniversityPress&Assessment, adepartmentoftheUniversityofCambridge.

WesharetheUniversity’smissiontocontributetosocietythroughthepursuitof education,learningandresearchatthehighestinternationallevelsofexcellence.

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Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisions ofrelevantcollectivelicensingagreements,noreproductionofanypartmaytake placewithoutthewrittenpermissionofCambridgeUniversityPress&Assessment.

AcataloguerecordforthispublicationisavailablefromtheBritishLibrary ACataloging-in-PublicationdatarecordforthisbookisavailablefromtheLibraryofCongress

Hardback CambridgeUniversityPress&Assessmenthasnoresponsibilityforthepersistence oraccuracyofURLsforexternalorthird-partyinternetwebsitesreferredtointhis publicationanddoesnotguaranteethatanycontentonsuchwebsitesis,orwill remain,accurateorappropriate.

INTUITIONINKANT

Inthisbook,DanielSmythoffersacomprehensiveoverviewof ImmanuelKant’sconceptionofintuitioninallitsspecies – divine, receptive,sensible,andhuman.Kantconsiderssenseperceptiona paradigmofintuition,yetclaimsthatwecanrepresentinfinitiesin intuition,despitethe finitudeofsenseperception.Smythexamines thisheterodoxcombinationofcommitmentsandarguesthatthe variousfeaturesKantascribestointuitionaremeanttoremedy specificcognitiveshortcomingsthatarisefromthediscursivityof ourintellect,withintuitionactingastheintellect’scognitivepartner tomakeknowledgepossible.HereconstructsKant’sconceptionof intuitionanditsroleinhisphilosophyofmind,epistemology,and philosophyofmathematics,andshowsthatKant’sconceptionof sensibilityisasinnovativeandrevolutionaryashismuch-debated theoryoftheunderstanding.

 isAssistantProfessorofLetters,Philosophy,and GermanStudiesatWesleyanUniversity,Connecticut.Hepublishes onKant,philosophyofmathematics,andaesthetictheoryandhas translatednumerousbooksandarticlesfromGerman.

INTUITIONINKANT

TheBoundlessnessofSense

DANIELSMYTH

WesleyanUniversity,Connecticut

ShaftesburyRoad,Cambridge   ,UnitedKingdom

OneLibertyPlaza, thFloor,NewYork,  ,USA

 WilliamstownRoad,PortMelbourne,  ,Australia 

, rdFloor,Plot ,SplendorForum,JasolaDistrictCentre,NewDelhi – ,India

 PenangRoad,#–/,VisioncrestCommercial,Singapore 

CambridgeUniversityPressispartofCambridgeUniversityPress&Assessment, adepartmentoftheUniversityofCambridge.

WesharetheUniversity’smissiontocontributetosocietythroughthepursuitof education,learningandresearchatthehighestinternationallevelsofexcellence.

www.cambridge.org

Informationonthistitle: www.cambridge.org/

Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisions ofrelevantcollectivelicensingagreements,noreproductionofanypartmaytake placewithoutthewrittenpermissionofCambridgeUniversityPress&Assessment.

AcataloguerecordforthispublicationisavailablefromtheBritishLibrary ACataloging-in-PublicationdatarecordforthisbookisavailablefromtheLibraryofCongress

Hardback CambridgeUniversityPress&Assessmenthasnoresponsibilityforthepersistence oraccuracyofURLsforexternalorthird-partyinternetwebsitesreferredtointhis publicationanddoesnotguaranteethatanycontentonsuchwebsitesis,orwill remain,accurateorappropriate.

INTUITIONINKANT

Inthisbook,DanielSmythoffersacomprehensiveoverviewof ImmanuelKant’sconceptionofintuitioninallitsspecies – divine, receptive,sensible,andhuman.Kantconsiderssenseperceptiona paradigmofintuition,yetclaimsthatwecanrepresentinfinitiesin intuition,despitethe finitudeofsenseperception.Smythexamines thisheterodoxcombinationofcommitmentsandarguesthatthe variousfeaturesKantascribestointuitionaremeanttoremedy specificcognitiveshortcomingsthatarisefromthediscursivityof ourintellect,withintuitionactingastheintellect’scognitivepartner tomakeknowledgepossible.HereconstructsKant’sconceptionof intuitionanditsroleinhisphilosophyofmind,epistemology,and philosophyofmathematics,andshowsthatKant’sconceptionof sensibilityisasinnovativeandrevolutionaryashismuch-debated theoryoftheunderstanding.

 isAssistantProfessorofLetters,Philosophy,and GermanStudiesatWesleyanUniversity,Connecticut.Hepublishes onKant,philosophyofmathematics,andaesthetictheoryandhas translatednumerousbooksandarticlesfromGerman.

INTUITIONINKANT

TheBoundlessnessofSense

DANIELSMYTH

WesleyanUniversity,Connecticut

ShaftesburyRoad,Cambridge   ,UnitedKingdom

OneLibertyPlaza, thFloor,NewYork,  ,USA

 WilliamstownRoad,PortMelbourne,  ,Australia 

, rdFloor,Plot ,SplendorForum,JasolaDistrictCentre,NewDelhi – ,India

 PenangRoad,#–/,VisioncrestCommercial,Singapore 

CambridgeUniversityPressispartofCambridgeUniversityPress&Assessment, adepartmentoftheUniversityofCambridge.

WesharetheUniversity’smissiontocontributetosocietythroughthepursuitof education,learningandresearchatthehighestinternationallevelsofexcellence.

www.cambridge.org

Informationonthistitle: www.cambridge.org/

Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisions ofrelevantcollectivelicensingagreements,noreproductionofanypartmaytake placewithoutthewrittenpermissionofCambridgeUniversityPress&Assessment.

AcataloguerecordforthispublicationisavailablefromtheBritishLibrary ACataloging-in-PublicationdatarecordforthisbookisavailablefromtheLibraryofCongress

Hardback CambridgeUniversityPress&Assessmenthasnoresponsibilityforthepersistence oraccuracyofURLsforexternalorthird-partyinternetwebsitesreferredtointhis publicationanddoesnotguaranteethatanycontentonsuchwebsitesis,orwill remain,accurateorappropriate.

Itistoolittletocall Man a littleWorld;Except God,Manisa diminutive tonothing.Manconsistsofmorepieces,moreparts, thantheworld;thantheworlddoeth,naythantheworldis.And ifthosepieceswereextended,andstretchedoutinMan,asthey areintheworld,Manwouldbethe Gyant,andtheWorldthe Dwarfe,theWorldbutthe Map,andtheManthe World JohnDonne, DevotionsuponEmergentOccasions, , MeditationIV

Variouspredicatesofspacethatonewouldotherwiseregardas objectivecannowbeexplainedthroughthisconcept[sc.ofspace]in viewofitsorigin. .Spaceisunitary[einig],becauseitistheformof representationsofeverypossibleouterobjectinaunitarysubject. . Spaceisinfinite.Forthecapacitytosuffer[Fähigkeitzuzulassen] variousimpressionsofouterthings,orreceptivity[Empfänglichkeit], hasnolimitations[Schranken]initself. .Spaceisnecessary;foritis thatuponwhichthepossibilityofthesensesisgrounded.

Kant,R

Whenamansummonedtoanimatedobservationbeginstodo battlewithnature,heinitiallyfeelsaprodigiousdrivetosubjugate itsobjectstohimself.Yetitdoesnottakelongforthemtointrude soviolentlyuponhimthathewellfeelshowmuchcausehehasto acknowledgetheirpowerandtoadmiretheirefficacy.Nosooner hasheconvincedhimselfofthisreciprocalinfluencethanhe becomesawareofadoubleinfinity,intheobjectsthe manifoldnessofbeingandbecomingandtheirlivelycriss-crossing relations,inhimself,however,thepossibilityofaninfinite development,asherefineshisreceptivityaswellashisjudgment toevernewformsofup-takeandreaction.

Goethe, “ApologyfortheUndertaking,” IdeasonOrganicFormation,

Contents

Acknowledgments page ix

Abbreviations,Citations,andOtherConventions xi

Introduction:FromInfinitytoGivenness:Kant’sApperceptive FacultyPsychologyandHisTop-DownApproachtoIntuition

ChapterSummaries

 Reason’sSelf-KnowledgeandKant’sCriticalMethodology

  UnfoldingAPrioritheMereConceptofaFacultyofKnowledge

. PureGeneralLogicasa Selbsterkenntnis ofReason

. Critiqueasa Selbsterkenntnis ofReason

. ProsecutingaCritiqueviaPureApperception

 SyntheticJudgmentandIntuition:TheSensibility/ UnderstandingDistinctioninthe “Introduction”

  KnowledgethatComestoBe

. AnalyticityandIntellectualGroundsofTruth

. SyntheticJudgmentandIntuition

. FeaturesandAdvantagesofThisInterpretation

. Self-ConsciouslyTrackingtheTruth

. IntuitionandReceptivity

 AnApperceptiveApproachtotheTranscendentalAesthetic

. ApperceptionandthePreliminaries

. Kant’sTeleologicalLanguageinthePreliminaries

. DiscursivityandGenerality;ImmediacyandGivenness

. ReceptivityandSensibility

  SensationintheAbstract:MatterandFormofIntuition

Conclusion

 Exposition,ConceptualAnalysis,andApperception

  IsolatingSensibility:EliminationversusAbstraction

  OriginalAcquisitionandAPriori,GivenConcepts

  ExpositionasConceptualAnalysis

. CompetentUseastheCriterionofMarkhood

. Conclusion

 Infinity,Discursivity,Givenness:TheIntuitiveRootsof SpatialRepresentation

  ApproachingtheThirdMetaphysicalExposition

  CriteriaofIntuitiveandDiscursiveRepresentation

. HolisticContainmentStructureandContinuity

. InfinitaryIntuitions,FiniteConcepts

. TheBoundlessnessofSense

 Prolegomenatoa Stufenleiter ofKantianIntuition

. PeculiaritiesofPorphyrianTrees

. PorphyrianClassificationsinKant

. The Stufenleiter Passage(A/B)

. Stufenleiter asTargetedAnalyticalTools

 A Stufenleiter ofKantianIntuition,PartI:Intuition u¨berhaupt andSpontaneousIntuition

  ATargetedAnalysisofHumanIntuition

. GivennessasCriterionofIntuition u¨berhaupt

. CognitiveSpontaneityasDifferentia

 A Stufenleiter ofKantianIntuition,PartII:Receptivity andSensibility

  Sensible-AffectionDependenceasDifferentia 

  Self-RepresentationasDifferentia 

  LevelsofAbstraction,TypesofEvidence,andFeaturesof KantianIntuition

Bibliography

Index

Acknowledgments

ThisprojectbeganasadissertationattheUniversityofChicagoovera decadeago.Nopartofthatdissertationsurvivesinthepresentbook,but theformativeinfluenceofmyadvisorsandmyfellowgraduatestudents endures.RobertPippin’sbreadthandsavvytaughtmethevalueofviewing issuesagainstawidehistoricalhorizonandofimaginativelyinhabiting unfamiliarposturesofthought.JimConant’scapacityforslow,generous readingshowedmetheimportanceofattendingcloselytophilosophical methodology.FromDanielSutherlandIlearnedtoappreciatethefecundityofKant’sphilosophyofmathematicsandtheacuityofitsscholars.And AnatSchechtmanintroducedmetotheprofundityofLeibniz’sand Descartes’sviewsoninfinityandhelpedmetoseetheirrelevanceto Kant.Iamforeverdiscoveringandre-discoveringgemsthattheymanaged toslipintomypockets.I’mgratefultoNathanBauer,ThomasLand, JustinShaddock,andClintonTolleyfordiscussingKantwithmebefore IknewwhatIwastalkingabout.AndI’mgratefultoSimonGurofsky, JoshuaMendelsohn,AndrewPitel,DanielRodriguez-Navas,JessTizzard, andAndyWernerforcontinuingthosediscussionsafterIwouldnot shutup.

IoweagreatdebttothebroadercommunityofKantscholarsfor cultivatinganintellectualestuaryforup-and-comersthatisatoncenurturingandrigorous.MyviewsandhabitsofmindhaveimprovedimmeasurablyfrombeinganactivememberoftheNorthAmericanKantSociety. Forencouragement,intellectualcamaraderie,andinvaluableinsightsat variousstagesalongtheway,IamgratefultoMattBoyle,EmilyCarson, RosalindChaplin,AndrewChignell,StephenEngstrom,AnilGomes, JohannesHaag,AndreaKern,PatKitcher,MichelleKosch,Samantha Matherne,ColinMcLear,BennettMcNulty,JamesMessina,Sasha Newton,SebastianRödl,TimothyRosenkoetter,UlrichSchlösser,Lisa Shabel,NickStang,andRachelZuckert.Ihaveparticularlybenefitted fromextendedconversationswithIanBlecher,ThomasLand,andTyke

Nunez.AndIcannotbegintosurveythedebtsIowetomyclosest interlocutorsaboutKant(auchallenDingenu¨berhaupt),TillHoeppner andJessTizzard.IshuddertothinkwhereIwouldbewithouttheirgood senseandgoodhumor.

Ialsobenefittedfromacuteandconstructivereportsbytwoanonymous reviewersforCambridgeUniversityPress.For findingsuchfantastic readersandforguidingmethroughthereviewandpublicationprocess withpatienceandpracticality,IamgratefultoHilaryGaskin.Thanksare alsoduetoCameronCookforcreatingthe Index andtomydepartment forpayingforit.

Theprocessofwritingthisbookwasnowalkinthepark,soIam especiallygratefultomywonderfulcolleaguesatWesleyanUniversityfor advice,moralsupport,andwalksinthepark.MycolleaguesintheCollege ofLetters,aswellasmycomradesinthePhilosophyDepartment,worked toensurethatIfeltvaluedandsecure,activelyprotectingmytimefor researchandfamily.Forgoingaboveandbeyondindifferentways,Imust singleoutJoeFitzpatrick,SteveHorst,TusharIrani,KatherineKuenzli, RogerMatthewGrant,UliPlass,JoeRouse,SanfordShieh,andCourtney WeissSmith.

Whatwritingthisbookhasrequiredmorethananythingelseistime. IamgratefulforWesleyan’sparentalleaveprogram,whichenabledmeto putresearchonholdduringthepreciousearlymonthsofmychildren’ s lives.Iamgratefultomymother-in-law,Kristin,fordroppingeverything whenthepandemichitinordertodevoteherselftohergrandkids.Iam gratefultotheteachersatNeighborhoodPreschoolinMiddletownforthe caretheypracticedduringthepandemicandforthelovetheypractice always.Iamgratefultomychildren,FionnandEva,forbeingrelentlessly amazing.AndIamgratefultomywife,LeighAnn,forherresilienceand forbearancewhenIhavebeenabsentorirritable,fortheintensityand generosityofherattention,forhercapacityforgentleness,andforher tenacity.Itistomyfamily,nottoKant,thatIowemymostvividsenseof theboundlessnessofourhumancapacities.

Abbreviations,Citations,andOtherConventions

ReferencestoKant

TranslationsofKantaremyown,butkeytermsaccordwithstandard Englisheditions.Iunderlinetexttosignifymyownemphasis,andnoteit parenthetically.IuseboldtypefacetoexpressKant’semphasis(wherehe wouldhaveusedSperrdruck),whichIgenerallyleaveunremarked.Iretain Kant’sitalicsinquotations,thoughonlytoindicateforeignwords,notto expressemphasis.

ReferencestoKant’swritingsfollowstandardpracticewithonerefinement:theadditionoflinenumbers.Iprovidevolume,page,andline numbersfromtheAkademieAusgabeofKant’swritings(Kant –), exceptforthe CritiqueofPureReason,whereIcitetheA()and B()pagination.TheA/Bpagenumberisfollowed,afteraperiod,by thelinenumbersoftheMeinerPhilosophischeBibliothekedition(Kant ).TheselinenumberstrackthepaginationoftheMeinervolume,not thepaginationoftheA,B,orAkademieeditions.Tolocatecitedpassages, first findtheA/BpageintheMeinereditionandthenlookforcitedline numberswithinthatA/Bpage.

BecauseanA/BpagemayextendacrossapagebreakintheMeiner edition,linenumbersmaysometimesappeartogobackward.Thus,A/ Bf.– referstothesentence, “Siehatalso[ ]gemeinen Verstandes.” Thissentencebeginsonline  ofpage  oftheMeiner editionandendsonline  ofpage .Forthesamereason,someearly portionsofB havehigherlinenumbersthanlaterones,sincethey appearbeforethepagebreak:B.– precedesB.–. Whennolinenumbersarespecified,Imeantorefertoanextended discussioninthatareaofthetext.IdothisonlywhenItakemy interpretationtobeuncontroversial.

xii Abbreviations,Citations,andOtherConventions

IsupplyAdickes’sestimateddatingofallReflectionsandofallunpublishedwritingsthatfalloutsidethepenumbraofKant’ s “criticalperiod” (–).Idonotprovidedatesfortextswithinthisperiodorfor publishedwritings.

IabbreviateKant’sworksasfollows:

A– Anthropologylectures,followedbyfulltitle(e.g. A-Collins;A-Menschenkunde)

Anthropology AnthropologieinpragmatischerHinsicht()

Critique KritikderreinenVernunft( =A/  =B)

Directions VondemerstenGrundedesUnterschiedesderGegenden imRaume()

Discovery ÜbereineEntdeckung,nachderalleneueKritikder reinenVernunftdurcheineältereentbehrlichgemacht werdensoll()

Dreams TräumeeinesGeistersehers,erläutertdurchTräumeder Metaphysik()

Groundwork GrundlegungzurMetaphysikderSitten()

Inaugural Demundisensibilisatqueintelligibilisformaet principiis()

Judgment KritikderUrteilskraft()

L– Logiclectures,followedbyabbreviatedtitle:

BlomBlomberg(early s) BusBusolt(c. )

DWDohna-Wundlacken()

JäscheImmanuelKantsLogik,einHandbuchzu Vorlesungen()

PhPhilippi()

PöPölitz(–)

WienWienerLogic(–)

M–

Metaphysicslectures,followedbyabbreviatedtitle:

DWDohna-Wundlacken(–)

HHerder(–)

MrMrongovius(–)

Pö/L Pölitz/L (–)

Pö/L Pölitz/L (–?)

SchönvonSchön(–)

Vi/K Vigilantius/K (/)

VoVolkmann(/)

Metaphysical Foundations

MetaphysischeAnfangsgru¨ndeder Naturwissenschaft()

OnKästner ÜberKästnersAbhandlungen()

Orient Washeißt:sichimDenkenorientieren?()

Physical Monadology

Metaphysicaecumgeometriaiunctaeususinphilosophia naturali,cuiusspecimenI.continetmonadologiam physicam()

Postumum Opuspostumum(c. –)

Practical KritikderpraktischenVernunft()

Prolegomena Prolegomenazueinerjedenku¨nftigenMetaphysik,dieals Wissenschaftwirdauftretenkönnen()

Proof DereinzigmöglicheBeweisgrundzueiner DemonstrationdesDaseinsGottes()

RReflections,citedwithAdickes’sestimateddating

Teleological ÜberdenGebrauchteleologischerPrincipieninder Philosophie()

Tone VoneinemneuerdingserhobenenvornehmenTonin derPhilosophie()

ReferencestoMajorHistoricalFigures

Igenerallycitecriticaleditionswiththestandardabbreviationsindicatedin mybibliography.Iprovidelinenumberswhenavailableanduseful. IdepartfromthispracticeonlywhenIthinkitwillbeeasierforreaders to findthepassagebysectionnumbersorinawidelyavailablecollection. Thus,citationsofAquinas,Wolff,Baumgarten,andMeieremploysection numbers,asdomanycitationsofLeibniz.

OtherReferences

Allotherreferences,includingcitationsofsecondaryliterature,employthe Chicago-style,name–dateformat.Whenapiecehasbeenrepublishedor translated,IcitetheversionIthinkiseasiesttoaccess,providingthe originaldateofpublicationinsquarebracketsforhistoricalcontext.Thus, “Parsons( [])” referstohisclassicessay “Kant’sPhilosophyof Arithmetic” asitappearsinPosy’sinvaluablecollection, Kant’sPhilosophy ofMathematics:ModernEssays.

xiv Abbreviations,Citations,andOtherConventions

OtherConventions

Ienclosewordsinangledbracketstomentiontheconceptstheyexpress. Thus <horse> and <Pferd> co-refertotheconceptofthenaturalspecies equusferus.Iusethesesameangledbracketstorefertothejudgment expressedbythesentencetheyenclose,whichIalsoitalicize.Thus <horses aremammals> isananalyticjudgment.

Iusesinglequotationmarkstomentionthewordsenclosedbythem. Thus ‘horse’ hastwovowels,but ‘Pferd’ onlyone.

Iusedoublequotationmarksbothtoquotetextandas “ scarequotes ” , tocallcriticalattentiontoaphraseoridea.

Introduction

FromInfinitytoGivenness:Kant’sApperceptiveFaculty PsychologyandHisTop-DownApproachtoIntuition

Distinguishingthesensiblefromtheintellectualaspectsofourknowledge isthekeystoneofKant’scriticalenterprise.Inhispracticalphilosophy,itis ouramphibiousstatusasrationalyetsensiblebeingsthatmakesussubject to,andsimultaneouslyauthorsof,ethicalimperatives.Andinhistheoreticalphilosophy,Kantarguesthataproperaccountofsensibilityand understanding – andtheirassociatedrepresentations,intuitionsandconcepts – revealsboththepossibilityofhumanknowledgeanditsinherent limits(Critique A/B

).NowKantishardlythe firstto contrast “ sense ” with “intellect” ortodistinguish “lower” from “higher” cognitivecapacities.Yettheconclusionshebasesonthisdistinctionareso heterodoxthathisconceptionsofitsdisjunctsmustdivergesignificantly fromtraditionalaccounts.

Kant’smostnotoriousheterodoxyis,ofcourse,his “transcendental idealism”:thetwinclaimsthat(a)spatiotemporalobjectsandproperties aremere “ appearances ”,i.e.mind-dependentor “transcendentallyideal” phenomena,andthat(b)humanknowledgeisrestrictedtosuchappearancesanddoesnotextendtothingsinthemselves.ButtheKantian heterodoxythatprecipitatedthepresentprojectisevenmoreunorthodox thanhisidealism:namely,hisclaimthatwecanrepresentthemathematicallyinfinitenot despite but invirtueof thesensible,intuitiveaspectsof ourcognition.

Thisisaviewunprecedentedinthehistoryofphilosophy.Rationalists andempiricistsalikeagreethat if wearecapableofknowledgeinvolving mathematicalinfinity,suchknowledgecannothaveasensiblefoundation. Theytakethistofollowfromtheundeniable finitudeofhumansense perception.Somephenomenaarejusttoosmallortoofaint,otherstoo largeortoointenseforoursensoryapparatustoregisterorperceptually discriminate.SoempiricistssuchasHobbes,Berkeley,andHumeargue that,sinceallknowledgemustbegroundedinsenseperception,whichis finite,cognitionofmathematicalinfinityisimpossible,andweshould 

insteaddevelopastrictly finitisticgeometrybasedon minimasensibilia.  Invertingthisreasoning,rationalistssuchasDescartes,Spinoza,and Leibnizpointtothemathematicallimitationsofhumansenseandimaginationasproofofahigherpowerofintellect,whichtheymakeresponsible forinfinitarycognition. Kantisuniqueindenyingtheirsharedassumption:thatsensible,intuitiverepresentationmustbe finite.

NowKantdoesrecognizetheobviouslimitsonsenseperception. Heinsists,however,that “theformofpossibleexperiencehasnothingat alltodowiththeir[sc.thesenses’]coarseness” (A/B).Themathematicalpropertiesofspaceandtime,includingtheirinfinitedivisibility, mustbeexhibitedinourempiricalintuitings(Af./Bf.),evenif thesepropertiesoutstripoursensoryorphenomenologicalacuity. Indeed,Kantseemstotreattherepresentationofmathematicalinfinity asadefiningcharacteristicofintuition: “Spaceisrepresentedasaninfinite given magnitude.[...]Therefore theoriginalrepresentationofspaceis intuition andnot concept” (B–,Kant’sbold,myunderlining).

Thisposesaninterpretivepuzzle:Whatconceptionofsensibleintuition wouldallowfortheintuitiverepresentationofmathematicalinfinities, whilerespectingtheundeniable finitudeofsenseperceptionandretaining thelatterastheparadigmcaseofintuition?Andwhatphilosophical rationalecouldKanthaveforrejectingthetraditional, finitisticconception ofsensibilityinfavorofonethatmakesasinglecapacityresponsiblefor

 Hobbesrejectstheveryideaofinfi nityonthegroundsthatoursensesare finite(Leviathan  ., ).Headvocatesamaterialist(corpuscularian)geometryinhis  DeCorpore andavarietyof mathematicaltreatises(seeJesseph ,esp.chs.  and ).Berkeleyarguesthatnogenuineideas arecommunicatedbyinfinitarytermsinhis  essay “OfInfi nities” andlaterattacksthe foundationsofinfi nitesimalcalculusin TheAnalyst ().Heoutlinesa fi nitisticgeometrybased on minimasensibilia in§§ – ofthe PrinciplesofHumanKnowledge ().Jesseph () remainstheauthorityontheseaspectsofBerkeley’ sphilosophyofmathematics.Hume’ s fi nitism emergesinhistreatmentofourideasofspaceandtimeinbook ,part  of Treatise () andin Enquiry part ,§ ().Jacquette ()off ersasympatheticreconstructionof Hume’ s finitism.

 InthesixthMeditation,Descartesdistinguishespureintellectfromimaginationbyobservingthat ourinabilitytoformadistinctquasi-perceptualimageofachiliagondoesnothinderusfrom mathematicallydemonstratingitsproperties(AT :–).OnDescartes’snotionofinfinity,see Schechtman (, ).Leibnizdeploysthechiliagonexampletodistinguishsymbolicfrom intuitiveknowledgeinhis  “MeditationsonKnowledge,Truth,andIdeas” (G :,AG –)andagaininhis  NewEssays todistinguishideasfromimages(II.xxix., A  :–).Similarly,forSpinoza,aprincipalsourceofconfusionaboutinfinityisthe “failuretodistinguishwhatwecanapprehendonlybytheintellectandnotbytheimagination, andwhatcanalsobeapprehendedbytheimagination” (Letter ,G :,SM ;cf. Ethics ps.).ForSpinoza’sinfluenceonLeibniz’sviewsaboutinfinityandinfinitarycognition,see Nachtomy ()

suchcontrarycognitiveachievements – viz.therepresentationofinfinitary structureandtheproductionof finitesenseperceptions?

Interpreterssometimestrytoresolvethisdifficultyby “charitably” minimizingKant’scommitmenttotheintuitiverepresentationofinfinity. Intuitions,theysuggest,exhibitonlya potential infinity:Werepresent spacemerelyasopen-ended,notasactuallyendless;asindefinitelydivisible,notascontaininganactualinfinityofdistinctspaces.Moreover,what holdsformathematicalabstractaneednotholdforperceptibleconcretaor theirrepresentations.

PerusalofKant’stextsunderminestheseresponses,however,asrecent scholarshiphasshown. Kantresolutelymaintainsthatspaceandtime,as formsofsensibleintuition,areactuallyinfiniteinthelargeandinthe small.Indeed,thepotentialinfinitiestowhichsomecommentatorsproposeweretreatarepossible,accordingtoKant,onlyinsofarastheyare groundedinactualinfinities,ofwhichwehavean “originalrepresentation” inourformofsensibleintuition. AndKantinsiststhatthemathematical propertiesoftheformofintuitionareinheritedbyallintuitiverepresentationsbearingthatform(A

).Thus,tocometogrips withKant’sepistemologyandphilosophyofmind – basedasitisinhis distinctionbetweensensibilityandintellect,intuitionandconcept – we mustrecoveraconceptionofsensibleintuitionforwhichtherepresentationofmathematicalinfinitiesisaconstitutivepossibility,despitethe undeniablesensoryandphenomenologicallimitsonthesensitivity,scope, andacuityofhumansenseperception.

 See,forexample,Bu¨chel (, –);Carson ();Friedman (, , );Domski ();Posy ();Patton ();OnofandSchulting (, );Smyth (,  []); Tolley ();Chaplin ();Rosefeldt ();andWinegar ().KempSmithemphasizes Kant’sacceptanceofactualinfinityinhisdiscussionofthe firstAntinomy ( [], –). Buthiswasaminorityopinion.Kant’sclearestendorsementoftheactuallyinfinitarycharacterof intuitionappearsin OnKästner.AndKant’sauthorshipofthistextwasdiscoveredonlyin , withDilthey’sanalysisoftheRostock Nachlass.Bythen, finitisticinterpretationsofKantweretoo entrenchedtobeoverturned.Thefew fin-de-siècle scholarswhoevenregisteredKant’scommitment toactualinfinitydismisseditasaninconsistencyinhisposition(Vaihinger , –) – aview thatstillhasadvocatestoday(Guyer ).Theideathatactualinfinityisaconsistentandessential featureofKant’sconceptionofsensibleintuitionremainedaminorityview,especiallyin Anglophonediscussions,wellintothe s.Ithasmanychampionstoday.

 WhenKästner () challengesKantonthispoint,arguingthatgeometryrequiresonlypotential infinities,notactualinfinities,Kantresponds: “[Toclaimthat]alinecanbeextendedintoinfinity amountstosayingthatthespaceinwhichIdescribethelineisgreaterthaneverylinethatIcan describeinit;andthusthegeometergroundsthepossibilityofhistaskofenlargingaspace(ofwhich therearemany)intoinfinityupontheoriginalrepresentationofaunitary,infinite, subjectively given space ” (OnKästner :,cf. ).Fordiscussion,seeSmyth ( [],section )and Section   

Myargumentin TheBoundlessnessofSense isthatthisheterodox, infinitaryconceptionofsensibleintuitionarisesfromanaspectofKant’ s philosophicalmethodthathasfallenintodisrepute:his “facultypsychology”,i.e.hisapproachtothemindasaseatofdiversebutcoordinated cognitivecapacities. Acapacityisdefinedthroughitscharacteristicfunction,itscontributiontoaspecifiedoutputorachievement.Inthecaseof Kant’stranscendentalepistemology,theoutputrelativetowhichcapacities areidentifiedanddiscriminatedishumanknowledgeofobjectivereality. Sincecognitivecapacitiesaredefinedbytheirfunction,i.e.theircontributiontoknowledge,anyrepresentationthatfulfillsthecognitiveroleofan intuition justis anintuition,whateveritsintrinsicpropertiesmaybe.This isthe firststeptowardsolvingourinterpretivepuzzle.Foritmakesroom forthepossibilitythatarepresentationcouldplaythedistinctivecognitive roleofanintuitionwithoutexhibitingtheintrinsiclimitations(sensory, phenomenological,orwhatever)thatarecharacteristicofhumansense perceptionandincompatiblewithinfinitarystructure.Iarguethat,for Kant,ourrepresentationsofspaceandtimedojustthat:theyfulfillthe cognitivefunctionofintuitionswhilesurpassingthesensoryandphenomenologicallimitsassociatedwithhumansenseperception.

SowhatisthedefiningcognitivefunctionofsensibleintuitionforKant? Andhowdoeshegoaboutidentifyingit?Whatsortsofarguments,what sortsofevidencearedispositiveinKant’sfacultypsychology?Kant’sEarly Modernpredecessorsrecognizedtwocomplementarymethodsfortheorizingthemindanditspowers:(i) “empiricalpsychology”,whichreliedon

 Iusetheneutralterm ‘capacity’ becauseKantreserves ‘faculty’ for spontaneous capacities.Kant classifiessensibilitynotasa faculty (facultas, Vermögen)butasa capacity (potentia, Fähigkeit)and, specifically,asapassivecapacityor receptivity (receptivitas, Empfänglichkeit).SeeR (–) :  RecentinterpretersstressthatKantiancognition(Erkenntnis)cannotbeidentifiedwithknowledge (Wissen);seeWatkinsandWillaschek (,  []).Iagreethatthereareimportant distinctionshere,buttheyareofapeculiarkind.Kant’saiminthe Critique istovindicatethe possibilityofhuman Wissen (and,ultimately, Begreifen:comprehension).Itisinserviceofthisgoal thatKantintroducessuchtermsas “Erkenntnis” , “Kenntnis” , “Anschauung” , “Sinnlichkeit” , “Empfänglichkeit”,andsoon.Itakethesetermstohavea “focalmeaning”,expressingamoreor lessintimaterelationtohumanknowledgeinitshighestform.Thus,ItakeallKantiancognitive capacitiesandactstobeepistemicinthattheiressentialfunctionistopromoteknowledge(Wissen, Begreifen).Incharacterizingarepresentationasanintuition,orasacognition,Kantishighlighting thefeaturesofthatrepresentationthathavethepotentialtocontributeto Wissen.Thisisnottodeny thattherepresentationmayhaveother,non-epistemicfeaturesorthattheintrinsicpropertiesthat serveanepistemicfunctionmayalsoservenon-epistemicfunctions.Norisittodenythatactsof cognitionoftenfallshortofthe Wissen thatistheirdefiningaim.Whatitdoesmeanisthatitwillnot benecessary,forourpurposes,tocontrastcognitionwithknowledgeinwhatfollows.Iregretthat Icannotdevotetothiscontentiousissuetheattentionitdeserves.Therudimentsofmypositionare outlinedin Sections   and  

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