Theprincipleswhicharisefromtheirreferencetothesensibleworld，onlyserveourunderstandingforempiricaluse。Beyondthistheyarearbitrarycombinations，withoutobjectivereality，andwecanneitherknowtheirpossibilityapriori，norverifytheirreferencetoobjects，letalonemakeitintelligiblebyanyexample;becauseexamplescanonlybeborrowedfromsomepossibleexperience，consequentlytheobjectsoftheseconceptscanbefoundnowherebutinapossibleexperience。Thiscomplete（thoughtoitsoriginatorunexpected）solutionofHume’sproblemrescuesforthepureconceptsoftheunderstandingtheiraprioriorigin，andfortheuniversallawsofnaturetheirvalidity，aslawsoftheunderstanding，yetinsuchawayastolimittheirusetoexperience，becausetheirpossibilitydependssolelyonthereferenceoftheunderstandingtoexperience，butwithacompletelyreversedmodeofconnectionwhichneveroccurredtoHume，notbyderivingthemfromexperience，butbyderivingexperiencefromthem。Thisisthereforetheresultofallourforegoinginquiries："Allsyntheticalprinciplesaprioriarenothingmorethanprinciplesofpossibleexperience，andcanneverbereferredtothingsinthemselves，buttoappearancesasobjectsofexperience。Andhencepuremathematicsaswellasapurescienceofnaturecanneverbereferredtoanythingmorethanmereappearances，andcanonlyrepresenteitherthatwhichmakesexperiencegenerallypossible，orelsethatwhich，asitisderivedfromtheseprinciples，mustalwaysbecapableofbeingrepresentedinsomepossibleexperience。"Sect。31。Andthuswehaveatlastsomethingdefinite，uponwhichtodependinallmetaphysicalenterprises，whichhavehitherto，boldlyenoughbutalwaysatrandom，attemptedeverythingwithoutdiscrimination。Thattheaimoftheirexertionsshouldbesonear，struckneitherthedogmaticalthinkersnorthosewho，confidentintheirsupposedsoundcommonsense，startedwithconceptsandprinciplesofpurereason（whichwerelegitimateandnatural，butdestinedformereempiricaluse）inquestoffieldsofknowledge，towhichtheyneitherknewnorcouldknowanydeterminatebounds，becausetheybadneverreflectednorwereabletoreflectonthenatureorevenonthepossibilityofsuchapureunderstanding。Manyanaturalistofpurereason（bywhichImeanthemanwhobelieveshecandecideinmattersofmetaphysicswithoutanyscience）maypretend，thatlielongagobythepropheticspiritofhissoundsense，notonlysuspected，butknewandcomprehended，whatisherepropoundedwithsomuchado，or，ifhelikes，withprolixandpedanticpomp："thatwithallourreasonwecanneverreachbeyondthefieldofexperience。"Butwhenheisquestionedabouthisrationalprinciplesindividually，hemustgrant，thattherearemanyofthemwhichbehasnottakenfromexperience，andwhicharethereforeindependentofitandvalidapriori。Howthenandonwhatgroundswillherestrainbothhimselfandthedogmatist，whomakesuseoftheseconceptsandprinciplesbeyondallpossibleexperience，becausetheyarerecognizedtobeindependentofit？Andevenhe，thisadeptinsoundsense，inspiteofallhisassumedandcheaplyacquiredwisdom，isnotexemptfromwanderinginadvertentlybeyondobjectsofexperienceintothefieldofchimeras。Heisoftendeeplyenoughinvolvedinthem，thoughinannouncingeverythingasmereprobability，rationalconjecture，oranalogy，begivesbyhispopularlanguageacolortohisgroundlesspretensions。Sect。32。Sincetheoldestdaysofphilosophyinquirersintopurereasonhaveconceived，besidesthethingsofsense，orappearances（phenomena），whichmakeupthesensibleworld，certaincreationsoftheunderstanding（Verstandeswesen），callednoumena，whichshouldconstituteanintelligibleworld。Andasappearanceandillusionwerebythosemenidentified（athingwhichwemaywellexcuseinanundevelopedepoch），actualitywasonlyconcededtothecreationsofthought。Andweindeed，rightlyconsideringobjectsofsenseasmereappearances，confesstherebythattheyarebaseduponathinginitself，thoughweknownotthisthinginitsinternalconstitution，butonlyknowitsappearances，viz。，thewayinwhichoursensesareaffectedbythisunknownsomething。
　　Theunderstandingtherefore，byassumingappearances，grantstheexistenceofthingsinthemselvesalso，andsofarwemaysay，thattherepresentationofsuchthingsasformthebasisofphenomena，consequentlyofmerecreationsoftheunderstanding，isnotonlyadmissible，butunavoidable。Ourcriticaldeductionbynomeansexcludesthingsofthatsort（noumena），butratherlimitstheprinciplesoftheAesthetic（thescienceofthesensibility）
　　tothis，thattheyshallnotextendtoallthings，aseverythingwouldthenbeturnedintomereappearance，butthattheyshallonlyholdgoodofobjectsofpossibleexperience。Herebythenobjectsoftheunderstandingaregranted，butwiththeinculcationofthisrulewhichadmitsofnoexception：
　　"thatweneitherknownorcanknowanythingatalldefiniteofthesepureobjectsoftheunderstanding，becauseourpureconceptsoftheunderstandingaswellasourpureintuitionsextendtonothingbutobjectsofpossibleexperience，consequentlytomerethingsofsense，andassoonasweleavethisspheretheseconceptsretainnomeaningwhatever。"Sect。33。Thereisindeedsomethingseductiveinourpureconceptsoftheunderstanding，whichtemptsustoatranscendentuse，——ausewhichtranscendsallpossibleexperience。Notonlyareourconceptsofsubstance，ofpower，ofaction，ofreality，andothers，quiteindependentofexperience，containingnothingofsenseappearance，andsoapparentlyapplicabletothingsinthemselves（noumena），but，whatstrengthensthisconjecture，theycontainanecessityofdeterminationinthemselves，whichexperienceneverattains。
　　Theconceptofcauseimpliesarule，accordingtowhichonestatefollowsanothernecessarily;butexperiencecanonlyshowus，thatonestateofthingsoften，oratmost，commonly，followsanother，an（ithereforeaffordsneitherstrictuniversality，nornecessity。HencetheCategoriesseemtohaveadeepermeaningandimportthancanbeexhaustedbytheirempiricaluse，andsotheunderstandinginadvertentlyaddsforitselftothehouseofexperienceamuchmoreextensivewing，whichitfillswithnothingbutcreaturesofthought，withouteverobservingthatithastransgressedwithitsotherwiselawfulconceptstheboundsoftheiruse。Sect。34。Twoimportant，andevenindispensable，thoughverydry，investigationshadthereforebecomeindispensableintheCritiqueofPureReason，—viz。，thetwochapters"VomSchematismusderreinenVerstandsbegriffe，"and"VomGrundederUnterscheidungallerVerstandesbegriffeuberhauptinPhenomenaundNoumena。"Intheformeritisshown，thatthesensesfurnishnotthepureconceptsoftheunderstandinginconcreto，butonlytheschedulefortheiruse，andthattheobjectconformabletoitoccursonlyinexperience（astheproductoftheunderstandingfrommaterialsofthesensibility）。
　　Inthelatteritisshown，that，althoughourpureconceptsoftheunderstandingandourprinciplesareindependentofexperience，anddespiteoftheapparentlygreatersphereoftheiruse，stillnothingwhatevercanbethoughtbythembeyondthefieldofexperience，becausetheycandonothingbutmerelydeterminethelogicalformofthejudgmentrelativelytogivenintuitions。
　　Butasthereisnointuitionatallbeyondthefieldofthesensibility，thesepureconcepts，astheycannotpossiblybeexhibitedinconcrete，arevoidofallmeaning;consequentlyallthesenoumena，togetherwiththeircomplex，theintelligibleworld，17arenothingbutrepresentationofaproblem，ofwhichtheobjectinitselfispossible，butthesolution，fromthenatureofourunderstanding，totallyimpossible。Forourunderstandingisnotafacultyofintuition，butoftheconnectionofgivenintuitionsinexperience。Experiencemustthereforecontainalltheobjectsforourconcepts;butbeyonditnoconceptshaveanysignificance，asthereisnointuitionthatmightofferthemafoundation。Sect。35。Theimaginationmayperhapsbeforgivenforoccasionalvagaries，andfornotkeepingcarefullywithinthelimitsofexperience，sinceitgainslifeandvigorbysuchflights，andsinceitisalwayseasiertomoderateitsboldness，thantostimulateitslanguor。Buttheunderstandingwhichoughttothinkcanneverbeforgivenforindulginginvagaries;forwedependuponitaloneforassistancetosetbounds，whennecessary，tothevagariesoftheimagination。Buttheunderstandingbeginsitsaberrationsveryinnocentlyandmodestly。
　　Itfirstelucidatestheelementarycognitions，whichinhereinitpriortoallexperience，butyetmustalwayshavetheirapplicationinexperience。
　　Itgraduallydropstheselimits，andwhatistheretopreventit，asithasquitefreelyderiveditsprinciplesfromitself？Andthenitproceedsfirsttonewly—imaginedpowersinnature，thentobeingsoutsidenature;
　　inshorttoaworld，forwhoseconstructionthematerialscannotbewanting，becausefertilefictionfurnishesthemabundantly，andthoughnotconfirmed，isneverrefuted，byexperience。Thisisthereasonthatyoungthinkersarcsopartialtonietaph3，sicsofthetrulydogmaticalkind，andoftensacrificetoittheirtimeandtheirtalents，whichmightbeotherwisebetteremployed。Butthereisnouseintryingtomoderatethesefruitlessendeavorsofpurereasonbyallmannerofcautionsastothedifficultiesofsolvingquestionssooccult，bycomplaintsofthelimitsofourreason，andbydegradingourassertionsintomereconjectures。Foriftheirimpossibilityisnotdistinctlyshown，andreason’scognitionofitsownessencedoesnotbecomeatruescience，inwhichthefieldofitsrightuseisdistinguished，sotosay，withmathematicalcertaintyfromthatofitsworthlessandidleuse，thesefruitlesseffortswillneverbeabandonedforgood。Sect。36。HowisNatureitselfpossible？Thisquestion——thehighestpointthattranscendentalphilosophycaneverreach，andtowhich，asitsboundaryandcompletion，itmustproceed—properlycontainstwoquestions。First：Howisnatureatallpossibleinthematerialsense，byintuition，consideredasthetotalityofappearances;howarespace，time，andthatwhichfillsboth——theobjectofsensation，ingeneralpossible？Theansweris：BymeansoftheconstitutionofourSensibility，accordingtowhichitisspecificallyaffectedbyobjects，whichareinthemselvesunknowntoit，andtotallydistinctfromthosephenomena。ThisanswerisgivenintheCritiqueitselfinthetranscendentalAesthetic，andintheseProlegomenabythesolutionofthefirstgeneralproblem。Secondly：Howisnaturepossibleintheformalsense，asthetotalityoftherules，underwhichallphenomenamustcome，inordertobethoughtasconnectedinexperience？Theanswermustbethis：itisonlypossiblebymeansoftheconstitutionofourUnderstanding，accordingtowhichalltheaboverepresentationsofthesensibilityarenecessarilyreferredtoaconsciousness，andbywhichthepeculiarwayinwhichwethink（viz。，byrules），andhenceexperiencealso，arepossible，butmustbeclearlydistinguishedfromaninsightintotheobjectsinthemselves。ThisanswerisgivenintheCritiqueitselfinthetranscendentalLogic，andintheseProlegomena，inthecourseofthesolutionofthesecondmainproblem。Buthowthispeculiarpropertyofoursensibilityitselfispossible，orthatofourunderstandingandoftheapperceptionwhichisnecessarilyitsbasisandthatofallthinking，cannotbefurtheranalyzedoranswered，becauseitisofthemthatweareinneedforallouranswersandforallourthinkingaboutobjects。Therearemanylawsofnature，whichwecanonlyknowbymeansofexperience;
　　butconformitytolawintheconnectionofappearances，i。e。，innatureingeneral，wecannotdiscoverbyanyexperience，becauseexperienceitselfrequireslawswhichareaprioriatthebasisofitspossibility。Thepossibilityofexperienceingeneralisthereforeatthesametimetheuniversallawofnature，andtheprinciplesoftheexperiencearetheverylawsofnature。Forwedonotknownaturebutasthetotalityofappearances，i。e。，ofrepresentationsinus，andhencewecanonlyderivethelawsofitsconnectionfromtheprinciplesoftheirconnectioninus，thatis，fromtheconditionsoftheirnecessaryunioninconsciousness，whichconstitutesthepossibilityofexperience。Eventhemainpropositionexpoundedthroughoutthissection——thatuniversallawsofnaturecanbedistinctlyknownapriori——leadsnaturallytotheproposition：thatthehighestlegislationofnaturemustlieinourselves，i。e。，inourunderstanding，andthatwemustnotseektheuniversallawsofnatureinnaturebymeansofexperience，butconverselymustseeknature，astoitsuniversalconformitytolaw，intheconditionsofthepossibilityofexperience，whichlieinoursensibilityandinourunderstanding。
　　Forbowwereitotherwisepossibletoknowaprioritheselaws，astheyarenotrulesofanalyticalcognition，buttrulysyntheticalextensionsofit？Suchanecessaryagreementoftheprinciplesofpossibleexperiencewiththelawsofthepossibilityofnature，canonlyproceedfromoneoftworeasons：eithertheselawsaredrawnfromnaturebymeansofexperience，orconverselynatureisderivedfromthelawsofthepossibilityofexperienceingeneral，andisquitethesameasthemereuniversalconformitytolawofthelatter。Theformerisself—contradictory，fortheuniversallawsofnaturecanandmustbeknownapriori（thatis，independentofallexperience），andbethefoundationofallempiricaluseoftheunderstanding;
　　thelatteralternativethereforealoneremains。18Butwemustdistinguishtheempiricallawsofnature，whichalwayspresupposeparticularperceptions，fromthepureoruniversallawsofnature，which，withoutbeingbasedonparticularperceptions，containmerelytheconditionsoftheirnecessaryunioninexperience。Inrelationtothelatter，natureandpossibleexperiencearequitethesame，andastheconformitytolawheredependsuponthe—necessaryconnectionofappearancesinexperience（withoutwhichwecannotknowanyobjectwhateverinthesensibleworld），consequentlyupontheoriginallawsoftheunderstanding，itseemsatfirststrange，butisnotthelesscertain，tosay：Theunderstandingdoesnotderiveitslaws（apriori）from，butprescribesthemto，nature。Sect。37。Weshallillustratethisseeminglyboldpropositionbyanexample，whichwillshow，thatlaws，whichwediscoverinobjectsofsensuousintuition（especiallywhentheselawsareknownasnecessary），arecommonlyheldbyustobesuchashavebeenplacedtherebytheunderstanding，inspiteoftheirbeingsimilarinallpointstothelawsofnature，whichweascribetoexperience。Sect。38。Ifweconsiderthepropertiesofthecircle，bywhichthisfigurecombinessomanyarbitrarydeterminationsofspaceinitself，atonceinauniversalrule，wecannotavoidattributingaconstitution（eineNatur）
　　tothisgeometricalthing。Tworightlines，forexample，whichintersectoneanotherandthecircle，howsoevertheymaybedrawn，arealwaysdividedsothattherectangleconstructedwiththesegmentsoftheoneisequaltothatconstructedwiththesegmentsoftheother。Thequestionnowis：
　　Doesthislawlieinthecircleorintheunderstanding，thatis，Doesthisfigure，independentlyoftheunderstanding，containinitselfthegroundofthelaw，ordoestheunderstanding，havingconstructedaccordingtoitsconcepts（accordingtothequalityoftheradii）thefigureitself，introduceintoitthislawofthechordscuttingoneanotheringeometricalproportion？Whenwefollowtheproofsofthislaw，wesoonperceive，thatitcanonlybederivedfromtheconditiononwhichtheunderstandingfoundstheconstructionofthisfigure，andwhichisthatoftheequalityoftheradii。But，ifweenlargethisconcept，topursuefurthertheunityofvariouspropertiesofgeometricalfiguresundercommonlaws，andconsiderthecircleasaconicsection，whichofcourseissubjecttothesamefundamentalconditionsofconstructionasotherconicsections，weshallfindthatallthechordswhichintersectwithintheellipse，parabola，andhyperbola，alwaysintersectsothattherectanglesoftheirsegmentsarenotindeedequal，butalwaysbearaconstantratiotooneanother。Ifweproceedstillfarther，tothefundamentallawsofphysicalastronomy，wefindaphysicallawofreciprocalattractiondiffusedoverallmaterialnature，theruleofwhichis：IIthatitdecreasesinverselyasthesquareofthedistancefromeachattractingpoint，i。e。，asthesphericalsurfacesincrease，overwhichthisforcespreads，"whichlawseemstobenecessarilyinherentintheverynatureofthings，andhenceisusuallypropoundedasknowableapriori。Simpleasthesourcesofthislaware，merelyrestingupontherelationofsphericalsurfacesofdifferentradii，itsconsequencesaresovaluablewithregardtothevarietyoftheiragreementanditsregularity，thatnotonlyareallpossibleorbitsofthecelestialbodiesconicsections，butsucharelationoftheseorbitstoeachotherresults，thatnootherlawofattraction，thanthatoftheinversesquareofthedistance，canbeimaginedasfitforacosmicalsystem。Hereaccordinglyisanaturethatrestsuponlawswhichtheunderstandingknowsapriori，andchieflyfromtheuniversalprinciplesofthedeterminationofspace。NowIask：Dothelawsofnaturelieinspace，anddoestheunderstandinglearnthembymerelyendeavoringtofindouttheenormouswealthofmeaningthatliesinspace;ordotheyinhereintheunderstandingandinthewayinwhichitdeterminesspaceaccordingtotheconditionsofthesyntheticalunityinwhichitsconceptsareallcentered？Spaceissomethingsouniformandastoallparticularpropertiessoindeterminate，thatweshouldcertainlynotseekastoreoflawsofnatureinit。Whereasthatwhichdeterminesspacetoassumetheformofacircleorthefiguresofaconeandasphere，istheunderstanding，sofarasitcontainsthegroundoftheunityoftheirconstructions。Themereuniversalformofintuition，calledspace，mustthereforebethesubstratumofallintuitionsdeterminabletoparticularobjects，andinitofcoursetheconditionofthepossibilityandofthevarietyoftheseintuitionslies。Buttheunityoftheobjectsisentirelydeterminedbytheunderstanding，andonconditionswhichlieinitsownnature;andthustheunderstandingistheoriginoftheuniversalorderofnature，inthatitcomprehendsallappearancesunderitsownlaws，andtherebyfirstconstructs，apriori，experience（astoitsform），bymeansofwhichwhateveristobeknownonlybyexperience，isnecessarilysubjectedtoitslaws。
　　Forwearenotnowconcernedwiththenatureofthingsinthemselves，whichisindependentoftheconditionsbothofoursensibilityandourunderstanding，butwithnature，asanobjectofpossibleexperience，andinthiscasetheunderstanding，whilstitmakesexperiencepossible，therebyinsiststhatthesensuousworldiseithernotanobjectofexperienceatall，ormustbenature[viz。，anexistenceofthings，determinedaccordingtouniversallaws19]。APPENDIXTOTHEPURESCIENCEOFNATURE。Sect。39。OftheSystemoftheCategories。Therecanbenothingmoredesirabletoaphilosopher，thantobeabletoderivethescatteredmultiplicityoftheconceptsortheprinciples，whichhadoccurredtohiminconcreteuse，fromaprincipleapriori，andtouniteeverythinginthiswayinonecognition。Heformerlyonlybelievedthatthosethings，whichremainedafteracertainabstraction，andseemedbycomparisonamongoneanothertoconstituteaparticularkindofcognitions，werecompletelycollected;butthiswasonlyanAggregate。
　　Nowheknows，thatjustsomany，neithermorenorless，canconstitutethemodeofcognition，andperceivesthenecessityofhisdivision，whichconstitutescomprehension;andnowonlyhehasattainedaSystem。Tosearchinourdailycognitionfortheconcepts，whichdonotrestuponparticularexperience，andyetoccurinallcognitionofexperience，wheretheyasitwereconstitutethemereformofconnection，presupposesneithergreaterreflectionnordeeperinsight，thantodetectinalanguagetherulesoftheactualuseofwordsgenerally，andthustocollectelementsforagrammar。Infactbothresearchesareverynearlyrelated，eventhoughwearenotabletogiveareasonwhyeachlanguagehasjustthisandnootherformalconstitution，andstilllesswhyanexactnumberofsuchformaldeterminationsingeneralarefoundinit。AristotlecollectedtenpureelementaryconceptsunderthenameofCategories。20Tothese，whicharealsocalledpredicaments，21hefoundhimselfobligedafterwardstoaddfivepost—predicaments，someofwhichhowever（prius，simul，andmolus）arecontainedintheformer;
　　butthisrandomcollectionmustbeconsidered（andcommended）asamerehintforfutureinquirers，notasaregularlydevelopedidea，andhenceithas，inthepresentmoreadvancedstateofphilosophy，beenrejectedasquiteuseless。Afterlongreflectiononthepureelementsofhumanknowledge（thosewhichcontainnothingempirical），IatlastsucceededindistinguishingwithcertaintyandinseparatingthepureelementarynotionsoftheSensibility（spaceandtime）fromthoseoftheUnderstanding。Thusthe7th，8th，and8thCategorieshadtobeexcludedfromtheoldlist。Andtheotherswereofnoservicetome;becausetherewasnoprinciple[inthem]，onwhichtheunderstandingcouldbeinvestigated，measuredinitscompletion，andallthefunctions，whenceitspureconceptsarise，determinedexhaustivelyandwithprecision。Butinordertodiscoversuchaprinciple，Ilookedaboutforanactoftheunderstandingwhichcomprisesalltherest，andisdistinguishedonlybyvariousmodificationsorphases，inreducingthemultiplicityofrepresentationtotheunityofthinkingingeneral：Ifoundthisactoftheunderstandingtoconsistinjudging。Herethenthelaborsofthelogicianswerereadyathand，thoughnotyetquitefreefromdefects，andwiththishelpIwasenabledtoexhibitacompletetableofthepurefunctionsoftheunderstanding，whicharehoweverundeterminedinregardtoanyobject。Ifinallyreferredthesefunctionsofjudgingtoobjectsingeneral，orrathertotheconditionofdeterminingjudgmentsasobjectivelyvalid，andsotherearosethepureconceptsoftheunderstanding，concerningwhichIcouldmakecertain，thatthese，andthisexactnumberonly，constituteourwholecognitionofthingsfrompureunderstanding。Iwasjustifiedincallingthembytheiroldname，Categories，whileIreservedformyselfthelibertyofadding，underthetitleof"Predicables，"acompletelistofalltheconceptsdeduciblefromthem，bycombinationswhetheramongthemselves，orwiththepureformoftheappearance，i。e。，spaceortime，orwithitsmatter，sofarasitisnotyetempiricallydetermined（viz。，theobjectofsensationingeneral），assoonasasystemoftranscendentalphilosophyshouldbecompletedwiththeconstructionofwhichIamengagedintheCritiqueofPureReasonitself。NowtheessentialpointinthissystemofCategories，whichdistinguishesitfromtheoldrhapsodicalcollectionwithoutanyprinciple，andforwhichaloneitdeservestobeconsideredasphilosophy，consistsinthis：thatbymeansofitthetruesignificanceofthepureconceptsoftheunderstandingandtheconditionoftheirusecouldbepreciselydetermined。Forhereitbecameobviousthattheyarethemselvesnothingbutlogicalfunctions，andassuchdonotproducetheleastconceptofanobject，butrequiresomesensuousintuitionasabasis。Theythereforeonlyservetodetermineempiricaljudgments，whichareotherwiseundeterminedandindifferentasregardsallfunctionsofjudging，relativelytothesefunctions，therebyprocuringthemuniversalvalidity，andbymeansofthemmakingjudgmentsofexperienceingeneralpossible。Suchaninsightintothenatureofthecategories，whichlimitsthematthesametimetothemereuseofexperience，neveroccurredeithertotheirfirstauthor，ortoanyofhissuccessors;butwithoutthisinsight（whichimmediatelydependsupontheirderivationordeduction），theyarequiteuselessandonlyamiserablelistofnames，withoutexplanationorrulefortheiruse。Hadtheancientseverconceivedsuchanotion，doubtlessthewholestudyofthepurerationalknowledge，whichunderthenameofmetaphysicshasforcenturiesspoiledmanyasoundmind，wouldhavereachedus。inquiteanothershape，andwouldhaveenlightenedthehumanunderstanding，insteadofactuallyexhaustingitinobscureandvainspeculations，therebyrenderingitunfitfortruescience。Thissystemofcategoriesmakesalltreatmentofeveryobjectofpurereasonitselfsystematic，andaffordsadirectionorcluehowandthroughwhatpointsofinquiryeverymetaphysicalconsiderationmustproceed，inordertobecomplete;foritexhaustsallthepossiblemovements（momenta）oftheunderstanding，amongwhicheveryconceptmustbeclassed。InlikemannerthetableofPrincipleshasbeenformulated，thecompletenessofwhichwecanonlyvouchforbythesystemofthecategories。Eveninthedivisionoftheconcepts，22whichmustgobeyondthephysicalapplicationoftheunderstanding，itisalwaystheverysameclue，which，asitmustalwaysbedeterminedaprioribythesamefixedpointsofthehumanunderstanding，alwaysformsaclosedcircle。Thereisnodoubtthattheobjectofapureconceptioneitheroftheunderstandingorofreason，sofarasitistobeestimatedphilosophicallyandonaprioriprinciples，caninthiswaybecompletelyknown。Icouldnotthereforeomittomakeuseofthiscluewithregardtooneofthemostabstractontologicaldivisions，viz。，thevariousdistinctionsof"thenotionsofsomethingandofnothing，"
　　andtoconstructaccordingly（Critique，P。207）aregularandnecessarytableoftheirdivisions。23Andthissystem，likeeveryothertrueonefoundedonauniversalprinciple，showsitsinestimablevalueinthis，thatitexcludesallforeignconcepts，whichmightotherwiseintrudeamongthepureconceptsoftheunderstanding，anddeterminestheplaceofeverycognition。Thoseconcepts，whichunderthenameof"conceptsofreflection"havebeenlikewisearrangedinatableaccordingtotheclueofthecategories，intrude，withouthavinganyprivilegeortitletobeamongthepureconceptsoftheunderstandinginOntology。
　　Theyareconceptsofconnection，andtherebyoftheobjectsthemselves，whereastheformerareonlyconceptsofamerecomparisonofconceptsalreadygiven，henceofquiteanothernatureanduse。Bymysystematicdivision24theyaresavedfromthisconfusion。Butthevalueofmyspecialtableofthecategorieswillbestillmoreobvious，whenweseparatethetableofthetranscendentalconceptsofReasonfromtheconceptsoftheunderstanding。
　　Thelatterbeingofquiteanothernatureandorigin，theymusthavequiteanotherformthantheformer。Thissonecessaryseparationhasneveryetbeenmadeinanysystemofmetaphysicsfor，asarule，theserationalconceptsallmixedupwiththecategories，likechildrenofonefamily，whichconfusionwasunavoidableintheabsenceofadefinitesystemofcategories。Kant’s"Prolegomena"—ThirdPart（InternetEncyclopediaofPhilosophy）ThirdPartOfTheMainTranscendentalProblem。HowIsMetaphysicsInGeneralPossible？Sect。40。Puremathematicsandpurescienceofnaturehadnooccasionforsuchadeduction，aswehavemadeofboth，fortheirownsafetyandcertainty。
　　Fortheformerrestsuponitsownevidence;andthelatter（thoughsprungfrompuresourcesoftheunderstanding）uponexperienceanditsthoroughconfirmation。Physicscannotaltogetherrefuseanddispensewiththetestimonyofthelatter;becausewithallitscertainty，itcannever，asphilosophy，rivalmathematics。Bothsciencesthereforestoodinneedofthisinquiry，notforthemselves，butforthesakeofanotherscience，metaphysics。Metaphysicshastodonotonlywithconceptsofnature，whichalwaysfindtheirapplicationinexperience，butalsowithpurerationalconcepts，whichnevercanbegiveninanypossibleexperience。Consequentlytheobjectiverealityoftheseconcepts（viz。，thattheyarenotmerechimeras），andthetruthorfalsityofmetaphysicalassertions，cannotbediscoveredorconfirmedbyanyexperience。Thispartofmetaphysicshoweverispreciselywhatconstitutesitsessentialend，towhichtherestisonlyameans，andthusthisscienceisinneedofsuchadeductionforits，ownsake。
　　Thethirdquestionnowproposedrelatesthereforeasitweretotherootandessentialdifferenceofmetaphysics，i。e。，theoccupationofReasonwithitself，andthesupposedknowledgeofobjectsarisingimmediatelyfromthisincubationofitsownconcepts，withoutrequiring，orindeedbeingabletoreachthatknowledgethrough，experience。25Withoutsolvingthisproblemreasonneverisjustified。Theempiricalusetowhichreasonlimitsthepureunderstanding，doesnotfullysatisfytheproperdestinationofthelatter。Everysingleexperienceisonlyapartofthewholesphereofitsdomain，buttheabsolutetotalityofallpossibleexperienceisitselfnotexperience。Yetitisanecessary[concrete]problemforreason，themererepresentationofwhichrequiresconceptsquitedifferentfromthecategories，whoseuseisonlyimmanent，orreferstoexperience，sofarasitcanbegiven。Whereastheconceptsofreasonaimatthecompleteness，i。e。，thecollectiveunityofallpossibleexperience，andtherebytranscendeverygivenexperience。Thustheybecometranscendent。Astheunderstandingstandsinneedofcategoriesforexperience，reasoncontainsinitselfthesourceofideas，bywhichImeannecessaryconcepts，whoseobjectcannotbegiveninanyexperience。Thelatterareinherentinthenatureofreason，astheformerareinthatoftheunderstanding。
　　Whiletheformercarrywiththemanillusionlikelytomislead，theillusionofthelatterisinevitable，thoughitcertainlycanbekeptfrommisleadingus。Sinceallillusionconsistsinholdingthesubjectivegroundofourjudgmentstobeobjective，aself—knowledgeofpurereasoninitstranscendent（exaggerated）
　　useisthesolepreservativefromtheaberrationsintowhichreasonfallswhenitmistakesitsdestination，andrefersthattotheobjecttranscendently，whichonlyregardsitsownsubjectanditsguidanceinallimmanentuse。Sect。41。Thedistinctionofideas，thatis，ofpureconceptsofreason，fromcategories，orpureconceptsoftheunderstanding，ascognitionsofaquitedistinctspecies，originanduse，issoimportantapointinfoundingasciencewhichistocontainthesystemofalltheseaprioricognitions，thatwithoutthisdistinctionmetaphysicsisabsolutelyimpossible，orisatbestarandom，bunglingattempttobuildacastleintheairwithoutaknowledgeofthematerialsoroftheirfitnessforanypurpose。HadtheCritiqueofPureReasondonenothingbutfirstpointoutthisdistinction，ithadtherebycontributedmoretoclearupourconceptionof，andtoguideourinquiryin，thefieldofmetaphysics，thanallthevaineffortswhichhavehithertobeenmadetosatisfythetranscendentproblemsofpurereason，withouteversurmisingthatwewereinquiteanotherfieldthanthatoftheunderstanding，andhenceclassingconceptsoftheunderstandingandthoseofreasontogether，asiftheywereofthesamekind。Sect。42。Allpurecognitionsoftheunderstandinghavethisfeature，thattheirconceptspresentthemselvesinexperience，andtheirprinciplescanbeconfirmedbyit;whereasthetranscendentcognitionsofreasoncannot，eitherasideas，appearinexperience，—oraspropositionseverbeconfirmedorrefutedbyit。Hencewhatevererrorsmayslipinunawares，canonlybediscoveredbypurereasonitself—adiscoveryofmuchdifficulty，becausethisveryreasonnaturallybecomesdialecticalbymeansofitsideas，andthisunavoidableillusioncannotbelimitedbyanyobjectiveanddogmaticalresearchesintothings，butbyasubjectiveinvestigationofreasonitselfasasourceofideas。Sect。43。IntheCritiqueofPureReasonitwasalwaysmygreatestcaretoendeavornotonlycarefullytodistinguishtheseveralspeciesofcognition，buttoderiveconceptsbelongingtoeachoneofthemfromtheircommonsource。Ididthisinorderthatbyknowingwhencetheyoriginated，Imightdeterminetheirusewithsafety，andalsohavetheunanticipatedbutinvaluableadvantageofknowingthecompletenessofmyenumeration，classificationandspecificationofconceptsapriori，andthereforeaccordingtoprinciples。Withoutthis，metaphysicsismererhapsody，inwhichnooneknowswhetherhehasenough，orwhetherandwheresomethingisstillwanting。Wecanindeedhavethisadvantageonlyinpurephilosophy，butofthisphilosophyitconstitutestheveryessence。AsIhadfoundtheoriginofthecategoriesinthefourlogicalfunctionsofallthejudgmentsoftheunderstanding，itwasquitenaturaltoseektheoriginoftheideasinthethreefunctionsofthesyllogismsofreason。
　　Forassoonasthesepureconceptsofreason（thetranscendentalideas）
　　aregiven，theycouldhardly，excepttheybeheldinnate，befoundanywhereelse，thaninthesameactivityofreason，which，sofarasitregardsmereform，constitutesthelogicalelementofthesyllogismsofreason;
　　but，sofarasitrepresentsjudgmentsoftheunderstandingwithrespecttotheoneortotheotherformapriori，constitutestranscendentalconceptsofpurereason。Theformaldistinctionofsyllogismsrenderstheirdivisionintocategorical，hypothetical，anddisjunctivenecessary。Theconceptsofreasonfoundedonthemcontainedtherefore，first，theideaofthecompletesubject（thesubstantial）;secondly，theideaofthecompleteseriesofconditions;
　　thirdly，thedeterminationofallconceptsintheideaofacompletecomplexofthatwhichispossible。26Thefirstideaispsychological，thesecondcosmological，thethirdtheological，and，asallthreegiveoccasiontoDialectics，yeteachinitsownway，thedivisionofthewholeDialectsofpurereasonintoitsParalogism，itsAntinomy，anditsIdeal，wasarrangedaccordingly。Throughthisdeductionwemayfeelassuredthatalltheclaimsofpurereasonarecompletelyrepresented，andthatnonecanbewanting;becausethefacultyofreasonitself，whencetheyalltaketheirorigin，istherebycompletelysurveyed。Sect。44。Inthesegeneralconsiderationsitisalsoremarkablethattheideasofreasonareunlikethecategories，ofnoservicetotheuseofourunderstandinginexperience，butquitedispensable，andbecomeevenanimpedimenttothemaximsofarationalcognitionofnature。Yetinanotheraspectstilltobedeterminedtheyarenecessary。Whetherthesoulisorisnotasimplesubstance，isofnoconsequencetousintheexplanationofitsphenomena。Forwecannotrenderthenotionofasimplebeingintelligiblebyanypossibleexperiencethatissensuousorconcrete。Thenotionisthereforequitevoidasregardsallhoped—forinsightintothecauseofphenomena，andcannotatallserveasaprincipleoftheexplanationofthatwhichinternalorexternalexperiencesupplies。Sothecosmologicalideasofthebeginningoftheworldorofitseternity（aparteante）cannotbeofanygreaterservicetousfortheexplanationofanyeventintheworlditself。Andfinallywemust，accordingtoarightmaximofthephilosophyofnature，refrainfromallexplanationsofthedesignofnature，drawnfromthewillofaSupremeBeing;becausethiswouldnotbenaturalphilosophy，butanacknowledgmentthatwehavecometotheendofit。Theuseoftheseideas，therefore，isquitedifferentfromthatofthosecategoriesbywhich（andbytheprinciplesbuiltuponwhich）experienceitselffirstbecomespossible。ButourlaboriousanalyticsoftheunderstandingwouldbesuperfluousifwehadnothingelseinviewthanthemerecognitionOfnatureasitcanbegiveninexperience;forreasondoesitswork，bothinmathematicsandinthescienceofnature，quitesafelyandwellwithoutanyofthissubtlededuction。ThereforeourCritiqueoftheUnderstandingcombineswiththeideasofpurereasonforapurposewhichliesbeyondtheempiricaluseoftheunderstanding;butthiswehaveabovedeclaredtobeinthisaspecttotallyinadmissible，andwithoutanyobjectormeaning。Yettheremustbeaharmonybetweenthatofthenatureofreasonandthatoftheunderstanding，andtheformermustcontributetotheperfectionofthelatter，andcannotpossiblyupsetit。Thesolutionofthisquestionisasfollows：Purereasondoesnotinitsideaspointtoparticularobjects，whichliebeyondthefieldofexperience，butonlyrequirescompletenessoftheuseoftheunderstandinginthesystemofexperience。Butthiscompletenesscanbeacompletenessofprinciplesonly，notofintuitions[i。e。，concreteatsightsorAnschauungen]
　　andofobjects。Inorderhowevertorepresenttheideasdefinitely，reasonconceivesthemafterthefashionofthecognitionofanobject。Thecognitionisasfarastheserulesareconcernedcompletelydetermined，buttheobjectisonlyanideainventedforthepurposeofbringingthecognitionoftheunderstandingasnearaspossibletothecompletenessrepresentedbythatidea。PrefatoryRemarktotheDialecticsofPureReason。Sect。45。WehaveaboveshowninSect。Sect。33and34thatthepurityofthecategoriesfromalladmixtureofsensuousdeterminationsmaymisleadreasonintoextendingtheiruse，quitebeyondallexperience，tothingsinthemselves;thoughasthesecategoriesthemselvesfindnointuitionwhichcangivethemmeaningorsenseinconcrete，they，asmerelogicalfunctions，canrepresentathingingeneral，butnotgivebythemselvesaloneadeterminateconceptofanything。SuchhyperbolicalobjectsaredistinguishedbytheappellationofNoumena，orpurebeingsoftheunderstanding（orbetter，beingsofthought），suchas，forexample，"substance，"butconceivedwithoutpermanenceintime，or"cause，"butnotactingintime，etc。Herepredicates，thatonlyservetomaketheconformity—to—lawofexperiencepossible，areappliedtotheseconcepts，andyettheyaredeprivedofalltheconditionsofintuition，onwhichaloneexperienceispossible，andsotheseconceptsloseallsignificance。Thereisnodanger，however，oftheunderstandingspontaneouslymakinganexcursionsoverywantonlybeyonditsownboundsintothefieldofthemerecreaturesofthought，withoutbeingimpelledbyforeignlaws。Butwhenreason，whichcannotbefullysatisfiedwithanyempiricaluseoftherulesoftheunderstanding，asbeingalwaysconditioned，requiresacompletionofthischainofconditions，thentheunderstandingisforcedoutofitssphere。Andthenitpartlyrepresentsobjectsofexperienceinaseriessoextendedthatnoexperiencecangrasp，partlyeven（withaviewtocompletetheseries）itseeksentirelybeyonditnoumena，towhichitcanattachthatchain，andso，havingatlastescapedfromtheconditionsofexperience，makeitsattitudeasitwerefinal。Thesearethenthetranscendentalideas，which，thoughaccordingtothetruebuthiddenendsofthenaturaldeterminationofourreason，theymayaimnotatextravagantconcepts，butatanunboundedextensionoftheirempiricaluse，yetseducetheunderstandingbyanunavoidableillusiontoatranscendentuse，which，thoughdeceitful，cannotberestrainedwithintheboundsofexperiencebyanyresolution，butonlybyscientificinstructionandwithmuchdifficulty。！。ThePsychologicalIdea。27Sect。46。Peoplehavelongsinceobserved，thatinallsubstancesthepropersubject，thatwhichremainsafteralltheaccidents（aspredicates）areabstracted，consequentlythatwhichformsthesubstanceofthingsremainsunknown，andvariouscomplaintshavebeenmadeconcerningtheselimitstoourknowledge。Butitwillbewelltoconsiderthatthehumanunderstandingisnottobeblamedforitsinabilitytoknowthesubstanceofthings，thatis，todetermineitbyitself，butratherforrequiringtoknowitwhichisamereideadefinitelyasthoughitwereagivenobject。Purereasonrequiresustoseekforeverypredicateofathingitspropersubject，andforthissubject，whichisitselfnecessarilynothingbutapredicate，itssubject，andsoonindefinitely（orasfaraswecanreach）。Buthenceitfollows，thatwemustnotholdanything，atwhichwecanarrive，tobeanultimatesubject，andthatsubstanceitselfnevercanbethoughtbyourunderstanding，howeverdeepwemaypenetrate，evenifallnaturewereunveiledtous。Forthespecificnatureofourunderstandingconsistsinthinkingeverythingdiscursively，thatis，representingitbyconcepts，andsobymerepredicates，towhichthereforetheabsolutesubjectmustalwaysbewanting。Hencealltherealproperties，bywhichweknowbodies，aremereaccidents，notexceptingimpenetrability，whichwecanonlyrepresenttoourselvesastheeffectofapowerofwhichthesubjectisunknowntous。Nowweappeartohavethissubstanceintheconsciousnessofourselves（inthethinkingsubject），andindeedinanimmediateintuition;forallthepredicatesofaninternalsenserefertotheego，asasubject，andIcannotconceivemyselfasthepredicateofanyothersubject。Hencecompletenessinthereferenceofthegivenconceptsaspredicatestoasubject——notmerelyanidea，butanobject—thatis，theabsolutesubjectitself，seemstobegiveninexperience。Butthisexpectationisdisappointed。Fortheegoisnotaconcept，28butonlytheindicationoftheobjectoftheinternalsense，sofarasweknowitbynofurtherpredicate。Consequentlyitcannotbeinitselfapredicateofanyotherthing;butjustaslittlecanitbeadeterminateconceptofanabsolutesubject，butis，asinallothercases，onlythereferenceoftheinternalphenomenatotheirunknownsubject。Yetthisidea（whichservesverywell，asaregulativeprinciple，totallytodestroyallmaterialisticexplanationsoftheinternalphenomenaofthesoul）occasionsbyaverynaturalmisunderstandingaveryspeciousargument，which，fromthissupposedcognitionofthesubstanceofourthinkingbeing，infersitsnature，sofarastheknowledgeofitfallsquitewithoutthecomplexofexperience。Sect。47。Butthoughwemaycallthisthinkingself（thesoul）substance，asbeingtheultimatesubjectofthinkingwhichcannotbefurtherrepresentedasthepredicateofanotherthing;itremainsquiteemptyandwithoutsignificance，ifpermanence—thequalitywhichrenderstheconceptofsubstancesinexperiencefruitful—cannotbeprovedofit。Butpermanencecanneverbeprovedoftheconceptofasubstance，asathinginitself，butforthepurposesofexperienceonly。ThisissufficientlyshownbythefirstAnalogyofExperience，29andwhoeverwillnotyieldtothisproofmaytryforhimselfwhetherhecansucceedinproving，fromtheconceptofasubjectwhichdoesnotexistitselfasthepredicateofanotherthing，thatitsexistenceisthoroughlypermanent，andthatitcannoteitherinitselforbyanynaturalcauseoriginalorbeannihilated。
　　Thesesyntheticalaprioripropositionscanneverbeprovedinthemselves，butonlyinreferencetothingsasobjectsofpossibleexperience。Sect。48。Ifthereforefromtheconceptofthesoulasasubstance，wewouldinferitspermanence，thiscanholdgoodasregardspossibleexperienceonly，not[ofthesoul]asathinginitselfandbeyondallpossibleexperience。
　　Butlifeisthesubjectiveconditionofallourpossibleexperience，consequentlywecanonlyinferthepermanenceofthesoulinlife;forthedeathofmanistheendofallexperiencewhichconcernsthesoulasanobjectofexperience，exceptthecontrarybeproved，whichistheveryquestioninhand。Thepermanenceofthesoulcanthereforeonlybeproved（andnoonecaresforthat）duringthelifeofman，butnot，aswedesiretodo，afterdeath;andforthisgeneralreason，thattheconceptofsubstance，sofarasitistobeconsiderednecessarilycombinedwiththeconceptofpermanence，canbesocombinedonlyaccordingtotheprinciplesofpossibleexperience，andthereforeforthepurposesofexperienceonly。30Sect。49。Thatthereissomethingrealwithoutuswhichnotonlycorresponds，butmustcorrespond，toourexternalperceptions，canlikewisebeprovedtobenotaconnectionofthingsinthemselves，butforthesakeofexperience。
　　Thismeansthatthereissomethingempirical，i。e。，somephenomenoninspacewithoutus，thatadmitsofasatisfactoryproof，forwehavenothingtodowithotherobjectsthanthosewhichbelongtopossibleexperience;
　　becauseobjectswhichcannotbegivenusinanyexperience，donotexistforus。Empiricallywithoutmeisthatwhichappearsinspace，andspace，togetherwithallthephenomenawhichitcontains，belongstotherepresentations，whoseconnectionaccordingtolawsofexperienceprovestheirobjectivetruth，justastheconnectionofthephenomenaoftheinternalsenseprovestheactualityofmysoul（asanobjectoftheinternalsense）。BymeansofexternalexperienceIamconsciousoftheactualityofbodies，asexternalphenomenainspace，inthesamemannerasbymeansoftheinternalexperienceIamconsciousoftheexistenceofmysoulintime，butthissoulisonlyknownasanobjectoftheinternalsensebyphenomenathatconstituteaninternalstate，andofwhichtheessenceinitself，whichformsthebasisofthesephenomena，isunknown。Cartesianidealismthereforedoesnothingbutdistinguishexternalexperiencefromdreaming;andtheconformitytolaw（asacriterionofitstruth）oftheformer，fromtheirregularityandthefalseillusionofthelatter。Inbothitpresupposesspaceandtimeasconditionsoftheexistenceofobjects，anditonlyinquireswhethertheobjectsoftheexternalsenses，whichwewhenawakeputinspace，areasactuallytobefoundinit，astheobjectoftheinternalsense，thesoul，isintime;thatis，whetherexperiencecarrieswithitsurecriteriatodistinguishitfromimagination。Thisdoubt，however，mayeasilybedisposedof，andwealwaysdosoincommonlifebyinvestigatingtheconnectionofphenomenainbothspaceandtimeaccordingtouniversallawsofexperience，andwecannotdoubt，whentherepresentationofexternalthingsthroughoutagreestherewith，thattheyconstitutetruthfulexperience。Materialidealism，inwhichphenomenaareconsideredassuchonlyaccordingtotheirconnectioninexperience，mayaccordinglybeveryeasilyrefuted;anditisjustassureanexperience，thatbodiesexistwithoutus（inspace），asthatI
　　myselfexistaccordingtotherepresentationoftheinternalsense（intime）：forthenotionwithoutus，onlysignifiesexistenceinspace。HoweverastheEgointheproposition，IIIam，"meansnotonlytheobjectofinternalintuition（intime），butthesubjectofconsciousness，justasbodymeansnotonlyexternalintuition（inspace），butthething—in—itself，whichisthebasisofthisphenomenon;[asthisisthecase]thequestion，whetherbodies（asphenomenaoftheexternalsense）existasbodiesapartfrommythoughts，maywithoutanyhesitationbedeniedinnature。Butthequestion，whetherImyselfasaphenomenonoftheinternalsense（thesoulaccordingtoempiricalpsychology）existapartfrommyfacultyofrepresentationintime，isanexactlysimilarinquiry，andmustlikewisebeansweredinthenegative。Aridinthismannereverything，whenitisreducedtoitstruemeaning，isdecidedandcertain。Theformal（whichIhavealsocalledtranscendental）actuallyabolishesthematerial，orCartesian，idealism。
　　Forifspacebenothingbutaformofmysensibility，itisasarepresentationinmejustasactualasImyselfam，andnothingbuttheempiricaltruthoftherepresentationsinitremainsforconsideration。But，ifthisisnotthecase，ifspaceandthephenomenainitaresomethingexistingwithoutus，thenallthecriteriaofexperiencebeyondourperceptioncanneverprovetheactualityoftheseobjectswithoutus。II。TheCosmologicalIdea。31Sect。50。Thisproductofpurereasoninitstranscendentuseisitsmostremarkablecuriosity。Itservesasaverypowerfulagenttorousephilosophyfromitsdogmaticslumber，andtostimulateittothearduoustaskofundertakingaCritiqueofReasonitself。Itermthisideacosmological，becauseitalwaystakesitsobjectonlyfromthesensibleworld，anddoesnotuseanyotherthanthosewhoseobjectisgiventosense，consequentlyitremainsinthisrespectinitsnativehome，itdoesnotbecometranscendent，andisthereforesofarnotmereidea;whereas，toconceivethesoulasasimplesubstance，—alreadymeanstoconceivesuchanobject（thesimple）ascannotbepresentedtothesenses。
　　Yetthecosmologicalideaextendstheconnectionoftheconditionedwithitscondition（whethertheconnectionismathematicalordynamical）sofar，thatexperiencenevercankeepupwithit。Itisthereforewithregardtothispointalwaysanidea，whoseobjectnevercanbeadequatelygiveninanyexperience。Sect。51。Inthefirstplace，theuseofasystemofcategoriesbecomesheresoobviousandunmistakable，thateveniftherewerenotseveralotherproofsofit，thisalonewouldsufficientlyproveitindispensableinthesystemofpurereason。Thereareonlyfoursuchtranscendentideas，astherearesomanyclassesofcategories;ineachofwhich，however，theyreferonlytotheabsolutecompletenessoftheseriesoftheconditionsforagivenconditioned。Inanalogytothesecosmologicalideasthereareonlyfourkindsofdialecticalassertionsofpurereason，which，astheyaredialectical，therebyprove，thattoeachofthem，oiiequallyspeciousprinciplesofpurereason，acontradictoryassertionstandsopposed。Asallthemetaphysicalartofthemostsubtledistinctioncannotpreventthisopposition，itcompelsthephilosophertorecurtothefirstsourcesofpurereasonitself。ThisAntinomy，notarbitrarilyinvented，butfoundedinthenatureofhumanreason，andhenceunavoidableandneverceasing，containsthefollowingfourthesestogetherwiththeirantitheses：1。
　　Thesis：TheWorldhas，asto，TimeandSpace，aBeginning（limit）。
　　Antithesis：TheWorldis，astoTimeandSpace，infinite。2。
　　Thesis：EverythingintheWorldconsistsof[elementsthatare]simple。
　　Antithesis：Thereisnothingsimple，buteverythingiscomposite。
　　3。
　　Thesis：ThereareintheWorldCausesthroughFreedom。
　　Antithesis：ThereisnoLiberty，butallisNature。
　　4。
　　Thesis：IntheSeriesoftheWorld—CausesthereissomenecessaryBeing。
　　Antithesis：ThereisNothingnecessaryintheWorld，butinthisSeriesAllisincidental。Sect。52。a。Hereisthemostsingularphenomenonofhumanreason，nootherinstanceofwhichcanbeshowninanyotheruse。Ifwe，asiscommonlydone，representtoourselvestheappearancesofthesensibleworldasthingsinthemselves，ifweassumetheprinciplesoftheircombinationasprinciplesuniversallyvalidofthingsinthemselvesandnotmerelyofexperience，asisusually，naywithoutourCritique，unavoidablydone，therearisesanunexpectedconflict，whichnevercanberemovedinthecommondogmaticalway;becausethethesis，aswellastheantithesis，canbeshownbyequallyclear，evident，andirresistibleproofs—forIpledgemyselfastothecorrectnessofalltheseproofs—andreasonthereforeperceivesthatitisdividedwithitself，astateatwhichtheskepticrejoices，butwhichmustmakethecriticalphilosopherpauseandfeelillatease。Sect。52。b。Wemayblunderinvariouswaysinmetaphysicswithoutanyfearofbeingdetectedinfalsehood。Forwenevercanberefutedbyexperienceifwebutavoidself—contradiction，whichinsynthetical，thoughpurelyfictitiouspropositions，maybedonewhenevertheconcepts，whichweconnect，aremereideas，thatcannotbegiven（intheirwholecontent）inexperience。
　　Forhowcanwemakeoutbyexperience，whethertheworldisfrometernityorhadabeginning，whethermatterisinfinitelydivisibleorconsistsofsimpleparts？Suchconceptcannotbegiveninanyexperience，beiteversoextensive，andconsequentlythefalsehoodeitherofthepositiveorthenegativepropositioncannotbediscoveredbythistouchstone。TheonlypossiblewayinwhichreasoncouldhaverevealedunintentionallyitssecretDialectics，falselyannouncedasDogmatics，wouldbewhenitweremadetogroundanassertionuponauniversallyadmittedprinciple，andtodeducetheexactcontrarywiththegreatestaccuracyofinferencefromanotherwhichisequallygranted。Thisisactuallyherethecasewithregardtofournaturalideasofreason，whencefourassertionsontheoneside，andasmanycounter—assertionsontheotherarise，eachconsistentlyfollowingfromuniversally—acknowledgedprinciples。Thustheyrevealbytheuseoftheseprinciplesthedialecticalillusionofpurereasonwhichwouldotherwiseforeverremainconcealed。Thisisthereforeadecisiveexperiment，whichmustnecessarilyexposeanyerrorlyinghiddenintheassumptionsofreason。32Contradictorypropositionscannotbothbefalse，excepttheconcept，whichisthesubjectofboth，isself—contradictory;forexample，thepropositions，"asquarecircleisround，andasquarecircleisnotround，"arebothfalse。For，astotheformeritisfalse，thatthecircleisround，becauseitisquadrangular;
　　anditislikewisefalse，thatitisnotround，thatis，angular，becauseitisacircle。Forthelogicalcriterionoftheimpossibilityofaconceptconsistsinthis，thatifwepresupposeit，twocontradictorypropositionsbothbecomefalse;consequently，asnomiddlebetweenthemisconceivable，nothingatallisthoughtbythatconcept。Sect。52。c。Thefirsttwoantinomies，whichIcallmathematical，becausetheyareconcernedwiththeadditionordivisionofthehomogeneous，arefoundedonsuchaself—contradictoryconcept;andhenceIexplainhowithappens，thatboththeThesisandAntithesisofthetwoarefalse。WhenIspeakofobjectsintimeandinspace，itisnotofthingsinthemselves，ofwhichIknownothing，butofthingsinappearance，thatis，ofexperience，astheparticularwayofcognisingobjectswhichisaffordedtoman。I
　　mustnotsayofwhatIthinkintimeorinspace，thatinitself，andindependentofthesemythoughts，itexistsinspaceandintime;forinthatcaseIshouldcontradictmyself;becausespaceandtime，togetherwiththeappearancesinthem，arenothingexistinginthemselvesandoutsideofmyrepresentations，butarethemselvesonlymodesofrepresentation，anditispalpablycontradictorytosay，thatameremodeofrepresentationexistswithoutourrepresentation。
　　Objectsofthesensesthereforeexistonlyinexperience;whereastogivethemaself—subsistingexistenceapartfromexperienceorbeforeit，ismerelytorepresenttoourselvesthatexperienceactuallyexistsapartfromexperienceorbeforeit。NowifIinquireafterthequantityoftheworld，astospaceandtime，itisequallyimpossible，asregardsallmynotions，todeclareitinfiniteortodeclareitfinite。Forneitherassertioncanbecontainedinexperience，becauseexperienceeitherofaninfinitespace，orofaninfinitetimeelapsed，oragain，oftheboundaryoftheworldbyavoidspace，orbyanantecedentvoidtime，isimpossible;thesearemereideas。Thisquantityoftheworld，whichisdeterminedineitherway，shouldthereforeexistintheworlditselfapartfromallexperience。Thiscontradictsthenotionofaworldofsense，whichismerelyacomplexoftheappearanceswhoseexistenceandconnectionoccuronlyinourrepresentations，thatis，inexperience，sincethislatterisnotanobjectinitself，butameremodeofrepresentation。Henceitfollows，thatastheconceptofanabsolutelyexistingworldofsenseisself—contradictory，thesolutionoftheproblemconcerningitsquantity，whetherattemptedaffirmativelyornegatively，isalwaysfalse。Thesameholdsgoodofthesecondantinomy，whichrelatestothedivisionofphenomena。Forthesearemererepresentations，andthepartsexistmerelyintheirrepresentation，consequentlyinthedivision，orinapossibleexperiencewheretheyaregiven，andthedivisionreachesonlyasfarasthislatterreaches。Toassumethatanappearance，e。g。，thatofbody，containsinitselfbeforeallexperiencealltheparts，whichanypossibleexperiencecaneverreach，istoimputetoamereappearance，whichcanexistonlyinexperience，anexistenceprevioustoexperience。Inotherwords，itwouldmeanthatmererepresentationsexistbeforetheycanbefoundinourfacultyofrepresentation。Suchanassertionisself—contradictory，asalsoeverysolutionofourmisunderstoodproblem，whetherwemaintain，thatbodiesinthemselvesconsistofaninfinitenumberofparts，orofafinitenumberofsimpleparts。Sect。53。Inthefirst（themathematical）classofantinomiesthefalsehoodoftheassumptionconsistsinrepresentinginoneconceptsomethingself—contradictoryasifitwerecompatible（i。e。，anappearanceasanobjectinitself）。
　　But，astothesecond（thedynamical）classofantinomies，thefalsehoodoftherepresentationconsistsinrepresentingascontradictorywhatiscompatible;sothat，asintheformercase，theopposedassertionsarebothfalse，inthiscase，ontheotherhand，wheretheyareopposedtooneanotherbymeremisunderstanding，theymaybothbetrue。Anymathematicalconnectionnecessarilypresupposeshomogeneityofwhatisconnected（intheconceptofmagnitude），whilethedynamicalonebynomeansrequiresthesame。Whenwehavetodealwithextendedmagnitudes，allthepartsmustbehomogeneouswithoneanotherandwiththewhole;