Kant’s\"Prolegomena\"—Introduction（InternetEncyclopediaofPhilosophy）IntroductionTheseProlegomenaaredestinedfortheuse，notofpupils，butoffutureteachers，andeventhelattershouldnotexpectthattheywillbeserviceableforthesystematicexpositionofaready—madescience，butmerelyforthediscoveryofthescienceitself。Therearescholarlymen，towhomthehistoryofphilosophy（bothancientandmodern）isphilosophyitself;forthesethepresentProlegomenaarenotwritten。Theymustwaittillthosewhoendeavortodrawfromthefountainofreasonitselfhavecompletedtheirwork;itwillthenbethehistorian’sturntoinformtheworldofwhathasbeendone。Unfortunately，nothingcanbesaid，whichintheiropinionhasnotbeensaidbefore，andtrulythesameprophecyappliestoallfuturetime;forsincethehumanreasonhasformanycenturiesspeculateduponinnumerableobjectsinvariousways，itishardlytobeexpectedthatweshouldnotbeabletodiscoveranalogiesforeverynewideaamongtheoldsayingsofpastages。MyobjectistopersuadeallthosewhothinkMetaphysicsworthstudying，thatitisabsolutelynecessarytopauseamoment，and，neglectingallthathasbeendone，toproposefirstthepreliminaryquestion，’Whethersuchathingasmetaphysicsbeatallpossible？’Ifitbeascience，howcomesitthatitcannot，likeothersciences，obtainuniversalandpermanentrecognition？Ifnot，howcanitmaintainitspretensions，andkeepthehumanmindinsuspensewithhopes，neverceasing，yetneverfulfilled？Whetherthenwedemonstrateourknowledgeorourignoranceinthisfield，wemustcomeonceforalltoadefiniteconclusionrespectingthenatureofthisso—calledscience，whichcannotpossiblyremainonitspresentfooting。Itseemsalmostridiculous，whileeveryotherscienceiscontinuallyadvancing，thatinthis，whichpretendstobeWisdomincarnate，forwhoseoracleeveryoneinquires，weshouldconstantlymoveroundthesamespot，withoutgainingasinglestep。Andsoitsfollowershavingmeltedaway，wedonotfindmenconfidentoftheirabilitytoshineinothersciencesventuringtheirreputationhere，whereeverybody，howeverignorantinothermatters，maydeliverafinalverdict，asinthisdomainthereisasyetnostandardweightandmeasuretodistinguishsoundknowledgefromshallowtalk。Afterallitisnothingextraordinaryintheelaborationofascience，whenmenbegintowonderhowfarithasadvanced，thatthequestionshouldatlastoccur，whetherandhowsuchascienceispossible？Humanreasonsodelightsinconstructions，thatithasseveraltimesbuiltupatower，andthenrazedittoexaminethenatureofthefoundation。Itisnevertoolatetobecomewise;butifthechangecomeslate，thereisalwaysmoredifficultyinstartingareform。Thequestionwhetherasciencebepossible，presupposesadoubtastoitsactuality。Butsuchadoubtoffendsthemenwhosewholepossessionsconsistofthissupposedjewel;hencehewhoraisesthedoubtmustexpectoppositionfromallsides。Some，intheproudconsciousnessoftheirpossessions，whichareancient，andthereforeconsideredlegitimate，willtaketheirmetaphysicalcompendiaintheirhands，andlookdownonhimwithcontempt;
others，whoneverseeanythingexceptitbeidenticalwithwhattheyhaveseenbefore，willnotunderstandhim，andeverythingwillremainforatime，asifnothinghadhappenedtoexcitetheconcern，orthehope，foranimpendingchange。Nevertheless，IventuretopredictthattheindependentreaderoftheseProlegomenawillnotonlydoubthispreviousscience，butultimatelybefullypersuaded，thatitcannotexistunlessthedemandsherestatedonwhichitspossibilitydepends，besatisfied;and，asthishasneverbeendone，thatthereis，asyet，nosuchthingasMetaphysics。Butasitcanneverceasetobeindemand，2——sincetheinterestsofcommonsenseareintimatelyinterwovenwithit，hemustconfessthataradicalreform，orratheranewbirthofthescienceafteranoriginalplan，areunavoidable，howevermenmaystruggleagainstitforawhile。SincetheEssaysofLockeandLeibniz，orrathersincetheoriginofmetaphysicssofarasweknowitshistory，nothinghaseverhappenedwhichwasmoredecisivetoitsfatethantheattackmadeuponitbyDavidHume。Hethrewnolightonthisspeciesofknowledge，buthecertainlystruckasparkfromwhichlightmighthavebeenobtained，haditcaughtsomeinflammablesubstanceandhaditssmolderingfirebeencarefullynursedanddeveloped。HumestartedfromasinglebutimportantconceptinMetaphysics，viz。，thatofCauseandEffect（includingitsderivativesforceandaction，etc。）。
Hechallengesreason，whichpretendstohavegivenbirthtothisideafromherself，toanswerhimbywhatrightshethinksanythingtobesoconstituted，thatifthatthingbeposited，somethingelsealsomustnecessarilybeposited;forthisisthemeaningoftheconceptofcause。Hedemonstratedirrefutablythatitwasperfectlyimpossibleforreasontothinkaprioriandbymeansofconceptsacombinationinvolvingnecessity。Wecannotatallseewhy，inconsequenceoftheexistenceofonething，anothermustnecessarilyexist，orhowtheconceptofsuchacombinationcanariseapriori。Henceheinferred，thatreasonwasaltogetherdeludedwithreferencetothisconcept，whichsheerroneouslyconsideredasoneofherchildren，whereasinrealityitwasnothingbutabastardofimagination，impregnatedbyexperience，whichsubsumedcertainrepresentationsundertheLawofAssociation，andmistookthesubjectivenecessityofhabitforanobjectivenecessityarisingfrominsight。Henceheinferredthatreasonhadnopowertothinksuch，combinations，evengenerally，becauseherconceptswouldthenbepurelyfictitious，andallherpretendedaprioricognitionsnothingbutcommonexperiencesmarkedwithafalsestamp。Inplainlanguagethereisnot，andcannotbe，anysuchthingasmetaphysicsatall。3HoweverhastyandmistakenHume’sconclusionmayappear，itwasatleastfoundeduponinvestigation，andthisinvestigationdeservedtheconcentratedattentionofthebrighterspiritsofhisdayaswellasdeterminedeffortsontheirparttodiscover，ifpossible，ahappiersolutionoftheprobleminthesenseproposedbyhim，allofwhichwouldhavespeedilyresultedinacompletereformofthescience。ButHumesufferedtheusualmisfortuneofmetaphysicians，ofnotbeingunderstood。Itispositivelypainfultoseebowutterlyhisopponents，Reid，Oswald，Beattie，andlastlyPriestley，missedthepointoftheproblem;
forwhiletheywereevertakingforgrantedthatwhichhedoubted，anddemonstratingwithzealandoftenwithimpudencethatwhichheneverthoughtofdoubting，theysomisconstruedhisvaluablesuggestionthateverythingremainedinitsoldcondition，asifnothinghadhappened。Thequestionwasnotwhethertheconceptofcausewasright，useful，andevenindispensableforourknowledgeofnature，forthisHumehadneverdoubted;butwhetherthatconceptcouldbethoughtbyreasonapriori，andconsequentlywhetheritpossessedaninnertruth，independentofallexperience，implyingawiderapplicationthanmerelytotheobjectsofexperience。ThiswasHume’sproblem。Itwasaquestionconcerningtheorigin，notconcerningtheindispensableneedoftheconcept。Weretheformerdecided，theconditionsoftheuseandthesphereofitsvalidapplicationwouldhavebeendeterminedasamatterofcourse。Buttosatisfytheconditionsoftheproblem，theopponentsofthegreatthinkershouldhavepenetratedverydeeplyintothenatureofreason，sofarasitisconcernedwithpurethinking，—ataskwhichdidnotsuitthem。
Theyfoundamoreconvenientmethodofbeingdefiantwithoutanyinsight，viz。，theappealtocommonsense。ItisindeedagreatgiftofGod，topossessright，or（astheynowcallit）plaincommonsense。Butthiscommonsensemustbeshownpractically，bywell—consideredandreasonablethoughtsandwords，notbyappealingtoitasanoracle，whennorationaljustificationcanbeadvanced。Toappealtocommonsense，wheninsightandsciencefail，andnosooner—thisisoneofthesubtlediscoveriesofmoderntimes，bymeansofwhichthemostsuperficialrantercansafelyenterthelistswiththemostthoroughthinker，andholdhisown。Butaslongasaparticleofinsightremains，noonewouldthinkofhavingrecoursetothissubterfuge。Forwhatisitbutanappealtotheopinionofthemultitude，ofwhoseapplausethephilosopherisashamed，whilethepopularcharlatangloriesandconfidesinit？IshouldthinkthatHumemightfairlyhavelaidasmuchclaimtocommonsenseasBeattie，andinadditiontoacriticalreason（suchasthelatterdidnotpossess），whichkeepscommonsenseincheckandpreventsitfromspeculating，or，ifspeculationsareunderdiscussionrestrainsthedesiretodecidebecauseitcannotsatisfyitselfconcerningitsownarguments。Bythismeansalonecancommonsenseremainsound。Chiselsandhammersmaysufficetoworkapieceofwood，butforsteel—engravingwerequireanengraver’sneedle。Thuscommonsenseandspeculativeunderstandingareeachserviceableintheirownway，theformerinjudgmentswhichapplyimmediatelytoexperience，thelatterwhenwejudgeuniversallyfrommereconcepts，asinmetaphysics，wheresoundcommonsense，socalledinspiteoftheinapplicabilityoftheword，hasnorighttojudgeatall。Iopenlyconfess，thesuggestionofDavidHumewastheverything，whichmanyyearsagofirstinterruptedmydogmaticslumber，andgavemyinvestigationsinthefieldofspeculativephilosophyquiteanewdirection。Iwasfarfromfollowinghimintheconclusionsatwhichhearrivedbyregarding，notthewholeofhisproblem，butapart，whichbyitselfcangiveusnoinformation。Ifwestartfromawell—founded，butundeveloped，thought，whichanotherhasbequeathedtous，wemaywellhopebycontinuedreflectiontoadvancefartherthantheacuteman，towhomweowethefirstsparkoflight。IthereforefirsttriedwhetherHume’sobjectioncouldnotbeputintoageneralform，andsoonfoundthattheconceptoftheconnectionofcauseandeffectwasbynomeanstheonlyideabywhichtheunderstandingthinkstheconnectionofthingsapriori，butratherthatmetaphysicsconsistsaltogetherofsuchconnections。Isoughttoascertaintheirnumber，andwhenIhadsatisfactorilysucceededinthisbystartingfromasingleprinciple，Iproceededtothedeductionoftheseconcepts，whichIwasnowcertainwerenotdeducedfromexperience，asHumehadapprehended，butsprangfromthepureunderstanding。Thisdeduction（whichseemedimpossibletomyacutepredecessor，whichbadneverevenoccurredtoanyoneelse，thoughnoonehadhesitatedtousetheconceptswithoutinvestigatingthebasisoftheirobjectivevalidity）wasthemostdifficulttaskeverundertakenintheserviceofmetaphysics;andtheworstwasthatmetaphysics，suchasitthenexisted，couldnotassistmeintheleast，becausethisdeductionalonecanrendermetaphysicspossible。ButassoonasIhadsucceededinsolvingHume’sproblemnotmerelyinaparticularcase，butwithrespecttothewholefacultyofpurereason，Icouldproceedsafely，thoughslowly，todeterminethewholesphereofpurereasoncompletelyandfromgeneralprinciples，initscircumferenceaswellasinitscontents。Thiswasrequiredformetaphysicsinordertoconstructitssystemaccordingtoareliablemethod。ButIfearthattheexecutionofHume’sprobleminitswidestextent（viz。，myCritiqueofthePureReason）willfareastheproblemitselffared，whenfirstproposed。Itwillbemisjudgedbecauseitismisunderstood，andmisunderstoodbecausemenchoosetoskimthroughthebook，andnottothinkthroughit—adisagreeabletask，becausetheworkisdry，obscure，opposedtoallordinarynotions，andmoreoverlong—winded。Iconfess，however，Ididnotexpect，tohearfromphilosopherscomplaintsofwantofpopularity，entertainment，andfacility，whentheexistenceofahighlyprizedandindispensablecognitionisatstake，whichcannotbeestablishedotherwise，thanbythestrictestrulesofmethodicprecision。Popularitymayfollow，butisinadmissibleatthebeginning。Yetasregardsacertainobscurity，arisingpartlyfromthediffusenessoftheplan，owingtowhich。theprincipalpointsoftheinvestigationareeasilylostsightof，thecomplaintisjust，andIintendtoremoveitbythepresentProlegomena。Thefirst—mentionedwork，whichdiscussesthepurefacultyofreasoninitswholecompassandbounds，willremainthefoundation，towhichtheProlegomena，asapreliminary，exercise，refer;forourcritiquemustfirstbeestablishedasacompleteandperfectedscience，beforewecanthinkoflettingMetaphysicsappearonthescene，orevenhavethemostdistanthopeofattainingit。Wehavebeenlongaccustomedtoseeingantiquatedknowledgeproducedasnewbytakingitoutofitsformercontext，andreducingittosysteminanewsuitofanyfancypatternundernewtitles。MostreaderswillsetoutbyexpectingnothingelsefromtheCritique;buttheseProlegomenamaypersuadehimthatitisaperfectlynewscience，ofwhichnoonehasevereventhought，theveryideaofwhichwasunknown，andforwhichnothinghithertoaccomplishedcanbeofthesmallestuse，exceptitbethesuggestionofHume’sdoubts。Yetevenhedidnotsuspectsuchaformalscience，butranhisshipashore，forsafety’ssake，landingonskepticism，theretoletitlieandrot;whereasmyobjectisrathertogiveitapilot，who，bymeansofsafeastronomicalprinciplesdrawnfromaknowledgeoftheglobe，andprovidedwithacompletechartandcompass，maysteertheshipsafely，whitherhelisteth。Ifinanewscience，whichiswhollyisolatedanduniqueinitskind，westartedwiththeprejudicethatwecanjudgeofthingsbymeansofourpreviouslyacquiredknowledge，which。，ispreciselywhathasfirsttobecalledinquestion，weshouldonlyfancywesaweverywherewhatwehadalreadyknown，。theexpressions，havingasimilarsound，onlythatallwouldappearutterlymetamorphosed，senselessandunintelligible，becauseweshouldhaveasafoundationoutownnotions，madebylonghabitasecondnature，insteadoftheauthor’s。Butthelongwindednessofthework，sofarasitdependsonthesubject，andnottheexposition，itsconsequentunavoidabledrynessanditsscholasticprecisionarequalitieswhichcanonlybenefitthescience，thoughtheymaydiscreditthebook。Fewwritersaregiftedwiththesubtlety，andatthesametimewiththegrace，ofDavidHume，orwiththedepth，aswellastheelegance，ofMosesMendelssohn。YetIflattermyselfImighthavemademyownexpositionpopular，hadmyobjectbeenmerelytosketchoutaplanandleaveitscompletiontoothersinsteadofhavingmyheartinthewelfareofthescience，towhichIhaddevotedmyselfsolong;intruth，itrequirednolittleconstancy，andevenself—denial，topostponethesweetsofanimmediatesuccesstotheprospectofaslower，butmorelasting，reputation。Makingplansisoftentheoccupationofanopulentandboastfulmind，whichthusobtainsthereputationofacreativegenius，bydemandingwhatitcannotitselfsupply;bycensuring，whatitcannotimprove;andbyproposing，whatitknowsnotwheretofind。Andyetsomethingmoreshouldbelongtoasoundplanofageneralcritiqueofpurereasonthanmereconjectures，ifthisplanistobeotherthantheusualdeclamationsofpiousaspirations。
Butpurereasonisaspheresoseparateandself—contained，thatwecannottouchapartwithoutaffectingalltherest。Wecanthereforedonothingwithoutfirstdeterminingtheposition;ofeachpart，anditsrelationtotherest;for，asourjudgmentcannotbecorrectedbyanythingwithout，thevalidityanduseofeverypartdependsupontherelationinwhichitstandstoalltherestwithinthedomainofreason。Sointhestructureofanorganizedbody，theendofeachmembercanonlybededucedfromthefullconceptionofthewhole。Itmay，then，besaidofsuchacritiquethatitisnevertrustworthyexceptitbeperfectlycomplete，downtothesmallestelementsofpurereason。Inthesphereofthisfacultyyoucandetermineeithereverythingornothing。Butalthoughameresketch，precedingtheCritiqueofPureReason，wouldbeunintelligible，unreliable，anduseless，itisallthemoreusefulasasequel。Forsoweareabletograspthewhole，toexamineindetailthechiefpointsofimportanceinthescience，andtoimproveinmanyrespectsourexposition，ascomparedwiththefirstexecutionofthework。AfterthecompletionoftheworkIofferheresuchaplanwhichissketchedoutafterananalyticalmethod，whiletheworkitselfhadtobeexecutedinthesyntheticalstyle，inorderthatthesciencemaypresentallitsarticulations，asthestructureofapeculiarcognitivefaculty，intheirnaturalcombination。Butshouldanyreaderfindthisplan，whichIpublishastheProlegomenatoanyfutureMetaphysics，stillobscure，lethimconsiderthatnoteveryoneisboundtostudyMetaphysics，thatmanymindswillsucceedverywell，intheexactandevenindeepsciences，morecloselyalliedtopracticalexperience，4whiletheycannotsucceedininvestigationsdealingexclusivelywithabstractconcepts。Insuchcasesmenshouldapplytheirtalentstoothersubjects。Buthewhoundertakestojudge，orstillmore，toconstruct，asystemofMetaphysics，mustsatisfythedemandsheremade，eitherbyadoptingmysolution，orbythoroughlyrefutingit，andsubstitutinganother。Toevadeitisimpossible。Inconclusion，letitberememberedthatthismuch—abusedobscurity（frequentlyservingasamerepretextunderwhichpeoplehidetheirownindolenceordullness）hasitsuses，sinceallwhoinothersciencesobserveajudicioussilence，speakauthoritativelyinmetaphysicsandmakebolddecisions，becausetheirignoranceisnotherecontrastedwiththeknowledgeofothers。
Yetitdoescontrastwithsoundcriticalprinciples，whichwemaythereforecommendinthewordsofVirgil：\"Ignavum，fucos，pecusapraesepibusarcent。\"
\"Beesaredefendingtheirhivesagainstdrones，thoseindolentcreatures。
\"Kant’s\"Prolegomena\"—Preamble（InternetEncyclopediaofPhilosophy）PreambleOnThePeculiaritiesOfAllMetaphysicalCognition。Sect。1：OftheSourcesofMetaphysicsIfitbecomesdesirabletoformulateanycognitionasscience，itwillbenecessaryfirsttodetermineaccuratelythosepeculiarfeatureswhichnoothersciencehasincommonwithit，constitutingitscharacteristics;
otherwisethe。boundariesofallsciencesbecomeconfused，andnoneofthemcanbetreatedthoroughlyaccordingtoitsnature。Thecharacteristicsofasciencemayconsistofasimpledifferenceofobject，orofthesourcesofcognition，orofthekindofcognition，orperhapsofallthreeconjointly。Onthis，therefore，dependstheideaofapossiblescienceanditsterritory。First，asconcernsthesourcesofmetaphysicalcognition，itsveryconceptimpliesthattheycannotbeempirical。Itsprinciples（includingnotonlyitsmaximsbutitsbasicnotions）mustneverbederivedfromexperience。
Itmustnotbephysicalbutmetaphysicalknowledge，viz。，knowledgelyingbeyondexperience。Itcanthereforehaveforitsbasisneitherexternalexperience，whichisthesourceofphysicsproper，norinternal，whichisthebasisofempiricalpsychology。Itisthereforeaprioriknowledge，comingfrompureUnderstandingandpureReason。ButsofarMetaphysicswouldnotbedistinguishablefrompureMathematics;
itmustthereforebecalledpurephilosophicalcognition;andforthemeaningofthistermIrefertotheCritiqueofthePureReason（II。\"MethodofTranscendentalism，\"Chap。I。，Sec。1），wherethedistinctionbetweenthesetwoemploymentsofthereasonissufficientlyexplained。Sofarconcerningthesourcesofmetaphysicalcognition。Sect。2。ConcerningtheKindofCognitionwhichcanalonebecalledMetaphysicala。OftheDistinctionbetweenAnalyticalandSyntheticaljudgmentsingeneral。
——Thepeculiarityofitssourcesdemandsthatmetaphysicalcognitionmustconsistofnothingbutapriorijudgments。Butwhateverbetheirorigin，ortheirlogicalform，thereisadistinctioninjudgments，astotheircontent，accordingtowhichtheyareeithermerelyexplicative，addingnothingtothecontentofthecognition，orexpansive，increasingthegivencognition：theformermaybecalledanalytical，thelattersynthetical，judgments。Analyticaljudgmentsexpressnothinginthepredicatebutwhathasbeenalreadyactuallythoughtintheconceptofthesubject，thoughnotsodistinctlyorwiththesame（full）consciousness。WhenIsay：Allbodiesareextended，Ihavenotamplifiedintheleastmyconceptofbody，buthaveonlyanalyzedit，asextensionwasreallythoughttobelongtothatconceptbeforethejudgmentwasmade，thoughitwasnotexpressed，thisjudgmentisthereforeanalytical。Onthecontrary，thisjudgment，Allbodieshaveweight，containsinitspredicatesomethingnotactuallythoughtinthegeneralconceptofthebody;itamplifiesmyknowledgebyaddingsomethingtomyconcept，andmustthereforebecalledsynthetical。b。TheCommonPrincipleofallAnalyticalJudgmentsistheLawofContradiction。
——AllanalyticaljudgmentsdependwhollyonthelawofContradiction，andareintheirnatureaprioricognitions，whethertheconceptsthatsupplythemwithmatterbeempiricalornot。Forthepredicateofanaffirmativeanalyticaljudgmentisalreadycontainedintheconceptofthesubject，ofwhichitcannotbedeniedwithoutcontradiction。Inthesamewayitsoppositeisnecessarilydeniedofthesubjectinananalytical，butnegative，judgment，bythesamelawofcontradiction。Suchisthenatureofthejudgments：allbodiesareextended，andnobodiesareunextended（i。e。，simple）。Forthisveryreasonallanalyticaljudgmentsarea。priorievenwhentheconceptsareempirical，as，forexample，Goldisayellowmetal;fortoknowthisIrequirenoexperiencebeyondmyconceptofgoldasayellowmetal：itis，infact，theveryconcept，andIneedonlyanalyzeit，withoutlookingbeyonditelsewhere。c。SyntheticaljudgmentsrequireadifferentPrinciplefromtheLawofContradiction。—Therearesyntheticalaposteriorijudgmentsofempiricalorigin;buttherearealsootherswhichareprovedtobecertainapriori，andwhichspringfrompureUnderstandingandReason。Yettheybothagreeinthis，thattheycannotpossiblyspringfromtheprincipleofanalysis，viz。，thelawofcontradiction，alone;theyrequireaquitedifferentprinciple，though，fromwhatevertheymaybededuced，theymustbesubjecttothelawofcontradiction，whichmustneverbeviolated，eventhougheverythingcannotbededucedfromit。Ishallfirstclassifysyntheticaljudgments。1。Empiricaljudgmentsarealwayssynthetical。Foritwouldbeabsurdtobaseananalyticaljudgmentonexperience，asourconceptsufficesforthepurposewithoutrequiringanytestimonyfromexperience。Thatbodyisextended，isajudgmentestablishedapriori，andnotanempiricaljudgment。Forbeforeappealingtoexperience，wealreadyhavealltheconditionsofthejudgmentintheconcept，fromwhichwehavebuttoelicitthepredicateaccordingtothelawofcontradiction，andtherebytobecomeconsciousofthenecessityofthejudgment，whichexperiencecouldnoteventeachus。2。Mathematicaljudgmentsareallsynthetical。Thisfactseemshithertotohavealtogetherescapedtheobservationofthosewhohaveanalyzedhumanreason;itevenseemsdirectlyopposedtoalltheirconjectures，thoughincontestablycertain，andmostimportantinitsconsequences。Forasitwasfoundthattheconclusionsofmathematiciansallproceedaccordingtothelawofcontradiction（asisdemandedbyallapodicticcertainty），menpersuadedthemselvesthatthefundamentalprincipleswereknownfromthesamelaw。Thiswasagreatmistake，forasyntheticalpropositioncanindeedbecomprehendedaccordingtothelawofcontradiction，butonlybypresupposinganothersyntheticalpropositionfromwhichitfollows，butneverinitself。Firstofall，wemustobservethatallpropermathematicaljudgmentsareapriori，andnotempirical，becausetheycarrywiththemnecessity，whichcannotbeobtainedfromexperience。Butifthisbenotconcededtome，verygood;IshallconfinemyassertionpureMathematics，theverynotionofwhichimpliesthatitcontainspureaprioriandnotempiricalcognitions。Itmightatfirstbethoughtthattheproposition7+5=12isamereanalyticaljudgment，followingfromtheconceptofthesumofsevenandfive，accordingtothelawofcontradiction。ButoncloserexaminationitappearsthattheconceptofthesumOf7+5containsmerelytheirunioninasinglenumber，withoutitsbeingatallthoughtwhattheparticularnumberisthatunitesthem。Theconceptoftwelveisbynomeansthoughtbymerelythinkingofthecombinationofsevenandfive;andanalyzethispossiblesumaswemay，weshallnotdiscovertwelveintheconcept。Wemustgobeyondtheseconcepts，bycallingtoouraidsomeconcreteimage[Anschauung]，i。e。，eitherourfivefingers，orfivepoints（asSegnerhasitinhisArithmetic），andwemustaddsuccessivelytheunitsofthefive，giveninsomeconcreteimage[Anschauung]，totheconceptofseven。Henceourconceptisreallyamplifiedbytheproposition7+
5=I2，andweaddtothefirstasecond，notthoughtinit。Arithmeticaljudgmentsarethereforesynthetical，andthemoreplainlyaccordingaswetakelargernumbers;forinsuchcasesitisclearthat，howevercloselyweanalyzeourconceptswithoutcallingvisualimages（Anscliauung）toouraid，wecanneverfindthesumbysuchmeredissection。Allprinciplesofgeometryarenolessanalytical。Thatastraightlineistheshortestpathbetweentwopoints，isasyntheticalproposition。
Formyconceptofstraightcontainsnothingofquantity，butonlyaquality。
Theattributeofshortnessisthereforealtogetheradditional，andcannotbeobtainedbyanyanalysisoftheconcept。Here，too，visualization[Anschauung]
mustcometoaidus。Italonemakesthesynthesispossible。Someotherprinciples，assumedbygeometers，areindeedactuallyanalytical，anddependonthelawofcontradiction;buttheyonlyserve，asidenticalpropositions，asamethodofconcatenation，andnotasprinciples，e。g。，a=a，thewholeisequaltoitself，ora+b>a，thewholeisgreaterthanitspart。Andyeteventhese，thoughtheyarerecognizedasvalidfrommereconcepts，areonlyadmittedinmathematics，becausetheycanberepresentedinsomevisualform[Anschauung]。Whatusuallymakesusbelievethatthepredicateofsuchapodictic5judgmentsisalreadycontainedinourconcept，andthatthejudgmentisthereforeanalytical，istheduplicityoftheexpression，requestingustothinkacertainpredicateasofnecessityimpliedinthethoughtofagivenconcept，whichnecessityattachestotheconcept。Butthequestionisnotwhatwearerequestedtojoininthoughttothegivenconcept，butwhatweactuallythinktogetherwithandinit，thoughobscurely;andsoitappearsthatthepredicatebelongstotheseconceptsnecessarilyindeed，yetnotdirectlybutindirectlybyanaddedvisualization[Anschauung]。Sect。3。ARemarkontheGeneralDivisionofjudgmentsintoAnalyticalandSyntheticalThisdivisionisindispensable，asconcernstheCritiqueofhumanunderstanding，andthereforedeservestobecalledclassical，thoughotherwiseitisoflittleuse，butthisisthereasonwhydogmaticphilosophers，whoalwaysseekthesourcesofmetaphysicaljudgmentsinMetaphysicsitself，andnotapartfromit，inthepurelawsofreasongenerally，altogetherneglectedthisapparentlyobviousdistinction。ThusthecelebratedWolf，andhisacutefollowerBaumgarten，cametoseektheproofoftheprincipleofSufficientReason，whichisclearlysynthetical，intheprincipleofContradiction。
InLocke’sEssay，however，Ifindanindicationofmydivision。Forinthefourthbook（chap。iii。Sect。9，seq。），havingdiscussedthevariousconnectionsofrepresentationsinjudgments，andtheirsources，oneofwhichhemakes—Iidentityandcontradiction\"（analyticaljudgments），andanotherthecoexistenceofrepresentationsinasubject，heconfesses（Sect。
10）thatouraprioriknowledgeofthelatterisverynarrow，andalmostnothing。Butinhisremarksonthisspeciesofcognition，thereissolittleofwhatisdefinite，andreducedtorules，thatwecannotwonderifnoone，notevenHume，wasledtomakeinvestigationsconcerningthissortofjudgments。Forsuchgeneralandyetdefiniteprinciplesarenoteasilylearnedfromothermen，whohavehadthemobscurelyintheirminds。Wemusthitonthemfirstbyourownreflection，thenwefindthemelsewhere，wherewecouldnotpossiblynavefoundthematfirst，becausetheauthorsthemselvesdidnotknowthatsuchanidealayatthebasisoftheirobservations。Menwhoneverthinkindependentlyhaveneverthelesstheacutenesstodiscovereverything，afterithasbeenonceshownthem，inwhatwassaidlongsince，thoughnooneeversawittherebefore。Sect。4。TheGeneralQuestionoftheProlegemena。
—IsMetaphysicsatallPossible？Wereametaphysics，whichcouldmaintainitsplaceasascience，reallyinexistence;couldwesay，hereismetaphysics，learnit，anditwillconvinceyouirresistiblyandirrevocablyofitstruth：thisquestionwouldbeuseless，andtherewouldonlyremainthatotherquestion（whichwouldratherbeatestofouracuteness，thanaproofoftheexistenceofthethingitself），\"Howisthesciencepossible，andhowdoesreasoncometoattainit？\"Buthumanreasonhasnotbeensofortunateinthiscase。ThereisnosinglebooktowhichyoucanpointasyoudotoEuclid，andsay：
ThisisMetaphysics;hereyoumayfindthenoblestobjectsofthisscience，theknowledgeofahighestBeing，andofafutureexistence，provedfromprinciplesofpurereason。Wecanbeshownindeedmanyjudgments，demonstrablycertain，andneverquestioned;buttheseareallanalytical，andratherconcernthematerialsandthescaffoldingforMetaphysics，thantheextensionofknowledge，whichisourproperobjectinstudyingit（Sect2）。Evensupposingyouproducesyntheticaljudgments（suchasthelawofSufficientReason，whichyouhaveneverproved，asyououghtto，frompurereasonapriori，thoughwegladlyconcedeitstruth），youlapsewhentheycometobeemployedforyourprincipalobject，intosuchdoubtfulassertions，thatinallagesoneMetaphysicshascontradictedanother，eitherinitsassertions，ortheirproofs，andthushasitselfdestroyeditsownclaimtolastingassent。Nay，theveryattemptstosetupsuchasciencearethemaincauseoftheearlyappearanceofskepticism，amentalattitudeinwhichreasontreatsitselfwithsuchviolencethatitcouldneverhavearisensavefromcompletedespairofeversatisfyingourmostimportantaspirations。Forlongbeforemenbegantoinquireintonaturemethodically，theyconsultedabstractreason，whichhadtosomeextentbeenexercisedbymeansofordinaryexperience;forreasoniseverpresent，whilelawsofnaturemustusuallybediscoveredwithlabor。SoMetaphysicsfloatedtothesurface，likefoam，whichdissolvedthemomentitwasscoopedoff。
Butimmediatelythereappearedanewsupplyonthesurface，tobeevereagerlygatheredupbysome，whileothers，insteadofseekinginthedepthsthecauseofthephenomenon，thoughttheyshowedtheirwisdombyridiculingtheidlelaboroftheirneighbors。Theessentialanddistinguishingfeatureofpuremathematicalcognitionamongallotheraprioricognitionsis，thatitcannotatallproceedfromconcepts，butonlybymeansoftheconstructionofconcepts（seeCritiqueII。，MethodofTranscendentalism，Chap。I。，sect。1）。Asthereforeinitsjudgmentsitmustproceedbeyondtheconcepttothatwhichitscorrespondingvisualization[Anschauung]contains，thesejudgmentsneithercan，noroughtto，ariseanalytically，bydissectingtheconcept，butareallsynthetical。Icannotrefrainfrompointingoutthedisadvantageresultingtophilosophyfromtheneglectofthiseasyandapparentlyinsignificantobservation。
Humebeingprompted（ataskworthyofaphilosopher）tocasthiseyeoverthewholefieldofaprioricognitionsinwhichhumanunderstandingclaimssuchmightypossessions，heedlesslyseveredfromitawhole，andindeeditsmostvaluable，province，viz。，puremathematics;forhethoughtitsnature，or，sotospeak，thestate—constitutionofthisempire，dependedontotallydifferentprinciples，namely，onthelawofcontradictionalone;
andalthoughhedidnotdividejudgmentsinthismannerformallyanduniversallyasIhavedonehere，whathesaidwasequivalenttothis：thatmathematicscontainsonlyanalytical，butmetaphysicssynthetical，apriorijudgments。Inthis，however，hewasgreatlymistaken，andthemistakehadadecidedlyinjuriouseffectuponhiswholeconception。Butforthis，hewouldhaveextendedhisquestionconcerningtheoriginofoursyntheticaljudgmentsfarbeyondthemetaphysicalconceptofCausality，andincludedinitthepossibilityofmathematicsapriorialso，forthislatterhemusthaveassumedtobeequallysynthetical。Andthenhecouldnothavebasedhismetaphysicaljudgmentsonmereexperiencewithoutsubjectingtheaxiomsofmathematicsequallytoexperience，athingwhichhewasfartooacutetodo。Thegoodcompanyintowhichmetaphysicswouldthushavebeenbrought，wouldhavesaveditfromthedangerofacontemptuousill—
treatment，forthethrustintendedforitmusthavereachedmathematics，whichwasnotandcouldnothavebeenHume’sintention。Thusthatacutemanwouldhavebeenledintoconsiderationswhichmustneedsbesimilartothosethatnowoccupyus，butwhichwouldhavegainedinestimablybyhisinimitablyelegantstyle。Metaphysicaljudgments，properlysocalled，areallsynthetical。Wemustdistinguishjudgmentspertainingtometaphysicsfrommetaphysicaljudgmentsproperlysocalled。Manyoftheformerareanalytical，buttheyonlyaffordthemeansformetaphysicaljudgments，whicharethewholeendofthescience，andwhicharealwayssynthetical。Foriftherebeconceptspertainingtometaphysics（as，forexample，thatofsubstance），thejudgmentsspringingfromsimpleanalysisofthemalsopertaintometaphysics，as，forexample，substanceisthatwhichonlyexistsassubject;andbymeansofseveralsuchanalyticaljudgments，weseektoapproachthedefinitionoftheconcept。
Butastheanalysisofapureconceptoftheunderstandingpertainingtometaphysics，doesnotproceedinanydifferentmannerfromthedissectionofanyother，evenempirical，concepts，notpertainingtometaphysics（suchas：airisanelasticfluid，theelasticityofwhichisnotdestroyedbyanyknowndegreeofcold），itfollowsthattheconceptindeed，butnottheanalyticaljudgment，isproperlymetaphysical。Thissciencehassomethingpeculiarintheproductionofitsaprioricognitions，whichmustthereforebedistinguishedfromthefeaturesithasincommonwithotherrationalknowledge。Thusthejudgment，thatallthesubstanceinthingsispermanent，isasyntheticalandproperlymetaphysicaljudgment。Iftheaprioriprinciples，whichconstitutethematerialsofmetaphysics，havefirstbeencollectedaccordingtofixedprinciples，thentheiranalysiswillbeofgreatvalue;itmightbetaughtasaparticularpart（asaphilosophiadefinitiva），containingnothingbutanalyticaljudgmentspertainingtometaphysics，andcouldbetreatedseparatelyfromthesyntheticalwhichconstitutemetaphysicsproper。Forindeedtheseanalysesarenotelsewhereofmuchvalue，exceptinmetaphysics，i。e。，asregardsthesyntheticaljudgments，whicharetobegeneratedbythesepreviouslyanalyzedconcepts。Theconclusiondrawninthissectionthenis，thatmetaphysicsisproperlyconcernedwithsyntheticalpropositionsapriori，andthesealoneconstituteitsend，forwhichitindeedrequiresvariousdissectionsofitsconcepts，viz。，ofitsanalyticaljudgments，butwhereintheprocedureisnotdifferentfromthatineveryotherkindofknowledge，inwhichwemerelyseektorenderourconceptsdistinctbyanalysis。Butthegenerationofaprioricognitionbyconcreteimagesaswellasbyconcepts，infineofsyntheticalpropositionsaprioriinphilosophicalcognition，constitutestheessentialsubjectofMetaphysics。Wearythereforeaswellofdogmatism，whichteachesusnothing，asofskepticism，whichdoesnotevenpromiseusanything，noteventhequietstateofacontentedignorance;disquietedbytheimportanceofknowledgesomuchneeded;andlastly，renderedsuspiciousbylongexperienceofallknowledgewhichwebelievewepossess，orwhichoffersitself，underthetitleofpurereason：thereremainsbutonecriticalquestionontheanswertowhichourfutureproceduredepends，viz。，IsMetaphysicsatallpossible？Butthisquestionmustbeanswerednotbyskepticalobjectionstotheasseverationsofsomeactualsystemofmetaphysics（forwedonotasyetadmitsuchathingtoexist），butfromtheconception，asyetonlyproblematical，ofascienceofthissort。IntheCritiqueofPureReasonIhavetreatedthisquestionsynthetically，bymakinginquiriesintopurereasonitself，andendeavoringinthissourcetodeterminetheelementsaswellasthelawsofitspureuseaccordingtoprinciples。Thetaskisdifficult，andrequiresaresolutereadertopenetratebydegreesintoasystem，basedonnodataexceptreasonitself，andwhichthereforeseeks，withoutrestinguponanyfact，tounfoldknowledgefromitsoriginalgerms。Prolegomena，however，aredesignedforpreparatoryexercises;theyareintendedrathertopointoutwhatwehavetodoinorderifpossibletoactualizeascience，thantopropoundit。Theymustthereforerestuponsomethingalreadyknownastrustworthy，fromwhichwecansetoutwithconfidence，andascendtosourcesasyetunknown，thediscoveryofwhichwillnotonlyexplaintouswhatweknew，butexhibitasphereofmanycognitionswhichallspringfromthesamesources。ThemethodofProlegomena，especiallyofthosedesignedasapreparationforfuturemetaphysics，isconsequentlyanalytical。Butithappensfortunately，thatthoughwecannotassumemetaphysicstobeanactualscience，wecansaywithconfidencethatcertainpureapriorisyntheticalcognitions，pureMathematicsandpurePhysicsareactualandgiven;forbothcontainpropositions，whicharethoroughlyrecognizedasapodicticallycertain，partlybymerereason，partlybygeneralconsentarisingfromexperience，andyetasindependentofexperience。Wehavethereforesomeatleastuncontestedsyntheticalknowledgeapriori，andneednotaskwhetheritbepossible，foritisactual，buthowitispossible，inorderthatwemaydeducefromtheprinciplewhichmakesthegivencognitionspossiblethepossibilityofalltherest。Sect。5。TheGeneralProblem：HowisCognitionfromPureReasonPossible？Wehaveabovelearnedthesignificantdistinctionbetweenanalyticalandsyntheticaljudgments。Thepossibilityofanalyticalpropositionswaseasilycomprehended，beingentirelyfoundedonthelawofContradiction。Thepossibilityofsyntheticalaposteriorijudgments，ofthosewhicharegatheredfromexperience，alsorequiresnoparticularexplanation;forexperienceisnothingbutacontinualsynthesisofperceptions。Thereremainthereforeonlysyntheticalpropositionsapriori，ofwhichthepossibilitymustbesoughtorinvestigated，becausetheymustdependuponotherprinciplesthanthelawofcontradiction。Buthereweneednotfirstestablishthepossibilityofsuchpropositionssoastoaskwhethertheyarepossible。Forthereareenoughofthemwhichindeedareofundoubtedcertainty，andasourpresentmethodisanalytical，weshallstartfromthefact，thatsuchsyntheticalbutpurelyrationalcognitionactuallyexists;butwemustnowinquireintothereasonofthispossibility，andask，howsuchcognitionispossible，inorderthatwemayfromtheprinciplesofitspossibilitybeenabledtodeterminetheconditionsofitsuse，itssphereanditslimits。Theproperproblemuponwhichalldepends，whenexpressedwithscholasticprecision，istherefore：
HowareSynthetheticPropositionsaprioripossible？ForthesakeofpopularityIhaveaboveexpressedthisproblemsomewhatdifferently，asaninquiryintopurelyrationalcognition，whichIcoulddoforoncewithoutdetrimenttothedesiredcomprehension，because，aswehaveonlytodoherewithmetaphysicsanditssources，thereaderwill，Ihope，aftertheforegoingremarks，keepinmindthatwhenwespeakofpurelyrationalcognition，wedonotmeananalytical，butsyntheticalcognition。6Metaphysicsstandsorfallswiththesolutionofthisproblem：itsveryexistencedependsuponit。Letanyonemakemetaphysicalassertionswitheversomuchplausibility，lethimoverwhelmuswithconclusions，ifhehasnotpreviouslyprovedabletoanswerthisquestionsatisfactorily，Ihavearighttosaythisisallvainbaselessphilosophyandfalsewisdom。
Youspeakthroughpurereason，andclaim，asitweretocreatecognitionsapriori。bynotonlydissectinggivenconcepts，butalsobyassertingconnectionswhichdonotrestuponthelawofcontradiction，andwhichyoubelieveyouconceivequiteindependentlyofallexperience;howdoyouarriveatthis，andhowwillyoujustifyyourpretensions？Anappealtotheconsentofthecommonsenseofmankindcannotbeallowed;forthatisawitnesswhoseauthoritydependsmerelyuponrumor。SaysHorace：\"Quodcunqueostendismihisic，incredulusodi。\"
\"Toallthatwhichthouprovestmethus，Irefusetogivecredence。\"Theanswertothisquestion，thoughindispensable，isdifficult;andthoughtheprincipalreasonthatitwasnotmadelongagois，thatthepossibilityofthequestionneveroccurredtoanybody，thereisyetanotherreason，whichisthisthatasatisfactoryanswertothisonequestionrequiresamuchmorepersistent，profound，andpainstakingreflection，thanthemostdiffuseworkonMetaphysics，whichonitsfirstappearancepromisedimmortalitytoitsauthor。Andeveryintelligentreader，whenhecarefullyreflectswhatthisproblemrequires，mustatfirstbestruckwithitsdifficulty，andwouldregarditasinsolubleandevenimpossible，didtherenotactuallyexistpuresyntheticalcognitionsapriori。ThisactuallyhappenedtoDavidHume，thoughhedidnotconceivethequestioninitsentireuniversalityasisdonehere，andasmustbedone，shouldtheanswerbedecisiveforallMetaphysics。Forhowisitpossible，saysthatacuteman，thatwhenaconceptisgivenme，Icangobeyonditandconnectwithitanother，whichisnotcontainedinit，insuchamannerasifthelatternecessarilybelongedtotheformer？Nothingbutexperiencecanfurnishuswithsuchconnections（thusheconcludedfromthedifficultywhichhetooktobeanimpossibility），andallthatvauntednecessity，or，whatisthesamething，allcognitionassumedtobeapriori，isnothingbutalonghabitofacceptingsomethingastrue，andhenceofmistakingsubjectivenecessityforobjective。ShouldmyreadercomplainofthedifficultyandthetroublewhichIoccasionhiminthesolutionofthisproblem，heisatlibertytosolveithimselfinaneasierway。Perhapshewillthenfeelunderobligationtothepersonwhohasundertakenforhimalaborofsoprofoundresearch，andwillratherbesurprisedatthefacilitywithwhich，consideringthenatureofthesubject，thesolutionhasbeenattained。Yetithascostyearsofworktosolvetheprobleminitswholeuniversality（usingtheterminthemathematicalsense，viz。，forthatwhichissufficientforallcases），andfinallytoexhibititintheanalyticalform，asthereaderfindsithere。Allmetaphysiciansarethereforesolemnlyandlegallysuspendedfromtheiroccupationstilltheyshallhaveansweredinasatisfactorymannerthequestion，\"Howaresyntheticcognitionsaprioripossible？\"Fortheanswercontainstheonlycredentialswhichtheymustshowwhentheyhaveanythingtoofferinthenameofpurereason。Butiftheydonotpossessthesecredentials，theycanexpectnothingelseofreasonablepeople，whohavebeendeceivedsooften，thantobedismissedwithoutfurtherado。Iftheyontheotherhanddesiretocarryontheirbusiness，notasascience，butasanartofwholesomeoratorysuitedtothecommonsenseofman，theycannotinjusticebeprevented。Theywillthenspeakthemodestlanguageofarationalbelief，theywillgrantthattheyarenotallowedeventoconjecture，farlesstoknow，anythingwhichliesbeyondtheboundsofallpossibleexperience，butonlytoassume（notforspeculativeuse，whichtheymustabandon，butforpracticalpurposesonly）theexistenceofsomethingthatispossibleandevenindispensablefortheguidanceoftheunderstandingandofthewillinlife。Inthismarineralonecantheybecalledusefulandwisemen，andthemoresoastheyrenouncethetitleofmetaphysicians;
forthelatterprofesstobespeculativephilosophers，andsince，whenjudgmentsaprior：areunderdiscussion，poorprobabilitiescannotbeadmitted（forwhatisdeclaredtobeknownaprioriistherebyannouncedasnecessary），suchmencannotbepermittedtoplaywithconjectures，buttheirassertionsmustbeeitherscience，orareworthnothingatall。Itmaybesaid，thattheentiretranscendentalphilosophy，whichnecessarilyprecedesallmetaphysics，isnothingbutthecompletesolutionoftheproblemherepropounded，insystematicalorderandcompleteness，andhithertowehaveneverhadanytranscendentalphilosophy;forwhatgoesbyitsnameisproperlyapartofmetaphysics，whereastheformersciencesintendedfirsttoconstitutethepossibilityofthe’matter，andmustthereforeprecedeallmetaphysics。Anditisnotsurprisingthatwhenawholescience，deprivedofallhelpfromothersciences，andconsequentlyinitselfquitenew，isrequiredtoanswera—singlequestionsatisfactorily，weshouldfindtheanswertroublesomeanddifficult，nayevenshroudedinobscurity。Aswenowproceedtothissolutionaccordingtotheanalyticalmethod，inwhichweassumethatsuchcognitionsfrompurereasonsactuallyexist，wecanonlyappealtotwosciencesoftheoreticalcognition。whichaloneisunderconsiderationhere），puremathematicsandpurenaturalscience（physics）。Forthesealonecanexhibittousobjectsinadefiniteandactualizableform（inderAnschauung），andconsequently（ifthereshouldoccurinthemacognitionapriori）canshowthetruthorconformityofthecognitiontotheobjectinconcrete，thatis，itsactuality，fromwhichwecouldproceedtothereasonofitspossibilitybytheanalyticmethod。Thisfacilitatesourworkgreatlyforhereuniversalconsiderationsarenotonlyappliedtofacts，butevenstartfromthem，whileinasyntheticproceduretheymuststrictlybederivedinabstractsfromconcepts。But，inordertorisefromtheseactualandatthesametimewell—groundedpurecognitionsaprioritosuchapossiblecognitionofthesameasweareseeking，viz。，tometaphysicsasascience，wemustcomprehendthatwhichoccasionsit，Imeanthemerenatural，thoughinspiteofitstruthnotunsuspected，cognitionaprioriwhichliesatthebottomofthatscience，theelaborationofwhichwithoutanycriticalinvestigationofitspossibilityiscommonlycalledmetaphysics。Inaword，wemustcomprehendthenaturalconditionsofsuchascienceasapartofourinquiry，andthusthetranscendentalproblemwillbegraduallyansweredbyadivisionintofourquestions：1。Howispuremathematicspossible？
2。Howispurenaturalsciencepossible？
3。Howismetaphysicsingeneralpossible？
4。Howismetaphysicsasasciencepossible？Itmaybeseenthatthesolutionoftheseproblems，thoughchieflydesignedtoexhibittheessentialmatteroftheCritique，hasyetsomethingpeculiar，whichforitselfalonedeservesattention。Thisisthesearchforthesourcesofgivensciencesinreasonitself，sothatitsfacultyofknowingsomethingapriorimaybyitsowndeedsbeinvestigatedandmeasured。Bythisprocedurethesesciencesgain，ifnotwithregardtotheircontents，yetastotheirproperuse，andwhiletheythrowlightonthehigherquestionconcerningtheircommonorigin，theygive，atthesametime，anoccasionbettertoexplaintheirownnature。Kant’s\"Prolegomena\"—FirstPart（InternetEncyclopediaofPhilosophy）FirstPartOfTheTranscendentalProblem：HowIsPureMathematicsPossible？Hereisagreatandestablishedbranchofknowledge，encompassingevennowawonderfullylargedomainandpromisinganunlimitedextensioninthefuture。Yetitcarrieswithitthoroughlyapodicticalcertainty，i。e。，absolutenecessity，whichthereforerestsuponnoempiricalgrounds。Consequentlyitisapureproductofreason，andmoreoveristhoroughlysynthetical。
[Herethequestionarises：]\"Howthenisitpossibleforhumanreasontoproduceacognitionofthisnatureentirelyapriori？\"Doesnotthisfaculty[whichproducesmathematics]，asitneitherisnorcanbebaseduponexperience，presupposesomegroundofcognitionapriori，whichliesdeeplyhidden，b，。——，whichmightrevealitselfbytheseitseffects，iftheirfirstbeginningswerebutdiligentlyferretedout？Sect。7。Butwefindthatallmathematicalcognitionhasthispeculiarity：
itmustfirstexhibititsconceptinavisualform[Anschauung]
andindeedapriori，thereforeinavisualformwhichisnotempirical，butpure。Withoutthismathematicscannottakeasinglestep;henceitsjudgmentsarealwaysvisual，viz。，\"Intuitive\";whereasphilosophymustbesatisfiedwithdiscursivejudgmentsfrommereconcepts，andthoughitmayillustrateitsdoctrinesthroughavisualfigure，canneverderivethemfromit。Thisobservationonthenatureofmathematicsgivesusacluetothefirstandhighestconditionofitspossibility，whichis，thatsomenon—sensuousvisualization[calledpureintuition，orreineAnschauung]
mustformitsbasis，inwhichallitsconceptscanbeexhibitedorconstructed，inconcreteandyetapriori。Ifwecanfindoutthispureintuitionanditspossibility，wemaythenceeasilyexplainhowsyntheticalpropositionsaprioriarepossibleinpuremathematics，andconsequentlyhowthisscienceitselfispossible。Empiricalintuition[viz。，sense—perception]
enablesuswithoutdifficultytoenlargetheconceptwhichweframeofanobjectofintuition[orsense—perception]，bynewpredicates，whichintuition[i。e。，sense—perception]itselfpresentssyntheticallyinexperience。
Pureintuition[viz。，thevisualizationofformsinourimagination，fromwhicheverythingsensual，i。e。，everythoughtofmaterialqualities，isexcluded]doessolikewise，onlywiththisdifference，thatinthelattercasethesyntheticaljudgmentisaprioricertainandapodictical，intheformer，onlyaposterioriandempiricallycertain;becausethislattercontainsonlythatwhichoccursincontingentempiricalintuition，buttheformer，thatwhichmustnecessarilybediscoveredinpureintuition。
He。—eintuition，beinganintuitionapriori，isbeforeallexperience，viz。，beforeanyperceptionofparticularobjects，inseparablyconjoinedwithitsconcept。Sect。8。Butwiththisstepourperplexityseemsrathertoincreasethantolessen。Forthequestionnowis，\"Howisitpossibletointuit[inavisualform]anythingapriori\"Anintuition[viz。，avisualsenseperception]issucharepresentationasimmediatelydependsuponthepresenceoftheobject。Henceitseemsimpossibletointuitfromtheoutsetapriori，becauseintuitionwouldinthateventtakeplacewithouteitheraformerorapresentobjecttoreferto，andbyconsequencecouldnotbeintuition。Conceptsindeedaresuch，thatwecaneasilyformsomeofthemapriori，viz。，suchascontainnothingbutthethoughtofanobjectingeneral;andweneednotfindourselvesinanimmediaterelationtotheobject。Take，forinstance，theconceptsofQuantity，ofCause，etc。Buteventheserequire，inordertomakethemunderstood，acertainconcreteuse—thatis，anapplicationtosomesense—experience[Anschauung]，bywhichanobjectofthemisgivenus。Buthowcantheintuitionoftheobject[itsvisualization]precedetheobjectitself？Sect。9。Ifourintuition[i。e。，oursense—experience]wereperforceofsuchanatureastorepresentthingsastheyareinthemselves，therewouldnotbeanyintuitionapriori，butintuitionwouldbealwaysempirical。
ForIcanonlyknowwhatiscontainedintheobjectinitselfwhenitispresentandgiventome。Itisindeedeventhenincomprehensiblehowthevisualizing[Anschauung]ofapresentthingshouldmakemeknowthisthingasitisinitself，asitspropertiescannotmigrateintomyfacultyofrepresentation。Butevengrantingthispossibility，avisualizingofthatsortwouldnottakeplaceapriori，thatis，beforetheobjectwerepresentedtome;forwithoutthislatterfactnoreasonofarelationbetweenmyrepresentationandtheobjectcanbeimagined，unlessitdependuponadirectinspiration。Thereforeinonewayonlycanmyintuition[Anschauung]anticipatetheactualityoftheobject，andbeacognitionapriori，viz。：
ifmyintuitioncontainsnothingbuttheformofsensibility，antedatinginmysubjectivityalltheactualimpressionsthroughwhichIamaffectedbyobjects。ForthatobjectsofsensecanonlybeintuitdaccordingtothisformofsensibilityIcanknowapriori。Henceitfollows：thatpropositions，whichconcernthisformofsensuousintuitiononly，arepossibleandvalidforobjectsofthesenses;asalso，conversely，thatintuitionswhicharepossibleaprioricanneverconcernanyotherthingsthanobjectsofoursenses。7Sect。10。Accordingly，itisonlytheformofsensuousintuitionbywhichwecanintuitthingsapriori，butbywhichwecanknowobjectsonlyastheyappeartous（tooursenses），notastheyareinthemselves;
andthisassumptionisabsolutelynecessaryifsyntheticalpropositionsaprioribegrantedaspossible，orif，incasetheyactuallyoccur，theirpossibilityistobecomprehendedanddeterminedbeforehand。Now，theintuitionswhichpuremathematicslaysatthefoundationofallitscognitionsandjudgmentswhichappearatonceapodicticandnecessaryareSpaceandTime。Formathematicsmustfirsthaveallitsconceptsinintuition，andpuremathematicsinpureintuition，thatis，itmustconstructthem。Ifitproceededinanyotherway，itwouldbeimpossibletomakeanyheadway，formathematicsproceeds，notanalyticallybydissectionofconcepts，butsynthetically，andifpureintuitionbewanting，thereisnothinginwhichthematterforsyntheticaljudgmentsaprioricanbegiven。Geometryisbaseduponthepureintuitionofspace。Arithmeticaccomplishesitsconceptofnumberbythesuccessiveadditionofunitsintime;andpuremechanicsespeciallycannotattainitsconceptsofmotionwithoutemployingtherepresentationoftime。Bothrepresentations，however，areonlyintuitions;forifweomitfromtheempiricalintuitionsofbodiesandtheiralterations（motion）everythingempirical，orbelongingtosensation，spaceandtimestillremain，whicharethereforepureintuitionsthatlieaprioriatthebasisoftheempirical。Hencetheycanneverbeomitted，butatthesametime，bytheirbeingpureintuitionsapriori，theyprovethattheyaremereformsofoursensibility，whichmustprecedeallempiricalintuition，orperceptionofactualobjects，andconformablytowhichobjectscanbeknownapriori，butonlyastheyappeartous。Sect。11。Theproblemofthepresentsectionisthereforesolved。Puremathematics，assyntheticalcognitionapriori，isonlypossiblebyreferringtonootherobjectsthanthoseofthesenses。Atthebasisoftheirempiricalintuitionliesapureintuition（ofspaceandoftime）
whichisapriori。Thisispossible，becausethelatterintuitionisnothingbutthemereformofsensibility，whichprecedestheactualappearanceoftheobjects，in，thatit，infact，makesthempossible。Yetthisfacultyofintuitingaprioriaffectsnotthematterofthephenomenon（thatis，thesense—elementinit，forthisconstitutesthatwhichisempirical），butitsform，viz。，spaceandtime。Shouldanymanventuretodoubtthatthesearedeterminationsadheringnottothingsinthemselves，buttotheirrelationtooursensibility，Ishouldbegladtoknowhowitcanbepossibletoknowtheconstitutionofthingsapriori，viz。，beforewehaveanyacquaintancewiththemandbeforetheyarepresentedtous。Such，however，isthecasewithspaceandtime。