第22章

Whenspeakingofuninvitingobjects，Imeanthosewhichdonotpassfromonesensationtotheopposite；invitingobjectsarethosewhichdo；inthislattercasethesensecomingupontheobject，whetheratadistanceornear，givesnomorevividideaofanythinginparticularthanofitsopposite。Anillustrationwillmakemymeaningclearer：——herearethreefingers——alittlefinger，asecondfinger，andamiddlefinger。 Verygood。 Youmaysupposethattheyareseenquiteclose：Andherecomesthepoint。 Whatisit？ Eachofthemequallyappearsafinger，whetherseeninthemiddleorattheextremity，whetherwhiteorblack，orthickorthin——itmakesnodifference；afingerisafingerallthesame。Inthesecasesamanisnotcompelledtoaskofthoughtthequestion，whatisafinger？forthesightneverintimatestothemindthatafingerisotherthanafinger。 True。 Andtherefore，Isaid，aswemightexpect，thereisnothingherewhichinvitesorexcitesintelligence。 Thereisnot，hesaid。 Butisthisequallytrueofthegreatnessandsmallnessofthefingers？Cansightadequatelyperceivethem？andisnodifferencemadebythecircumstancethatoneofthefingersisinthemiddleandanotherattheextremity？Andinlikemannerdoesthetouchadequatelyperceivethequalitiesofthicknessorthinness，orsoftnessorhardness？Andsooftheothersenses；dotheygiveperfectintimationsofsuchmatters？Isnottheirmodeofoperationonthiswise——thesensewhichisconcernedwiththequalityofhardnessisnecessarilyconcernedalsowiththequalityofsoftness，andonlyintimatestothesoulthatthesamethingisfelttobebothhardandsoft？ Youarequiteright，hesaid。 Andmustnotthesoulbeperplexedatthisintimationwhichthesensegivesofahardwhichisalsosoft？What，again，isthemeaningoflightandheavy，ifthatwhichislightisalsoheavy，andthatwhichisheavy，light？ Yes，hesaid，theseintimationswhichthesoulreceivesareverycuriousandrequiretobeexplained。 Yes，Isaid，andintheseperplexitiesthesoulnaturallysummonstoheraidcalculationandintelligence，thatshemayseewhethertheseveralobjectsannouncedtoherareoneortwo。 True。 Andiftheyturnouttobetwo，isnoteachofthemoneanddifferent？ Certainly。 Andifeachisone，andbotharetwo，shewillconceivethetwoasinastateofdivision，foriftherewereundividedtheycouldonlybeconceivedofasone？ True。 Theeyecertainlydidseebothsmallandgreat，butonlyinaconfusedmanner；theywerenotdistinguished。 Yes。 Whereasthethinkingmind，intendingtolightupthechaos，wascompelledtoreversetheprocess，andlookatsmallandgreatasseparateandnotconfused。 Verytrue。 Wasnotthisthebeginningoftheenquiry’Whatisgreat？’and’Whatissmall？’ Exactlyso。 Andthusarosethedistinctionofthevisibleandtheintelligible。 Mosttrue。 ThiswaswhatImeantwhenIspokeofimpressionswhichinvitedtheintellect，orthereverse——thosewhicharesimultaneouswithoppositeimpressions，invitethought；thosewhicharenotsimultaneousdonot。 Iunderstand，hesaid，andagreewithyou。 Andtowhichclassdounityandnumberbelong？ Idonotknow，hereplied。 Thinkalittleandyouwillseethatwhathasprecededwillsupplytheanswer；forifsimpleunitycouldbeadequatelyperceivedbythesightorbyanyothersense，then，asweweresayinginthecaseofthefinger，therewouldbenothingtoattracttowardsbeing；butwhenthereissomecontradictionalwayspresent，andoneisthereverseofoneandinvolvestheconceptionofplurality，thenthoughtbeginstobearousedwithinus，andthesoulperplexedandwantingtoarriveatadecisionasks’Whatisabsoluteunity？’Thisisthewayinwhichthestudyoftheonehasapowerofdrawingandconvertingthemindtothecontemplationoftruebeing。 Andsurely，hesaid，thisoccursnotablyinthecaseofone；forweseethesamethingtobebothoneandinfiniteinmultitude？ Yes，Isaid；andthisbeingtrueofonemustbeequallytrueofallnumber？ Certainly。 Andallarithmeticandcalculationhavetodowithnumber？ Yes。 Andtheyappeartoleadthemindtowardstruth？ Yes，inaveryremarkablemanner。 Thenthisisknowledgeofthekindforwhichweareseeking，havingadoubleuse，militaryandphilosophical；forthemanofwarmustlearntheartofnumberorhewillnotknowhowtoarrayhistroops，andthephilosopheralso，becausehehastoriseoutoftheseaofchangeandlayholdoftruebeing，andthereforehemustbeanarithmetician。 Thatistrue。 Andourguardianisbothwarriorandphilosopher？ Certainly。 Thenthisisakindofknowledgewhichlegislationmayfitlyprescribe；andwemustendeavourtopersuadethosewhoareprescribetobetheprincipalmenofourStatetogoandlearnarithmetic，notasamateurs，buttheymustcarryonthestudyuntiltheyseethenatureofnumberswiththemindonly；noragain，likemerchantsorretail—traders，withaviewtobuyingorselling，butforthesakeoftheirmilitaryuse，andofthesoulherself；andbecausethiswillbetheeasiestwayforhertopassfrombecomingtotruthandbeing。 Thatisexcellent，hesaid。 Yes，Isaid，andnowhavingspokenofit，Imustaddhowcharmingthescienceis！andinhowmanywaysitconducestoourdesiredend，ifpursuedinthespiritofaphilosopher，andnotofashopkeeper！ Howdoyoumean？ Imean，asIwassaying，thatarithmetichasaverygreatandelevatingeffect，compellingthesoultoreasonaboutabstractnumber，andrebellingagainsttheintroductionofvisibleortangibleobjectsintotheargument。Youknowhowsteadilythemastersoftheartrepelandridiculeanyonewhoattemptstodivideabsoluteunitywhenheiscalculating，andifyoudivide，theymultiply，takingcarethatoneshallcontinueoneandnotbecomelostinfractions。 Thatisverytrue。 Now，supposeapersonweretosaytothem：Omyfriends，whatarethesewonderfulnumbersaboutwhichyouarereasoning，inwhich，asyousay，thereisaunitysuchasyoudemand，andeachunitisequal，invariable，indivisible，——whatwouldtheyanswer？ Theywouldanswer，asIshouldconceive，thattheywerespeakingofthosenumberswhichcanonlyberealisedinthought。 Thenyouseethatthisknowledgemaybetrulycallednecessary，necessitatingasitclearlydoestheuseofthepureintelligenceintheattainmentofpuretruth？ Yes；thatisamarkedcharacteristicofit。 Andhaveyoufurtherobserved，thatthosewhohaveanaturaltalentforcalculationaregenerallyquickateveryotherkindofknowledge；andeventhedulliftheyhavehadanarithmeticaltraining，althoughtheymayderivenootheradvantagefromit，alwaysbecomemuchquickerthantheywouldotherwisehavebeen。 Verytrue，hesaid。 Andindeed，youwillnoteasilyfindamoredifficultstudy，andnotmanyasdifficult。 Youwillnot。 And，forallthesereasons，arithmeticisakindofknowledgeinwhichthebestnaturesshouldbetrained，andwhichmustnotbegivenup。 Iagree。 Letthisthenbemadeoneofoursubjectsofeducation。Andnext，shallweenquirewhetherthekindredsciencealsoconcernsus？ Youmeangeometry？ Exactlyso。 Clearly，hesaid，weareconcernedwiththatpartofgeometrywhichrelatestowar；forinpitchingacamp，ortakingupaposition，orclosingorextendingthelinesofanarmy，oranyothermilitarymanoeuvre，whetherinactualbattleoronamarch，itwillmakeallthedifferencewhetherageneralisorisnotageometrician。 Yes，Isaid，butforthatpurposeaverylittleofeithergeometryorcalculationwillbeenough；thequestionrelatesrathertothegreaterandmoreadvancedpartofgeometry——whetherthattendsinanydegreetomakemoreeasythevisionoftheideaofgood；andthither，asIwassaying，allthingstendwhichcompelthesoultoturnhergazetowardsthatplace，whereisthefullperfectionofbeing，whichsheought，byallmeans，tobehold。 True，hesaid。 Thenifgeometrycompelsustoviewbeing，itconcernsus；ifbecomingonly，itdoesnotconcernus？ Yes，thatiswhatweassert。 Yetanybodywhohastheleastacquaintancewithgeometrywillnotdenythatsuchaconceptionofthescienceisinflatcontradictiontotheordinarylanguageofgeometricians。 Howso？ Theyhaveinviewpracticeonly，andarealwaysspeaking？inanarrowandridiculousmanner，ofsquaringandextendingandapplyingandthelike——theyconfusethenecessitiesofgeometrywiththoseofdailylife；whereasknowledgeistherealobjectofthewholescience。 Certainly，hesaid。 Thenmustnotafurtheradmissionbemade？ Whatadmission？ Thattheknowledgeatwhichgeometryaimsisknowledgeoftheeternal，andnotofaughtperishingandtransient。 That，hereplied，maybereadilyallowed，andistrue。 Then，mynoblefriend，geometrywilldrawthesoultowardstruth，andcreatethespiritofphilosophy，andraiseupthatwhichisnowunhappilyallowedtofalldown。 Nothingwillbemorelikelytohavesuchaneffect。 Thennothingshouldbemoresternlylaiddownthanthattheinhabitantsofyourfaircityshouldbyallmeanslearngeometry。 Moreoverthesciencehasindirecteffects，whicharenotsmall。 Ofwhatkind？hesaid。 Therearethemilitaryadvantagesofwhichyouspoke，Isaid；andinalldepartmentsofknowledge，asexperienceproves，anyonewhohasstudiedgeometryisinfinitelyquickerofapprehensionthanonewhohasnot。 Yesindeed，hesaid，thereisaninfinitedifferencebetweenthem。 Thenshallweproposethisasasecondbranchofknowledgewhichouryouthwillstudy？ Letusdoso，hereplied。 Andsupposewemakeastronomythethird——whatdoyousay？ Iamstronglyinclinedtoit，hesaid；theobservationoftheseasonsandofmonthsandyearsisasessentialtothegeneralasitistothefarmerorsailor。 Iamamused，Isaid，atyourfearoftheworld，whichmakesyouguardagainsttheappearanceofinsistinguponuselessstudies；andIquiteadmitthedifficultyofbelievingthatineverymanthereisaneyeofthesoulwhich，whenbyotherpursuitslostanddimmed，isbythesepurifiedandre—illumined；andismorepreciousfarthantenthousandbodilyeyes，forbyitaloneistruthseen。Nowtherearetwoclassesofpersons：oneclassofthosewhowillagreewithyouandwilltakeyourwordsasarevelation；anotherclasstowhomtheywillbeutterlyunmeaning，andwhowillnaturallydeemthemtobeidletales，fortheyseenosortofprofitwhichistobeobtainedfromthem。Andthereforeyouhadbetterdecideatoncewithwhichofthetwoyouareproposingtoargue。Youwillverylikelysaywithneither，andthatyourchiefaimincarryingontheargumentisyourownimprovement；atthesametimeyoudonotgrudgetoothersanybenefitwhichtheymayreceive。 IthinkthatIshouldprefertocarryontheargumentmainlyonmyownbehalf。 Thentakeastepbackward，forwehavegonewrongintheorderofthesciences。 Whatwasthemistake？hesaid。 Afterplanegeometry，Isaid，weproceededatoncetosolidsinrevolution，insteadoftakingsolidsinthemselves；whereasaftertheseconddimensionthethird，whichisconcernedwithcubesanddimensionsofdepth，oughttohavefollowed。 Thatistrue，Socrates；butsolittleseemstobeknownasyetaboutthesesubjects。 Why，yes，Isaid，andfortworeasons：——inthefirstplace，nogovernmentpatronisesthem；thisleadstoawantofenergyinthepursuitofthem，andtheyaredifficult；inthesecondplace，studentscannotlearnthemunlesstheyhaveadirector。Butthenadirectorcanhardlybefound，andevenifhecould，asmattersnowstand，thestudents，whoareveryconceited，wouldnotattendtohim。That，however，wouldbeotherwiseifthewholeStatebecamethedirectorofthesestudiesandgavehonourtothem；thendiscipleswouldwanttocome，andtherewouldbecontinuousandearnestsearch，anddiscoverieswouldbemade；sinceevennow，disregardedastheyarebytheworld，andmaimedoftheirfairproportions，andalthoughnoneoftheirvotariescantelltheuseofthem，stillthesestudiesforcetheirwaybytheirnaturalcharm，andverylikely，iftheyhadthehelpoftheState，theywouldsomedayemergeintolight。 Yes，hesaid，thereisaremarkablecharminthem。ButIdonotclearlyunderstandthechangeintheorder。Firstyoubeganwithageometryofplanesurfaces？ Yes，Isaid。 Andyouplacedastronomynext，andthenyoumadeastepbackward？ Yes，andIhavedelayedyoubymyhurry；theludicrousstateofsolidgeometry，which，innaturalorder，shouldhavefollowed，mademepassoverthisbranchandgoontoastronomy，ormotionofsolids。 True，hesaid。 ThenassumingthatthesciencenowomittedwouldcomeintoexistenceifencouragedbytheState，letusgoontoastronomy，whichwillbefourth。 Therightorder，hereplied。Andnow，Socrates，asyourebukedthevulgarmannerinwhichIpraisedastronomybefore，mypraiseshallbegiveninyourownspirit。Foreveryone，asIthink，mustseethatastronomycompelsthesoultolookupwardsandleadsusfromthisworldtoanother。 Everyonebutmyself，Isaid；toeveryoneelsethismaybeclear，butnottome。 Andwhatthenwouldyousay？ Ishouldrathersaythatthosewhoelevateastronomyintophilosophyappeartometomakeuslookdownwardsandnotupwards。 Whatdoyoumean？heasked。 You，Ireplied，haveinyourmindatrulysublimeconceptionofourknowledgeofthethingsabove。AndIdaresaythatifapersonweretothrowhisheadbackandstudythefrettedceiling，youwouldstillthinkthathismindwasthepercipient，andnothiseyes。Andyouareverylikelyright，andImaybeasimpleton：but，inmyopinion，thatknowledgeonlywhichisofbeingandoftheunseencanmakethesoullookupwards，andwhetheramangapesattheheavensorblinksontheground，seekingtolearnsomeparticularofsense，Iwoulddenythathecanlearn，fornothingofthatsortismatterofscience；hissoulislookingdownwards，notupwards，whetherhiswaytoknowledgeisbywaterorbyland，whetherhefloats，oronlyliesonhisback。 Iacknowledge，hesaid，thejusticeofyourrebuke。Still，I shouldliketoascertainhowastronomycanbelearnedinanymannermoreconducivetothatknowledgeofwhichwearespeaking？ Iwilltellyou，Isaid：Thestarryheavenwhichwebeholdiswroughtuponavisibleground，andtherefore，althoughthefairestandmostperfectofvisiblethings，mustnecessarilybedeemedinferiorfartothetruemotionsofabsoluteswiftnessandabsoluteslowness，whicharerelativetoeachother，andcarrywiththemthatwhichiscontainedinthem，inthetruenumberandineverytruefigure。Now，thesearetobeapprehendedbyreasonandintelligence，butnotbysight。 True，hereplied。 Thespangledheavensshouldbeusedasapatternandwithaviewtothathigherknowledge；theirbeautyislikethebeautyoffiguresorpicturesexcellentlywroughtbythehandofDaedalus，orsomeothergreatartist，whichwemaychancetobehold；anygeometricianwhosawthemwouldappreciatetheexquisitenessoftheirworkmanship，buthewouldneverdreamofthinkingthatinthemhecouldfindthetrueequalorthetruedouble，orthetruthofanyotherproportion。 No，hereplied，suchanideawouldberidiculous。 Andwillnotatrueastronomerhavethesamefeelingwhenhelooksatthemovementsofthestars？WillhenotthinkthatheavenandthethingsinheavenareframedbytheCreatoroftheminthemostperfectmanner？Buthewillneverimaginethattheproportionsofnightandday，orofbothtothemonth，orofthemonthtotheyear，orofthestarstotheseandtooneanother，andanyotherthingsthatarematerialandvisiblecanalsobeeternalandsubjecttonodeviation——thatwouldbeabsurd；anditisequallyabsurdtotakesomuchpainsininvestigatingtheirexacttruth。 Iquiteagree，thoughIneverthoughtofthisbefore。 Then，Isaid，inastronomy，asingeometry，weshouldemployproblems，andlettheheavensaloneifwewouldapproachthesubjectintherightwayandsomakethenaturalgiftofreasontobeofanyrealuse。 That，hesaid，isaworkinfinitelybeyondourpresentastronomers。 Yes，Isaid；andtherearemanyotherthingswhichmustalsohaveasimilarextensiongiventothem，ifourlegislationistobeofanyvalue。Butcanyoutellmeofanyothersuitablestudy？ No，hesaid，notwithoutthinking。 Motion，Isaid，hasmanyforms，andnotoneonly；twoofthemareobviousenougheventowitsnobetterthanours；andthereareothers，asIimagine，whichmaybelefttowiserpersons。 Butwherearethetwo？ Thereisasecond，Isaid，whichisthecounterpartoftheonealreadynamed。 Andwhatmaythatbe？ Thesecond，Isaid，wouldseemrelativelytotheearstobewhatthefirstistotheeyes；forIconceivethatastheeyesaredesignedtolookupatthestars，soaretheearstohearharmoniousmotions； andthesearesistersciences——asthePythagoreanssay，andwe，Glaucon，agreewiththem？ Yes，hereplied。 Butthis，Isaid，isalaboriousstudy，andthereforewehadbettergoandlearnofthem；andtheywilltelluswhetherthereareanyotherapplicationsofthesesciences。Atthesametime，wemustnotlosesightofourownhigherobject。 Whatisthat？ Thereisaperfectionwhichallknowledgeoughttoreach，andwhichourpupilsoughtalsotoattain，andnottofallshortof，asIwassayingthattheydidinastronomy。Forinthescienceofharmony，asyouprobablyknow，thesamethinghappens。Theteachersofharmonycomparethesoundsandconsonanceswhichareheardonly，andtheirlabour，likethatoftheastronomers，isinvain。 Yes，byheaven！hesaid；and’tisasgoodasaplaytohearthemtalkingabouttheircondensednotes，astheycallthem；theyputtheirearsclosealongsideofthestringslikepersonscatchingasoundfromtheirneighbour’swall——onesetofthemdeclaringthattheydistinguishanintermediatenoteandhavefoundtheleastintervalwhichshouldbetheunitofmeasurement；theothersinsistingthatthetwosoundshavepassedintothesame——eitherpartysettingtheirearsbeforetheirunderstanding。 Youmean，Isaid，thosegentlemenwhoteaseandtorturethestringsandrackthemonthepegsoftheinstrument：mightcarryonthemetaphorandspeakaftertheirmanneroftheblowswhichtheplectrumgives，andmakeaccusationsagainstthestrings，bothofbackwardnessandforwardnesstosound；butthiswouldbetedious，andthereforeIwillonlysaythatthesearenotthemen，andthatI amreferringtothePythagoreans，ofwhomIwasjustnowproposingtoenquireaboutharmony。Fortheytooareinerror，liketheastronomers；theyinvestigatethenumbersoftheharmonieswhichareheard，buttheyneverattaintoproblems—thatistosay，theyneverreachthenaturalharmoniesofnumber，orreflectwhysomenumbersareharmoniousandothersnot。 That，hesaid，isathingofmorethanmortalknowledge。 Athing，Ireplied，whichIwouldrathercalluseful；thatis，ifsoughtafterwithaviewtothebeautifulandgood；butifpursuedinanyotherspirit，useless。Verytrue，hesaid。 Now，whenallthesestudiesreachthepointofinter—communionandconnectionwithoneanother，andcometobeconsideredintheirmutualaffinities，then，Ithink，butnottillthen，willthepursuitofthemhaveavalueforourobjects；otherwisethereisnoprofitinthem。 Isuspectso；butyouarespeaking，Socrates，ofavastwork。 Whatdoyoumean？Isaid；thepreludeorwhat？Doyounotknowthatallthisisbutthepreludetotheactualstrainwhichwehavetolearn？Foryousurelywouldnotregardtheskilledmathematicianasadialectician？ Assuredlynot，hesaid；Ihavehardlyeverknownamathematicianwhowascapableofreasoning。 Butdoyouimaginethatmenwhoareunabletogiveandtakeareasonwillhavetheknowledgewhichwerequireofthem？ Neithercanthisbesupposed。 Andso，Glaucon，Isaid，wehaveatlastarrivedatthehymnofdialectic。Thisisthatstrainwhichisoftheintellectonly，butwhichthefacultyofsightwillneverthelessbefoundtoimitate； forsight，asyoumayremember，wasimaginedbyusafterawhiletobeholdtherealanimalsandstars，andlastofallthesunhimself。 Andsowithdialectic；whenapersonstartsonthediscoveryoftheabsolutebythelightofreasononly，andwithoutanyassistanceofsense，andperseveresuntilbypureintelligencehearrivesattheperceptionoftheabsolutegood，heatlastfindshimselfattheendoftheintellectualworld，asinthecaseofsightattheendofthevisible。 Exactly，hesaid。 Thenthisistheprogresswhichyoucalldialectic？ True。 Butthereleaseoftheprisonersfromchains，andtheirtranslationfromtheshadowstotheimagesandtothelight，andtheascentfromtheundergrounddentothesun，whileinhispresencetheyarevainlytryingtolookonanimalsandplantsandthelightofthesun，butareabletoperceiveevenwiththeirweakeyestheimagesinthewater（whicharedivine），andaretheshadowsoftrueexistence（notshadowsofimagescastbyalightoffire，whichcomparedwiththesunisonlyanimage）——thispowerofelevatingthehighestprincipleinthesoultothecontemplationofthatwhichisbestinexistence，withwhichwemaycomparetheraisingofthatfacultywhichistheverylightofthebodytothesightofthatwhichisbrightestinthematerialandvisibleworld——thispowerisgiven，asIwassaying，byallthatstudyandpursuitoftheartswhichhasbeendescribed。 Iagreeinwhatyouaresaying，hereplied，whichmaybehardtobelieve，yet，fromanotherpointofview，isharderstilltodeny。 This，however，isnotathemetobetreatedofinpassingonly，butwillhavetobediscussedagainandagain。Andso，whetherourconclusionbetrueorfalse，letusassumeallthis，andproceedatoncefromthepreludeorpreambletothechiefstrain，anddescribethatinlikemanner。Say，then，whatisthenatureandwhatarethedivisionsofdialectic，andwhatarethepathswhichleadthither；forthesepathswillalsoleadtoourfinalrest？ DearGlaucon，Isaid，youwillnotbeabletofollowmehere，thoughIwoulddomybest，andyoushouldbeholdnotanimageonlybuttheabsolutetruth，accordingtomynotion。WhetherwhatItoldyouwouldorwouldnothavebeenarealityIcannotventuretosay；butyouwouldhaveseensomethinglikereality；ofthatIamconfident。 Doubtless，hereplied。