2019

Preprint N°492 Everyday Language and Technical Terminology: Reflective Abstractions in the Long-term History of Spatial Terms Matthias Schemmel

 

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EverydayLanguageandTechnicalTerminology:ReflectiveAbstractionsintheLong-termHistoryofSpatialTermsMatthiasSchemmel

Abstract:Thispaper1discussestheoriginoftechnicalterminologyineverydaylanguage

byoutliningstagesinalong-termhistoryoftechnicalterminologymarkedbyincreasing

degreesofreflexivity.ItusestheexamplesofspatialterminologyinanancientChinese

theoreticaltext,inNewtonianmechanics,andinrelativitytheory,andattemptsto

explaintheincreasingdistanceofthemeaningsoftechnicaltermsfromtheireveryday

counterpartsbyrelatingittohistoricalprocessesofknowledgeintegration.

1. Aparadoxandaquestion

Letmestartwithaparadox.Weusuallythinkthat,intechnicallanguage,terminology

holdsakeyrole.Weusuallythinkthatitisprimarilythetechnicaltermsthatmakethe

languagetechnical.Letmecontrastthisviewwithanallegedquoteoftheturn-of-the-

centurymathematicianDavidHilbert(1862–1943):

Onemustbeabletosayeachtime—insteadof‘points’,‘straightlines’,and

‘planes’—‘tables’,‘chairs’,and‘beermugs’.2

Hilbertsupposedlysaidthisinthecontextofadiscussionaboutthefoundationsof

geometry,aboutwhichhewouldlaterwriteagroundbreakingwork,DieGrundlagender

Geometrie,firstpublishedin1899.3Inthatwork,HilbertreformulatedEuclidean

1ThispaperisbasedonapresentationgivenattheworkshopTerminologyin(ancient)

scienceorganizedbyMarkusAsperinthecontextoftheTOPOIprojectclusterandheld

May5–6,2014attheHumboldtUniversityofBerlin.2“ManmußjederzeitanStellevon‘Punkte,Geraden,Ebenen’‘Tische,Stühle,Bierseidel’

sagenkönnen”(Hilbert1970,403).Thestatementisfoundinthesection

LebensgeschichtewrittenbythemathematicianOttoBlumenthal(1876–1944).3Hilbert1899.

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geometryinsuchawaythatitbecameindependentfromgeometricalintuitionandthe

everydaymeaningoftermssuchas‘point’,‘straightline’,and‘plane’.Themeaningofthe

termsisfixedsolelythroughtheiruseintheaxioms,anditthereforebecomesarbitrary

whatwordsareused.Thisiswhatiscalledimplicitdefinition.4

Hilbert’squotethusarguesthat,inaxiomatictheories,themeaningsoftechnicalterms

shouldbefixedbymeansofimplicitdefinitionsandthereforebecompletely

independentfromthemeaningsofthewordsofeverydaylanguage.Euclid,bycontrast,

definedmanyofhistermsexplicitly.Apoint,forinstance,isaccordingtohisElements

thatwhichhasnopart.5

Thisdefinitionreflectstheintuitiveideathatapointissosmall,itcannotbefurther

dividedintoparts.

ThedisparitybetweenHilbert’sandEuclid’scasesgivesrisetoafundamentalquestion

withregardtotheoreticaltermsintheexactsciences:Whatistherelationbetween

everydaylanguageandintuitionononehandandscientificterminologyontheother?As

Ishallargueinthispaper,thisrelationchangesoverhistoryanddependsonthetypesof

theoreticalknowledgeconsideredandtheirrelationtoexperience.Inparticular,Ishall

arguethattheoreticaltermsmayhavedifferentdegreesofreflexivity,i.e.,theymay

embodydifferent,anddifferentlyprogressed,historiesofreflection.

Asbefitsthewidercontextofthiscontribution,6Ishallparticularlydiscussexamplesof

theoreticaltermsrelatedtospatialknowledge.Myexamplesrelatetothefollowing

threehistoricalepisodes:

– theoriginsoftheoreticalscienceinantiquity(section2);

– theemergenceofclassicalmechanicsinearlymoderntimes(section3);and

4ForanintroductiontotheconceptofimplicitdefinitionanditsrelationtoHilbert’s

FoundationsofGeometry,seeSchlick2009,205–217.5Euclid1956,153.6TheprojectclusterTOPOI,whichprovidedtheframeworkoftheworkshopatwhich

thistextwasfirstpresented,isdevotedtothestudyoftheformationandtransformation

ofspaceandknowledgeinancientcivilizations.

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– thetransformationofphysicsintheearlytwentiethcentury(section4).

Theseareallwell-studiedepisodes,whicharewidelyconsideredturningpointsinthe

historyoftheexactsciences.WhileIdonotargueforalinear,letalonepredetermined,

developmentconnectingthethreeepisodes,weshallseethatonemayunderstandthem

asdisplayingprogressivelyhigherdegreesofreflexivityinthetheoreticaltermsthey

bringabout.Thisoverallresultwillbesummarizedintheconcludingsection.

2. Technicalterminologyattheoriginsoftheoreticalscience

Technicalterminologypredatestheriseoftheoreticalscience.Technicaltermsmay

formwheneverspecializedknowledgeiscommunicated.Thismayhappeninthecontext

ofjointactionwithinagroupofexperts,inthecontextofteachingtoapprentices,orin

thecontextofcommunicatingknowledgetoanappropriatelyinformedaudienceoutside

thegroupofexperts.Theformationoftechnicalterminologymaythusoccurinfieldsof

variousculturalpracticessuchastool-making,construction,navigation,surveying,

administration,orastronomicalobservationandrecord-keeping.Allthesepractices

havedevelopedpriortotheemergenceoftheoreticalscience,whichismarkedbya

reflectiononthelinguisticorotherwisematerialrepresentationsofthemorepractical

formsofknowledge.7

Theearliestevidenceforthistypeoftheoreticalknowledgestemsfromantiquity.

Aristotle’sPhysicsandEuclid’sElementspresentprominentexamplesoftheoretical

reflectionsonspatialknowledgeandarepartofanintellectualtraditionthatreaches

backtoPre-Socratictimes.Lessknownisthefactthatsimilarreflectionsare

documentedinsourcesfromancientChina.Inparticulartheso-calledMohistCanon,a

textfromaround300BCEandoneofthemostformalandmostrigorouslyarguedtexts

fromancientChina,containspassagesthatdefineanddiscussspatialterms.

Thus,paralleltotheEuclideandefinitionofapointwefind,intheMohistCanon,a

definitionofan‘end-point’.

7SeeSchemmel2016andfurtherreferencesgiventherein.

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duān端‘end-point’istheelementthat,havingnomagnitude,comesforemost.8

Theeverydayword‘duān’端,whichdenotesanextreme,oranendofanelongateobject,

ishereturnedintoatechnicalterm.Howdoweknowthatitistobeunderstoodasa

technicalterm?Notonlyisitdefined,but,mostimportantly,itispartofanetworkof

definedterms.Thus,‘element’and‘magnitude’arebothdefinedinothersectionsofthe

text.Letusheretakeacloserlookatthedefinitionof‘magnitude’.

hòu厚‘havingmagnitude’meansthatthereissomethinginrelationtowhichit

(i.e.,thethingthathasmagnitude)isbigger.

hòu厚‘havingmagnitude’:Onlyanend-pointhasnothinginrelationtowhichit

isbigger.9

Hòu厚 ineverydaylanguagemeans‘thick’(inthesenseofamaterial,physical

dimension).Hereitisturnedintoanabstracttermthatimpliesspatialmagnitudeand

canbeusedinotherdefinitionsorexplanations.Alatersection,forinstance,reads:

yíng盈‘beingfilledout’isnowherenothavingsomething.

yíng盈‘beingfilledout’:Wherethereisnofillingoutthereisnomagnitude(hòu

厚).Onthemeasuringrodthereisnoplacetowhichitextendssuchthatyoudo

notgetboth(i.e.,fillingoutandmagnitude).10

Thuswehaveapairofterms,hòu厚‘havingmagnitude’(beingextended)andyíng盈

‘fillingout’,thatconsistentlydifferentiatethematerialandthespatialaspectsofbodies.

Takingintoaccountallthesectionsonspatial,temporalandmaterialconcepts,we

obtainanetworkoftermswhichispresentedinfig.1.

8ThisisCanonA61,followingtheenumerationbyA.C.Graham(Graham1978).The

translationsfromancientChinesehavebeendoneincooperationwithWilliamG.Boltz,

seeBoltzandSchemmel2016.9CanonandExplanationofsectionA55.10CanonandExplanationofsectionA65.

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Figure1:Terminologicalrelationsbetweensectionsonspace,timeandmatter.Definitions

arerepresentedbysquares,propositionsbyovals.Aboldarrowindicatesthatadefined

termisusedintheCanonofanothersection,athinarrowthatitisusedintheco-ordinated

Explanation.Dottedarrowsindicatethattheoccurrenceofthetermisonlyconjectural.

Althoughthetermsformanetwork,theyarenotimplicitlydefined,asinHilbert’s

axiomaticgeometry.Rather,theirmeaningispartlyderivedfromtheireveryday

meaning.Theeverydaylanguagetermsreflecteverydaystructuresofcognition.The

materialandthespatialaspectsofbodies,forinstance,areaspectsofeverydayintuitive

thinkingandformpartofwhatmaybetermedanthropomorphicknowledge.11

Anthropomorphicknowledgeisstudiedbydevelopmentalpsychologyanditsstructures

arepriortoanytheory.Furthermore,owingtothesimilarbiologicalmake-upofall

humansandthesimilarexperiencestheymakeinasharedenvironmentwhose

fundamentalphysicalfeaturesarethesameeverywhere,largepartsofthis

anthropomorphicknowledgeareuniversal.

Buttheuniversalityofanthropomorphicknowledgestructuresdoesnotgenerally

translateintoauniversalityoftheirlinguisticrepresentations.Thisisbecause,in

11Onthegradualdifferentiationofthecorporealandspatialaspectsoftheenvironment

intheprocessofontogenesis,see,forinstance,Piaget1959(inparticular97–101).

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language,theuniversalaspectsofcognitionmaybecomemixedupwith,andmodified

by,other,culture-specificpartsofcognitionandwithculture-specificaspectsoftheir

representation.Thisholds,inparticular,forthelinguisticrepresentationof

anthropomorphicknowledgestructuresprovidedbytheoreticalterms.

Themeaningoftheoreticaltermsissetapartfromthatoftheireverydaycounterparts

byanactofexplicitreflectioninthemediumofrepresentation.Thismaybeadefinition

oranyotheruseofmaterialmeansofrepresentationdesignedtodelineatemeaning.As

aconsequence,termsreferringtoreal-worldobjectsandeventsnowbecome

themselvesobjectsofreflectionandareconsideredwithrespecttotheirmutual

relations.Thismaybeunderstoodasaprocessofreflectiveabstraction:Thereflection

abstractsfromtheparticularcontextsofthetermsintheireverydayuse.Onthehigher

levelofreflection,newmeaningisconstructedbyconcretization,i.e.,byexplicitly

establishingrelationstoothertermsofthetheory.12

Thus,when‘fillingout’istakenoutofallpracticalcontextsoffillingsomethingout,and

consideredregardlessofsuchcontextsandappliedtomaterialobjects,attributes,and

timesandspaces(ashappensintheMohistCanon)13,thisisaprocessofabstractionand

generalization.Anthropomorphicknowledgestructuresremaineffectivebutare

modifiedintheirreconstructiononthetheoreticallevelofreflection.Theshiftsinthe

meaningoftermsmay,inparticular,bringaboutwhatmaybecalledartifactsoftheory:

Owingtotheirgeneralizationandabsolutization,themeaningoftermsmaynowinvolve

typicallytheoreticalproperties,likethoserelatingtoinfinity,whicharealientotheir

everydaycounterparts,andwhichareoftenatthecoreofphilosophical-mathematical

problems.Thus,whilea‘point’isintuitivelyunderstoodassomethingverysmalllikea

dotofverysmallsize,itisnowclaimedtobeinfinitelysmall,therebyforcingthe

reconsiderationofnotionssuchascomposition,extension,andmotion.

12TheconceptofreflectiveabstractionistakenoverfromtheworkofPiaget(Piaget

1985),butwefollowheretheenhancementoftheconceptofreflectionproposedby

Damerow(1996,1–27),accordingtowhichtheobjectofreflectionconsistsnotonlyof

theactionsofthereflectingsubjectbutcruciallyincludesthematerialmeansofaction.13SectionsA65(seeabove),A66,andB15;seeBoltzandSchemmel2016.

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Thattheresultsofsuchabstractionsarenotuniversallythesameisalreadyindicatedby

thisexample.WhileintheGreekcontexttheabstracttermisthepoint(σημεῖον),inthe

Chinesecaseitistheend-point(duān端).14

Besidesthesectionsonspatialterms,therearesectionsoftheMohistCanonthatreflect

onknowledgestructuresrelatedtomechanicalandopticalphenomena.Thefollowing

section,forinstance,documentstheoccupationwithunexpectedeffectswhen

mechanicaldevicesareinvolved:

Thebeam(héng衡):Ifyouaddaweight(zhòng重)tooneofitssides[thatside]

willnecessarilydropdown.Thisisduetotheeffectiveness(quán權)andthe

weightmatchingeachother.Iftheyaremadelevelwitheachother,thenthebase

isshortandthetipislong.Addequalweightstobothsides,thenthetipwill

necessarilygodown.Thisisduetothetiphavinggainedeffectiveness.15

Thesectiondealswithasituationinwhichaleverisinvolved,sothatequalweightsmay

havedifferenteffectsonitstwoends.Thepuzzleistheoreticallyresolvedby

complementingthetermzhòng重‘weight’withatermquán權‘effectiveness’,to

accountforthedifferentbehaviorofweightsindifferentdistancesfromthefulcrum.

Thisdifferentiationoftheterm‘weight’maybeunderstoodasatheoreticalresponseto

instrumentalknowledge,namelyknowledgeobtainedinthehandlingofcultural

artifacts,inthiscaseinstrumentsinvolvingalever.16

14Note,however,thattherearealternativedefinitionsofapointinancientGreektexts,

inparticularonedefiningthepointastheextremityofaline;seeEuclid1956,155–158.

ThissimilaritybetweentheGreekandChinesecases(whichhavetobeconsidered

independentwithregardtothetheoreticallayerofknowledge)maybetakenas

indicativeoftheshapingforceofmaterialityevenonthechoiceofourtheoretical

abstractions.15ExplanationofsectionB25b.Thetranslationresultedfromjointworkinthecontext

ofaworkinggrouponthehistoryofmechanicsattheMaxPlanckInstituteforthe

Historyofscience,whichincludedWilliamBoltz,JürgenRenn,andtheauthor.16ThisinterpretationhasfirstbeengiveninRennandSchemmel2006.

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Wemaythusdistinguishbetweenanthropomorphicandinstrumentalknowledge,the

firstobtainedthroughexperienceswithrespecttouniversalfeaturesofthephysical

environment,thelatterobtainedthroughexperiencesinhandlingculture-specific

artifacts.Theoreticalknowledgeemergesfromthesystematicreflectiononthesemore

elementarytypesofknowledge.Whiletherearemarkeddifferencesinthespecific

theoreticaltermsthatforminthecaseofancientGreekandancientChinesetheoretical

sciences,thephenomenonitselfturnsouttobeacross-culturalone.Letusformulate

generalcharacteristicsoftheformationoftechnicalterminologyattheoriginsof

theoreticalscience.

Origin:Thetechnicaltermsattheoriginsoftheoreticalsciencearetakenfromeveryday

language,possiblyincludingthespecializedlanguageofpractitioners.

Knowledgestructures:Theirmeaningreflectsstructuresofanthropomorphicand

instrumentalknowledge.Atthesametime,theirmeaningisdistinguishedfromthatin

everydaylanguagebythedecontextualizationfromconcreteactionandthe

recontextualizationwithintheory.Theoreticaldemandssuchasconsistency,

comprehensiveness,andtheresolutionofparadoxesgiverisetodifferentiationsand

fixationsofthetermsthatarealientotheireverydaycounterparts.

Externalrepresentation:Thesystemoftheoreticaltermsistransmittedandstabilized

throughexternalrepresentationintexts.Thetheoreticaltextsmaybehandeddown

orally,butmostoftenawrittencomponentplaysacrucialrole.Thiswrittencomponent

entailsthepossibilityofcommunicatingtheoreticalknowledgetolatergenerationseven

aftertheoraltraditioninthecontextofwhichitemergedhasceased.

ThelastpointbringsustothequestionofthefateofMohistscience.TheMohistCanon

originatedintheWarringStatesperiodwhenChinawaspoliticallyfragmentedinto

manysmallerstates,oftenatwarwitheachother.Atthetime,avarietyofaristocratic

thinkersstroveforanappointmenttohighofficeandofferedtheirservicesasadvisors

tothevariousrulersandgovernments.Avividcultureofdisputationflourishedandwe

evenseetheemergenceofatypeofsophists,thebianzhe,whodisputedforthesakeof

disputationandbecamefamousforframingparadoxes.Inthisenvironment,itseems,

thelaterMohistsstrovetoshowthatconsistentreasoningispossibleandthat

paradoxescouldbeavoidedorresolvedbyreflectingonlanguageanddelineatingthe

meaningofterms.Inthiscontext,theydealtwithavarietyofsubjectsrangingfrom

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mattersofconduct,governmentandethicstosubjectsthatwewouldtodayclassifyas

geometry,mechanicsandoptics,asisdocumentedintheMohistCanon.

ThetheoreticaltraditionofthelaterMohistsdidnotlastlong,however.Itprobably

ceasedunderthechangedsocio-politicalconditionsoftheunifiedempireand

centralizedadministrationoftheQindynastyinthethirdcenturyBCE.Thetextwas

garbledinitstransmission,andalthoughitwashandeddowntothepresent,itdidnot

becomeeffectiveinChineseintellectualhistoryforalongtime.Whenitwascommented

onagainstartingattheendoftheeighteenthcentury,ithadbecomeanobjectof

historicalandphilologicalinterestratherthanasourceinforminganactualtraditionof

theoreticalthinking.

Greektheoreticaltextsongeometry,mechanics,andoptics,bycontrast,didhavean

impactonlaterEuropeanandNearEasternknowledgetraditionsandservedasmodels

forrepresentingtheoreticalknowledgewellintomoderntimes.

3. Technicalterminologyintheemergenceofclassicalmechanics

TurningtoearlymodernEurope,onemayaskwhatthemaindifferenceisbetweenthe

ancienttheoreticalreflectionsdiscussedintheprevioussectionandtheirearlymodern

counterparts.Concerningthescienceofmechanics,onemajordifferenceisclearlythe

challengetointegrateavastbodyofsystematicallyexpandedexperientialknowledge.

Themodernscienceofclassicalmechanicsresultedfromtheintegrationofthe

cumulatedastronomicalknowledgeembodiedinKepler’slawsofplanetarymotionand

thecumulatedmechanicalknowledgeembodiedinGalileo’slawsoffreefalland

projectilemotion.Theintegrativereflectiononthesebodiesofknowledgebrought

aboutafundamentalchangeoftheconceptofforcewhichliesattheheartofclassical

mechanics.

Thereisananthropomorphicknowledgestructurethatwemayrefertoasthemotion-

implies-forcemodel.17Wheneverwewanttosetsomethinginmotion,wehavetoexerta

force.Andthemoreforceweexert,thequickermovesthemobile.Thisintuitiverelation

17RennandDamerow2007.

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was,inmedievalscience,mathematicallyquantifiedbythestatementthatthemoving

forceisproportionaltothevelocityofthemobile.

Theaspectofmathematizationisimportantinthiscontext.Itprovidesanadditional

wayofrelatingtermsinanetwork:therelationsmaynotonlybesemantical,asinthe

caseoftheMohists,butalsomathematical.Now,classicalmechanicsisdistinguished

frompre-classicalmechanicsbyareconceptualizationofforcewhichonlymadepossible

theintegrationofterrestrialandcelestialmechanics:Inclassicalmechanics,forceis

conceivedproportionaltoacceleration,ratherthanvelocity.Inertialmotion,i.e.uniform

motioninastraightline,isnotinneedofacausalexplanationintermsofforces,and

onlychangeofvelocity(acceleration)is.Thedeep-structureoftheanthropomorphic

relationbetweenmotionandforceispreserved,butthemodifiedstructurerelates

accelerationtoforce,whileuniformmotioninastraightlineisequivalenttorest.

LetustakealookattheterminologyinNewton’sPhilosophiaenaturalisprincipia

mathematica,firstpublishedin1687.Thebookisusuallyconsideredthefirstconsistent

expositionoftheconceptualframeworkofclassicalmechanics.InanalogytoEuclid’s

Elements,Newtonbeginswithaseriesofdefinitionsoftechnicaltermssuchas‘quantity

ofmatter’,‘quantityofmotion’,‘inherentforce’,‘impressedforce’etc.Definition3,for

instance,reads:

Inherentforceofmatteristhepowerofresistingbywhicheverybody,sofarasit

isable,perseveresinitsstateeitherofrestingorofmovinguniformlystraight

forward.18

Newtonthusintroducesaninherentforce(visinsita)toexplaininertia.Hedoesexactly

whatwehavejuststatediswronginclassicalmechanics!Tointroduceaforcefor

maintainingamotioniscompatiblewiththemedievalconceptionofforceandmotion,

notwiththeclassicalone,whichNewtonpioneersinthisbook.Thismeansthat,despite

thenewmathematical-conceptualstructureofclassicalmechanics,Newton,inchoosing

histechnicalterms,isinfluencedbyatheoreticaltraditionthatdirectlyrelatestoour

intuitionsandtheirreflectionineverydaylanguage.

18Newton1999,404.

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SimilarreminiscencesofearliercognitivestructuresarefoundinNewton’s

understandingofspace,atermhedoesnotdefine,becauseitis“familiartoeveryone”19,

butdiscussesinalongScholium.Space,accordingtoNewton,isinastateofabsolute

restanddoesnotmove.Butinclassicalmechanicsabsoluterestisindistinguishable

fromuniformmotioninastraightline!

ButNewton’sunderstandingofforceandspace,whichisatoddswiththemathematical

structureofthesciencehepioneers,isnothisindividualblunder.Rather,itisindicative

ofhowconceptualdevelopmentproceedsintheexactsciences.Newton’sintegration

waspossibleonlyonthebasisofavailableconceptualframeworks,whichinformedthe

meaningofthetechnicalterms.Atthesametime,theknowledgeintegrationemployed

mathematicalmeans,andthereorganizationofthemathematical-conceptualstructure

ledtochangesinthemeaningsoftheterms.Thiscreatedthetensionswithinthe

conceptualframeworkthatwewitnessinNewton’swritings.

Letussummarizethecharacteristicsoftheoreticaltermsintheemergenceofclassical

mechanics:

Origin:Thetechnicaltermsarepartofatheoreticaltradition,whichitselfrelatesbackto

everydaylanguage.Adisciplinarilyfixedsystemoftechnicalterminologyisonly

emergingandcontroversiesoverthemeaningoftermsshowthatterminologyistoa

certainextentstillamatterofindividualsystem-building.20

KnowledgeStructures:Themeaningsofthetheoreticaltermsreflectthecognitive

structuresofprevioustheories(whichthemselvesincorporateanthropomorphicand

instrumentalknowledgestructures),modifiedastointegratesystematically

accumulatedempiricalknowledge.Buttensionsbetweenestablishedmeaningsandnew

mathematical-conceptualstructuresexist.

ExternalRepresentation:Thesystemoftermsistransmittedandstabilizedthrough

externalrepresentationmostlybymeansofwrittentext,diagrams,andsymbolic

formalisms.Themathematicalformalismplaysacrucialroleinintegratingnew

19Newton1999,408.20AsexamplesconsidertheterminologicaldiscussionsintheLeibniz-Clarke

correspondence(Alexander1970),orthevisvivacontroversy.

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empiricalknowledgeandservesasamediumbetweenexperienceandconceptual

structure.Itisameansbywhichnewexperiencesaretranslatedintoconceptsthat

createtensionswithintheexistingconceptualstructures.

Inthecaseofclassicalmechanics,itwasonlyinthecontextoflaterreflectionsona

mathematical-conceptualframeworkthathad,notleastowingtoitsempiricalsuccess,

becomefirmlyestablished,thatthetensionbetweenthetraditionalmeaningsofterms

anchoredinintuitionsandeverydayuseandthenewmathematicalstructurecouldbe

resolved.Thus,itwasonlywiththedevelopmentoftheconceptof‘inertialframes’inthe

late19thcenturythatthemathematical-conceptualstructureofspaceinclassical

mechanicsfoundanadequateterminologicalexpression.Ataroundthesametime,

however,thedistinguishedstatusofmechanicsasafundamentaltheoryforallof

physicsbecameincreasinglydisputed.

4. Technicalterminologyinthetransformationof

early-twentieth-centuryphysics

Inthelate19thcentury,fieldsofphysicsotherthanmechanics,inparticular

thermodynamicsandelectrodynamics,haddevelopedtheirownmathematical-

conceptualstructuresandtechnicalterminologies,partlyoverlappingwithmechanics,

butpartlyindependentofit.Theconceptualrevolutionsofearlytwentieth-century

physicsoccurredattheborderlinesbetweenthesesubfieldsofphysics.21Thetheoryof

specialrelativity,forinstance,resultedfromconsiderationsaboutelectromagnetic

phenomenainrelativemechanicalmotionandcanthusbeviewedashavingemergedat

theborderlinebetweenelectrodynamicsandmechanics.

Theconceptualrevolutionsofearlytwentieth-centuryphysicsarenotoriousforhaving

renderedthatsciencemore‘abstract’,tohaveremoveditevenfurtherfromeveryday

intuitionandeverydaylanguageashadpreviouslybeenthecase.Andinfact,central

termsofmodernphysics,suchas‘energy-stresstensor’or‘quantumstate’seemhardly

relatabletoeverydayknowledge.Arethenthetermsofmodernphysicstobeimplicitly

definedwithoutreferencetoeverydaymeanings,asHilbert’saxiomaticmethod

suggests?

21SeeRenn2006,inparticular87–127.

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Hilberthimselfattemptedanaxiomatizationofphysics.22Tothisendhecombined

Einstein’snascenttheoryofgeneralrelativitywithatheoryofmatter,whichis

nowadaysonlyknowntohistoriansofscience.23Butbesidesthetransientcharacterof

theingredientsofHilbert’saxiomaticprogramforphysics,Einsteinhadsomemore

fundamentalreservationsconcerningtheideaofanaxiomaticfoundationofmodern

physics.InhisessayGeometryandExperienceof1921,hesayswithrespecttothe

applicationofHilbert’saxiomaticgeometrytophysics:

Itisclearthatthesystemofconceptsofaxiomaticgeometryalonecannotmake

anyassertionsastothebehaviorofrealobjects[…].Tobeabletomakesuch

assertions,geometrymustbestrippedofitsmerelylogical-formalcharacterby

thecoordinationofrealobjectsofexperiencewiththeemptyconceptual

schemataofaxiomaticgeometry.24

Infact,inordertore-interpretcentraltermsofclassicalphysicsrelatedtospaceand

time,Einsteinhadtodisentanglethedifferentlayersofknowledgethatcontributedto

theirmeaning.Ontheonehandtherewasthelayeroftheoperationsofmeasurement.

Thislayerisclearlyrootedinpracticalknowledgeandinvolvesconceptssuchas

measuringrodsandclocks.Inordertoapplythisknowledge,Einsteinhadtomakebasic

assumptionsconcerningtheexistenceofrigidbodiesandthepossibilitytosynchronize

clocks,allrootedinanthropomorphicandinstrumentalknowledgestructuresandallin

accordwithclassicalphysics.Ontheotherhand,thereisthelayeroftheoretical

assumptionsaboutthecomparisonofspaceandtimemeasuresinsystemsinrelative

motion,whichimpliesgeneralstatementsaboutthestructureofspaceandtime.While

theseassumptionsmayappearintuitivelyobvious,Einsteinnoticedthattheyarenot

impliedbytheassumptionsaboutmeasurementoperations.Givinguptheideasofthe

independenceoflength,duration,andsimultaneityfromthestateofmotion,Einstein

arrivedatanewgeometricalframeworkforphysics,laterdescribedwithtechnical

termssuchas‘space-time’and‘chronogeometry’.22Hilbert,DieGrundlagenderPhysik,firstpublishedasHilbert1915andHilbert1916.23ThisisGustavMie’sunifyingtheory.FordiscussionsofMie’sandHilbert’stheories,

andfortranslationsintoEnglishoftheiroriginalwritings,seethecorresponding

sectionsinRennandSchemmel2007.24Einstein1921.ThetranslationistakenfromEinstein1982,234–235.

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Accordingly,Einsteinfurtherexplains:

Theideaofthemeasuring-rodandtheideaoftheclockcoordinatedwithitinthe

theoryofrelativitydonotfindtheirexactcorrespondenceintherealworld.[…]

Butitismyconvictionthatinthepresentstageofdevelopmentoftheoretical

physicstheseconceptsmuststillbeemployedasindependentconcepts;forwe

arestillfarfrompossessingsuchcertainknowledgeofthetheoreticalprinciples

[…]astobeabletoconstructsolidbodiesandclockstheoreticallyfrom

elementaryconcepts.25

Thismeans,thetheoryof(general)relativitystillreliesoneverydayconceptssuchasa

measuringrod(whichweencounteredwiththeMohists!),althoughfromtheviewpoint

ofmodernphysicstheseobjectsareidealizations.Thecrucialpointhereisthat,inorder

toidentifythecorrespondingmathematicalstructureswithinanewtheoryasphysical

space(orspace-time),theymustbeconnectedtoformertheoreticalorpre-theoretical

knowledge,fromwhichtheyderivetheirspatial(orspatio-temporal)meaning.26

Letusagainsummarizesomeofthecharacteristicsoftheoreticalterminologyinthe

transformationofearly-twentieth-centuryphysics.

Origin:Technicaltermsarepartofvariousexperttraditionsorganizedinadisciplinary

hierarchy.

KnowledgeStructures:Theirmeaningispartlyfixedbythemathematicalstructureofa

particulartheory,butrelationstoknowledgeoutsidethisstructureandeventopre-

theoreticalknowledgeareneededtoprovidephysicalmeaning.Thismultiplerelation

constitutingmeaningalsoexplainshowthesametermmayhavedifferentbut

overlappingmeaningsindifferenttheoriesand(sub-)disciplines.

ExternalRepresentation:Thesystemoftermsistransmittedthroughexternal

representationmostlybymeansofwrittentext,diagrams,andsymbolicformalisms.

Theserepresentationsstabilizethesystemoftermswithinafield,buttensionsmay

occurattheborderlineswherefundamentalchangestaketheirstartwhenthemeaning

oftermshastobere-negotiated.

25Einstein1921.ThetranslationistakenfromEinstein1982,236–237.26SeeBlum,Renn,andSchemmel2016.

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5. Reflectiveabstractionsinthelong-termhistoryof

spatialterms

Inthispaperwehavediscussedtherelationbetweeneverydaylanguageandthe

technicalterminologyintheoreticaltextsrelatedtospatialknowledge.Inthiscontext

weconceivedofeverydaylanguageasexternallyrepresentinganthropomorphicand

instrumentalknowledgestructures,i.e.knowledgestructuresbuiltupinthemindofany

individualintheprocessofontogenesis,whichcompriseuniversalaspectsofsensori-

motorintelligenceaswellasknowledgerelatedtoculture-specificpracticessuchasthe

handlingofinstrumentsandotherculturalartifacts.

Wehavedescribedthespatialterminologythataroseattheoriginoftheoreticalscience

inantiquityasresultingfromaprocessofreflectiveabstraction.Inthiscontext,the

mediumofreflectionislinguisticexpressions,inparticularspatialterminology.In

theoreticaltextsfromantiquity,themeaningsoftermsareexplicitlyreflectedinthe

mediumofwrittenlanguage,bringingforthareconstructionofanthropomorphicand

instrumentalknowledgestructuresonatheoreticallevel.Atthesametime,this

reconstructionmodifiestheseknowledgestructures,sinceitabstractsfromtheconcrete

contextsofactionfromwhichtheyderivetheiroriginalmeaningandre-contextualizes

themwithinanetworkoftheoreticalterms,whichaimsatfulfillingtheoreticaldemands

suchasgeneralityandconsistency.Whileitisthisnetworkthatmakestheterms

theoretical,thenetworkisnotclosedinthesensethatthemeaningoftermswouldbe

sufficientlyfixedwithoutreferencetoknowledgeoutsideit,aswouldbethecaseina

completelyaxiomatizedtheoryofthekindofHilbert’sfoundationsofgeometry.

Thetheoreticalterminologyrelatedtospacethatformedintheemergenceofclassical

mechanicsmayalsobeviewedasresultingfromaprocessofreflectiveabstraction.In

additiontothesemanticrelationsbetweentermsencounteredinMohistscience,

relationsexpressedbymeansofmathematicalformalismsplayacentralroleinthis

context.Thesemathematicalrelationsinparticularservetheintegrationofhuge

corporaofexperientialknowledgeoncelestialandterrestrialmotions,experiential

knowledgethatwasmathematicallyandconceptuallypre-processed,asdocumentedin

earlierwritingslikethoseofKeplerandGalileo.Thereflectiononthemeaningofterms

nowtakesplaceinthemediumofsuchmathematical-conceptualwritings.The

mathematicalrelationsbetweentheoreticaltermsarere-negotiatedastoallowforthe

16

integrationoftheexperientialknowledgetobecaptured.Atthesametime,theterms

inherittheirmeaningsfromtheoreticaltraditions,whicharethemselves,aswehave

seen,rootedinanthropomorphicandinstrumentalknowledge.Theensuingtensions

withinthenetworkoftermswereonlyresolvedcenturiesafterthepioneeringworkof

Newtonandhiscontemporaries.Theresultwasafurtherstepofreflectiveabstraction

separatingtheoreticalknowledgestructuresfromtheknowledgestructuresrepresented

ineverydaylanguage:afurthermodificationofthesestructuresbyrebuildingtheir

relationsinthecontextofamathematical-semanticstructureabletointegratethe

relevant(pre-processed)experientialknowledge.

Intheradicalconceptualtransformationsofearly-twentieth-centuryphysicswecan

identifyyetanotherstepofreflectiveabstraction,removingphysicalspatialterminology

evenfurtherfromitsoriginsineverydaylanguage,without,however,cuttingthe

connection.Thenewreorderingofknowledgethatbringsaboutthechangesinthe

meaningsofterms(andthecreationofnewterms)isagainimposedbyknowledge

integration.Butthistimetheknowledgeunderquestionisknowledgepre-processedin

developedsub-disciplines.Itsintegrationagaindemandsabstraction:aspectsofthe

existingrepresentationsthatdonotcorrespondtostructuresofexperientialknowledge

butarerelicsofthecognitivehistoryoftheoryareupforre-negotiation.Anexampleis

theconstancyoflengths,durationsandsimultaneityundertransformationsbetween

inertialframesinrelativeuniformmotion,whichisassumedwithinclassicalmechanics,

butnotimpliedbytheoperationsofspaceandtimemeasurements.Byabstractingfrom

suchaspects,generalizationsarepossiblethatenabletheintegrationofknowledgefrom

differentdisciplines.Thenewconcretizationisguidedbythepropertiesofborderline

objects,whosetreatmentdemandsknowledgestructuresfrommorethanonediscipline

tobetakenintoaccount.

Fromtheaboveitbecomesclearthathistoricalprocessesofreflectiveabstractionbuild

oneupontheother.Notinalinearorapredeterminedway:theexampleofMohist

scienceanditsfateclearlyshowsthattheoccurrenceofreflectiveabstractionsdoesnot

implytheprogressiontofurtherones.Buttheexternalknowledgerepresentations

resultingfrominstancesofcollectivereflectionserveasthepreconditionsforlater

reflectiveabstractionsthatbuildonthem,sinceeachprocessofreflectiveabstractionis

thetransformativereconstructionofanexistingknowledgestructure.Thereflectionon

disciplinarilystructuredknowledgeatthebeginningofthetwentiethcentury,for

17

instance,wasonlypossibleinthemediumofthemathematical-conceptualstructures

thatoriginatedin,andhaddevelopedsince,earlymoderntimes.Ouremphasisonthe

threeturningpointsinantiquity,earlymoderntimes,andtheearlytwentiethcentury

doesnotmeantodenytheimportanceofthedevelopmentsbetweentheseturning

points,ofcourse.ThemathematizationofAristotelianphilosophyinmedievaltimesand

theformationandadvancementofanalyticalmechanicsinthecourseoftheeighteenth

andnineteenthcenturiesareimportantexamplesforsuchdevelopments.Butthe

turningpointsarecharacterizedbyfundamentalconceptualreorganizationsof

knowledge.Theseprocessesofknowledgereorganizationare,atthesametime,

processesofknowledgeintegration,inwhichexperientialknowledge—beitdifferent

partsofanthropomorphicknowledge,beittheknowledgeofpractitioners,orbeit

knowledgesystematicallyaccumulatedinscientifictraditionsanddisciplines—is

assimilatedtotheoreticalstructures,whilethesestructuresareaccommodatedtothe

newknowledge.Thetheoreticaltermstherebybecomeincreasinglyabstractinthe

sensethattheirmeaningbecomesincreasinglyremovedfromthemeaningoftheterms

ineverydaylanguage.

Willthesuccessionofreflectiveabstractionseventuallyremoveourspatialconceptsso

farfromtheiroriginineverydaylanguagethattheymaybecomeimplicitlydefined

withinanaxiomatictheorysuchasHilbert’sgeometry?WasEinsteinreferringtosucha

developmentwhen(inthelastquotegivenabove)hestatedthatatthepresentstateof

thedevelopmentoftheoreticalphysicswearestillinneedofconceptsestablishinga

relationtoeveryday,practical,oroperativeknowledge?Willtheoreticalphysics

eventuallybecomeindependentfromsuchconcepts?InHilbert’sfoundationof

geometry,themeaningsofthecentraltermsaredecoupledfromallexteriorknowledge

wherebythetheorybecomespurelystructural.Itisnolongeratheoryofphysicalspace,

butonethatmaybeappliedtoit.Fromthisitbecomesclearthataphysicaltheoryof

spacemustalwaysretainarelationtoknowledgeexteriortoitsmathematicalstructure

bytheverydemandthatitbeatheoryofphysicalspace.Ontheotherhand,thereare

indicationsthatinfuturetheoriesofphysics,spacemaynolongerplaythefundamental

roleitstilldoesatthepresent.Theroleofpre-theoreticalknowledgeinconstitutingthe

meaningofthecentraltermsofatheorymaytherebybecomeevenmoremediated.

Physicalspacemay,forinstance,turnouttobeaphenomenonemergingfrommore

fundamentalnon-spatialentities.Themeaningsofthetechnicaltermsbywhichthese

18

entitiesaredescribedwouldthenalsostandinanemergencerelationtothemore

traditionalconceptsandcouldaccordinglyhavelittleornothingincommonwiththe

meaningsofeverydaylanguageterms.

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Max Planck Institute for the History of Science

Preprints since 2014 (a full list can be found at our website)

454 Klaus Geus and Mark Geller (eds.) Esoteric Knowledge in Antiquity (TOPOI - Dahlem Seminar for the History of Ancient Sciences Vol. II) 455 Carola Sachse Grundlagenforschung. Zur Historisierung eines wissenschaftspolitischen Ordnungsprinzips am Beispiel der Max-Planck-Gesellschaft (1945–1970) 456 David E. Rowe and Robert Schulmann General Relativity in the Context of Weimar Culture 457 F. Jamil Ragep From Tūn to Turun: The Twists and Turns of the Ṭūsī-Couple 458 Pietro Daniel Omodeo Efemeridi e critica all’astrologia tra filosofia naturale ed etica: La contesa tra Benedetti e Altavilla nel tardo Rinascimento torinese 459 Simone Mammola Il problema della grandezza della terra e dell’acqua negli scritti di Alessandro Piccolomini, Antonio Berga e G. B. Benedetti e la progressiva dissoluzione della cosmologia delle sfere elementari nel secondo ’500 460 Stefano Bordoni Unexpected Convergence between Science and Philosophy: A debate on determinism in France around 1880 461 Angelo Baracca Subalternity vs. Hegemony – Cuba’s Unique Way of Overcoming Subalternity through the Development of Science 462 Eric Hounshell & Daniel Midena “Historicizing Big Data” Conference, MPIWG, October 31 – November 2, 2013 (Report) 463 Dieter Suisky Emilie Du Châtelet und Leonhard Euler über die Rolle von Hypothesen. Zur nach-Newtonschen Entwicklung der Methodologie 464 Irina Tupikova Ptolemy’s Circumference of the Earth (TOPOI - Towards a Historical Epistemology of Space) 465 Irina Tupikova, Matthias Schemmel, Klaus Geus Travelling along the Silk Road: A new interpretation of Ptolemy’s coordinates 466 Fernando Vidal and Nélia Dias The Endangerment Sensibility 467 Carl H. Meyer & Günter Schwarz The Theory of Nuclear Explosives That Heisenberg Did not Present to the German Military 468 William G. Boltz and Matthias Schemmel Theoretical Reflections on Elementary Actions and Instrumental Practices: The Example of the Mohist Canon (TOPOI - Towards a Historical Epistemology of Space) 469 Dominic Olariu The Misfortune of Philippus de Lignamine’s Herbal or New Research Perspectives in Herbal Illustrations From an Iconological Point of View 470 Fidel Castro Díaz-Balart On the Development of Nuclear Physics in Cuba 471 Manfred D. Laubichler and Jürgen Renn Extended Evolution 472 John R. R. Christie Chemistry through the ‘Two Revolutions’: Chemical Glasgow and its Chemical Entrepreneurs, 1760-1860 473 Christoph Lehner, Helge Wendt Mechanik in der Querelle des Anciens et des Modernes 474 N. Bulatovic, B. Saquet, M. Schlender, D. Wintergrün, F. Sander Digital Scrapbook – can we enable interlinked and recursive knowledge equilibrium? 475 Dirk Wintergrün, Jürgen Renn, Roberto Lalli, Manfred Laubichler, Matteo Valleriani Netzwerke als Wissensspeicher 476 Wolfgang Lefèvre „Das Ende der Naturgeschichte“ neu verhandelt 477 Martin Fechner Kommunikation von Wissenschaft in der Neuzeit: Vom Labor in die Öffentlichkeit 478 Alexander Blum, Jürgen Renn, Matthias Schemmel Experience and Representation in Modern Physics: The Reshaping of Space (TOPOI - Towards a Historical Epistemology of Space) 479 Carola Sachse Die Max-Planck-Gesellschaft und die Pugwash Conferences on Science and World Affairs (1955–1984) 480 Yvonne Fourès-Bruhat Existence theorem for certain systems of nonlinear partial differential equations 481 Thomas Morel, Giuditta Parolini, Cesare Pastorino (eds.) The Making of Useful Knowledge

482 Wolfgang Gebhardt Erich Kretschmann. The Life of a Theoretical Physicist in Difficult Times 483 Elena Serrano Spreading the Revolution: Guyton’s Fumigating Machine in Spain. Politics, Technology, and Material Culture (1796–1808) 484 Jenny Bangham, Judith Kaplan (eds.) Invisibility and Labour in the Human Sciences 485 Dieter Hoffman, Ingo Peschel (eds.) Man möchte ja zu seinem Fach etwas beitragen 486 Elisabeth Hsu, Chee Han Lim Enskilment into the Environment: the Yijin jing Worlds of Jin and Qi 487 Jens Høyrup Archimedes: Knowledge and Lore from Latin Antiquity to the Outgoing European Renaissance 488 Jens Høyrup Otto Neugebauer and the Exploration of Ancient Near Eastern Mathematics 489 Matteo Valleriani, Yifat-Sara Pearl, Liron Ben Arzi (eds.) Images Don’t Lie(?) 490 Frank W. Stahnisch (ed.) Émigré Psychiatrists, Psychologists, and Cognitive Scientists in North America since the Second World War 491 María Sánchez Colina, Angelo Baracca, Carlos Cabal Mirabal, Arbelio Pentón Madrigal, Jürgen Renn, Helge Wendt (eds.) Historia de la física en Cuba (siglo XX) 492 Matthias Schemmel Everyday Language and Technical Terminology: Reflective Abstractions in the Long-term History of Spatial Terms