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title: Formal, Transcendental, and Dialectical Thinking : Logic and Reality SUNY Series in Philosophy author: Harris, Errol E. publisher: State University of New York Press isbn10 | asin: 0887064299 print isbn13: 9780887064296 ebook isbn13: 9780585068329 language: English subject Logic, Dialectic. publication date: 1987 lcc: BC71.H24 1987eb ddc: 160 subject: Logic, Dialectic.

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My aim has been to reassess the importance of logic and its place in philosophical as well as other forms of thinking, and to consider the question whether the presuppositions of contemporary science may not demand something beyond the current style of mathematical logic to express the principles of structure of scientific thinking. To do this, I have had to present the reader first with an analysis of the presuppositions of formal logic, and a discussion of their adequacy to twentieth century scientific discoveries; then with the alternative possibilities.http://en.wikipedia.org/wiki/Errol_Harris

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  • title: Formal,Transcendental,andDialecticalThinking:LogicandRealitySUNYSeriesinPhilosophyauthor: Harris,ErrolE.

    publisher: StateUniversityofNewYorkPressisbn10|asin: 0887064299printisbn13: 9780887064296

    ebookisbn13: 9780585068329language: Englishsubject Logic,Dialectic.

    publicationdate: 1987lcc: BC71.H241987ebddc: 160

    subject: Logic,Dialectic.

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    Formal,Transcendental,andDialecticalThinking

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    SUNYSeriesinPhilosophy

    RobertCummingsNeville,Editor

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    Formal,Transcendental,AndDialecticalThinkingLogicandReality

    ErrolE.Harris

    StateUniversityofNewYorkPress

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    PublishedbyStateUniversityofNewYorkPress,Albany

    1987StateUniversityofNewYork

    Allrightsreserved

    PrintedintheUnitedStatesofAmerica

    Nopartofthisbookmaybeusedorreproducedinanymannerwhatsoeverwithoutwrittenpermissionexceptinthecaseofbriefquotationsembodiedincriticalarticlesandreviews.

    Forinformation,addressStateUniversityofNewYorkPress,StateUniversityPlaza,Albany,N.Y.,12246

    LibraryofCongressCataloginginPublicationData

    Harris,ErrolE.Formal,transcendental,anddialecticalthinking.(SUNYseriesinphilosophy)Includesindex.1.Logic.2.Dialectic.I.Title.II.Series.BC71.H24198716086-14463ISBN0-88706-429-9ISBN0-88706-430-2(pbk.)

    10987654321

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    CONTENTSPreface ix

    Introduction:ContemporaryProblems 1

    IsLogicRelevant? 1

    ThePredicamentofModernMan 3

    ScienceasObjectiveKnowledge 6

    Bankruptcyof"theScientificOutlook" 11

    TheWhirligigofTime 13

    PartIFormalLogic

    Chapter1ThePresuppositionsofFormalLogic 23

    LogicandMetaphysics 23

    Frege'sGrundlagenderArithmatik 25

    TheThesisofthisChapter 31

    Commutation,AssociationandDistribution 32

    Implication 33

    Chapter2FormalLogicandScientificMethod 49

    EmpiricismandInduction 49

    Physicsand"theInterrelatednessofThings" 58

    TheMethodologyofScience 62

    Perception 65

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    PartIITranscendentalLogic

    Chapter3KantandFichte 75

    SynthesisandTranscendentalSubjectivity 75

    Coherence 81

    TheEmergenceofDialectic 82

    Chapter4Husserl'sTranscendentalLogic 89

    Psychologismvs.Formalism 89

    InadequaciesofFormalLogic 92

    TheTaskofTranscendentalLogic 97

    UndevelopedImplications 100

    Chapter5DialecticalTranscendentalism 105

    AReformulationofTranscendentalPhilosophy 105

    DialecticalParallel 110

    Chapter6TranscendentalIdealism 113

    TheProblemofSelf-constitution 113

    MeritsandDemeritsofTranscendentalism 117

    Chapter7"Independent"and"Nonindependent"Objects 121

    WholesandParts 121

    UnresolvedProblems 124

    PartIIIDialectic

    Chapter8TheLogicofSystem 131

    Relations,ExternalandInternal 131

    OverlapofTerms 135

    OrganizationandSystem 140

    TheSelf-differentiationofSystem 144

    SummaryandExemplification 149

  • Chapter9NegationandtheLawsofThought 157

    IdentityandDifference 157

    DialecticandtheLawofContradiction 163

    CriticismsandMisconceptions 165

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    Chapter10CategoriesofPerception 171

    TheFormoftheFacts 171

    BeingandBecoming 173

    Quantity,Number,andFormalLogic 182

    Chapter11CategoriesofReflection 189

    CommonSense 189

    CommonSenseandNewtonianScience 190

    ContemporaryScience 193

    Chapter12CategoriesofSystematicThinking 199

    TheConcept,TheoreticalandObjective 199

    ConceptualMoments 200

    ScientificJudgement 202

    ScientificInference 206

    (1)Deduction 209

    (2)Induction 215

    ScientificAdvance 221

    Chapter13Objectivity 227

    ThreeWorldViews 227

    RelationofSubjectivetoObjective 233

    TheoryandPractice 236

    IdentityofSubjectivityandObjectivity 237

    Chapter14Value 243

    DialecticalGenerationofValue 243

    Desire,Purpose,andObjectiveStandards 244

    DialecticandWorldProblems 249

    ManandNature 250

  • ResidualQuestions 257

    (1)Thefreedomandindividualityofman 258

    (2)Theultimatecharacteroftheuniversalwhole 261

    (3)Man'srelationtouniversalnature 262

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    PREFACE"Theconclusionisthatlogic,conceivedasanadequateanalysisoftheadvanceofthought,isafake.Itisasuperbinstrument,butitrequiresabackgroundofcommonsense...

    "Mypointisthatthefinaloutlookofphilosophicthoughtcannotbebasedupontheexactstatementswhichformthebasisofthespecialsciences.

    "Theexactnessisafake."

    AlfredNorthWhitehead

    Withcloseapproximation,theabovestatementexpressesthemainthesisofthisbook.Iarguethatformalprecisionisaspecificlevelofthinking,howeversophisticated,whichisausefulinstrumentformanypurposes,butwhichislimitedinitsapplicability,eveninscience.Thereisamoreconcreteformofthought,moreuniversalinitsscope,ofwhichinsufficientheedhasbeentaken,whoseprinciplesneedfurtherdevelopmentandmeritcloserreflection.

    Whatisreveredas"thescientificoutlook"hasbeen,andstillis,toooftenconfusedwiththeexactitudewhichWhitehead,intheabovequotation,repudiatesWhitehead,whoincollaborationwithBertrandRussell,wrotethegreatesttreatiseonformallogicofthepresentcentury.BymanyphilosophersitisalsoconfusedwithphilosophicalEmpiricism.Butthescientificoutlookofcontemporarysciencehaschangedinmanywaysfromwhatitwasintheseventeenthcentury,andthetypeoflogicappropriatetotheworld-viewoftheRenaissancerequiresatleastconsiderablesupplementationifitistobeadequatetothescienceoftodayandtotheproblemsfacingmoderncivilization.

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    IntheIntroductionwhichfollowsIhavecriticizedthisoutdatedandnowobsolete"scientificoutlook";andinsodoingIhavespokenofscienceinwhatsomemayconsidertooharshatone.Buttheymaybereassuredthatitisnotscience,assuch,whichisherebeingcastigated,butonlyaprescribedandlimitedtheoreticalattitude,whichhasrunitselfintoaculdesac,fromwhichitcanfindnooutlet,andfromwhichtheescapeisindicatedinthelaterchaptersofthebook,wherescienceonceagaincomesintoitsown.

    Myaimhasbeentoreassesstheimportanceoflogicanditsplaceinphilosophicalaswellasotherformsofthinking,andtoconsiderthequestionwhetherthepresuppositionsofcontemporarysciencemaynotdemandsomethingbeyondthecurrentstyleofmathematicallogictoexpresstheprinciplesofstructureofscientificthinking.Todothis,Ihavehadtopresentthereaderfirstwithananalysisofthepresuppositionsofformallogic,andadiscussionoftheiradequacytotwentiethcenturyscientificdiscoveries;thenwiththealternativepossibilities.ThefirstoftheseisTranscendentalLogic,whichisneitherveryfamiliarnorverymuchdiscussedamongcontemporaryphilosophers,soIhavepresumedthatmanyreaderswouldbegratefulforacertainamountofintroductoryexplanation,bothofitstechnicaltermsandofitsbasicdoctrines.Thisitseemedbesttodobydirectreferencetothemajorworksoftheauthorswhooriginallyexpoundedit(involvingsomebriefattentiontoitshistory).Chapters4and5may,inconsequence,seemtoholduptheargument;butifthereaderwillbepatient(forneitherchapterisverylong),heorshewillfindthatthethreadistakenupagaininwhatfollowsinsuchawayastomakecleartherelevanceofwhathasgonebefore.

    Havingsetthisprecedent,itmayseemsomewhatinconsistentnottohavedealtwithDialecticalLogicinthesamefashion;but,althoughPartIIIisunashamedlyHegelian,IhavenotpresenteditintheformofacommentaryonHegel'slogic.OnegoodreasonisthatIhavedonethatatlengthelsewhere.AnotheristhatIwishedtosetoutthefundamentalpresuppositionsofthistypeoflogic,asIhaddoneoftheprevioustwo,andsohaveofferedwhatisineffectapropaedeutictoHegel,followedbyanapplicationofthelogico-epistemologicalprinciplessetouttoscientificmethodandrecentscientifictheory.TheconcludingchaptersreturntotheissuesraisedintheIntroduction,

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    forminginpartacompletionofthedialecticalsystem,andinpartanillustrativedevelopmentofitsconsequences.

    If,inthenotes,Ihavemadewhatsomemayconsidertoomanyreferencestomyownwritings,ithasbeenonlytosparethereaderthetediumofrepetition,sothatIshouldnotneedtosayoveragainwhatIhadarguedatmorelengthelsewhere.Thosewhohavereadtheearlierworksneedonlyignoretherelatednotes,whilethosewhohavenotmaywishtolookthemupinordertosupplementwhatisarguedinthepresenttext.

    Onecritic,whoreadthebookintypescript,hasurgedmetodrawattentionfurthertowriterslikeBrandBlanshardandNicholasRescher,whoseworks(asheputit)lendsupporttomyoverallposition.Ihaveacknowledgedinformerwritings(e.g.,HypothesisandPerception)mydeepdebttoProfessorBlanshardandmybroadagreementwithhisviews.ButinrecentyearsIhavebeenengagedindebatewithhimoveratleastonecrucialmattergermanetotheargumentofthepresentwork(seeIdealisticStudies,vols.IX,2;X,2;andXII,3),andIhesitatetoappealtohimasasupporterwithoutreservationswhenIamunsureofhisunqualifiedapproval.AndIcanhardlyciteProfessorRescherasonewho''lendssupporttothisoverallposition,"becausehisintriguingandingeniousversionofthecoherencetheoryoftruth,nodoubthighlyusefulheruisticallyinmanyfields,isexpounded,asheputsit,"inamannerconsonantwithmodernstandardsofrigourandprecision."Hesaysitaimsatbeing"exactandformalized,"andheusesthroughoutthetechniquesofthecurrentsymboliclogic.1Now,inwhatfollows,Iarguethatthetacitbutinevitablepresuppositionsofthislogic,andofitscharacteristicformalization,arealtogetherincompatiblewiththekindofcoherencetheorythatIespouse,soIcanhardlyclaimsupportfromProfessorRescher.Alsoheexplicitlyallows,asthedefinitionoftruth,correspondencewithwhat"isactuallythecase"inasensewhichIcannot,andheadmitsbyimplicationseverallogicalandepistemologicalthesesthatIamcompelledbythethrustofmyargumenttoreject.ToembarkhereonanextendedcritiqueofRescher'stheorywouldbeoutofplace,andtohavedonesointhebodyofthetextwouldhavebeenanunwarranteddigression.

    Mysinceregratitudeisdue,andfreelygiven,toDr.Willem

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    Klever,oftheErasmusUniversityinRotterdam,whoreadanearlierdraftofthisbookandmadesympatheticandhelpfulsuggestionsforimprovement;alsototheInstituteforAdvancedStudiesintheHumanities,oftheUniversityofEdinburgh,forthehospitalityandfacilitiesitgrantedme,asaResearchFellow,atthetimewhenIwasdoingtheworkofwhichthisbookisthefruit.IhavetothanktheEditoroftheInternationalPhilosophicalQuarterlyforpermissiontoreproduceinmodifiedform,aspartoftheIntroduction,andofChapters13and14,materialwhichhasappearedinarticlespublishedinVols.XVandXIXofthatjournal.

    E.E.H.HIGHWRAYJUNE30,1986

    1.Cf.TheCoherenceTheoryofTruth,Oxford,attheClarendonPress,1973.

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    INTRODUCTIONIIsLogic"Relevant"?

    Logicispopularlythoughtofasaverydryandabstractdisciplinequitedevoidofpracticalrelevance.Indeed,contemporarylogicianshaveassertedthatalllogicaltruthsareanalyticandtautological,sothattheycannevergiveusnewknowledge,eventhoughtheymayservetoderivehithertounnoticedconsequencesfromwhatisalreadyknown.Butthisviewoflogicisamisconception.Afterall,itisadmittedonallhandsthatlogicisthesciencethatsetsoutanddevelopstheprinciplesfundamentaltothemethodofeveryscienceandidentifiesthenormsthatjustifytheclaimofanydisciplinetobeascienceatall.Andnobodynowadaysislikelytodenythatscienceisofpracticalimportance.Ifso,surelylogic,atleastindirectly,musthaverelevancetotheinterestsofpracticalliving.

    Moreover,thesignificanceandachievementofanyphilosophyiscloselyboundupwiththetheoryoflogicthatitespousesanduponitwilldependwhateffect,ifany,thephilosophywillhaveonpracticalaffairs.Philosophy,priortothelasthalf-century,wasgenerallycreditedwithgreatpracticalinfluence,especiallyinthespheresofmoralsandpolitics;butmorerecentlysuchphilosophyhasbeenrankedasideologyandhasbeen,forthemostpart,frowneduponinprofessionalacademiccircles.Thatagainhasbeenbecausephilosophershaveassumedwhattheyregardasascientificattitude,consideringscienceasproperlyobjectiveknowledgedisinterestedlyconcernedwithfactsandeschewingeveryprejudiceorevaluation.Values,onceheldtobetheprovinceofthephilosopher,arenowassignedtothepsychologist,whoishimselfascientistandtreatsthemsimplyasfacts,asthedeterminantsofbehaviour.Hedoesnotandwillnotclaimtopronouncenormativemaxims.Theideologiesrejectedbythephilosopherthus

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    becomegristtothepsychologist'smillandformatleastpartofthesubject-matteralsoofthesocialsciences.

    Whatthenisleftforthephilosopher?Itwouldbeanimpertinenceforhimtoencroachuponthefieldsofthespecialsciences,whethernaturalorsocial;buttheprinciplesonwhichtheirreasoningisbased,thosewhichdeterminethevalidityoftheirarguments,theruleswhichgoverntheirprocedureandthearchitectonicoftheirsystemsarematterswhichscientiststhemselvesdonotusuallyinvestigate,takingthemsimplyforgranted.Theseformtheprovinceofthelogicianandarefairgameforthephilosopher.Consequently,inrecenttimes,philosophyhascometobeidentifiedalmost,ifnotquite,whollywithlogic.

    Thisretreatofphilosophymoreorlessintothebackgroundhasleftthenaturalsciencesasthemostpervasiveintellectualinfluencesinourcivilization,whichisdominatedbytheirtheoriesandpermeatedbyscientifictechnologyineveryphaseofitsactivity.Initiallythisseemedalltothegoodandtheadvanceofsciencewashailedasbeneficentprogress.Latterly,however,scientifictechnology,thoughitseemedatonetimetopromisethesolutionofallproblemsandthecureforallills,hasprovedtobethesourceandrootcauseofthemostmenacingproblemsofall;problems,moreover,that,whileinseparablefromtheveryprogressofourcivilization,threatenitscontinuedexistence,yettowhichthatprogressseemstooffernoprospectofsolution.

    Iflogic,asseemsclear,hassomebearingonthemethodofscience,itshouldalsohavesomerelevance,evenifindirect,tothesevitalissues.Butinfactitisnotquitesoindirectasmayappearatfirstsight,becausethepracticalproblemsturnouttobenotpurelyscientificandtheaboveconceptionofscienceproves,underscutiny,torestonshakypresuppositions,sothatourconceptionsoflogicandphilosophymaywellrequirerevisionandtheirimportanceforpracticallivingmayprovetobefundamental.

    Toconvincethereaderofthis,Iproposetobegininthisintroductionbydiscussingatsomelengthmatterswhichmightnotseemgermanetothesubjectannouncedinthetitleofthisbook,but,aswilllaterappear,aretheultimategoalofitsargument.Formymainthesisisthatlogic,properlyconceived,isinseparablefromthestructureoftheactualworld,aswellasfromourunderstandingofit.Itmusttherefore,bedirectlyandintimatelyrelevanttothesolutionofpracticalproblems.

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    IIThePredicamentofModemMan

    Europeancivilizationhasnotalwaysbeenscientific,althoughearlyinitshistorythespiritofsciencewasbornamongtheGreeks;butinourowndayscienceanditsproductsaccompanyallouractivitiesandpermeateourwayoflife.Further,whatwasonceknownasWesterncivilizationhas,inthetwentiethcentury,becomepervasivethroughouttheworld.Itisthecivilizationofthescientificoutlook,fromtheeffectsofwhichnoteventheremotestcornersoftheeartharetodaywhollyimmune.ScienceandtechnologyarenolongerthemonopolyoftheWest.TheyflourishequallyinIndia,China,andJapan,andtheyaffectthelifestyleofallthepeoplesoftheworld.Infact,thepracticeofmankindtodayisdirectedbytheadvanceofscience,andlifeisdominatedbythemachine.Thosewhostillbelieveinandvaluespiritualendswillseethisasacauseforsorrowanddismay;butthosewho,borneontheresistlesstideofscientificprogress,havecometoregardthehumanminditselfasamachineandthebeliefinthespiritasjustoneofthemachine'saberrations,may(ifthewordisstillappropriate)thinkitoffersanattractiveprospect.Theymightadoptthisviewwereitnot,indeed,thattechnologicaladvancehasbroughtuponmankindasituationinwhichtheverycivilizationwhichhasnurturedscience,andthesocialstructureuponwhichitrestsandfromwhichitderives,isthreatenedwithextinction.

    Inanoverpopulatedworld,scientificmethodsofproductionexhausttheworld'sresources,betheyofenergyorofnutriment.Industrialwastepollutestheatmosphereandthehydrosphere,producingacidrainwhichpoisonstheearth,itslakes,anditsrivers.Otherlivingspecies,onwhichthehumandependsforfood,arebeingdecimated,andthewholeecologyoftheearthisbeingdisrupted.Destructionofthetropicalforestswithcontemporarymachinesonascalehithertoimpracticablethreatenstoupsetclimaticequilibria,aswellastodeprivetheatmosphereofitschiefsourceofoxygen.Oilspillage,unprecedentedintheearth'shistory,pollutestheseas,destroyingmarinelife,bothbirdandfish,andsettlinguponthebreedinggroundsoftheplanktonwhichisitsmainfoodsupply.Thecontinuedadvanceofscienceseemsonlytoincreaseandcomplicatethesetroubles,and,apartfromcreatingnewproblems,hasasyetofferedlittlebywayofmitigation.

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    Asifthiswerenotenough,sciencehasgivenusatomicenergy,theproductionofwhichisaccompaniedbyappallingdangers:thepossibleoverheatingandmeltdownofatomiccores,threateningexplosionsofstupendousdestructiveforce;theescapeofdeadlyradioactivegasesandtheseepageofharmfulradioactiveliquids;theaccumulationofatomicwastesremainingradioactivelylethalforhundreds-eventhousands-ofyears,thesafestorageofwhichscientistshavenotyetdevised,andwhich,whendiscovered,nationaleconomiesmaywellnotbeabletoafford.Andthesearetheby-productsofgeneratingatomicenergyonlyforpeacefulanddomesticpurposes.Itsmainpurpose,however,atthepresenttime,istheproliferationofatomicweapons,theuseofwhichinamajorconflictwouldundoubtedlywipeoutallcivilization,alltechnology,andallscience.

    Hereagain,theveryfabric.ofourcivilization,itspoliticalform,threatensitssurvival.Sciencehasflourishedandcouldonlydosoinasocietyorganizedtosupplymaterialneedsoflifeandgovernedsoastomaintainsocialorder.Suchgovernmentisnecessarilyembodiedinapoliticalstructure,andthatentailslegislationandtheenforcementoflaw.Thisisthefunctionofthestate,whichcanoperateonlyifitwieldssupremelegalauthorityandpowerinthecommunity.Moderncivilizationisorganizedinnation-states,eachsovereignandindependent,andsovereigntyis,byitsverynatureanddefinition,legallysupreme,sothatinpracticeitcannotbesubjecttoanyhigherlaw.Themutualdealingsofsovereignstates,therefore,cannotbeeffectivelyregulated.Whatparadesasinternationallaw,byitsownprinciplesrecognizesandpurportstomaintaintherightsofindependentnationalsovereignty.Insodoingitdisqualifiesitselffrompoliticalenforcement.Noauthorityexists,orcouldexistwithoutextinguishingnationalsovereignindependence,toenforceinternationallaw.TheUnitedNations,committedbyitsChartertorespectandmaintainnationalsovereigntyissimilarlydisqualified.Itfollowsthatinternationalrelationsarelegallyunregulable.

    Inconsequence,thereisnowayofensuringthattreatieswillbekeptanditmustbenotedthatinternationallawitselfhasonlytreatystatus.Theonlysecurityagainstexternalaggressionanddominationavailabletoanynation,therefore,liesinitsownanditsallies'power.Itiscompelledtodependforitsownsafetyonitsownmeansofdefence,bolsteredwhenpossiblebyalliances.Yetagainitmustberememberedthatalliancesdependupontreaties,whichmay,inthefinalissue,notbeobserved.Allinternationalpolitics,therefore,isinevitablypower

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    politics,anditsaimisalwaystomaintainabalanceofpowerinthenationalinterest.Theunavoidableresultisanarmsrace,whichnothingcancurbbecauseanyadvanceoneithersidemustalwaysbematchedontheother.Itcannotbecurbedbecausearmslimitationcanbesecuredonlybytreaty,andthereisnomeansofensuringtheobservanceoftreatiesapartfromthethreatofmilitaryretaliationfortheirbreach.Disarmamenttreatiesthusbecomeself-defeating,becausetheycommitthepartiestodivestthemselvesoftheonlymeanstoensuretheirobservance.

    Amountingarmsraceisthusunavoidableandincurable.Thiswasbadenoughinearliertimes,buttodayithasbecomeintolerableandthreatenstobefinallyfatal,becausesciencehasputintoourhandsnuclearweapons,alreadystock-piledtoanextentsufficienttodestroytheworld'spopulationseveraltimesover.

    Politiciansnevertireofassuringusthatwhatpreventsandhasforfortyyearspreventedtheoutbreakofnuclearwaristhepolicyofdeterrence.Thepossiblityof"mutuallyassureddestruction"(appropriatelyacronymizedasMAD)restrainseithersidefromusingnuclearweapons.Butinthestrategicalthinkingofthemilitary,thisdoctrinehasalreadybeenabandoned.Strategiesofso-calledlimitednuclearwararenowbeingdevised,ontheassumptionsthatsuchawarcanbewonandthatitsvictorcansurviveasanorderedandcivilizedsociety.Thattheassumptionsarepalpablyfalse,however,mustbeseenbyanyintelligentpersonwhocarefullyconsidersthescientificevidence.1Butiftheseassumptionsweretrue,astheycontradictthosesupportingthedoctrineofdeterrence,theywouldremovetheallegedsafeguardagainstnuclearannihilation.Moreover,nonuclearwar,oncestarted,couldbelimited,forneithersidecouldrelyontheothertoobserveanypresumedlimit.Norisdeterrenceavalidconcept.Itdependsonthebalanceofpower,andtherecordofhistoryshowsthatthebalanceofpowerisalwaysunstable.Atanytime,achangeofgovernment,orideology,oralliance,byanypower,mayalterthearrayofopposingforcestogiveonesidetheadvantage.Thatwouldimmediatelyremovethedeterrent.

    Tohavemaintainedthebalanceformorethanthirty-fiveyearsisnoextraordinaryprecedent.TherewerenomajorwarsinEuropebetween1815and1914,andminorwarshavebeenmorenumerousandmoreominoussnce1946thanwerethoseofthenineteenthcentury.anyoneofthemcouldhaveescalatedtobecomeaworld-wideconflict.Evennow,thoseinprogressmightgetoutofhandandembroilthe

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    superpowers.Theverynatureofpowerpoliticsgeneratesinternationalcrises,andnonationhasareliablemeansofensuringthattheycanbecontained.Inshort,asinternationalpoliticsareconductedtoday,nothinglessthanaradicalchangeofthinkingandpoliticalpracticeislikelytosavemankindfromtheinevitablenuclearholocausttowardwhich,liketheGedareneswine,thenationsoftheworldunheedinglyplungeforward.2Theseverityofthispoliticalcrisisisasmuchduetoscientificadvanceasanyother,forthenatureofinternationalpowerpoliticshasnotchangedsincetheeighteenthcentury,onlythedestructivepowerandthesophisticationoftheweaponsatthedisposalofsovereignnations.Butitisnottosciencethatwecanlookforanymitigationofthethreatoranysolutionoftheproblems.

    ThattherearesolutionsIamconvinced,foritisbynomeansimpossibleforustoextricateourselvesfromourpresentdesperatepredicament,althoughitcannotbebycontinuingtorelyonscience.Itwillrequirefirstadeepinvestigationintothecausesofthecrisisandthesourcesoftheimpasseinwhichwehavebecomeimmured.Thisagainwilldemandexaminationandrethinkingofthefundamentalpresuppositionsofourculture.Itisthescientificoutlookinparticularthatneedstobescrutinizedafresh,forbythatourcivilizationhasbecomesaturated,asitisdominatedinitspracticebywhatsciencehasproduced.Clearly,thistaskcannotsuitablybeundertakenbyscientists,unlesstheycanstepbackfromtheirpracticetouncoverandexamineitspresuppositionsinacritiquewhichwouldproperlybephilosophical.Thetaskis,infact,thatofphilosophy,butcontemporaryphilosophy,byadoptinghatittakestobeascientificattitude,haslargelydisqualifieditselffromundertakingthisservice.Myaiminwhatfollowswillbetodiscoverhowandwhythishascomeaboutandtosuggesthowitmightberemedied.Onemaycallthisattemptthepropaedeutictothesolutionofthecontemporarypredicament.

    IIIScienceasObjectiveKnowledge

    Tosaythatknowledgeandtrutharenecessarilyconnectedisitselfatruism.Ifabelieforopinionisfalse,itcannotbeknowledge.Ofwhateverweclaimtoknowwemustbeassured,andifourassuranceis

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    notfullyjustifiedtheclaimwillbedenied.Further,itwouldbemeaninglesstosaythatabelieforopinionwastrueifitwereamereconcoctionofthebelievingsubjectwithoutanyreferencetoanindependentlyrealworld.Tobeknown,knowledgemustindeedbesubjectivelyentertained,buttobeknowledge,itmusthavesomeobjectivereference,itmustbetrueofsomeindependentrealitywhichisthesameforallknowersandthereforeuniversalinitsvalidity.

    Devotiontotheobjectivityoftrueknowledgeis,andhasbeensincethesixthcenturyB.C.,thecharacteristicmarkofWesterncivilization.Forthisreason,ourcultureisuniversallyacclaimedas"scientific,"andtheformofitspraxishasbecomedistinctivelytechnological;forscienceisthecommonlyapprovedformofobjectiveknowing,scientificresearchtheonerecognizedformandmethodofdiscoveringthenatureoftheindependentlyexistingworld,andthepracticalapplicationofwhatsciencehasfoundthemosteffectivewayofcontrollingnatureandofharnessingitsforcesintheserviceofhumanaims.

    Thisviewofscienceandknowledgewouldnot,untilveryrecently,havebeenseriouslyquestionedbymany,andeventodayitwouldbemerelyperversetodeny,ashistoricalfact,thisgeneralcharacterizationofourWesterncivilization.Butthehumansituationthathasresultedfromthisveryprevalenceofscientismhas,inrecentdecades,raiseddoubtsinsomemindsaboutthevalidityofthepresuppositionsofthescientificattitude;andtheoutcomeofscientificthinkingitselfwarrants,andisproducing,amodificationofoutlook,asyetnomorethangerminal,whichshouldtransformourwholeapproachtoobjectivity.

    Toseehowthisisso,letusfirstbrieflyrecallthehistoricaloriginofobjectivismandexaminesomeofitsmajorconsequences.TheideaofuniversalobjectiveknowledgegoesbackatleasttoPlato,forwhomtheknowableesentiallyandexclusivelywaswhatwascompletelytranslucenttotheintellect,absolutelyprecise,andfinallyevidenttothought:theultimatelyintelligible.Theonedisciplinewhichcould,inpractice,approachthisidealwasmathematics(foritremainedproblematicaljustwhatPlato'sdialectic,forhimthesupremescience,reallywas).Mathematics,therefore,remainedthemodelforallreliableandself-justifyingknowledgeuntilwellintotheseventeenthcentury.Accordingly,theseventeenthcenturyarchitectsofthemodernscientificrevolutionsegregatedallmathematizableelementsofourexperienceandallowednothingelsetorankasscientificallyknowable.These

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    elementsincludethespatiotemporalandthenumerable,whatevercouldbemeasuredandsubjectedtoalgebraicalcalculation.Thus,therealandobjectivebecameconfinedtotheso-calledprimaryqualitiesofthings,theirspatialandmechanicalproperties.Everythingelsewasrelegatedtothemerelysubjective.Allsecondaryqualities,suchascolour,sound,andthelikethepurelysensiblewereclassedasmind-dependentandthereforemerelyapparent.

    Thescientificallyknowableworldwasthusconceivedasanextendedaggregationofmaterial(ormass-)pointswhichmovedinthespatialfieldinaccordancewithfixedlaws.Theirmovementwasdeterminedbyforcesdependentsolelyupontheirpositionandmass.Theobjectiveworldwasthusavastmachinewithextended,measurable,kinematic,anddynamicproperties,altogetherforeigntoandexclusiveofconsciousnessandfeeling,oranyothertypicalpropertyofmind.Values,therefore,whichdependupondesire,purpose,andconsciousestimation,wouldbeseenasbelongingexclusivelytothesubjectivemindandwerenottobefoundintheobjectiveworld.

    Thismaterial,mechanicalworld,however,wastheobjectparexcellenceofscientificknowledgeandsowasconceivedaspresentedtothemindindependentlyofitsownactivity.Yetthemindhadsomehowtobecomeapprisedofitsexternalpresenceandofitsnature.Beingthusmutuallyexclusive,theextendedworldandtheconsciousmindwererelatedtoeachotheronlyexternally.Themethodbywhichthemindwasallegedtobecomeawareofthepresenceandcharacterofexternalnature,therefore,wasconceivedasthetransmission,insomewayneverfullyexplained,ofrepresentative"ideas"fromexternalbodiesthroughthesenses.Thesimplestandmostprimitiveformoftheseideasweretakentobesensations,andthesenseswereregardedastheprimarychannelofcommunicationbetweenthematerialworldandtheknowingmindofthescientist.Theobjectivityofscience,therefore,dependednotonlyonitsmathematicalreasoning,whichaspurelyformalandalgorithmichadnofactualsignificance,butalsouponitsreferencetoempiricallyperceiveddataintermsofwhichthealgorithmwasinterpreted.

    Thetwinpillarsofobjectiveknowledge,accordingly,cametoberecognizedasmathematicaldeductivereasoningandinductivegeneralizationfromdirectobservation.Restinguponthesetwosupportsanedificeofvalue-freescientificknowledgewasbuilt,progressivelyaugmentedbysuccessivediscoveriesofaworlddevoidofanytraceoffinalcausationoranyvestigeofconsciousness,noteventhatofthescientisthimself.

  • Page9

    Empiricistphilosophy,whicharoseintheseventeenthcenturyco-temporaneouslywithmodernscience,wasitsnaturalcounterpart.Allknowledge,onthisview,originatesfromsense-observationwhichistocountasthebasiccriterionoftruthandthewarrantoffactualrealiability,evenmathematicalknowledgebeinganabstractionfromwhatoriginallycomesthroughsense.Initsepistemologyafirmdistinctionissetbetweenmattersoffact(discoveredbyobservation)andmattersintuitivelyknownthrough''comparisonofideas,"definingstrictlythelimitbetweeninductiveanddeductivelogic.Anequallyfirmseparationismadebetweentheseformsof"rational"knowledgeandthefeelingsandsentimentsbywhichmen'sevaluationsandmoraljudgementsaredetermined.

    Empiricism,whiletypicaloftheseventeenthandeighteenthcenturies,haspersistedtoourowndayandhas,infact,beenstrongerthaneverinthemid-twentieth.Today,itshowssignsinmanyrespectsofdecline,buttheonebranchwhichcontinuestoflourishvirtuallyunchallengedisitsdevelopmentofthetraditionalformallogicintocontemporarysymboliclogic,asabranch,orratherastheveryfoundation,ofmathematicstheage-oldparadigmofrigourandintuitivecertaintyanidealofperfection,however,purchasedinourowndayatthecostofpureabstractionandanalyticity,whichdisqualifiesbothmathematicsandlogicfromprovidinganyfactualknowledge,anddeprivesreasonofallbutapurelyinstrumentalrole.Modernlogiciscommonlydescribedbyitsexponentsasa"powerfultool,"butwhateveritspower,itsfunctiondoesnotincludethediscoveryofnewfactsortheprescriptionofpracticalobjectives.

    Sorapidweretheachievementsofthenewscienceandsocompellingintheirtriumphantsuccesswereitsmethodsthattheareasoriginallyexcludedbecameprogressivelydrawnintotheirsphereofoperation.First,secondaryqualitiesbecamecorrelatedwithphysicalmotions,andthentheprocessesoflifeandofthehumanbody,asobjectsforthegrowingsciencesofbiologyandphysiology.Finally,theactivitiesoftheminditselfbecamesubjectmatterfortheempiricalscienceofpsychologyandinitswakethesocialsciencescameintobeing,adaptingthemethodsofthephysicalsciencestothestudyofsocialandculturalphenomena.

    Inordertobedrawnintothecircleofthescientificallyknowable,however,life,mind,andsocietyhadtobetransformedintothekindofobjectswhichalonesuchsciencerecognizedasreal.Theyhadtobepubliclyobservableandreducibletoquantifiableproperties.Tothisend,throughthemediationofbiochemistry,biologicalprocessescame

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    tobeexplainedintermsofphysicsandchemistry;physiologyfollowedsuitand,withthehelpofneurophysiology,psychologicalphenomenabecameaccessibletotheapprovedmethods.Further,thesciencesofthemindandofsocietycametobeviewedasbehaviouralsciences,concernedonlywithpubliclyobservableandovertmovementsofhumanbodies.Whencyberneticssuppliedthemeansofmechanizingandmathematizingtheprocessesofthinkingandtheoperationsofintelligence,thefullyobjectiveworldpictureseemedtohavebeencompletedbyathoroughgoingphysicalism,reducingeverythingwithoutexceptiontomaterialandmechanistictermsinauniversal,unified,value-freescience.

    Atthisstage,valueitselfbecomesdevalued.Thescienceofpsychology,inalliancewiththoseofanthropologyandsociology,revealsevaluativebehaviourasexpressiveoffeelingsandmouldedbysocialpressuresintoculturaltraditions.Allvaluesanderstwhilephilosophicaltheoriesofvalueareshowntoberelative,primarilytothechemicalmechanismoftheindividualhumanorganismandsecondarilytotheculturalunitinwhichtheindividualisintegrated.

    Anthropologistsreinforcetheseresultsbythediscoveryofdifferingandapparentlyincommensurablecodesindifferentcultures,sothatthestandardsrecognizedinonesocietyarequiteinapplicableinothers.Thegenerallyacceptedscientificdoctrineisthusuniversalrelativism,whichrendersthenotionofobjectivevalueinvalid.Ethics,accordingly,becomesnoncognitive,andobligationisreducedtotheincidenceofsocialandpsychologicalpressures,whichappearasthesolebasisforthemoralregulationofconduct.Butifallvaluesarethusrelative,nostandardofvaluehasobjectivevalidityevenwithinaparticularsociety;for,apartfromthefactthatallculturesbreakupintosubcultures,towhichthesamescientificconsiderationsmustapply,differencesoftemperamentbetweenpersonsareunbridgeable.So,evenifpsychologicalinfluencessubjecteveryindividualtoconditioningbysocialpractices,therecanbenoexternalyardstickwithwhichtomeasureconclusivelyevenindividualjudgements.Muchlesscouldanystandardberegardedasuniversallybindinguponallmankind.

    Paripassuwiththisthoroughgoingobjectivizationofscientificknowledge,theadvanceoftechnologyhasoverwhelmedeverysphereofhumanpractice.Technologyistheapplicationofscientifictheorytothepracticalaccomplishmentofhumanpurposes.Itsadvanceisbuiltintothestructureandmethodofmodernempiricalscience.Sciencereliesforitsdiscoveriesonobservation,experiment,andmeasurement,themethodsofwhichareimprovedandmademorepreciseby

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    thepracticalapplicationofitsownresults.Discoveriesrevealnewmeansofconstructingmoreefficientinstrumentsforobservationwhichmakenewdiscoveriespossible.Disclosureofthelawsofmechanismwhichregulatethecosmicmachineprompttheinventionofmachineswhich,byincreasingthepowerandprecisionofobservation,helptorevealnewlaws.Lawsofnatureoncediscoveredcanbeputtouseandinspannedtoservetheneedsofhumanlifeandcomfort;andnotonlyisthispossible,butthetechnizationofhumanskillsitselfministerstotheadvanceofscientificknowledge.Discoveryofthestructureoftheatomandofthebehaviourofelementaryparticlesteachesengineershowtobuildelectronmicroscopesandcyclotrons,whichrevealtophysicistsnewfactsaboutthestructureofatomsandthebehaviourofelementaryparticles.Discoveriesinelectronicsprompttheconstructionofcomputerswhichenablescientistsinallfieldstomakeyetmorediscoveries.

    Thefinaloutcomeisarangeoftechnicaldevelopmentthatgivesmanunprecedentedpowersbothofproductionanddestruction.Regulationofhumanbehaviourbymeansofdrugsaswellasbyimplantingelectrodesinthebrainisalreadypossible.Modificationofthegeneticcodesoastoaffectfutureevolutionofthespeciesiswellwithintheboundsofpossibility.Theprospectofprolonginglifebycounteractingtheadvanceofsenilityisconfidentlyentertained.Astheresultoftechniquesalreadyinuse,drastictransformationoftheterrestrialenvironmentwithfar-reachingconsequencesfortheconditionsofhumanandotherlifeisalreadytakingplace.Thisisnolongerevenamatterofconsciouschoice,forthetechniquesalreadyadoptedare(aswehaveseen)exhaustingsomeofthekeyresourcesoftheplanet,pollutingitswateranditsatmosphere,andexterminatingusefulspeciesofplantandanimallife,orinjectingintothemsubstanceswhichrenderthemharmfulasfoodforhumanbeings.Destructivecapabilitiesareevenmoredramatic,formoderntechnologyhasproducednuclearweaponsthatcouldannihilateallhumanityandpossiblyalllifeontheplanetifusedwithoutrestraint.

    IVBankruptcyof"theScientificOutlook"

    Allthiswecontemplatewithapprehensionandbewilderment.Whatitmeansisthattheseventeenthcenturyconceptionofobjective

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    sciencehasgeneratedamethodofdiscoverywhichhasbeenspectacularlysuccessfulwithinitsfield,butwhichhasbroughtman,byitsverysuccess,toapasswhereheisfacedwithproblemsofsurvival,thesolutionsofwhicharehardlyobvious.Toappealagaintoscienceandtechnologyseemsonlytoproducenewandgreaterproblemsinthecourseofsolvingoldones.Buttherealdifficultyisthattheproblemsarenotsimplytechnicalbutaremoral.Itisnotjustaquestionofhowweshallconsumetheearth'sresources,orhowwemaysavethem,orhowtoconservetheenvironmentortoregulateitschange.Itisnotsimplyamatterofhowwecanvarythegeneticcodeanddirectfutureevolution;norhowtomodifysocialbehaviourbyartificialmeansandwhatsortofbehaviourtopromote.Weshouldnotasksimplywhentoresorttonuclearwarfareorwhatwouldbethebeststrategy.Theessentialquestioniswhetherweshoulddoanyofthesethingsorallowthemtobedoneatall.Thequestionisnotoneofwhatwecandobutofwhatweoughttodo:oneofrightandduty,notsimplyourownrightanddutyandtherightsanddutiesofourimmediateassociates,butalsooftherestofmankind,howeverremotelyplaced,andoffuturegenerationsincenturiestocome.

    Thesearemoralquestionsunprecedentedinanyculturaltraditionandunanticipatedinanyprevioustheoryofethics.Astheyareglobalintheirscope,theyarequestions,theanswerstowhichdemandreferencetouniversalstandardsofvalue;andastheybearuponthedeepestandmostfar-reachinginterestsofthehumanrace,theprinciplestowhichanswersshouldconformmustbeultimateandobjective.Foritisnotonlyapredictionthatwearecalledontomakeastowhatmayorwillhappen,butajudgementofwhatoughttobedoneandonewhichmustbevalidforeverybodywithoutexception.

    Objectiveanduniversalstandardsofvalue,however,arepreciselywhatthepursuitofobjectivescientifictruthhaseliminated.Suchscienceisvalue-free,and,havingdrawnintoitsdomaineveryformofhumaninvestigation,ithaspronouncedvaluejudgementstobesubjectiveandrelativetolocalandtemporalconditions.

    TheissuehasbeendiscussedinabrilliantessaybyHansJonas.3Moderntechnology,hepointsout,is"utopian"initscharacterbecauseitprofessesacapacitytoremodelandregulatethetotalstructureoffutureliving.Hewrites:

    Inconsequenceoftheinevitable"utopian"scaleofmoderntechnology,thesalutarygapbetweeneverydayandultimateissues

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    ...issteadilyclosingLivingnowconstantlyintheshadowofunwanted,built-in,automaticutopianism,weareconstantlyconfrontedwithissueswhosepositivechoicerequiressupremewisdomanimpossiblesituationformaningeneralandinparticularforcontemporaryman,whodeniestheveryexistenceofitsobject:viz.,objectivevalueandtruth.Weneedwisdommostwhenwebelieveinitleast.4

    Butitisthepursuitofobjectivetruththathasdestroyedthefoundationsofobjectivevalue.Theveryauthorityofsciencehasbroughtustothecriticalimpasse.Recentreflectionsonthenatureofscienceanditsmethods,however,convergingfromdiversepointsofdeparture,arenowcallinginquestiontheauthorityofscienceitself,inmuchthesamewayassciencehascalledinquestiontheauthorityofvaluejudgements,and,atleastbyimplication,theresultingcritiquehasunderminedtheveryclaimofsciencetoultimatereliability.

    VTheWhirligigofTime

    PursuingHusserl'searlyinsightintothebeginningsofthecrisiswehavebeenoutlining,5phenomenologistsarguethattheobjectiveoutlook,ofwhichscienceisthetypicalexpression,isitselfderivativefromamorefundamentalsubjectiveexperience.Theoriginalinvolvementoftheexperiencingsubjectinhis"life-world,"fromwhichthescientificviewisanabstraction,isforgottenbythescientist,andaccordingtoHusserlitisonlybytracingscientificthinkingbacktoitsoriginalsourcethatwearelikelytograspthenatureofthecrisisintowhichithasledus.Insodoinghereducessciencetoaconstructioneffectedbythetranscendentalegowithinthesubjectiveawarenessoftheultimatesubjectofconsciousness.6Existentialistshaveemphasizedthisoriginatingfunctionoftheconscioussubject,some,likeSartre,stressingitscompletefreedomtoviewandconstructtheworldaccordingtoitsownunrestrictedchoice.Inmuchthesamevein,Heideggercontendsinafamousessay7thatmodernscienceischaracterizedasresearch,throughthepredelineationofanareaofinvestigationwhichprescribesbothitsmethodofprocedureandthesortofobjectwhichistocountasrealandasevidence.Inconsequence,scientificinquirybecomesthepursuitofaninstitu-

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    tionalizedprofessionalcommunity,towhichitsideasandthecanonsofitsmethodologyareesoteric.Inshort,itsmethodsandresultsarerelativetoaselectedgroupwitharestrictedoutlook.Meanwhile,R.G.Collingwoodhasmaintainedthatscience,ineveryperiodofitshistory,restsuponaconstellationofabsolutepresuppositions,whichareneitherempiricallyderivednorrationallysupportedandcannotproperlybedescribedastrue.8Theyaresimplypresupposedabsolutely,andtheyarepeculiartothehistoricalperiodunderscrutiny.Thus,fromthreedifferentdirections,criticismsuggeststhatobjectivistscienceitselfisrelativetoamorefundamentalsubjectiveawareness,ortoaclosedsocialgroup,ortoahistoricalperiod,ortoallthreetogether.

    TheboatoftraditionalempiricismhadalreadybeguntorockwhenKarlPopperrejectedaspsychologisticthecriterionofscientificvalidityintheevidenceofsense-perception,whenheabandonedinductivereasoningaslogicallyinvalidandmaintainedthatscientifichypothesesweremereconjectures,thesourceofwhichmightpossiblybepsychologicallyaccountablebutwasnotlogicallyexplicable.Thehypothesesthemselves,heheld,wereacceptableonlysolongastheyremainedunrefutedbyempiricalevidence.Theultimately"basic"characterofsuchevidence,however,hedeclaredtobeamatterofconvention,becauseultimatedatacanneverbereached,allbeingsubjecttointerpretation.9Empiricists(includingPopperhimself)didnotimmediatelynoticehowcompletelythisviewsubjectivizedscience(atendencypushedevenfurtherbyPopper'sfollowerImrLakatos).TheytoleratedandevenwelcomeditatfirstbecauseoftheapparentlyempiricalcharacterofwhatPopperdemandedasfalsifiyingevidence.

    ButthedovecotesoftheacceptedphilosophyofscienceweremoredisturbinglyflutteredwhenThomasKuhndeclaredthatsciencealwaysoperateswithinthelimitsofa"paradigm"or"exemplar"whichprescribesthegeneraloutlinesoftheoreticalstructureandthemethodsofprocedure.Thepradigmalsodeterminesthefundamentalconceptsanddefinesultimateentitiesandthenatureofreality.Thisparadigmhasnojustificationotherthanthatthescientificcommunityacceptsit;soonceagainitisesoteric.Andevidenceisassimilatedtotheparadigmthatis,totheoryratherthantheorytoevidence.Asaresult,allobservationbecomes"theory-laden,"athesismaintainedoriginally(ineffect)bytheBritishidealistsattheturnofthecentury,andrevived(unwittingly)byN.R.Hansoninthemiddlefifties.10Changesofparadigm,whentheyoccur,aresaidtoberevolutionary,sothatthoseprevailingindifferentepochsaremutuallyincommen-

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    surable,andeachisestablishedsolelybyevidenceandargumentsrecognizedandinterpretedinthelightofitsowntheoreticaltermsandconcepts.Revolutionarychangesoccurwhenthenormalprocessof"puzzle-solving,"whicharticulatestheparadigm,breaksdownbecauseofanaccumulationof"anomalies,"eachofwhichtakenalone,solongasitdoesnotobstructthecourseofresearch,tendslargelytobeignored.Butwhenrevolutionsdooccur,thegenerationofthenewparadigmisnotrationallyaccountableandarisesfromaproliferationofrivalhypothesesguided(itwouldseem)bynosystematicprinciple.11Thehistoryofsciencethuscomestoberegardedasasuccessionofconceptualschemesirrationallygeneratedandselectedfromamongalternativesmoreorlessarbitrarily,eachofwhichispeculiartoitsownperiodandesoterictoaspecialprofessionalcommunity,eachprescribingitsownmethods,procedures,andcanonsofacceptability,interpretingitsownevidenceaccordingtoitsownprinciples,recognizingasfactonlywhatconformstoitsownconcepts,noneofwhichmaybelegitimatelycomparedwithorcriticizedfromtheviewpointofanyother.

    Finally,inthehandsofPaulFeyerabend,scienceisextolledasapurelyandproperlysubjectivepursuit.Theproliferationofhypotheses,themorediverseandegregiousthebetter,heregardsasadvantageous.Noneofthemhas,orneedhave,anylogicallyjustifiableorigin;theadoptionofanyofthem(ascientificrevolutioninKuhn'ssense)"cannotbeaccountedforinanyreasonablefashion."12Whatintheoryorpracticeisconsidered"rational"dependsuponruleseitheracceptedatthetimeor''inventedinthecourseofitsdevelopment."13Butnosuchrulesarepermanent,fortheyareallhistoricallyrelative.Scienceisahumancreation,constructingitsownworldinitsownwayaccordingtoitsownstandards.Thechoiceofourbasiccosmologyisamatteroftaste,andscienceisinthisrespect,asinallothers,onaparwithart,aestheticcriteriaofsatisfactionbeingparamountinboth.14Thestudyofitschangesisasociologicalstudyandtheirexplanationifany,isapsychologicalexplanation,butthestatusofpsychologyandsociologyassciencesis(presumably)nodifferentfromtherest."Andthusthewhirligigoftimebringsinhisrevenges."

    Thescientificapproachtothestudyofvalues,astudytakentobewhollyobjectiveandvalue-free,pronouncedallstandardsofvaluetobesubjectiveandrelative.Itnowtranspiresthatscientificcanonsandconceptsarethemselves,inpreciselythesamewayandfrompreciselythesamecauses,subjectiveandrelative.But,ifthisissowehavelost

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    allholdonobjectivityandallgraspoftruth.Forwhatissubjectiveandrelative,ischangeablefromindividualtoindividualandfromtimetotime,andnoassertioncancompelourassentifitisliabletosuchinstability.Ifwhatisheldtobetrueatonetimeisheldtobefalseatanotherandwhatisacceptedtodaywillberejectedtomorrow,nothinghasanyjustifiableclaimandallopinionsalikewillprovefalse.Ifallallegedtruthsarebuttemporaryillusionsthatverywordwillhavelostitsmeaning.Fornoclaimtotruthisevermadewhichdoesnotpresumethat,howeverwellorillitmaybefounded,yetthereissomeuniversalcriterionbywhichitmaybejudgedandwhichgivesitsignificance.Nothingcanberejectedasillusoryexceptbyreferencetosomesuchcriterion,andnothingcanbeacceptedastrueunlessitconformstosomesuchstandard.Ifthereisnone,noclaimscouldeithersensiblybemadeorrightlyinvalidated.

    Thatstandardsaremerelyrelative,whetherofvalueorofscientificrigour,isanassertionwhichpresumablyclaimstruth.Therefore,byimplicationitappealstosomepresumedstandardoftruthwhichisuniversalandobjective.Thepositionis,therefore,self-destructiveanduntenable.Whatthisstandardishastobeuncovered.Wemustfindawayofviewingsciencewhichallowsforandcanrelatetothisuniversalandobjectivestandard,evenifconceivedonlyingeneralterms;andonewhichdoesnotatthesametimeeliminateasimilarrelationshipinthesphereofvalues.

    Wehavealreadyseenthatsciencealonecannotsolvetheproblemswhichweface.Infact,notonlydoesitproduceandexacerbatethem,butbythecontemporarycritiqueitsownvalidityandauthorityhavebeenundermined.Theproblemsarenot,indeed,essentiallyscientific,butaremoreporperlyphilosophical,fortheyconcernvaluesandthestandardswhichoughttoberespectednotsimplythosethatareinfactacceptedorneglected,asthecasemaybe.Themainphilosophicalquestionisthatofthestatusandvalidityofthesestandards,whichhavebeendissolvedawaybyscientifictreatment,whilescienceitself,byasimilarargument,hasbeendisqualifiedfromreturningaverdict.Contemporaryphilosophyhassofarcontributednothingtowardsasolutionofthepracticalproblemsnorofferedanyanswertothephilosophicalquestion.Empiricism,strengtheningtheseventeenthcenturyoutlook,hasbeenanaccompliceinthecreationofthefirst,andbyitsownlogicrenouncesitsownrightanddeniesitsowncom-

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    petencetoanswerthesecond,todefinestandardsofvalueortojudgeoftheirvalidity.Forempiricistscontendthatmattersoffactbelongsolelytotheprovinceofthespecialsciences,thatallvaluesderivefromsentimentandfeelingwithoutrationalbasis,andthatlogicispurelyanalyticandinstrumentalincapableoforiginatingsubstantiveknowledge.Yetitissuchlogicalonethatcontemporaryanalyticphilosophyadmitsascompetent.

    Inarecentlectureoncontemporaryphilosophy,Mr.AnthonyQuinton,havingexplainedhowthelogicalpositivismofthethirtiesanditssuccessorsinlaterdecadeshadlosttheirholdonorthodoxy,remarks,"Moregenerally,therehastakenplaceaverymarkedreestablishmentofthelinksbetweenphilosophyandformallogic."theeffectofthisreestablishment,hemaintains,isthereaffirmation(especiallybyW.V.O.Quine)of"theviewthatformallogicinthetraditionofFregeandRusselldisplaystheessentialstructureofthoughtandlanguage."15Ifthisisindeedthecase,theabilityofcurrentphilosophytocontendwiththeproblemssetoutabovewillbecircumscribedbyformallogic;andasphilosophyisthedisciplineuponwhichthemainburdenmustfall(thenatureoftheproblemsbeingwhatitis),itscapacitytosolvethemwillbeproportionaltotheadequacyofthelogicitespouses.Ifallitrecognizesiseitherinduction,astheallegedlogicofempiricalscience,whichhasengenderedtheproblems,ordeduction,theformalprocedurelimitedtopurelyanalytictautologies,philosophywillbebroken-backedanddisqualifiedabinitiofromrenderingassistanceinthemodernpredicament.Soweshallbeleftinoursorryplightwithoutrefugeorresource.

    Schools,otherthantheanalytic,criticalastheyareofthemorepositivistformsofempiricism,haveerodedawaytheclaimtoobjectivitywithoutwhichjudgementishamstrunganddebilitated.Wehave,ineffect,beendeprivedofanyconceptionofreasonwhichwouldmakeitsuseeffectualinourpresentcriticalsituation.Thetypeoflogicwhichempiricismhasbequeathedtous,theonlysortcurrentlyinvogue,hasabandonedeveryformofrationalitythatcouldbeproductiveofremediestoourills.Ourfirsttask,therefore,mustbetoinvestigatethenatureandfoundationofthislogicinoursearchfortherootcausesofourdilemmas.Wemaythendeterminewhatsortofrationality,ifany,canshowusthewayoutofthelabyrinthinwhichwehavelostalldirection.

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    Notes

    1.Cf.TheEffectsofNuclearWeapons,ReportbytheUnitedStatesAtomicEnergyCommission,1964;TheHolifieldCommitteeHearingsonRadiation,UnitedStatesCongress,1959;andNuclearDisasterbyTomStonier,PenguinBooks,Harmondsworth,1963.Neitherthefactsnortheargumentspresentedinthesedocumentshaveyetbeensuperseded;infact,recentinternationalconferencesofscientistshavereachedstillmorealarmingconclusionsoffinalcatastrophe.

    2.IhavesetouttheaboveargumentsmoreatlengthinTheSurvivalofPoliticalMan(UniversityoftheWitwatersrandPress,1950)andAnnihilationandUtopia(GeorgeAllenandUnwin,London,1966).

    3."TechnologyandResponsibility,ReflectionsontheNewTasksofEthics,"SocialResearch,Spring1973.ReprintedinPhilosophicalEssays(EnglewoodCliffs,NJ),1974.

    4.Ibid.,p.50f.

    5.Cf.E.HusserlTheCrisisofEuropeanSciences,trans.D.Carr(NorthwesternUniversityPress,Evanston,IL1970).

    6.Cf.E.Husserl,op.cit.,esp.TheCrisisofEuropeanHumanityandPhilosophy,TheViennaLectureof1935,(Husserliana,BandVI,p.343),trans.DavidCarr,p.295:"Asanaccomplishmentit[mathematicalscience]isatriumphofthehumanspirit.Butsofarastherationalityofitsmethodsandtheoriesareconcerneditisathoroughlyrelativeone.Itpresupposesattheoutsetthefundamentalassumptionwhichitselfexcludestruerationality.Sincetheperceivedsurroundingworld,asmerelysubjectiveexperienceisforgottenandthescientistisnotmadeatheme[ofinvestigation]."andTheCrisisofEuropeanSciences,Carr,p.97,Husserliana,BandVI,p.100:Imyselfusetheword'transcendental'inthewidersense,forthe...originalmotif...whichisthemostfruitfulofmeaninginallmodernphilosophy....Itisthemotifofinquiringbackintotheultimatesourcesofallknowledge,ofself-reflectionbytheknowerintohimselfandhisknowinglife,inwhichallscientificstructureswhicharevalidforhimhaveoccurredaspurposiveactivity,arepreservedasacquisition,andhavebecomeandcontinuetobecomefreelyavailable."

    7.DieZeitdesWeltbilds,"inHolzwege(Frankfurt-am-Main,1952).

    8.Cf.AnEssaryonMetaphysics(Oxford,1940).

    9.Cf.TheLogicofScientificDiscovery(London,1959),pp.40-47,94,104f.

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    10.Cf.PatternsofDiscovery(Cambridge,1958).

    11.Cf.T.Kuhn,TheStructureofScientificRevolutions(Chicago,1962-1970).

    12.Cf."ConsolationsfortheSpecialist"inCriticismandtheGrowthofKnowledge,eds.I.LakatosandA.Musgrave(Cambridge,1970),p.214.

    13.Opcit.,p.216.

    14.Cf.op.cit.,p.228.

    15."CurrentTrendsinPhilosophy,"TheListener,22nd.April1976,pp.495-496.

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    PARTIFORMALLOGIC

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    Chapter1ThePresuppositionsofFormalLogicILogicandMetaphysics

    Thesuggestionthatlogicrestsuponmetaphysicalpresuppositionsisliableinthesedaystoberejectedwithscorn.First,therearesomephilosophersstillwhomaintainthatmetaphysicsisanimpossibleandillegitimateinquiry.Ifthisisstatedmerelydogmatically,itdeservesnoattention;butthereasonwhichinthepasthaspersuadedthinkersoftheimpossibilityofmetaphysicshaslongbeenabandonedasunfounded.Thatreasonwasoriginally,thatmetaphysicsclaimstorevealthenatureofthings,butthatthiscanonlybedone,ifatall,byempiricalinvestigation,theonlypropermethodofwhichisthemethodofthenaturalsciences.Anypronouncementaboutfactualmattersmustbebasedonobservationalevidence,andthatmetaphysicsneithercannorattemptstooffer.Sucharguments,however,havelongsincebeenexposedasunwarranted,ifonlybecauseaccordingtothecurrentconceptionofscientificmethod,asheldbothbypractisingscientistsandbyphilosophersofscience,allsciencehasbeenshowntopresupposenonempiricalpresuppositions;butmainlybecausetheveryanti-metaphysicalargumentitselfhasbeenrecognizedbysomeofitsownoriginalproponents(e.g.,LudwigWittgenstein)asrestinguponmetaphysicalassumptions.1Theverypositivistswhooriginallyhaddeclaredthatmetaphysicalpropositionscouldhaveno(factual)senselatercametorevisetheirposition."Thatmetaphysicsisnonsenseisnonsense,"declaredFriedrichWaismann.

  • Page24

    Evenifthisisconceded,however,therearesomewhowillmaintainthatlogicisapurelyformaldisciplineabstractingentirelyfromthematerialcontentofdiscourseandconcernedsolelywiththeformandtheformalrelationsofitsexpressionsandthatthesearewhollyindependentofmetaphysicaltheories,thesubjectmatterofwhichisthefundamental(orelementary)natureofthings,andwhich,therefore,isconcerneddirectlywiththematerialcontentofdiscourse,whatitisabout.Further,itiswidelyheld,thelogicalstructureofthought(orofitsexpression)neitherdictatesnorisdeterminedbymetaphysicaldoctrine.Thatmaybewhateveritwillwithoutintheleastaffectingtheprincipleswhichgoverninferentialprocedures.Infact,theargumentwillcontinue,theprinciplesofvalidinference,whichitisthebusinessoflogictoinvestigate,mustbepriortoanymetaphysicalspeculation,forinsofarasmetaphysicsderivesitsconclusionsfrompremissesbyreasoning,theprinciplesofthatreasoningmustbeindependentofandpriortoboththematerialpremissesandtheconclusions.Theprinciplesaccordingtowhichthelatterarereachedfromtheformercannotthemselvesbetheconsequenceofeither,andmust,therefore,beindependentoftheircontent.Moreover,criticismofmetaphysicalpresuppositionsispossibleonlogicalgrounds.Theymaybeself-contradictory,ormutuallyincompatible,orimproperlyformulated.Iflogicalprincipleswereconsequencesofmetaphysicalpresuppositions,suchcriticismwouldbeimpossibleandself-destructive.

    Butalltheseargumentspresuppose,first,thatformandcontentareunrelatedandmutuallyindependent,whichisitselfametaphysicalassumption.Andsecondly,validityinreasoningiswhatguaranteestrueconclusionsfromtruepremisses,andthatcanbeensuredonlyonthegroundofsomerealconnectioninthecontent.Principlesofvalidinference,therefore,canhardlybeindependententirelyofthenatureofthesubjectmatter,unlesstheyaretobealtogethertrivialandineffectual.

    Inference,however,isanoperationofthoughtthoughmostcontemporarylogicians,anxioustopurgetheirdisciplineofalltaintofpsychologism,prefertosubstituteforprinciplesofinferencerulesofimplicationorentailment.Nevertheless,fewwouldwishtodenythatlogicisconcernedwithconcepts,withtherelationsbetweenthem,andbetweenthemandtheentitiesofwhichtheyaretheconcepts.Here,whetherwelikeitornot,thereisinevitableinvolvementwiththought,foraconceptisobviouslyaproductofconceiving;andrelationsbetweenconceptsandthattowhichtheyapplyinescapablyimpliesthe

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    relationofconceptiontoitsobjects.Howweviewthatrelation,moreover,is,orinvolves,ametaphysicaltheory.Indeed,logicaltheoryandpracticealwaysdopresupposesomeconceptofthestructureoffact,which,whenmadeexplicit,isametaphysic.Byexaminingthedoctrinesandpracticesoflogicians,therefore,weshouldbeabletodiscoverwhattheirpresuppositionsare,theirassumptionsaboutwhat,ifthelogicalproceduresaretobeviable,thenatureoftheconceptanditsrelationtoexistingthingsmustbe.

    Logicians,moreover,despiteprotestationsagainstthedependenceoflogiconmetaphysics,dofromtimetotimeadmitbyimplicationthatthelogicalcharacterofconceptsdoesdependuponthenatureoftheobjectstowhichtheyapply.Frege,forinstance,saysthatstrictlytheonlywaywecanestablishthataconceptisfreefromcontradictionistoshowthatsomethingfallsunderit.2Presumably,then,thenatureoftheobjectsfallingundertheconceptdeterminewhetheritisself-consistent.Fregealsomaintainsthattherulesofcalculationarenotchosenarbitrarilybutdependonthemeaningswehaveassignedtooursymbols.3

    IIFregeandDieGrundlagenderArithmetik

    Despiteseveralprecursors,thefounderofcontemporarylogicisundoubtedlyGottlobFrege,whoseinfluenceuponBertrandRussellwasprofoundand,throughhimandhisworkincollaborationwithA.N.Whitehead,haspersistedtothepresentday.ThefundamentalprinciplesFregeestablishedhaveneverbeenseriouslyquestionedormodifiedbyanyexponentofmathematicallogic.Thechangeswhichhavebeenmade,thoughconsiderable,havebeenmostlyinnotationandthemethodsofitsoperation,butnotofthefundamentalideaswhichFregesetoutinsuchworksasDieGrundlagenderArithmetik,DieBegriffsschrift,andGrundgezetzederArithmetik.Itwillbesufficientformyimmediatepurposetoconfineattentiontothefirstofthese,forsuchchangesintheoryandpracticeashavesubsequentlybeenmadeaffectitlessthantheydotheotherworks.

    InhisconclusiontoDieGrundlagen,Fregeclaimstohaveshownthatitisatleastprobable,thatarithmetic"becomessimplyadevelopmentoflogic"inconsequenceofthedefinitionofnumberwhichhehas

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    given.Bytheuseoftheexpression"one-onecorrelation"(beiderseitseindeutigeZuordnung)andthedefinitionwhichhegivesofthat,heclaimstohavereducedtheconceptionofnumbertooneofpurelylogicalrelations.Thesearerelationsbetweenconceptsandtheirextensions,forFregemaintainsthatnumbers,althoughtheyare"objects"(inhissenseoftheword),areneitherphysicalnormentalentities.Therelationsdonotpertainto"objects''assuch,butonlytoconcepts.ThenumberthatbelongstotheconceptF,hetellsus,istheextensionoftheconcept"like-numberedtotheconceptF,"where"like-numbered"(gleichzahlig)isdefinedintermsofone-onecorrelation.Fromthisclaimitfollowsthatlogicisconcernedonlywiththenatureofconceptsandtherelationsbetweenthem,alongwiththerelationofaconcepttotheobjectswhichfallunderiti.e.,itsextension.

    Thereshouldbenoobjectionstothisviewoflogic,forevenifonewishedtomaintainthatlogicisalsoconcernedwithpropositionsandtheirmutualrelations,itmustbeconcededthatpropositionsarethemselvesenunciationsoftherelationsbetweenconcepts,betweenconceptsandobjects,andbetweenobjectssofarastheyfallunderconcepts.Or,ifonewishedtosay,withMarthaandWilliamKneale,that"logicisconcernedwiththeprinciplesofvalidinference,"4itmustbeadmittedthatinferencedependsupontherelationsbetweenconcepts,forevenifitisformulatedinpurelytruth-functionalterms,thetruthorfalsityofapropositionmustdependontherelationsbetweentheconceptsandtheobjectstowhichthepropositionrefers,andinferenceupontherelationbetweentheseandotherstowhichotherpropositionsrefer.

    Fregeinsiststhat"concept"shouldalwaysbeunderstood,inlogicandmathematics,onlyinitslogicalsenseandnotinanypsychologicalsense,nor,asoftenoccurs,inamixtureofthetwo.Whatpreciselyitslogicalsenseshouldbeisnotimmediatelyapparent,butwemayagreethatpsychologismandconfusionbetweenlogicandempiricalpsychologyaretobedeplored.Frege,however,doesnotalwaysgivequitethesameaccountoftheconceptindifferentwritings.Inhisessayon"FunctionandConcept"(1891),5heidentifiestheconceptwiththefunctioninmathematics,sayingthatitisafunctionwhosevalueisalwaysatruth-value.ObjectionshavebeenraisedtotheconsequencesofthisdoctrinewhichIshallnotdiscuss.6Itsinterestinthepresentcontextliesinthefactthatamathematicalfunctiongivesexpressiontoaprincipleofsystematicrelationshipsbetweenterms,andthatitsvalues(orexemplifications)fordifferentargumentsmaydifferwidely

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    althoughtheyallsatisfythefunction.Whattheyhaveincommonneedbenothingbeyondthefactthattheydosatisfythefunction.AndthischaracteroffunctionsismuchnearertotheaccountoftheconceptthatIshallseektoadvocatelaterthanwhatFregesaysofitelsewhere.

    Frege,infact,consistentlyignoresthefactorofdifferenceintheexemplificationoftheconcept(orfunction)except,ofcourse,sofarasargumentsmaydiffer.Hedistinguishessharplybetweenconceptandtheobjectswhichfallunderit,orinalternativemathematicallanguage,betweenthefunctionanditsvaluerange."Object,"hesays,isindefinablebutisanythingthatisnotafunction(orconcept),sothatnoexpressionforitcontainsanemptyspace.7Thevaluerangeofafunctioni.e.,itsvaluesfordifferentargumentscorrespondsto(oristhesameas)theextensionofaconcept,whichpresumablyconsistsofthesetorcollectionofobjectsthatfallunderit.

    Thesymbolforanobject,therefore,canneversignificantlybeusedtofilltheplaceofthepredicateinaproposition.Thatcanbedoneonlybythesymbolforaconcept.Andwhenthenameofanobjectisusedinasentenceasifitwerethepredicate(e.g.,in"ThemorningstarisVenus")theword"is"hasbeenusedinadifferentsensefromthatofthenormalcopulaandstandsforidentity,oristhesameastheequalsign,=.Onlytermsthatrepresentconceptscanbeusedpredicatively.

    Allthisstronglysuggeststhataconceptisacommoncharacter,property,orquality,abstractedfromanumberofobjectswhichareinstancesofitpurelybecauseandinvirtueoftheirhavingthatcharacter,propertyorquality.Theconceptisabstract,aclassconcept,anditsinstancesareconcreteobjectsfallingunderitbecauseeachhasthepropertywhichisthedistinguishingmarkoftheclass.ThatthisishowFregeunderstandsthematterisborneoutbyhistreatmentofnumber.

    Indevelopinghisfamousdefinitionofnumber,Frege,criticizingearlierviews,deniesthatanumberisapropertyofthings,8oraset(Menge),collection,orgroupofobjectsofanykind,orthepropertyofsuchagroup.9Itisnothingmerelysubjective,noritisaconcept,foritcanbegivenapropername("nought,"one,""two,"forinstance)whichcannotrightlybeusedintheplural.Itisthereforeanobject;10butitisnotthepropertyofanobject,norofagroupofobjects,norisitamanifold,asseveralearlierwritersalleged.Anassertionaboutnumber,heholds,isalwaysaboutaconcept,becauseitistheconceptthatdeterminestheunitstobecounted.Theconceptisolatestheinstanceswhichfallunderit,distinguishingthemfromotherobjectsaswellasfromoneanother,yetitisidenticalinallofthemandsoadmitsofno

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    divisibilitywithinthem.Noteveryconceptisofthissort,butthosewhichare,forinstance,"moonofJupiter,"arethosetowhichwecanassignnumbers.11Itthusappearsthattheconceptiswhatisidenticalinallitsinstancestheircommoncharacterandtheunitsofthenumberwhichbelongstoitareitsinstances.Takentogetherasagroup,collection,orset,theyconstituteitsextension.

    NowFregedoesnotdefinethenumberwhichbelongstoaconceptFasitsextension,butastheextensionoftheconceptgleichzahligdemBegriffF("equi-numberedwiththeconceptF")andtoavoidcircularityhedefines"equi-numbered"as"beiderseitseindeutigzugeordnet"("arrangedinone-onerelation").Butwhatareequi-numberedandwhatarearrangedinone-onerelationareobviouslytheobjectsfallingunderF.

    Theextensionofaconceptisthecollectionorsetofalltheobjectswhichfallundertheconcept.ButFregehastoldusthatanumberisnotaset.Sohisdefinitioncannotbetakentomeanpreciselywhatitsays.CertainlythenumberthatbelongstoFisnotthenumberthatbelongsto"gleichzahligdemBegriffF"althoughitissaidtobe(isdefinedas)itsextension.Itsextensionisallthoseconceptsequi-numberedtoF;buthowcanthenumberbelongingtoFandtoallotherequi-numberedconceptsbethecollectionoftheseconcepts?Obviously,whatFregemeansisthatthenumberiswhatalltheseconceptshaveincommon,what(asthewordgleichzahligindicates)makesthemgleich.Ratherthanitsextension,itistheintentionorcommonpropertydefiningtheconcept,"gleichzahligdemBegriffF";thatis,thepropertywhichtheextensionofFhasincommonwiththeextensionofeveryotherconceptequi-numerouswithit.

    Theseconsiderationsleadusoncemoretotheviewoftheconceptasacommonorclasspropertyembracingasetofinstancesitsextension.TheinstancesarewhatFregecalls"objects"whichareobviouslyparticulars,asopposedtotheconceptwhichisabstractandgeneral.Moreover,theinstancesarerelatedtooneanothersimplyasinstances;thatis,inrespectoffallingundertheconcept,theyareidentical.Sotheycanrankasunitsinadenumberableset.

    Itwouldseemthen,thatnotallFrege'searlierdenialscanbemaintainedconsonantlywithhisowndefinitionofnumber.Foranumberis,afterall,apropertyofwhatCantorcalledeinemengethesetorcollectionofobjectsconstitutingtheextensionofaconcept.Certainly,itisnotthesetitself,butitisthepropertywhichithasincom-

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    monwithallothersetswhoseelementscanbeputinone-onerelationtoit.Frege'sdefinitionlosesnothinginthetranslation,givenbytheKneales,12intoCantor'sterminology:"Thecardinalnumberofasetisthesetofallsetsequivalenttoit"(whereequivalenceistherelationbetweensetsofone-onecorrelation).Buttobestrictlycorrect,weoughttosay"thecommonpropertyofallsetsequivalenttoit,"andsotopreferRussell'swording:"theclassofallclassessimilartoagivenclass,"becausetheword"class"hasaconvenientambiguity,meaningcommonproperty(orclassconcept)aswellascollectionorset.InRussell'sdefinition,therefore,''class"atitsfirstoccurrencehasthefirstmeaningandatalllateroccurrencesthesecond.

    Further,astheKnealespointout,13Fregesometimesallowshimselftotalkasifnumberwereasecond-levelconcept."Accordingtotheproposeddefinition,"saytheKneales,"anumberwouldbejustthecommoncharacterofallsetsofthesamesize."Itwouldthusbethe(second-level)conceptofbeinggleichzahligwithagivenconceptthecommonproperty(orconcept)ofallconceptswhicharesogleichzahligwhichissurelypreciselywhatthatworddenotes.

    Yet,althoughFregeinsiststhatnumbersbelongonlytoconcepts,andthatweshouldnotidentifyaconceptwithitsextension,14itisobviousfromhistreatmentofthematterthatnumberspertainsolelytotheextensionofconcepts,andtheextensionofaconceptis,clearly,envisagedasasetorcollectionofparticulars(eineMenge)relatedonetoanotheronlyinthattheybelongtothatcollection,whichtheydobyfallingunderthesameconcept.Itisamereaggregate,theelementsofwhicharewhollyexternaltooneanotherand,apartfromtheircommoncharacteroffallingunderthesameconcept,arerelatedsolelybyaggregation.Onlyonthisaccountcantheybearrangedinone-to-onecorrelationwiththeelementsofotheraggregatestheextensionsofotherconceptsandsocanbeassignednumbers.Thispurelyexternalrelationshipbetweentheelementsofanaggregateistypicalofunitswhicharecountableandtowhichnumberscanthereforebeapplied.

    Ifobjectsareinthiswayparticularscollectedtogetherunderconcepts,eachthedistinguishingcharacterofadeterminateset,15andtheextensionofeachbeingsusceptibletonumeration,therelationbetweenconceptswillbeofthesamekindastherelationbetweennumbers;sothatlogicwillinconsequencebemathematicalthroughout.

    ThatthisinterpretationofFregeiscorrect,thatitinvolvestheassimilationoflogicalobjectstotheobjectsofmathematics,iscorroboratedbytheKnealesasfollows:

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    Furthermore,itisFrege'sviewthatwhenasatisfactorychainofdefinitionshasbeensetforthitwillbeclearthattheonlyundefinednotionsrequiredforthepresentationofarithmeticarenotionsofformallogic.Inparticularhewishestoshowthattalkaboutnaturalnumberscanbereducedtotalkaboutsets,classes,ormanifolds,whichintheterminologyoflogiciansaretheextensionsofconcepts,andhesaysexplicitlythattheobjectsofarithmeticarelogicalobjects.16

    Themetaphysicalbackgroundtothistheoryis,obviously,theconceptionofapluralisticworldofparticularentitiesor"objects"classifiableintosetsidentifiedbycommonpropertiesorconcepts.Theattributiverelationbetweenpropertyandobjectremainsundefined,butwemayassumethatitisacontingentrelation.Thatbetweenobjectsiswhollyexternal,dependingonlyuponhowtheyarecollectedtogetherintoclassesorsets,andsolikewiseistherelationbetweensets.Theappropriatemetaphysicaltheoryislogicalatomism,asitwaspropoundedbyBertrandRussellearlyinthiscentury,andbyWittgensteininhisTractatus.Itisthetheorywhichconceivestheworldasmadeupof,orasacollectionof,facts,eachindependentofalltherest,sothatanyoneofthemmaybethecaseormaynotbethecasewithoutmakinganydifferencetoanyoftheothers.Thefactsarethereforeatomicandtheirmutualrelationsareexternal.17Afactconsistseitheroftheinherenceinanobject(oragroupofobjects)ofaproperty(orseveralproperties),orinarelationbetweenobjects.Butbetweenfactsthereisnoconnectionsuchthatitwouldbepossibletoinferonefromanyother.Thisbeingso,ourpresumptionaboveisconfirmedthattherelationbetweenobjectandpropertyiscontingent,forifitwerenotso,inferencefromonefacttoanotherwouldbepossibleandthealterationofonewouldentailthatofothers.Anatomicfactcanbestatedinanatomicproposition,and,asanatomicfactmaybecombinedwithothersintoacomplexfact,soatomicpropositionsmaybejoinedinacomplexproposition.ThesearethemetaphysicalpresuppositionsofthelogicdevelopedfromFrege'sphilosophyofarithmetic,oftheBegriffschriftanditssuccessorsfromPrincipiaMathematicaonwards.

    Attemptshavebeenmadetodeny,ortoevade,thisconclusionbyallegingthatthemetaphysicaldoctrineisanadjunctunnecessarytothelogic,andthatitsauthorsweresimplymisledbythelanguageofmathematicsintoconstructingthemetaphysicaltheory.Soindeedtheymayhavebeenmisledbythelanguageofmathematicsinto

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    believingthatthemetaphysicaltheorywastrue.Butthatinnowayaltersthefactthatthelogicpresupposesandisfoundeduponthemetaphysic.Forthelanguageofmathematicsisaboutsetsofexternallyrelatedunits,aboutnumbers,asFregesoaptlydefinesthem,arealmofdiscoursethemetaphysicalcharacterofwhichisrightlysetoutinthetheoryoflogicalatomism.Whatmaywellbedoubted,however,isthatthefundamentalstructureoftheworld,oftheconcretelyreal,isthesameasthatofthisessentiallyabstractsphereofcomputationandcalculation.Itisundoubtedlypossibletoregardalldistinguishableobjectsintheworldasiftheywereexternallyrelatedparticularunitswhichcanbevariouslygroupedaccordingtoarbitraryprinciplesofclassification,and,forsomepurposes,thisassumptionmayproveveryuseful.Whenitismade,objectscanbeenumeratedandmathematicalprocedurescanbeappliedtothem.Butthelogicappropriatetomathematicalcalculationmaywellproveinadequateifthepresupposedmetaphysicisnottrueofthingsastheyreallyareinconcretefact.

    IIITheThesisofthisChapter

    Beforeconsideringtheadequacyofthemetaphysics,evidencemustbeinspectedwhichconfirmsthethesisthatcontemporaryformallogic,initsassimilationtomathematics,isindeedfoundeduponthemetaphysicthusbrieflyindicated.

    ThethesisthatIshalltrytoestablishinwhatfollowsisthatlogicalatomismisanindispensablepresuppositionandisimplicitintheproceduresofformalsymboliclogic.Iamwellawarethatmanylogicianstodayrejectthemetaphysic,butIshallarguethattheirlogicalpracticeneverthelessrequiresitasapresupposition.Andthismaywellbethecaseevenifandalthoughtheyrejectthe"logicism"ofFregeandRussellinregardtomathematics.NordoIinanywaywishtosuggestthat,becausethisisthecase,mathematicianseithersubscribetothemetaphysicorpresupposeitintheirownthinking.

    Itis,however,onlycalculationtowhichproceduresofformallogicareassimilated,andmathematicalreasoningisbynomeansrestrictedtocalculation.Itshouldnotbesurprising,therefore,ifitturnedoutthatmathematicalreasoningitselfinsomeofitsbranchesexemplifiedprinciplesoutsidethescopeofformallogic.Nevertheless,sofarasthe

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    objectsofdiscourseare,canbereducedto,ormayberepresentedas,"sets,classes,ormanifolds,"wemayexpectformallogicaselaboratedatthepresenttimetobeappropriate.StilllessdoIbelievethatthismetaphysicispresupposedbynaturalscience.Infact,inthenextchapterIshallarguethatitisnotandthat,forthatreason,contemporaryphilosophicalanalysisofallegedscientificmethodoftengoesastray.

    IVCommutation,Association,andDistribution

    Mathematicianshaveextendedtheconceptofnumbertoincludenegative,irrational,andimaginarynumbers,andtheyinterpretthesymbolsforthesehighertypesofnumberssothat,incalculationwiththem,thefundamentalalgebraicallawsarenotviolated.Thesearethelawsofcommutation,association,anddistribution.SuchlawsobviouslyholdonlyifthesymbolsemployedstandforentitiesofthekinddefinedbyFrege;thatis,setsofunitaryparticularsmutuallyinexternalrelation.Basically,allarithmeticalcalculationisadditionandsubtraction,theaggregationandseparationofmutuallyindifferentandexternallyrelatedunits.Multiplication,division,raisinganumbertohigherpowers,andextractingrootsarealljustcomplicationsofthebasicoperationsofadditionandsubtraction.Itfollowsthattheseoperationswillconformtocommutative,associative,anddistributivelawsaslongastheentitiesonwhichtheyareperformedareexternallyrelatedparticularunits.Underthiscondition,theorderinwhichnumbersareaddedwillbeofnoconsequence:

    andasmultiplicationissimplytheadditionofequalsetsornumbers

    Forxandyaremerelygroupsofindependentunitscollectedtogether,themutualjuxtapositionofwhichisentirelyindifferent.Suchacollectioncan,ofcourse,beempty,ormaycontainonlyoneunit,butthatwillmakenodifferencetoitsobeyingthecommutativeprinciple.Associativeanddistributivelawsdependonpreciselythesamecondition.Inthecaseoftheassociativerulethisisobvious:

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    Andthedistibutiveruleholdsbecausethesumoftwocollectionsofunitsmultipliedagivennumberoftimesisthesameasthesumofeachofthecollectionsseparatelymultipliedthatnumberoftimes:

    If,however,theunitsthatmadeupacollectionwereinternallyrelatedsothattheyaffectedoneanotherincertainwaysorconstitutedoneanotherbytheirmutualrelations,if,inshort,weweredealingwithwholesandnotwithmerecollections,theorderinwhichtheelementswereaggregatedwouldnotbeindifferentandthealgebraiclawswouldnolongerhold.

    Logicianshavebeenparticularlycarefultoensurethattheirmanipulationofthesymbolswhichtheyemployshouldconformtothethreefundamentalalgebraiclaws,andwenowseethattheconditionforthisisthatthesesymbolsshouldrepresententitiesthatareexternallyrelatedorarecomposedofexternallyrelatedelements.That,wefound,waspreciselyhowFregeviewedconceptsandtheobjectswhichfallunderthem;thesearewhatlogicisabout,andthemetaphysicalpresuppositionofapluralisticatomismisagainapparent.

    Moreover,notonlyisitthecasethatformalproceduresconformingtothelawsofcommutation,association;anddistributionpresupposeanatomicandparticulatesubjectmatter,but,indeed,apartfromthispresuppositionformalization(inthesenseofsymbolization)isimpossible.Symbols,iftheyaretobeuseful,andiftheyaretobemanipulatedalgebraically,mustrepresentidenticalandunchangingtermsorentities.Collectionsofbareparticularsaresoconceived.Theparticularsareeachidentical,constant,andseparatefromeveryother.Butinasysteminwhichtheelementsareinternallyrelated,sothatanychangeineitherpartorwholeisliabletoaffectanyandeveryelementinthesystem,symbolsrepresentingtheelementswouldbeunstableandalgorithmicoperationswiththemwouldbreakdown.Thepresuppositionsofformallogicwhichwehaveuncoveredarenotfortuitousnoraretheycontingentlymade.Theyareessentialtoit,andwithoutthemformalizationisnotfeasible.

    VImplication

    Theprimaryruleofinferenceisgenerallyknownastheruleofdetachment,theschemaforwhichis

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    IfPthenQ;butP,thereforeQ.

    Therelationexpressedby"IfPthenQ"isthatofimplicationandtheinterpretationofthisrelationfundamentaltocontemporaryformallogiciswhatisknownasmaterialimplication,thedoctrineof"thePhilonianconditional."18Theformulaformaterialimplicationis ,andthatitisfundamentalincontemporarylogicisclearfromthefactthatitappears(inoneformoranother)attheheadofeverysetofaxiomsforgenerallogicwhichhassofarbeenoffered.19.

    TheauthorsofPrincipiaMathematicaarequiteexplicitastoitssignificance.Amongthefunctionsofpropositionstheylist"fourspecialcaseswhichareoffundamentalimportance,sincealltheaggregationsofsubordinatepropositionsintoonecomplexpropositionwhichoccurinthesequel[i.e.,therestofthework]areformedoutofthemstepbystep."20thesearethelogicalproduct(orconjunction),thelogicalsum(oralternation),thecontradictoryfunctionandtheimplicativefunction.Thelastincludesallfourbecause isequivalentto andto .Mypurposewillbeserved,therefore,byconsideringtheimplicativefunctiononly.Thepeculiaritiesoftherelationrepresentedbythefunction

    haveoftenbeennoticedbefore,anditisgenerallyagreedthatitdiffersfromthenotionofimplicationincommonuseoutsideformallogic,bywhichweunderstandthatifaproposition(q)isimpliedbyanother(p),theformercanbederivedfromthelattercanbeinferredordeducedfromit.Thatthisisnotalwaysthecasewhenlogicianswrite iscommonlyadmitted,butthelogicalconditionalisusuallyconsideredtoincludesuchcasesofpossibleinference.This,however,isnotandcannotbeso,becausethepresuppositionofatomicparticularsnoticedabovedoesnotpermitofit,asIshallnowproceedtoexplain.

    Theconditionalfunctor,,issodefinedthat istruewheneverbothpropositionsaretrue,orbothfalse,orpisfalseandqistrue.Attentionhasbeendrawn,byH.W.B.Joseph,BrandBlanshard,andothers,21tothefactthatthisisnotarelationbetweentwopropositionssomuchasadisjunctionofrelations.Noessentialconnectionisrequiredbetweenthetruthorfalsityofthepropositionsconcernedinordertosatisfytheconditionsforthiskindofimplication.Thereisnoessentialconnectionbetweenthefalsityof"Alldogsarecats"andthetruthof"thesunishot,"yet,accordingtotheprescribedrule,thefirstimpliesthesecondbecauseitisfalse.Now,ifallpropositionsare

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    atomicandstatefactswhichareunconnected,wenevercantellinadvanceofexperienceandsimplyfromourknowledgeofotherpropositionswhetherapropositionistrueorfalse.Intheusualsenseof"imply",noelementarypropositionshouldeverimplyanyother.Butifwecandiscoverthataproposition,p,istrueandanother,q,isalsotrue,orthatpisfalseandqinsomecasestrueandinothersfalse,wecanassertthatpmateriallyimpliesq.Thus,ifelementrypropositionsdostateatomicandmutuallyindependentfacts,thedoctrineofmaterialimplicationislogicallyimportantanduseful.Butifimplicationbetweenpropositionsrequiredinterdependencebetweenfactsuponwhichtheirtruthorfalsitywasconsequent,thedoctrineofmaterialimplication(asa"logical"relationholdingbetweenpropositionsirrespectiveoftheirlogicalinterdependence)wouldhavenologicalforce.

    Thisconclusioncannotbeevadedbyallowingthatmaterialimplicationincludessuchcasesasinvolvelogicalinterdependencebetweenthecomponents.Ifthetruthofqislogicallydependentuponthatofp,itmaybesaid,everythingdemandedbythedoctrinewillbefulfilled:whenpistrue,qwillbetrue;whenpisfalse,qwillbefalse;butifpshouldhappentobefalse,qmayneverthelessbetrue.Thisconformitywiththerequirementsofthedoctrineis,however,purelyaccidentalandmaterialimplicationcanneverbeacriterionoflogicalinterconnection.Ifitwere,casesinwhichthepropositionswerelogicallyindependent(liketheexamplegivenabove)wouldnotbepermissible.Morethanthis,theconditionalconnectiveneverdenoteslogicalinterdependence,evenwhereithappenstoexist,thoughsymboliclogiciansfrequentlyoverlookthefactbecausetheytendtoconfusetherulefortheuseofthesymbolwithalogicalrelationbetweenpropositions.

    doesnotentitleustoassertqastrueifweknowthatpistrue,forwecannot,withthatknowledgealone,assert .Wecandothatonlyifwealsoknowthatqistrue;and,ofcourse,ifwedo,theostensibleconclusionisnotaninferencefromp.Consequently,thesecondimplicationsigndoesnotsignifylogicalinterdependenceanymorethanthefirst,foritisnotthematerialimplicativerelationbetweenpandqthatentailsqwhenpistrue.Likewise,evenifthefirstimplicationwerestrict,thesecondneednotbe,becausethematerialimplicationwouldstillholdifeither werefalse.Accordingly,thesigncanneverindicatelogicalinterdependence.

    Thisissometimesheldtobedisprovedbytheexample:

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    Here,thetwocompoundexpressionsarethoughttoberelatedbyastrictlogicalimplication,asarethecomponentsofthesecondcompound.Butthisisamistake.Ifthefirstconnectiveisnotastrictimplication,neitheraretheothertwo,andifitis,althoughtheywillbealso,this,ashasbeenshown,isnotwhattheimplicationsigndenotes.Icanconcludefromthefalsityoftheconsequentofaconditionaltothatoftheantecedentonlyifthereisastrictlogicalconnectionbetweentheantecedentandtheconsequentinthefirstplace.Thereisnostrictlogicalconnectionbetween

    Thesunishot

    andNewtonwasaman;

    therefore,itdoesnotfollowstrictlythatifNewtonwasawomanthesunmustbecold.Thevalidityofthesymbolicexpressionmustdependthroughouteitheruponthelogicalinterdependenceofallitscomponentsorofnone.Iftheformeristhecasethenthesignhassurreptitiouslybeengivenadifferentmeaningfromtherelationsbetweenpropositionsintermsofwhichmaterialimplicationhasbeendefined,andthatdoctrinewillnotapply(becauseitcannotguaranteethelogicaldependenceofquponp).Ifthelatteristhecase,thentherelationbetweennoneofthecomponentsisthatofstrictlogicalinterdependence.

    But isdefinedas ,itwillbemaintained,therefore,~qleavesnoalternativeexcept~p;thus,theimplicationisstrict.Butthisisnotastrictimplicationbetweenpropositions,butmerelyaruledeterminingtheuseofasymbol.Thetruthof

    Newtonwasaman

    doesnotdependonthatofThesunishot,

    butmustbeknownindependentlybeforewecanwritebetweenthem.Andwhenknownindependently,itdoesnotentitleustoinferfromitsoppositetothefalsityoftheproposition,"Thesunishot,"althoughweareentitledbytheruletoconnectitscontradictorywiththedenialoftheconsequentbythematerialimplicationsign.Whereweareentitledtoinfer,andthetruthoftheconsequentisdependentuponthatoftheantecedent,theconnectivedoesnotrepresentthelogicalrelationbetweenthepropositions.Itremainstrue,therefore,thatthedoctrineofmaterialimplicationmakessenseonlyifthepropositionstowhichitappliesareallatomicandlogicallyindependent.

  • Wherearealconnectiondoesexist,thedoctrineiswhollyinap-

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    propriate.IfNewtonwasaman,itfollowsofnecessitythathismotherwasawoman,andifhismotherwasnotawomanhecouldhavebeennoman;butalthough"Newtonwasaman'materiallyimplies"Newton'smotherwasawoman'(becausebothhappentobetrue),"Newton'smotherwasnotawoman'alsoimplies"Newtonwasaman"(becausethefirstpropositionhappenstobefalseandthesecondtrue).Thus,

    doesnotholdstrictly,forifqisfalseitstillmateriallyimpliesp,andifqistrueitcanequallybeimpliedmateriallyby~p.Wemayequallywellwrite

    (whenpandqareeitherorbothfalse),

    or

    (whenpandqareeitherorbothtrue);

    andifpistrueandqisfalse,

    isstillcorrecteventhoughpdoesnotmateriallyimplyq.

    Clearly,then,thedoctrineofmaterialimplicationalwayspresupposesthemutuallogicalindependenceofelementarypropositions,asuppositionjustifiedonlyiftheystateactuallyindependentfacts.Inotherwords,theimplicativefunction,whichisfundamentaltothewholesystemofPrincipiaMathematica,presupposeslogicalatomism.Asalmosteverytheoremanddemonstrationinthelogicalcalculusthereelaboratedincludesthisfunction,itwouldbefairtosaythatwithoutit(andsowithoutthepresuppositionofatomism)thecalculuscouldnotoperate.Thesubstitutionofadifferentnotationmakesnodifference;forinstance or involvesthelogicalindependenceofthetruthandfalsityofthepropositionsinpreciselythesamewayas ,fortheincompatibilitysignisdefinedasmeaningnomorethanthateitherorbothpropositionsarefalse.22Whatistrueofmaterialimplicationisequallytrueofformalimplication,whichisthegeneralizedversionofmaterialimplicationandisexpressedbythefunction

    InThePrinciplesofMathematics(Ch.III,40-41),Russellequatesthisformulawiththeuniversalpropositionofthetraditionallogic."Allmenaremortal"issaidtobeequivalentto"Forallvaluesofx,xisamanimpliesxismortal"23Thevariablecannot,however,berestrictedtomen,

  • Page38

    becausethatwouldeliminatetheimplicationbyeliminating"xisaman."Wecandeterminethetruthorfalsityoftheantecedent(xisaman)onlybyinspectionofeachparticularcaseofsubstitution,which,ifxisunrestricted,isaninterminabletask.Wecannotavailourselvesforthispurposeofanygeneralruleofrecognition,suchas"Notreesaremen,"becauseanysuchruleisitselfaformalimplication(inthiscase,"Forallvaluesofx,xisatreeimpliesxisnotaman")andtheestablishmentofitstruthwouldinvolveasimilarinfiniteprocessofinvestigationofparticulars.Thepresumptionthroughoutisthattheatomicpropositionsconcernedpredicatepropertiesofparticularobjectswhicharenotessentiallyrelatedtothoseobjects,foranyparticularmaybesubstitutedforxandthetruthoftheresultingpropositionmustbecheckedbysomeexternalcriterion(for"xisatree''or"xisaman"cannotbeanalytic).Theissueisnotsimplythattheverificationprocedureinvolvesaninfiniteprocess,butthatthetruthconditionfortheconditionalimpliesthatitscomponentsarelogicallyindependentfortheirtruthvalue.Theatomicpropositionsarenotthemselvesessentiallyrelated.Theformalimplicationisnotaconnectionofpropertiesinherentintheirnatures,itissimplyadisjunctionofconjoinedtruthvalues(aswehaveseen).Onlyiftheworldwerecomposedofbareparticulars,externallyrelatedtooneanotherandtotheirproperties,andonlyifthefactsoftheworldcomposedofsuchconjunctionsofparticularswerewithoutanymutualconnection,wouldtherebeneedofaninfiniteprocessofinspectiontoestablishanimplicativerelationbetweentwoclassesofsubjects,sothatapropositionalfunctionlikefxcanbesaidformallytoimplyanotherjxonlyifeverypossiblecasehasbeeninspected.Onceagaintheprinciplesofthelogicalcalculuspresupposesatomicityintheworldandwemustconcludethatthemetaphysicisindispensabletoit,forifthatwereabandoned,thewholedoctrineofimplicationuponwhichthelogicalsystemisbuiltwouldhavetoberevised.

    Sometimesanexcuseisofferedfortheparadoxical(onemightsay,illogical)characterofmaterialimplicationonthegroundthatthePhilonianinterpretationoftheconditionalistheweakestwhichwillsatisfytherequirementthattheruleofdetachmentgivesavalidinference.24Butitisobviousfromtheforegoingthatitdoesnotsatisfythisrequirement;forunlessthereissomeessentialconnectionbetweenpandqwecannotvalidlyargue"Ifpthenq,andp;thereforeq."Weoughtnoteventoassert,"Ifpthenq"exceptontheconditionthatthereisaconnectionbetweenwhatthepropositionsexpress.ThePhilonianinterpretation

  • Page39

    licensestheschema"IfPthenO"whetherornotthereisanyconnection,sothatwemightargue

    Ifpigscannotfly,Socratesismortal;butpigscannotfly,therefore,Socratesismortal.

    Althoughthisargumentisvalidaccordingtothecurrentdoctrine,theconclusion,aslongasitincludestheword"therefore"isfalse,becauseitallegesineffectthatthereasonforSocrates'mortalityisthefiightlessnessofpigs.Accordingly,wehaveanimplicitlyfalseconclusionfromtruepremisses,andthatispreciselywhattheruleofdetachmentissupposedtopreclude.

    Wemight,ofcourse,changetheschemaslightlytotheform,"IfP,andifPthenQ,thenQ":

    Butthisineffectistheemptytautology

    which,ifthePhilonianinterpretationismaintainedthroughout,issubjecttoallthestricturesdiscussedabove,andifitappliesonlytothefirstconditional,thelastexpressionbecomesfalse.Thematerialimplication,

    Ifpigscannotfly,Socratesismortal,

    doesnotimplythatSocratesismortalbecausepigscannotfly.

    Quine,inMethodsofLogic,reservestheterm"implication"foraconditionalwhichis,inhisterminology,"valid";thatis,truewhateverinterpretationisgiventoitsliteralsymbols.25Forexample,ifnointerpretationofpandqcanmaketheconsequentoftheconditionalfalseandtheantecedenttrue,theconditionalisvalidandamountstoanimplication.If,onsomeinterpretations,theconditionalistrueandonothersfalse,itis"consistent,''inQuine'sterminology,butnot"valid";andifnointerpretationmakesittrue,itis"inconsistent".Thus,

    istruehoweverweinterpretpandq.

    "IfCassiusisnothungry,thenCassiusisnotbothleanandhungry."

    i.Ifbothantecedentandconsequentaretrue,thewholeconditionalistrue.ii.Suppose"Cassiusisnothungry"tobefalse,thenitwillmateriallyimplyanyproposition,sotheconditionalremainstrue.

  • Page40

    iii.Suppose"Cassiusislean"tobefalse,thentheconsequentofthecontitionalwillbetrueandwillbeimpliedbyeveryproposition.

    Hence,theconditionalcannotbefalsifiedbyanyinterpretationofitsliterals,anditisavalidimplication.26Nowalogicalschemathatistrueforallinterpretationsofitscomponentliteralsisatautology,soanimplicationturnsouttobeatautologicalconditional.Thisispatentfromtheexamplegiven,for

    andtosaythatCassiusisnothungryistosaythatheisnothungry,whetherornotheisalsolean.

    Note,however,thatthelogicalproofofthevalidityofaconditionalpreservesanddependsuponthePhilonianinterpretation,accordingtowhichthecoincidenttruth-valuesofthecomponents(bothtrue,bothfalse,orantecedentfalseandconsequenttrue)aresufficient.Quine'sversionofimplication,therefore,innowayremovesthepresuppositionthatelementarypropositionsareatomicandhavenologicalinterdependence.Validinference,onthisview,mustberestrictedtotautologiesanditspropersymbolizationoughttobe .ButevensotheanomaliesconsequentuponthePhilonianinterpretationarenotremoved,becauseifpisfalseitwillimplyeveryotherproposition,includingitsowncontradictory,andeveryvalidimplicationwillbeaninstanceofconsequentiamirabilis,inwhichtheconclusionfollowsfromitsowndenial,andthiswillbethecase,moreover,whateverpropositionissubstitutedforp.Suchaconclusion,however,iswhollyunacceptableandshouldleadustodistrustthePhiloniandoctrinerootandbranch.

    Myconclusionisnotsimplythatformalizedlogicisandmustalwaysbetruth-functional,andthattruth-functionallogicimplieslogicalatomism.Itisthatformalizationpresupposestheviewoftheconceptasabstractandofitsextensionasamerecollectionorsetof"objects,"aviewcommontoFrege,Russell,andtheWittgensteinoftheTractatus,aswellastothemajorityofcontemporarylogicians.Truth-functionalvarietiesoflogicmerelyservetoconfirmthisthesis,butanyformalizedsystem,truth-functionalornot,presupposesthistheoryoftheconcept,fromwhichlogicalatomismfollowsnaturally.Torejectlogicalatomismistoholdthatpropositionscanexpressinternalrelationsbetweennon-synonymoustermsandtoadmitthenotionofnon-tautologicalnecessityinlogic.Suchanadmission,Icontend,mustwreckanysystemofformalization,forthereasongivenonpage33abovethatthecommutative,associative,anddistributivelaws

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    wouldnolongerhold.Further,whererelationsareinternaltherecanbenobareparticulars,andinconsequencetheruleofsubstitutionforvariablescannotbemaintained,becausetheirsignificancewouldchangeindifferingcontexts(i.e.,indifferentformulae).

    ThereplacementofmaterialimplicationbystrictimplicationincontemporarymodallogichasmadenodifferencetothepresuppositionsIamimputingtomathematicallogicingeneral.Inextendinggenerallogictoincludemodalforms,C.I.Lewisintroducedstrictimplication(symbolizedby )inplaceofmaterialimplicationinordertoremovetheinconveniencestowhichattentionhasbeendrawn.Buthedidnotsucceed,becausestrictimplicationisdefinedbythesubstitutionof"impossible"forthenegativeinthedefinitionofmaterialimplication.Wherebeforewewrote

    wenowwrite

    andthismakesnodifferencebecauseitisequallytrueofmaterialimplication.Theretoo,itisnotpossibleforthePhilonianconditionaltoholdiftheconsequentisfalsewhiletheantecedentistrue.

    Therelationsbetweenstatementsofpossibilityandnecessitysetoutinmodallogic,becauseitspureformalismmustbemaintained,leaveasidethegroundsbothofpossibility'andofnecessity,justasgeneralformallogicabstractsfromthegroundsofthetruthorfalsityofatomicpropositions.Itisconcernedonlywithformaltransformationsofexpressionsformodalstatements;andexceptfortautologyandself-contradiction,whatmakesapropositionpossibly,actually,ornecessarilytrueisnottheconcernofformallogic.Infact,ifIamright,itspresuppositionisthatnopropositioniseithernecessaryorimpossibleexceptanalytically.Ifitisimpossible,then,forqtobefalseandptrue,ifpstrictlyimpliesq,itisfornootherreasonthanthattheimplicationistautologous.

    Accordinglyittranspires,asbefore,thatanimpossiblepropositionimplieseverypropositionandanecessaryoneisimpliedbyeveryproposition,which,inthecommonmeaningof"implies,"isnotthecase.TheequalityoftheanglesofanequilateralEuclideantriangleisnotimpliedbythemortalityofSocrates,noryetbytheinnocenceofJudasIscariot;andthatthesumoftheanglesofthetriangleexceeds180degreesdoesnotimplythatthewhaleisamammalnoryetthatitisafish.Iflogicalatomismistrue,strictimplicationcannotholdbetweenatomicpropositionsunlessstrictandmaterial(orformal)im-

  • Page42

    plicationamounttothesamething.Thedifference,ifany,canonlybepurelylogical;inotherwords,tobestrict,ornecessary,theimplicationmustbeatautology,whereasamaterialconditionalneedonlybeconsistent.Yetifstrictimplicationissimplyatautologicalconditionaltheconsequencesofthedoctrine,aswehaveseen,becomealtogetherincoherentforordinarythought.27Solongastheconceptisview


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