1st:2nd:3rd:4th:

LogicOverviewI–SyllogisticTerms(seeChapter6)

Everystandard-formcategoricalsyllogismhasexactlythreeterms,towit:Themajortermisthepredicatetermoftheconclusion(P).Theminortermisthesubjecttermoftheconclusion(S).Themiddletermisthetermappearinginbothpremisesbutnotintheconclusion(M).Thepremiseinwhichthemajortermappearsisthemajorpremise.Thepremiseinwhichtheminortermappearsistheminorpremise.Asyllogismis instandard formwhen its threepropositionsare inexactly thisorder:majorpremise,minorpremise,conclusion.Everypropositioninacategoricalsyllogismmustbeoneofthefollowingfour:

AnAproposition—universalaffirmative (e.g.,Allpoliticiansareliars.)

AnEproposition—universalnegative (e.g.,Nopoliticiansareliars.)

AnIproposition—particularaffirmative (e.g.,Somepoliticiansareliars.)

AnOproposition—particularnegative (e.g.,Somepoliticiansarenotliars.)

Themoodofasyllogismisdeterminedbythetypesofitsthreepropositions,AAA,EIO,etc.Thefigureofastandard-formsyllogismisdeterminedbythepositionofitsmiddleterm:

Middletermisthesubjectofthemajorpremiseandthepredicateoftheminorpremise.Middletermisthepredicateofbothpremises.Middletermisthesubjectofbothpremises.Middletermisthepredicateofthemajorpremiseandthesubjectoftheminorpremises.

1.2.3.4.5.6.

LogicOverviewII—ValidFormsoftheCategoricalSyllogism(seeChapter6)

Any syllogistic form is completely determined by the combination of its mood and figure.Thereareexactly15validformsofthecategoricalsyllogism,eachwithauniquename:

Rulesgoverningeveryvalidcategoricalsyllogism:Thesyllogismmustcontainexactlythreeterms,usedconsistently.Themiddletermofthesyllogismmustbedistributedinatleastonepremise.*Ifeithertermisdistributedintheconclusion,itmustbedistributedinthepremises.*Avalidsyllogismcannothavetwonegativepremises.Ifeitherpremiseofthesyllogismisnegative,theconclusionmustbenegative.Fromtwouniversalpremisesnoparticularconclusionmaybedrawn.

1.2.3.4.5.6.7.

LogicOverviewIII—TheSevenStagesofScientificInvestigation:TheScientificMethod(seeChapter13)

IdentifytheproblemDevisepreliminaryhypothesesCollectadditionalfactsFormulatearefinedexplanatoryhypothesisDeduceconsequencesfromtherefinedhypothesisTesttheconsequencesdeducedApplythetheory

1.

LogicOverviewIV—Mill’sMethodsofInductiveInference(seeChapter12)

TheMethodofAgreement:Theonefactororcircumstancethatiscommontoallthecasesofthephenomenonunderinvestigationislikelytobethecause(oreffect)ofthatphenomenon.ABCDoccurtogetherwithwxyz.AEFGoccurtogetherwithwtuv.

Note

*(Note:Atermisdistributedwhenthepropositioninwhichthetermappearsreferstoallmembersoftheclasstowhichthetermrefers.Thus,intheproposition“Allhumansaremortal”theterm“humans”isdistributed,buttheterm“mortal”isnot.)

INTRODUCTIONTOLOGIC

INTRODUCTIONTOLOGIC

FOURTEENTHEDITION

IrvingM.CopiUniversityofHawaii

CarlCohenUniversityofMichigan

KennethMcMahonHawaiiPacificUniversity

Firstpublished2011,2009,2005,2002,1998byPearsonEducation,Inc.

Published2016byRoutledge2ParkSquare,MiltonPark,Abingdon,OxonOX144RN711ThirdAvenue,NewYork,NY10017,USA

RoutledgeisanimprintoftheTaylor&FrancisGroup,aninformabusiness

Copyright©2011,2009,2005,2002,1998Taylor&Francis

Allrightsreserved.Nopartofthisbookmaybereprintedorreproducedorutilisedinanyformorbyanyelectronic,mechanical,orothermeans,nowknownorhereafterinvented,includingphotocopyingandrecording,orinanyinformationstorageorretrievalsystem,withoutpermissioninwritingfromthepublishers.

Notice:Productorcorporatenamesmaybetrademarksorregisteredtrademarks,andareusedonlyforidentificationandexplanationwithoutintenttoinfringe.

Creditsandacknowledgmentsborrowedfromothersourcesandreproduced,withpermission,inthistextbookappearonappropriatepagewithintext(oronpage607).

Manyofthedesignationsbymanufacturersandsellertodistinguishtheirproductsareclaimedastrademarks.Wherethosedesignationsappearinthisbook,andthepublisherwasawareofatrademarkclaim,thedesignationshavebeenprintedininitialcapsorallcaps.

ISBN-13:9780205820375(hbk)

LibraryofCongressCataloging-in-PublicationDataCopi,IrvingM.Introductiontologic.—14thed./IrvingM.Copi,CarlCohen,K.D.McMahon.p.cm.Includesindex.

1.Logic—Textbooks.I.Cohen,Carl,1931-II.McMahon,K.D.(KennethD.)III.Title.BC108.C692011160—dc22

2010036272

WededicatethisfourteentheditionofIntroductiontoLogictothemanythousandsofstudentsandtheirteachers,athundredsofuniversitiesintheUnitedStatesandaroundtheworld,whohavereliedonearliereditionsofthebook,andhavegreatlyhelpedtoimproveit,overfivedecades.

PartI

chapter1

chapter2

chapter3

chapter4

PartII

chapter5

chapter6

chapter7

chapter8

chapter9

chapter10

PartIII

chapter11

chapter12

chapter13

chapter14

BriefContents

LOGICANDLANGUAGESECTIONAREASONING

BasicLogicalConcepts

AnalyzingArguments

SECTIONBINFORMALLOGIC

LanguageandDefinitions

Fallacies

DEDUCTION

SECTIONACLASSICALLOGIC

CategoricalPropositions

CategoricalSyllogisms

SyllogismsinOrdinaryLanguage

SECTIONBMODERNLOGIC

SymbolicLogic

MethodsofDeduction

QuantificationTheory

INDUCTION

SECTIONAANALOGYANDCAUSATION

AnalogicalReasoning

CausalReasoning

SECTIONBSCIENCEANDPROBABILITY

ScienceandHypothesis

Probability

PartI

chapter1

1.11.21.31.41.51.6

chapter2

2.12.22.32.4

chapter3

3.13.23.33.43.53.6

chapter4

4.14.24.34.44.5

ContentsForewordPrefaceAcknowledgmentsAVeryBriefHistoryofLogic

LOGICANDLANGUAGESECTIONAREASONING

BasicLogicalConcepts

WhatLogicIsPropositionsandArgumentsRecognizingArgumentsArgumentsandExplanationsDeductiveandInductiveArgumentsValidityandTruth

AnalyzingArguments

ParaphrasingArgumentsDiagrammingArgumentsComplexArgumentativePassagesProblemsinReasoning

SECTIONBINFORMALLOGIC

LanguageandDefinitions

LanguageFunctionsEmotiveLanguage,NeutralLanguage,andDisputesDisputesandAmbiguityDefinitionsandTheirUsesTheStructureofDefinitions:ExtensionandIntensionDefinitionbyGenusandDifference

Fallacies

WhatIsaFallacy?ClassificationofFallaciesFallaciesofRelevanceFallaciesofDefectiveInductionFallaciesofPresumption

4.6

PartII

chapter5

5.15.25.35.45.55.65.75.8

chapter6

6.16.26.36.46.5

chapter7

7.17.27.37.47.57.67.77.8

chapter8

8.18.28.38.48.5

FallaciesofAmbiguityLogicintheRealWorld

DEDUCTION

SECTIONACLASSICALLOGIC

CategoricalPropositions

TheTheoryofDeductionClassesandCategoricalPropositionsTheFourKindsofCategoricalPropositionsQuality,Quantity,andDistributionTheTraditionalSquareofOppositionFurtherImmediateInferencesExistentialImportandtheInterpretationofCategoricalPropositionsSymbolismandDiagramsforCategoricalPropositions

CategoricalSyllogisms

Standard-FormCategoricalSyllogismsTheFormalNatureofSyllogisticArgumentVennDiagramTechniqueforTestingSyllogismsSyllogisticRulesandSyllogisticFallaciesExpositionoftheFifteenValidFormsoftheCategoricalSyllogismAppendix:DeductionoftheFifteenValidFormsoftheCategoricalSyllogism

SyllogismsinOrdinaryLanguage

SyllogisticArgumentsReducingtheNumberofTermstoThreeTranslatingCategoricalPropositionsintoStandardFormUniformTranslationEnthymemesSoritesDisjunctiveandHypotheticalSyllogismsTheDilemma

SECTIONBMODERNLOGIC

SymbolicLogic

ModernLogicandItsSymbolicLanguageTheSymbolsforConjunction,Negation,andDisjunctionConditionalStatementsandMaterialImplicationArgumentFormsandRefutationbyLogicalAnalogyThePreciseMeaningof“Invalid”and“Valid”

8.68.78.88.98.10

chapter9

9.19.29.39.49.59.69.79.89.99.109.119.12

chapter10

10.110.210.310.410.510.610.7

PartIII

chapter11

11.111.211.311.4

chapter12

12.112.2

TestingArgumentValidityUsingTruthTablesSomeCommonArgumentFormsStatementFormsandMaterialEquivalenceLogicalEquivalenceTheThree“LawsofThought”

MethodsofDeduction

FormalProofofValidityTheElementaryValidArgumentFormsFormalProofsofValidityExhibitedConstructingFormalProofsofValidityConstructingMoreExtendedFormalProofsExpandingtheRulesofInference:ReplacementRulesTheSystemofNaturalDeductionConstructingFormalProofsUsingtheNineteenRulesofInferenceProofofInvalidityInconsistencyIndirectProofofValidityShorterTruth-TableTechnique

QuantificationTheory

TheNeedforQuantificationSingularPropositionsUniversalandExistentialQuantifiersTraditionalSubject–PredicatePropositionsProvingValidityProvingInvalidityAsyllogisticInferenceLogicintheRealWorld

INDUCTION

SECTIONAANALOGYANDCAUSATION

AnalogicalReasoning

InductionandDeductionRevisitedArgumentbyAnalogyAppraisingAnalogicalArgumentsRefutationbyLogicalAnalogy

CausalReasoning

CauseandEffectCausalLawsandtheUniformityofNature

12.312.412.5

chapter13

13.113.213.313.4

chapter14

14.114.214.3

InductionbySimpleEnumerationMethodsofCausalAnalysisLimitationsofInductiveTechniques

SECTIONBSCIENCEANDPROBABILITY

ScienceandHypothesis

ScientificExplanationScientificInquiry:HypothesisandConfirmationEvaluatingScientificExplanationsClassificationasHypothesis

Probability

AlternativeConceptionsofProbabilityTheProbabilityCalculusProbabilityinEverydayLifeLogicintheRealWorld

Appendix:Graduate-LevelAdmissionTestsSolutionstoSelectedExercisesPhotocreditsGlossary/Index

L

Foreword

“Inarepublicannation,whosecitizensaretobeledbypersuasionandnotbyforce,theartofreasoningbecomesofthefirstimportance.

—ThomasJefferson”ogichassometimesbeendefinedasthescienceofthelawsofthought.Thisisinaccurate.Thinkingisoneoftheprocessesstudiedbypsychologists.Ifthoughtreferstoanyprocess

thatoccursinpeople’sminds,notallthoughtisanobjectofstudyforthelogician.Thus,onemaythinkofanumberbetweenoneandtenwithoutdoinganyreasoningaboutit.Onemayalsoremember, imagine, free-associate, or perform any of a number of mental processes. Allreasoningisthinking,butnotallthinkingisreasoning.Thelawsthatdescribethemovementsofthemindarepsychologicallawsratherthanlogicalprinciples.Todefinelogicinthiswayistoincludetoomuch.

Logichasalsobeencalledthescienceofreasoning.Thisisbetter,butreasoningisakindof thinking in which inference takes place and conclusions are drawn from premises. Thisprocessisextremelycomplex,characterizedbyacombinationoftrialanderror,occasionallyilluminatedbyflashesofinsight.Logiciansarenotconcernedwiththewaysinwhichthemindarrives at its conclusions in the process of reasoning; they are concerned only with thecorrectnessof thecompletedprocess:Doestheconclusionreached followbynecessity fromthe premises? The study of the methods and principles used to distinguish correct fromincorrectreasoningisthecentralissuewithwhichlogicdeals.

Reasonistheinstrumentonwhichonemustdependwhenreliablejudgmentsareneeded.Nonrational instruments—feelings, beliefs, habits, hunches, and the like—are commonlyemployed,butwhenagreatdealdependsonthejudgmentsonemakes—whenonemustdecidehow to act in complicated circumstances, or determine what is true in matters that have aseriousimpact—reasonisourbestrecourse;nothingcanreplaceit.

There are rationalmethods,methodswell tested and confirmed, for determiningwhat istrue.Therearewell-established,rationaltechniques,fordrawingnewinferencesfromwhatisalready known to be true.Our ignorance is vast, and therefore people often resort to someauthorityinreachingjudgment—buttheneedforreasoncannotbeescapedeventhen,becauseonemust decidewhich authorities deserve respect.Every serious intellectual pursuit comesultimatelytorelyonreasoning,becausethereisnothingthatcansuccessfullyreplaceit.

Bynaturehumansareendowedwithpowersofreasoning.Logicisthestudyoftheusesofthosepowers. Intuitively,wemayhave longactedon soundprinciples,onlypartlygrasped.With care, these principles canbe brought to the surface, formulatedprecisely, and appliedwithconfidencetoproblemssolvablebyreason.Throughstudyinglogic,peoplecomefirsttorecognize their ownnative capacities, then to learn to strengthen them throughpractice.Thestudyoflogichelpsonetoreasonwellbyilluminatingtheprinciplesofcorrectreasoning.

Whateverthesphereinwhichknowledgeissought—whetherinscience,politics,orinthe

conductofone’sprivatelife—logicisusedtoreachwarrantedconclusions.Intheformalstudyoflogic,withwhichthisbookisconcerned, thestudentwill learnhowtoacquire truthsandhowtoevaluatecompetingclaims for truth, tocritiquearguments, recognize inconsistencies,detect logical fallacies, and construct formal arguments according to demonstrably validinferencepatterns.Insum,thestudyoflogicwillhelpthestudenttoreasonmorecarefullyand,ingeneral,tothinkandactmorerationally.

Ideally,everycollegecourseshouldcontributetothisend,yetmanydonot.Muchthatistaught in college classes soon grows out of date. But the skills of accurate thinking neverbecomeobsolete,andthedevelopmentoftheseskillsliessquarelywithintheprovinceofthestudyoflogic.Thestudyoflogichelpsustoidentifyargumentsthataregoodandtounderstandwhy they are good. The study of logic helps us to identify arguments that are bad and tounderstand why they are bad. No study is more useful or more widely relevant to seriousconcernsthanthis.

This considered assurance we give to our readers: A command of the fundamentalprinciples of correct reasoning,which the study of this book promotes,willmake a deeplysatisfying,significant,andpermanentcontributiontoone’sintellectuallife.

E

■■

■

PrefacearliereditionsofIntroductiontoLogichavebeenwarmlyreceivedbyourphilosophicalcolleaguesaroundtheworld.JamesDruleyfromReedleyCollege,Madera,CA,whowas

oneofthereviewersofthetwelfthedition,wrote:“Severaltimes,afterreadingapartofthetextIhavethought,‘Thatcouldnothavebeenwrittenanymoreinsightfullyorelegantly; thatcouldnothavebeenexplainedbetter.’”Wearegratifiedbysuchkindwords,ofcourse,butweare not content. As a consequence, a number of alterations have beenmade in an effort torefine,polish,andimproveanalreadyexcellenttext.CertainfallacieshavebeenreclassifiedinChapter 4, and the flowchart in Chapter 6 has been restructured. In Chapter 8 we haveprovidedandexplainedalternativesymbols thatareused inother texts; inaddition,muchofthematerialinChapters8–10hasbeenreorganized.Somearguments,definitions,explanations,and formulations have been tightened up and clarified, while the essential structure andsubstanceofthebookhavebeenretained.

NewtoThisEdition

InPartOne,thebasicconceptsoflogicarepresented.Weexplorethedifficultiesencounteredineverydayusesoflanguage,andthedifferentfunctionsoflanguage.Weexplainthenatureandfunctionsofdefinitionsinordinarydiscourse,andthenidentifyandexhibitthemanyinformalfallaciesthatarecommonlyencountered.InPartTwothemethodsofdeductivereasoningarepresentedandanalyzed.Herewefirstgiveanaccountoftraditionalorclassicalsyllogistics,and then introduce the more powerful notation and techniques of modern symbolic logic.Finally, in Part Three, the techniques of inductive logic are presented, beginning with theappraisalof simpleanalogicalargumentsandproceeding toananalysisofcausal reasoning,and the canons of scientificmethod.We concludewith an account of alternative theories ofprobability,andtheusesofthetheoremsintheelementarycalculusofprobability.

AshorthistoryoflogicappearsjustbeforethebeginningofPartOne.Briefbiographiesofanumberofthegreatlogicianshavebeenincludedthroughoutthechapters,bothinordertohistoricallycontextualizelogic,aswellastoindicatehowcontributionstologicarenotsomethingremoteanddetachedfromlife,butanexpressionofthelivesandpassionsofveryhumanbeings.AnewAppendixdescribesthepracticalapplicationsoflogictothetakingofadmissionstests,suchastheGRE(GraduateRecordExamination),LSAT(LawSchoolAdmissionTest),GMAT(GraduateManagementAdmissionTest),andMAT(MillerAnalogiesTest).

Finally,IntroductiontoLogicinallofitseditionshasbeenrichwithillustrativematerialsandexercises taken from events and controversies in real life, from history and some classicalsources,butmainlyfromcontemporaryperiodicalsandbooks.Wetakeprideinthefactthat,asourreviewershavenoted,thosestudyingIntroductiontoLogicareinescapablyintroducedto

a verywide range of intellectual concerns and thus learnmuchmore than logic. Exhibitingargumentsandtheories(goodandbad)byillustratingthemwithgenuinecontroversies in theworldofcollegestudents,ratherthanwithillustrationsartificiallydevisedforthepurpose,hasbeenourcontinuingconcern.Logicaltheoryismostfullygraspedwhenitisvividlyappliedtocontemporaryhumanaffairs.InthiseditionofIntroductiontoLogicwehaveaddedmanyfreshillustrations,replacingthosemoredated,alongwithsomenewargumentsarisinginconnectionwith the lively issuesof the firstdecadeof the twenty-first century. In the selectionof theseillustrations and exercises we seek scrupulously to avoid partisanship. On all sides ofcontroversial issues, good arguments, and bad ones, may appear. Support for one view oranother in current controversy is not our proper business; the understanding and analysis ofargumentsis.

InalleditionsofIntroductiontoLogicwestrovetoachievethatcombinationofaccuracy,clarity,andpenetrationthathasalwaysbeenourobjective.Tothisendwehavereliedonthesupportandadviceofstudentsandinstructorswhousethebookandwhoaresensitivetoitsshortcomings.Weconclude, therefore,withanearnest invitation toour readers to joinus inadvancingthisnever-endingproject.Senduscorrectionsasneeded,andsuggestionsofeverykind.Yourcontributions,warmlywelcome,maybemostconvenientlyaddressedtoCarlCohenatccohen@umich.eduorKennethD.McMahonatkmcmahon@campus.hpu.edu.Thefeedbackfrom students and instructors who rely on Introduction to Logic has helped to make it theworld’smostwidelyusedbookinthestudyoflogic.Wewillreceiveyourresponsestoitwithrespectandheartfeltgratitude.

CarlCohenTheUniversityofMichigan,AnnArbor

KennethMcMahonHawaiiPacificUniversity,Honolulu

ANoteonColor

Logic is often perceived as a “black-and-white” subject. However, in this edition ofIntroductiontoLogicwehave introducedcolor.Colorplaysa role inguiding theeyemorereadily to sections, subsections, and text boxes, but it also serves important pedagogicalfunctions.InChapter6, for instance,colorhasbeenused tostrengthen theapplicationof theVenndiagramtechniquefortheevaluationofcategoricalsyllogisms.Masteryofthistechniqueismorereadilyachievedifthecirclesrepresentingthesubject,predicate,andmiddletermsofcategoricalsyllogismsareconsistentlypositionedrelativetoeachother.Accordingly,previouseditions maintained a consistent and predictable placement. This edition strengthens thosespatial clues by consistently assigning a specific color to each circle. This provides anadditionalvisualreminderofthenatureofeachcircle.

F

Acknowledgmentsor accurate corrections, penetrating observations, and wise suggestions in very greatnumber,twopersonsdeserveourheartfeltthanks:

Prof.VictorCosculluela,PolkStateCollege,WinterHaven,FloridaMr.ManuelSanchezNazario,Chicago,Illinois

Contributors to this edition have been very numerous. College students, as well asinstructors,havewrittentosuggestimprovements,topointoutambiguitiesorinaccuracies,tonote typographical errors, to suggest useful illustrative materials. All receive our directresponse,ofcourse;butwetakesatisfactioninlistingherealsothenamesofsomeofthosetowhom we are indebted for contributions large and small to this fourteenth edition ofIntroductiontoLogic:Prof.JohnM.Abbarno,D’YouvilleCollege,Buffalo,NewYorkProf.BenjaminAbellera,DCFFoundation,SilverSpring,MarylandDr.GeraldAbrams,UniversityofMichigan,AnnArbor,MichiganMr.RussellAlfonso,UniversityofHawaii,Honolulu,HawaiiMr.WyattDeanAmmon,HamlineUniversity,St.Paul,MinnesotaMs.TamaraAndrade,AnnArbor,MichiganEmilBadici,UniversityofFlorida,Gainesville,FloridaStephenBarnes,NorthwestVistaCollege,SanAntonio,TexasMr.JasonBates,UniversityofMichigan,AnnArbor,MichiganMr.MaximilianBauer,AnnArbor,MichiganMr.GeorgeBeals,MichiganBibleSchool,Plymouth,MichiganDrewBerkowitz,BridgewaterStateUniversity,Bridgewater,MassachusettsMs.AmeliaBischof,IthacaCollege,Ithaca,NewYorkMr.EvanBlanchard,AnnArbor,MichiganMr.BenjaminBlock,AnnArbor,MichiganProf.JefferyBorrowdale,CuestaCollege,SanLuisObispo,CaliforniaMr.JohnBransfield,UniversityofConnecticut,Storrs,ConnecticutMr.NicholasBratton,Seattle,WashingtonTeresaBritton,EasternIllinoisUniversity,Charleston,IllinoisProf.KeithBurgess-Jackson,UniversityofTexasatArlington,TexasMr.BryanCampbell,VanderbiltUniversity,Nashville,TennesseeProf.RebeccaCarr,GeorgeWashingtonUniversity,Washington,D.C.Prof.SidneyChapman,RichlandCollege,Dallas,TexasMr.Kun-HungChen,NationalTaiwanUniversity,TaipeiProf.ZoeClose,GrossmontCollege,ElCajon,CaliforniaJenniferCaseldine-Bracht,IndianaUniversity/PurdueUniversity,Ft.Wayne,IndianaProf.WilliamS.Cobb,UniversityofMichigan,AnnArbor,MichiganProf.MalcolmS.Cohen,UniversityofMichigan,AnnArbor,MichiganMr.KeithColeman,UniversityofKansas,Lawrence,KansasMs.MeredithCrimp,AnnArbor,MichiganMr.DennisA.DeVera,Dept.ofSocialSciences,CAS,CLSU,PhilippinesMr.JoshuaDeYoung,UniversityofMichigan,AnnArbor,MichiganJamesDruly,ReedleyCollege,MaderaCenter,Madera,CaliforniaProf.ElmerH.Duncan,BaylorUniversity,Waco,TexasR.ValentineDusek,UniversityofNewHampshire,Durham,NewHampshireMr.EricDyer,UniversityofMichigan,AnnArbor,MichiganMr.KumarEswaran,TempleUniversity,Philadelphia,PennsylvaniaMr.JoshuaFayWilliamFerraiolo,SanJoaquinDeltaCollege,Stockton,California

Ms.MorganFett,AnnArbor,MichiganProf.DanielE.Flage,JamesMadisonUniversity,Harrisonburg,VirginiaJasonFlato,GeorgiaPerimeterCollege,Clarkston,GeorgiaProf.KevinFunchion,SalemStateCollege,Salem,MassachusettsMs.ElizabethGartner,UniversityofMichigan,AnnArbor,MichiganProf.FaithGielow,VillanovaUniversity,Villanova,PennsylvaniaProf.JosephGilbert,StateUniversityofNewYorkatBrockport,NewYorkMr.AnandGiridharadas,Mumbai,IndiaProf.SidneyGospe,UniversityofWashington,Seattle,WashingtonMr.MichaelGraubert,London,EnglandMr.JosephGrcic,IndianaStateUniversity,TerreHaute,IndianaDr.RobertA.Greene,UniversityofMichigan,AnnArbor,MichiganMs.JaniceGrzankowski,Cheektowaga,NewYorkMr.MatthewHampel,UniversityofMichigan,AnnArbor,MichiganProf.AllanHancock,CuestaCollege,SanLuisObispo,CaliforniaProf.WarrenHarbison,BoiseStateUniversity,Boise,IdahoMr.AbdulHalimB.AbdulKarim,oftheNationalUniversityofSingaporeProf.ClareSwiftHeiller,ofBakersfieldCollege,Bakersfield,CaliforniaProf.JeremiahJoaquin,DeLaSalleUniversity,Manila,PhilippinesProf.RoyceJones,IllinoisCollege,Jacksonville,IllinoisProf.GaleJustin,CaliforniaStateUniversityatSacramentoMr.RoryKraft,Jr.,MichiganStateUniversity,EastLansing,MichiganProf.RichardT.Lambert,CarrollCollege,Helena,MontanaMr.CharlesLambros,StateUniversityofNewYorkatBuffaloMr.AndrewLaZella,HamlineUniversity,St.Paul,MinnesotaProf.GeraldW.Lilje,WashingtonStateUniversity,Pullman,WashingtonMr.JamesLipscomb,Tarrytown,NewYorkMs.LindaLorenz,AnnArbor,MichiganProf.E.M.Macierowski,BenedictineCollege,Atchison,KansasMs.ErikaMalinoski,UniversityofMichigan,AnnArbor,MichiganProf.KrishnaMallik,BentleyCollege,Waltham,MassachusettsMr.NeilManson,UniversityofAberdeen,UnitedKingdomProf.EdwinMartin,NorthCarolinaStateUniversity,Raleigh,NorthCarolinaProf.MichaelJ.Matthis,KutztownUniversity,Kutztown,PennsylvaniaProf.GeorgeMavrodes,UniversityofMichigan,AnnArbor,MichiganProf.LeemonMcHenry,WittenbergUniversity,Springfield,OhioMr.ChristopherMelley,Univ.ofMaryland,AsianDivision,Okinawa,JapanMs.MedelineMetzger,AnnArbor,MichiganMr.DavidA.Mihaila,Honolulu,HawaiiProf.RichardW.Miller,UniversityofMissouriatRolla,MissouriProf.MasatoMitsuda,SanFranciscoStateUniversity,SanFrancisco,CaliforniaMs.ErinMoore,OhioStateUniversity,Columbus,OhioMs.SusanMoore,Fairgrove,MichiganProf.KippyMyers,Freed-HardemanUniversity,Henderson,TennesseeMr.MichaelNorth,UniversityofMichigan,AnnArbor,MichiganDavidO’Connor,SetonHallUniversity,SouthOrange,NewJerseyMr.JohnOltean,AnnArbor,MichiganProf.SumerPek,UniversityofMichigan,AnnArbor,MichiganProf.RayPerkins,PlymouthStateCollege,Plymouth,NewHampshireMr.RobertPicciotto,Gastonia,NorthCarolinaProf.HowardPospesel,UniversityofMiami,CoralGables,FloridaMr.WaynePraeder,oftheU.S.ChessFederationMs.DeborahPugh,Stanford,CaliforniaProf.DennisP.Quinn,St.VincentCollege,Latrobe,PennsylvaniaMr.NicholasQuiring,UniversityofMichigan,AnnArbor,MichiganMr.ChrisRaabe,ofYakatut,AlaskaMr.JayRapaport,UniversityofMichigan,AnnArbor,MichiganDr.PatrickRarden,AppalachianStateUniversity,Boone,NorthCarolina

Prof.LeeC.Rice,MarquetteUniversity,Milwaukee,WisconsinDr.ThomasRiggins,NewYorkUniversity,NewYorkCityDavidC.Ring,OrangeCoastCollege,CostaMesa,CaliforniaProf.BlaineB.Robinson,SouthDakotaSchoolofMines,RapidCity,SouthDakotaEricSaidel,GeorgeWashingtonUniversity,Washington,D.C.RudySaldana,CitrusCollege,Glendora,CaliforniaMr.MiltonSchwartz,Esq.,NewYorkCityMr.AmitSharma,ofV.S.NiketanCollege,Kathmandu,NepalProf.EmeritusAlbertC.Shaw,RowanCollege,Glassboro,NewJerseyProf.EdwardSherline,UniversityofWyoming,Laramie,WyomingMr.AmjolShrestha,HawaiiPacificUniversity,Honolulu,HawaiiMs.LaurenShubow,UniversityofMichigan,AnnArbor,MichiganMr.JasonA.Sickler,UniversityofNorthDakota,GrandForks,NorthDakotaMs.StefanieSilverman,UniversityofMichigan,AnnArbor,MichiganProf.MichaelSlattery,VillanovaUniversity,Villanova,PennsylvaniaDr.BarbaraM.Sloat,UniversityofMichigan,AnnArbor,MichiganMahadevanSrinivasan,UniversityofTennessee,Knoxville,TennesseeProf.JamesStewart,BowlingGreenStateUniversity,BowlingGreen,OhioMr.PaulTang,CaliforniaStateUniversity,LongBeach,CaliforniaMr.AndrewTardiff,NorthKingstown,RhodeIslandMarkL.Thomas,BlinnCollege,Bryan,TexasDavidA.Truncellito,GeorgeWashingtonUniversity,Washington,DCMs.MeghanUrisko,AnnArbor,MichiganMr.J.A.VandeMortel,CerritosCollege,Norwalk,CaliforniaDavidVessey,GrandValleyStateUniversity,Allendale,MichiganMr.ChrisViger,UniversityofWesternOntarioMr.RoyWeatherford,UniversityofSouthFlorida,Tampa,FloridaProf.AllenWeingarten,Morristown,NewJerseyProf.WarrenWeinstein,CaliforniaStateUniversityatLongBeach,CaliforniaMs.JessicaWheeler,Springfield,MissouriProf.PhilipH.Wiebe,TrinityWesternUniversity,BritishColumbia,CanadaMr.MichaelWingfield,LakeDallas,TexasMr.IsaiahWunsch,UniversityofMichigan,AnnArbor,MichiganMs.CynthiaYuen,AnnArbor,MichiganMariaZaccaria,GeorgiaPerimeterCollege,Dunwoody,Georgia

PAVeryBriefHistoryofLogic

hilosophybeginswithwonder.Whatistheworldmadeof?Wheredoesitcomefrom?Whyarewehere?Thespeculationsofprimitivepeopleswereoftenimaginative,but

wereunfounded,irrational.PhilosophyaswethinkofittodaydidnotariseuntiltheGreekphilosophersofthesixthcenturyBCEsoughtsomeoverridingtheoriesabouttheworld.Isthereonestuffofwhichtheworldismade?Oneprinciplethatisfundamentalthroughout?

WethinkofSocratesandPlatoasthegreatfiguresinthebirthofWesternphilosophy,andwestudythemstilltoday.Theirgreatnessliesinpartintheireffortstobringthingsintointellectualorder—toprovide,oratleasttoseek,somecoherentsystemthatcanexplainwhythingsarethewaytheyare.ButevenbeforeSocratestherehadbeendeepthinkers—Thales,Parmenides,Heraclitus,Democritusandotherswhohadproposedassortedaccountsofthefundamentalstuffoftheworld,orofthefundamentalprinciplebywhichallisgoverned.

Theyweretheorizing,notmerelyguessing—buttherewasnorealscienceintheseearlyspeculations.Dogmaticsuppositions,supernaturalforces,thegods,ancientmythsandlegendshadalwaystobecalledupon.Asphilosophygraduallymaturedtheregrewthedrivetoknow,todiscoverprinciplesthatcouldberelieduponingivingexplanations.

Thuslogicbegins.Judgmentsaresoughtthatcanbetestedandconfirmed.Themethodswithwhichwediscoverandconfirmwhateverwereallyknowneedtobeidentifiedandrefined.Wemustreasonaboutthings,andwehungertounderstandtheprinciplesofrightreasoning.

Thatfirstclimbfromchaoticthoughtintosomewell-orderedsystemofreasoningwasanenterpriseofextraordinarydifficulty.Itsfirstmaster,Aristotle(seep.3),havingdevelopedasystemwithinwhichtheprinciplesofreasoningcouldbepreciselyformulated,wasrightlyheldinawebyrationalthinkersfromhisdaytoours.Hewasthefirstgreatlogician.

Aristotleapproachedreasoningasanactivityinwhichwefirstidentifyclassesofthings.Wethenrecognizetherelationsamongtheseclasses.Thenwecanmanipulatethepropositionsinwhichtheserelationsarespecified.Thefundamentalelementsofreasoningare,hethought,thegroupsthemselves,thecategoriesintowhichwecanputthings.Hethereforedistinguishedtypesofcategoricalpropositions(e.g.,“AllXsareYs”—auniversalaffirmativeproposition;“SomeYsarenotXs”—aparticularnegativeproposition;andsoon)andwiththoseunderstoodwecanreasonimmediatelytoconclusionsabouttherelationsamongthesepropositions(e.g.,“IfsomeXsareYs,thenitcannotbetruethatnoYsareXs”).Moreimportantly,bycombiningcategoricalpropositionsinvolvingthreeterms(say,Xs,Ys,andZs)invariousways,wecanreasonaccuratelybyconstructingcategoricalsyllogisms(e.g.,“IfallXsareYs,andsomeXsareZs,itmustbethatsomeZsareYs”).Usingsuchtechniques,agreatsystemofdeductivelogiccanbebuilt,aswillbeshowninChapters5,6and7ofthisbook.

AcenturyafterAristotletheworkoftheStoicphilosopher,Chrysippus(seep.7),

carriedlogicalanalysistoahigherlevel.ThefundamentalelementsofreasoningweretakentobenottheAristoteliancategories,butpropositions,theunitswithwhichwecanaffirmordenysomestatesofaffairs(e.g.,“XisinAthens,”or“XisinSparta”).Wecanthendiscoverthelogicalrelationsamongpropositions:“IfXisinAthensthenXisnotinSparta.”Wecanthenidentifyelementaryargumentsthatdependuponthesevariousrelations:“IfXisinAthensthenXisnotinSparta.XisinAthens.ThereforeXisnotinSparta.”Theformofthissimpleargument,calledmodusponens,iscommonanduseful;manyothersuchelementaryformsmaybeidentifiedandappliedinrationaldiscourse,aswewillseeinlaterportionsofthisbook.

Withtheseadvancesitsoonbecomesclearthatthevalidityofadeductiveargument,thesoliditywithwhichaconclusionmaybeinferredifthepremisesaretrue,dependsupontheformoftheargument,itsshaperatherthanitscontent—oraslogicianssay,itssyntacticfeaturesratherthanitssemanticcontent.Modusponens,andeverysuchargumentform,canhaveanunlimitednumberofrealizations,orinstances.Theconsequencesofthisformalnatureofvalidityremainedtobeinvestigated.WiththedeclineoftheRomanEmpire,theworkoftheGreeklogicianshadbeenpreservedbyMuslimscholars,mostnotablyAl-Farabi(c.872-c.950),whowrote,inBaghdad,acommentaryontheworksofAristotle,andcametobecalled“theSecondTeacher,”secondonlytoAristotleinbreadthanddepthoflearning.HewasfollowedbythegreatMuslimpolymath,IbnSina,knownbyhisLatinizedname,Avicenna.TheirscholarshipeventuallypenetratedandrefreshedWesternthought.Syntacticformscameagaintobeofcentralinterestinlogicinthetwelfthcentury,inFrance,withtheworkofthemonk,PeterAbelard(1079–1142).

InEnglandthegreatlogicalfigureofthoseearlymodernyearswasWilliamofOckham(1287–1348).Heidentifiedsomeofthetheoremsmorepreciselyformulatedmanyyearslaterbythemathematicallogician,AugustusDeMorgan;DeMorgan’stheoremswewillencounterandapplyinthesecondpartofthisbook.Ockhamsoughttoridmetaphysics,inwhichhewaschieflyinterested,ofuselessconcepts.Heurgedthatwhenatermornotionhasbeenshownfruitlessitshouldbesimplycutoutanddiscarded.Thisimperativeprinciple,“Ockham’srazor,”remainsacommonguideline:Inallrationalthinking,entitiesmustnotbemultipliedbeyondnecessity.

DeductivelogichadlargelybegunwithAristotle’scompiledtreatises,TheOrganon.Thatlogicallowedandencouragedthepowerfulmanipulationofwhatisalreadyknown,andthatisindeedextremelyuseful.However,thelong-studiedanalysisofpropositionsandtheirrelationsdidnotprovidethestuffofnewknowledge,desperatelyneededandwidelysoughtintheearlymoderncenturies.Whattheintellectualworldrequired,manythought,wasanewOrganon.ThatNovumOrganumwaspublishedbyFrancisBacon(1561–1626)inEnglandin1620.TheBaconianmethodaimedtocodifytheproceduresusedbyscientistswheninvestigatingallnaturalthings.Called“thefatherofempiricism”,Bacon,withotherpioneersofthescientificrevolutioninastronomyandmedicine,didnotrejecttheworkofclassicallogicians,butsupplementedthatworkbyformulatingthemethodsthatmakepossibletheacquisitionofempiricaltruths.Facts—whatwelearnabouttheworld—constitutethepremisesuponwhichdeductiveargumentscanbebuilt.Thesewerethefirstgreatstepsinformulatingtheprinciplesofinductivelogic.

Itwastimetogatherthethreadsoflogicalanalysis,deductiveandinductive,intoonecoherentfabric.Thefirsttextbookoflogic(Logic,ortheArtofThinking),waspublishedanonymouslyin1662byagroupknownasthePort-Royallogicians.Theprincipalauthors,AntoineArnauld(famousforhispublisheddisputeswithDescartes)andPierreNicole,werejoinedbyBlaisePascal(1623–1662),agreatFrenchmathematicianwhohadinvented,whileateenager,afunctioningmechanicalcalculator.Pascalwasalsooneoftheoriginatorsofthetheoryofprobability—asphereoflogicthatwewillenterinthefinalchapterofthisbook.Othertextbooksfollowed,includingLogick,ortheRightUseofReason(1725)byIsaacWatts;thenLogic(1826)byRichardWhately.Then,in1843,therewaspublishedinEnglandoneofthegreatestofalllogictextbooks:ASystemofLogic,byJohnStuartMill(1806–1873).Inthisworkthetechniqueswithwhichweuncoverandconfirmcausalconnectionsintherealworldwereforthefirsttimesetforthinaccuratedetail.Mill’smethods,hisstillrelevantcontributionstothestudyofinductivelogic,wediscussatlengthinPartIIIofthisbook.

Indeductivelogicmuchcreativeworkremainedtobedone.Reasoningwasknowntobeburdenedbytheambiguitiesandimprecisionofordinarylanguage.Oneofthegreatestofearlymodernthinkers,GottfriedWilhelmLeibniz(1646–1716),sethimselfthetaskofovercomingthesedeficienciesbydevelopingamathematicallyexactsymboliclanguage,oneinwhichconceptsmightbeexpressedwithunambiguousclarity.Leibniz(alsooneoftheindependentinventorsoftheinfinitesimalcalculus)hadenvisionedasortoflogicmachine—onewithwhichoperationsofalogicalnaturemightbeperformedefficientlyandaccurately,ascanbedoneinthealgebrathatheknewwell.Thatgreatlogicmachineheneverproduced,buthisdreamofitmaybeseenastheforeshadowingofthemodernelectroniccomputer.

AmajoradvancetowardLeibniz’sgoalwasmadebytheEnglishlogicianGeorgeBoole(seep.189),whodevised,inhisInvestigationintotheLawsofThought(1854),ageneralsystemfortheaccurateexpressionandthusmanipulationofpropositions.PropositionshadplayedacentralroleinlogicsincethetimeofAristotleandChrysippus.ButitwasonlywithBoole’sdeepanalysisofpropositions—theBooleaninterpretationdiscussedingreatdetailinChapter5ofthisbook—thatafullyconsistentsystemofthelogicofpropositionswasatlastpossible.

Othermathematiciansandlogiciansmadesignificantadvancesthatbroughtgreaterprecisionandefficiencytotherealmofdeductivelogic.OneofthesewasAugustusDeMorgan(1806–1871),alludedtoaboveinconnectionwiththeworkofWilliamofOckham.Thetheoremsthatstillcarryhisnameremaintothisdaycriticallogicaltoolsinprovingthevalidityofdeductivearguments.AnotherEnglishlogician,JohnVenn(1834–1923),contributedbrilliantlytotheprocessofdeterminingdeductivevaliditybydesigningasystem,asbeautifulasitissimple,fortheiconicexhibitionoftherelationsofthetermsincategoricalpropositions.Venndiagrams,consistingofinterlockingcircles,arenowverywidelyused.Theyserveasaneasilyapplieddevicewithwhichthesenseofpropositionscanbegivenvisualforce,andwithwhichthevalidityorinvalidityofcategoricalsyllogismscanbeestablished.WeuseVenndiagramsextensivelyinPartIIofthisbook.

OneofthegreatestAmericanphilosophers,CharlesSandersPeirce(1839–1914),best

knownasthefounderofthemovementknownaspragmatism,thoughtofhimselfprimarilyasalogician.Logicwasforhimaverybroadstudy,involvingthemethodsofallinquiry;formaldeductivelogic,towhichhemadesomenotablecontributions,hetooktobeoneofitsbranches.Wethinkwithsigns,saidPeirce,andlogicistheformaltheoryofsigns.Heintroducedsomenewconcepts,suchasinclusionandlogicalsum;hedevisedsymbolsfortheexpressionofnovellogicaloperations;heexploredthelogicofrelations—andheanticipatedworklaterdoneinexpressingBooleanoperationsusingthefeaturesofelectricalswitchingcircuits,akeysteptowardtheactualdevelopmentoftheall-conqueringlogicmachinethathadbeenenvisionedbyGottfriedLeibniz.

Arigorous,formalsystemofpropositionallogicwasproducedbytheGermanlogicianGottlobFrege(1848–1925).Thatsystem,andhisinventionoftheconceptofquantification,establishhimasoneofthegreatestofmodernlogicians.Withquantification—asweexplainindetailinChapter10ofthisbook—itispossibletodealaccuratelywithahugebodyofdeductiveargumentthatcannototherwisebereadilypenetratedbythemachineryofmodernsymboliclogic.

BertrandRussell(1872–1970)andAlfredNorthWhitehead(1861–1947)soughttointegrateallthismodernworkondeductivelogicinonegreatandremarkabletreatise:PrincipiaMathematica,publishedinsegmentsfrom1910to1913.Using(withsomeadjustments)thenotationthathadbeendevisedbytheItalianlogicianGiuseppePeano(1858–1932),aswellasthelogicalsystemearlierdevelopedbyFrege,RussellandWhiteheadattemptedtoshowthatthewholeofmathematicscouldbederivedfromafewbasiclogicalaxioms.Muchofwhatappearsinchapters8,9,and10ofthisbookisderivedfromtheirwork.

Deductivelogiccontinuedtodevelop.Thecompletenessofaxiomaticsystemsbecameamatterofgreatinterestinthetwentiethcentury.KurtGödel(1906–1978)wasabletodemonstratethatanyformalaxiomaticsystem,ifitisconsistent,mustinfactbeincomplete,andfromGödel’sincompletenesstheoremsitfollowsthatwithinanyformalsystemtherewillbesomeformulasthatmustremainundecidable.Otheraspectsofdeductivelogichavebeenmorerecentlyinvestigated:thedistinctionbetween“fuzzy”and“crisp”logichasbeenexplored;modallogic,inwhichtheconceptsofpossibilityandnecessityaremanipulated,hasbeenhighlydeveloped.

Butperhapsnothingthatmodernlogicianshaveaccomplishedhashadmoreprofoundimpactthanthedevelopment—byJohnvonNeumann(1903–1957)andothers—oftheintellectualarchitectureofthecircuitsofdigitalcomputers.Notlongthereafter,withtheactualconstructionandgradualperfectionoftheelectronicdigitalcomputerduringthetwentiethcentury,Leibniz’sgreatvisionwasatlastmadereal.

TheaccountabovesketchesthehistoryoflogicintheWest,mainlyinEuropeandNorthAmerica.Elsewhereontheplanetlogicwasalsostudied,ofcourse—butwedonothaveaccessibleandaccuraterecordsofthediscoveriesmadelongagoinChinaandIndia.WeknowthatinIndiamuchworkhadbeendoneontheprinciplesoflogic.AugustusDeMorganwasinfluencedbythatwork;thetheoremsthatbearhisname,explainedinChapter9ofthisbook,weredevelopedindependentlyinIndia.GeorgeBoolewasinfluencedbyIndianthinkersaswell.Therulesofimmediateinference,discussedinthisbookinchapter5,

appearalsotohavebeenarticulatedinIndia,butlogicthereemphasizedeffectivephilosophicalargumentation,includingbothdeductiveandinductiveelements,ratherthanformalsystems.InChina,atthetimeofthephilosopherMozi(470–391BCE),theprinciplesofanalogicalreasoning,discussedinchapter11ofthisbook,weredeveloped.Butofthathistorywecannotbesure,becauseintheyears213–206BCEtheQindynasty,toeraseallmarksofprecedingdynasties,burnedmanybooksandkilledmanyscholars.Muchworkdoneinearlierperiodswasthuspermanentlylost.

FromthetimeofAristotle’sOrganontothetwenty-firstcenturymorepeoplehavestudiedlogicfromonebookthanfromanyother;thatbook,nowinyourhands,isIntroductiontoLogic,originallyconceivedandwrittenbyoneofthemostpowerfulandincisivethinkersofthetwentiethcentury,thelateIrvingCopi(1917–2002).

INTRODUCTIONTOLOGIC

Waterfall,byM.C.Escher,isallwrong.Thewaterflowsaway,andgoingawaycomescloser;itflowsdownward,andgoingdownitcomesup,returningtothepointfromwhichitbegan.Whatcanaccountfortheplausibleappearanceofwhatweknowtobeimpossible?Theartistplayswiththenormalassumptionsofourvision.Thecornerpointsofthecentralcubeinthispictureareconnectedinwaysthatcauseustoperceivewhatisfarthestawayonthestructureasclosest,andtoperceiveitshighestpointsasalsoitslowest.WearedupedbyEscher’sartistry.

Asperceptionmaybetrickedbyacleverpicture,ourthinkingmaybetrickedbyacleverargument.Thereareprinciplesthatunderliegoodreasoning,butwhenweviolatethemwearelikelytobemisled—orbycarelessnesstomisleadourselves.InWaterfallweconfrontdisorderinseeing,andthenwithscrutinydetectitscause.Inthestudyoflogicweconfrontmanybadarguments,andthenwithscrutinylearnwhatmakesthembad.

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M.C.Escher’sWaterfall©2005TheM.C.EscherCompany—Holland.Allrightsreserved.www.mcescher.com

SECTIONA

SECTIONB

chapter1

chapter2

chapter3

chapter4

partI LogicandLanguage

REASONING

BasicLogicalConcepts

AnalyzingArguments

INFORMALLOGIC

LanguageandDefinitions

Fallacies

“Comenow,andletusreasontogether.—Isaiah1:18

Allourliveswearegivingandacceptingreasons.Reasonsarethecoinwepayforthebeliefswehold.

—EdithWatsonSchipper

”

1.1

1.2

1.3

1.4

1.5

1.6

chapter1BasicLogicalConcepts

WhatLogicIs

PropositionsandArguments

RecognizingArguments

ArgumentsandExplanations

DeductiveandInductiveArguments

ValidityandTruth

1.1WhatLogicIs

Logic is the study of themethods and principles used to distinguish correct from incorrectreasoning.

Whenwereasonaboutanymatter,weproduceargumentstosupportourconclusions.Ourargumentsincludereasonsthatwethinkjustifyourbeliefs.However,notallreasonsaregoodreasons.Thereforewemayalwaysask,whenweconfrontanargument:Doestheconclusionreached follow from the premises assumed? To answer this question there are objectivecriteria;inthestudyoflogicweseektodiscoverandapplythosecriteria.

Reasoning is not the onlyway inwhich people support assertions theymake or accept.Theymayappealtoauthorityortoemotion,whichcanbeverypersuasive,ortheymayrely,without reflection, simplyonhabits.However,when someonewants tomake judgments thatcanbecompletelyreliedupon,theironlysolidfoundationwillbecorrectreasoning.Usingthemethodsandtechniquesoflogic—thesubjectmatterofthisbook—onecandistinguishreliablybetweensoundandfaultyreasoning.

LogicThestudyofthemethodsandprinciplesusedtodistinguishcorrectfromincorrectreasoning.

PropositionAstatement;whatistypicallyassertedusingadeclarativesentence,andhencealwayseithertrueorfalse—althoughitstruthorfalsitymaybeunknown.

1.2PropositionsandArguments

We begin by examining more closely the most fundamental concepts in the study of logic,concepts presupposed in the paragraphs just above. In reasoningwe construct and evaluate

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arguments; arguments are built with propositions. Although these concepts are apparentlysimple,theyrequirecarefulanalysis.

A.PropositionsPropositionsarethebuildingblocksofourreasoning.Apropositionassertsthatsomethingisthecaseoritassertsthatsomethingisnot.Wemayaffirmaproposition,ordenyit—buteverypropositioneitherassertswhatreallyisthecase,oritassertssomethingthatisnot.Thereforeeverypropositioniseithertrueorfalse.

Biography

Aristotle

fallthegreatphilosophersandlogicians,ancientandmodern,noneisgreaterthanAristotle(384–322BCE),whoseworksandinfluencelargelyruledtheworldofintellectfortwomillennia.Hewasoftenreferredtoas“ThePhilosopher”;his

authority(evenwhenhewasmistaken!)wasrarelyquestioned.BorninMacedonia,inthecityofStagira,wherehisfatherwasphysiciantotheking,he

wasviewedfrombirthasamemberofthearistocracy,andwasafriendoftheking’sson,Philip.WhenPhilipbecamekingofMacedonia,hesummonedAristotle,whohadformanyyearsbeenstudyinginAthensatPlato’sschool,TheAcademy,toreturntoMacedoniaastutortohissonAlexander(wholaterwouldbeknownasAlexandertheGreat).AsheadvancedonhissubsequentconquestsinAsia,Alexanderremainedincontactwithhisrespectedteacher,sendingback,atAristotle’srequest,specimensandartifactsthatcontributedtotheearlygrowthofthesciences.

Aristotle—oneofthetrio,withPlatoandSocrates,wholargelyfoundedWesternphilosophy—hadatrulyencyclopedicmind.Heinvestigated,contributedto,wroteabout,andtaughtvirtuallyallsubjectsonwhichsomeknowledgehadbeenaccumulatedathistime:thenaturalsciences(biology,zoology,embryology,anatomy,astronomy,meteorology,physics,andoptics);thearts(poetry,music,theater,andrhetoric);governmentandpolitics;psychologyandeducation;economics;ethics;metaphysics—andofcourselogic,ofwhichhealonewasthesystematicfounder.Histreatisesonlogic,latercombinedintoonegreatworkentitledTheOrganon(“TheInstrument”),constitutetheearliestformalstudyofoursubject.Thepenetrationandcoherenceofhislogicalanalyses,andthecomprehensivenessandgeneralaccuracyofhisscientificstudies,justifyhisacknowledgedstatusasoneofthefinestthinkersevertohavegracedourplanet.

Attheageof49AristotlereturnedtoAthensandestablishedhisownhighlyinfluentialschool,theLyceum,wherehetaughtfortwelveyears.Hediedofnaturalcausesin322BCE.Inhiswill,heaskedtobeburiednexttohiswife,Pythias.

InlogicAristotlegraspedtheoverridingnecessityofdeterminingtherulesofcorrectreasoning.Heexplainedvalidityandcharacterizedthefourfundamentaltypesofcategoricalpropositionsandtheirrelations.InthePriorAnalytics,oneofthesixbooksofTheOrganon,hedevelopedasophisticatedtheoreticalaccountofcategoricalsyllogisms,anaccountthatlongdominatedtherealmofdeductivelogicandthatremainstodayaneffectivetoolofsoundreasoning.

ItissaidofAristotlethathewasprobablythelastpersontoknoweverythingtherewastobeknowninhisowntime.■

Therearemanypropositionsaboutwhose truthweareuncertain.“There is lifeonsome

otherplanetinourgalaxy,”forexample,isapropositionthat,sofaraswenowknow,maybetrueormaybefalse.Its“truthvalue”isunknown,butthisproposition,likeeveryproposition,mustbeeithertrueorfalse.

Aquestionassertsnothing,andthereforeitisnotaproposition.“Doyouknowhowtoplaychess?”is indeedasentence,but thatsentencemakesnoclaimabout theworld.Neither isacommand a proposition (“Come quickly!”), nor is an exclamation a proposition (“Oh mygosh!”).Questions, commands, and exclamations—unlike propositions—are neither true norfalse.

Whenweassertsomeproposition,wedosousingasentenceinsomelanguage.However,thepropositionweassertisnotidenticaltothatsentence.Thisisevidentbecausetwodifferentsentences,consistingofdifferentwordsdifferentlyarranged,mayhavethesamemeaningand

maybeusedtoasserttheverysameproposition.Forexample,“Lesliewontheelection”and“The election was won by Leslie” are plainly two different sentences that make the sameassertion.

Sentencesarealwayspartsofsomelanguage,butpropositionsarenottiedtoEnglishortoany given language. The four sentences are in different languages, but they have a singlemeaning:all four,usingdifferentwords,maybeuttered toassert theverysameproposition.Proposition is the termweuse to refer towhat it is thatdeclarative sentencesare typicallyusedtoassert.

Itisraining. (English)

Estálloviendo. (Spanish)

Ilpleut. (French)

Esregnet. (German)

Thetermstatementisnotanexactsynonymofproposition,butitisoftenusedinlogicinmuchthesamesense.Somelogicianspreferstatementtoproposition,although the latterhasbeen more commonly used in the history of logic. Other logicians eschew both terms asmetaphysical,usingonlythetermsentence.However,theconceptofapropositionisseenbymany as making a useful distinction between a sentence and what the sentence asserts.Consequently,inthisbookweusebothterms.

StatementAproposition;whatistypicallyassertedbyadeclarativesentence,butnotthesentenceitself.Everystatementmustbeeithertrueorfalse,althoughthetruthorfalsityofagivenstatementmaybeunknown.

Theverysamesentencecanbeused tomakeverydifferent statements (or toassertverydifferent propositions), depending on the context inwhich it is expressed. For example, thesentence, “The largest state in the United States was once an independent republic,” onceexpressedatruestatementorproposition(aboutTexas),butifassertedtodaywouldexpressafalsestatementorproposition(aboutAlaska).Thesamewordsassertdifferentpropositionsatdifferenttimes.

Propositionsmay be simple, like those used in the preceding illustrations, but theymayalsobecompound, containing other propositionswithin themselves.Consider the followingproposition,fromarecentaccountoftheexploitationoftheAmazonBasininBrazil:

TheAmazonBasinproducesroughly20percentoftheEarth’soxygen,createsmuchofitsownrainfall,andharborsmanyunknownspecies.1

This sentence simultaneously asserts three propositions, concerning what the AmazonBasin produces and what it creates and what it harbors. The passage thus constitutes aconjunctiveproposition.Assertingaconjunctivepropositionisequivalenttoassertingeachofitscomponentpropositionsseparately.

Somecompoundpropositionsdonotassertthetruthoftheircomponents.Indisjunctive(oralternative) propositions, no one of the components is asserted. Abraham Lincoln (in amessage to Congress in December 1861) said, “Circuit courts are useful, or they are notuseful.”Thisdisjunctivepropositionisplainlytrue,buteitheroneofitscomponentsmightbe

false.Other compound propositions that do not assert their components are hypothetical (or

conditional)propositions.Theeighteenth-century freethinker,Voltaire, said, “IfGoddidnotexist, it would be necessary to invent him.” Here, again, neither of the two components isasserted.Theproposition“Goddoesnotexist,” isnotasserted,nor is theproposition,“it isnecessary to invent him.” Only the “if-then” proposition is asserted by the hypothetical orconditionalstatement,andthatcompoundstatementmightbetrueevenifbothofitscomponentswerefalse.

In logic, the internal structure of propositions is important. To evaluate an argumentweneedafullunderstandingofthepropositionsthatappearinthatargument.Propositionsofmanydifferentkindswillbeanalyzedinthisbook.

B.ArgumentsWithpropositionsasbuildingblocks,weconstructarguments.Inanyargumentweaffirmoneproposition on the basis of some other propositions. In doing this, an inference is drawn.Inference is a process thatmay tie together a cluster of propositions. Some inferences arewarranted (or correct); others are not. The logician analyzes these clusters, examining thepropositionswithwhich theprocessbeginsandwithwhich it ends,aswell as the relationsamongthesepropositions.Suchaclusterofpropositionsconstitutesanargument.Argumentsarethechiefconcernoflogic.

Inference Aprocessbywhichonepropositionisarrivedatandaffirmedonthebasisofsomeotherpropositionorpropositions.

Argumentisatechnicalterminlogic.Itneednotinvolvedisagreement,orcontroversy.Inlogic,argumentrefersstrictlytoanygroupofpropositionsofwhichoneisclaimedtofollowfromtheothers,whichareregardedasprovidingsupport for the truthof thatone.Foreverypossibleinferencethereisacorrespondingargument.

Inwritingorinspeech,apassagewilloftencontainseveralrelatedpropositionsandyetcontainnoargument.Anargumentisnotmerelyacollectionofpropositions;itisaclusterwithastructurethatcapturesorexhibitssomeinference.Wedescribethisstructurewiththetermsconclusionandpremise.Theconclusionofanargumentisthepropositionthatisaffirmedonthe basis of the other propositions of the argument. Those other propositions, which areaffirmed (or assumed) as providing support for the conclusion, are the premises of theargument.

Wewill encounter a vast range of arguments in this book—arguments ofmany differentkinds,onmanydifferenttopics.Wewillanalyzeargumentsinpolitics,inethics,insports,inreligion,inscience,inlaw,andineverydaylife.Thosewhodefendthesearguments,orwhoattack them, are usually aiming to establish the truth (or the falsehood) of the conclusionsdrawn.Aslogicians,however,ourinterestisintheargumentsassuch.Asagentsorascitizenswemaybedeeplyconcernedaboutthetruthorfalsityoftheconclusionsdrawn.However,aslogicianswe put those interests aside.Our concernswill be chiefly two. First,wewill beconcernedabouttheformofanargumentunderconsideration,todetermineifthatargumentisofakindthatislikelytoyieldawarrantedconclusion.Second,wewillbeconcernedabout

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thequalityoftheargument,todeterminewhetheritdoesinfactyieldawarrantedconclusion.

ArgumentAnygroupofpropositionsofwhichoneisclaimedtofollowfromtheothers,whichareregardedasprovidingsupportorgroundsforthetruthofthatone.

ConclusionInanyargument,thepropositiontowhichtheotherpropositionsintheargumentareclaimedtogivesupport,orforwhichtheyaregivenasreasons.

Premises Inanargument,thepropositionsuponwhichinferenceisbased;thepropositionsthatareclaimedtoprovidegroundsorreasonsfortheconclusion.

Arguments vary greatly in the degree of their complexity. Some are very simple. Otherarguments, as we will see, are quite intricate, sometimes because of the structure orformulation of the propositions they contain, sometimes because of the relations among thepremises,andsometimesbecauseoftherelationsbetweenpremisesandconclusion.

Thesimplestkindofargumentconsistsofonepremiseandaconclusionthatisclaimedtofollowfrom it.Eachmaybestated ina separate sentence,as in the followingargument thatappearsonastickeraffixedtobiologytextbooksinthestateofAlabama:

Noonewaspresentwhenlifefirstappearedonearth.Thereforeanystatementaboutlife’soriginsshouldbeconsideredastheory,notfact.

Bothpremiseandconclusionmaybestatedwithinthesamesentence,asinthisargumentarisingoutofrecentadvancesinthescienceofhumangenetics:

SinceitturnsoutthatallhumansaredescendedfromasmallnumberofAfricanancestorsinourrecentevolutionarypast,believinginprofounddifferencesbetweentheracesisasridiculousasbelievinginaflatearth.2

Biography

fallthelogiciansofancienttimes,AristotleandChrysippusstandoutasthetwogreatest.TheenormousinfluenceofAristotle,whofirstsystematizedlogicandwasitsprincipalauthorityfortwothousandyears,hasalreadybeenrecognized.Borna

centurylater,Chrysippus(c.279–c.206BCE)developedaconceptualschemewhoseinfluencehasonlymorerecentlybeenappreciated.

ThelogicofAristotlewasoneofclasses.IntheAristotelianargument“Allmenaremortal;Greeksaremen;thereforeGreeksaremortal,”thefundamentalelementsarethecategories,orterms(“men,”“mortalthings,”and“Greeks”).Incontrast,thelogicofChrysippuswasonebuiltofpropositionsandtheconnectionsbetweenthem(e.g.,“Ifitisnowday,itisnowlight.Itisnowday.Thereforeitisnowlight.”).Thissimpleargumentform(nowcalledmodusponens)andmanyotherfundamentalargumentforms,Chrysippusanalyzedandclassified.Hislogicalinsightswerecreativeandprofound.

BorninAsiaMinor,inSoli,ChrysippusstudiedthephilosophyoftheStoics—mostfamousamongthemZenoandCleanthes—andeventuallybecameheadoftheStoicschoolinAthens.

Inthatcapacityhetaughttheneedtocontrolone’semotions,whichhethoughttobedisordersordiseases.Heurgedthepatientacceptanceoftheoutcomesofafateonecannot

control,andtherecognitionthattheoneGod(ofwhichthetraditionalGreekgodsarebutaspects)istheuniverseitself.

Butitisasalogicianthathisinfluencehasbeengreatest.Hegrasped,asAristotledidnot,thecentralroleoftheproposition—”thatwhichis,initself,capableofbeingdeniedoraffirmed.”Fromthisbasehedevelopedthefirstcoherentsystemofpropositionallogic.■

Theorderinwhichpremisesandconclusionappearcanalsovary,butitisnotcriticalin

determining the quality of the argument. It is common for the conclusion of an argument toprecedethestatementofitspremiseorpremises.OnthedayBabeRuthhithis700thhomerun(13July1934),thefollowingargumentappearedinTheNewYorkTimes:

ArecordthatpromisestoendureforalltimewasattainedonNavinFieldtodaywhenBabeRuthsmashedhisseven-hundredthhomeruninalifetimecareer.Itpromisestolive,firstbecausefewplayersinhistoryhaveenjoyedthelongevityonthediamondoftheimmortalBambino,and,second,becauseonlytwootherplayersinthehistoryofbaseballhavehitmorethan300homeruns.

Thisisanexampleofanargumentwhosetwopremises,eachnumbered,appearaftertheconclusion isstated. It isalsoanexampleofaveryplausibleargumentwhoseconclusion isfalse,giventhatHankAaronhithis700thhomerunon21July1973,thirty-nineyearslater.

Even when premise and conclusion are united in one sentence, the conclusion of theargumentmaycomefirst.TheEnglishutilitarianphilosopher,JeremyBentham,presentedthiscrispargumentinhisPrinciplesofLegislation(1802):

Everylawisanevil,foreverylawisaninfractionofliberty.

Although this is only one short sentence, it is an argument because it contains twopropositions,ofwhichthefirst(everylawisanevil)istheconclusionandthesecond(everylaw is an infraction of liberty) is the premise. However, no single proposition can be an

1.

argument,becauseanargumentismadeupofagroupofpropositions.Yetsomepropositions,because they are compound, do sound like arguments, and caremust be taken to distinguishthemfromtheargumentstheyresemble.Considerthefollowinghypotheticalproposition:

Ifastateaimstobeasocietycomposedofequals,thenastatethatisbasedonthemiddleclassisboundtobethebestconstituted.

Neither the first nor the second component of this proposition is asserted. All that isasserted is that the former implies the latter, and bothmightwell be false.No inference isdrawn,noconclusionisclaimedtobetrue.Aristotle,whostudiedtheconstitutionandqualityof actual states inGreecemore than two thousand years ago,wrote confidently inPolitics,BookIV,Chapter11:

Astateaimsatbeingasocietycomposedofequals,andthereforeastatethatisbasedonthemiddleclassisboundtobethebestconstituted.

Inthiscasewedohaveanargument.ThisargumentofAristotleisshortandsimple;mostargumentsarelongerandmorecomplicated.Everyargument,however—shortorlong,simpleor complex—consists of a group of propositions of which one is the conclusion and theother(s)arethepremisesofferedtosupportit.

Althougheveryargumentisastructuredclusterofpropositions,noteverystructuredclusterofpropositionsisanargument.Considerthisveryrecentaccountofglobalinequality:

Inthesameworldinwhichmorethanabillionpeopleliveatalevelofaffluenceneverpreviouslyknown,roughlyabillionotherpeoplestruggletosurviveonthepurchasingpowerequivalentoflessthanoneU.S.dollarperday.Mostoftheworld’spoorestpeopleareundernourished-lackaccesstosafedrinkingwateroreventhemostbasichealthservicesandcannotsendtheirchildrentoschool.AccordingtoUNICEF,morethan10millionchildrendieeveryyear-about30,000perday-fromavoidable,poverty-relatedcauses.3

Thisreportisdeeplytroubling—butthereisnoargumenthere.Reasoningisanart,aswellasascience.Itissomethingwedo,aswellassomethingwe

understand. Giving reasons for our beliefs comes naturally, but skill in the art of buildingarguments,andtestingthem,requirespractice.Onewhohaspracticedandstrengthenedtheseskills ismore likely toreasoncorrectly thanonewhohasnever thoughtabout theprinciplesinvolved. Therefore we provide in this book very many opportunities for practice in theanalysisofarguments.

EXERCISES

Identifythepremisesandconclusionsinthefollowingpassages.Somepremisesdosupporttheconclusion,othersdonot.Note thatpremisesmay support conclusionsdirectlyor indirectlyandthatevensimplepassagesmaycontainmorethanoneargument.

EXAMPLE

Awell-regulatedmilitiabeingnecessarytothesecurityofafreestate,therightofthe

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peopletokeepandbeararmsshallnotbeinfringed.—TheConstitutionoftheUnitedStates,Amendment2

SOLUTION

Premise:Awell-regulatedmilitiaisnecessaryforthesecurityofafreestate.Conclusion:Therightofthepeopletokeepandbeararmsshallnotbeinfringed.

Whatstopsmanypeoplefromphotocopyingabookandgivingittoapalisnotintegritybutlogistics;it’seasierandinexpensivetobuyyourfriendapaperbackcopy.

—RandyCohen,TheNewYorkTimesMagazine,26March2000

ThomasAquinasarguedthathumanintelligenceisagiftfromGodandtherefore“toapplyhumanintelligencetounderstandtheworldisnotanaffronttoGod,butispleasingtohim.”

—RecountedbyCharlesMurrayinHumanAccomplishment(NewYork:HarperCollins,2003)

SirEdmundHillaryisahero,notbecausehewasthefirsttoclimbMountEverest,butbecauseheneverforgottheSherpaswhohelpedhimachievethisimpossiblefeat.Hededicatedhislifetohelpingbuildschoolsandhospitalsforthem.

—PatreS.Rajashekhar,“MountEverest,”NationalGeographic,September2003

Standardizedtestshaveadisparateracialandethnicimpact;whiteandAsianstudentsscore,onaverage,markedlyhigherthantheirblackandHispanicpeers.Thisistrueforfourth-gradetests,collegeentranceexams,andeveryotherassessmentonthebooks.Ifaracialgapisevidenceofdiscrimination,thenalltestsdiscriminate.

—AbigailThernstrom,“Testing,theEasyTarget,”TheNewYorkTimes,15January2000

Goodsenseis,ofallthingsintheworld,themostequallydistributed,foreverybodythinkshimselfsoabundantlyprovidedwithitthateventhosemostdifficulttopleaseinallothermattersdonotcommonlydesiremoreofitthantheyalreadypossess.

—RenéDescartes,ADiscourseonMethod,1637

WhenNoahWebsterproposedaDictionaryoftheAmericanLanguage,hisearly19th-centurycriticspresentedthefollowingargumentagainstit:“BecauseanywordsnewtotheUnitedStatesareeitherstupidorforeign,thereisnosuchthingastheAmericanlanguage;there’sjustbadEnglish.”

—JillLepore,“Noah’sMark,”TheNewYorker,6November2006

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Thedeathpenaltyistoocostly.InNewYorkStatealonetaxpayersspentmorethan$200millioninourstate’sfaileddeathpenaltyexperiment,withnooneexecuted.

Inadditiontobeingtoocostly,capitalpunishmentisunfairinitsapplication.Thestrongestreasonremainstheepidemicofexonerationsofdeathrowinmatesuponpost-conviction investigation, including tenNewYork inmates freed in the last18monthsfromlongsentencesbeingservedformurdersorrapestheydidnotcommit.

—L.Porter,“Costly,FlawedJustice,”TheNewYorkTimes,26March2007

Housesarebuilttolivein,nottolookon;therefore,letusebepreferredbeforeuniformity.

—FrancisBacon,“OfBuilding,”inEssays,1597

Toboycottabusinessoracity[asaprotest]isnotanactofviolence,butitcancauseeconomicharmtomanypeople.Thegreatertheeconomicimpactofaboycott,themoreimpressivethestatementitmakes.Atthesametime,theeconomicconsequencesarelikelytobesharedbypeoplewhoareinnocentofanywrongdoing,andwhocanillaffordthelossofincome:hotelworkers,cabdrivers,restaurateurs,andmerchants.Theboycottweaponoughttobeusedsparingly,iffornootherreasonthantheharmitcancausesuchbystanders.

—AlanWolfe,“TheRiskyPoweroftheAcademicBoycott,”TheChronicleofHigherEducation,17March2000

Ethniccleansingwasviewednotsolongagoasalegitimatetoolofforeignpolicy.Intheearlypartofthe20thcenturyforcedpopulationshiftswerenotuncommon;multiculturalempirescrumbledandnationalismdrovetheformationofnew,ethnicallyhomogenouscountries

—BelindaCooper,“TradingPlaces,”TheNewYorkTimesBookReview,17September2006

Ifajuryissufficientlyunhappywiththegovernment’scaseorthegovernment’sconduct,itcansimplyrefusetoconvict.Thispossibilityputspowerfulpressureonthestatetobehaveproperly.Forthisreasonajuryisoneofthemostimportantprotectionsofademocracy

—RobertPrecht,“Japan,theJury,”TheNewYorkTimes,1December2006

Withoutforests,orangutanscannotsurvive.Theyspendmorethan95percentoftheirtimeinthetrees,which,alongwithvinesandtermites,providemorethan99percentoftheirfood.TheironlyhabitatisformedbythetropicalrainforestsofBorneoandSumatra

—BiruteGaldikas,“TheVanishingManoftheForest,”TheNewYorkTimes,6January2007

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Omniscienceandomnipotencearemutuallyincompatible.IfGodisomniscient,hemustalreadyknowhowheisgoingtointervenetochangethecourseofhistoryusinghisomnipotence.Butthatmeanshecan’tchangehismindabouthisintervention,whichmeansheisnotomnipotent

—RichardDawkins,TheGodDelusion(NewYork:HoughtonMifflin,2006)

Reasonisthegreatestenemythatfaithhas;itnevercomestotheaidofspiritualthings,butmorefrequentlythannotstrugglesagainstthedivineWord,treatingwithcontemptallthatemanatesfromGod

—MartinLuther,LastSermoninWittenberg,17January1546

1.3RecognizingArguments

Beforewe can evaluate an argument,wemust recognize it.Wemust be able to distinguishargumentativepassagesinwritingorspeech.Doingthisassumes,ofcourse,anunderstandingofthelanguageofthepassage.However,evenwithathoroughcomprehensionofthelanguage,the identification of an argument can be problematic because of the peculiarities of itsformulation.Evenwhenweareconfidentthatanargumentisintendedinsomecontext,wemaybeunsureaboutwhichpropositionsareservingasitspremisesandwhichasitsconclusion.Aswehaveseen,thatjudgmentcannotbemadeonthebasisoftheorderinwhichthepropositionsappear.Howthenshallweproceed?

A.ConclusionIndicatorsandPremiseIndicatorsOneusefulmethoddependsontheappearanceofcertaincommonindicators,certainwordsorphrases that typically serve to signal the appearance of an argument’s conclusion or of itspremises.Hereisapartiallistofconclusionindicators:

therefore forthesereasons

hence itfollowsthat

so Iconcludethat

accordingly whichshowsthat

inconsequence whichmeansthat

consequently whichentailsthat

provesthat whichimpliesthat

asaresult whichallowsustoinferthat

forthisreason whichpointstotheconclusionthat

thus wemayinfer

ConclusionindicatorAwordorphrase(suchas“therefore”or“thus”)appearinginanargumentandusuallyindicatingthatwhatfollowsitistheconclusionofthatargument.

Otherwordsorphrasestypicallyservetomarkthepremisesofanargumentandhencearecalledpremiseindicators.Usually,butnotalways,whatfollowsanyoneofthesewillbethepremiseofsomeargument.Hereisapartiallistofpremiseindicators:

since asindicatedby

because thereasonisthat

for forthereasonthat

as maybeinferredfrom

followsfrom maybederivedfrom

asshownby maybededucedfrom

inasmuchas inviewofthefactthat

B.ArgumentsinContextThewords andphraseswehave listedmayhelp to indicate thepresenceof an argumentoridentifyitspremisesorconclusion,butsuchindicatorsdonotnecessarilyappear.Sometimesitisjustthemeaningofthepassage,oritssetting,thatindicatesthepresenceofanargument.Forexample,duringtheintensecontroversyoverthedeploymentofadditionalU.S.troopstoIraqin2007,onecriticofthatdeploymentwrote:

AswesendouryoungmenandwomenabroadtobringordertoIraq,manyofitsso-calledleadershaveabandonedtheirposts.WehavegiventheIraqisanopportunitytoironouttheirdifferencesandtheythrowitbackinourfaces.Iraqdoesnotdeserveourhelp.4

Nopremise indicators or conclusion indicators are usedhere, yet the argument is clear.Indicators are also absent in the following argument in SamHarris’sLetter to a ChristianNation,whosepremisesandconclusionsareunmistakable:

HalftheAmericanpopulationbelievesthattheuniverseis6,000yearsold.Theyarewrongaboutthis.Declaringthemsoisnot“irreligiousintolerance.”Itisintellectualhonesty5

Often,however,theforceofanargumentcanbeappreciatedonlywhenoneunderstandsthecontextinwhichthatargumentispresented.Forexample,theundergraduateadmissionsystemoftheUniversityofMichiganthatgaveafixednumberofextrapointstoallmembersofcertainminoritygroupswasheldunconstitutionalbytheU.S.SupremeCourtinGratzv.Bollinger in2003. Justice Ruth Bader Ginsburg dissented, defending the Michigan system with thefollowingargument:

Universitieswillseektomaintaintheirminorityenrollment…whetherornottheycandosoinfullcandor….[They]mayresorttocamouflage.Ifhonestyisthebestpolicy,surelyMichigan’saccuratelydescribed,fullydisclosedCollegeaffirmativeactionprogramispreferabletoachievingsimilarnumbersthroughwinks,nods,anddisguises.6

PremiseindicatorInanargument,awordorphrase(like“because”and“since”)thatnormallysignalsthatwhatfollowsitarestatementsservingaspremises.

This argument derives its force from the realization that universities had in fact longdisguisedtheirpreferentialadmissionprogramstoavoidattacksbasedontheequalprotectionclause of the 14th Amendment to the U.S. Constitution. Chief Justice William Rehnquist’sresponsetoJusticeGinsburg’sargumentisalsointelligibleonlyinthecontextofherdefenseofthepreferentialadmissionsystem.Rehnquistwrotethefollowing:

Theseobservationsareremarkablefortworeasons.First,theysuggestthatuniversities—towhoseacademicjudgmentwearetoldweshoulddefer—willpursuetheiraffirmativeactionprogramswhetherornottheyviolatetheUnitedStatesConstitution.Second,theyrecommendthattheseviolationsshouldbedealtwith,notbyrequiringtheUniversitiestoobeytheConstitution,butbychangingtheConstitutionsothatitconformstotheconductoftheuniversities.7

Rehnquist’sreferenceto“changingtheConstitution”mustbeunderstoodinlightofthefactthat the Michigan undergraduate admission system had been held unconstitutional. Hisreferencetothepursuitofaffirmativeactionprograms“whetherornottheyviolatetheUnitedStates Constitution” can best be understood in light of Ginsburg’s earlier reference to thepossibleuseof“winks,nods,anddisguises.”

The full force of argument and counterargument can be grasped, inmost circumstances,onlywithanunderstandingofthecontextinwhichthoseargumentsarepresented.Inreallife,contextiscritical.Forexample,ifyouaretoldthatIambringingalobsterhomefordinner,youwillhavelittledoubtthatIintendtoeatit,notfeedit.

C.PremisesorConclusionsNotinDeclarativeFormIt isnotuncommonforthepremisesofanargumenttobepresentedintheformofquestions.However, ifquestionsassertnothing,anddonotexpresspropositions,howis thispossible?Onthesurfacetheymakenoassertions;beneaththesurfaceaninterrogativesentencecanserveasapremisewhenitsquestionisrhetorical—thatis,whenitsuggestsorassumesananswerthat ismadetoserveas thepremiseofanargument.Thesentencemaybeinterrogativeeventhoughitsmeaningisdeclarative.

Thisuseofquestionsissometimesobvious,asinaletterdated7January2007toTheNewYorkTimes,objectingtoanewseriesofU.S.coinsthatwillhonorformerpresidentialwives.IritR.Rasoolywrote:

Iamirkedbythenewsetofcoinsbeingissued.Whilesomefirstladieshaveinfluencedourcountry,shouldwebestowthishonoronpeoplewhoareunelected,whoseonlycredentialishavingaprominentspouse?

Plainly,thecriticmeanstoaffirmthepropositionthatweshouldnotbestowthishonoronsuchpeople.Hecontinues:

Wouldn’thonoringwomenwhohaveservedasgovernors,SupremeCourtjusticesorlegislatorsbeamorefittingtributetothisnation’swomenthancoinsfeaturing“FirstSpouses”?

RhetoricalquestionAnutteranceusedtomakeastatement,butwhich,becauseitisininterrogativeformandisthereforeneithertruenorfalse,doesnotliterallyassertanything.

This critic obviously believes that honoring such achievementswould be amore fittingtribute, but he again expresses that propositionwith a question.His letter also provides anillustrationof theneed to relyoncontext to interpretdeclarativestatements thatareactuallymade.Thewriter’sreportthatheis“irked”bythenewsetofcoinsisnodoubttrue,butthisstatement is more than a mere description of his state of mind; he means to express thejudgmentthatsuchasetofcoinsoughtnotbeissued.

Usingquestionstoexpressapremiseissometimescounterproductive,however,becauseitmay inviteanswers (by the listener,or silentlyby the reader) that threaten theconclusionatwhichtheargumentaims.Forexample,thearchbishopoftheAnglicanChurchinNigeria,whoisanardentopponentofhomosexualityandviewsitasdeeplysinful,arguesthus:

Whydidn’tGodmakealiontobeaman’scompanion?Whydidn’tHemakeatreetobeaman’scompanion?Orbetterstill,whydidn’tHemakeanothermantobeaman’scompanion?SoevenfromthecreationstoryyoucanseethatthemindofGod,God’sintention,isformanandwomantobetogether.8

ConclusionsdrawnaboutGod’sintentions,usingaspremisesquestionsthatinviteamyriadofdifferentresponses,maybeunderminedbytheanswerstheyelicit.

Questions can servemost effectively as premises when the answers assumed really doseemtobeclearandinescapable.Insuchcasesthereaders(orhearers)areledtoprovidetheapparently evident answers for themselves, thus augmenting the persuasiveness of theargument. Here is an example: Some who find euthanasia morally unacceptable reject thedefense of that practice as grounded in the right to self-determination possessed by theterminallyillpatient.Theyargueasfollows:

Ifarighttoeuthanasiaisgroundedinself-determination,itcannotreasonablybelimitedtotheterminallyill.Ifpeoplehavearighttodie,whymusttheywaituntiltheyareactuallydyingbeforetheyarepermittedtoexercisethatright?9

Thequestionisforcefulbecauseitsanswerappearstobeundeniable.Itseemsobviousthatthereisnogoodreasonwhy,ifpeoplehavearighttodiegroundedinself-determination,theymustwaituntiltheyaredyingtoexercisethatright.Hence(thiscritiqueconcludes)therighttoeuthanasia,ifthereisone,cannotbelimitedtotheterminallyill.Theargumenthasmuchmerit,butfromtheperspectiveofitsreligiousadvocates,itmayprovetobeatwo-edgedsword.

Argumentsthatdependonrhetoricalquestionsarealwayssuspect.Becausethequestionisneither truenor false, itmaybeservingasadevice tosuggest the truthofsomepropositionwhileavoidingresponsibilityforassertingit.Thatpropositionislikelytobedubious,anditmayinfactbefalse.Toillustrate:In2007ArableadersinJerusalemexpressedgreatanxietyabout thesafetyof theAl-AqsamosquewhentheIsraeligovernmentbeganconstructionofaramp leading to the platform (also sacred to the Jews) on which that very holymosque issituated.Inreviewingthesituation,DavidGelernter,anIsraelipartisanasked:“IsitpossiblethatArableadersaremoreinterestedinattackingIsraelthanprotectingreligiousandculturalmonuments?”10Well,yes,thatispossible,ofcourse—butitmaynotbetrue,andthequestionframedin thiswayisplainly intendedtocause thereader tobelieve thatArableaderswerebeingduplicitousinvoicingtheirconcerns.DidtheauthorassertthatsuchduplicitylaybehindtheArabobjections?No,hedidn’tsaythat!

Gossipcolumniststhriveonsuggestivequestions.Celebritytidbitscommonlyappearintheform,“DoesParisHiltonhaveanytalentasanactress?”Similarly,indiscussingsocialissues,rhetorical questions can be an effective method of covert assertion. When riots in France

spread through Islamic neighborhoods, many wondered what motivated those rioters.JournalistChristopherCaldwellwrote:

WeretheyadmirersofFrance’smajorityculture,frustratedatnotbeingabletojoinitonequalterms?Ordidtheysimplyaspiretoburntothegroundasocietytheydespised?11

Accuserswhoprotect themselvesby framing their accusations in interrogative sentencesmay shield themselves from the indignant complaints of their target. “No,” theymay insist,“thatisnotwhatIsaid!”

Itiswisepolicytorefrainfromarguingwithquestions.In some arguments the conclusion appears in the form of an imperative. The reason, or

reasons,weoughttoperformagivenactaresetforthaspremises,andwearethendirectedtoactinthatway.ThusinProverbs4:7weread:

Wisdomistheprincipalthing;thereforegetwisdom.

Herethesecondclauseisacommand,andacommand,likeaquestion,isneithertruenorfalseandcannotexpressaproposition.Therefore,strictlyspeaking,itcannotbetheconclusionof an argument. Nonetheless, it surely ismeant to be the conclusion of an argument in thispassagefromProverbs.Howcanweexplainthisapparentinconsistency?Itisusefulinmanycontextstoregardacommandasnodifferentfromapropositioninwhichhearers(orreaders)aretoldthattheywouldbewisetoact,oroughttoact,inthemannerspecifiedinthecommand.ThustheconclusionoftheargumentinProverbsmayberephrasedas“Gettingwisdomiswhatyou should do.” Assertions of this kind may be true or false, as most will agree. Whatdifferencethereisbetweenacommandtodosomethingandastatementthatitshouldbedoneisanissuethatneednotbeexploredhere.Byignoringthatdifference(iftherereallyisone),weareabletodealuniformlywithargumentswhoseconclusionsareexpressedinthisform.

Reformulationsofthiskindcanclarifytherolesofanargument’sconstituentpropositions.Itisnecessarytograspthesubstanceofwhatisbeingasserted,tounderstandwhichclaimsareserving to support which inferences, whatever their external forms. Some neededreformulationsaremerelygrammatical.Apropositionthatfunctionsasapremisemaytaketheformofaphrase rather thanadeclarative sentence.This iswell illustrated in the followingargumentativepassage,whoseconclusionisaverysharpcriticismoftheUnitedStates:

Whatisafailedstate?Itisonethatfailstoprovidesecurityforthepopulation,toguaranteerightsathomeorabroad,ortomaintainfunctioningdemocraticinstitutions.OnthisdefinitiontheUnitedStatesistheworld’sbiggestfailedstate.12

The second and third premises of this argument are compressed into phrases, but thepropositionsforwhichthesephrasesareshorthandareclearenough,andtheircriticalroleintheauthor’sreasoningisevident.

D.UnstatedPropositionsArgumentsaresometimesobscurebecauseone (ormore)of theirconstituentpropositions isnotstatedbutisassumedtobeunderstood.Anillustrationwillbehelpfulhere.ThechairoftheDepartment of Sociology at City College, CUNY, presented two strong but controversialarguments,inparallel,regardingthejustifiabilityofthedeathpenalty.Thefirstpremiseofeachargumentisthehypothesisthatthefactualbelief(oftheproponent,oroftheopponent,ofthe

penalty) about what does in fact deter homicide is mistaken. The second premise of eachargument,althoughentirelyplausible,isnotstated,leavingthereaderthetaskofreconstructingit.

Thefirstargumentwentlikethis:Iftheproponentofthedeathpenaltyisincorrectinhisbeliefthatthe[death]penaltydetershomicide,thenheisresponsiblefortheexecutionofmurdererswhoshouldnotbeexecuted.13

This argument relies on the unstated second premise: “No one should be executed toadvanceanobjectivethatisnotpromotedbyexecution.”Henceonewhomistakenlybelievesthattheobjective(deterringmurders)isachievedbyexecutingthoseconvictedisresponsiblefortheexecutionofmurdererswhoshouldnotbeexecuted.

Thesecondargumentwentlikethis:Iftheopponentofthedeathpenaltyisincorrectinhisbeliefthatthedeathpenaltydoesn’tdeter,heisresponsibleforthemurderofinnocentindividualswhowouldnothavebeenmurderedifthedeathpenaltyhadbeeninvoked.14

This argument relies on the unstated second premise: “Protecting the lives of innocentindividuals from murder justifies the execution of murderers if other murderers are thendeterredbythefearofexecution.”Henceonewhomistakenlybelievesthatthedeathpenaltydoes not deter murderers is responsible for the lives of innocents who are subsequentlymurdered.

Ineachoftheseargumentstheassumedbutunstatedsecondpremiseisplausible.Onemightfind both arguments persuasive—leaving open for empirical investigation the question ofwhether, in fact, the death penalty does deter murder. However, the force of each of theargumentsdependsonthetruthoftheunstatedpremiseonwhichitrelies.

Apremisemaybeleftunstatedbecausethearguersupposesthatitisunquestionedcommonknowledge.Inthecontroversyoverthecloningofhumanbeings,oneangrycriticwrote:

Humancloning—likeabortion,contraception,pornographyandeuthanasia—isintrinsicallyevilandthusshouldneverbeallowed.15

This is plainly an argument, but part of it is missing. The argument relies on the veryplausible but unstated premise that “what is intrinsically evil should never be allowed.”Argumentsineverydaydiscourseveryoftenrelyonsomepropositionthatisunderstoodbutnotstated.Suchargumentsarecalledenthymemes.Wewillexamine themmoreclosely later inthisbook.

Theunstatedpremiseonwhich an enthymeme reliesmaynot beuniversally accepted; itmay be uncertain or controversial.An arguermay deliberately refrain from formulating thatcritical premise, believing that by allowing it to remain tacit, the premise is shielded fromattack.For example,medical researchusingembryonic stemcells (cells found in thehumanembryo that can develop into other types of cells and into most types of tissue) is highlycontroversial. One U.S. senator used the following enthymeme in attacking legislation thatwouldpermitgovernmentfinancingofsuchresearch:

Thisresearch[involvingtheuseofembryonicstemcells]isillegal,forthisreason:Thedeliberatekillingofahumanembryoisanessentialcomponentofthecontemplatedresearch.16

The stated premise is true: Research of this kind is not possiblewithout destroying theembryo.However,theconclusionthatsuchresearchisillegaldependsontheunstatedpremise

1.

2.

thatthekillingofahumanembryoisillegal—andthatclaimisverymuchindispute.The effectiveness of an enthymeme may depend on the hearer’s knowledge that some

propositionisfalse.Toemphasizethefalsityofsomeproposition,aspeakermayconstructanargumentinwhichthefirstpremiseisahypotheticalpropositionofwhichtheantecedent(the“if” component), is the proposition whose falsity the speaker wishes to show, and theconsequent (the “then” component) is a proposition known by everyone to be false. Theunstated falsehood of this second component is the second premise of the enthymematicargument.Theunstatedfalsehoodofthefirstcomponentistheconclusionoftheargument.Toillustrate:ThedistinguishedpoliticalphilosopherJohnRawlsadmiredAbrahamLincolnasthepresidentwhomostappreciatedthemoralequalityofhumanbeings.RawlsfrequentlyquotedLincoln’senthymematicargument,“Ifslaveryisnotwrong,nothingiswrong.”17Itisofcoursewildlyfalsetosaythatnothingiswrong—fromwhichitfollowsthatitisequallyfalsetosaythatslavery isnotwrong.Similarly,distinguishedpsychiatristBrunoBettelheim,survivorofboth Dachau and Buchenwald, wrote: “If all men are good, then there never was anAuschwitz.”

Enthymeme Anargumentthatisstatedincompletely,theunstatedpartofitbeingtakenforgranted.

1.4ArgumentsandExplanations

Passages that appear to be arguments are sometimes not arguments but explanations. Theappearance of words that are common indicators—such as “because,” “for,” “since,” and“therefore”—cannotsettlethematter,becausethosewordsareusedbothinexplanationsandinarguments(although“since”cansometimesrefertotemporalsuccession).Weneedtoknowtheintentionoftheauthor.Comparethefollowingtwopassages:

Layupforyourselvestreasuresinheaven,whereneithermothnorrustconsumesandwherethievesdonotbreakinandsteal.Forwhereyourtreasureis,therewillyourheartbealso

—Matt.7:19

Thereforeisthenameofit[thetower]calledBabel;becausetheLorddidthereconfoundthelanguageofalltheearth

—Gen.11:19Thefirstpassageisclearlyanargument.Itsconclusion,thatoneoughttolayuptreasuresin

heaven,issupportedbythepremise(heremarkedbytheword“for”)thatone’sheartwillbewhereone’s treasure is laidup.Thesecondpassage,whichuses theword“therefore”quiteappropriately,isnotanargument.Itexplainswhythetower(whoseconstructionisrecountedinGenesis)iscalledBabel.Thetowerwasgiventhisname,wearetold,becauseitwastheplace where humankind, formerly speaking one language, became confounded by manylanguages—the name is derived from aHebrewwordmeaning “to confound.” The passageassumesthatthereaderknowsthatthetowerhadthatname;theintentionistoexplainwhythatname was given to it. The phrase, “Therefore is the name of it called Babel,” is not a

conclusionbutacompletionoftheexplanationofthenaming.Inaddition,theclause,“becausetheLorddidthereconfoundthelanguageofalltheearth,”isnotapremise;itcouldnotserveasareasonforbelievingthatBabelwasthenameofthetower,becausethefactthatthatwasthe name is known by those to whom the passage is addressed. In this context, “because”indicatesthatwhatfollowswillexplainthegivingofthatname,Babel,tothattower.

These two passages illustrate the fact that superficially similar passagesmay have verydifferent functions.Whether some passage is an argument or an explanation depends on thepurposetobeservedbyit.Ifouraimistoestablishthetruthofsomeproposition,Q,andweoffersomeevidence,P,insupportofQ,wemayappropriatelysay“QbecauseP.”InthiscasewearegivinganargumentforQ,andPisourpremise.Alternatively,supposethatQisknowntobetrue.Inthatcasewedon’thavetogiveanyreasonstosupportitstruth,butwemaywishtogiveanaccountofwhyitistrue.Herealsowemaysay“QbecauseP”—butinthiscasewearegivingnotanargumentforQ,butanexplanationofQ.

In responding to a query about the apparent color of quasars (celestial objects lying farbeyondourgalaxy),onescientistwrote:

Themostdistantquasarslooklikeintensepointsofinfraredradiation.Thisisbecausespaceisscatteredwithhydrogenatoms(abouttwopercubicmeter)thatabsorbbluelight,andifyoufilterthebluefromvisiblewhitelight,rediswhat’sleft.Onitsmultibillion-light-yearjourneytoearthquasarlightlosessomuchbluethatonlyinfraredremains.18

Theauthorisnotseekingtoconvincehisreaderthatquasarshavetheapparentcolortheydo,butrathergivingthecausesofthisfact;heisexplaining,notarguing.

However, it may be difficult at times to determine whether an author intends to beexplaining some stateof affairs, or tobe arguing for someconclusion that is critical in thatexplanation.Here,forexample,isapassagethatmaybeinterpretedineitherway

Iwouldliketohighlightanotherpropertyofwater,uniquebutalsovitaltomakinglifeonEarthpossible.Aswatercools,approachingitsfreezingpoint,itsdensitysuddenlydecreases,reversingtheusual“naturalconvection”patternsinwhichcolderfluidssink.Thisreversalcausesthecoldeststrataofwatertorisetothetopofanoceanorlake.Theselargebodiesofwaternowfreezefromthetopdown.Wereitnotforthisuniquepropertyofwater,theoceansandlakeswouldhavelongandcompletelyfrozenoverfromthebottomupwithdireconsequencesforanylife-sustainingliquidwateronEarth.19

More than one conclusionmay be inferred from the same premise, thus presenting twoarguments. Similarly, more than one thing may be accounted for by the same fact, thuspresentingtwoexplanations.Hereisanillustration:

TheOxfordEnglishDictionaryisahistoricaldictionary,providingcitationsmeanttoshowtheevolutionofeveryword,beginningwiththeearliestknownusage.Therefore,akeytask,andapopularsportforthousandsofvolunteerwordaficionados,isantedating:findingearliercitationsthanthosealreadyknown.20

Thatantedatingisakeytaskforthemakersofthatdictionaryisaccountedforbythefactthat theOxfordEnglishDictionary is ahistorical dictionary.This fact about the dictionaryalsoexplainswhy,forwordaficionados,antedatingisapopularsport.

If anauthorwrites“QbecauseP,” howcanwe tellwhether he intends to explain or topersuade?Wecanask:WhatisthestatusofQinthatcontext?IsQapropositionwhosetruthneedstobeestablishedorconfirmed?Inthatcase,“becauseP”isprobablyofferingapremiseinitssupport;“QbecauseP”isinthatinstanceanargument.OrisQapropositionwhosetruthisknown,oratleastnotindoubtinthatcontext?Inthatcase,“becauseP”isprobablyofferingsomeaccountofwhyQhascometobetrue;“QbecauseP”isinthatinstanceanexplanation.

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Inanexplanation,onemustdistinguishwhatisbeingexplainedfromwhattheexplanationis. In the explanation from Genesis given at the beginning of this section, what is beingexplained is how the towerofBabel came tohave that name; the explanation is that itwasthere that the Lord did confound the language of all the Earth. In the astronomical examplegiven subsequently, what is being explained is the fact that quasars appear to be red; theexplanationisthataslighttravelsfromtheverydistantquasartoEarthalltheblueinthatlightisfilteredout.

Ifwe are sensitive to the context,wewill usually be able to distinguish an explanationfromanargument.However,therewillalwaysbesomepassageswhosepurposeisuncertain,andsuchpassagesmaydeservetobegivenalternative,equallyplausible“readings”—viewedasargumentswheninterpretedinonewayandasexplanationswheninterpretedinanother.

EXERCISES

Someofthefollowingpassagescontainexplanations,somecontainarguments,andsomemaybeinterpretedaseitheranargumentoranexplanation.Whatisyourjudgmentaboutthechieffunctionofeachpassage?Whatwouldhavetobethecaseforthepassageinquestiontobeanargument? To be an explanation? Where you find an argument, identify its premises andconclusion.Where you find an explanation, indicate what is being explained and what theexplanationis.

EXAMPLE

HumanshavevaryingskincolorsasaconsequenceofthedistanceourancestorslivedfromtheEquator.It’sallaboutsun.Skincoloriswhatregulatesourbody’sreactiontothesunanditsrays.Darkskinevolvedtoprotectthebodyfromexcessivesunrays.LightskinevolvedwhenpeoplemigratedawayfromtheEquatorandneededtomakevitaminDintheirskin.Todothattheyhadtolosepigment.Repeatedlyoverhistory,manypeoplemoveddarktolightandlighttodark.Thatshowsthatcolorisnotapermanenttrait

—NinaJablonski,“TheStoryofSkin,”TheNewYorkTimes,9January2007

SOLUTION

This is essentially an explanation.What is being explained is the fact that humans havevaryingskincolors.Theexplanationisthatdifferentskincolorsevolvedashumanscameto live at different distances from the Equator and hence needed different degrees ofprotectionfromtheraysofthesun.Onemightinterpretthepassageasanargumentwhoseconclusion is that skin color is not a permanent trait of all humans. Under this

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interpretation, all the propositions preceding the final sentence of the passage serve aspremises.

DavidBernstein[inOnlyOnePlaceofRedress:AfricanAmericans,LaborRegulations,andtheCourtsfromReconstructiontotheNewDeal,2001]placeslaborlawsatthecenterofthecontemporaryplightofblackAmericans.Manyoftheseostensiblyneutrallaws(e.g.,licensinglaws,minimum-wagelaws,andcollectivebargaininglaws