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1 Basic Concepts 1.1 Arguments, Premises, and Conclusions Logic may be defined as the science that evaluates arguments. All of us encounter arguments in our day-to-day experience. We read them in books and newspapers, hearthem ontelevision,andformulate themwhencommunicatingwithfriendsand associates.Theaimoflogicistodevelopasystemofmethodsandprinciplesthatwe mayuseascriteriaforevaluatingtheargumentsofothersandasguidesinconstructing argumentsofourown.Amongthebenefitstobeexpectedfromthestudyoflogicis anincreaseinconfidencethatwearemakingsensewhenwecriticizethearguments ofothersandwhenweadvanceargumentsofourown. Anargument,asitoccursinlogic,isagroupofstatements,oneormoreofwhich (the premises) are claimed to provide support for, or reasons to believe, one of the others (the conclusion). All arguments may be placed in one of two basic groups: thoseinwhichthepremisesreallydosupporttheconclusionandthoseinwhichthey donot,eventhoughthey are claimedto.Theformeraresaidtobegoodarguments (atleasttothatextent),thelatterbadarguments.Thepurposeoflogic,asthescience thatevaluatesarguments,isthustodevelopmethodsandtechniquesthatallowusto distinguishgoodargumentsfrombad. Asisapparentfromtheabovedefinition,theterm‘‘argument’’hasaveryspecific meaning in logic. It does not mean, for example, a mere verbal fight, as one might havewithone’sparent,spouse,orfriend.Letusexaminethefeaturesofthisdefinition in greater detail. First of all, an argument is a group of statements. A statementisa sentence thatis eithertrueorfalse—inotherwords,typicallyadeclarativesentence or a sentence component that could stand as a declarative sentence. The following sentencesarestatements: Aluminumisattackedbyhydrochloricacid. BroccoliisagoodsourceofvitaminA. ArgentinaislocatedinNorthAmerica. S NapoleonprevailedatWaterloo. RembrandtwasapainterandShelleywasapoet. N L The first two statements are true, the second two false. The last one expresses two statements,bothofwhicharetrue.Truthandfalsityarecalledthetwopossibletruth valuesofastatement.Thus,thetruthvalueofthefirsttwostatementsistrue,thetruth value of the second two is false, and the truthvalue of the laststatement,as wellas thatofitscomponents,istrue. Unlike statements, many sentences cannot be said to be either true or false. Questions, proposals, suggestions, commands, and exclamations usually cannot, and so are not usually classified as statements. The following sentences are not statements: Whatistheatomicweightofcarbon? (question) Let’sgototheparktoday. (proposal) Wesuggestthatyoutravelbybus. (suggestion) Turntotheleftatthenextcorner. (command) Allright! (exclamation) Thestatementsthatmakeupanargumentaredividedintooneormorepremises andoneandonlyoneconclusion.Thepremisesarethestatementsthatsetforththe reasonsorevidence,andtheconclusionisthestatementthattheevidenceisclaimed tosupportorimply.Inotherwords,theconclusionisthestatementthatisclaimedto followfromthepremises.Hereisanexampleofanargument: Allcrimesareviolationsofthelaw. Theftisacrime. Therefore,theftisaviolationofthelaw. Thefirsttwostatementsarethepremises;thethirdistheconclusion.(Theclaimthat thepremisessupportorimplytheconclusionisindicatedbytheword‘‘therefore.’’)In thisargumentthepremisesreallydosupporttheconclusion,andsotheargumentisa goodone.Butconsiderthisargument: Somecrimesaremisdemeanors. Murderisacrime. Therefore,murderisamisdemeanor. In this argument the premises do not support the conclusion, even though they are claimedto,andsotheargumentisnotagoodone. One of the most important tasks in the analysis of arguments is being able to distinguishpremisesfromconclusion.Ifwhatisthoughttobeaconclusionisreallya premise, and vice versa, the subsequent analysis cannot possibly be correct. Fre- quently, arguments contain certain indicator words that provide clues in identifying premisesandconclusion.Sometypicalconclusionindicatorsare 2 Chapter1: BasicConcepts therefore accordingly entailsthat wherefore wemayconclude hence thus itmustbethat itfollowsthat consequently whence impliesthat wemayinfer so asaresult Wheneverastatementfollowsoneoftheseindicators,itcanusuallybeidentifiedas theconclusion.Byprocessofeliminationtheotherstatementsintheargumentarethe premises.Example: Corporateraidersleavetheirtargetcorporationwithaheavydebtburdenandno increaseinproductivecapacity.Consequently,corporateraidersarebadforthe businesscommunity. The conclusionof this argumentis‘‘Corporateraidersarebadforthebusinesscom- munity,’’ and the premise is ‘‘Corporate raiders leave their target corporation with a heavydebtburdenandnoincreaseinproductivecapacity.’’ Claimed Premises evidence What is claimed to follow Conclusion from the evidence If an argument does not contain a conclusion indicator, it may containa premise indicator.Sometypicalpremiseindicatorsare since inthat seeingthat asindicatedby maybeinferredfrom forthereasonthat because as inasmuchas for giventhat owingto Anystatementfollowingoneoftheseindicatorscanusuallybeidentifiedasapremise. Example: Expectantmothersshouldneveruserecreationaldrugs,sincetheuseofthese drugscanjeopardizethedevelopmentofthefetus. S N L Arguments,Premises, and Conclusions 3 Thepremiseofthisargumentis‘‘Theuseofthesedrugscanjeopardizethedevelop- mentofthefetus,’’andtheconclusionis‘‘Expectantmothersshouldneveruserecre- ationaldrugs.’’ One premise indicator not included in the above list is ‘‘for this reason.’’ This indicatorisspecialinthatitcomesimmediatelyafterthepremisethatitindicates.‘‘For thisreason’’(exceptwhenfollowedbyacolon)meansforthereason(premise)that wasjustgiven.Inotherwords,thepremiseisthestatementthatoccursimmediately before‘‘forthisreason.’’Oneshouldbecarefulnottoconfuse‘‘forthisreason’’with ‘‘forthereasonthat.’’ Sometimesasingleindicatorcanbeusedtoidentifymorethanonepremise.Con- siderthefollowingargument: Thedevelopmentofhigh-temperaturesuperconductingmaterialsistechnolog- icallyjustified,forsuchmaterialswillallowelectricitytobetransmittedwithout lossovergreatdistances,andtheywillpavethewayfortrainsthatlevitate magnetically. Thepremiseindicator‘‘for’’goeswithboth‘‘Suchmaterialswillallowelectricitytobe transmittedwithoutlossovergreatdistances’’and‘‘Theywillpavethewayfortrains that levitate magnetically.’’ These are the premises. By process of elimination, ‘‘The development ofhigh-temperaturesuperconductingmaterialsistechnologicallyjusti- fied’’istheconclusion. Sometimes an argument contains no indicators. When this occurs, the reader/ listenermustaskhimselforherselfsuchquestionsas:Whatsinglestatementisclaimed (implicitly)tofollowfromtheothers?Whatisthearguertryingtoprove?Whatisthe mainpointinthepassage?Theanswerstothesequestionsshouldpointtotheconclu- sion.Example: Thespaceprogramdeservesincreasedexpendituresintheyearsahead.Notonly doesthenationaldefensedependuponit,buttheprogramwillmorethanpay foritselfintermsoftechnologicalspinoffs.Furthermore,atcurrentfunding levelstheprogramcannotfulfillitsanticipatedpotential. Theconclusionofthisargumentisthefirststatement,andalloftheotherstatements arepremises.Theargumentillustratesthepatternfoundinmostargumentsthatlackin- dicatorwords:theintendedconclusionisstatedfirst,andtheremainingstatementsare thenofferedinsupportofthisfirststatement.Whentheargumentisrestructuredaccord- ingtologicalprinciples,however,theconclusionisalwayslistedafterthepremises: P : Thenationaldefenseisdependentuponthespaceprogram. 1 P : Thespaceprogramwillmorethanpayforitselfintermsoftechnological 2 spinoffs. P : Atcurrentfundinglevelsthespaceprogramcannotfulfillitsanticipated 3 potential. C: Thespaceprogramdeservesincreasedexpendituresintheyearsahead. 4 Chapter1: BasicConcepts Whenrestructuringargumentssuchasthis,oneshouldremainascloseaspossible totheoriginalversion,whileatthesametimeattendingtotherequirementthatprem- isesandconclusionbecompletesentencesthataremeaningfulintheorderinwhich theyarelisted. Notethatthefirsttwopremisesareincludedwithinthescopeofasinglesentence intheoriginalargument.Forthepurposesofthischapter,compoundarrangementsof statementsinwhichthevariouscomponentsareallclaimedtobetruewillbeconsid- eredasseparatestatements. Passages that contain arguments sometimes contain statements that are neither premises nor conclusion. Only statements that are actually intended to support the conclusionshouldbeincludedinthelistofpremises.Ifastatementhasnothingtodo withtheconclusionor,forexample,simplymakesapassingcomment,itshouldnot beincludedwithinthecontextoftheargument.Example: Socializedmedicineisnotrecommendedbecauseitwouldresultinareductionin theoverallqualityofmedicalcareavailabletotheaveragecitizen.Inaddition, itmightverywellbankruptthefederaltreasury.Thisisthewholecaseagainst socializedmedicineinanutshell. The conclusion of this argument is ‘‘Socialized medicine is not recommended,’’and thetwostatementsfollowingtheword‘‘because’’arethepremises.Thelaststatement makes only a passing comment about the argument itself and is therefore neither a premisenoraconclusion. Closely related to the concepts of argument and statement are those of inference and proposition. An inference, in the technical sense of the term, is the reasoning processexpressedbyanargument.Aswewillseeinthenextsection,inferencesmay beexpressednotonlythroughargumentsbutthroughconditionalstatementsaswell. Intheloosesenseoftheterm,‘‘inference’’isusedinterchangeablywith‘‘argument.’’ Analogously,aproposition,inthetechnicalsense,isthemeaningorinformation content of a statement. For the purposes of this book, however, ‘‘proposition’’ and ‘‘statement’’areusedinterchangeably. NoteontheHistoryofLogic ThepersonwhoisgenerallycreditedasbeingthefatheroflogicistheancientGreek philosopher Aristotle (384–322 B.C.). Aristotle’s predecessors had been interestedin theartofconstructingpersuasiveargumentsandintechniquesforrefutingtheargu- mentsofothers,butitwasAristotlewhofirstdevisedsystematiccriteriaforanalyzing and evaluating arguments. Aristotle’s logic is called syllogistic logic and includes muchofwhatistreatedinChapters4and5ofthistext.Thefundamentalelementsin thislogicareterms,andargumentsareevaluatedasgoodorbaddependingonhow thetermsarearrangedintheargument.Inadditiontohisdevelopmentofsyllogistic logic,Aristotlecatalogedanumberofinformalfallacies,atopictreatedinChapter3of S thistext. N L Arguments,Premises, and Conclusions 5 AfterAristotle’sdeath,anotherGreekphilosopher,Chrysippus(279–206B.C.),one of the founders of the Stoic school, developed a logic in which the fundamental elementswerewholepropositions.Chrysippustreatedeverypropositionaseithertrue orfalseanddevelopedrulesfordeterminingthetruthorfalsityofcompoundpropo- sitionsfromthetruthorfalsityoftheircomponents.Inthecourseofdoingso,helaid the foundation for the truth functional interpretation of the logical connectives pre- sentedinChapter6ofthistextandintroducedthenotionofnaturaldeduction,treated inChapter7. For thirteen hundred years after the death of Chrysippus, relatively little creative workwasdoneinlogic.ThephysicianGalen(A.D.129–ca.199)developedthetheory of the compound categorical syllogism, but for the most partphilosophersconfined themselves to writing commentaries on the works of Aristotle andChrysippus.Boe- thius(ca.480–524)isanoteworthyexample. ThefirstmajorlogicianoftheMiddleAgeswasPeterAbelard(1079–1142).Abelard reconstructedandrefinedthelogicofAristotleandChrysippusascommunicatedby Boethius,andheoriginatedatheoryofuniversalsthattracedtheuniversalcharacter ofgeneraltermstoconceptsinthemindratherthanto‘‘natures’’existingoutsidethe mind,asAristotlehadheld.Inaddition,Abelarddistinguishedargumentsthatarevalid becauseoftheirformfromthosethatarevalidbecauseoftheircontent,butheheld thatonlyformalvalidityisthe‘‘perfect’’orconclusivevariety.Thepresenttextfollows Abelardonthispoint. AfterAbelard,thestudyoflogicduringtheMiddleAgesblossomedandflourished through the work of numerous philosophers. It attained its final expression in the writingsoftheOxfordphilosopherWilliamofOccam(ca.1285–1349).Occamdevoted much of his attention to modal logic, a kind of logic that involves such notionsas possibility, necessity, belief, and doubt. He also conducted an exhaustive study of formsofvalidandinvalidsyllogismsandcontributedtothedevelopmentofthecon- cept of a metalanguage—that is, a higher-level language used to discuss linguistic entitiessuchaswords,terms,propositions,andsoon. Towardthemiddleofthefifteenthcentury,areactionsetinagainstthelogicofthe Middle Ages. Rhetoric largely displaced logic as the primary focus of attention; the logicofChrysippus,whichhadalreadybeguntoloseitsuniqueidentityintheMiddle Ages, was ignored altogether, and the logic of Aristotle was studied only in highly simplistic presentations. A reawakening did not occur until two hundred years later throughtheworkofGottfriedWilhelmLeibniz(1646–1716). Leibniz,ageniusinnumerousfields,attemptedtodevelopasymboliclanguageor ‘‘calculus’’ that could be used to settle all forms of disputes, whether in theology, philosophy, or international relations. As a result of this work, Leibniz is sometimes credited with being the father of symbolic logic. Leibniz’s efforts to symbolize logic werecarriedintothenineteenthcenturybyBernardBolzano(1781–1848). With the arrival of the middle of the nineteenth century, logic commenced an extremelyrapidperiodofdevelopmentthathascontinuedtothisday.Workinsym- 6 Chapter1: BasicConcepts bolic logic was done by a number of philosophers and mathematicians, including AugustusDeMorgan(1806–1871),GeorgeBoole(1815–1864),WilliamStanleyJevons (1835–1882),andJohnVenn(1834–1923),someofwhomarepopularlyknowntoday by the logical theorems and techniques that bear their names. At the same time, a revival in inductive logic was initiated by the British philosopher John Stuart Mill (1806–1873),whosemethodsofinductionarepresentedinChapter9ofthistext. Towardtheendofthenineteenthcentury,thefoundationsofmodernmathematical logicwerelaidbyGottlobFrege(1848–1925).HisBegriffsschriftsetsforththetheory ofquantificationpresentedinChapter8ofthistext.Frege’sworkwascontinuedinto the twentieth century by Alfred North Whitehead (1861–1947) and Bertrand Russell (1872–1970), whose monumental Principia Mathematica attempted to reduce the whole of pure mathematics to logic. The Principia is the source of much of the symbolismthatappearsinChapters6,7,and8ofthistext. Duringthetwentiethcentury,muchoftheworkinlogichasfocusedontheformal- izationoflogicalsystemsandonquestionsdealingwiththecompletenessandconsis- tency of such systems. A now-famous theorem proved by Kurt Goedel(1906–1978) statesthatinanyformalsystemadequatefornumbertheorythereexistsanundecidable formula—thatis,aformulasuchthatneitheritnoritsnegationisderivablefromthe axiomsofthesystem.Otherdevelopmentsincludemultivaluedlogicsandtheformal- izationofmodallogic.Mostrecently,logichasmadeamajorcontributiontotechnology byprovidingtheconceptualfoundationfortheelectroniccircuitryofdigitalcomputers. EXERCISE1.1 I.Each ofthe followingpassagescontainsasingleargument.Usingtheletters‘‘P’’ and‘‘C,’’identifythepremisesandconclusionofeachargument,writingpremises first and conclusion last. List the premises in the order in which they make the most sense, and write both premises and conclusion in the form of separate declarative sentences. Indicator words may be eliminated once premises and conclusionhavebeenappropriatelylabeled.Theexercisesmarkedwithastarare answeredinthebackofthetext. (cid:1) 1. Titaniumcombinesreadilywithoxygen,nitrogen,andhydrogen,allofwhich haveanadverseeffectonitsmechanicalproperties.Asaresult,titaniummust beprocessedintheirabsence. (IllustratedWorldofScienceEncyclopedia) 2. Since the good, according to Plato, is that which furthers a person’s real interests,itfollowsthatinanygivencasewhenthegoodisknown,menwill seekit. (AvrumStrollandRichardPopkin,PhilosophyandtheHumanSpirit) 3. Asthedenialorperversionofjusticebythesentencesofcourts,aswellasin S anyothermanner,iswithreasonclassedamongthejustcausesofwar,itwill N L Arguments,Premises, and Conclusions 7 follow that the federal judiciary ought to have cognizance of all causes in whichthecitizensofothercountriesareconcerned. (AlexanderHamilton,FederalistPapers,No.80) (cid:1) 4. Whenindividualsvoluntarilyabandonproperty,theyforfeitanyexpectationof privacyinitthattheymighthavehad.Therefore,awarrantlesssearchorsei- zureofabandonedpropertyisnotunreasonableundertheFourthAmendment. (JudgeStephanieKulpSeymour,UnitedStatesv.Jones) 5. Artistsandpoetslookattheworldandseekrelationshipsandorder.Butthey translatetheirideastocanvas,ortomarble,orintopoeticimages.Scientists trytofindrelationshipsbetweendifferentobjectsandevents.Toexpressthe ordertheyfind,theycreatehypothesesandtheories.Thusthegreatscientific theoriesareeasilycomparedtogreatartandgreatliterature. (DouglasC.Giancoli,TheIdeasofPhysics,3rdedition) 6. ThefactthattherewasneveralandbridgebetweenAustraliaandmainland Asiaisevidencedbythefactthattheanimalspeciesinthetwoareasarevery different.AsianplacentalmammalsandAustralianmarsupialmammalshave notbeenincontactinthelastseveralmillionyears. (T.DouglasPriceandGaryM.Feinman,ImagesofthePast) (cid:1) 7. The psychological impact and crisis created by birth of a defective infant is devastating. Not only is the mother denied the normaltensionreleasefrom thestressofpregnancy,butbothparentsfeelacrushingblowtotheirdignity, self-esteem, and self-confidence. In a very short time, they feel grief forthe lossofthenormalexpectedchild,angeratfate,numbness,disgust,wavesof helplessnessanddisbelief. (JohnA.Robertson,‘‘InvoluntaryEuthanasiaofDefectiveNewborns’’) 8. Theclassroomteacheriscrucialtothedevelopmentandacademicsuccessof theaveragestudent,andadministratorssimplyareancillarytothiseffort.For this reason, classroom teachers ought to be paid at least the equivalent of administratorsatalllevels,includingthesuperintendent. (PeterF.Falstrup,LettertotheEditor) 9. Anagreementcannotbindunlessbothpartiestotheagreementknowwhat they are doing and freely choose to do it. This implies that the seller who intendstoenteracontractwithacustomerhasadutytodiscloseexactlywhat thecustomerisbuyingandwhatthetermsofthesaleare. (ManuelG.Velasquez,‘‘TheEthicsofConsumerProduction’’) (cid:1) 10. Punishment,whenspeedyandspecific,maysuppressundesirablebehavior, butitcannotteachorencouragedesirablealternatives.Therefore,itiscrucial tousepositivetechniquestomodelandreinforceappropriatebehaviorthat the person can use in place of the unacceptable response that has to be suppressed. (WalterMischelandHarrietMischel,EssentialsofPsychology) 8 Chapter1: BasicConcepts 11. Profitservesaverycrucialfunctioninafreeenterpriseeconomy,suchasour own. Highprofitsare the signal that consumerswantmoreoftheoutputof the industry. High profits provide the incentive for firms to expand output andformorefirmstoentertheindustryinthelongrun.Forafirmofabove- averageefficiency,profitsrepresenttherewardforgreaterefficiency. (DominicSalvatore,ManagerialEconomics,3rdedition) 12. Cats can think circles around dogs! My cat regularly used to close and lock the door to my neighbor’s doghouse, trapping their sleepingDobermanin- side.Trytellingacatwhattodo,orputtingaleashonhim—he’llglareatyou andsay,‘‘Idon’tthinkso.Youshouldhavegottenadog.’’ (KevinPurkiser,LettertotheEditor) (cid:1) 13. Sinceprivatepropertyhelpspeopledefinethemselves,sinceitfreespeople frommundanecaresofdailysubsistence,andsinceitisfinite,noindividual should accumulate so much property that others are prevented from accu- mulatingthenecessitiesoflife. (LeonP.Baradat,PoliticalIdeologies,TheirOriginsandImpact) 14. ToeveryexistingthingGodwillssomegood.Hence,sincetoloveanything is nothing else than to will good to that thing, it is manifest that God loves everythingthatexists. (ThomasAquinas,SummaTheologica) 15. Women of the working class, especially wage workers, should not have more than two children at most. The average working man can support no more and the average working woman can take care of no more in de- centfashion. (MargaretSanger,FamilyLimitations) (cid:1) 16. Radioactive fallout isn’t the only concern in the aftermath of nuclearexplo- sions. The nations of planet Earth have acquired nuclear weapons with an explosive power equal to more than a million Hiroshima bombs. Studies suggest that explosion of only half these weapons would produce enough soot,smoke,anddusttoblankettheEarth,blockoutthesun,andbringona nuclearwinterthatwouldthreatenthesurvivalofthehumanrace. (JohnW.HillandDorisK.Kolb,ChemistryforChangingTimes,7thedition) 17. Anantreleasesachemicalwhenitdies,anditsfellowsthencarryitawayto the compost heap. Apparently the communication is highly effective; a healthy ant painted with the death chemical will be dragged to the funeral heapagainandagain. (CarolR.EmberandMelvinEmber,CulturalAnthropology,7thedition) 18. Everyartandeveryinquiry,andsimilarlyeveryactionandpursuit,isthought toaimatsomegood;andforthisreasonthegoodhasrightlybeendeclared tobethatatwhichallthingsaim. S (Aristotle,NicomacheanEthics) N L Arguments,Premises, and Conclusions 9