Inductive and Deductive Reasoning实用文档.docx
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Inductive and Deductive Reasoning实用文档.docx
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InductiveandDeductiveReasoning实用文档
InductiveandDeductiveReasoning
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CriticalThinking
Excerptedfrom:
//sjsu.edu/depts/itl/7/index.html
InductiveandDeductiveReasoning
Manypeopledistinguishbetweentwobasickindsofargument:
inductiveanddeductive.Inductionisusuallydescribedasmovingfromthespecifictothegeneral,whiledeductionbeginswiththegeneralandendswiththespecific;argumentsbasedonexperienceorobservationarebestexpressedinductively,whileargumentsbasedonlaws,rules,orotherwidelyacceptedprinciplesarebestexpresseddeductively.Considerthefollowingexample:
Adham:
I'venoticedpreviouslythateverytimeIkickaballup,itcomesbackdown,soIguessthisnexttimewhenIkickitup,itwillcomebackdown,too.
Rizik:
That'sNewton'sLaw.Everythingthatgoesupmustcomedown.Andso,ifyoukicktheballup,itmustcomedown.
Adhamisusinginductivereasoning,arguingfromobservation,whileRizikisusingdeductivereasoning,arguingfromthelawofgravity.Rizik'sargumentisclearlyfromthegeneral(thelawofgravity)tothespecific(thiskick);Adham'sargumentmaybelessobviouslyfromthespecific(eachindividualinstanceinwhichhehasobservedballsbeingkickedupandcomingbackdown)tothegeneral(thepredictionthatasimilareventwillresultinasimilaroutcomeinthefuture)becausehehasstateditintermsonlyofthenextsimilarevent--thenexttimehekickstheball.
Asyoucansee,thedifferencebetweeninductiveanddeducativereasoningismostlyinthewaytheargumentsareexpressed.Anyinductiveargumentcanalsobeexpresseddeductively,andanydeductiveargumentcanalsobeexpressedinductively.
Evenso,itisimportanttorecognizewhethertheformofanargumentisinductiveordeductive,becauseeachrequiresdifferentsortsofsupport.Adham'sinductiveargument,above,issupportedbyhispreviousobservations,whileRizik'sdeductiveargumentissupportedbyhisreferencetothelawofgravity.Thus,Adhamcouldprovideadditionalsupportbydetailingthoseobservations,withoutanyrecoursetobooksortheoriesofphysics,whileRizikcouldprovideadditionalsupportbydiscussingNewton'slaw,evenifRizikhimselfhadneverseenaballkicked.
Theappropriateselectionofaninductiveordeductiveformatforaspecificfirststepstowardsoundargumentation.
IntroductiontoInduction
AscoveredinthesectiononInductiveandDeductiveReasoning,inductiveargumentsareusuallybasedonexperienceorobservation.Ineffect,then,inductiveargumentsareallcomparisonsbetweentwosetsofevents,ideas,orthings;asaresult,inductiveargumentsaresometimescalledanalogicalarguments.Thepointofthosecomparisons,oranalogies,istoestablishwhetherthetwosetsunderconsideration,similarinanumberofotherways,arealsosimilarinthewayofinteresttotheargument.Considerthisexample:
Marikosays,"EverytimeI'veseenared-tintedsunset,thenextday'sweatherhasbeenbeautiful.Todayhadared-tintedsunset,sotomorrowwillbebeautiful."
Essentially,Marikoiscomparingonesetofevents(observedred-tintedsunsetsandeachfollowingday'sweather)withanother(today'sobservedsunsetandtomorrow'spredictedweather).Thesesetsaresimilarinanimportantway(red-tintedsunsets),andtheinductiveargumentisthattheywillalsobesimilarinanotherway(niceweatheronthefollowingday).Inthiscase,Marikoisarguingfromparticularcasesinthepasttoaparticularcaseinthepresentandfuture,butshecouldalsoargueinductivelyfromthoseparticularcasestoageneralone,suchas"It'salwaysbeautifulthedayafterared-tintedsunset."
Thestrengthofsuchanargumentdependsinlargepartonthreeofitselements:
1.howaccurateandcomprehensivethepreviousobservationsare;
2.howstrongthecausallinkseemstobe;
3.howsimilarthetwocasesare.
InMariko'sargument,tosatisfythefirstelement,wewouldwanttobesurethatshe'sseenmanysuchsunsets,andthat"redness"and"beauty"havebeenjudgedconsistently.Tosatisfythesecond,wewouldwanttofeelconfidentthatthereisastrongcorrelationbetweenweatherpatternsonsuccessivedays.Tosatisfythethird,wewouldwanttoknowwhetherthereareanysignificantdifferencesbetweentheobservationoftoday'ssunsetandofthepreviousones.Adifferenceinseason,adifferenceingeographicalortopographicallocation,adifferenceinclimate,oranyothersignificantvariationmightaffectthecomparabilityofthetwosetsofobservations.
Infact,weshouldalwaysunderstandthesecondpremiseofaninductiveargumenttocontainaclaimlike"thereisotherwisenosignificantdifference."ThesecondpremiseofMariko'sargument,then,mightread,"Today'ssunsetwasred-tinted(andtherewerenosignificantdifferencesbetweenthisandpreviousred-tintedsunsets)."Keepingsuchadisclaimerinmindisimportant,becausethisiswheremanyinductiveargumentsareweakest.
Becauseweargueinductivelyfromtheparticulartothegeneral,suchargumentsareoftencalledgeneralizations,orinductivegeneralizations.Otherkindsofargumentswithasimilarformatincludecausalarguments.
ExercisesforInduction
1.Whichofthefollowingclaimswouldbebestexpressedbyinductivereasoning?
Yourfirstquizgradeusuallyindicateshowyouwilldointhecourse.
Thefinalexamaccountsfor30%ofthecoursegrade.
Latepaperswillnotbeaccepted.
Gravity'sRainbowisrequiredreadinginyourcourse.
2.EverytimeJorgehasseenabaseballgamebetweentheGiantsandtheDodgersatCandlestickPark,theGiantshavewon.Tomorrow,theGiantsplaytheDodgersatCandlestick.WhichofthefollowingisleastsignificantwhenarguingthattheGiantswillwintomorrow?
JorgehasonlyseentheGiantsplaytheDodgerstwice.
Bothteamshavemanynewplayers.
Jorgewon'tbegoingtothegametomorrow.
ThefieldatCandlestickwillbeunusuallymuddytomorrow.
IntroductiontoCausalArguments
Oneofthemostimportantusesforinductivereasoningistoarguecausation.Considerthefollowingexample:
Abicyclistmovesintothetrafficlaneinordertopassatruckillegallyparkedinthebikelane.Thedriverofacarapproachingfromtherearslamsonherbrakesinordertoavoidhittingthebicycle.Afollowingcarfailstostopintime,andsmashesintothebackofthefirst.Theinsurancecompaniesdisagreeaboutwhoshouldbeheldresponsible,andtheygotocourttodecidewhocausedtheaccident.
Whatargumentsarelikelytobemadeincourt?
Thebicyclist'slawyerwillprobablyclaimthattheillegallyparkedtruckcausedherclienttoswerveintothelaneoftraffic.Thelawyerforthedriverofthefirstcarwillprobablyclaimthatthebicyclist'sactionscausedherclienttoslamonthebrakes.Thelawyerfortheseconddriverwillprobablyclaimthatthefirstcar'ssuddenstopcausedhisclienttosmashintoitsback.
Noneoftheseclaimsseemstofitthepatternofaninductiveargument,becausenoneofthemseemsbasedonobservationorexperience.But,infact,theydofitthatpattern.Thebicyclist'slawyer,forexample,isactuallyarguingthat:
∙Normallythebicyclistwouldhavecontinuedinthebikelane,butinthisinstanceheswervedintothelaneoftraffic.
∙Theonlysignificantdifferencebetween"normally"and"inthiscase"isthepresenceoftheillegallyparkedtruck.
∙Therefore,thetruckcausedthebicyclisttoswerve.
Thelawyersforthedriversaremakingsimilararguments:
thefirst,thattheonlysignificantdifferencewastheswervingbicycle;andthesecond,thattheonlysignificantdifferencewasthesuddenlybrakingcar.Likeinductivereasoning,then,thesecausalargumentsarebasedonobservedinstances.(Inthiscase,noobservationsareneededtoconvinceusthatthebicyclistwouldnotnormallyhaveswervedorthefirstdriverwouldnotnormallyhavebrakedsuddenly.Butif,forsomereason,observationswerenecessary,wecoulddesignastudyofautomobileandbicycletrafficonthatstreet,orsurveydriversandbicyclistsabouttheirexperiences,orinotherwaysprovideevidencetoverifythepartofthepremisedescribingthenormalpatternoftraffic.
Thesecausalarguments,then,followtheformofaninductiveargumentwithoneimportantexception:
whereasaninductiveargumentcarriesaspartofitssecondpremisetheimplicationthatthereisotherwisenosignificantdifference,thesecausalargumentscarrytheimplicationthatthereisonlyonesignificantdifference:
forthebicyclist,thetruck;forthefirstdriver,thebicycle;fortheseconddriver,thefirstcar.
Howcanweknowthatthereisreallyonlyonesignificantdifference?
Inreal-lifesituations,wecannotusuallybecertainofthat,sincetheworldinwhichweliveisaverycomplicatedandintricateplace.If,however,thereisastronglikelihoodofcausationandtherearenootherapparentcausesinevidence,thentheargumentwillseemconvincing.Tworulestorememberindealingwithcausationare:
1.Thecausemustprecedetheeventintime.Ononehand,argumentsthathavetheeffectbeforethecauseareexamplesoftherelativelyrarefallacyofreversecausation.Onetheother,argumentswhoseonlyproofofcausationisthattheeffectfollowedthecauseareexamplesoffallaciousposthocreasoning.
2.Evenastrongcorrelationisinsufficienttoprovecausation.Otherpossibleexplanationsforsuchastrongcorrelationincludecoincidence,reversedcausation,andmissingsomethingthatisthecauseofboththeoriginal"cause"anditspurported"effect."
Inthetrial,forexample,theseconddriver'slawyerco
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