Inductive and Deductive Reasoning实用文档.docx

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