assumes

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曼哈顿笔记

目录

uttheArgument.................................................................................................................................1

rgument..............................................................................................................1

OntheGMAT.....................................................................................................................................................2

Thearguer’sjobandyourjob.........................................................................................................................2

Listofthetwelveflaws.....................................................................................................................................2

Detailsofthetwelveflaws...............................................................................................................................3

ifiedAssumptions......................................................................................................................3

ionErrors..................................................................................................................................4

isonErrors...............................................................................................................................5

rors...........................................................................................................................................6

icationErrors.........................................................................................................................7

Findthegapsinarguments.............................................................................................................................7

ngtheQuestionStemandStratege..............................................................................................8

uttheArgument

rgument

Everycompleteargumenthastwocomponentswrittendownonpaper:

•Premis—supportingstatements

•Conclusion—themainpointorbiggestclaimoftheargument

Asoundargumentissuccessfuloneverylevel:thepremisaretrue,andtheconclusionlogicallyfollows

onclusionfollowslogicallyfromtruepremis,thatconclusionistherefore

true.

Avalidargumentisoneinwhichtheconclusionfollowslogicallyfromthepremis—butthepremis

idargument,ifthepremisaretrue,thentheconclusionwillalso

betrue.

Inagood,validargument,ovideenough

evidencetoguaranteethetruthoftheconclusion(whichisoccasionallyimpliedratherthanstated

explicitly).

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OntheGMAT

Whilesoundnessisthegoalinreal-lifereasoning,,

ontheGMAT,avoidchallengingthetruthofthepremisthemlves.

Focusonwhethertheargumentisvalid.

Thearguer’sjobandyourjob

People’sbrainsaredesignedtomakeconnectionsandtogobeyondthearguer’sconclusion.

OntheGMAT,however,youshouldnotethespeaker’sconclusionprecily.

It’sthejobofthearguertoprovehisorhercatoyoubybuildingasoundargumentbackedby

bissimplytorecognizeflawsandomissions.

Listofthetwelveflaws

Theflawsoverlapsomewhat;itdoesn’n’’smore

y,youcanspotanyofthemon

thetest.

ifiedAssumptions

sSharedBeliefs

xtremeConclusion

sSkilland/orWill

gueorAlteredTerms

sSignsofaThing=ThingItlf

ionErrors–oversimplification

pCorrelationandCausation

stheFuture=thePast–ngsareequal

stheBestMeansSuccess

isonErrors

ectionBias(Unreprentativesample,survivorbias,ever-changingpool)–

isdoubtful

ubledAnalogy–nalogy

rors

estheQuantities(percent,rates,ratios)

icationErrors

gthePoint

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Detailsofthetwelveflaws

ifiedAssumptions

Anargumentwiththissortofflawrequiresanunspokenandunsupportedpremi—thatis,the

authorisdependingonapremithatheorshedidn’twritedownandhasn’,the

conclusioncan’tbevalidatedunlesstheassumptioncanbeproven.

sSharedBeliefs

Thearguerassumesthatthelistenerwillsharecertainbasicbeliefs—someofwhicharemere

impressions,prejudices,andsoon.

Thespeaker’sargumentdependsontheideathat―teenagersunder16aremorelikelytomaketheaters

dirtyandtodamagethefacilities,‖thespeakerdidn’tevenbothertowritethat—andheorshecertainly

didn’tproveit.

Don’ttakeanythingforgranted,anddon’tbringinoutsideideas.

It’sthearguer’’syourjobtonoticethatthearguerhasn’tdoneso.

xtremeConclusion

Theconclusionuslanguagesoextremethatthepremiscannotjustifythatconclusion:

Watchoutfortheextremewords:only,never,always,cannot,certainly,obviously,inevitably,

most,least,best,worst.

gisthebestmethodever?Betterthanswimming,tennis,anda

millionotherthings?Evenifyouprovethatjoggingisbetterinsomerespectthanstationarybicycling,

allyoucansayisthatjoggingisbetterthanoneotheractivity,notthatit’sthebest.

Keepinmindthatevenaperfectlyreasonableargumentcanbedestroyedbytoostrongaconclusion.

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sSkilland/orWill

Forpeopletodosomething,theyhavetobeabletodoit,andtheyhavetowantto.

Someargumentsgiveyouonepiecebutnottheother.

Butbothskillandwillarenecessary.

gueorAlteredTerms

Justasyouareonthelookoutforextremelanguage,you’realsoonthelookoutforvagueoraltered

languagethroughouttheargument.

RecallthePeoplewhojogargument:Whatonearthdoesitmeantoexercithesameamountas

someonewhoisjogging10miles?Doesitmeanbikingforthesameamountoftimeorthesamedistance?

Thesamenumberofcaloriesburned?It’smuchfastertoride10milesonastationarybikethantojog10

miles,soifthearguermeansthatthedistancesarethesame,thenthere’sanotherreason(besidesthe

author’sconclusion)thatthejoggershavelessheartdia:theyareexercisingmorehoursperweek.

onanytermthat’sinsufficientlypreci.

Likewi,anychangeintermsthroughthecouroftheargumentshouldmakeyouarchaneyebrow.

Whetherthetermsbecomemoregeneralormorespecific,theargumentnowhasafissureinitslogic.

sSignsofaThing=ThingItlf

Don’ften,reportingeffectis

especiallyacutewhenpeoplehaveanincentive(suchasmoney)toover-report,oranincentive(suchas

fearorlaziness)tounder-report.

Forinstance,reportsofcrimessuchaslitteringandjaywalkingareinfrequent—thatdoesn’t

meanpeoplearen’sofwhiplashfromcar

accidents,however,tendtobehighlyinflated(atleastintheU.S.),sincevictimsareoftenina

sofworkplaceharassmentorother

improperworkingconditionsmaybelessfrequentthanactualincidentsifworkersfearlosing

theirjobs.

Anothercommonvariationonthisproblemassumesthat,becaualawexists,peoplemustbe

notthesameascompliancewithalaw.

ionErrors

Manyconclusionsasrtthatsomethingisthecauofsomethingel,usuallywithouttheword―cau‖

olyattheverb:cau,make,force,leadto,prevent,protect,increa,decrea,

okatinfinitives(ce),ievementofgoals

requirescausation.

pCorrelationandCausation

Iftwothingsoccurtogether(correlation),youcan’tautomaticallyconcludethataparticularcausalmodelis

,ifXhappenedshortlyafterY,youcannotnecessarilyconcludethatXwascaudby

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ew:IfXandYemtobecorrelated,andthentherearefourpossibilities:

(1)XcausY.

(2)YcausX.

(3)Z(someotherphenomenon)causbothXandY.

(4)It’sanaccident;youdon’thaveallthedata.

Logically,MAT,you’ll

minatingevenonewillstrengthenyourca.

stheFuture=thePast

stheBestMeansSuccess

Sometimes,avarietyofoptionsareavailabletosolveaproblem,butnoneofthooptionsarevery

esnotaffectwhetheranoptioncanbeconsideredthebest,whetherithad

somebeneficialeffect,orwhetheritcouldstillbethebestsolutiontoalessvereversionoftheproblem.

Forinstance,ifanewCEOishiredtotrytorescueacompanyonthebrinkofbankruptcy,even

onediesofaterriblediathat

doesnotmeanthathedidnotreceiveoptimalmedicalcare.

Sometimeventhebestthingfails.

isonErrors

Theassumptiontypicallybeingthatthetwothingsaresimilarenoughintheimportantwaystobe

compared.

ectionBias

Wheneveryoucomparetwogroups,youhavetomakesurethatthetwogroupsarelegitimately

particularlytricky

whenthetwogroupsemcomparable—forinstance,whentheyarebothdrawnfromthesame

reafewvariationsoflectionbias:

9.1UnreprentativeSample

Wouldn’tthatsampleofcustomersbebiadtowardpeoplewholikeyou?Afterall,theyfilledoutalong

entialforlf-lectionbiasisstronghere.

Somecustomerswhofilledoutalongsurveyforfreesaidthattheyloveourcompany.

Soourcustomersloveourcompany.

9.2SurvivorBias

Here,itislikelythatthowholivedtobe100didsoinpartbynotsmoking,andthatplentyofpeopleborn

100ormoreyearsagodidsmokeanddidnotlivetobe100.

Asurveyoflivingpeopleover100showedlowerratesofcigarettesmokingthanwereshownin

ore,smokingisontheri.

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9.3Ever-ChangingPool

Fiveyearsago,peopleoppodthenewdorm,andnow80%ofrespondentstoapolllikethedorm.

Arethepollrespondentsthesamepopulationasthevoters?Maybethepollwasconductedonor

nearcampus;ahighpercentageofstudentsinthepollwouldcertainlyskewresults.

ApetitioniscirculatinginCapitalCityopposingthebuildingofanewsportscenteratState

University,arsago,manycityresidents

oppodthebuildingofthenewStateUniversitydormitorycomplex,yetinapollthisyear,80%

oeople

whocurrentlyoppothenewSportsCenterarepatient,theywillchangetheirminds.

10．TheTroubledAnalogy

There’snothingwrongwithagoodanalogy,ime

youmakeananalogy,you’resayingthatsomethingislikesomethingel—exceptthatitisn’texactlylike

that,oryou’djustbetalkingabouttheoriginaltopic.

It’syourjobtopointoutthatthearguerhasnotestablishedenoughsimilaritiesbetweenthetwoobjectsto

drawaneffectiveanalogybetweenthem.

rors

Tovalidatethisclaim,evenjustforonecatowner,youwouldneedtoknow1)howmuchmorethe

catfoodcoststhanthekindthatthecatownercurrentlybuys,2)howmuchtimethecatowner

spendscleaninguphair,and3)themonetaryvalueofthecatowner’’ssubstantial!

Accordingtoarecentstudy,catsthateatPremiumCatFoodhavehealthiercoatsandshedless

hairthanthothatdon'remiumCatFoodcostsmore,thetimesavedcleaninguppet

hairfromfurnitureandrugsmakesPremiumCatFoodawichoiceforcatowners.

estheQuantities

Celadon,anewtherapyforthetreatmentofaddictiontotheillegaldrugtaroCaine,hasbeen

proveneffectiveinastudycenteredaroundRegisHospitalinthewesternpartofthestateof

dyinvolvedlocaltaroCaineaddictswhorespondedtoanewspaperad

ipantswhoreceivedceladonandcounlingwere40%more

likelytorecoverthanwerepatientsassignedtoacontrolgroupandwhoreceivedonly

tionaltherapieshaveonlya20%ore,thebestway

toreducedeathsfromtaroCaineoverdothroughoutallofNewPortsmouthwouldbetofund

celadontherapyforalltaroCaineaddicts.

40%certainlylookslikeahighernumberthan20%.However,the20%isanactualrecoveryratefor

40%isapercentincreaonanunknownfigure—therecoveryrateofthe

enowaytocomparethistoanactual20%tance,whatifthe

controlgrouphada50%recoveryrate?Thenthecetadonegroupwouldhave70%recoveryrate(1.4x

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50).Butwhatifthecontrolgrouphada1%recoveryrate?Thenthecetadonegroupwouldhavea1.4%

recoveryrate,thatyouarementally

ytodothesame.

Inshort,ifanynumbersornumericrelationshipsareprentedinanargument,determinewhether

theyarebeingcitedinalogicalway.

AfewotherstandardmathematicalrelationshipsshowupinCriticalReasoningaswell:

RatexTime=Distance

Profit=Revenue-Costs

(DollarsperHour)xHours=Dollars

icationErrors

gthePoint

Somepeoplesayweshouldconsumelessoiltolowerourdependenceonsuppliesfrom

nehasyetproventhelinkbetweenoilconsumptionand

climatechange.

Thistypeofflawisverycommonwhenpeopleargueovercaustheyfeeldeepemotionsabout.

Findthegapsinarguments

Foreachargument,regapsmuchlargerthanothers

udentsare

ore,aprogramoffree

schoollunchesshouldhelpthestudentsperformatgradelevel.

Youmightdiagramitinthisway:

Notethatthet

tscan’taffordlunch,sotheydon’teatlunch,e

agap?

Whileitcertainlydoesemreasonablethatalackoffoodwouldcontributetopooracademic

performance,,thestudentsarehungryandtheyaredoingpoorly,

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butisthehungerreallycausingthepoorperformance?Howmuchofthepoorperformanceisit

causing?Couldtherebesomeotherfactorcontributingtothepoorperformance?

Thecondgapismuchlarger,nchwillhelpstudentsperformatgradelevel?That’s

unately,thereareentireschoolsinwhichthemajorityofchildrenperformfar

belowgradelevel,anditisdoubtfulthatlunchalonewouldfixtheentireproblem.

ngtheQuestionStemandStrategy

GMATQuestionstemsfallintoafewbroadcategories:

QuestionsaboutAssumptions

QuestionsaboutEvidence

QuestionsaboutStructure

ItcanbehelpfultocategorizeeachquestionasinvolvingAssumptions,Evidence,t

important

alsorecommendedthatyouwritedownabriefnoteaboutthequestionasareminder.

Justremembertomaintaingoodstrategy:

readthequestionstemfirst,

diagramtheargument,

anticipatetheanswer,

anduprocessofelimination.

Anexample:

Whilemanypeoplethinkofthelotteryasaharmlesswaytohavefunandpossiblywinsome

money,ore,publicofficialsshouldn'tbuy

lotterytickets.

Whichofthefollowing,iftrue,wouldmoststrengthentheconclusion?

Youcanmentallydismissthatpartandthinkoftheargumentthisway:

ore,publicofficialsshouldn'tbuy

lotterytickets.

Diagramtheargument:

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ral,identifyassumptions

beforereadingtheanswerchoices,soyoudon’tgettrickedbyevilwronganswersthatarethereto

distractyou.

Keepinmindthatyou’looking

specificalldananswer

thatlinksthepremitotheconclusion.

Ifyou’rehavingtroublewithyouroriginalargument,translateittoasimpler,

beeasiertofigureouttheassumption.

ore,publicofficialsshouldn'tliftweights.

Thengobacktotheargument:TheassumptionhereisPublicofficialsshouldn'diagram,

youwouldeitasPO'sshouldn'tG.

Someotherpointsfromthecommentsoftheexercis:

AsacorrectGMATanswerwillnotgenerallyinsultanyone.

Somechoicesemtobetryingtoargueagainstthepremimentionedintheargument,butsince

wealreadytakethepremiasafact,thechoicesdon’treallyhaveanimpactontheargument—

surely,theymightbetrue,age,thefactin

premiisstillvalid.