Knowledge occurs at the intersec3on of belief and truth. In this...
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We begin the course by reviewing what scien3sts call “cri3cal thinking skills.” How do you KNOW what you know? This is also known by the more daun3ng name: epistemology. We are going to spend today talking about the difference between opinion, belief and knowledge and the two different systems we have in our brain for making decisions between what we think is true and what we think is false. The 3tle “Thinking Fast and Slow” comes from a 2011 book by Daniel Kahneman. He and his colleague Amos Tversky (now deceased) developed the two-system model we’ll discuss today. They received a Nobel Prize for their work and helped to found the discipline of behavioral economics. 1
Transcript of Knowledge occurs at the intersec3on of belief and truth. In this...
Webeginthecoursebyreviewingwhatscien3stscall“cri3calthinkingskills.”HowdoyouKNOWwhatyouknow?Thisisalsoknownbythemoredaun3ngname:epistemology.Wearegoingtospendtodaytalkingaboutthedifferencebetweenopinion,beliefandknowledgeandthetwodifferentsystemswehaveinourbrainformakingdecisionsbetweenwhatwethinkistrueandwhatwethinkisfalse.The3tle“ThinkingFastandSlow”comesfroma2011bookbyDanielKahneman.HeandhiscolleagueAmosTversky(nowdeceased)developedthetwo-systemmodelwe’lldiscusstoday.TheyreceivedaNobelPrizefortheirworkandhelpedtofoundthedisciplineofbehavioraleconomics.
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Knowledgeoccursattheintersec3onofbeliefandtruth.Inthisdiagram,thingsareeithertrue(ornot)andtheyareeitherbelieved(ornot).No3cethatnotalltruethingsarebelievedandthatthereisplentyofroomontheright-handsideofthediagramforthingsthatwebelieve–butthatarenottrue.Whatisanexampleofsomethingthatwebelieveinbutwhichisn’ttrue?(Un3lwe’reabout7or8,probablySantaClaus).Knowledgeoccursattheintersec3onoftruthandbelief.Knowledgeiscreatedwhenwetakeabelief(youcancallitahypothesisoranopinionifyouwantto)andputittothetest.Ifourbeliefpassesthetest,wenowsayitistrue.
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Aswetrytoexpandourknowledge,wecanusethingswealreadyknowforsuretotryandprovethingsweareunsureof.Thismethod,oftakingpiecesofknowledge(alsoknownas“facts”)andlinkingthemthroughlogictoformaconclusion,isknownasconstruc3nganargument.Theclassicformofanargumentiscalledasyllogism.Here,statementsoffact(called“premises”)arelinkedthroughlogictoreachaconclusion.Example:
Premise1:SocratesishumanPremise2:Allhumansaremortal
Therefore(usingthelogicofthetransi3veproperty)
Conclusion:Socratesismortal.
Note:thetransi3vepropertyshouldbefamiliarfrommathclass.IfA=BandB=Cthen,A=C.
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Anotherwayoflookingatthesyllogismisthroughsettheory.Here,letSetAbeSocrateswhoisasubsetofSetB(allhumans).SetBisitselfasubsetofSetC(allthingsthataremortal).Therefore,SetA(Socrates)isasubsetofSetC(thingsthataremortal).
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Youneedtoseparatethetruthofthepremisesfromthelogicusedtoconnectthem.Youcanhaveavalidargument(thatis,onewithvalidlogic)butthepremisescanbeflawed,resul3nginafalseconclusion.Argumentscangobadoneoftwoways.First,thelogiccanbeflawed(invalidorfalseorfallacious)asinthethirdexampleabove.Orthepremisescanbeflawed(orfalse).Asinthesecondexampleabove–weknowthatnotallmenaremad.Thatpremiseisfalse.You’lldiscovertomorrowthatargumentsbuiltonbadlogicarewaymorecommonthanyoumighthavethought.
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Thetypeofreasoningwe’vebeendescribingisobenreferredtoasdeduc3velogicordeduc3vereasoning.Mostmathema3csfollowsthistypeofreasoning.Youstartoffwithsomeaxiomsorpremisesandyouwindupwithaconclusion.Indeduc3velogic,ifthepremisesaretrueandthelogicisvalid,theresultisalwaystrue.Completelytrue,not“probablytrue”.
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Hereisagoodexampleoftheflawedorfalsepremise.IsSoutheastnormalortypicalforahighschool?Thatgetstowhatdowemeanby“normal”or“typical”?TheGreekphilosopherSocratessaidwemustfirstdefineourtermsbeforewecanusededuc3on.InthatWakeCountyisonlyabout20%African-American,Southeastisnot“normal”.InthatSoutheasthasthesamebasicclassesasallotherWakeCountyhighschools,Southeastis“normal”.
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Induc3vereasoningisfamiliartoanyonewhohasstudiedtheScien3ficMethod.Wemakeobserva3onsandformahypothesis.Wetestourhypothesisbymakingmoreobserva3ons.Weeitheracceptorrejectourhypothesisandreachaconclusion.Withinduc3on,wecanneverbe100%sureofourconclusion.Newobserva3onsmightforceustorejectourconclusion.Induc3veconclusionsareeitherstring(backedupbylotsofobserva3ons)orweak(backedupbyveryfewobserva3ons).
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Asitstandsnow,myconclusionisweak.TherearecertainlymanyotherobjectsthatareyellowandsourthatareNOTlemons.Icouldimprovethequalityofmyinduc3veargumentbyincreasingthedetailonthepremises.IfIrewriteitas“MostFRUITSthatareyellowandsourarealsolemons”andthenturnthesecondpremiseinto“ThisFRUITisbothyellowandsour”,Ihaveamuchstrongerargument.
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Mostpeopledon’tusededuc3onorinduc3ontomaketheirdecisionsonwhatisorisn’ttrue.Mostpeoplerelyon“gutfeelings”or“ins3nct”.Twopsychologists,AmosTverskyandDanielKahneman,studiedthisandrealizedthathumanshaveevolvedtwoseparate,independentsystemsinourbrainsfordecidingwhatistrueorfalse.Thefirstandmostcommonisthequick“gutfeeling”orins3nctualapproach.Thesecondoneinvolvesdeduc3onandinduc3onandismuchslowerthanthefirst.The“System2”asdescribedbyKahnemanandTverskyisalsouniquetohumans.Itmaybewhatmakesushuman.
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System#1isfast.Itisemo3onal.Itisbasedonins3nct.Formostpeople,relyingonSystem#1heuris3csishowtheygetthroughlife.Examplesofheuris3cs:theavailabilityheuris3csaysthatifwehearalotoflionroarsinthedistance,theremustbelionsnearby.Workspremygoodwithlionsbutbreaksdowninmodernsitua3ons.Eventhoughcrimehasbeendecliningsteadilyfordecades,wes3llhearaboutitfrequentlyinthenewsmedia,givingusthemistakenimpressionthatcrimeratesareactuallygoingup.Mostracismisbasedonafaultyheuris3c.
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WhileSystem#1mayworkfinewhenitcomestolionsandtheprobabilityoflionamacks,itbreaksdownwhenfacedwitheventhesimplestquan3ta3veques3on.Intheproblemabove,themajorityofstudentssaytheballmustcosttencents.Theyareusingaruleofthumbtoarriveattheiranswerandtheyarewrong.Theballactuallycostsanickel.
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System#2isafairlyrecentaddi3ontohumanbehavior.Itseemstorequirewri3ngtoreallymakeitworkandwe’veonlyhadwri3ngforabout5,000years.System#2isslowandlogicalandprecise.WhenSystem#2arrivesatadecision,usingpremisesthataretrueandlogicthatisvalid,theconclusionisalmostalwayscorrect.It’shardtofoolSystem#2.Intheballandbatexampleonthepreviousslide,Ifollowedanalgorithmtoconvertmyworkproblemtoanequa3onandthenusdanotheralgorithmtosolvetheequa3onandinterprettheanswer.
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“Analysisparalysis”referstotheinabilitytomakeasimpledecision(likewhattowatchonNenlix)ifyouhavetochoosebetweendozensorhundreds(orthousands)ofpossiblechoices.Alotofourbaddecisions,alotofourfalsebeliefsarisebecauseweuseSystem#1whenweshouldbeusingSystem#2.Iontheotherhand,usingSystem#2foreverythingcanbeexhaus3ngandcounter-produc3ve.
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Here’sanexampleofhowSystem#1thinkingor“commonsense”canleadyouastray.Inournexttwoexamples,we’regoingtofocusontherepresenta3venessheuris3c,whichsaysthateverythingcanbeputintocategories.Ifitquackslikeaduck,it’sprobablyaduck,right?Simplecommonsense.Buthowrealis3cwouldthatassump3onbeifIheardaquacking-typenoisewhileinAntarc3ca?DucksarenotcommonplaceinAntarc3ca.I’mprobablyhearingthenoisesmadebyapenguininstead.KnowinghowcommonorappropriatethecategoriesareforwhereIamin3meandspaceiscalledthebaserate.ThebaserateforducksinAntarc3caispremylow,butI’dneedtobeusingSystem#2torealizethat.
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Roughly1%ofthena3onisemployeddirectlyinagriculture.That’safewmillionpeople.Onlya3ny,3nyfrac3onofthepopula3onplaytrumpetinmajorsymphonyorchestras.Maybelessthanahundredintotal.Thus,thebaserateforfarmersisfargreaterthanthebaseratefortrumpetplayers.System#1saysTomplaystrumpet.System#2saysitismorelikelythatTomisafarmer.
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ItlookspremyobviousthatLindaisprobablyafeminist.Butremember,ourchoicesare“bankteller”versus“feministbankteller”.Here,youneedtorealizethatthesetoffeministbanktellersisasubsetofthesetofallbanktellersandthus,hasasmallerbaserate.
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InFrance,GermanyandBelgium–youareautoma3callysignedupasanorgandonorwhenyougetadriver’slicense.Youcanoptoutifyouwant,butthatrequiresaseparateform.InEngland,theNetherlandsandAustria,thesitua3onisreversed.Youhavetooptinfororgandona3onandcheckaspecialboxonyourlicenseform.ThisdemonstrateshowlimlepeopleliketothinkandhowcommimedtheyaretousingSystem#1thoughtprocesses.
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