deductive

LegalReasoning

LegalReasoning

InductiveandDeductivepatterninargumentInductiveanddeductiverefertotwodistinctlogicalprocess.

Inductivereasoningisamovementfromaspecificexamplesoractivitiestogeneralizationorrule.

Deductivereasoningisamovementfromageneralizationtospecific.

(⼀)InductiveReasoning

Inductivereasoningisreasoninginwhichthepremisektosupplystrongevidencefor(notabsoluteproofof)thetruthof

heconclusionofadeductiveargumentiscertain,thetruthoftheconclusionofaninductiveargument

isprobable,badupontheevidencegiven.

Thephilosophicaldefinitionofinductivereasoningismorenuancedthansimpleprogressionfromparticular/individual

,thepremisofaninductivelogicalargumentindicatesomedegreeofsupport

(inductiveprobability)fortheconclusionbutdonotentailit;thatis,manner,

thereisthepossibilityofmovingfromgeneralstatementstoindividualinstances(forexample,statisticalsyllogisms,

discusdbelow).

Anexampleofaninductiveargument:

90%ofbiologicallifeformsthatweknowofdependonliquidwatertoexist.

Therefore,ifwediscoveranewbiologicallifeformitwillprobablydependonliquidwatertoexist.

Thisargumentcouldhavebeenmadeeverytimeanewbiologicallifeformwasfound,andwouldhavebeencorrectevery

time;however,itisstillpossiblethatinthefutureabiologicallifeformnotrequiringwatercouldbediscovered.

Asaresult,theargumentmaybestatedlessformallyas:

Allbiologicallifeformsthatweknowofdependonliquidwatertoexist.

Allbiologicallifeprobablydependsonliquidwatertoexist.

Theformsofinductivereasoning

1.1Generalization

Ageneralization(moreaccurately,aninductivegeneralization)proceedsfromapremiaboutasampletoaconclusion

aboutthepopulation.

TheproportionQofthesamplehasattributeA.

Therefore:

TheproportionQofthepopulationhasattributeA.

Example

Thereare20balls—eitherblackorwhite—matetheirrespectivenumbers,youdrawasampleoffourballs

nductivegeneralizationwouldbethatthereare15black,andfive

white,ballsintheurn.

Howmuchthepremissupporttheconclusiondependsupon(a)thenumberinthesamplegroup,(b)thenumberinthe

population,and(c)thedegreetowhichthesamplereprentsthepopulation(whichmaybeachievedbytakingarandom

sample).Thehastygeneralizationandthebiadsamplearegeneralizationfallacies.

1.2Statisticalsyllogism

Mainarticle:Statisticalsyllogism

Astatisticalsyllogismproceedsfromageneralizationtoaconclusionaboutanindividual.

AproportionQofpopulationPhasattributeA.

AnindividualXisamemberofP.

Therefore:

ThereisaprobabilitywhichcorrespondstoQthatXhasA.

Theproportioninthefirstpremiwouldbesomethinglike"3/5thsof","all","few",tosimpliciterfallaciescan

occurinstatisticalsyllogisms:"accident"and"converaccident".

1.3Simpleinduction

Simpleinductionproceedsfromapremiaboutasamplegrouptoaconclusionaboutanotherindividual.

ProportionQoftheknowninstancesofpopulationPhasattributeA.

IndividualIisanothermemberofP.

Therefore:

ThereisaprobabilitycorrespondingtoQthatIhasA.

Thisisacombinationofageneralizationandastatisticalsyllogism,wheretheconclusionofthegeneralizationisalsothe

firstpremiofthestatisticalsyllogism.

1.4Argumentfromanalogy

Mainarticle:Argumentfromanalogy

Theprocessofanalogicalinferenceinvolvesnotingthesharedpropertiesoftwoormorethings,andfromthisbasisinferring

thattheyalsosharesomefurtherproperty:

PandQaresimilarinrespecttopropertiesa,b,andc.

ObjectPhasbeenobrvedtohavefurtherpropertyx.

Therefore,Qprobablyhaspropertyxalso.

Analogicalreasoningisveryfrequentincommonn,science,philosophyandthehumanities,butsometimesitis

edapproachisca-badreasoning.

1.5Causalinference

Acausalinferencedrawsaconclusionaboutacausalconnectionbadontheconditionsoftheoccurrenceofaneffect.

Premisaboutthecorrelationoftwothingscanindicateacausalrelationshipbetweenthem,butadditionalfactorsmustbe

confirmedtoestablishtheexactformofthecausalrelationship.

1.6Prediction

Apredictiondrawsaconclusionaboutafutureindividualfromapastsample.

ProportionQofobrvedmembersofgroupGhavehadattributeA.

Therefore:

ThereisaprobabilitycorrespondingtoQthatothermembersofgroupGwillhaveattributeAwhennextobrved.

(⼆)DeductiveReasoning

Deductivereasoning,alsodeductivelogic,logicaldeductionor,informally,top-down"logic,istheprocessofreasoningfrom

oneormorestatements(premis)ersfrominductivereasoningorabductive

reasoning.

remisaretrue,thetermsareclear,andtherulesofdeductive

logicarefollowed,thentheconclusionreachedisnecessarilytrue.

Deductivereasoning(top-downlogic)contrastswithinductivereasoning(bottom-uplogic)inthefollowingway:Indeductive

reasoning,aconclusionisreachedreductivelybyapplyinggeneralrulesthatholdovertheentiretyofacloddomainof

discour,narrowingtherangeunderconsiderationuntilonlytheconclusion(s)ctivereasoning,theconclusion

isreachedbygeneralizingorextrapolatingfrom,i.e.,,however,thattheinductive

reasoningmentionedhereisnotthesameasinductionudin

mathematicalproofs–mathematicalinductionisactuallyaformofdeductivereasoning.

Forexample:

Majorpremi:Allmenaremortal.

Minorpremi:Socratesisaman.

Conclusion:Socratesismortal.

Rule:Tobeenforceable,thecontractforthesaleofgoodsforapriceof$500ormoremustbeinwriting.

Facts:Theoralcontractforthesaleofthegoodswasnotfor$500ormore.

Legalconclusion:Thecontractinthiscainforceable.

Summary:

Derienceisthesyllogism.

Legalproblemsolvinginthecivillawtraditionisakindofdeductivereasoning,whichisbadonrulesthecontentsofwhich

arepositedpriortotheproblemstowhichtheymustbeapplied.

Forlegaldeductivereasoning,ybefromtheconstitution,astatute,an

administrativeregulation,treaty,executiveorder,,,conclude.

Theformsofdeductivereasoning

1.1Thelawofdetachment

econditionalstatementismade,andahypothesis(P)

clusion(Q)tbasicformislistedbelow:

1.P→Q(conditionalstatement)

2.P(hypothesisstated)

3.Q(conclusiondeduced)

Indeductivereasoning,wecanconcludeQfromPbyusingthelawofdetachment.[3]However,iftheconclusion(Q)isgiven

insteadofthehypothesis(P)thenthereisnodefinitiveconclusion.

Thefollowingisanexampleofanargumentusingthelawofdetachmentintheformofanif-thenstatement:

glesatisfies90°

2.A=120°.

btuangle.

SincethemeasurementofangleAisgreaterthan90°andlessthan180°,

however,wearegiventheconclusionthatAisanobtuanglewecannotdeducethepremithatA=120°.

1.2Thelawofsyllogism

Thelawofsyllogismtakestwoconditionalstatementsandformsaconclusionbycombiningthehypothesisofonestatement

thegeneralform:

1.P→Q

2.Q→R

ore,P→R.

Thefollowingisanexample:

yissick,thenhewillbeabnt.

yisabnt,thenhewillmisshisclasswork.

ore,ifLarryissick,thenhewillmisshisclasswork.

Wededucedthefinalstatementbycombiningthehypothesisofthefirststatementwiththeconclusionofthecond

anexampleoftheTransitivePropertyinmathematics.

TheTransitivePropertyissometimesphradinthisform:

1.A=B.

2.B=C.

ore,A=C.

1.3Thelawofcontrapositive

Thelawofcontrapositivestatesthat,inaconditional,iftheconclusionisfal,

generalformisthefollowing:

1.P→Q.

2.~Q.

ore,wecanconclude~P.

Thefollowingareexamples:

raining,thentherearecloudsinthesky.

renocloudsinthesky.

,itisnotraining.