AS Lecture 6 26 7.docx
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AS Lecture 6 26 7.docx
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ASLecture6267
FormsofArgument
Inductivearguments=Argumentsthatarenotintendedtoconcludewithcertainty(i.e.,notintendedtobevalid)
Examples:
60%SMUstudentsarebusinessstudents.
MinisanSMUstudent.
>Minisabusinessstudent.
70%ofSMUstudentsarebusinessstudents.
MinisanSMUstudent.
>Minisabusinessstudent.
90%ofSMUstudentsarebusinessstudents
MinisanSMUstudent.
>Minisabusinessstudent.
StatisticalSyllogism
N%ofFsareGs
XisanF
>XisaG
StrongInduction=theimprobabilityofalltruepremises&afalseconclusion
CogentInduction=stronginduction&alltruepremises&allrelevantinformationknowntothearguerincluded
ArgumentfromAnalogy
‘Jane’scarisJapanese,lessthantwo-yearsold,hasafuelinjectionsystemandanenginecapacityoflessthan1300cc.SoisJill’scar.SinceJanegetsgoodmileagepergallon,youcanbeprettysurethatJilldoestoo.’
Xhaspropertiesa,b,c………andz
Yhaspropertiesa,b,c………
_____________________________
SoprobablyYhaspropertyz
InductiveGeneralisation
’10,000Singaporeanswereselectedatrandomand66%ofthesewerefoundtoeatoutatleasttwiceaweek.Probablyabouttwo-thirdsofSingaporeanseatoutatleasttwiceaweek.’
N%ofmembersofarepresentativesampleofclassShavepropertyF
__________________________________________
SoprobablyaboutN%ofS’sareF
ArgumentfromAuthority
‘Singaporeequitieswillprobablydecreaseinvalueduringthenextyear,becausetheMinisterofFinancesaystheywill.’
XsaysthatP(whereXisarelevantauthority)
_____________________________________
SoprobablyP
DeductiveArguments=Argumentsintendedtobevalid
CategoricalSyllogisms
Fivecommonandusefulvalidformsforconstructingandreconstructingarguments
(1)AllSareM
AllMareP
>AllSareP
AllmentaleventsarebraineventsAllbraineventsarephysicalevents
>Allmentaleventsarephysicalevents
(2)AllSareM
NoMareP
>NoSareP
Allastrologicalpredictionsareunfalsifiable
Nounfalsifiableclaimsarefactualclaims
>Noastrologicalpredictionsarefactualclaims
(3)AllMareP
SomeSareM
>SomeSareP
Allgoodchessplayerscanreason
Somecomputersaregoodchessplayers
>Somecomputerscanreason
(4)NoMareP
SomeSareM
>SomeSarenotP
Noactsintendedtosavelivesareimmoral
Someactsoftortureareactsintendedtosavelives
>Someactsoftorturearenotimmoral
(5)AllPareM
SomeSarenotM
>SomeSarenotP
Alldemocraciesareopensocieties
Someregimesarenotopensocieties
>Someregimesarenotdemocracies
PropositionalLogic:
FormsorRulesofInference
Note:
Formsmarkedwith**areinvalid.Theyareunreliableandwearealsolikelytoconfusethemwithvalidforms.Don’tusethem!
ThebutlerisnotnotguiltynotnotP
>Thebutlerisguilty>P
ThebutlerisguiltyP
>Thebutlerisnotnotguilty>notnotP
DoubleNegation(DN)
Wemayalsoarguefromconclusiontopremise
MarkisAmericanP
>MarkisAmericanorJohnisAustralian>PorQ
Addition(A)
ThebutlerisguiltyandthemaidisguiltyPandQ
>Thebutlerisguilty>P
Simplification(S)
JohnisworkingorJohnisathomePorQ
Johnisnotworkingnot-P
>Johnisathome>Q
DisjunctiveSyllogism(DS)
JohnisworkingorJohnisathomePorQ
JohnisworkingP
>Johnisnotathome>not-Q
**FalseDilemma(**FD)
DeMorgan’sLaws(DM)
ItisnotthecaseboththatPolly’sprettyandshe’switty
>EitherPolly’snotprettyorshe’snotwitty
not-(PandQ)
>not-Pornot-Q
Wemayalsoarguefromconclusiontopremise
ItisnoteitherthecasethatPolly’sprettyorshe’switty
>Polly’snotprettyandshe’snotwitty
not-(PorQ)
>not-Pandnot-Q
Wemayalsoarguefromconclusiontopremise
ReasoningwithConditionals
AntecedentConsequent
IfJohnisauniversitystudent,thenJohncanread
=JohnisauniversitystudentonlyifJohncanread
=JohncanreadifJohnisauniversitystudent
IfJohnisauniversitystudent,thenJohncanread
Johnisauniversitystudent
>JohncanreadIfPthenQ
P
ModusPonens(MP)>Q
IfJohnisauniversitystudent,thenJohncanread
Johncannotread
>JohnisnotauniversitystudentIfPthenQ
Not-Q
ModusTollens(MT)>Not-P
IfJohnisauniversitystudent,thenJohncanread
Johncanread
>Johnisauniversitystudent
IfPthenQ
Q
**AffirmingtheConsequent(**AC)>P
IfJohnisauniversitystudent,thenJohncanread
Johnisnotauniversitystudent
>Johncannotread
IfPthenQ
Not-P
**DenyingtheAntecedent(**DA)>Not-Q
IfJohnisauniversitystudentthenJohncanread
>IfJohncannotreadthenJohnisnotauniversitystudent
IfPthenQ
Transposition(T)>Ifnot-Qthennot-P
Ifdeterminismistrue,thenthereisnofreewill
Ifthereisnofreewill,thenthereisnomoralresponsibility
>Ifdeterminismistrue,thenthereisnomoralresponsibility
IfPthenQ
IfQthenR
HypotheticalSyllogism(HS)>IfPthenR
Dilemma(D)
Form1Form2Form3
PorQPornot-PPorQ
IfPthenRIfPthenRIfPthenR
IfQthenSIfnot-PthenRIfQthenR
>RorS>R>R
Eitherouractionsaredetermined,inwhichcasewearenotresponsibleforthem,ortheyaretheresultsofrandomevents,inwhichcasewearenotresponsibleforthem.(DavidHume)
ReductioAdAbsurdum(RAA)
ToprovethatP
(1)Assume:
Not-P.
(2)ShowthatNot-Pentailsafalseproposition(ideallyacontradiction)
(3)ConcludethatP.
1.HeavyobjectsfallfasterthanlightonesAssume
2.m-MisheavierthanM
3.>m-MwillfallfasterthanM1,2
4.mislighterthanM
5.>mwillfallslowerthanM1,4
6.IfmfallsslowerthanMthenmwillslow
Mdownwhenthetwoobjectsarejoined.
7.>m-MwillfallslowerthanM5,6,MP
8.>m-MwillfallfasterandslowerthanM3,7
Contradiction
9.>Heavyobjectsdonotfallfasterthan
lightones1-8,RAA
Themoralrightsofelephants
Elephantshavebeenknowntoburytheirdead.Buttheywoulddosoonlyiftheyhaveaconceptoftheirownspeciesandunderstandwhatdeathmeans.Iftheyunderstandwhatdeathmeans,theyhaveacapacityforabstraction,andiftheyhaveacapacityforabstraction,theycanthink.Yetyouadmitthatelephantshavenomoralrightsonlyiftheycan’tthink.Youmustthereforeacceptthatelephantshavemoralrights.
KeyofPropositions
B=Elephantsburytheirdead
C=Elephantshaveaconceptoftheirownspecies
U=Elephantsunderstandwhatdeathmeans
A=Elephantshaveacapacityforabstraction
T=Elephantscanthink
M=Elephantshavemoralrights
Translation:
B
Bonlyif(CandU)=IfBthen(CandU)
IfU,thenA
IfA,thenT
Not-Monlyifnot-T=Ifnot-M,thennot-T
>M
Argument-Form:
B
IfBthen(CandU)
IfU,thenA
IfA,thenT
Ifnot-M,thennot-T
>M
ProvingvaliditybyrulesofinferenceinVSAF
SAF=StandardArgument-Form
VSAF=ValidStandardArgumentForm
1.BPremise
2.IfB,then(CandU)Premise
3.>CandU1,2,MP
4.>U3,S
5.IfU,thenAPremise
6.>A4,5,MP
7.IfA,thenTPremise
8.>T6,7,MP
9.>notnotT8,DN
10.Ifnot-M,thennot-TPremise
11.>notnotM9,10,MT
12.>M11,DN
ListofEquivalences
Theseareallcommonlyencounteredwaysofsayingthesamething.
AllAareB=Allnon-Barenon-A
NoAarenon-B
OnlyBareA
IfathingisanA,thenitisaB
AthingisanAonlyifitisaB
ItisfalsethatsomeAarenotB
NoAareB=NoBareA
AllAarenon-B
NotanyAareB
NothingisbothAandB
ItisfalsethatsomeAareB
SomeAareB=SomeBareA
SomeAarenotnon-B
ItisfalsethatnoAareB
NoteveryAarenon-B
SomeAarenotB=SomeAarenon-B
ItisfalsethatallAareB
NoteveryAisaB
pandq=qandp
pbutq
p,eventhoughq
p,neverthelessq
porq=qorp
punlessq
qunlessp
Ifnot-p,thenq
Ifnot-q,thenp
Ifpthenq=ponlyifq
Ifnot-q,thennot-p
Not-porq
Not-qorp
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