Table Of Content1
Basic Concepts
1.1
Arguments, Premises, and Conclusions
Logic may be defined as the science that evaluates arguments. All of us encounter
arguments in our day-to-day experience. We read them in books and newspapers,
hearthem ontelevision,andformulate themwhencommunicatingwithfriendsand
associates.Theaimoflogicistodevelopasystemofmethodsandprinciplesthatwe
mayuseascriteriaforevaluatingtheargumentsofothersandasguidesinconstructing
argumentsofourown.Amongthebenefitstobeexpectedfromthestudyoflogicis
anincreaseinconfidencethatwearemakingsensewhenwecriticizethearguments
ofothersandwhenweadvanceargumentsofourown.
Anargument,asitoccursinlogic,isagroupofstatements,oneormoreofwhich
(the premises) are claimed to provide support for, or reasons to believe, one of the
others (the conclusion). All arguments may be placed in one of two basic groups:
thoseinwhichthepremisesreallydosupporttheconclusionandthoseinwhichthey
donot,eventhoughthey are claimedto.Theformeraresaidtobegoodarguments
(atleasttothatextent),thelatterbadarguments.Thepurposeoflogic,asthescience
thatevaluatesarguments,isthustodevelopmethodsandtechniquesthatallowusto
distinguishgoodargumentsfrombad.
Asisapparentfromtheabovedefinition,theterm‘‘argument’’hasaveryspecific
meaning in logic. It does not mean, for example, a mere verbal fight, as one might
havewithone’sparent,spouse,orfriend.Letusexaminethefeaturesofthisdefinition
in greater detail. First of all, an argument is a group of statements. A statementisa
sentence thatis eithertrueorfalse—inotherwords,typicallyadeclarativesentence
or a sentence component that could stand as a declarative sentence. The following
sentencesarestatements:
Aluminumisattackedbyhydrochloricacid.
BroccoliisagoodsourceofvitaminA.
ArgentinaislocatedinNorthAmerica.
S
NapoleonprevailedatWaterloo.
RembrandtwasapainterandShelleywasapoet. N
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The first two statements are true, the second two false. The last one expresses two
statements,bothofwhicharetrue.Truthandfalsityarecalledthetwopossibletruth
valuesofastatement.Thus,thetruthvalueofthefirsttwostatementsistrue,thetruth
value of the second two is false, and the truthvalue of the laststatement,as wellas
thatofitscomponents,istrue.
Unlike statements, many sentences cannot be said to be either true or false.
Questions, proposals, suggestions, commands, and exclamations usually cannot,
and so are not usually classified as statements. The following sentences are not
statements:
Whatistheatomicweightofcarbon? (question)
Let’sgototheparktoday. (proposal)
Wesuggestthatyoutravelbybus. (suggestion)
Turntotheleftatthenextcorner. (command)
Allright! (exclamation)
Thestatementsthatmakeupanargumentaredividedintooneormorepremises
andoneandonlyoneconclusion.Thepremisesarethestatementsthatsetforththe
reasonsorevidence,andtheconclusionisthestatementthattheevidenceisclaimed
tosupportorimply.Inotherwords,theconclusionisthestatementthatisclaimedto
followfromthepremises.Hereisanexampleofanargument:
Allcrimesareviolationsofthelaw.
Theftisacrime.
Therefore,theftisaviolationofthelaw.
Thefirsttwostatementsarethepremises;thethirdistheconclusion.(Theclaimthat
thepremisessupportorimplytheconclusionisindicatedbytheword‘‘therefore.’’)In
thisargumentthepremisesreallydosupporttheconclusion,andsotheargumentisa
goodone.Butconsiderthisargument:
Somecrimesaremisdemeanors.
Murderisacrime.
Therefore,murderisamisdemeanor.
In this argument the premises do not support the conclusion, even though they are
claimedto,andsotheargumentisnotagoodone.
One of the most important tasks in the analysis of arguments is being able to
distinguishpremisesfromconclusion.Ifwhatisthoughttobeaconclusionisreallya
premise, and vice versa, the subsequent analysis cannot possibly be correct. Fre-
quently, arguments contain certain indicator words that provide clues in identifying
premisesandconclusion.Sometypicalconclusionindicatorsare
2 Chapter1: BasicConcepts
therefore accordingly entailsthat
wherefore wemayconclude hence
thus itmustbethat itfollowsthat
consequently whence impliesthat
wemayinfer so asaresult
Wheneverastatementfollowsoneoftheseindicators,itcanusuallybeidentifiedas
theconclusion.Byprocessofeliminationtheotherstatementsintheargumentarethe
premises.Example:
Corporateraidersleavetheirtargetcorporationwithaheavydebtburdenandno
increaseinproductivecapacity.Consequently,corporateraidersarebadforthe
businesscommunity.
The conclusionof this argumentis‘‘Corporateraidersarebadforthebusinesscom-
munity,’’ and the premise is ‘‘Corporate raiders leave their target corporation with a
heavydebtburdenandnoincreaseinproductivecapacity.’’
Claimed
Premises
evidence
What is claimed to follow
Conclusion
from the evidence
If an argument does not contain a conclusion indicator, it may containa premise
indicator.Sometypicalpremiseindicatorsare
since inthat seeingthat
asindicatedby maybeinferredfrom forthereasonthat
because as inasmuchas
for giventhat owingto
Anystatementfollowingoneoftheseindicatorscanusuallybeidentifiedasapremise.
Example:
Expectantmothersshouldneveruserecreationaldrugs,sincetheuseofthese
drugscanjeopardizethedevelopmentofthefetus. S
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Arguments,Premises, and Conclusions 3
Thepremiseofthisargumentis‘‘Theuseofthesedrugscanjeopardizethedevelop-
mentofthefetus,’’andtheconclusionis‘‘Expectantmothersshouldneveruserecre-
ationaldrugs.’’
One premise indicator not included in the above list is ‘‘for this reason.’’ This
indicatorisspecialinthatitcomesimmediatelyafterthepremisethatitindicates.‘‘For
thisreason’’(exceptwhenfollowedbyacolon)meansforthereason(premise)that
wasjustgiven.Inotherwords,thepremiseisthestatementthatoccursimmediately
before‘‘forthisreason.’’Oneshouldbecarefulnottoconfuse‘‘forthisreason’’with
‘‘forthereasonthat.’’
Sometimesasingleindicatorcanbeusedtoidentifymorethanonepremise.Con-
siderthefollowingargument:
Thedevelopmentofhigh-temperaturesuperconductingmaterialsistechnolog-
icallyjustified,forsuchmaterialswillallowelectricitytobetransmittedwithout
lossovergreatdistances,andtheywillpavethewayfortrainsthatlevitate
magnetically.
Thepremiseindicator‘‘for’’goeswithboth‘‘Suchmaterialswillallowelectricitytobe
transmittedwithoutlossovergreatdistances’’and‘‘Theywillpavethewayfortrains
that levitate magnetically.’’ These are the premises. By process of elimination, ‘‘The
development ofhigh-temperaturesuperconductingmaterialsistechnologicallyjusti-
fied’’istheconclusion.
Sometimes an argument contains no indicators. When this occurs, the reader/
listenermustaskhimselforherselfsuchquestionsas:Whatsinglestatementisclaimed
(implicitly)tofollowfromtheothers?Whatisthearguertryingtoprove?Whatisthe
mainpointinthepassage?Theanswerstothesequestionsshouldpointtotheconclu-
sion.Example:
Thespaceprogramdeservesincreasedexpendituresintheyearsahead.Notonly
doesthenationaldefensedependuponit,buttheprogramwillmorethanpay
foritselfintermsoftechnologicalspinoffs.Furthermore,atcurrentfunding
levelstheprogramcannotfulfillitsanticipatedpotential.
Theconclusionofthisargumentisthefirststatement,andalloftheotherstatements
arepremises.Theargumentillustratesthepatternfoundinmostargumentsthatlackin-
dicatorwords:theintendedconclusionisstatedfirst,andtheremainingstatementsare
thenofferedinsupportofthisfirststatement.Whentheargumentisrestructuredaccord-
ingtologicalprinciples,however,theconclusionisalwayslistedafterthepremises:
P : Thenationaldefenseisdependentuponthespaceprogram.
1
P : Thespaceprogramwillmorethanpayforitselfintermsoftechnological
2
spinoffs.
P : Atcurrentfundinglevelsthespaceprogramcannotfulfillitsanticipated
3
potential.
C: Thespaceprogramdeservesincreasedexpendituresintheyearsahead.
4 Chapter1: BasicConcepts
Whenrestructuringargumentssuchasthis,oneshouldremainascloseaspossible
totheoriginalversion,whileatthesametimeattendingtotherequirementthatprem-
isesandconclusionbecompletesentencesthataremeaningfulintheorderinwhich
theyarelisted.
Notethatthefirsttwopremisesareincludedwithinthescopeofasinglesentence
intheoriginalargument.Forthepurposesofthischapter,compoundarrangementsof
statementsinwhichthevariouscomponentsareallclaimedtobetruewillbeconsid-
eredasseparatestatements.
Passages that contain arguments sometimes contain statements that are neither
premises nor conclusion. Only statements that are actually intended to support the
conclusionshouldbeincludedinthelistofpremises.Ifastatementhasnothingtodo
withtheconclusionor,forexample,simplymakesapassingcomment,itshouldnot
beincludedwithinthecontextoftheargument.Example:
Socializedmedicineisnotrecommendedbecauseitwouldresultinareductionin
theoverallqualityofmedicalcareavailabletotheaveragecitizen.Inaddition,
itmightverywellbankruptthefederaltreasury.Thisisthewholecaseagainst
socializedmedicineinanutshell.
The conclusion of this argument is ‘‘Socialized medicine is not recommended,’’and
thetwostatementsfollowingtheword‘‘because’’arethepremises.Thelaststatement
makes only a passing comment about the argument itself and is therefore neither a
premisenoraconclusion.
Closely related to the concepts of argument and statement are those of inference
and proposition. An inference, in the technical sense of the term, is the reasoning
processexpressedbyanargument.Aswewillseeinthenextsection,inferencesmay
beexpressednotonlythroughargumentsbutthroughconditionalstatementsaswell.
Intheloosesenseoftheterm,‘‘inference’’isusedinterchangeablywith‘‘argument.’’
Analogously,aproposition,inthetechnicalsense,isthemeaningorinformation
content of a statement. For the purposes of this book, however, ‘‘proposition’’ and
‘‘statement’’areusedinterchangeably.
NoteontheHistoryofLogic
ThepersonwhoisgenerallycreditedasbeingthefatheroflogicistheancientGreek
philosopher Aristotle (384–322 B.C.). Aristotle’s predecessors had been interestedin
theartofconstructingpersuasiveargumentsandintechniquesforrefutingtheargu-
mentsofothers,butitwasAristotlewhofirstdevisedsystematiccriteriaforanalyzing
and evaluating arguments. Aristotle’s logic is called syllogistic logic and includes
muchofwhatistreatedinChapters4and5ofthistext.Thefundamentalelementsin
thislogicareterms,andargumentsareevaluatedasgoodorbaddependingonhow
thetermsarearrangedintheargument.Inadditiontohisdevelopmentofsyllogistic
logic,Aristotlecatalogedanumberofinformalfallacies,atopictreatedinChapter3of S
thistext. N
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Arguments,Premises, and Conclusions 5
AfterAristotle’sdeath,anotherGreekphilosopher,Chrysippus(279–206B.C.),one
of the founders of the Stoic school, developed a logic in which the fundamental
elementswerewholepropositions.Chrysippustreatedeverypropositionaseithertrue
orfalseanddevelopedrulesfordeterminingthetruthorfalsityofcompoundpropo-
sitionsfromthetruthorfalsityoftheircomponents.Inthecourseofdoingso,helaid
the foundation for the truth functional interpretation of the logical connectives pre-
sentedinChapter6ofthistextandintroducedthenotionofnaturaldeduction,treated
inChapter7.
For thirteen hundred years after the death of Chrysippus, relatively little creative
workwasdoneinlogic.ThephysicianGalen(A.D.129–ca.199)developedthetheory
of the compound categorical syllogism, but for the most partphilosophersconfined
themselves to writing commentaries on the works of Aristotle andChrysippus.Boe-
thius(ca.480–524)isanoteworthyexample.
ThefirstmajorlogicianoftheMiddleAgeswasPeterAbelard(1079–1142).Abelard
reconstructedandrefinedthelogicofAristotleandChrysippusascommunicatedby
Boethius,andheoriginatedatheoryofuniversalsthattracedtheuniversalcharacter
ofgeneraltermstoconceptsinthemindratherthanto‘‘natures’’existingoutsidethe
mind,asAristotlehadheld.Inaddition,Abelarddistinguishedargumentsthatarevalid
becauseoftheirformfromthosethatarevalidbecauseoftheircontent,butheheld
thatonlyformalvalidityisthe‘‘perfect’’orconclusivevariety.Thepresenttextfollows
Abelardonthispoint.
AfterAbelard,thestudyoflogicduringtheMiddleAgesblossomedandflourished
through the work of numerous philosophers. It attained its final expression in the
writingsoftheOxfordphilosopherWilliamofOccam(ca.1285–1349).Occamdevoted
much of his attention to modal logic, a kind of logic that involves such notionsas
possibility, necessity, belief, and doubt. He also conducted an exhaustive study of
formsofvalidandinvalidsyllogismsandcontributedtothedevelopmentofthecon-
cept of a metalanguage—that is, a higher-level language used to discuss linguistic
entitiessuchaswords,terms,propositions,andsoon.
Towardthemiddleofthefifteenthcentury,areactionsetinagainstthelogicofthe
Middle Ages. Rhetoric largely displaced logic as the primary focus of attention; the
logicofChrysippus,whichhadalreadybeguntoloseitsuniqueidentityintheMiddle
Ages, was ignored altogether, and the logic of Aristotle was studied only in highly
simplistic presentations. A reawakening did not occur until two hundred years later
throughtheworkofGottfriedWilhelmLeibniz(1646–1716).
Leibniz,ageniusinnumerousfields,attemptedtodevelopasymboliclanguageor
‘‘calculus’’ that could be used to settle all forms of disputes, whether in theology,
philosophy, or international relations. As a result of this work, Leibniz is sometimes
credited with being the father of symbolic logic. Leibniz’s efforts to symbolize logic
werecarriedintothenineteenthcenturybyBernardBolzano(1781–1848).
With the arrival of the middle of the nineteenth century, logic commenced an
extremelyrapidperiodofdevelopmentthathascontinuedtothisday.Workinsym-
6 Chapter1: BasicConcepts
bolic logic was done by a number of philosophers and mathematicians, including
AugustusDeMorgan(1806–1871),GeorgeBoole(1815–1864),WilliamStanleyJevons
(1835–1882),andJohnVenn(1834–1923),someofwhomarepopularlyknowntoday
by the logical theorems and techniques that bear their names. At the same time, a
revival in inductive logic was initiated by the British philosopher John Stuart Mill
(1806–1873),whosemethodsofinductionarepresentedinChapter9ofthistext.
Towardtheendofthenineteenthcentury,thefoundationsofmodernmathematical
logicwerelaidbyGottlobFrege(1848–1925).HisBegriffsschriftsetsforththetheory
ofquantificationpresentedinChapter8ofthistext.Frege’sworkwascontinuedinto
the twentieth century by Alfred North Whitehead (1861–1947) and Bertrand Russell
(1872–1970), whose monumental Principia Mathematica attempted to reduce the
whole of pure mathematics to logic. The Principia is the source of much of the
symbolismthatappearsinChapters6,7,and8ofthistext.
Duringthetwentiethcentury,muchoftheworkinlogichasfocusedontheformal-
izationoflogicalsystemsandonquestionsdealingwiththecompletenessandconsis-
tency of such systems. A now-famous theorem proved by Kurt Goedel(1906–1978)
statesthatinanyformalsystemadequatefornumbertheorythereexistsanundecidable
formula—thatis,aformulasuchthatneitheritnoritsnegationisderivablefromthe
axiomsofthesystem.Otherdevelopmentsincludemultivaluedlogicsandtheformal-
izationofmodallogic.Mostrecently,logichasmadeamajorcontributiontotechnology
byprovidingtheconceptualfoundationfortheelectroniccircuitryofdigitalcomputers.
EXERCISE1.1
I.Each ofthe followingpassagescontainsasingleargument.Usingtheletters‘‘P’’
and‘‘C,’’identifythepremisesandconclusionofeachargument,writingpremises
first and conclusion last. List the premises in the order in which they make the
most sense, and write both premises and conclusion in the form of separate
declarative sentences. Indicator words may be eliminated once premises and
conclusionhavebeenappropriatelylabeled.Theexercisesmarkedwithastarare
answeredinthebackofthetext.
(cid:1) 1. Titaniumcombinesreadilywithoxygen,nitrogen,andhydrogen,allofwhich
haveanadverseeffectonitsmechanicalproperties.Asaresult,titaniummust
beprocessedintheirabsence.
(IllustratedWorldofScienceEncyclopedia)
2. Since the good, according to Plato, is that which furthers a person’s real
interests,itfollowsthatinanygivencasewhenthegoodisknown,menwill
seekit.
(AvrumStrollandRichardPopkin,PhilosophyandtheHumanSpirit)
3. Asthedenialorperversionofjusticebythesentencesofcourts,aswellasin S
anyothermanner,iswithreasonclassedamongthejustcausesofwar,itwill N
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Arguments,Premises, and Conclusions 7
follow that the federal judiciary ought to have cognizance of all causes in
whichthecitizensofothercountriesareconcerned.
(AlexanderHamilton,FederalistPapers,No.80)
(cid:1) 4. Whenindividualsvoluntarilyabandonproperty,theyforfeitanyexpectationof
privacyinitthattheymighthavehad.Therefore,awarrantlesssearchorsei-
zureofabandonedpropertyisnotunreasonableundertheFourthAmendment.
(JudgeStephanieKulpSeymour,UnitedStatesv.Jones)
5. Artistsandpoetslookattheworldandseekrelationshipsandorder.Butthey
translatetheirideastocanvas,ortomarble,orintopoeticimages.Scientists
trytofindrelationshipsbetweendifferentobjectsandevents.Toexpressthe
ordertheyfind,theycreatehypothesesandtheories.Thusthegreatscientific
theoriesareeasilycomparedtogreatartandgreatliterature.
(DouglasC.Giancoli,TheIdeasofPhysics,3rdedition)
6. ThefactthattherewasneveralandbridgebetweenAustraliaandmainland
Asiaisevidencedbythefactthattheanimalspeciesinthetwoareasarevery
different.AsianplacentalmammalsandAustralianmarsupialmammalshave
notbeenincontactinthelastseveralmillionyears.
(T.DouglasPriceandGaryM.Feinman,ImagesofthePast)
(cid:1) 7. The psychological impact and crisis created by birth of a defective infant is
devastating. Not only is the mother denied the normaltensionreleasefrom
thestressofpregnancy,butbothparentsfeelacrushingblowtotheirdignity,
self-esteem, and self-confidence. In a very short time, they feel grief forthe
lossofthenormalexpectedchild,angeratfate,numbness,disgust,wavesof
helplessnessanddisbelief.
(JohnA.Robertson,‘‘InvoluntaryEuthanasiaofDefectiveNewborns’’)
8. Theclassroomteacheriscrucialtothedevelopmentandacademicsuccessof
theaveragestudent,andadministratorssimplyareancillarytothiseffort.For
this reason, classroom teachers ought to be paid at least the equivalent of
administratorsatalllevels,includingthesuperintendent.
(PeterF.Falstrup,LettertotheEditor)
9. Anagreementcannotbindunlessbothpartiestotheagreementknowwhat
they are doing and freely choose to do it. This implies that the seller who
intendstoenteracontractwithacustomerhasadutytodiscloseexactlywhat
thecustomerisbuyingandwhatthetermsofthesaleare.
(ManuelG.Velasquez,‘‘TheEthicsofConsumerProduction’’)
(cid:1) 10. Punishment,whenspeedyandspecific,maysuppressundesirablebehavior,
butitcannotteachorencouragedesirablealternatives.Therefore,itiscrucial
tousepositivetechniquestomodelandreinforceappropriatebehaviorthat
the person can use in place of the unacceptable response that has to be
suppressed.
(WalterMischelandHarrietMischel,EssentialsofPsychology)
8 Chapter1: BasicConcepts
11. Profitservesaverycrucialfunctioninafreeenterpriseeconomy,suchasour
own. Highprofitsare the signal that consumerswantmoreoftheoutputof
the industry. High profits provide the incentive for firms to expand output
andformorefirmstoentertheindustryinthelongrun.Forafirmofabove-
averageefficiency,profitsrepresenttherewardforgreaterefficiency.
(DominicSalvatore,ManagerialEconomics,3rdedition)
12. Cats can think circles around dogs! My cat regularly used to close and lock
the door to my neighbor’s doghouse, trapping their sleepingDobermanin-
side.Trytellingacatwhattodo,orputtingaleashonhim—he’llglareatyou
andsay,‘‘Idon’tthinkso.Youshouldhavegottenadog.’’
(KevinPurkiser,LettertotheEditor)
(cid:1) 13. Sinceprivatepropertyhelpspeopledefinethemselves,sinceitfreespeople
frommundanecaresofdailysubsistence,andsinceitisfinite,noindividual
should accumulate so much property that others are prevented from accu-
mulatingthenecessitiesoflife.
(LeonP.Baradat,PoliticalIdeologies,TheirOriginsandImpact)
14. ToeveryexistingthingGodwillssomegood.Hence,sincetoloveanything
is nothing else than to will good to that thing, it is manifest that God loves
everythingthatexists.
(ThomasAquinas,SummaTheologica)
15. Women of the working class, especially wage workers, should not have
more than two children at most. The average working man can support
no more and the average working woman can take care of no more in de-
centfashion.
(MargaretSanger,FamilyLimitations)
(cid:1) 16. Radioactive fallout isn’t the only concern in the aftermath of nuclearexplo-
sions. The nations of planet Earth have acquired nuclear weapons with an
explosive power equal to more than a million Hiroshima bombs. Studies
suggest that explosion of only half these weapons would produce enough
soot,smoke,anddusttoblankettheEarth,blockoutthesun,andbringona
nuclearwinterthatwouldthreatenthesurvivalofthehumanrace.
(JohnW.HillandDorisK.Kolb,ChemistryforChangingTimes,7thedition)
17. Anantreleasesachemicalwhenitdies,anditsfellowsthencarryitawayto
the compost heap. Apparently the communication is highly effective; a
healthy ant painted with the death chemical will be dragged to the funeral
heapagainandagain.
(CarolR.EmberandMelvinEmber,CulturalAnthropology,7thedition)
18. Everyartandeveryinquiry,andsimilarlyeveryactionandpursuit,isthought
toaimatsomegood;andforthisreasonthegoodhasrightlybeendeclared
tobethatatwhichallthingsaim. S
(Aristotle,NicomacheanEthics) N
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Arguments,Premises, and Conclusions 9
