the game of logic by lewis carroll

7/31/2019 The Game of Logic by Lewis Carroll

http://slidepdf.com/reader/full/the-game-of-logic-by-lewis-carroll 1/68



SeetheSunisoverhead,|--y-------y'-|Shiningonus,FULLand|||RED!|x'||7|8|NowtheSunisgoneaway,-------------AndtheEMPTYskyisGREY!___

THEGAMEOFLOGIC

ByLewisCarrol

TomyChild-friend.

Icharminvain;forneveragain,AllkeenlyasmyglanceIbend,WillMemory,goddesscoy,EmbodyformyjoyDeparteddays,norletmegaze

Onthee,myfairyfriend!

Yetcouldthyface,inmysticgrace,Amomentsmileonme,'twouldsendFar-dartingraysoflightFromHeavenathwartthenight,BywhichtoreadinverydeedThyspirit,sweetestfriend!

SomaythestreamofLife'slongdreamFlowgentlyonwardtoitsend,Withmanyafloweretgay,Adownitswillowyway:

Maynosighvex,nocareperplex,Mylovinglittlefriend!

NOTABENE.

WitheachcopyofthisBookisgivenanEnvelope,containingaDiagram(similartothefrontispiece)oncard,andnineCounters,fourredandfivegrey.

TheEnvelope,&c.canbehadseparately,at3d.each.

TheAuthorwillbeverygratefulforsuggestions,especiallyfrombeginnersinLogic,ofanyalterations,orfurtherexplanations,thatmayseemdesirable.Lettersshouldbeaddressedtohimat"29,BedfordStreet,CoventGarden,London."

PREFACE



"Therefoam'drebelliousLogic,gagg'dandbound."

ThisGamerequiresnineCounters--fourofonecolourandfiveofanother:sayfourredandfivegrey.

BesidesthenineCounters,italsorequiresonePlayer,ATLEAST.IamnotawareofanyGamethatcanbeplayedwithLESSthanthisnumber:whilethereareseveralthatrequireMORE:takeCricket,forinstance,whichrequirestwenty-two.Howmucheasieritis,whenyouwanttoplayaGame,tofindONEPlayerthantwenty-two.Atthesametime,thoughonePlayerisenough,agooddealmoreamusementmaybegotbytwoworkingatittogether,andcorrectingeachother'smistakes.

Asecondadvantage,possessedbythisGame,isthat,besidesbeinganendlesssourceofamusement(thenumberofarguments,thatmaybeworkedbyit,beinginfinite),itwillgivethePlayersalittleinstructionaswell.ButisthereanygreatharminTHAT,solongasyougetplentyofamusement?

CONTENTS.

CHAPTERPAGE

I.NEWLAMPSFOROLD.1.Propositions.......12.Syllogisms........203.Fallacies........32

II.CROSSQUESTIONS.1.Elementary........372.HalfofSmallerDiagram.Propositions

toberepresented.....403.Do.Symbolstobeinterpreted..424.SmallerDiagram.Propositionstoberepresented.......445.Do.Symbolstobeinterpreted..466.LargerDiagram.Propositionstoberepresented.......487.BothDiagramstobeemployed..51

III.CROOKEDANSWERS.1.Elementary........552.HalfofSmallerDiagram.Propositionsrepresented.......59

3.Do.Symbolsinterpreted...614.SmallerDiagram.Propositionsrepresented.625.Do.Symbolsinterpreted...656.LargerDiagram.Propositionsrepresented.677.BothDiagramsemployed....72

IV.HITORMISS.........85



CHAPTERI.

NEWLAMPSFOROLD.

"Lightcome,lightgo."_________

1.Propositions.

"SomenewCakesarenice.""NonewCakesarenice.""Allnewcakesarenice."

Therearethree'PROPOSITIONS'foryou--theonlythreekindswearegoingtouseinthisGame:andthefirstthingtobedoneistolearnhowtoexpressthemontheBoard.

Letusbeginwith

"SomenewCakesarenice."

Butbeforedoingso,aremarkhastobemade--onethatisratherimportant,andbynomeanseasytounderstandallinamoment:sopleasetoreadthisVERYcarefully.

TheworldcontainsmanyTHINGS(suchas"Buns","Babies","Beetles"."Battledores".&c.);andtheseThingspossessmanyATTRIBUTES(suchas"baked","beautiful","black","broken",&c.:infact,whatevercanbe"attributedto",thatis"saidtobelongto",anyThing,isanAttribute).WheneverwewishtomentionaThing,weuseaSUBSTANTIVE:whenwewishtomentionanAttribute,weuseanADJECTIVE.Peoplehaveaskedthequestion"CanaThingexist

withoutanyAttributesbelongingtoit?"Itisaverypuzzlingquestion,andI'mnotgoingtotrytoanswerit:letusturnupournoses,andtreatitwithcontemptuoussilence,asifitreallywasn'tworthnoticing.But,iftheyputittheotherway,andask"CananAttributeexistwithoutanyThingforittobelongto?",wemaysayatonce"No:nomorethanaBabycouldgoarailway-journeywithnoonetotakecareofit!"Youneversaw"beautiful"floatingaboutintheair,orlitteredaboutonthefloor,withoutanyThingtoBEbeautiful,nowdidyou?

AndnowwhatamIdrivingat,inallthislongrigmarole?Itisthis.Youmayput"is"or"are"betweennamesoftwoTHINGS(forexample,"somePigsarefatAnimals"),orbetweenthenamesoftwo

ATTRIBUTES(forexample,"pinkislight-red"),andineachcaseitwillmakegoodsense.But,ifyouput"is"or"are"betweenthenameofaTHINGandthenameofanATTRIBUTE(forexample,"somePigsarepink"),youdoNOTmakegoodsense(forhowcanaThingBEanAttribute?)unlessyouhaveanunderstandingwiththepersontowhomyouarespeaking.Andthesimplestunderstandingwould,Ithink,bethis--thattheSubstantiveshallbesupposedtoberepeatedattheendofthesentence,sothatthesentence,ifwrittenoutinfull,wouldbe"somePigsarepink(Pigs)".Andnowtheword"are"makesquitegoodsense.



Thus,inordertomakegoodsenseoftheProposition"somenewCakesarenice",wemustsupposeittobewrittenoutinfull,intheform"somenewCakesarenice(Cakes)".Nowthiscontainstwo'TERMS'--"newCakes"beingoneofthem,and"nice(Cakes)"theother."NewCakes,"beingtheonewearetalkingabout,iscalledthe'SUBJECT'oftheProposition,and"nice(Cakes)"the'PREDICATE'.AlsothisPropositionissaidtobea'PARTICULAR'one,sinceitdoesnotspeakoftheWHOLEofitsSubject,butonlyofaPARTofit.Theothertwokindsaresaidtobe'UNIVERSAL',becausetheyspeakoftheWHOLEoftheirSubjects--theonedenyingniceness,andtheotherassertingit,oftheWHOLEclassof"newCakes".Lastly,ifyouwouldliketohaveadefinitionoftheword'PROPOSITION'itself,youmaytakethis:--"asentencestatingthatsome,ornone,orall,oftheThingsbelongingtoacertainclass,calledits'Subject',arealsoThingsbelongingtoacertainotherclass,calledits'Predicate'".

Youwillfindthesesevenwords--PROPOSITION,ATTRIBUTE,TERM,SUBJECT,PREDICATE,PARTICULAR,UNIVERSAL--charminglyuseful,ifanyfriendshouldhappentoaskifyouhaveeverstudiedLogic.Mindyoubringallsevenwordsintoyouranswer,andyoufriendwillgoawaydeeplyimpressed--'asadderandawiserman'.

NowpleasetolookatthesmallerDiagramontheBoard,andsupposeittobeacupboard,intendedforalltheCakesintheworld(itwouldhavetobeagoodlargeone,ofcourse).Andletussupposeallthenewonestobeputintotheupperhalf(marked'x'),andalltherest(thatis,theNOT-newones)intothelowerhalf(marked'x'').ThusthelowerhalfwouldcontainELDERLYCakes,AGEDCakes,ANTE-DILUVIANCakes--ifthereareany:Ihaven'tseenmany,myself--andsoon.LetusalsosupposealltheniceCakestobeputintotheleft-handhalf(marked'y'),andalltherest(thatis,thenot-niceones)intotheright-handhalf(marked'y'').Atpresent,then,wemustunderstandxtomean"new",x'"not-new",y"nice",andy'"not-nice."

AndnowwhatkindofCakeswouldyouexpecttofindincompartmentNo.5?

Itispartoftheupperhalf,yousee;sothat,ifithasanyCakesinit,theymustbeNEW:anditispartoftheleft-handhalf;sothattheymustbeNICE.HenceifthereareanyCakesinthiscompartment,theymusthavethedouble'ATTRIBUTE'"newandnice":or,ifweuseletters,themustbe"xy."

Observethatthelettersx,yarewrittenontwooftheedgesofthiscompartment.ThisyouwillfindaveryconvenientruleforknowingwhatAttributesbelongtotheThingsinanycompartment.TakeNo.7,forinstance.IfthereareanyCakesthere,theymust

be"x'y",thatis,theymustbe"not-newandnice."

Nowletusmakeanotheragreement--thataredcounterinacompartmentshallmeanthatitis'OCCUPIED',thatis,thatthereareSOMECakesinit.(Theword'some,'inLogic,means'oneormore'sothatasingleCakeinacompartmentwouldbequiteenoughreasonforsaying"thereareSOMECakeshere").Alsoletusagreethatagreycounterinacompartmentshallmeanthatitis'EMPTY',thatisthatthereareNOCakesinit.InthefollowingDiagrams,Ishallput'1'(meaning'oneormore')whereyouaretoputaRED



counter,and'0'(meaning'none')whereyouaretoputaGREYone.

AstheSubjectofourPropositionistobe"newCakes",weareonlyconcerned,atpresent,withtheUPPERhalfofthecupboard,wherealltheCakeshavetheattributex,thatis,"new."

Now,fixingourattentiononthisupperhalf,supposewefounditmarkedlikethis,

-----------||||1|||||-----------

thatis,witharedcounterinNo.5.Whatwouldthistellus,withregardtotheclassof"newCakes"?

WoulditnottellusthatthereareSOMEoftheminthexy-compartment?Thatis,thatsomeofthem(besideshavingtheAttributex,whichbelongstobothcompartments)havetheAttributey(thatis,"nice").Thiswemightexpressbysaying"somex-Cakesarey-(Cakes)",or,

puttingwordsinsteadofletters,

"SomenewCakesarenice(Cakes)",

or,inashorterform,

"SomenewCakesarenice".

AtlastwehavefoundouthowtorepresentthefirstProposition

ofthisSection.IfyouhavenotCLEARLYunderstoodallIhavesaid,gonofurther,butreaditoverandoveragain,tillyouDOunderstandit.Afterthatisoncemastered,youwillfindalltherestquiteeasy.

Itwillsavealittletrouble,indoingtheotherPropositions,ifweagreetoleaveouttheword"Cakes"altogether.IfinditconvenienttocallthewholeclassofThings,forwhichthecupboardisintended,the'UNIVERSE.'Thuswemighthavebegunthisbusinessbysaying"LetustakeaUniverseofCakes."(Soundsnice,doesn'tit?)

OfcourseanyotherThingswouldhavedonejustaswellasCakes.

WemightmakePropositionsabout"aUniverseofLizards",oreven"aUniverseofHornets".(Wouldn'tTHATbeacharmingUniversetolivein?)

Sofar,then,wehavelearnedthat

-----------||||1||



|||-----------

means"somexandy,"i.e."somenewarenice."

Ithinkyouwillseewithoutfurtherexplanation,that

-----------|||||1||||-----------

means"somexarey',"i.e."somenewarenot-nice."

NowletusputaGREYcounterintoNo.5,andaskourselvesthemeaningof

-----------|||

|0|||||-----------

Thistellsusthatthexy-compartmentisEMPTY,whichwemayexpressby"noxarey",or,"nonewCakesarenice".ThisisthesecondofthethreePropositionsattheheadofthisSection.

Inthesameway,

-----------

|||||0||||-----------

wouldmean"noxarey',"or,"nonewCakesarenot-nice."

Whatwouldyoumakeofthis,Iwonder?

-----------|||

|1|1||||-----------

IhopeyouwillnothavemuchtroubleinmakingoutthatthisrepresentsaDOUBLEProposition:namely,"somexarey,ANDsomearey',"i.e."somenewarenice,andsomearenot-nice."

Thefollowingisalittleharder,perhaps:



-----------||||0|0||||-----------

Thismeans"noxarey,ANDnonearey',"i.e."nonewarenice,ANDnonearenot-nice":whichleadstotherathercuriousresultthat"nonewexist,"i.e."noCakesarenew."Thisisbecause"nice"and"not-nice"makewhatwecallan'EXHAUSTIVE'divisionoftheclass"newCakes":i.e.betweenthem,theyEXHAUSTthewholeclass,sothatallthenewCakes,thatexist,mustbefoundinoneortheotherofthem.

Andnowsupposeyouhadtorepresent,withcountersthecontradictoryto"noCakesarenew",whichwouldbe"someCakesarenew",or,puttinglettersforwords,"someCakesarex",howwouldyoudoit?

Thiswillpuzzleyoualittle,Iexpect.EvidentlyyoumustputaredcounterSOMEWHEREinthex-halfofthecupboard,sinceyou

knowthereareSOMEnewCakes.ButyoumustnotputitintotheLEFT-HANDcompartment,sinceyoudonotknowthemtobeNICE:normayyouputitintotheRIGHT-HANDone,sinceyoudonotknowthemtobeNOT-NICE.

What,then,areyoutodo?IthinkthebestwayoutofthedifficultyistoplacetheredcounterONTHEDIVISION-LINEbetweenthexy-compartmentandthexy'-compartment.ThisIshallrepresent(asIalwaysput'1'whereyouaretoputaredcounter)bythediagram

-----------

||||-1-||||-----------

OuringeniousAmericancousinshaveinventedaphrasetoexpressthepositionofamanwhowantstojoinoneortheotheroftwoparties--suchastheirtwoparties'Democrats'and'Republicans'--butcan'tmakeuphismindWHICH.Suchamanissaidtobe"sittingonthefence."Nowthatisexactlythepositionoftheredcounteryouhavejustplacedonthedivision-line.HelikesthelookofNo.5,andhelikesthelookofNo.6,andhedoesn'tknowWHICHto

jumpdowninto.Sotherehesitsastride,sillyfellow,danglinghislegs,oneoneachsideofthefence!

NowIamgoingtogiveyouamuchharderonetomakeout.Whatdoesthismean?

-----------||||1|0|



|||-----------

ThisisclearlyaDOUBLEProposition.Ittellsusnotonlythat"somexarey,"butalsothe"noxareNOTy."Hencetheresultis"ALLxarey,"i.e."allnewCakesarenice",whichisthelastofthethreePropositionsattheheadofthisSection.

Wesee,then,thattheUniversalProposition

"AllnewCakesarenice"

consistsofTWOPropositionstakentogether,namely,

"SomenewCakesarenice,"and"NonewCakesarenot-nice."

Inthesameway

-----------||||0|1||||-----------

wouldmean"allxarey'",thatis,

"AllnewCakesarenot-nice."

NowwhatwouldyoumakeofsuchaPropositionas"TheCakeyouhavegivenmeisnice"?IsitParticularorUniversal?

"Particular,ofcourse,"youreadilyreply."OnesingleCakeishardlyworthcalling'some,'even."

No,mydearimpulsiveReader,itis'Universal'.Rememberthat,fewastheyare(andIgrantyoutheycouldn'twellbefewer),theyare(orrather'itis')ALLthatyouhavegivenme!Thus,if(leaving'red'outofthequestion)IdividemyUniverseofCakes

intotwoclasses--theCakesyouhavegivenme(towhichIassigntheupperhalfofthecupboard),andthoseyouHAVEN'Tgivenme(whicharetogobelow)--Ifindthelowerhalffairlyfull,andtheupperoneasnearlyaspossibleempty.Andthen,whenIamtoldtoputanuprightdivisionintoeachhalf,keepingtheNICECakestotheleft,andtheNOT-NICEonestotheright,IbeginbycarefullycollectingALLtheCakesyouhavegivenme(sayingtomyself,fromtimetotime,"Generouscreature!HowshallIeverrepaysuchkindness?"),andpilingthemupintheleft-handcompartment.ANDITDOESN'TTAKELONGTODOIT!



HereisanotherUniversalPropositionforyou."BarzillaiBeckaleggisanhonestman."Thatmeans"ALLtheBarzillaiBeckaleggs,thatIamnowconsidering,arehonestmen."(YouthinkIinventedthatname,nowdon'tyou?ButIdidn't.It'sonacarrier'scart,somewheredowninCornwall.)

ThiskindofUniversalProposition(wheretheSubjectisasingleThing)iscalledan'INDIVIDUAL'Proposition.

Nowletustake"NICECakes"astheSubjectofProposition:thatis,letusfixourthoughtsontheLEFT-HANDhalfofthecupboard,wherealltheCakeshaveattributey,thatis,"nice."

-----Supposewefinditmarkedlikethis:--|||1|Whatwouldthattellus?||-----||||||-----

Ihopethatitisnotnecessary,afterexplainingtheHORIZONTALoblongsofully,tospendmuchtimeovertheUPRIGHTone.Ihopeyouwillsee,foryourself,thatthismeans"someyarex",thatis,

"SomeniceCakesarenew."

"But,"youwillsay,"wehavehadthiscasebefore.YouputaredcounterintoNo.5,andyoutoldusitmeant'somenewCakesare

nice';andNOWyoutellusthatitmeans'someNICECakesareNEW'!CanitmeanBOTH?"

Thequestionisaverythoughtfulone,anddoesyouGREATcredit,dearReader!ItDOESmeanboth.Ifyouchoosetotakex(thatis,"newCakes")asyourSubject,andtoregardNo.5aspartofaHORIZONTALoblong,youmayreadit"somexarey",thatis,"somenewCakesarenice":but,ifyouchoosetotakey(thatis,"niceCake")asyourSubject,andtoregardNo.5aspartofanUPRIGHToblong,THENyoumayreadit"someyarex",thatis,"someniceCakesarenew".Theyaremerelytwodifferentwaysofexpressingtheverysametruth.

Withoutmorewords,Iwillsimplysetdowntheotherwaysinwhichthisuprightoblongmightbemarked,addingthemeaningineachcase.Bycomparingthemwiththevariouscasesofthehorizontaloblong,youwill,Ihope,beabletounderstandthemclearly.

Youwillfinditagoodplantoexamineyourselfonthistable,bycoveringupfirstonecolumnandthentheother,and'dodgingabout',asthechildrensay.

Alsoyouwilldowelltowriteoutforyourselftwoothertables--one



fortheLOWERhalfofthecupboard,andtheotherforitsRIGHT-HANDhalf.

AndnowIthinkwehavesaidallweneedtosayaboutthesmallerDiagram,andmaygoontothelargerone.

_________________________________________________ |Symbols.|Meanings._______________|_________________________________ -----|||||||Someyarex';|||i.e.Somenicearenot-new.-----|||||1|||||-----||-----||||Noyarex;|0||i.e.Nonicearenew.|||

-----|[Observethatthisismerelyanotherwayof|||expressing"Nonewarenice."]||||||-----||-----|||||||Noyarex';|||i.e.Nonicearenot-new.-----|||||0||

|||-----||-----|||||1||Someyarex,andsomearex';|||i.e.Somenicearenew,andsomeare-----|not-new.||||1|||||-----||

-----|||||0||Noyarex,andnonearex';i.e.Noy|||exist;-----|i.e.NoCakesarenice.||||0|||||-----||



-----|||||1||Allyarex;|||i.e.Allnicearenew.-----|||||0|||||-----||-----|||||0||Allyarex';|||i.e.Allnicearenot-new.-----|||||1|||||-----|_______________|_________________________________

Thismaybetakentobeacupboarddividedinthesamewayasthelast,butALSOdividedintotwoportions,fortheAttributem.Let

usgivetomthemeaning"wholesome":andletussupposethatallWHOLESOMECakesareplacedINSIDEthecentralSquare,andalltheUNWHOLESOMEonesOUTSIDEit,thatis,inoneorotherofthefourqueer-shapedOUTERcompartments.

Weseethat,justas,inthesmallerDiagram,theCakesineachcompartmenthadTWOAttributes,so,here,theCakesineachcompartmenthaveTHREEAttributes:and,justastheletters,representingtheTWOAttributes,werewrittenontheEDGESofthecompartment,so,here,theyarewrittenattheCORNERS.(Observethatm'issupposedtobewrittenateachofthefouroutercorners.)Sothatwecantellinamoment,bylookingatacompartment,whatthreeAttributesbelongtotheThingsinit.Forinstance,takeNo.12.Herewe

findx,y',m,atthecorners:soweknowthattheCakesinit,ifthereareany,havethetripleAttribute,'xy'm',thatis,"new,not-nice,andwholesome."Again,takeNo.16.Herewefind,atthecorners,x',y',m':sotheCakesinitare"not-new,not-nice,andunwholesome."(RemarkablyuntemptingCakes!)

ItwouldtakefartoolongtogothroughallthePropositions,containingxandy,xandm,andyandmwhichcanberepresentedonthisdiagram(thereareninety-sixaltogether,soIamsureyouwillexcuseme!)andImustcontentmyselfwithdoingtwoorthree,asspecimens.Youwilldowelltoworkoutalotmoreforyourself.

Takingtheupperhalfbyitself,sothatourSubjectis"newCakes",

howarewetorepresent"nonewCakesarewholesome"?

Thisis,writinglettersforwords,"noxarem."NowthistellsusthatnoneoftheCakes,belongingtotheupperhalfofthecupboard,aretobefoundINSIDEthecentralSquare:thatis,thetwocompartments,No.11andNo.12,areEMPTY.Andthis,ofcourse,isrepresentedby

-------------------



||||_____|_____||||||||0|0|||||||-------------------

AndnowhowarewetorepresentthecontradictoryProposition"SOMExarem"?ThisisadifficultyIhavealreadyconsidered.IthinkthebestwayistoplacearedcounterONTHEDIVISION-LINEbetweenNo.11andNo.12,andtounderstandthistomeanthatONEofthetwocompartmentsis'occupied,'butthatwedonotatpresentknowWHICH.ThisIshallrepresentthus:--

-------------------||||_____|_____||||||||-1-|||||||-------------------

Nowletusexpress"allxarem."

Thisconsists,weknow,ofTWOPropositions,

"Somexarem,"and"Noxarem'."

Letusexpressthenegativepartfirst.ThistellsusthatnoneoftheCakes,belongingtotheupperhalfofthecupboard,aretobefoundOUTSIDEthecentralSquare:thatis,thetwocompartments,No.9andNo.10,areEMPTY.This,ofcourse,isrepresentedby

-------------------|0|0||_____|_____||||||||||||||||-------------------

Butwehaveyettorepresent"Somexarem."ThistellsusthatthereareSOMECakesintheoblongconsistingofNo.11andNo.12:soweplaceourredcounter,asinthepreviousexample,onthedivision-linebetweenNo.11andNo.12,andtheresultis

-------------------|0|0||_____|_____||||||||-1-|||||||-------------------



Nowletustryoneortwointerpretations.

Whatarewetomakeofthis,withregardtoxandy?

-------------------||0||_____|_____||||||||1|0|||||||-------------------

Thistellsus,withregardtothexy'-Square,thatitiswholly'empty',sinceBOTHcompartmentsaresomarked.Withregardtothexy-Square,ittellsusthatitis'occupied'.True,itisonlyONEcompartmentofitthatissomarked;butthatisquiteenough,whethertheotherbe'occupied'or'empty',tosettlethefactthatthereisSOMETHINGintheSquare.

If,then,wetransferourmarkstothesmallerDiagram,soastogetridofthem-subdivisions,wehavearighttomarkit

-----------||||1|0||||-----------

whichmeans,youknow,"allxarey."

Theresultwouldhavebeenexactlythesame,ifthegivenoblonghadbeenmarkedthus:--

-------------------|1|0||_____|_____|||||||||0|||||||-------------------

Oncemore:howshallweinterpretthis,withregardtoxandy?

-------------------|0|1||_____|_____||||||||||||||||-------------------



Thistellsus,astothexy-Square,thatONEofitscompartmentsis'empty'.Butthisinformationisquiteuseless,asthereisnomarkintheOTHERcompartment.Iftheothercompartmenthappenedtobe'empty'too,theSquarewouldbe'empty':and,ifithappenedtobe'occupied',theSquarewouldbe'occupied'.So,aswedonotknowWHICHisthecase,wecansaynothingaboutTHISSquare.

TheotherSquare,thexy'-Square,weknow(asinthepreviousexample)tobe'occupied'.

If,then,wetransferourmarkstothesmallerDiagram,wegetmerelythis:--

-----------|||||1||||-----------

whichmeans,youknow,"somexarey'."

Theseprinciplesmaybeappliedtoalltheother

oblongs.Forinstance,torepresent"ally'arem'"weshouldmarkthe-------RIGHT-HANDUPRIGHTOBLONG(theone||thathastheattributey')thus:--|---||0|||---|-1-||0|||---|||-------

and,ifweweretoldtointerpretthelowerhalfofthecupboard,markedasfollows,withregardtoxandy,

-------------------||||||||0||||||||-----|-----||1|0|-------------------

weshouldtransferittothesmallerDiagramthus,

-----------||||1|0||||-----------

andreadit"allx'arey."



TwomoreremarksaboutPropositionsneedtobemade.

Oneisthat,ineveryPropositionbeginningwith"some"or"all",theACTUALEXISTENCEofthe'Subject'isasserted.If,forinstance,Isay"allmisersareselfish,"ImeanthatmisersACTUALLYEXIST.IfIwishedtoavoidmakingthisassertion,andmerelytostatetheLAWthatmiserlinessnecessarilyinvolvesselfishness,Ishouldsay"nomisersareunselfish"whichdoesnotassertthatanymisersexistatall,butmerelythat,ifanyDIDexist,theyWOULDbeselfish.

Theotheristhat,whenaPropositionbeginswith"some"or"no",andcontainsmorethattwoAttributes,theseAttributesmaybere-arranged,andshiftedfromoneTermtotheother,"adlibitum."Forexample,"someabcaredef"maybere-arrangedas"somebfareacde,"eachbeingequivalentto"someThingsareabcdef".Again"Nowiseoldmenarerashandrecklessgamblers"maybere-arrangedas"Norasholdgamblersarewiseandreckless,"eachbeingequivalentto"Nomenarewiseoldrashrecklessgamblers."

2.Syllogisms

NowsupposewedivideourUniverseofThingsinthreeways,withregardtothreedifferentAttributes.OutofthesethreeAttributes,wemaymakeupthreedifferentcouples(forinstance,iftheywerea,b,c,wemightmakeupthethreecouplesab,ac,bc).AlsosupposewehavetwoPropositionsgivenus,containingtwoofthesethreecouples,andthatfromthemwecanproveathirdPropositioncontainingthethirdcouple.(Forexample,ifwedivideourUniverseform,x,andy;andifwehavethetwoPropositionsgivenus,"nomarex'"and"allm'arey",containingthetwocouplesmxandmy,itmightbepossibletoprovefromthemathirdProposition,containingxandy.)

InsuchacasewecallthegivenPropositions'THEPREMISSES',thethirdone'THECONCLUSION'andthewholeset'ASYLLOGISM'.

Evidently,ONEoftheAttributesmustoccurinbothPremisses;orelseonemustoccurinONEPremiss,anditsCONTRADICTORYintheother.

Inthefirstcase(when,forexample,thePremissesare"somemarex"and"nomarey'")theTerm,whichoccurstwice,iscalled'THEMIDDLETERM',becauseitservesasasortoflinkbetweentheothertwoTerms.

Inthesecondcase(when,forexample,thePremissesare"no

marex'"and"allm'arey")thetwoTerms,whichcontainthesecontradictoryAttributes,maybecalled'THEMIDDLETERMS'.

Thus,inthefirstcase,theclassof"m-Things"istheMiddleTerm;and,inthesecondcase,thetwoclassesof"m-Things"and"m'-Things"aretheMiddleTerms.

TheAttribute,whichoccursintheMiddleTermorTerms,disappearsintheConclusion,andissaidtobe"eliminated",whichliterallymeans"turnedoutofdoors".



NowletustrytodrawaConclusionfromthetwoPremisses--

"SomenewCakesareunwholesome;NoniceCakesareunwholesome."

Inordertoexpressthemwithcounters,weneedtodivideCakesinTHREEdifferentways,withregardtonewness,toniceness,andtowholesomeness.ForthiswemustusethelargerDiagram,makingxmean"new",y"nice",andm"wholesome".(EverythingINSIDEthecentralSquareissupposedtohavetheattributem,andeverythingOUTSIDEittheattributem',i.e."not-m".)

YouhadbetteradopttheruletomakemmeantheAttributewhichoccursintheMIDDLETermorTerms.(Ihavechosenmasthesymbol,because'middle'beginswith'm'.)

Now,inrepresentingthetwoPremisses,IprefertobeginwiththeNEGATIVEone(theonebeginningwith"no"),becauseGREYcounterscanalwaysbeplacedwithCERTAINTY,andwillthenhelptofixthepositionoftheredcounters,whicharesometimesalittleuncertainwheretheywillbemostwelcome.

Letusexpress,the"noniceCakesareunwholesome(Cakes)",i.e.

"noy-Cakesarem'-(Cakes)".ThistellsusthatnoneoftheCakesbelongingtothey-halfofthecupboardareinitsm'-compartments(i.e.theonesoutsidethecentralSquare).Hencethetwocompartments,No.9andNo.15,areboth'EMPTY';andwemustplaceagreycounterinEACHofthem,thus:--

-----------|0|||--|--|||||||--|-----|--||||||

|--|--||0||-----------

WehavenowtoexpresstheotherPremiss,namely,"somenewCakesareunwholesome(Cakes)",i.e."somex-Cakesarem'-(Cakes)".ThistellsusthatsomeoftheCakesinthex-halfofthecupboardareinitsm'-compartments.HenceONEofthetwocompartments,No.9andNo.10,is'occupied':and,aswearenottoldinWHICHofthesetwocompartmentstoplacetheredcounter,theusualrulewouldbetolayitonthedivision-linebetweenthem:but,inthiscase,theotherPremisshassettledthematterforus,bydeclaring

No.9tobeEMPTY.Hencetheredcounterhasnochoice,andMUSTgointoNo.10,thus:--

-----------|0|1||--|--|||||||--|-----|--||||||



|--|--||0||-----------

AndnowwhatcounterswillthisinformationenableustoplaceintheSMALLERDiagram,soastogetsomePropositioninvolvingxandyonly,leavingoutm?Letustakeitsfourcompartments,onebyone.

First,No.5.AllweknowaboutTHISisthatitsOUTERportionisempty:butweknownothingaboutitsinnerportion.ThustheSquareMAYbeempty,oritMAYhavesomethinginit.Whocantell?SowedarenotplaceANYcounterinthisSquare.

Secondly,whatofNo.6?Herewearealittlebetteroff.WeknowthatthereisSOMETHINGinit,forthereisaredcounterinitsouterportion.Itistruewedonotknowwhetheritsinnerportionisemptyoroccupied:butwhatdoesTHATmatter?OnesolitaryCake,inonecorneroftheSquare,isquitesufficientexcuseforsaying"THISSQUAREISOCCUPIED",andformarkingitwitharedcounter.

AstoNo.7,weareinthesameconditionaswithNo.5--wefind

itPARTLY'empty',butwedonotknowwhethertheotherpartisemptyoroccupied:sowedarenotmarkthisSquare.

AndastoNo.8,wehavesimplynoinformationatall.

Theresultis

-------||1||---|---||||-------

Our'Conclusion',then,mustbegotoutoftherathermeagerpieceofinformationthatthereisaredcounterinthexy'-Square.HenceourConclusionis"somexarey'",i.e."somenewCakesarenot-nice(Cakes)":or,ifyouprefertotakey'asyourSubject,"somenot-niceCakesarenew(Cakes)";buttheotherlooksneatest.

WewillnowwriteoutthewholeSyllogism,puttingthesymbol&there4[*]for"therefore",andomitting"Cakes",forthesakeofbrevity,attheendofeachProposition.

[*][NOTEfromBrett:Theuseof"&there4"isaratherarbitraryselection.Thereisnofontavailableingeneralpractice

whichrendersthe"therefore"symbolcorrection(threedotsinatriangularformation).Thiscanbedone,however,inHTML,soifthisdocumentisreadinabrowser,thenthesymbolwillbeproperlyrecognized.Thisisapoorman'sexcuse.]

"SomenewCakesareunwholesome;NoniceCakesareunwholesome&there4SomenewCakesarenot-nice."

Andyouhavenowworkedout,successfully,yourfirst'SYLLOGISM'.



Permitmetocongratulateyou,andtoexpressthehopethatitisbutthebeginningofalongandgloriousseriesofsimilarvictories!

WewillworkoutoneotherSyllogism--aratherharderonethanthelast--andthen,Ithink,youmaybesafelylefttoplaytheGamebyyourself,or(better)withanyfriendwhomyoucanfind,thatisableandwillingtotakeashareinthesport.

LetusseewhatwecanmakeofthetwoPremisses--

"AllDragonsareuncanny;AllScotchmenarecanny."

Remember,Idon'tguaranteethePremissestobeFACTS.Inthefirstplace,IneverevensawaDragon:and,inthesecondplace,itisn'toftheslightestconsequencetous,asLOGICIANS,whetherourPremissesaretrueorfalse:allWEhavetodoistomakeoutwhethertheyLEADLOGICALLYTOTHECONCLUSION,sothat,ifTHEYweretrue,ITwouldbetruealso.

Yousee,wemustgiveupthe"Cakes"now,orourcupboardwillbeofnousetous.Wemusttake,asour'Universe',someclass

ofthingswhichwillincludeDragonsandScotchmen:shallwesay'Animals'?And,as"canny"isevidentlytheAttributebelongingtothe'MiddleTerms',wewillletmstandfor"canny",xfor"Dragons",andyfor"Scotchmen".SothatourtwoPremissesare,infull,

"AllDragon-Animalsareuncanny(Animals);AllScotchman-Animalsarecanny(Animals)."

Andthesemaybeexpressed,usinglettersforwords,thus:--

"Allxarem';Allyarem."

ThefirstPremissconsists,asyoualreadyknow,oftwoparts:--

"Somexarem',"and"Noxarem."

Andthesecondalsoconsistsoftwoparts:--

"Someyarem,"and"Noyarem'."

Letustakethenegativeportionsfirst.

Wehave,then,tomark,onthelargerDiagram,first,"noxarem",andsecondly,"noyarem'".Ithinkyouwillsee,without



furtherexplanation,thatthetworesults,separately,are

----------------------||||0|||--|--||--|--|||0|0||||||||--|--|--|--||--|--|--|--||||||||||||--|--||--|--|||||0||----------------------

andthatthesetwo,whencombined,giveus

-----------|0|||--|--|||0|0|||--|--|--|--||||||

|--|--||0||-----------

Wehavenowtomarkthetwopositiveportions,"somexarem'"and"someyarem".

Theonlytwocompartments,availableforThingswhicharexm',areNo.9andNo.10.Ofthese,No.9isalreadymarkedas'empty';soourredcountermustgointoNo.10.

Similarly,theonlytwo,availableforym,areNo.11andNo.13.

Ofthese,No.11isalreadymarkedas'empty';soourredcounterMUSTgointoNo.13.

Thefinalresultis

-----------|0|1||--|--|||0|0|||--|--|--|--|||1||||--|--|

|0||-----------

AndnowhowmuchofthisinformationcanusefullybetransferredtothesmallerDiagram?

Letustakeitsfourcompartments,onebyone.



AstoNo.5?This,wesee,iswholly'empty'.(Somarkitwithagreycounter.)

AstoNo.6?This,wesee,is'occupied'.(Somarkitwitharedcounter.)

AstoNo.7?Ditto,ditto.

AstoNo.8?Noinformation.

ThesmallerDiagramisnowprettyliberallymarked:--

-------|0|1||---|---||1||-------

AndnowwhatConclusioncanwereadofffromthis?Well,itisimpossibletopacksuchabundantinformationintoONEProposition:weshallhavetoindulgeinTWO,thistime.

First,bytakingxasSubject,weget"allxarey'",thatis,

"AllDragonsarenot-Scotchmen":

secondly,bytakingyasSubject,weget"allyarex'",thatis,

"AllScotchmenarenot-Dragons".

Letusnowwriteout,alltogether,ourtwoPremissesandourbrace

ofConclusions.

"AllDragonsareuncanny;AllScotchmenarecanny.&there4AllDragonsarenot-Scotchmen;AllScotchmenarenot-Dragons."

Letmemention,inconclusion,thatyoumayperhapsmeetwithlogicaltreatisesinwhichitisnotassumedthatanyThingEXISTSatall,by"somexarey"isunderstoodtomean"theAttributesx,yareCOMPATIBLE,sothataThingcanhavebothatonce",and"no

xarey"tomean"theAttributesx,yareINCOMPATIBLE,sothatnothingcanhavebothatonce".

Insuchtreatises,Propositionshavequitedifferentmeaningsfromwhattheyhaveinour'GameofLogic',anditwillbewelltounderstandexactlywhatthedifferenceis.

Firsttake"somexarey".HereWEunderstand"are"tomean"are,asanactualFACT"--whichofcourseimpliesthatsomex-ThingsEXIST.ButTHEY(thewritersoftheseothertreatises)onlyunderstand



"are"tomean"CANbe",whichdoesnotatallimplythatanyEXIST.SotheymeanLESSthanwedo:ourmeaningincludestheirs(forofcourse"somexAREy"includes"somexCANBEy"),buttheirsdoesNOTincludeours.Forexample,"someWelshhippopotamiareheavy"wouldbeTRUE,accordingtothesewriters(sincetheAttributes"Welsh"and"heavy"arequiteCOMPATIBLEinahippopotamus),butitwouldbeFALSEinourGame(sincetherearenoWelshhippopotamitoBEheavy).

Secondly,take"noxarey".HereWEonlyunderstand"are"tomean"are,asanactualFACT"--whichdoesnotatallimplythatnoxCANbey.ButTHEYunderstandthePropositiontomean,notonlythatnoneAREy,butthatnoneCANPOSSIBLYbey.Sotheymeanmorethanwedo:theirmeaningincludesours(forofcourse"noxCANbey"includes"noxAREy"),butoursdoesNOTincludetheirs.Forexample,"noPolicemenareeightfeethigh"wouldbeTRUEinourGame(since,asanactualfact,nosuchsplendidspecimensareeverfound),butitwouldbeFALSE,accordingtothesewriters(sincetheAttributes"belongingtothePoliceForce"and"eightfeethigh"arequiteCOMPATIBLE:thereisnothingtoPREVENTaPolicemanfromgrowingtothatheight,ifsufficientlyrubbedwithRowland'sMacassarOil--whichsaidtomakeHAIRgrow,whenrubbedonhair,andsoofcoursewillmakeaPOLICEMANgrow,whenrubbedonaPoliceman).

Thirdly,take"allxarey",whichconsistsofthetwopartialPropositions"somexarey"and"noxarey'".Here,ofcourse,thetreatisesmeanLESSthanwedointheFIRSTpart,andmorethanwedointheSECOND.Butthetwooperationsdon'tbalanceeachother--anymorethanyoucanconsoleaman,forhavingknockeddownoneofhischimneys,bygivinghimanextradoor-step.

IfyoumeetwithSyllogismsofthiskind,youmayworkthem,quiteeasily,bythesystemIhavegivenyou:youhaveonlytomake'are'mean'areCAPABLEofbeing',andallwillgosmoothly.For"somexarey"willbecome"somexarecapableofbeingy",thatis,"theAttributesx,yareCOMPATIBLE".And"noxarey"will

become"noxarecapableofbeingy",thatis,"theAttributesx,yareINCOMPATIBLE".And,ofcourse,"allxarey"willbecome"somexarecapableofbeingy,andnonearecapableofbeingy'",thatis,"theAttributesx,yareCOMPATIBLE,andtheAttributesx,y'areINCOMPATIBLE."InusingtheDiagramsforthissystem,youmustunderstandaredcountertomean"theremayPOSSIBLYbesomethinginthiscompartment,"andagreyonetomean"therecannotPOSSIBLYbeanythinginthiscompartment."

3.Fallacies.

Andsoyouthink,doyou,thatthechiefuseofLogic,inreallife,istodeduceConclusionsfromworkablePremisses,andtosatisfyyourselfthattheConclusions,deducedbyotherpeople,arecorrect?Ionlywishitwere!Societywouldbemuchlessliabletopanicsandotherdelusions,andPOLITICALlife,especially,wouldbeatotallydifferentthing,ifevenamajorityofthearguments,thatscatteredbroadcastovertheworld,werecorrect!Butitisalltheotherway,Ifear.ForONEworkablePairofPremisses(ImeanaPairthatleadtoalogicalConclusion)thatyoumeetwithin



readingyournewspaperormagazine,youwillprobablyfindFIVEthatleadtonoConclusionatall:and,evenwhenthePremissesAREworkable,forONEinstance,wherethewriterdrawsacorrectConclusion,thereareprobablyTENwherehedrawsanincorrectone.

Inthefirstcase,youmaysay"thePREMISSESarefallacious":inthesecond,"theCONCLUSIONisfallacious."

Thechiefuseyouwillfind,insuchLogicalskillasthisGamemayteachyou,willbeindetecting'FALLACIES'ofthesetwokinds.

ThefirstkindofFallacy--'FallaciousPremisses'--youwilldetectwhen,aftermarkingthemonthelargerDiagram,youtrytotransferthemarkstothesmaller.Youwilltakeitsfourcompartments,onebyone,andask,foreachinturn,"WhatmarkcanIplaceHERE?";andinEVERYonetheanswerwillbe"Noinformation!",showingthatthereisNOCONCLUSIONATALL.Forinstance,

"Allsoldiersarebrave;SomeEnglishmenarebrave.&there4SomeEnglishmenaresoldiers."

looksuncommonlyLIKEaSyllogism,andmighteasilytakeinalessexperiencedLogician.ButYOUarenottobecaughtbysuchatrick!YouwouldsimplysetoutthePremisses,andwouldthencalmlyremark"FallaciousPREMISSES!":youwouldn'tcondescendtoaskwhatCONCLUSIONthewriterprofessedtodraw--knowingthat,WHATEVERitis,itMUSTbewrong.Youwouldbejustassafeasthatwisemotherwas,whosaid"Mary,justgouptothenursery,andseewhatBaby'sdoing,ANDTELLHIMNOTTODOIT!"

TheotherkindofFallacy--'FallaciousConclusion'--youwillnotdetecttillyouhavemarkedBOTHDiagrams,andhavereadoffthecorrectConclusion,andhavecompareditwiththeConclusionwhichthewriterhasdrawn.

Butmind,youmustn'tsay"FALLACIOUSConclusion,"simplybecauseitisnotIDENTICALwiththecorrectone:itmaybeaPARTofthecorrectConclusion,andsobequitecorrect,ASFARASITGOES.Inthiscaseyouwouldmerelyremark,withapityingsmile,"DEFECTIVEConclusion!"Suppose,ofexample,youweretomeetwiththisSyllogism:--

"Allunselfishpeoplearegenerous;Nomisersaregenerous.&there4Nomisersareunselfish."

thePremissesofwhichmightbethusexpressedinletters:--

"Allx'arem;Noyarem."

HerethecorrectConclusionwouldbe"Allx'arey'"(thatis,"Allunselfishpeoplearenotmisers"),whiletheConclusion,drawn



bythewriter,is"Noyarex',"(whichisthesameas"Nox'arey,"andsoisPARTof"Allx'arey'.")Hereyouwouldsimplysay"DEFECTIVEConclusion!"Thesamethingwouldhappen,ifyouwereinaconfectioner'sshop,andifalittleboyweretocomein,putdowntwopence,andmarchofftriumphantlywithasinglepenny-bun.Youwouldshakeyourheadmournfully,andwouldremark"DefectiveConclusion!Poorlittlechap!"AndperhapsyouwouldasktheyoungladybehindthecounterwhethershewouldletYOUeatthebun,whichthelittleboyhadpaidforandleftbehindhim:andperhapsSHEwouldreply"Sha'n't!"

Butif,intheaboveexample,thewriterhaddrawntheConclusion"Allmisersareselfish"(thatis,"Allyarex"),thiswouldbegoingBEYONDhislegitimaterights(sinceitwouldasserttheEXISTENCEofy,whichisnotcontainedinthePremisses),andyouwouldveryproperlysay"FallaciousConclusion!"

Now,whenyoureadothertreatisesonLogic,youwillmeetwithvariouskindsof(so-called)'Fallacies'whicharebynomeansALWAYSso.Forexample,ifyouweretoputbeforeoneoftheseLogiciansthePairofPremisses

"Nohonestmencheat;

Nodishonestmenaretrustworthy."

andweretoaskhimwhatConclusionfollowed,hewouldprobablysay"Noneatall!YourPremissesoffendagainstTWOdistinctRules,andareasfallaciousastheycanwellbe!"Thensupposeyouwereboldenoughtosay"TheConclusionis'Nomenwhocheataretrustworthy',"IfearyourLogicalfriendwouldturnawayhastily--perhapsangry,perhapsonlyscornful:inanycase,theresultwouldbeunpleasant.IADVISEYOUNOTTOTRYTHEEXPERIMENT!

"Butwhyisthis?"youwillsay."DoyoumeantotellusthatalltheseLogiciansarewrong?"Farfromit,dearReader!FromTHEIR

pointofview,theyareperfectlyright.Buttheydonotinclude,intheirsystem,anythinglikeALLthepossibleformsofSyllogisms.

TheyhaveasortofnervousdreadofAttributesbeginningwithanegativeparticle.Forexample,suchPropositionsas"Allnot-xarey,""Noxarenot-y,"arequiteoutsidetheirsystem.Andthus,having(fromsheernervousness)excludedaquantityofveryusefulforms,theyhavemaderuleswhich,thoughquiteapplicabletothefewformswhichtheyallowof,arenouseatallwhenyouconsiderallpossibleforms.

Letusnotquarrelwiththem,dearReader!Thereisroomenoughintheworldforbothofus.Letusquietlytakeourbroadersystem:

and,iftheychoosetoshuttheireyestoalltheseusefulforms,andtosay"TheyarenotSyllogismsatall!"wecanbutstandaside,andletthemRushupontheirFate!Thereisscarcelyanythingofyours,uponwhichitissodangeroustoRush,asyourFate.YoumayRushuponyourPotato-beds,oryourStrawberry-beds,withoutdoingmuchharm:youmayevenRushuponyourBalcony(unlessitisanewhouse,builtbycontract,andwithnoclerkoftheworks)andmaysurvivethefoolhardyenterprise:butifyouonceRushuponyourFATE--why,youmusttaketheconsequences!



CHAPTERII.

CROSSQUESTIONS.

"TheManintheWildernessaskedofme'Howmanystrawberriesgrowinthesea?'"__________

1.Elementary.

1.Whatisan'Attribute'?Giveexamples.

2.Whenisitgoodsensetoput"is"or"are"betweentwonames?Giveexamples.

3.WhenisitNOTgoodsense?Giveexamples.

4.WhenitisNOTgoodsense,whatisthesimplestagreementtomake,inordertomakegoodsense?

5.Explain'Proposition','Term','Subject',and'Predicate'.Giveexamples.

6.Whatare'Particular'and'Universal'Propositions?Giveexamples.

7.Givearuleforknowing,whenwelookatthesmallerDiagram,whatAttributesbelongtothethingsineachcompartment.

8.Whatdoes"some"meaninLogic?[Seepp.55,6]

9.Inwhatsensedoweusetheword'Universe'inthisGame?

10.Whatisa'Double'Proposition?Giveexamples.

11.WhenisaclassofThingssaidtobe'exhaustively'divided?Giveexamples.

12.Explainthephrase"sittingonthefence."

13.WhattwopartialPropositionsmakeup,whentakentogether,"allxarey"?

14.Whatare'Individual'Propositions?Giveexamples.

15.WhatkindsofPropositionsimply,inthisGame,theEXISTENCEoftheirSubjects?

16.WhenaPropositioncontainsmorethantwoAttributes,theseAttributesmayinsomecasesbere-arranged,andshiftedfromoneTermtotheother.Inwhatcasesmaythisbedone?Giveexamples.



__________

BreakupeachofthefollowingintotwopartialPropositions:

17.Alltigersarefierce.

18.Allhard-boiledeggsareunwholesome.

19.Iamhappy.

20.Johnisnotathome.

__________

[Seepp.56,7]

21.Givearuleforknowing,whenwelookatthelargerDiagram,whatAttributesbelongtotheThingscontainedineachcompartment.

22.Explain'Premisses','Conclusion',and'Syllogism'.Giveexamples.

23.Explainthephrases'MiddleTerm'and'MiddleTerms'.

24.InmarkingapairofPremissesonthelargerDiagram,whyisitbesttomarkNEGATIVEPropositionsbeforeAFFIRMATIVEones?

25.Whyisitofnoconsequencetous,asLogicians,whetherthePremissesaretrueorfalse?

26.HowcanweworkSyllogismsinwhichwearetoldthat"somexarey"istobeunderstoodtomean"theAttributex,yareCOMPATIBLE",and"noxarey"tomean"theAttributesx,yareINCOMPATIBLE"?

27.Whatarethetwokindsof'Fallacies'?

28.Howmaywedetect'FallaciousPremisses'?

29.Howmaywedetecta'FallaciousConclusion'?

30.SometimestheConclusion,offeredtous,isnotidenticalwiththecorrectConclusion,andyetcannotbefairlycalled'Fallacious'.Whendoesthishappen?AndwhatnamemaywegivetosuchaConclusion?

[Seepp.57-59]

2.HalfofSmallerDiagram.

Propositionstoberepresented.

-----------|||



|x||||--y-----y'-

__________

1.Somexarenot-y.

2.Allxarenot-y.

3.Somexarey,andsomearenot-y.

4.Noxexist.

5.Somexexist.

6.Noxarenot-y.

7.Somexarenot-y,andsomexexist.

__________

Takingx="judges";y="just";

8.Nojudgesarejust.

9.Somejudgesareunjust.

10.Alljudgesarejust.

__________

Takingx="plums";y="wholesome";

11.Someplumsarewholesome.

12.Therearenowholesomeplums.

13.Plumsaresomeofthemwholesome,andsomenot.

14.Allplumsareunwholesome.

[Seepp.59,60]

-----|||x|||--y--|||

|x'||-----

__________

Takingy="diligentstudents";x="successful";

15.Nodiligentstudentsareunsuccessful.



16.Alldiligentstudentsaresuccessful.

17.Nostudentsarediligent.

18.Therearesomediligent,butunsuccessful,students.

19.Somestudentsarediligent.

[Seepp.60,1]


Symbolstobeinterpreted.

__________

-----------|||

|x||||--y-----y'-

__________

--------------||||||1.||0|2.|0|0|||||||--------------

--------------||||||3.|-|4.|0|1|||||||--------------

__________

Takingx="goodriddles";y="hard";

--------------

||||||5.|1||6.|1|0|||||||--------------

--------------||||||7.|0|0|8.|0||||||||--------------



__________

[Seepp.61,2]

Takingx="lobster";y="selfish";

--------------||||||9.||1|10.|0||||||||--------------

--------------||||||11.|0|1|12.|1|1|||||||--------------

__________

-----||

x||||--y'-|||x'|||-----

Takingy="healthypeople";x="happy";

------------|0||||1||0|13.|---|14.|-1-|15.|---|16.|---|

|1||||1|||------------

[Seep.62]

4.SmallerDiagram.


-----------||||x||--y--|--y'-||x'||||-----------

__________



1.Allyarex.

2.Someyarenot-x.

3.Nonot-xarenot-y.

4.Somexarenot-y.

5.Somenot-yarex.

6.Nonot-xarey.

7.Somenot-xarenot-y.

8.Allnot-xarenot-y.

9.Somenot-yexist.

10.Nonot-xexist.

11.Someyarex,andsomearenot-x.

12.Allxarey,andallnot-yarenot-x.

[Seepp.62,3]

Taking"nations"asUniverse;x="civilised";y="warlike";

13.Nouncivilisednationiswarlike.

14.Allunwarlikenationsareuncivilised.

15.Somenationsareunwarlike.

16.Allwarlikenationsarecivilised,andallcivilisednationsarewarlike.

17.Nonationisuncivilised.

__________

Taking"crocodiles"asUniverse;x="hungry";andy="amiable";

18.Allhungrycrocodilesareunamiable.

19.Nocrocodilesareamiablewhenhungry.

20.Somecrocodiles,whennothungry,areamiable;butsomearenot.

21.Nocrocodilesareamiable,andsomearehungry.

22.Allcrocodiles,whennothungry,areamiable;andallunamiablecrocodilesarehungry.



23.Somehungrycrocodilesareamiable,andsomethatarenothungryareunamiable.

[Seepp.63,4]

5.SmallerDiagram.

Symbolstobeinterpreted.

__________

-----------||||x||--y--|--y'-||x'||||-----------

__________

--------------||||||1.|---|---|2.|---|---||1||||0|--------------

--------------||1||||3.|---|---|4.|---|---|

||0||0|0|--------------

__________

Taking"houses"asUniverse;x="builtofbrick";andy="two-storied";interpret

--------------|0|||||5.|---|---|6.|---|---||0|||-|----------|---

--------------||0||||7.|---|---|8.|---|---|||||0|1|--------------

[Seep.65]

Taking"boys"asUniverse;x="fat";andy="active";



interpret

--------------|1|1|||0|9.|---|---|10.|---|---||||||1|--------------

--------------|0|1||1||11.|---|---|12.|---|---|||0||0|1|--------------

__________

Taking"cats"asUniverse;x="green-eyed";andy="good-tempered";interpret

--------------|0|0|||1|13.|---|---|14.|---|---|||0||1||--------------

--------------|1|||0|1|15.|---|---|16.|---|---|||0||1|0|--------------

[Seepp.65,6]

6.LargerDiagram.


__________

-----------||||--x--|||||||--y--m--y'-|

||||||--x'-||||-----------

__________

1.Noxarem.



2.Someyarem'.

3.Allmarex'.

4.Nom'arey'.

5.Nomarex;Allyarem.

6.Somexarem;Noyarem.

7.Allmarex';Nomarey.

8.Nox'arem;Noy'arem'.

[Seepp.67,8]

Taking"rabbits"asUniverse;m="greedy";x="old";andy="black";represent

9.Nooldrabbitsaregreedy.

10.Somenot-greedyrabbitsareblack.

11.Allwhiterabbitsarefreefromgreediness.

12.Allgreedyrabbitsareyoung.

13.Nooldrabbitsaregreedy;Allblackrabbitsaregreedy.

14.Allrabbits,thatarenotgreedy,areblack;Nooldrabbitsarefreefromgreediness.

__________

Taking"birds"asUniverse;m="thatsingloud";x="well-fed";andy="happy";represent

15.Allwell-fedbirdssingloud;Nobirds,thatsingloud,areunhappy.

16.Allbirds,thatdonotsingloud,areunhappy;Nowell-fedbirdsfailtosingloud.

__________

Taking"persons"asUniverse;m="inthehouse";x="John";andy="havingatooth-ache";represent

17.Johnisinthehouse;Everybodyinthehouseissufferingfromtooth-ache.

18.ThereisnooneinthehousebutJohn;Nobody,outofthehouse,hasatooth-ache.

__________

[Seepp.68-70]

Taking"persons"asUniverse;m="I";x="thathastakenawalk";y="thatfeelsbetter";represent



19.Ihavebeenoutforawalk;Ifeelmuchbetter.

__________

Choosingyourown'Universe'&c.,represent

20.Isenthimtobringmeakitten;Hebroughtmeakettlebymistake.

[Seepp.70,1]

7.BothDiagramstobeemployed.

__________

-----------|||-----------|--x--||||

||||||x||--y--m--y'-||--y--|--y'-|||||||x'||--x'-|||||||----------------------

__________

N.B.IneachQuestion,asmallDiagramshouldbedrawn,forxandyonly,andmarkedinaccordancewiththegivenlargeDiagram:andthenasmanyPropositionsaspossible,forxandy,shouldberead

offfromthissmallDiagram.

----------------------|0||||||--|--||--|--|||0|0||||0|1||1.|--|--|--|--|2.|--|--|--|--|||1|||||0||||--|--||--|--||0|||||----------------------

[Seep.72]

----------------------|||||0||--|--||--|--|||0|0|||||||3.|--|--|--|--|4.|--|--|--|--|||1|0||||0||||--|--||--|--||||||0|



----------------------

__________

Mark,inalargeDiagram,thefollowingpairsofPropositionsfromtheprecedingSection:thenmarkasmallDiagraminaccordancewithit,&c.

5.No.13.[seep.49]9.No.17.6.No.14.10.No.18.7.No.15.11.No.19.[seep.50]8.No.16.12.No.20.

__________

Mark,onalargeDiagram,thefollowingPairsofPropositions:thenmarkasmallDiagram,&c.Theseare,infact,PairsofPREMISSESforSyllogisms:andtheresults,readofffromthesmallDiagram,aretheCONCLUSIONS.

13.Noexcitingbookssuitfeverishpatients;Unexcitingbooksmakeonedrowsy.

14.Some,whodeservethefair,gettheirdeserts;Nonebutthebravedeservethefair.

15.Nochildrenarepatient;Noimpatientpersoncansitstill.

[Seepp.72-5]

16.Allpigsarefat;Noskeletonsarefat.

17.Nomonkeysaresoldiers;Allmonkeysaremischievous.

18.Noneofmycousinsarejust;Nojudgesareunjust.

19.Somedaysarerainy;Rainydaysaretiresome.

20.Allmedicineisnasty;Sennaisamedicine.

21.SomeJewsarerich;AllPatagoniansareGentiles.

22.Allteetotalerslikesugar;Nonightingaledrinkswine.

23.Nomuffinsarewholesome;Allbunsareunwholesome.

24.Nofatcreaturesrunwell;Somegreyhoundsrunwell.

25.Allsoldiersmarch;Someyouthsarenotsoldiers.

26.Sugarissweet;Saltisnotsweet.

27.Someeggsarehard-boiled;Noeggsareuncrackable.

28.TherearenoJewsinthehouse;TherearenoGentilesinthegarden.

[Seepp.75-82]



29.Allbattlesarenoisy;Whatmakesnonoisemayescapenotice.

30.NoJewsaremad;AllRabbisareJews.

31.Therearenofishthatcannotswim;Someskatesarefish.

32.Allpassionatepeopleareunreasonable;Someoratorsarepassionate.

[Seepp.82-84]

CHAPTERIII.

CROOKEDANSWERS.

"Iansweredhim,asIthoughtgood,'Asmanyasred-herringsgrowinthewood'."

__________

1.Elementary.

1.Whatevercanbe"attributedto",thatis"saidtobelongto",aThing,iscalledan'Attribute'.Forexample,"baked",whichcan(frequently)beattributedto"Buns",and"beautiful",whichcan(seldom)beattributedto"Babies".

2.WhentheyaretheNamesoftwoThings(forexample,"thesePigsarefatAnimals"),oroftwoAttributes(forexample,"pinkislightred").

3.WhenoneistheNameofaThing,andtheothertheNameofanAttribute(forexample,"thesePigsarepink"),sinceaThingcannot

actuallyBEanAttribute.

4.ThattheSubstantiveshallbesupposedtoberepeatedattheendofthesentence(forexample,"thesePigsarepink(Pigs)").

5.A'Proposition'isasentencestatingthatsome,ornone,orall,oftheThingsbelongingtoacertainclass,calledthe'Subject',arealsoThingsbelongingtoacertainotherclass,calledthe'Predicate'.Forexample,"somenewCakesarenotnice",thatis(writteninfull)"somenewCakesarenotniceCakes";wherethe



class"newCakes"istheSubject,andtheclass"not-niceCakes"isthePredicate.

6.AProposition,statingthatSOMEoftheThingsbelongingtoitsSubjectareso-and-so,iscalled'Particular'.Forexample,"somenewCakesarenice","somenewCakesarenotnice."

AProposition,statingthatNONEoftheThingsbelongingtoitsSubject,orthatALLofthem,areso-and-so,iscalled'Universal'.Forexample,"nonewCakesarenice","allnewCakesarenotnice".

7.TheThingsineachcompartmentpossessTWOAttributes,whosesymbolswillbefoundwrittenontwooftheEDGESofthatcompartment.

8."Oneormore."

9.AsanameoftheclassofThingstowhichthewholeDiagramisassigned.

10.APropositioncontainingtwostatements.Forexample,"somenewCakesareniceandsomearenot-nice."

11.Whenthewholeclass,thusdivided,is"exhausted"amongthesetsintowhichitisdivided,therebeingnomemberofitwhich

doesnotbelongtosomeoneofthem.Forexample,theclass"newCakes"is"exhaustively"dividedinto"nice"and"not-nice"sinceEVERYnewCakemustbeoneortheother.

12.Whenamancannotmakeuphismindwhichoftwopartieshewilljoin,heissaidtobe"sittingonthefence"--notbeingabletodecideonwhichsidehewilljumpdown.

13."Somexarey"and"noxarey'".

14.AProposition,whoseSubjectisasingleThing,iscalled'Individual'.Forexample,"Iamhappy","Johnisnotathome".TheseareUniversalPropositions,beingthesameas"alltheI's

thatexistarehappy","ALLtheJohns,thatIamnowconsidering,arenotathome".

15.Propositionsbeginningwith"some"or"all".

16.Whentheybeginwith"some"or"no".Forexample,"someabcaredef"maybere-arrangedas"somebfareacde",eachbeingequivalentto"someabcdefexist".

17.Sometigersarefierce,Notigersarenot-fierce.

18.Somehard-boiledeggsareunwholesome,Nohard-boiledeggsarewholesome.

19.SomeI'sarehappy,NoI'sareunhappy.

20.SomeJohnsarenotathome,NoJohnsareathome.

21.TheThings,ineachcompartmentofthelargerDiagram,possessTHREEAttributes,whosesymbolswillbefoundwrittenatthreeoftheCORNERSofthecompartment(exceptinthecaseofm',whichisnotactuallyinsertedintheDiagram,butisSUPPOSEDtostandateachofitsfouroutercorners).



22.IftheUniverseofThingsbedividedwithregardtothreedifferentAttributes;andiftwoPropositionsbegiven,containingtwodifferentcouplesoftheseAttributes;andiffromthesewecanproveathirdProposition,containingthetwoAttributesthathavenotyetoccurredtogether;thegivenPropositionsarecalled'thePremisses',thethirdone'theConclusion',andthewholeset'aSyllogism'.Forexample,thePremissesmightbe"nomarex'"and"allm'arey";anditmightbepossibletoprovefromthemaConclusioncontainingxandy.

23.IfanAttributeoccursinbothPremisses,theTermcontainingitiscalled'theMiddleTerm'.Forexample,ifthePremissesare"somemarex"and"nomarey'",theclassof"m-Things"is'theMiddleTerm.'

IfanAttributeoccursinonePremiss,anditscontradictoryintheother,theTermscontainingthemmaybecalled'theMiddleTerms'.Forexample,ifthePremissesare"nomarex'"and"allm'arey",thetwoclassesof"m-Things"and"m'-Things"maybecalled'theMiddleTerms'.

24.BecausetheycanbemarkedwithCERTAINTY:whereasAFFIRMATIVEPropositions(thatis,thosethatbeginwith"some"or"all")

sometimesrequireustoplacearedcounter'sittingonafence'.

25.BecausetheonlyquestionweareconcernedwithiswhethertheConclusionFOLLOWSLOGICALLYfromthePremisses,sothat,ifTHEYweretrue,ITalsowouldbetrue.

26.Byunderstandingaredcountertomean"thiscompartmentCANbeoccupied",andagreyonetomean"thiscompartmentCANNOTbeoccupied"or"thiscompartmentMUSTbeempty".

27.'FallaciousPremisses'and'FallaciousConclusion'.

28.Byfinding,whenwetrytotransfermarksfromthelarger

Diagramtothesmaller,thatthereis'noinformation'foranyofitsfourcompartments.

29.ByfindingthecorrectConclusion,andthenobservingthattheConclusion,offeredtous,isneitheridenticalwithitnorapartofit.

30.WhentheofferedConclusionisPARTofthecorrectConclusion.Inthiscase,wemaycallita'DefectiveConclusion'.


Propositionsrepresented.

__________

--------------



||||||1.||1|2.|0|1|||||||--------------

--------------||||||3.|1|1|4.|0|0|||||||--------------

--------------||||||5.|1|6.||0|||||||--------------

-------|||7.|1|1|Itmightbethoughtthattheproper|||--------------|||

Diagramwouldbe|11|,inordertoexpress"some|||-------xexist":butthisisreallycontainedin"somexarey'."Toputaredcounteronthedivision-linewouldonlytellus"ONEOFTHEcompartmentsisoccupied",whichweknowalready,inknowingthatONEisoccupied.-------|||8.Noxarey.i.e.|0|||||-------

-------|||9.Somexarey'.i.e.||1||||-------

-------|||10.Allxarey.i.e.|1|0||||-------

-------

|||11.Somexarey.i.e.|1|||||-------

-------|||12.Noxarey.i.e.|0|||||-------



-------|||13.Somexarey,andsomearey'.i.e.|1|1||||-------

-------|||14.Allxarey'.i.e.|0|1||||----------||15.Noyarex'.i.e.|---||0|---

---|1|16.Allyarex.i.e.|---||0|---

---|0|17.Noyexist.i.e.|---||0|---

---||18.Someyarex'.i.e.|---||1|---

---

||15.Someyexist.i.e.|-1-|||---


Symbolsinterpreted.

__________

1.Noxarey'.

2.Noxexist.

3.Somexexist.

4.Allxarey'.



5.Somexarey.i.e.Somegoodriddlesarehard.

6.Allxarey.i.e.Allgoodriddlesarehard.

7.Noxexist.i.e.Noriddlesaregood.

8.Noxarey.i.e.Nogoodriddlesarehard.

9.Somexarey'.i.e.Somelobstersareunselfish.

10.Noxarey.i.e.Nolobstersareselfish.

11.Allxarey'.i.e.Alllobstersareunselfish.

12.Somexarey,andsomearey'.i.e.Somelobstersareselfish,andsomeareunselfish.

13.Ally'arex'.i.e.Allinvalidsareunhappy.

14.Somey'exist.i.e.Somepeopleareunhealthy.

15.Somey'arex,andsomearex'.i.e.Someinvalidsarehappy,andsomeareunhappy.

16.Noy'exist.i.e.Nobodyisunhealthy.

4.SmallerDiagram.


__________

--------------|1|||||1.|---|---|2.|---|---||0|||1||--------------

--------------|||||1|3.|---|---|4.|---|---|||0||||--------------

--------------||1||||5.|---|---|6.|---|---|||||0||--------------

--------------||||||7.|---|---|8.|---|---|



||1||0|1|--------------

--------------||||||9.|---|-1-|10.|---|---|||||0|0|--------------

--------------|1|||1|0|11.|---|---|12.|---|---||1||||1|--------------

-------|||13.Nox'arey.i.e.|---|---||0||-------

-------||0|

14.Ally'arex'.i.e.|---|---|||1|-------

-------|||15.Somey'exist.i.e.|---|-1-||||-------

-------|1|0|

16.Allyarex,andallxarey.i.e.|---|---||0||--------------|||17.Nox'exist.i.e.|---|---||0|0|-------

-------|0|1|18.Allxarey'.i.e.|---|---||||

-------

-------|0||19.Noxarey.i.e.|---|---||||-------

-------



|||20.Somex'arey,andsomearey'.i.e.|---|---||1|1|-------

-------|0|1|21.Noyexist,andsomexexist.i.e.|---|---||0||-------

-------||1|22.Allx'arey,andally'arex.i.e.|---|---||1|0|-------

-------|1||17.Somexarey,andsomex'arey'.i.e.|---|---|||1|-------

5.SmallerDiagram.

Symbolsinterpreted.

__________

1.Someyarenot-x,or,Somenot-xarey.

2.Nonot-xarenot-y,or,Nonot-yarenot-x.

3.Nonot-yarex.

4.Nonot-xexist.i.e.NoThingsarenot-x.

5.Noyexist.i.e.Nohousesaretwo-storied.

6.Somex'exist.i.e.Somehousesarenotbuiltofbrick.

7.Noxarey'.Or,noy'arex.i.e.Nohouses,builtofbrick,areotherthantwo-storied.Or,nohouses,that

arenottwo-storied,arebuiltofbrick.

8.Allx'arey'.i.e.Allhouses,thatarenotbuiltofbrick,arenottwo-storied.

9.Somexarey,andsomearey'.i.e.Somefatboysareactive,andsomearenot.

10.Ally'arex'.i.e.Alllazyboysarethin.



11.Allxarey',andally'arex.i.e.Allfatboysarelazy,andalllazyonesarefat.

12.Allyarex,andallx'arey.i.e.Allactiveboysarefat,andallthinonesarelazy.

13.Noxexist,andnoy'exist.i.e.Nocatshavegreeneyes,andnonehavebadtempers.

14.Somexarey',andsomex'arey.Orsomeyarex',andsomey'arex.i.e.Somegreen-eyedcatsarebad-tempered,andsome,thathavenotgreeneyes,aregood-tempered.Or,somegood-temperedcatshavenotgreeneyes,andsomebad-temperedoneshavegreeneyes.

15.Somexarey,andnox'arey'.Or,someyarex,andnoy'arex'.i.e.Somegreen-eyedcatsaregood-tempered,andnone,thatarenotgreen-eyed,arebad-tempered.Or,somegood-temperedcatshavegreeneyes,andnone,thatarebad-tempered,havenotgreeneyes.

16.Allxarey',andallx'arey.Or,allyarex',andally'arex.i.e.Allgreen-eyedcatsarebad-temperedandall,thathavenotgreeneyes,aregood-tempered.Or,all

good-temperedoneshaveeyesthatarenotgreen,andallbad-temperedoneshavegreeneyes.

6.LargerDiagram.


__________

------------------------------|||||||---|---||---|---|||0|0|||||||1.|---|---|---|---|2.|-1-|---|---|---||||||||||||---|---||---|---|||||||------------------------------

------------------------------

|||||0||---|---||---|---|||0|0|||||||3.|---|---|---|---|4.|---|---|---|---|||-||||||||---|---||---|---||||||0|------------------------------



------------------------------|0||||||---|---||---|---|||0|0||||0|1||5.|---|---|---|---|6.|---|---|---|---|||1|||||0||||---|---||---|---||0|||||------------------------------

------------------------------|||||0||---|---||---|---|||0|0|||||||7.|---|---|---|---|8.|---|---|---|---|||0|1||||0|0|||---|---||---|---||||||0|------------------------------

---------------|||

|---|---|||0|0||9.Noxarem.i.e.|---|---|---|---|||0||||---|---||||---------------

---------------||||---|---||||||

10.Somem'arey.i.e.|-1-|---|---|---|||||||---|---||||---------------

---------------||||---|---||||0||11.Ally'arem'.i.e.|---|---|---|-1-||||0||

|---|---||||---------------

---------------||||---|---|||0|0||12.Allmarex'.i.e.|---|---|---|---|||1||



|---|---||||---------------

---------------|0|||---|---|||0|0||13.Noxarem;i.e.|---|---|---|---|Allyarem.||1||||---|---||0||---------------

---------------|0|0||---|---||||||14.Allm'arey;i.e.|---|---|---|---|Noxarem'.||||||---|---||1|0|---------------

---------------|0|0||---|---|||1|0||15.Allxarem;i.e.|---|---|---|---|Nomarey'.|||0|||---|---||||---------------

---------------|0|0|

|---|---||||||16.Allm'arey';i.e.|---|---|---|---|Noxarem'.||||||---|---||0|1|---------------

---------------|0|0||---|---|||1|0||17.Allxarem;i.e.|---|---|---|---|

Allmarey.|||0|||---|---|[SeeremarksonNo.7,p.60.]|||---------------

---------------|0|||---|---||||||18.Nox'arem;i.e.|---|---|---|---|



Nom'arey.||0|0|||---|---||0||---------------

---------------||||---|---|||1|0||19.Allmarex;i.e.|---|---|---|---|Allmarey.||0|0|||---|---||||---------------

20.Wehadbettertake"persons"asUniverse.Wemaychoose"myself"as'MiddleTerm',inwhichcasethePremisseswilltaketheform

Iama-person-who-sent-him-to-bring-a-kitten;Iama-person-to-whom-he-brought-a-kettle-by-mistake.

Orwemaychoose"he"as'MiddleTerm',inwhichcasethePremisseswilltaketheform

Heisa-person-whom-I-sent-to-bring-me-a-kitten;Heisa-person-who-brought-me-a-kettle-by-mistake.

Thelatterformseemsbest,astheinterestoftheanecdoteclearlydependsonHISstupidity--notonwhathappenedtoME.Letusthenmakem="he";x="personswhomIsent,&c.";andy="personswhobrought,&c."

Hence,Allmarex;Allmarey.andtherequiredDiagramis

---------------||||---|---|||1|0|||---|---|---|---|||0|0|||---|---||||---------------

7.BothDiagramsemployed.

-------|0||1.|---|---|i.e.Allyarex'.|1||-------

-------||1|



2.|---|---|i.e.Somexarey';or,Somey'arex.|||-------

-------|||3.|---|---|i.e.Someyarex';or,Somex'arey.|1||-------

-------|||4.|---|---|i.e.Nox'arey';or,Noy'arex'.||0|-------

-------|0||5.|---|---|i.e.Allyarex'.i.e.Allblackrabbits|1||areyoung.-------

-------|||

6.|---|---|i.e.Someyarex'.i.e.Someblack|1||rabbitsareyoung.-------

-------|1|0|7.|---|---|i.e.Allxarey.i.e.Allwell-fedbirds|||arehappy.-------

-------|||i.e.Somex'arey'.i.e.Somebirds,

8.|---|---|thatarenotwell-fed,areunhappy;||1|or,Someunhappybirdsarenot-------well-fed.

-------|1|0|9.|---|---|i.e.Allxarey.i.e.Johnhasgota|||tooth-ache.-------

-------

|||10.|---|---|i.e.Nox'arey.i.e.Noone,butJohn,|0||hasgotatooth-ache.-------

-------|1||11.|---|---|i.e.Somexarey.i.e.Someone,who|||hastakenawalk,feelsbetter.



-------

-------|1||i.e.Somexarey.i.e.Someone,12.|---|---|whomIsenttobringmeakitten,|||broughtmeakettlebymistake.-------

---------------||0||---|---|||0|0||13.|-1-|---|---|---|-------|||||||0||---|---||---|---|||0||||----------------------

Let"books"beUniverse;m="exciting",x="thatsuitfeverishpatients";y="thatmakeonedrowsy".

Nomarex;&there4Noy'arex.Allm'arey.

i.e.Nobookssuitfeverishpatients,exceptsuchasmakeonedrowsy.

---------------||||---|---|||1|0||14.|---|---|---|---|-------|||0|||1|||---|---||---|---|

||||||----------------------

Let"persons"beUniverse;m="thatdeservethefair";x="thatgettheirdeserts";y="brave".

Somemarex;&there4Someyarex.Noy'arem.

i.e.Somebravepersonsgettheirdeserts.

---------------

|0|||---|---|||0|0||15.|---|---|---|---|-------||||||0|||---|---||---|---||0|||||----------------------

Let"persons"beUniverse;m="patient";



x="children";y="thatcansitstill".

Noxarem;&there4Noxarey.Nom'arey.

i.e.Nochildrencansitstill.

---------------|0|0||---|---|||0|1||16.|---|---|---|---|-------||0||||0|1||---|---||---|---|||||||----------------------

Let"things"beUniverse;m="fat";x="pigs";y="skeletons".

Allxarem;&there4Allxarey'.Noyarem.

i.e.Allpigsarenot-skeletons.

---------------||||---|---|||0|0||17.|---|---|---|---|-------||1|0||||||---|---||---|---|||||1||----------------------

Let"creatures"beUniverse;m="monkeys";x="soldiers";y="mischievous".

Nomarex;&there4Someyarex'.Allmarey.

i.e.Somemischievouscreaturesarenotsoldiers.

---------------|0|||---|---|||0|0||

18.|---|---|---|---|-------||||||0|||---|---||---|---||0|||||----------------------

Let"persons"beUniverse;m="just";x="mycousins";y="judges".

Noxarem;&there4Noxarey.



Noyarem'.

i.e.Noneofmycousinsarejudges.

---------------||||---|---|||1|0||19.|---|---|---|---|-------||||||1|||---|---||---|---|||||||----------------------

Let"periods"beUniverse;m="days";x="rainy";y="tiresome".

Somemarex;&there4Somexarey.Allxmarey.

i.e.Somerainyperiodsaretiresome.

N.B.ThesearenotlegitimatePremisses,sincetheConclusionisreallypartofthesecondPremiss,sothatthe

firstPremississuperfluous.Thismaybeshown,inletters,thus:--

"Allxmarey"contains"Somexmarey",whichcontains"Somexarey".Or,inwords,"Allrainydaysaretiresome"contains"Somerainydaysaretiresome",whichcontains"Somerainyperiodsaretiresome".

Moreover,thefirstPremiss,besidesbeingsuperfluous,isactuallycontainedinthesecond;sinceitisequivalentto"Somerainydaysexist",which,asweknow,isimpliedintheProposition"Allrainydaysaretiresome".

Altogether,amostunsatisfactoryPairofPremisses!

---------------|0|||---|---|||1|||20.|---|---|---|---|-------||0|0|||1|||---|---||---|---||0|||0||----------------------

Let"things"beUniverse;m="medicine";

x="nasty";y="senna".

Allmarex;&there4Allyarex.Allyarem.

i.e.Sennaisnasty.

[SeeremarksonNo.7,p60.]

---------------



||||---|---|||0|1||21.|-1-|---|---|---|-------||0|||||1||---|---||---|---|||||||----------------------

Let"persons"beUniverse;m="Jews";x="rich";y="Patagonians".

Somemarex;&there4Somexarey'.Allyarem'.

i.e.SomerichpersonsarenotPatagonians.

---------------|0|||---|---|||-||22.|---|---|---|---|-------||0|0||||||---|---||---|---|

|0|||0||----------------------

Let"creatures"beUniverse;m="teetotalers";x="thatlikesugar";y="nightingales".

Allmarex;&there4Noyarex'.Noyarem'.

i.e.Nonightingalesdislikesugar.

---------------|||

|---|---|||0|0||23.|-1-|---|---|---|-------||0|||||||---|---||---|---|||||||----------------------

Let"food"beUniverse;m="wholesome";x="muffins";y="buns".

Noxarem;Allyarem.

Thereis'noinformation'forthesmallerDiagram;sonoConclusioncanbedrawn.

---------------||||---|---|||0|0||24.|---|---|---|---|-------||1||||||



|---|---||---|---|||||1||----------------------

Let"creatures"beUniverse;m="thatrunwell";x="fat";y="greyhounds".

Noxarem;&there4Someyarex'.Someyarem.

i.e.Somegreyhoundsarenotfat.

---------------||||---|---|||-||25.|-1-|---|---|---|-------||0|0||||||---|---||---|---|||||||----------------------

Let"persons"beUniverse;m="soldiers";

x="thatmarch";y="youths".

Allmarex;Someyarem'.

Thereis'noinformation'forthesmallerDiagram;sonoConclusioncanbedrawn.

---------------|0|0||---|---|||0|1||26.|---|---|---|---|-------

||0||||0|1||---|---||---|---||1|||1||----------------------

Let"food"beUniverse;m="sweet";x="sugar";y="salt".

Allxarem;&there4Allxarey'.Allyarem'.Allyarex'.

i.e.Sugarisnotsalt.Saltisnotsugar.

---------------||||---|---|||1|0||27.|---|---|---|---|-------|||0|||1|||---|---||---|---|



||||||----------------------

Let"Things"beUniverse;m="eggs";x="hard-boiled";y="crackable".

Somemarex;&there4Somexarey.Nomarey'.

i.e.Somehard-boiledthingscanbecracked.

---------------|0|||---|---|||0|0||28.|---|---|---|---|-------||||||0|||---|---||---|---||0|||||----------------------

Let"persons"beUniverse;m="Jews";x="thatareinthehouse";y="thatareinthegarden".

Nomarex;&there4Noxarey.Nom'arey.

i.e.Nopersons,thatareinthehouse,arealsointhegarden.

---------------|0|0||---|---|||-||29.|---|---|---|---|-------||||||||

|---|---||---|---||1|0||1||----------------------

Let"Things"beUniverse;m="noisy";x="battles";y="thatmayescapenotice".

Allxarem;&there4Somex'arey.Allm'arey.

i.e.Somethings,thatarenotbattles,mayescapenotice.

---------------|0|||---|---|||0|0||30.|---|---|---|---|-------||1||||0|||---|---||---|---||0|||1||----------------------



Let"persons"beUniverse;m="Jews";x="mad";y="Rabbis".

Nomarex;&there4Allyarex'.Allyarem.

i.e.AllRabbisaresane.

---------------||||---|---|||1|||31.|---|---|---|---|-------||0|0|||1|||---|---||---|---|||||||----------------------

Let"Things"beUniverse;m="fish";x="thatcanswim";y="skates".

Nomarex';&there4Someyarex.Someyarem.

i.e.Someskatescanswim.

---------------||||---|---|||0|0||32.|---|---|---|---|-------||1|||||||---|---||---|---|||||1||----------------------

Let"people"beUniverse;m="passionate";

x="reasonable";y="orators".

Allmarex';&there4Someyarex'.Someyarem.

i.e.Someoratorsareunreasonable.

[SeeremarksonNo.7,p.60.]

CHAPTERIV.

HITORMISS.

"Thoucanstnothitit,hitit,hitit,Thoucanstnothitit,mygoodman."



__________

1.Painiswearisome;Nopainiseagerlywishedfor.

2.Nobaldpersonneedsahair-brush;Nolizardshavehair.

3.Allthoughtlesspeopledomischief;Nothoughtfulpersonforgetsapromise.

4.IdonotlikeJohn;SomeofmyfriendslikeJohn.

5.Nopotatoesarepine-apples;Allpine-applesarenice.

6.Nopinsareambitious;Noneedlesarepins.

7.Allmyfriendshavecolds;Noonecansingwhohasacold.

8.Allthesedishesarewell-cooked;Somedishesareunwholesomeifnotwell-cooked.

9.Nomedicineisnice;Sennaisamedicine.

10.Someoystersaresilent;Nosilentcreaturesareamusing.

11.Allwisemenwalkontheirfeet;Allunwisemenwalkontheirhands.

12."Mindyourownbusiness;Thisquarrelisnobusinessofyours."

13.Nobridgesaremadeofsugar;Somebridgesarepicturesque.

14.Noriddlesinterestmethatcanbesolved;Alltheseriddlesareinsoluble.

15.Johnisindustrious;Allindustriouspeoplearehappy.

16.Nofrogswritebooks;Somepeopleuseinkinwritingbooks.

17.Nopokersaresoft;Allpillowsaresoft.

18.Noantelopeisungraceful;Gracefulanimalsdelighttheeye.

19.Someunclesareungenerous;Allmerchantsaregenerous.

20.Nounhappypeoplechuckle;Nohappypeoplegroan.

21.Audiblemusiccausesvibrationintheair;Inaudiblemusicisnotworthpayingfor.

22.Hegavemefivepounds;Iwasdelighted.

23.NooldJewsarefatmillers;Allmyfriendsareoldmillers.

24.Flourisgoodforfood;Oatmealisakindofflour.



25.Somedreamsareterrible;Nolambsareterrible.

26.Norichmanbegsinthestreet;Allwhoarenotrichshouldkeepaccounts.

27.Nothievesarehonest;Somedishonestpeoplearefoundout.

28.Allwaspsareunfriendly;Allpuppiesarefriendly.

29.Allimprobablestoriesaredoubted;Noneofthesestoriesareprobable.

30."Hetoldmeyouhadgoneaway.""Heneversaysonewordoftruth."

31.Hissongsneverlastanhour;Asong,thatlastsanhour,istedious.

32.Nobride-cakesarewholesome;Unwholesomefoodshouldbeavoided.

33.Nooldmisersarecheerful;Someoldmisersarethin.

34.Allduckswaddle;Nothingthatwaddlesisgraceful.

35.NoProfessorsareignorant;Someignorantpeopleareconceited.

36.Toothacheisneverpleasant;Warmthisneverunpleasant.

37.Boresareterrible;Youareabore.

38.Somemountainsareinsurmountable;Allstilescanbesurmounted.

39.NoFrenchmenlikeplumpudding;AllEnglishmenlike

plumpudding.

40.Noidlerswinfame;Somepaintersarenotidle.

41.Nolobstersareunreasonable;Noreasonablecreaturesexpectimpossibilities.

42.Nokinddeedisunlawful;Whatislawfulmaybedonewithoutfear.

43.Nofossilscanbecrossedinlove;Anyoystermaybecrossedinlove.

44."Thisisbeyondendurance!""Well,nothingbeyondendurancehaseverhappenedtome."

45.Alluneducatedmenareshallow;Allthesestudentsareeducated.

46.Allmycousinsareunjust;Nojudgesareunjust.

47.Nocountry,thathasbeenexplored,isinfestedbydragons;Unexploredcountriesarefascinating.



48.Nomisersaregenerous;Someoldmenarenotgenerous.

49.Aprudentmanshunshyaenas;Nobankerisimprudent.

50.Somepoetryisoriginal;Nooriginalworkisproducibleatwill.

51.Nomisersareunselfish;Nonebutmiserssaveegg-shells.

52.Allpalepeoplearephlegmatic;Noone,whoisnotpale,lookspoetical.

53.Allspidersspinwebs;Somecreatures,thatdonotspinwebs,aresavage.

54.Noneofmycousinsarejust;Alljudgesarejust.

55.Johnisindustrious;Noindustriouspeopleareunhappy.

56.Umbrellasareusefulonajourney;Whatisuselessonajourneyshouldbeleftbehind.

57.Somepillowsaresoft;Nopokersaresoft.

58.Iamoldandlame;Nooldmerchantisalamegambler.

59.Noeventfuljourneyiseverforgotten;Uneventfuljourneysarenotworthwritingabookabout.

60.Sugarissweet;Somesweetthingsarelikedbychildren.

61.Richardisoutoftemper;NoonebutRichardcanridethathorse.

62.Alljokesaremeanttoamuse;NoActofParliamentisajoke.

63."Isawitinanewspaper.""Allnewspaperstelllies."

64.Nonightmareispleasant;Unpleasantexperiencesarenotanxiouslydesired.

65.Prudenttravellerscarryplentyofsmallchange;Imprudenttravellerslosetheirluggage.

66.Allwaspsareunfriendly;Nopuppiesareunfriendly.

67.Hecalledhereyesterday;Heisnofriendofmine.

68.Noquadrupedscanwhistle;Somecatsarequadrupeds.

69.Nocookedmeatissoldbybutchers;Nouncookedmeatisservedatdinner.

70.Goldisheavy;Nothingbutgoldwillsilencehim.

71.Somepigsarewild;Therearenopigsthatarenotfat.

72.Noemperorsaredentists;Alldentistsaredreadedby



children.

73.All,whoarenotold,likewalking;NeitheryounorIareold.

74.Allbladesaresharp;Somegrassesareblades.

75.Nodictatorialpersonispopular;Sheisdictatorial.

76.Somesweetthingsareunwholesome;Nomuffinsaresweet.

77.Nomilitarymenwritepoetry;Nogeneralsarecivilians.

78.Boresaredreaded;Aboreisneverbeggedtoprolonghisvisit.

79.Allowlsaresatisfactory;Someexcusesareunsatisfactory.

80.Allmycousinsareunjust;Alljudgesarejust.

81.Somebunsarerich;Allbunsarenice.

82.Nomedicineisnice;Nopillsareunmedicinal.

83.Somelessonsaredifficult;Whatisdifficultneedsattention.

84.Nounexpectedpleasureannoysme;Yourvisitisanunexpectedpleasure.

85.Caterpillarsarenoteloquent;Jonesiseloquent.

86.Somebaldpeoplewearwigs;Allyourchildrenhavehair.

87.Allwaspsareunfriendly;Unfriendlycreaturesarealwaysunwelcome.

88.Nobankruptsarerich;Somemerchantsarenotbankrupts.

89.Weaselssometimessleep;Allanimalssometimessleep.

90.Ill-managedconcernsareunprofitable;Railwaysareneverill-managed.

91.Everybodyhasseenapig;Nobodyadmiresapig.

______________

ExtractaPairofPremissesoutofeachofthefollowing:anddeducetheConclusion,ifthereisone:--

92."TheLion,asanyonecantellyouwhohasbeenchasedbythemasoftenasIhave,isaverysavageanimal:andtherearecertainindividualsamongthem,thoughIwillnotguaranteeitasagenerallaw,whodonotdrinkcoffee."

93."Itwasmostabsurdofyoutoofferit!Youmighthaveknown,ifyouhadhadanysense,thatnooldsailorseverlikegruel!"



"ButIthought,ashewasanuncleofyours--"

"Anuncleofmine,indeed!Stuff!"

"Youmaycallitstuff,ifyoulike.AllIknowis,MYunclesarealloldmen:andtheylikegruellikeanything!"

"Well,thenYOURunclesare--"

94."Docomeaway!Ican'tstandthissqueezinganymore.Nocrowdedshopsarecomfortable,youknowverywell."

"Well,whoexpectstobecomfortable,outshopping?"

"Why,Ido,ofcourse!AndI'msuretherearesomeshops,furtherdownthestreet,thatarenotcrowded.So--"

95."Theysaynodoctorsaremetaphysicalorganists:andthatletsmeintoalittlefactaboutYOU,youknow."

"Why,howdoyoumakeTHATout?Youneverheardmeplaytheorgan."

"No,doctor,butI'veheardyoutalkaboutBrowning'spoetry:and

thatshowedmethatyou'reMETAPHYSICAL,atanyrate.So--"

___________________

ExtractaSyllogismoutofeachofthefollowing:andtestitscorrectness:--

96."Don'ttalktome!I'veknownmorerichmerchantsthanyouhave:andIcantellyounotONEofthemwaseveranoldmisersincetheworldbegan!"

"AndwhathasthatgottodowitholdMr.Brown?"

"Why,isn'theveryrich?"

"Yes,ofcourseheis.Andwhatthen?"

"Why,don'tyouseethatit'sabsurdtocallhimamiserlymerchant?Eitherhe'snotamerchant,orhe'snotamiser!"

97."ItISsokindofyoutoenquire!I'mreallyfeelingagreatdealbetterto-day."

"AndisitNature,orArt,thatistohavethecreditofthishappychange?"

"Art,Ithink.TheDoctorhasgivenmesomeofthatpatentmedicineofhis."

"Well,I'llnevercallhimahumbugagain.There'sSOMEBODY,atanyrate,thatfeelsbetteraftertakinghismedicine!"

98."No,Idon'tlikeyouonebit.AndI'llgoandplaywithmydoll.DOLLSareneverunkind."

"Soyoulikeadollbetterthanacousin?Ohyoulittlesilly!"



"OfcourseIdo!COUSINSareneverkind--atleastnocousinsI'veeverseen."

"Well,andwhatdoesTHATprove,I'dliketoknow!Ifyoumeanthatcousinsaren'tdolls,whoeversaidtheywere?"

99."Whatareyoutalkingaboutgeraniumsfor?Youcan'ttelloneflowerfromanother,atthisdistance!Igrantyouthey'reallREDflowers:itdoesn'tneedatelescopetoknowTHAT."

"Well,somegeraniumsarered,aren'tthey?"

"Idon'tdenyit.Andwhatthen?Isupposeyou'llbetellingmesomeofthoseflowersaregeraniums!"

"Ofcoursethat'swhatIshouldtellyou,ifyou'dthesensetofollowanargument!Butwhat'sthegoodofprovinganythingtoYOU,Ishouldliketoknow?"

100."Boys,you'vepassedafairlygoodexamination,allthingsconsidered.NowletmegiveyouawordofadvicebeforeIgo.Rememberthatall,whoarereallyanxioustolearn,workHARD."

"Ithankyou,Sir,inthenameofmyscholars!AndproudamItothinkthereareSOMEofthem,atleast,thatarereallyANXIOUStolearn."

"Verygladtohearit:andhowdoyoumakeitouttobeso?"

"Why,Sir,Iknowhowhardtheywork--someofthem,thatis.Whoshouldknowbetter?"

___________________

ExtractfromthefollowingspeechaseriesofSyllogisms,orargumentshavingtheformofSyllogisms:andtesttheircorrectness.

Itissupposedtobespokenbyafondmother,inanswertoafriend'scautioussuggestionthatsheisperhapsaLITTLEoverdoingit,inthewayoflessons,withherchildren.

101."Well,they'vegottheirownwaytomakeintheworld.WEcan'tleavethemafortuneapiece.Andmoney'snottobehad,asYOUknow,withoutmoney'sworth:theymustWORKiftheywanttolive.Andhowaretheytowork,iftheydon'tknowanything?Takemywordforit,there'snoplaceforignoranceinTHESEtimes!Andallauthoritiesagreethatthetimetolearniswhenyou'reyoung.One'sgotnomemoryafterwards,worthspeakingof.Achildwilllearnmoreinanhourthanagrownmaninfive.Sothose,that

havetolearn,mustlearnwhenthey'reyoung,ifeverthey'retolearnatall.Ofcoursethatdoesn'tdounlesschildrenareHEALTHY:IquiteallowTHAT.Well,thedoctortellsmenochildrenarehealthyunlessthey'vegotagoodcolourintheircheeks.Andonlyjustlookatmydarlings!Why,theircheeksbloomlikepeonies!Well,now,theytellmethat,tokeepchildreninhealth,youshouldnevergivethemmorethansixhoursaltogetheratlessonsintheday,andatleasttwohalf-holidaysintheweek.Andthat'sEXACTLYourplanIcanassureyou!Wenevergobeyondsixhours,andeveryWednesdayandSaturday,aseveris,notonesyllableof



lessonsdotheydoaftertheironeo'clockdinner!SohowyoucanimagineI'mrunninganyriskintheeducationofmypreciouspetsismorethanIcanunderstand,Ipromiseyou!"

THEEND.

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the game of logic by lewis carroll

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