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SuppositionasQuantificationversus
SuppositionasGlobalQuantificational
Effect1
TerenceParsons
Amajorthemeinthesecondaryliteratureofthelastthreedecadeshasbeen
thequestion:Whatisthemedievaltheoryofthemodesofpersonalsupposition
atheoryof?Itisbeyondquestion(andhasneverbeenquestioned)thatthis
theoryisastudyofquantificationalphenomena,butwhatkindofstudy,and
whichquantificationalphenomena?
Spade1988suggeststhatthereareactuallytwotheoriestoaddressthis
questionto,anearlyoneandalaterone.2Mostofthepresentpaperisa
developmentofthisidea.IsuggestthatearlyworkbySherwoodandothers
wasastudyofquantifiers:theirsemanticsandtheeffectsofcontexton
inferencesthatcanbemadefromquantifiedterms.Later,inthehandsof
Burleyandothers,itchangedintoastudyofsomethingelse,astudyofwhat
Icallglobalquantificationaleffect.Insection1,Iexplainwhatthesetwo
optionsare.
Insection2,Ilookattheearlytradition,whichisfoundinmanythirteenth
centurywriters,includingWilliamofSherwood,PeterofSpain,Lambertof
Auxerre,andinseveralanonymoustexts,withremnantsofitextendingalsoto
muchlaterworks,suchastheLogicaParvaofPaulofVenice.Thisisan
investigationofthesemanticsofquantifiers,coupledwithaninvestigation
ofascentanddescent,whicharekindsofinferencethatareconsequenton,
butdistinctfrom,thesemanticsofthequantifiers.
Inthefourteenthcentury,thattraditionevolvedintoaquitedifferentone,
representedprimarilybyWalterBurley,WilliamOckham,andJohnBuridan.In
thislaterdevelopmenttheterminologyofmodesofcommonsuppositioncomesto
bedefinedintermsofthepossibilityofdescentandascent.Theresult,
discussedinsection3,isatheorythatisnolongeratheoryofquantifiers,
butatheoryofglobalquantificationaleffect.Thiswasagreatstepforward
intheclarificationoftechnicalterms,butastepbackwardinstudyingwhat
isimportantfromatwentiethcenturypointofview,sinceglobal
quantificationaleffectisconsequentuponanunderlyingsystemof
quantifiers,andthetheoryhasturneditsbackontheirstudy.
Finally,insection4,Ireturntothelong-standingquestionofthepurpose
ofsuppositiontheory.Settlingthequestionofwhatitwasatheoryofdoes
3
notsettlethequestionofwhatitwasthoughttoaccomplish.Isuggestthat
themedievalstudiesofsuppositionparallelmoderntheoriesofopacityand
transparency;inbothtraditionsthereisnosinglepurpose;instead,there
aredifferentstagesanddifferentparticipants,allwiththeirowndifferent
purposes.
Ontheusualinterpretation,therewasanaccountofquantifiersintheearly
medievalperiodwhichwasobscure;itwas"cleanedup"byfourteenthcentury
theoristsbybeingdefinedintermsofascentanddescent.Iamsuggesting
thatthecleaningupresultedinatotallynewtheory.Butthisisnot
compellingiftheobscurityoftheearlierviewpreventsusfrommakingany
senseofitatall.IntheAppendix,IclarifyhowIamreadingtheearlier
accounts.Theyareobscure,butIthinktheycanbereadsoastomakegood
sense.Thesesameissuesariseininterpretingtheinfamousnineteenth
centurydoctrineofdistribution;Itouchbrieflyonthis.
1QuantificationversusGlobalQuantificationalEffect
Alloftheauthorsunderdiscussionhereclassifythefunctioningofcommon
termsinpropositionsintothreecategories:Determinate,Distributive,and
4
MerelyConfused3.Determinatehassomethingtodowithwide-scopeexistential
quantification,distributivewithuniversalquantification,andmerely
confusedwithsomethinglikenarrow-scopeexistentialquantification.
Paradigmexamplesarethese:
Somedonkeyisarunner. `Donkey=hasDeterminate
supposition.
Everydonkeyisarunner. `Donkey=hasDistributive
supposition.
Everydonkeyisarunner. `Runner=hasMerelyConfused
supposition.
Althoughvirtuallyallauthorsagreeabouthowtoclassifytermsinsimple
propositions,ithasalwaysbeenpuzzlingwhattheythoughtthisrepresentsor
accomplishes.Thepointofthispaperistomakeasmalladvanceinexploring
thisquestion.IwillarguethatWilliamSherwood,PeterofSpain,and
LambertofAuxerrehaveatheoryofmodesofcommonsuppositionthatamounts
toasemanticsofquantifiers,whereasWalterBurley,WilliamOckham,andJohn
Buridanhaveaquitedifferenttheory,onethatamountstoatheoryofglobal
quantificationaleffect.Thepurposeofthissectionistoexplainthe
5
differencebetweentheseoptions.
1.1TheSemanticsofQuantifiers
Letussupposethatwehavegivenanexplanationofthesemanticsof
quantifiersandconnectives,andthatsomeonethenasksuswhatourtheoryhas
tosayabout`�x'asitoccursin
!�xPx.
Anaturalreplywouldbe:
Well,it'sauniversalquantifier,justasitwasbeforeanegationsign
appearedinfrontofit.Infact,thereisnothingnewtosayaboutit
atall;wehavegiventhesemanticsofthequantifier,andofnegation,
andeverythingthereistosayfollowsfromthese.
Thisreplyconstruesthequestionasaquestionaboutthesemanticsof
quantifiers.
1.2GlobalQuantificationalEffect
6
Wecouldalsogiveadifferentreply,consistentwiththefirst.Wecould
say:
Inthecontext`!�xPx=,thequantifierhasanexistentialeffect.In
thatcontext,thequantifierhastheactualeffectthatitwouldhaveif
itweremovedinfrontofthenegationandchangedtoexistential:
`�x!Px=.Soitsglobaleffecthereisexistential,notuniversal.
Itisfairlyeasytoseewhatthisamountsto,andtheideacanbemade
precisewithinthetheoryof"normalforms".Ifnobiconditionalsignappears
inaformulaofquantificationtheory,thenyoucantakeanyquantifierin
thatformulaandmoveitinstagestowardthefrontoftheformula,eachstage
beingequivalenttotheoriginalformula,providedthatyouswitchthe
quantifierfromuniversaltoexistential(orviceversa)wheneveryoumoveit
pastanegationsignoroutoftheantecedentofaconditional,andprovided
thatyoudonotmoveitpastaquantifierofoppositequantity(i.e.youdon't
moveauniversalpastanexistential,orviceversa).Forexample,youcan
taketheuniversalquantifierin`!(�xPx"G)'andmoveitontothefront
oftheconditionalasanexistential,toget`!�x(Px"G)',andthenthe
resultingexistentialcanbemovedfurtherfront,turningintoauniversal
7
again:`�x!(Px"G)'.Ifyoudothissystematicallytoallthequantifiers
inaformula,theresultisaformulain"prenexnormalform,"andintermsof
theseformsyoucandefinetheglobalquantificationaleffectofany
quantifierinanyformulaasfollows:
Aquantifierisgloballystronglyuniversalinaformulaifitbecomesa
widescopeuniversalquantifierin(oneof)theprenexnormalform(s)of
thatformula.
Aquantifierisgloballystronglyexistentialinaformulaifitbecomes
awidescopeexistentialquantifierin(oneof)theprenexnormal
form(s)ofthatformula.
Aquantifierisgloballyweaklyuniversalinaformulaifitbecomesa
universalquantifierin(oneof)theprenexnormalform(s)ofthat
formula,butithasscopeinsideanexistentialquantifierinanysuch
form.
Aquantifierisgloballyweaklyexistentialinaformulaifitbecomes
anexistentialquantifierin(oneof)theprenexnormalform(s)ofthat
formula,butithasscopeinsideauniversalquantifierinanysuch
8
form.
Forexample,theseconduniversalquantifierinthefollowingformulais
globallyweaklyexistential,asisshownbytheequivalences:
�x(Px"!�yRxy)┌┘
�x(Px"�y!Rxy)┌──┘�x�y(Px"!Rxy)
(Itcannotbemovedinfrontoftheinitialuniversalquantifierinanyway
whilepreservingequivalencewiththeoriginalformula.)
Thecontrastbetweentheearlysuppositiontheoryandthelateroneshowsup
asthefollowingcontrast,usingdistributivesuppositionasanexample:
TheEarlyTheory:Theearlytheoryisatheoryofthequantificationof
terms,analogoustoamodernsemanticsofquantifiers.Inthiskindof
account,auniversallyquantifiedtermsuchas`man'in`everyman'has
distributivesuppositionasaresultofthepresenceoftheword`every'.
Whenthisterm(withthe`every')appearsinmorecomplexcontexts,itstill
hasdistributivesupposition.Thisisbecausedistributivesuppositionisthe
9
statusatermhasinvirtueofitsbeingdirectlyquantifiedbyaquantifying
signsuchas`every'or`no'.Soin
Noteverymanisananimal
theterm`man'hasdistributivesuppositionbecauseofthe`every'.Thefact
thatthewholesentencehasanegationonthefrontdoesnotaffectthemode
ofsuppositionof`man'(justas`�x'isauniversalquantifierevenin
`!�xPx').
TheLaterTheory:Thelatertheoryisanaccountofglobalquantificational
effect,withdistributivesuppositionbeinganalogoustoglobaluniversal
effect.Asintheearlieraccount,the`man'in`everyman'hasdistributive
suppositionasaresultofthepresenceoftheword`every'.Butwhenthis
term(withthe`every')appearsinmorecomplexcontexts,itcanlosethis
distributivesupposition.Thisisbecausedistributivesuppositionisthe
statusatermhasinvirtueofitsglobaleffect.Soin
Noteverymanisananimal
10
theterm`man'losesitsdistributivesuppositionbecauseofthenegationon
thefront.
Inthelatertheory,determinatesuppositionisanalogoustoglobalstrongly
existentialeffect,merelyconfusedsuppositionisanalogoustoglobalweakly
existentialeffect,anddistributivesuppositionisanalogoustoglobal
universaleffect(lumpingtogetherstrongandweak).
11
1.3DistinguishingtheTheories
Whatdistinguishestheearliertheoryfromthelateroneiswhetherthemode
ofsuppositionofaterminapropositionissomethingthatthattermretains
whenitspropositionisembeddedinfurthercontexts.Nobodywilldispute
thatquantificationremainsunchangedunderembeddingwhileglobal
quantificationaleffectchanges.Thequestioniswhichphenomenonissupposed
tobecapturedbythemodeofsuppositionofaterm.Theearlykindoftheory
usesmodesofsuppositiontostandforquantificationalstatus,andthusthis
kindoftheoryisastudyofquantification;thelaterkindoftheoryuses
modesofsuppositiontostandforglobalquantificationaleffect,andsothat
iswhatitstudies.
Alltheoristsinfactspendagreatdealoftimeinstudyinginferences,a
pointrightlystressedbyKarger1993.Theyevenstudymuchthesame
inferencesinmuchthesameexamples.Buttheyexpresstheirfindings
differently.Intheearlytheorythereismuchdiscussionof"mobility,"i.e.
whetherornotonecanmakeinferencestosingularsundertheterm.Here,one
findsamplediscussionofcontextsinwhichinferencesareimmobilized.For
example,from`Everymanisrunning',onemaydescendunder`man'toinfer
12
`Thismanisrunning';butin`Noteverymanisrunning'thenegation
immobilizesthatinference,sothatoneisnotabletodescendfrom`Notevery
manisrunning'to`Thismanisnotrunning'.Onthisaccountthemodeof
suppositionof`man=(thatis,itsquantificationsemantics)remains
unchangedwhenthe`not=isadded,butthe`not=affectswhatinferencescan
bedrawn,becausemobilityhasentirelytodowithinferences..
Inthelatertheorylittleissaidofimmobiledistributivesupposition,4
sincedistributivesuppositionisdefinedintermsofthepossibilityof
descent.Onthatapproach,theanalysesofinferencefailuresarecouchedin
termsofthenegation'salteringthesuppositionoftheterm.In`Everyman
isrunning',theterm`man'hasdistributivesupposition(onboththeories),
andifdistributivesuppositionisnotimmobilized,onemaydescendunderthe
term.Inthelatertheorythenegationin`noteverymanisrunning'doesnot
immobilizethedistributivesuppositionof`man';itchangesitinto
determinatesupposition,anditisalreadyknownthatdescentisnot
sanctionedbydeterminatesupposition.Sotheaccountofinferencefailurein
`noteverymanisrunning=doesnotneedanappealtoimmobilization.
Ofcourse,boththeoriesneedtogetthesameanswersregardingwhat
13
inferencesarecorrect,andthustheyproceedinparallel,evenregardingmany
ofthedetails.Thedifferenceisthatintheearlyaccountoneneedsa
theoryofimmobilizationaddedontoatheoryofthesemanticsofquantifiers;
inthelattertheoryoneneedsanaccountofshift-of-mode-of-suppositionto
explainthesamecases.Itisnosurprisethenthatthedetailsofthe
conditionsunderwhichinferencesareimmobilizedintheearlytheoryare
closelyparalleledbythedetailsoftheconditionsunderwhichsuppositionis
alteredinthelatertheory.Theseparallelsgivetheimpressionofdifferent
articulationsofacommontheory.Ithinkthatinsteadwehavequitedistinct
theoriesthatruninparallelpartlybecauseofacommonheritage,andpartly
becausetheybothaimataccountingformuchthesamedata.
Eachapproachhasitsownapparentadvantages.Anadvantageofthelater
theoriesisthatinferencepatternscanbestatedquitegenerally.For
example,onecantakeitasaperfectlygeneralprinciplethat"distributive
entailsdeterminate,"thatis,fromanypropositioncontainingatermwith
distributivesupposition,ifthattermgetsitssuppositionchangedto
determinate(withoutanyotherchangesintheproposition)thentheresultant
propositionfollowsfromtheoriginal.Intheearliertheoriesthegeneral
14
principlehastobe"distributiveentailsdeterminate,unlessimmobilized."
Thisappearstobeafarlessusefulprinciple,sinceoneneedstocheckfor
immobilizationbeforeapplyingtheprinciple,andthatcanbeacomplicated
matter.Butsomethingsimilaralreadyhappensinthelatertheory,sincein
thattheoryitisanequallytrickymattertotellwhetheratermis
distributiveordeterminate.Sothereisatradeoffhere,anditisnotclear
thateithertheoryisbetteroverallataddressinginferences.
2:SuppositionasaTheoryofQuantification:TheEarly
Accounts
Thepurposeofthissectionistoargueindetailthefirstclaimmadeabove,
thattheearlyaccountsofsuppositionconstruedthemodesofsuppositionas
kindsofquantification,notaskindsofglobalquantificationaleffect.
2.1Howitgoesoverall
15
Atheoryofquantifiersgenerallyworksasfollows.First,eachquantifieris
understoodtohaveacanonicalposition.Thenthesemanticsofthequantifier
areexplainedforanoccurrenceofthequantifierinthatcanonicalposition,
intermsofanassumedunderstandingoftherestoftheelementspresent.For
example,inmodernfirstorderlogic,thecanonicalpositionofaquantifier
isonthefrontofaformula,withscopeoverthewholeformula.The
semanticsofthequantifierarethenexplainedintermsofaprior
understandingofhowtherestoftheformulaworks,inparticular,interms
ofwhatobjectssatisfytheformula.Forexample,theexistentialquantifier
isexplainedbysayingthat`(�x)(...x...)'istrueiffsomethingsatisfies
`...x...'.
Themedievaltheoryofsuppositiondiscussesquantifiedterms,notquantifiers
themselves,butthisisonlyamatterofformulation.Inallversionsof
suppositiontheory,thecanonicalpositionsforquantifiedtermsareas
subjecttermoraspredicatetermofacategoricalproposition.Thusthe
theoryneedstoaddresshowtheyworkintheseplaces.
Theaccountofwhichmodeofsuppositionatermhasinitscanonicalposition
isusuallyspecifiedintermsofrulessuchasthese:
16
Atermnotprecededbyaspecialsign(orprecededonlyby`some')has
determinatesupposition.
Auniversalaffirmativesign(e.g.`every')distributesthetermitis
adjoinedto,andmerelyconfusesanyothertermtoitsright.
Anegativeterm(e.g.`no'or`not')distributesanytermtoitsright.
Theresultsforstandardformcategoricalpropositionsarethese:
In`SomeSisP'neithertermisprecededbyasignotherthan`some',
andsobothhavedeterminatesupposition.
In`SomeSisnotP'thesubjecttermhasdeterminatesupposition,and
the`not'makesthepredicatetermsuppositdistributively.
In`NoSisP'the`no'makesbothtermssuppositdistributively.
In`EverySisP'the`every'makesthesubjecttermdistributiveand
makesthepredicatetermmerelyconfused.
17
Theserules(intheearlytheory)giveanalgorithmthatisnodifferentin
principlethanamodernaccountthatreads:
Ifaquantifiercontainsavariableallbyitselforprecededby`�'it
isuniversal;ifitcontainsavariableprecededby`�'itis
existential.
Theaboverulesthusgivesyntactictestsfordeterminingmodeofsupposition.
Theuniformaccountofthesemanticsofthesetermsthengoessomethinglike
this(thisisa"generic"version):
Atermhasdeterminatesuppositioninacategoricalpropositionwhenthe
locutioncontainingitcanbeexpoundedbymeansofitsbeingtruefor
somesinglething.
Atermhasdistributivesuppositioninacategoricalpropositionwhenit
suppositsthereforallofitssupposita.
Atermhasmerelyconfusedsuppositioninacategoricalpropositionwhen
itcanbetakenthereforseveralofitssupposita,notnecessarilyfor
18
all.
Theseaccountswillappearfrustratinglyvaguetomanycontemporaryreaders
(theywillbeclarifiedsomewhatintheappendix).Buttheirunclarityisnot
necessarilyanimpedimenttoclassifyingthem.First,itisclearthatthey
makenoappealtoascentordescent.Second,theaccountsyield(unclear)
accountsofthesemanticsofquantifiedterms,accountswhichdonotchange
whencategoricalpropositionsappearembeddedinmorecomplexconstructions.
Inparticular,justasinmodernquantificationtheory,oncethesemanticsof
thequantifiedtermsaregiven,wearedonewiththem;theydonot
metamorphizeintooneanotherwhensentencescontainingthemareembeddedin
largersentences(asinthelatertheory),noristheirsemanticsaffectedby
suchembedding.(Thisclaimwillbejustifiedbelow.)
Itisespeciallyeasytomisreadcertainrulesoftheearlytheoryasrules
foralteringsuppositionalstatuswithembedding.Therearetwosortsofsuch
rulessusceptibleofsuchmisreading,andIneedtoexplainwhythesearenot
rulesforalteringmodesofsupposition.
Firstaretherulesgivenabovethatexplainhowthepresenceofsignssuchas
`every',`no'and`not'affectthesuppositionalstatusoftermsfollowing
19
them.Thesecouldbe(mis)interpretedasalteringsuppositionalstatus;for
example,onecouldimaginethatthe(distributive)termsof`NoSisP'had
determinatesuppositionbeforethe`no'wasaddedtotheproposition,andthat
the`no'changedthesuppositionfromdeterminatetodistributive.Butthis
wouldbelikemistaking`(�x)Px'assomethingthatbecameanexistentially
quantifiedsentencebystartingwiththeuniversallyquantified`(x)Px'and
havingtheexistentialsignadded.Thatisn'thowmodernquantification
theoryworks,anditisn'thowtoreadtherulesabove(inthecontextofthe
earlytheory)thatspecifysuppositionalstatus.Inneithercasearethe
semanticsoftheresultingformulaexplainedintermsofthesemanticsofthe
allegedinputformula;itisonlyasyntacticaccidentthattheresulting
formulalookslikeanothermeaningfulformulawithasignadded.Onemight
thinkotherwise,becausethereismuchtalke.g.about`every'confusingor
distributingtermsthatfollowit,withthetermspresentbeforethe`every'
showsuptodosomethingtothem.But`every'distributesorconfusesthe
termsthemselves,notthetermsconstruedasthingsalreadyhaving
(determinate)supposition.
Second,therearerulesthatexplainhowthepresenceofsignssuchas`not'
affectmobility(ascentanddescent)uponembedding.Rulessuchas"What
20
mobilizestheimmobile,immobilizesthemobile."Theserulesforman
importantpartofbothenterprises.Thelatertheoriesdefinesuppositional
statusintermsofdescentandascent,andsointhesetheoriessuchrulesare
rulesabouthowembeddingaffectssuppositonalstatus.Butinthetheories
underdiscussion,ascentanddescentareneverpartofthesemanticsofthe
quantifiers;themodesofsuppositionarecharacterizedwithoutthesenotions.
Sointheearlyaccounts,rulesaboutmobilitysaynothingabout
suppositionalstatus.(Theysayinsteadwhattheysayliterally:theysay
whatmayormaynotbeinferredfromasentencecontainingtermsinsuchand
suchpositions.)
Ihavesketchedatheoryinwhichquantifiedtermshavetheirsemantics
explainedintheircanonicalpositionsincategoricalpropositions,andin
whichthetermsretaintheirsuppositionalstatusandsemanticswhensentences
containingthemarecombinedintolargersentences.Onthisaccount,since
`dog'hasdistributivesuppositionin`Everydogisspotted'italsohasthat
statusin`Necessarily,everydogisspotted',`Ifeverydogisspottedthen
everygiraffeisspotted',andsoon.ButsofarIhavesimplyassertedthat
thisistherightinterpretationoftheearlier(thirteenthcentury)authors.
Thecaseisyettobemade.IntheremainderofthissectionIconsiderthe
21
evidencethatWilliamofSherwood,PeterofSpain,andLambertofAuxerre
actuallyheldtheoriesofthissort.5
2.2WilliamofSherwood'sTheoryofQuantification
Williamgivesthefollowingsortsofexplanationsofthemodesofcommon
personalsupposition(Kretzmann1966,'5.2):
Suppositionisdeterminatewhenthelocutioncanbeexpoundedbymeans
ofsomesinglething.Whichisthecasewhenthewordsuppositsfor
somesinglething.Thereforein`amanisrunning'itcanbetruefor
anyonerunning.
Suppositionisdistributivewhen[theword]suppositsformanyinsucha
wayastosuppositforany.
Suppositionismerelyconfusedwhen[theword]suppositsasdoes
22
`animal'in`everymanisananimal'.
Williamalsodefinesmobility(fordistributivesuppositiononly)intermsof
descent,independentlyof(thoughimmediatelyafter)theaccountof
supposition.Ourpresentconcernisnottogetclearontheprecisemeaning
ofthesedefinitions(forthat,seetheappendix),buttogetclearaboutwhat
thedefinitionsaredefinitionsof:quantification,orglobalquantificational
effect?
WhatevidenceistherethatSherwoodhasatheoryofquantificationandnota
theoryofglobalquantificationaleffect?Thebestevidencewouldbeforhim
tomakethedistinctionandchoose,butnoauthorseemstohavedonethis.
Instead,wehavetwokindsofevidence:
A.SofarasIcanfind,Sherwoodnevergivesanexampleofatermthat
changessuppositionalstatusasaresultofembeddingthecategorical
propositioncontainingitinalargercontext.Ifhisgoalhadbeento
discussglobalquantificationaleffect,thiswouldbeastrangelapseonhis
part.
23
B.InatleastonecaseSherwoodcitesanexampleofatermwhoseglobal
quantificationaleffectisatoddswithitsquantificationalclassification.
Theexampleistheterm`man'in`noteverymanisrunning'.Inthisexample,
hesaysthat`man'hasimmobiledistributivesupposition,whichisexactly
whatonewouldexpectifthequantificationalword`every'hasa
distributionalsemantics,andifthenegationisseenasnotaffecting
suppositionalstatus,butaffectingmobility.The`every'gives`man'
distributivesupposition,andthe`not'createsacontextinwhichdescent
underthedistributivetermisinvalid,thatis,itmakesthetermimmobile
withoutchangingitsdistributivesupposition.IfSherwood'ssuppositional
statuswereakindofglobalquantificationaleffect,thenthenegationwould
affectthesuppositionoftheterm`man',makingitsomethingotherthan
distributive.(Onthelateraccount,itwouldmakethetermhavedeterminate
supposition.)
2.1.1Adoubtconcerningthispoint
Certaincommentatorswouldchallengetheinterpretationofthisexample;I
willspendsometimeonthereason.(Thissubsectionmaybeskippedwithout
24
lossofcontinuity.)
Thefullsentenceinwhichtheabovequoteoccursis:
Sometimes,however,distributionremainsimmobile,asin`noteveryman
isrunning'`onlyeverymanisrunning',andothercasesofthatsort.
Kretzmann1966,119-20suggeststhatSherwoodisnottalkinghereabout
distributivesuppositionatall,butratheraboutanindependentnotionof
distribution.Andthisclaimcannoteasilybediscounted.Afterall,
Sherwooddoesn'tsay"distributivesuppositionremainsimmobile,"hesays
"distributionremainsimmobile,"andtheterm`distribute'doeshaveameaning
independentofsuppositiontheoryproper.Forexample,Sherwoodhimselfgoes
ontoclassifycopulationintodeterminate,distributive,andmerelyconfused.
(Copulationistheanalogueforadjectivesofsuppositionfornouns.)And
distributionissometimesdefinedindependentlyofanyapplication.6Itis
clearthatSherwood'sdistributivesuppositionismeanttobethesortof
suppositionthattypicallyresultsfromdistribution.Soonemightmakesense
ofsayingthatatermisdistributedandhassuppositionbutnonethelesslacks
distributivesupposition.Butthiswouldbehighlymisleading,andonewould
expectafairlypointedandlengthyexplanation,whichSherwooddoesnotgive.
Thiswouldbeespeciallypertinent,sincehehasearlierdefined`mobile'
25
specificallyfordistributivesupposition,andforhimtouse`immobile'(in
connectionwithatermwithsupposition)foraquitedifferentpurposewould
bedisconcertinginawaythathewouldnotbelikelytooverlook.
Further,thereisaparallelpassagewhereimmobilityisdiscussed,andwhere
distributionalonecannotbewhatismeant.ItisinWilliam'sdiscussionof
copulation,whichimmediatelyfollowstheoneonsupposition.Inthis
section,copulationispresentedasaphenomenonparalleltosupposition,and
here,incomparingthetwonotions,wefindthecomment('5.14):
Wealsofindimmobiledistributivecopulation,asin`noteverysortof
...'
Thiscannotbeacommentaboutdistributioninisolation,sincehesays
`immobiledistributivecopulation'.Theparalleltotheprecedingremark
aboutimmobiledistributionfortermsthatsuppositisclose,andindicates
thatmobilityisnotanissueofdistributionperse,butratherofsomething
createdfromit.
ThereisonemorepieceofevidencethatKretzmanncitesinfavoroftheview
thatSherwoodisdiscussingdistribution,andnotdistributivesupposition.
ItistheincongruityofthelastsentenceofthewholecontextinKretzmann's
translation(Kretzmann1966'5.13.5):
26
Sometimes,however,distributionremainsimmobile,asin`not
everymanisrunning'`onlyeverymanisrunning',andothercasesof
thatsort.Itiscalledimmobile,however,notbecausewecannotascend
inthesubjectbutbecausewecannotdescend.Thisisduetothefact
thatdistributionisofthesuppositathemselves,andthereforewhenwe
cannotdescendtooneofthemitisacaseofwhatisproperlycalled
immobiledistribution.
Suppositioniscalledimmobileforasimilarreason,viz.,thatwe
cannotdescendtothesupposita;forsuppositionisforasuppositum.
Kretzmannsuggeststhatthelastlineismeanttocontrastimmobile
suppositionwithimmobiledistribution.ButonthisinterpretationSherwood
saysthatsuppositioncanbeimmobile,butnevergiveseitheranexampleoran
explanationofimmobilesupposition,andwearecompletelyinthedarkabout
whatitcouldbe.
IntheLatinfromwhichthisistranslated,thetextissomewhatdifferently
organized.Thesingle-sentencelastparagraphisnotseparatedfromthe
previousoneatall;itisaconjunctofthelastsentenceofthepreceding
paragraph.Sothewholequotehasthisform:
27
Sometimes,however,distributionremainsimmobile,asin`not
everymanisrunning'`onlyeverymanisrunning',andothercasesof
thatsort.Itiscalledimmobile,however,notbecausewecannotascend
inthesubjectbutbecausewecannotdescend.Thisisduetothefact
thatdistributionisofthesuppositathemselves,andthereforewhenwe
cannotdescendtooneofthemitisacaseofwhatisproperlycalled
immobiledistribution;andsuppositioniscalledimmobileforasimilar
reason,viz.,thatwecannotdescendtothesupposita;forsupposition
isforasuppositum.
Withthisparsing,theselectionappearstobeaslightlycomplicated
explanationofwhydistributivesuppositioniscalledAimmobile@inthese
examples.7
Still,thisisonlyoneexample,andonemightwonderifitcouldhavebeena
blunderonSherwood'spart.Butinanapparentlylatertext(Treatiseon
SyncategorematicWords)healsogivesanexamplewithimmobiledistributive
supposition.Heisillustratingtherulethat
Whentherearetwodistributionsoverthesamepartofalocutionthe
firstimmobilizesthesecond.
28
Theillustrationistheexample
Everymanseeingeverymanisrunning,
regardingwhichheindicatesthatthesecond`man'hasimmobilesupposition.8
Thisexampleisacomplexpropositioninwhichthetermunderdiscussion
occursinasubordinateclause(omnishomovidensomnemhominemcurrit).It
isreallynotclearhowthetheoryissupposedtohandleembeddingsofthis
sort;thisisthesortofissuewithwhichSherwoodstrugglesthroughoutthe
text.9Butitisclearthathesees`man'inthesubordinateclauseas
gettingdistributivesuppositionfromits`every',andthisdistributive
suppositionremainsintactinthelargersentence,eventhoughitgets
immobilizedbythefirst`every'.(Inthelatertheoriesthesecond`man'
wouldhaveitsdistributivesuppositiondestroyedbytheembedding.Itisnot
clearwhatkindofsuppositionwouldresult.10)
Noristhereanyindicationinthelatertextofanexpressionthatchanges
suppositionuponembedding.Theevidenceisnotconclusive,andprobably
cannotinprinciplebefurtherclarified.ThisisbecauseSherwoodoften
discusseswhatkindofsuppositionatermhasinwhatwewouldseeasan
embeddedcontextwithoutdiscussingwhatkindofsuppositionitmighthavehad
29
wereitslocalcontextnotembedded.Indeed,inthecontextsofmostinterest
tous,heprobablywasnotthinkingintermsofpropositionsbecomingembedded
inothers,andofhowthatmighthaveaffectedakindofsuppositionthey
alreadyhave.Andsoinevenposingthisquestionweareindangerofreading
ourthoughtsbackintohis.Butwhatisclear,Ithink,isthatitisboth
possibleandnaturaltoattributetohimaviewaccordingtowhichtermsget
theirkindsofsuppositionassignedtothembythepatternsof(mostly
syncategorematic)signsincategoricalpropositions,withoutanyattentionat
allbeingpaidtotheglobalquantificationaleffectofthattermwhenits
localcategoricalispartofalargersentence.
2.3LambertofAuxerre
Lambert,likeSherwood,definesthemodesofsuppositionindependentof
mobility.Hedefinesdeterminatesuppositionasfollows:
Determinatesuppositioniswhatacommontermhaswhenitcanbetaken
equallywellforoneorformorethanone,aswhenonesays`Amanis
running'.Inthatproposition`man'hasdeterminatesuppositionbecause
itistrueifonemanisrunningorifmorethanonearerunning.11
Insteadof`distributive'and`merelyconfused',Lambertusestheterminology
30
`strong'and`weak'.Strongiswhenthetermisinterpretedforallits
suppositanecessarily;weakiswhenthetermisinterpretednecessarilyfor
morethanonesuppositumcontainedunderitbutnotforall.Theseaccounts
arenotunproblematic,butforpresentpurposestheissueisnottheunclarity
oftheaccounts,buttheirindependencefromconsiderationsofascentand
descent,andthequestionofhowtheyareaffectedbyembeddings.
LambertgivesoneofSherwood'sexamplestoillustratestrongimmobile
supposition:`Onlyeverymanisrunning'.Thisexampleisnotconclusive,
sinceitisnotexactlyclearwhatitmeans.Butitisnaturaltointerpret
itasbeingequivalenttotheconjunctionof`everymanisrunning'and`no
non-manisrunning',withthesecondconjunctbeingaddedbythe`only'.
Presumably,thesingularsunder`man'in`onlyeverymanisrunning'areof
theform`onlythismanisrunning'12;sincethesecannotbeinferred,the
suppositionisimmobile.Themostnaturalinterpretationthenisthat`every'
gives`man'strong(=distributive)supposition,andthatthe`only'changes
theoverallimportoftheproposition,butwithoutchangingthefactthat
`man'hasdistributivesupposition.Thisisconsistentwiththeviewthat
suppositionisamatterofhowtermsarequantified,anditisinconsistent
31
withtheviewthatsuppositionisamatterofaterm'sglobalquantificational
effect.Butthediscussionissotersethatitishardtomakeagreatdeal
outofit,andLambertterminateshisdiscussionofsuppositionatthis
point.13
2.4PeterofSpain
TheviewsofPeterofSpainonpersonalsupposition,iftakenliterally,can
fitnicelyintothesamecategoryasSherwood.Buttheyaresomeagerthatit
ishardtoknowwhetherheputthingsinacertainwaybecausehemeantthem
strictlythatway,orbecausehejustwasn'tthinkingbeyondacertain
restrictedsetofapplications.
Peterdefinesthemodeswithoutreferencetoascentordescent,withheavy
relianceonsyntax.Wefind(VI.8):14
Determinatesuppositionlabelswhatacommontermhaswhentaken
indefinitelyorwithaparticularmarker,asin`manruns=or`someman
runs=.
By`takenindefinitely'heseemstohavemeantthatnoquantifier-likesign
(suchastheAparticular@sign`some=)precedesitsyntactically.15He
32
definesconfusedsupposition(VI.9)as
[Confused]16suppositionistheacceptanceofacommontermforseveral
thingsbymeansofauniversalsign.
Thereisnodiscussionofatermchangingitssuppositionalstatusupon
embedding.ButPeterdoesclearlydistinguishthequestionofthe
suppositionalstatusofatermfromthequestionofwhatinferences(descents
andascents)canbemadeusingit(VI.9):
[In`Everymanisananimal=theterm`man=]Astandsfor@[confusedly]
anddistributively,sincetakenforeveryman;mobilely,sincedescent
canbemadefromittoanysupposit,..
Thisseemstodriveawedgebetweensuppositionalstatusandmobilitywhich
wouldatleastprecludedefiningoneintermsoftheother.
Inthesectiononsupposition,hedoesnotdivideconfusedsuppositioninto
distributiveandmerelyconfused.Instead,hehasalonglatersectionon
distributioninwhichmuchisdiscussed,butlittlethatbearsdirectlyonthe
presentissue,sincethewords`distributive'and`supposition'(indicating
modeofsupposition)rarelyoccur.Butwhenhedoesdiscussdistribution
directlyheseemstotakesidesagainstviewingitintermsofglobaleffect.
Anillustration:Peterasks(XII.24)whetherthenegationin`Notmanis
33
just'{Nonhomoestiustus}distributes`man'.Heconcludesnot.17Heargues
thatifthereweredistribution,thereshouldbeacommontermtaken
universally,andsothereshouldbeasignsignifyinguniversality.But,he
says,auniversalsignsignifiesuniversality,whilenegationdoesnot;so
thereisnodistribution.NowifPetersawdistributionasamatterofglobal
quantificationaleffect,therewouldbenoreasontothinkthatasign
signifyinguniversalityshouldbeneededtoachievethis.Nordidheoverlook
thispossibility,forhethinksthatthecaseunderexaminationisjustsucha
case.Heconcludesthat`Notmanisjust'isuniversal,butonlybecausethe
negationnegates,andnotbecauseitcausesdistribution:18
Thesolutiontotheobjectionisnowclear,forthefactthat`Notman
isjust'isuniversalisnotbecauseofthenatureofdistributionfound
innegation,butbecausemanincommonisnegated,andoncethatis
removed,soisanyinferior.
Sothisisacaseinwhichoneclearlyhas"universal"globalquantificational
effect,butwithoutdistribution,andsoPetercannotviewdistributionasa
matterofglobalquantificationaleffect.
3SuppositionasaTheoryofGlobalQuantificational
34
Effect:TheLaterAccounts
3.1HowitGoes
Inthelatertheory,themodeofsuppositionofaterminanyproposition,no
matterhowcomplex,isdefinedintermsofdescentfromandascenttothat
propositionundertheterminquestion.Anaccountofdeterminatesupposition
goessomethinglikethis:
AtermFhasdeterminatesuppositioninaproposition`...F...'ifand
onlyif:
(i)From`...F...'onemayinfer`...thisF...or...thatF...or
...'
assumingthatthedemonstratedF'sincludealltheF'sthatthere
are,and
(ii)Onemayinfertheoriginalproposition`...F...'fromany
singularoftheform`...thisF...'.
Example:Theterm`donkey=hasdeterminatesuppositionin`Somedonkeyis
grey=because:
(i)From`Somedonkeyisgrey=onemayinfer`Thisdonkeyisgrey,or
thatdonkeyisgrey,orthatdonkeyisgrey,or...,assumingthat
35
theseareallthedonkeys.And:
(ii)Onemayinfer`Somedonkeyisgrey=fromanysingularoftheform
`Thisdonkeyisgrey=.
Complicationsabound;issuesthatwillnotbeaddressedhereincludethese:
⨿Indescending,youneedtomakechangesintheoriginalproposition.
E.g.,youdescendfrom`Everymanisrunning'to`Thismanisrunning',
notto`Everythismanisrunning'.Howcanyoutellingeneralwhat
changestomake?(E.g.Indescendingfrom`Onlydonkeysaregrey=do
youdescendto`Brownieisgrey=orto`OnlyBrownieisgrey=?)
⨿Whatistheforceof`ontheassumptionthatthedemonstratedF's
includealltheF's'?
⨿WhatifthereisonlyoneF,ornoF'satall?Whatifnecessarily
therearenoF'satall?
⨿Exactlyhowaretheothermodestobecharacterized?
Thesearemattersthatarewelldiscussedinbothprimaryandsecondary
sources;thepointsIammakinghereareindependentofthem.
Althoughmyuseoftheterminology`globalquantificationaleffect'isnew,
theclassificationofthelatertheoriesunderthistitlereliesonanalready
36
developedconsensusabouthowtotestformodesofsuppositioninthelater
theories,andtheremainingsubsectionsofthissectionare(Ithink)just
well-knownfactsbroughttogetherasevidenceforatheoreticalanalysisof
thesubjectmatterofthetheory.
3.2WalterBurley
Burleywrote(atleast)twotractsonsupposition.Thefirstinfluenced
Ockham'sownviews,andthesecondwaswrittenpartlyinreactiontoOckham=s
writing.IfBurley=sfirstwritingconstruedsuppositionasglobal
quantificationaleffect,thenwemightspeculatethatBurleyinventedthis
approach;otherwiseOckhamisagoodbet.Inmyopinion,theevidenceis
unclear.Hereishowitgoes.
3.2.1Burley=sEarlyWork:
InBurley'sfirstwork,DeSuppositionibus,heclearlydefinesmodesof
supposition(exceptdeterminate)intermsofthepossibilitiesofascentand
descent,andmobilityisnotanindependentnotionatall.Infact,Burley
hasfourmodesofcommonpersonalsupposition:determinate,merelyconfused,
mobilelydistributed,andimmobilelydistributed.Hisaccountofdeterminate
suppositionisprimarilybyexample:19
37
(32)...Determinatesuppositioniswhenacommontermsupposits
distributivelyforitssupposita,asin`Somemanruns'.
(Hisuseof`distributively'ismisleadinghere,sinceitisdisjointfrom
confusedanddistributivesupposition.)Hisaccountsofthesecondmodeisin
termsofascentanddescent:
(34)Atermsuppositsmerelyconfusedlywhenitsuppositsforseveral
thingsinsuchawaythatitisimpliedbyanyofthemandonecan
descendtononeofthem[either]copulativelyordisjunctively.
`Animal'suppositsthiswayin`Everymanisananimal'.Foritis
impliedby[its]supposita.Foritfollows:`Everymanisthisanimal;
thereforeeverymanisananimal'.Butitdoesnotfollow:`Everyman
isananimal;thereforeeverymanisthisanimal',anditalsodoesnot
follow:`Everymanisananimal;thereforeeverymanisthisanimalor
thatone'.
Bycontrastwiththisaccount,wecanassumethatthepreviouslyintroduced
determinatesuppositioniswhenthepropositioncontainingthetermisimplied
byanyinstance,andonecandescendtoadisjunctionofinstances.
Thetwoformsofconfused-and-distributivesuppositionaremobileand
38
immobile,bothexplainedhere:
(44)Confusedanddistributivesuppositionis...mobilewhena
commontermhassuppositionandthepowerofdistributingandonecan
descendtosomesuppositumofit.[Itis]immobilewhenacommonterm
suppositsforitssuppositaandonecannotdescendtothesesupposita.
Theterm`man'suppositsinthelatterwayin`Everymanbesides
Socratesruns'.Fortheterm`man'isdistributed,andonecannot
descendtoasuppositum.
Thisprovidesroughlythefollowingoperationaldefinition:atermis
distributedmobilelywhenthereisnoascentfromaninstancebutonecan
descendtoaninstance,anditisdistributedimmobilelywhenthereisno
ascentfromaninstanceandonecannotdescendtoaninstance.20(An
additionalconditionisgivenformobiledistribution,thatthetermbe
distributedbyasign.Thisisnotdefined,butitsrationaleisexplained
later(section46);itistoruleoutpossibledescentsthatareunrelatedto
supposition,asintheinference`Somepropositionistrue;thereforethis
propositionistrue',pointingto`Somepropositionistrue'.)
Itiscertainlypossibletoreadtheseexplanationsasdefinitionsofmodesof
suppositionintermsofascentanddescent,meanttobeappliedglobally.
39
Readinthisway,Burleyhadthisviewofsuppositionsapparentlybefore
eitherOckhamorBuridan.Butthisinterpretationisnotconclusive,fortwo
reasons.Oneisthatthesemightnotbedefinitions,butjustsymptomsof
anothermorebasicaccountofsupposition,notarticulated.Secondly,if
thesedefinitionsweretobeconfinedtoatomic(categorical)propositions,
theycouldbeconstruedasprovidinglocal,notglobal,truthconditionsfor
thequantifiers,asintheearlieraccounts.Thetesttodistinguishthese
wouldbetoseewhathappenstosuppositionwhencategoricalpropositionsare
embeddedinothercontexts.Ihavenotfounddiscussionofsuchanexamplein
Burley'searlytract.
3.2.1Burley=sLaterWork:
ThematterisdifferentinBurley=slaterwork,TheLongerTreatiseonthe
PurityoftheArtofLogic.Herehegivesessentiallythesameaccountsof
themodes,buthegivesanexampleinwhichhetestsforthesuppositionofa
terminanembeddedcontextbytestingthedescentsforthewholecontext.
Thisillustratesthatthetestformodeofsuppositionistobeapplied
globally,notlocally.Hereisthequote:21
(91)...asyncategoricwordconveyingamultitude[ofthingsand]
occurringinonecategoricaldoesnothavethepowerofconfusingaterm
40
occurringinanothercategorical.Thusthecopulative`Everymanisan
animalandsomemanishe'isfalseonaccountofitssecondpart.For
theterm`man'occurringinthesecondcategoricalisnotconfusedby
thepreceding[universal]sign.Therefore,itsuppositsdeterminately,
anditisdenoted[bytheproposition]thateverymanisananimaland
SocratesisheoreverymanisananimalandPlatoishe,andsoon.
Thisillustratesdescentunderthesecondterm`man=.Theimportantpointis
thatthedescentisfromthewholecomplexproposition`Everymanisananimal
andsomemanishe',notjustfromthesecondconjunct.Ifdeterminate
suppositionwereamatterofhowatermbehavesinitsowncategorical
proposition,thedescentunderdiscussioncouldnotbetakentobedirectly
relevanttothemodeoftheterm.22
3.3WilliamOckham
Ockham=sworkisasdifficulttoclassifyasisBurley=searlywork.One
thingisclear:Ockhamgivessystematicaccountsofallthemodesof
supposition(includingdeterminate!)entirelyintermsofthepossibilitiesof
ascentanddescent,andhemaybethefirsttodoso.Herearehis
41
accounts:23
Commonpersonalsuppositionisdividedintoconfusedanddeterminate
supposition.
Thereisdeterminatesuppositionwhenitispossibletodescendbysome
disjunctiontosingulars.Thusthisisagoodinference,`Amanruns,
thereforethismanruns,orthat,=andsoonforsingulars....It
isthereforeanestablishedrulethatwhentherecanbedescentto
singularsunderacommontermbyadisjunctivepropositionandthesaid
propositioncanbeinferredfromanyoneofthesingulars,thentheterm
hasdeterminatepersonalsupposition.
Confusedpersonalsupposition...isdivided,sincesomeismerely
confusedsuppositionandsomeisconfusedanddistributivesupposition.
Thereismerelyconfusedsuppositionwhenacommontermsupposits
personallyanditisnotpossibletodescendtosingularsthrougha
disjunctionifnochangehasbeenmadetotheotherextreme,but[itis
42
possibletodescend]throughapropositionwithadisjunctivepredicate
anditispossibletoinferthe[original]propositionfromany
singular.Forexample,inthisproposition,`Everymanisananimal,=
the`animal=hasmerelyconfusedsuppositionbecauseitisnotpossible
todescendunder`animal=toitsreferentsbydisjunction,sincewe
cannotinfer:`Everymanisananimal,thereforeeverymanisthis
animal,oreachmanisthatanimal,=andsoonforthesingulars.But
itiscertainlypossibletodescendtoapropositionwithadisjunctive
predicateofsingulars.Forthisisagoodinference:`Everymanisan
animal,thereforeeverymanisthisanimalorthatorthat,andsoon
forthesingulars=.
Thereisconfusedanddistributivesuppositionwhenitispossiblein
somewaytodescendconjunctively,if[theterm]hasmultiplereferents,
butnoformalinference[totheoriginalcan]bemadefromany[ofthe
conjuncts],asinthisproposition,`Eachmanisananimal.=Its
subjecthasconfusedanddistributivesupposition,forthisfollows:
`Eachmanisananimal,thereforethismanisananimal,andthat,and
soonforthesingulars.=Moreover,thisdoesnotfollowformally:
`Thatmanisananimal,=someoneorotherhavingbeenpointedto,
43
`thereforeeachmanisananimal.=
Whatisnotcompletelycleariswhethertheseaccountsaremeanttobeapplied
locallyorglobally.Onecoulddecreethattheyaretobeappliedonly
locally,totermsincategoricalpropositions;thiswouldyieldaversionof
theearlytheorywithanewaccountofthesemanticsofquantifiers,couched
entirelyintermsofascentanddescent.ButOckhamneversuggestssucha
limitation.Still,Ihavenotfoundclearexamplesthatwouldcommithimto
applyingthetheoryglobally.Ileavethisasalooseend.
3.4JohnBuridan
Buridanbeginswithhisfeetplantedinthepast,characterizingdeterminate
supposition(3.5.1)as24
whenitisnecessaryforthetruthofthesentence...thatitistrue
forsomedeterminatesupposit,
butheimmediatelycashesthisout(3.5.5-6)intermsofrequirementson
ascentanddescent:
Fromanygivensuppositofatermthecommontermcanbeinferredwith
44
theother[terms]unchangedinthegivensentence,
and
Fromacommontermsuppositingthisway,allthesingularscanbe
inferreddisjunctivelyinadisjunctivesentence.
Distributivesuppositionisgivenasimilardefinition,andmerelyconfused
suppositionisdefinedascommonpersonalsuppositionthatisneither
determinatenordistributive.
ItisclearfromBuridan=swritingsthatthenewtheoryisnowfully
developed,inthattheseconditionsarepresentedasconditionsthataretobe
appliedglobally,sothattheresultisaclassificationoftermsintermsof
theirglobalquantificationaleffect.Herearesomeillustrations:
(3.7.7):Hesaysthattheterm`man'in`Noteverymanisrunning'is
notdistributed;thisisbecausethenegation"removes"thedistribution
of`man'.
(3.7.37):Wefindthatin`Amandoesnotrunandahorseiswhite'the
terms`horse'and`white'arenotdistributed,butin`Not:amanis
runningandahorseiswhite'both`horse'and`white'aredistributed.
45
(3.7.44):Hespeaksofembeddingsignsasalteringthesuppositionof
termscontainedinwhattheyembed:"whatnaturallydistributesan
undistributedtermcanremovethedistributionofadistributedterm."
(Theexampleisof`No'removingthedistributionof`man'in`non-man
runs'whencombinedtoyield`Nonon-manruns'.)
(3.8.18):Wefindthat`man'hasdeterminatesuppositioninboth`Not:
nomanruns'andin`Socratesdoesnotseenoman'.
Clearlytheseexamplesillustrateatheoryinwhichatermhasakindof
suppositioninagivensentence,butthatkindcanbealteredwhenthe
sentencebecomesmorecomplex.Thetestineverycaseisintermsof
conditionsofascentanddescentappliedtothewholesentenceinwhichthe
termoccurs,andtheresultisatheoryofglobalquantificationaleffect.
3.5AlbertofSaxony
AlbertwroteataboutthesametimeasBurley,Ockham,andBuridan.His
accountisnotcompletelyclear,butoverallitappearstobeinthelater
46
tradition.
Asnotedabove,thereisnonecessaryconnectionbetweenappealingtoascent
anddescentinthedefinitionofmodesofsuppositionandhavingatheoryof
globalquantificationaleffectinsteadofquantification.Onecoulduse
ascentanddescenttoexplainthemeaningsofquantifiersincanonical
position,andthenholdthattheydonotchangemodewhenembedded.Italmost
looksasifAlbertofSaxonydoesthis.Hebeginswithanaccountofmodes
suppositionintermsofascentanddescent,virtuallyidenticaltoOckham=s:25
(II.4)Determinatesuppositionistheuseofageneraltermforeachof
thethingsitsignifiesbyitsimposition,...,insuchmannerthata
descenttoitssingularscanbeaffectedbyadisjunctiveproposition.
Inthissentence,`Amanruns=,theterm`man=hasdeterminate
supposition,becausetheterm`man=inthissentencestands,
disjunctively,foreverythingwhichitsignifiesbyitsimposition.For
itissufficientforthetruthoftheproposition`Amanruns=that
thisdisjunctivepropositionbetrue:`Thismanruns,orthatman
runs=,andsoonforallsingulars.
47
Merelyconfusedsuppositionistheinterpretationofatermforeach
thingitsignifiesbyitsimposition,...,insuchmannerthata
descenttoitssingularscanbemadebyapropositionofdisjunct
predicate,butnotbyadisjunctiveoraconjunctiveproposition....
Thiskindofsuppositionishadbytheterm`animal=inthesentence
`Everymanisananimal=;forthisisavalidconsequence,`Everyman
isananimal,thereforeeverymaniseitherthisanimalorthatanimal,
etc.=,...
(II.5)Confusedanddistributivesuppositionistheinterpretationofa
spokenorwrittenterm,inconjunctivemanner,foreachthing...
whichitisinstitutedtosignify,...,suchthatadescenttothe
singularsforwhichitstandscanbemadeinconjunctivemanner,by
reasonofthatsupposition.
Later,however,heexplainsuniversalandparticularsignsasfollows:
(III.2)Asignofuniversalityisonewhichindicatesthatthegeneral
term,towhichitisjoined,standsconjunctivelyforeachofitsvalues
...
Asignofparticularityisthatbywhichitisindicatedthatageneral
48
termstandsdisjunctivelyforeachofitsvalues...
Iftheselastpointsaretakenliterally,onewouldbeforcedtotreatthe
subjectof`Noteverymanruns'ashavingdistributivesupposition,sincethe
universalsignisclearlypresent;thiswouldmakeAlbert=sviewacaseof
theearlytraditionasoutlinedabove.ButAlbertexplicitlydeniesthis,
saying
(I.6)Everygeneraltermwhichfollowsimmediatelyonasignof
universality,withoutaprecedingnegation,hasconfusedand
distributivesupposition....AndIsayexpressly,`withouta
precedingnegation=,becauseifitissaid`Noteverymanruns',the
term`man'doesnothaveconfusedanddistributivesupposition,even
thoughitdoesfollowimmediatelyonthesignofuniversality.
ItisthusclearincontextthatAlbert=slinkingoftheuniversalsignwith
confusedanddistributivesuppositionismeanttoapplytonon-embedded
propositionsonly,andonbalancehisaccountturnsouttobesubstantially
thesameasBuridan's.
3.6PaulofVenice:theLogicaParva
49
TheLogicaParvaisaneclecticworkwrittenaboutahalfcenturyafterOckham
andBuridan,andthussubsequenttowhatIamcallingtheAlater@period..
Itseemstodrawonawidevarietyofsources,anditissomewhathaphazardin
itspresentation.Thereisasectiononsupposition,andatraditional
coverageofthemodes,whicharedefinedintermsofdescentandascent,as
follows:26
Determinatesuppositionistheacceptanceofacommontermsuppositing
personallybeneathwhichdescendingoccurstoallofitssingulars
disjunctively,e.g.`manrunsandtheseareallmen;therefore,thisman
runsorthismanrunsandthusofsingulars'.
Commonmobilepersonalsuppositionwhichismerelyconfusedisthe
acceptanceofacommontermstandingpersonallybeneathwhichone
descendstoallofitssuppositaindisjuncts,asin`everymanis[an]
animal,andtheseareall[the]animals;therefore,everymanisthis
animalorthatanimalandthusofsingulars'.
Mobiledistributivesuppositionistheacceptanceofacommonterm
standingpersonallybeneathwhichonedescendstoallofitsreferents
conjunctively;e.g.`everymanrunsandtheseareallmen';therefore
50
`thismanrunsandthiswomanrunsandthusofsingulars'.
Theseappealstoascentanddescentdonotentailthatthisisatheoryof
globalquantificationaleffect,forifthesedefinitionsweremeanttoapply
totermsonlyincanonicalpositionincategoricalpropositions,theresulting
theorycouldstillbeatheoryofquantifiers.Thekeyliesinhowthetheory
istobeappliedtotermsinpropositionsthatareembeddedinsuchawaythat
theirsuppositionwouldbealteredundertheBurley-Buridanapproach:does
suchembeddingalterthemodeofsupposition,oronlytheterm'smobility?
Paulseemstohaveitbothways,andthetextsupportsbothconclusions.
3.5.1VestigesoftheEarlyTheory:
First,thereisonecentralthemeaccordingtowhichembeddedtermsretain
theiroriginalmodeofsupposition,butarerenderedimmobile.Theseexamples
aregivenalongwithPaul's(paradoxical)characterizationsofimmobile
supposition.Hisdefinitionofimmobiledistributivesuppositionisthis
(II.4):
Immobiledistributivepersonalsuppositionistheacceptanceofaterm
withcommonpersonalsuppositionbeneathwhichdescendingdoesnot
happen,butifitdidhappen,onewoulddescendconjunctively,as
`necessarilyeverymanis[an]animal';here`man'suppositsinthis
51
way,becauseitdoesnotfollow[even]withaduemean:`therefore
necessarilythismanis[an]animal,andsoonforsingulars'...
Itisdifficulttomakesenseoftheideathatalthoughnodescenthappens,
thereisawayforittohappenifitshouldhappen.Hereisonespeculation
aboutwhatthismeans.27InallthecasesPaulgives,thetermsinquestion
areincategoricalsthatareembeddedinlargercontexts.Thetermshave
(mobile)distributivesuppositioninthecategoricalsconsideredinisolation,
sincedescentispossiblethere;e.g.thecategoricalembeddedin`necessarily
everymanisananimal'is`everymanisananimal',andfromthisproposition
onemaydescendunder`man'totheconjunction`thismanisananimalandthat
manisananimal,andsoon'.Apparently,whenembeddedunder`necessarily'
thetermretainsitsdistributivesupposition,butlosesitsmobilitybecause
descentisnolongerpossible.Thisisexactlywhatonewouldexpectif
distributionwereakindofquantification,whichretainsitsintegrityunder
embedding.Theotherexamples(stillinII.4)thataregivenimmediately
afterthisdefinitionarealsoarguablyofthiskind;theyclassifyas
immobilelydistributivetheindicatedtermsin:28
Ifeveryanimalruns,everyhumanruns.
EverymanexceptSocratesruns.
Noanimalexceptmanisrational.
52
[For]everymantobeananimalisknownbyme.
3.5.2VestigesoftheLaterTheory:
Thisthemeiscontradictedinothersectionsofthetext.Thesectionon
suppositionisfollowedimmediatelybyoneonconfoundingterms,which
containsthisdiscussion(II.5):
...inthisproposition`noteverymanis[an]animal',`man'doesnot
suppositdistributively,butdeterminately,accordingtoonerule
pertinenttothismatter,viz.,whatevermobilizestheimmobile
immobilizesthemobile.Thatis:Ifanysignhavingthepowerto
distributesometermfindsagainthesametermundistributed,thesign
makesthetermstanddistributively;andifthesignfindsagainthe
sametermdistributed,thesignmakesthesametermstandwithout
distribution,i.e.,itmakesitstanddeterminatelyormerelyconfused.
The`thatis'clauseiscrucial;contrarytothedistinctionsofthepreceding
sectiononsupposition,itidentifiesdistributionwithmobiledistribution.
Theresultisthattheterm`man'in`noteverymanisananimal'isnotjust
renderedimmobilebythe`not',ithasitsdistributivesuppositionturned
intodeterminate.Thisisclearlypartofthelaterheritageinwhichthe
distributivemodeofsuppositionisamatterofglobalquantificational
53
import.Thissamepatternisfoundinalatersectiononrulesofinference
(III.3).Here,wearegiventheexampleofabadinference:`Notnoanimal
runs,thereforenotnomanruns'andwearetoldthatthisisaninferencein
whichthetermisnotdistributed.Apparently,placingtheadditional`not'
infrontdoesnotjustimmobilizethedistributionof`animal'in`noanimal
runs';itremovesitentirely.
IconcludefromthisthattheLogicaParvaisapiecingtogetherof
ingredientsofabroadlydevelopedtraditionwithoutthecarefulthoughtthat
isnecessarytoseewhetherandhowtheyfittogether.Itcontainselements
ofbothoftheearliertraditionsthatIhavediscussed.
4WhatisSuppositionTheoryFor?
Onedebateinthecurrentliteraturetakesthisform:Therearegrave
difficultieswiththeideathatsuppositiontheorywasintendedtobeeithera
theoryofthetruthconditionsforquantifiers,oratheoryofinference,ora
theoryofmeaning,oratheoryofunderstanding.Butthenwhatcouldits
purposebe?Ihavesuggestedthatthecontentofthetheorychangedsomewhere
inthemiddleofitsdevelopment,fromsomethinglikeatheoryofquantifiers
toatheoryofglobalquantificationaleffect.Butthisdoesnotanswerthe
54
long-standingquestionregardingthepurposeofthetheory.Whatdidits
authorsthinkitaccomplished?Herearesomebriefremarksaboutthis
(different)topic,informedbythehistoricalviewputforthabove.
Thisquestionhasamodernparallel.Supposeahistorianoftwentiethcentury
philosophyweretonoticeourpreoccupationwithopaquecontexts,andwhatis
saidaboutthem.(S)hemightnaturallywonder:Whatisthepurposeofthe
theoryofopacity/transparency?Itisneitheratheoryofthetruth
conditionsforquantifiers,noratheoryofinference,noratheoryof
meaning,noratheoryofunderstanding.Butthenwhatcoulditspurposebe?
Thereisnosinglepurposebehindopacitytheory.Itsearlierdevelopers,
suchasFregeandCarnap,hadtheirpurposes,Quinehashis,andothershave
theirs.Andthesameistrueofsuppositiontheory.
Ininquiringaboutsuppositiontheory,peopleusuallystartinthemiddle,by
focusingonWilliamOckham.Supposewemakethesimilarmovewithopacity
theory,correlatingWilliamofOckhamwithWillardvanOrman.Wejumpinto
themiddleofcurrentconcernswithvanOrman'scriteriafor
opacity/transparency:
55
Atermtoccurstransparentlyin...t...iffwecaninfer...s...onthe
assumptionthats=t,andwecanalsoinferintheotherdirectiononthe
sameassumption.
Atermtoccurstransparentlyin...t...iffwecaninfer�x(...x...).
Atermtoccursopaquelyin...t...iffitdoesnotoccurtransparently
in...t...
Isthisatheoryofquantification?No,thoughit'spartlyatheoryabout
quantification.Isitaningredientofasemantictheoryatall?Itseems
nottobe,sincewhenpeoplegivesemanticrulesforlanguagestheyrarelyuse
thenotionofopacityortransparencyingivingtheserules.29Instead,itis
usedintwoways.Oneisinclassifyingtheresultsofoursemantic
treatment;e.g.wegiveasemanticsthatdoes/doesnotresultincertain
contextsbeingopaque.Theotherwayisthatweclassifyconstructionsfor
whichwedonothaveasemanticaccount;itisthoughttobeimportantinhow
toapproachthephenomenatobeabletosaywhetherweareattemptingto
produceanaccountofanopaquecontextoranon-opaqueone.
Wecancomparethiswithmedievalaccountsofsupposition.First,changethe
56
terminologyslightly;insteadof`inference',speakof`descent'and`ascent'.
Thenthefirstcharacterizationofreferentialtransparencyis:
Atermtoccurstransparentlyin...t...iffwecandescendto...s...
ontheassumptionthats=t,andwecanalsoascendfrom...s...backto
...t...onthatsameassumption.
Clearly,themodernnotionofnon-opacityandthemedievalnotionofpersonal
supposition(inthelatertradition)haveakindofparallelstructurein
theirexposition.Thereareotherparallelsaswell.Eachtheorytestsfor
thestatusofaterminasentence(oneforasingularterm,theotherfora
generalterm),andeachtestsforthestatusofatermthatoccursanywherein
thesentence,nomatterhowdeeplyembeddedinthesentenceitmaybe.More
strikingly,boththeoriesconsistentirelyofdefinitions!30Sowhatarethe
definitionsfor?
Opacitytheorydidn'tbeginthisway,itbeganwithadifferentperson(Frege)
withdifferentpurposes.ItbeganwithanattemptinFrege=sworkonsense
andreferencetodevelopthetheoryofreference.Fregeneededtodistinguish
sensefromreferenceinordertoindicatehowopaquecontextsmaybehandled
soasnottothreatenhistheoryofreference,andthisinturnwasinorder
tohavealogicthatwouldsecurethelogicalfoundationsofmathematics.His
57
discussionofindirect(=opaque31)contextsallowedhimtomaintainhis
thesisofintersubstitutivity;i.e.thegeneralvalidityofakindofmodified
lawofidentity.Asasidebenefithegaveafertileproposalforthe
semanticsofpropositionalattitudecontexts,thoughthatwasfarfromhis
mainpurpose.
Quine'spurposesweredifferent.Hewantedtoshowthatcertainconstructions
aremeaningless:theopaquecontextsthemselves,inhismoststringentmoods,
andquantifyingintotheminallofhismoods.Thiswaspartofhiscampaign
toavoidintensions,entitieswhoseidentityconditionshefoundunclear.And
thisinturnwasmotivatedbyhisnominalism.Quinedefendedhisnominalism
by"cleaningup"talkofintensions;heabjuredFrege=ssortofreferenceto
them,andinsteadclassifiedcontextsasAopaque@orAtransparent@using
operationallydefinedtestsfortheclassification.JustasOckhamdefended
hisnominalismbyreplacingobscureaccountsofthemeaningsofquantifiersby
cleaned-uptestsforthemodesofsuppositionintermsofascentand
descent.32
WhataboutpeopleotherthanQuine?Theyarenowinterestedinopacitysimply
becausetheyseeitasanimportantphenomenonthataffectsthesemanticsof
58
certainconstructions,invirtueofwhichthesecontextsseemtorequire
"specialhandling".
Boththeorieshaveparallelhistories,consistingroughlyofthreestages.In
thefirststage,theearlierdevelopers(FregeandCarnap/WilliamofSherwood
et.al.)wererealistmindedlogiciansinterestedinafertiledomainof
study.Theydevelopedtheoriesthatcutatthejoints,theoriesthatcouldbe
developedlateronintorecursiveaccountsoftruthandmeaning.Inthe
secondstage,thenominalists(Quine/Ockham)simplifiedandclarifiedthe
study,takingaglobalperspective,therebydiscardingintheprocessmuch
thatwasofinterestintheearlierstudy,byusingnotionsthatare
consequentonarecursivesemantics,butthatdonotthemselvesleadnaturally
tosuchanaccount.Finally,laterwritersinbothtraditionsarewillingto
drawonnotionsfrombothenterprises.Atalmostanypointintheongoing
work,everyoneiswritingwithinanongoingtraditionthatismostlytakenfor
granted;fewwriterspausetoaskbasicquestionsaboutwhytheyarefocusing
ontheproblemsathand.Thatisleftforfuturehistorians,whomaythusbe
leftwithaquestionwithnoclearanswer.
60
Appendix:MakingSenseofSuppositionwithoutDescent
Iarguedabovethattheearlyaccountsexplainedsuppositionwithoutappealto
ascentanddescent.Thisseemsclear.Buttheaccountsthemselvesarenot
onlynotclear,theycanseempositivelybewildering,atleastiftaken
literally.Ithinkthattheseaccountsareactuallyprimitiveversionsof
goodaccountsofthesemanticsofquantification.Inthisappendix,Iexplain
howonemightinterpretthetextssoastogetthisresult.Themodern
paraphrasesIproducearenotintendedtostatewhattheoriginalauthorshad
tosay,fortheseauthorssaidnothinginmodernterms.Theyarerather
explanationsinmoderngarbofwhattheoriginalpassagesmeant.
TheexplanationsIgivecannotbejustifiedfromtheoriginalpassagesalone;
theyaregiveninthelightoftheconsequencestheauthorsthoughttheir
explanationshad,consequencesthatarefoundinthesurroundingwritings.
Theyarenottheonlypossibleinterpretations.Forexample,itisclearto
anyonereadingtheoriginalexplanationsthatitispossibletointerpret
thesewriterssoastohavethemassertingunreconcilablenonsenseorsheer
falsehoods.Idonotdisputethatsuchinterpretationsarepossible;Ionly
wishtomakeclearthattherearedifferent,coherentoptions.
61
InA.1,ItrytoclarifyandmakecoherenttheaccountofWilliamofSherwood.
InA.2,IbrieflyindicatehowthisrelatestotheaccountsofPeterof
Spain,andLambertofAuxerre.Then,inA.3,Iexplainhowonecanseethe
nineteenthcenturydoctrineofdistributionasanexampleofthissortof
theory.
A.1WilliamofSherwood'sAccount
DeterminateSupposition:William('5.2)33givesthefollowingaccountof
determinatesupposition:
Personalsuppositionisdeterminatewhenthelocutioncanbeexpounded
bymeansofsomesinglething.Whichisthecasewhentheword
suppositsforsomesinglething.Thereforein`amanisrunning'itcan
betrueforanyonerunning.
Headds:
Thesentence`Amanisrunning'meansthatthepredicateisinsomeone
individual,notinmany,eventhoughthepredicateisinmanyCfora
sentencesometimespermitsthisbutitdoesnotsignifyit.
Iassumethatthebasicaccountisinthefirstsentence;suppositionis
determinatewhenthelocutioncanbeexpoundedbymeansofsomesingle
62
thing.34Buthowarewetoexpoundit?Toexpoundmeanstoprovidean
analysis,butwhatanalysis?Theanswerliesattheendofthefirstquote:
theexpoundingshouldsaysomethingabouttheoriginalpropositionbeingtrue
forthe(single)thing.IsuggestthatWilliam'sbasicaccountisthis:
WILLIAM'SACCOUNTOFDETERMINATESUPPOSITION:
TermAhasdeterminatesuppositionin`...A...'when`...A...'can
beexpoundedbymeansofitsbeingtrueforsomesinglething.
Thisisacompleteandaccuratecharacterizationofdeterminatesupposition.
Itstandsinneedofexplanation,butnotcorrection.Thatis,itisnot
clearfromthewordingalone,asitstands,whatitmeans,butonceitis
understood,itcanbeseenthatitisexactlyright.Sothediscussionbelow
isnotanefforttoreplaceWilliam'sdefinitionbyabetterone,itisan
attempttoclarifythisone.
Therearethreeingredientstoclarify:"toexpound,""bymeansofsomesingle
thing,"and"tobetruefor."Itaketheseinturn.
Toexpoundapropositionistoanalyzeitbyprovidingadifferent,
necessarilyequivalentproposition.Soweneedtofindanecessarily
equivalentpropositionwhichmakessomekindofappealto"somesinglething".
63
Itisclearfrombothcommentsandapplicationsthatthisthingmustbeone
ofthesuppositaoftheterm.Itisalsoclearfrombothcommentsand
applicationsthatselectionofanyparticularthingtoplaythisrolewouldbe
incorrect.(Recallthatin`Amanisrunning'itcanbetrueforanyone
running.)Sowearelookingforananalysisofthisform:
TermAhasdeterminatesuppositionin`...A...'when:Necessarily,
...A...ifandonlyifforsomexwhichisA:`...A...'istrue
forx.
Butwhatdoesitmeanforafull-fledgedproposition`...A...'tobetruefor
something?Forexample,whatdoesitmeanfor`Someanimalisrunning'tobe
trueforagiventhing?Whatismeant,ofcourse,isthatthepropositionis
trueforathingwithrespecttotheterm`A'intheproposition,and,in
particular,thatthepropositionistruewhenthesuppositaof`A'inthat
propositionarelimitedtothatthing:
Aproposition`...A...'istrueforxwithrespectto`A'ifandonlyif
thepropositionistruewhenyou"limit"thesuppositaof`A'tox
itself.
Soweneedtoclarifywhatitistolimitthesuppositionof`A'tox(inthe
propositionunderdiscussion).Therearetwowaystodothis,withdifferent
virtues.
64
WAY#1:Wecanmostsimply"limitthesuppositaof`A'tox"by
consideringtheoriginalpropositionwiththerelevantoccurrenceoftheterm
`A'replacedby`Athatisx'.Forexample,toaskwhether`Everyanimalis
spotted'istrueforBrownie(withrespectto`animal'),youconsiderthe
revisedproposition`EveryanimalthatisBrownieisspotted'.Tosaythat
`Everymanisrunning'istrueforSocrates(withrespectto`man')istosay
that`EverymanthatisSocratesisrunning'istrue.Andsoon.Usingthis
technique,theexplanationfromabovebecomes:
Aterm`A'hasdeterminatesuppositionin`...A...'when:Necessarily,
...A...ifandonlyifforsomexwhichisA:...Athatisx...
Theresultsarewhatweexpectofdeterminatesupposition.Forexample,the
term`dog'hasdeterminatesuppositionin`Somedogisspotted'because
Necessarily:
Somedogisspottediffthereissomedogxsuchthatsomedogthatisx
isspotted.
Theterm`dog'doesnothavedeterminatesuppositionin`Everydogisspotted'
becauseitisfalsethat
Necessarily:
Everydogisspottediffthereissomedogxsuchthateverydogthatis
xisspotted.
65
Itiseasytocheckthatunderthisclarification,William'saccountgivesthe
intendedresultsforallofthestandardformpropositions.Italsoprovides
anaccountofthesemanticsofquantification,inthesensethatwhenaterm
hasdeterminatesupposition,itsoccurrenceincanonicalpositionisstatedto
beequivalenttosomethingthatwenowwouldrecognizeasastatementofthe
truthconditionsforanexistentiallyquantifiedstatement.
TheproblemwithWAY#1isthatitproducesartificiallycomplexpropositions,
inthefaceoftheobviousfactthattheycanbesimplified.Thissuggests
the(equivalent)WAY#2.
WAY#2:ThisisjustlikeWAY#1exceptthatyousimplify`Athatisx'
to`x'allbyitself,whileremovinganyquantifyingsigndirectlygoverning
`A'(andalsoaddinganegationifthatsignisitselfnegative).Thus,
insteadofconsidering:
Somedogthatisxisspotted
oneconsiders:
xisspotted,
andinsteadofconsidering:
Nodogthatisxisspotted
oneconsiders:
66
xisnotspotted.
Theexplanationofdeterminatesuppositiononthiswaybecomes:
AtermAhasdeterminatesuppositionin`...A...'when:Necessarily,
...A...ifandonlyifforsomexwhichisA:[...x...]*
wherethenotation`[...x...]*'indicatesthattherelevantadjustmentshave
beenmadetothepropositioninquestion.Wenowgettheexpectedresults:
Theterm`dog'hasdeterminatesuppositionin`Somedogisspotted'because
Necessarily:Somedogisspottediffthereissomedogxsuchthatxis
spotted.
Theterm`dog'doesnothavedeterminatesuppositionin`Everydogisspotted'
becauseitisfalsethat
Necessarily:Everydogisspottediffthereissomedogxsuchthatxis
spotted.
Itiseasytocheckthatunderthissecondclarification,William'saccount
alsogivestheintendedresultsforallofthestandardformpropositions.
Thisexplanationrestsonanassumptionthatthescopeforanalysishasbeen
determined.Butsupposethatatermoccursinapropositionthatisitself
partofalargerproposition;whichdowepickforthe`...A...'inthe
explanation?Iarguedinsection2thatWilliam'sapproachistopickthe
67
smallerpropositionforthispurpose,sothatthe"testingscope"fordeciding
whetheratermhasdeterminatesuppositionisthecategoricalpropositionin
whichitoccurs,notanylargerpropositioncontainingthecategorical
proposition.Thisiswhatmakesthetheoryintoanaccountofquantification,
andnotanaccountofglobalquantificationaleffect.Theanalysesdiscussed
abovecouldbeincorporatedintoeithersortoftheory.35
DistributiveSupposition:William('5.2)definesconfusedanddistributive
suppositionasfollows:
Personalsuppositionisconfused...whenthewordsuppositsformany,
anddistributivewhenitsuppositsformanyinsuchawayastosupposit
forany.
Toassessthisweneedtoknowfirstwhatitisforatermto"suppositfor
many".Ithinkthatthisisaveryweakclaim;itonlydeniesthattheterm
hasdeterminatesupposition,i.e.itonlydeniesthatitsuppositsforone.
Thatis,itsaysthatthepropositioninquestioncannotbeexpoundedin
termsofanythinginvolving"somesinglething."Itisclearthatnothing
strongerisintendedthanthis,or,ifsomethingstrongerisintended,itis
soonretracted.Forexample,Williamsayssoonafterthisdefinition(in
'5.12)thatawordhasconfusedsuppositionwheneveritsuppositseitherfor
68
manythingsorforonethingtakenrepeatedly.(Heisworriedaboutthe
second`man'in`Everymanseesaman'wheneveryoneseesthesamemanCso
thatitisfalsethatmanymenareseen.)Sothe`many'ismerelyawayof
denyingthatwehaveacaseof`one',thatis,ofdeterminatesupposition.
Thisreducesthecharacterizationofdistributivesuppositionto:
WILLIAM'SACCOUNTOFDISTRIBUTIVESUPPOSITION:
Atermhasdistributivesuppositionwhenitdoesnothavedeterminate
suppositionanditsuppositsforany.
Itisclearincontextthat`suppositsforany'meansthatthetermsupposits
foranyofitssupposita;Iwilltakethislimitationforgranted.Thetrick
istoseehowtogetthistomeananythingotherthanatautology.Afterall,
howcouldatermnot"suppositforany"ofitssupposita?Theanswermustbe
thatforatermtosuppositforsomethinginapropositionrequiresmorethan
justthatthethinginquestionbeamongtheterm'ssupposita.Isuggestthat
aterm"suppositsforanyofitssuppositainaproposition"justincasethat
proposition'sbeingtrueentailsthatit(thatveryproposition)istruefor
anyofthesuppositaoftheterm(withrespecttotheterminquestion),in
thesenseof`truefor'discussedabove.Thus,anecessaryandsufficient
conditionfor:
`A'suppositsforanyofitssuppositain`...A...'
69
isthis:
`...A...'entailsthat`...A...'istrueforanyofA'ssupposita(with
respectto`A').
Thiscanthenbefurtherspelledoutasfollows:
Necessarily,if...A...,thenforanyxthatisA:`...A...'istruefor
x(withrespectto`A'),
thatis,appealingtoWAY#2above:
Necessarily,if...A...,thenforanyxthatisA:[...x...]*
Forexample,theterm`dog'hasdistributivesuppositionin`everydogis
spotted'becauseitdoesnothavedeterminatesuppositionthere,and:
Necessarily:ifeverydogisspotted,then,foranyxthatisadog:x
isspotted.
Again,onecancheckthatthisaccountgivestheintendedresultsfortermsin
standardformcategoricalpropositions.(Again,thisisanexplanationofhow
tounderstandWilliam'saccount,notaproposalforhowtoreplacehisaccount
withsomethingclearer.Hisaccountwasalreadyfullystatedabove,andI
havenotsuggestedrevisingit.)
OnemightwonderwhyIhaveformulatedtheconditionfordistributive
suppositionintermsofaconditionalinsteadofabiconditional.HereIam
70
guidedbytheintendedapplications;inorderforthepredicateof`SomeSis
notP'tohavedistributivesupposition(whichisrequiredbyWilliam'srule
at'13.1),oneneedsaconditional,notabiconditional36.
MerelyConfusedSupposition:Thedefinitionofmerelyconfusedsuppositionis
thehardesttogetclearon.Sherwood'sexplanationisvirtuallyno
explanationatall('5.2):
[Personalsupposition]ismerelyconfused[whenthewordsuppositsas
does]theword`animal'[in`everymanisananimal'].
Thereareanumberofadditionalexamples,butlittleinthewayof
explanation.Soeitherthereissomespecificnotioninmindthatisnot
stated,ormerelyconfusedsuppositionisnothingotherthanpersonalcommon
suppositionthatisneitherdeterminatenordistributive.
A.2PeterofSpainandLambertofAuxerre
PeterandLambertareeasytocoversincetheirdiscussionsofthemodesof
personalsuppositionaresoterse.
DeterminateSupposition:PeterofSpainsaysthisregardingdeterminate
supposition(VI.8,Dinneen1990,71):
71
Determinatesuppositionlabelswhatacommontermhaswhentaken
indefinitelyorwithaparticularmarker,asin`manruns'or`someman
runs'.Eachoftheseiscalleddeterminate,sincethoughineach,the
term`man'standsforeverymanrunningornot,theyaretrueonlyif
onemanisrunning.Tostandforisonething,tomakealocutiontrue
forsomethinganother.Intheexamplesabove,...theterm`man'stands
foreveryman,runningornot,butitmakestheutterancetrueforone
manrunning.
Thisformulationisdisconcertinglyloose,andthereislittleprofitin
exploringallofthereadingsthatclearlydonotcoherewiththeintended
applications.Itispossibletoreadtheremarkssothattheyareconsistent
withWilliam'saccountasexplainedabove,andthisseemstocoherealsowith
Peter'sapplications.SoIpresumethatthisiswhatisintended.
Lambertsaysthis(3g(iv),Kretzmann&Stump,111):
Determinatesuppositioniswhatacommontermhaswhenitcanbetaken
equallywellforoneorformorethanone,aswhenonesays`Amanis
running'.Inthatproposition`man'hasdeterminatesuppositionbecause
itistrueifonemanisrunningorifmorethanonearerunning.But
itiscalleddeterminatebecauseforthetruthofapropositioninwhich
72
acommontermthathasthatsortofsuppositionisused,itisenough
thatthecommontermisinterpretednecessarilyforsomesuppositum,and
itisnotrequiredthatitbeinterpretednecessarilyformorethanone,
althoughinsuppositionofthissortitcanbeinterpretedformorethan
one.
Itakeitthattheheartofthisaccountis:
LAMBERT'SACCOUNTOFDETERMINATESUPPOSITION:
TermAhasdeterminatesuppositionin`...A...'whenitis
sufficientforthetruthof`...A...'that`A'beinterpretedin
`...A...'foroneofitssupposita.
WhenLamberttalksaboutinterpretingaterminapropositionforone,itmay
bethatthisisthesameaswhenWilliamtalksaboutthepropositionbeing
trueforasinglething(withrespecttothatterm).Onthisinterpretation
Lambert'sremarksyieldaslightlydifferentaccountthanWilliam's;Lambert's
accountisaconditionalinsteadofabiconditional:
TermAhasdeterminatesuppositionin`...A...'whenitis
sufficientforthetruthof`...A...'that`...A...'betruefor
oneofA'ssuppositawithrespectto`A'.
Ifwelookatthetermsofstandardformcategoricalpropositions,thisyields
thestandardresultsexceptthatitmakespredicatesofuniversalaffirmatives
73
havedeterminatesupposition;itdoesthissince`EverySisP'doesfollow
from`ForsomexthatisP,everySisaPthatisx'.Thiscannotbewhat
Lambertintended,sincehesaysthatthesepredicateshaveconfused
supposition.PerhapsLambertwastakingforgrantedthatindeterminate
suppositionitisalsonecessaryforthetruthof`...A...'that`...A...'be
trueforoneofA'ssuppositawithrespectto`A'.Ifthisisaddedtothe
aboveaccount,itbecomesequivalenttoWilliam's.
DistributiveSupposition:PeterofSpainsays(XII.1,Dinneen1990,185):
Distributionisthemultiplicationofacommontermeffectedbya
universalsign.
Hedoesn'tsaymuchmore.Whateverhehasinmind,hisaccountisnotthe
sameasWilliam's,forheinsiststhatauniversalsignisneededfor
distribution,andhethinksthatnegationisnotauniversalsign.(Thiswas
discussedin'2.4.)Sothepredicateofaparticularnegativecannothave
distributivesuppositionforPeter;instead,hesaysthatsuchpredicateshave
simplesupposition.37
Ignoringpredicates,thebestwaytoreadPeterisprobablytoassumethathe
meansroughlythesameasWilliamexceptthatheholdstheadditionalview
74
thatdistributionoccursonlyinconnectionwithadistributingsign,38
coupledwiththeviewthat`every'and`no'aredistributingsignsbut`not'
isnot.Hethusagreeswiththeothersforthemostpart,thoughhediffers
insomedetails.
Lambert'saccountismuchclosertoSherwood's.Hesays:
[Distributive]...suppositioniswhatacommontermhaswhenitis
interpretedforallofitssuppositanecessarily...39
AboveIsuggestedthatLambert's`thetermisinterpretedfor'isthesameas
William's`thepropositionistruefor'.Ifwemakethissameequationhere,
Lambert'saccountisthesameasWilliam's.
MerelyConfusedSupposition:PeterofSpaindoesnotdefine`merely
confused'.40Hisviewseemstobethatwhereothersseeaneedformerely
confusedsupposition(mostprominently,inthepredicatesofuniversal
affirmatives)heseesonlysimplesupposition.SoprobablyPeterparts
companywiththeothersonthiscategory.
Lambertdefinesmerelyconfusedsuppositionasfollows:
[Merelyconfused]...suppositioniswhatacommontermhaswhenitis
75
interpretednecessarilyformorethanonesuppositumcontainedunderit
butnotforall...41
Howthisworksdependsonhowitisinterpreted.Suppose,forexample,that
weinterpretitasweaklyaspossible.ThenweconstrueLambert's`morethan
one'aswedidWilliam's`many',thatis,merelyasawaytodenythatthe
term"canbeinterpretedforone."Thispartoftheclausethensimplydenies
thatthetermhasdeterminatesupposition.Thenweinterpret`butnotfor
all'asmerelydenyingthatthetermis"interpretedforallofits
supposita,"thatis,asmerelydenyingthatthetermisuseddistributively.
Theoverallresultisthatatermisdefinedtohavemerelyconfused
suppositionwhenithaspersonalsuppositionthatisneitherdeterminatenor
distributive.Thisisasatisfactoryaccountthatcohereswitheverybody
else's.42Strongerconstrualsarepossible,butIdonotseeanynaturalway
toproduceonethatcohereswiththeapplicationofthetheorytothesubjects
andpredicatesofsimplecategoricalpropositions.
76
A.3DistributionintheNineteenthCentury
Thesortofclarificationandexplanationthatwasneededabovefor
suppositionisalsoneededforthenineteenthcenturynotionofdistribution.
Itakeasasamplethedefinitionof`distribution'offeredbyRichard
WhatelyinwhatwasapparentlythemostwidelyusedtextinGreatBritainand
Americathroughoutthatcentury.Whately(1826,40)givesthisdefinition:
...atermissaidtobe"distributed"whenitistakenuniversally,so
astostandforeverythingitiscapableofbeingappliedto...
Inanimportantclarification,Whatelydiscussesauniversalaffirmative
propositioninwhichthesubjectandpredicatetermsaredistinctbut
coextensive.Henotesthatthisfactshouldnotmakethepredicateterm
distributed,eventhoughitdoesstandforeverythingitiscapableofbeing
appliedto,becausethisfactisaccidentaltothelogicalformofthe
proposition:
...yetthisisnotimpliedbytheformoftheexpression;...
Puttingthesetwoideastogether,Whately'saccountseemstobe:
WHATELY'SACCOUNTOFDISTRIBUTEDTERM:
Atermisdistributediffitisimpliedbytheformoftheexpression
thatitstandsforeverythingitiscapableofbeingappliedto.
Clearlythe"standingfor"inquestionisinvirtueofhowthetermisusedin
77
"theexpression,"soitseemsfairtoexpandthisto:
Atermisdistributedinapropositioniffitisimpliedbytheformof
thatpropositionthatinthatpropositionthetermstandsforeverything
itiscapableofbeingappliedto.
Aterm`F'ispresumablycapableofapplyingtoalltheF's,andnothingelse.
Soitappearsthatwecanofferthefollowingelucidation:
Aterm`F'isdistributedin`...F...'iff`...F...'formallyentails
thatin`...F...'theterm`F'standsforeveryF.
ThisisalmostaperfectparalleltoSherwood'sdefinitionofdistributive
supposition,which,withaslightemendation43is:
Aterm`F'isdistributedin`...F...'iff`...F...'formallyentails
thatin`...F...'theterm`F'standsforanyofitssupposita.
DuplicatingthediscussionofA.1makesWhately'saccountofdistributedterm
essentiallythesameasSherwood'saccountofdistributivesupposition.The
explanationiscoherent;itresultsinthetraditionalclassificationofterms
intothosethataredistributedandthosethatarenot.
Muchhasbeenmadeoftheparallelaccountofnon-distribution.Afuller
quotefromWhately(p.40)yieldsthis:
...atermissaidtobe"distributed,"whenitistakenuniversally,so
78
astostandforeverythingitiscapableofbeingappliedto;and
consequently"undistributed,"whenitstandsforaportiononlyofthe
thingssignifiedbyit...
Theaccountof`undistributed'makesitappearthatweneedanindependent
accountofnon-distributionintermsofaterm'sstandingforaportionofa
class,anditiseasytoexpoundthisideasoastorenderitincoherent,as
PeterGeachhaspointedoutinseveralplaces.44Onecancertainlyblame
Whately(andothers;hisexpositionistypical)offaultyexpositionhere.
Butthereisanotheroption,whichistoseetheaccountof`undistributed'as
merelyanunfortunatewaytotrytoexpressthenegationoftheaccountof
`distributed'.Itreallyisapoorchoiceofterminology,butitisclear
whatisbeinggotat.
Isuggest,then,thatonecanmakegoodsenseofthenineteenthcentury
doctrineofdistributionalongthesamelinesthatonecanmakesenseofthe
thirteenthcenturyaccountsofdistributivesupposition.45
References
Barney,Steve,Lewis,Wendy,Normore,Calvin,andParsons,Terence(trans.)
AOnthePropertiesofDiscourse,@thisvolume.Translationofthe
79
firsttwo-thirdsofATractatusdeProprietatibusSermonum,@indeRijk
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Buridan,John.14thcentury.TractatusdeSuppositionibus.InReina,Maria
Elena,"GiovanniBuridano:TractatusdeSuppositionibus,"Rivista
criticadistoriadellafilosofia(1957),175-208.TranslatedinKing
1985.
Buridan,John.14thcentury.TractatusdeConsequentiis.InHubien,Hubert,
IohannisBuridanitractatusdeconsequentiis:Éditioncritique,Volume
XVIofPhilosophesmédiévaux,UniversitédeLouvain,1976.Translated
inKing1985.
Burley,Walter.14thcentury.ADeSuppositionibus,@inBrown,Stephen,
AWalterBurleigh=sTreatiseDeSuppositionibusandItsInfluenceon
WilliamofOckham,@FranciscanStudies32,1972,15-64.Translatedin
thisvolumeinSpade1997.
Burley,Walter.14thcentury.WalterBurleigh:Depuritateartislogicae
tractatuslongior,withaRevisedEditionoftheTractatusbrevior,
PhilotheusBoehner(ed),TheFranciscanInstitute,StBonaventure,NY,
80
1955.TranslatedinSpade[forthcoming].
DeRijk,L.M.1967LogicaModernorum,VolumeIIPart2.KoninklijkeVan
Gorcum&CompanyN.V.;Assen,TheNetherlands.
Dinneen,FrancisP.1990.PeterofSpain:LanguageinDispute.John
BenjaminsPublishingCompany,Amsterdam/Philadelphia.
Geach,Peter.1956"TheDoctrineofDistribution,"Mind67-74.
Geach,Peter.1962.ReferenceandGenerality.CornellUniversityPress,
Ithaca,NewYork.
Geach,Peter.1972."HistoryofaFallacy,"inLogicMatters,Oxford,
Blackwell,1-13.
Geach,Peter.1976."DistributionandSuppositio,"Mind85,432-35.
Karger,Elizabeth.1993."ATheoryofImmediateInferencesContainedin
Buridan=sLogic,"inKlausJacobi(ed.)Argumentationstheorie:
81
ScholasticForschungenzudenlogischenunesemantischenRegeln
korrektenFolgerns.E.J.Brill,Leiden-NewYork-Köln,407-29.
King,Peter.1985.JeanBuridan'sLogic:TheTreatiseonSupposition,The
TreatiseonConsequences.D.Reidel,Dordrecht.
Kretzmann,Norman.1966.WILLIAMOFSHERWOOD'SIntroductiontoLogic.
UniversityofMinnesotaPress,Minneapolis.
Kretzmann,Norman.1968.WILLIAMOFSHERWOOD'STreatiseonSyncategorematic
Words.UniversityofMinnesotaPress,Minneapolis.
Kretzmann,Norman,andEleonoreStump.1988.TheCambridgeTranslationsof
MedievalPhilosophicalTextsVolume1.CambridgeUniversityPress,
Cambridge.
LambertofAuxerre.14thcentury.PropertiesofTerms.Logica(Summa
Lamberti),ed.FrancoAlessio;VIII:Desuppositionibusetde
significationibus,pp.205045.Florence:LeNuovaItalia,1971.
TranslatedinKretzmann&Stump1988.
82
Mates,Benson.1972.ElementaryLogic.OxfordUniversityPress,N.Y.
Matthews,Gareth.1997.ATwoTheoriesofSupposition?,@thisvolume.
Ockham,William.14thCentury.SummaLogicae.
PaulofVenice.14thcentury.LogicaParva(1472edition),Venice.
ReprintedbyGeorgOlmsVerlag,Hildesheim/NewYork,1970.Translated
inPerreiah1984.
Perreiah,Alan.1984.LogicaParva:Translationofthe1472Edition.
PhilosophiaVerlag,München.
PeterofSpain.13thcentury.Tractatus:SummuleLogicales.DeRijk,L.M.
(ed.).VanGorcum,Assen,1972.TranslatedinDinneen1990.
Read,Stephen.1991."ThomasClevesandCollectiveSupposition,"Vivarium
XXIX,50-84.
83
Spade,PaulVincent.1988."TheLogicoftheCategorical:TheMedieval
TheoryofDescentandAscent,"inNormanKretzmann(ed.)Meaningand
InferenceinMedievalPhilosophy,Kluwer,Dordrecht,187-224.
Spade,PaulVincent.1997.TranslationofthebeginningofWalterBurley=s
TreatiseontheKindsofSupposition(DeSuppositionibus),translated
fromBrown,Stephen,AWalterBurleigh=sTreatiseDeSuppositionibusand
ItsInfluenceonWilliamofOckham,@FranciscanStudies32,1972,15-
64.Thisvolume.
84
Spade,PaulVincent.[forthcoming]TranslationofWalterBurley=sThelonger
TreatiseonthePurityoftheArtofLogic,Tract1:AOntheProperties
ofTerms.@TranslationofthesecondBurleyitemabove.
Whately,Richard.1975.ElementsofLogic.Scholar'sFacsimiles&Reprints,
Delmar,N.Y.(Reprintofthe1827edition.)
WilliamofSherwood.13thcentury.Introductionesinlogicam.Grabman,
Martin(ed.).SitzungsberichtederBayersichenAkademieder
Wissenschaften,Philosophisch-historischeAbteilung,Jahrgang1937,H.
10.Munich,1937.TranslatedinKretzmann1966.
WilliamofSherwood.13thcentury.Syncategoremata.O'Donnell,J.R.(ed.).
MediaevalStudiesIII,46-93.Toronto:PontificalInstituteof
MediaevalStudies,1941.TranslatedinKretzmann1968.
85
Notes
1.IamindebtedtotheparticipantsintheUCIconferenceonSignifierand
Supposita(Spring1995),especiallytoElizabethKarger,GarethMatthews,Calvin
Normore,StephenRead,andPaulVincentSpade.Iamresponsibleforanyandall
inadequacies.
2.Iamuncomfortable,however,withcharacterizingtheearlytheoryasatheoryof
reference,inthesensethatitisintendedtoanswerthequestionwhatatermrefers
toonagivenoccasion(Spade1988,208),withthetypicaloptionsbeingoneof,
severalof,oralloftheterm'ssupposita.Thispatterniscertainlythere,butI
suggestthattheearlytheorywasmoresophisticatedthanthis.(Cf.Matthews=
paperinthisvolume.)
3.Thereasonfortheterminology`merelyconfused=isthis.Onmostaccounts,a
commonterm(suchasacommonnoun,oranadjectiveorintransitiveverb)thatis
unaffectedbyanyspecialsignhasdeterminatesupposition.Specialsignssuchas
`every=or`[email protected].
Insomecasesthesignconfusesthetermbydistributingit;thusAdistributive@
supposition(frequentlycalledAconfusedanddistributed@supposition).But
sometimesthesuppositionofthetermisconfusedwithoutdistributingit,sothat
86
thetermismerelyconfused.
4.OckhamgivesithisbestshotinSummaLogicaeI.70,buthissuggestionisad
hoc;itisnotclearhowtogeneralizeittoothercases.(Burleyusestheterms
`mobile=and`immobile=differentlyfromotherauthors;seesection3.2.1below.)
5.IdiscussWilliamofSherwoodfirstbecauseheisthemostexplicit.Peter
apparentlywrotebeforeLambert,anditisveryunclearwhenWilliamwrote,thoughit
islikelytohavebeenafterPeter.Allofthesewritersseemtobediscussingan
alreadyestablishedtradition.
6.Lambert(inKretzmann&Stump1988,'7):"Distributionisthedivisionofone
thingintodivided[parts]."
7.Theodddiscussionofascentinthisselectionmaybeinresponsetoatopic
existingintheliteratureatSherwood'stime.TheanonymousauthorofOnthe
PropertiesofDiscourse(indeRijk1967;translationinthisvolume),anearlier
text,worriesabouttheproprietyofcallingsupposition"immobile"whenalthoughone
cannotmovedownward,onecanmoveupwards,asin`Everyhumanisananimal,
thereforeeveryhumanisasubstance'.Thatauthorexplainsthattheuseof
`immobile'withsuppositionisnotintendedtocoversuchupwardmovements.
Sherwood'sdiscussionhereseemstoterselyechothispoint.
87
8.Hesays(Kretzmann1968,'1.17):
...Supposetherearethreemenwhoseeeverymanandarerunningwhileall
theothersseeSocrates[only]andarenotrunning.Theneverymanwhoseesevery
manisrunning.(Inductiveproof.)Someonemayinfer`thereforeeverymanwhosees
Socratesisrunning',whichisfalse.
...thereisafallacyoffiguradictionishere[inmoving]fromimmobileto
mobilesupposition,andaqualequidistransformedintoahocaliquid.Whensucha
termstandsformanyimmobilelyitstandsasaqualequid,butwhenitstandsfor
manymobilelyitalsostandsforeachofthemasahocaliquid....
9.Wewouldsaythathewasintheprocessofformulatingatheoryofscope
distinctions.Hissolutionsconstantlyinvokestructuralambiguities(the
"compounded/divided"distinction,andthe"fallacyoffigureofspeech")thatwecall
scopeambiguities,andhefrequentlytalksofonelocutionhaving"power"over
another,and/orofalocution(thatwewouldseeascausingscope)being(un)ableto
"passover"toadifferent(later)partofthesentence.E.g.hesaysof`qualelibet
currit'that"Thedistributioncanstayinthesubjectandnotpassovertothe
predicate..."(VI.2).
10.Thequestionofwhatmodeofsuppositionresultsturnsonwhatyoutaketobe
thesingularsofthesentenceunderthesecondoccurrenceof`man'.Thenatural
88
hypothesisisthattheyareoftheform:
`everymanseeingthismanisrunning'.
Onthishypothesisthesecondoccurrenceof`man'hasnokindofpersonalsupposition
onOckham'stheory,butithasmerelyconfusedsupposition(bydefault)onBuridan's
theory.Foringeniousalternatives,seesection7ofRead1991.
11.FromKretzmann&Stump1988,'3g(iv).Theexplanationgoesonfurther;itis
discussedintheappendix.
12.Sherwoodassumedthatthesingularswouldhavethisform(Kretzmann1966,'5.2),
anditwouldbeoddforLamberttoassumesomethingelsewithoutcomment.
13.Later,Lambertusestheexample`noteverymanisrunning'toillustratehow
negationcanimmobilizeatermthatispreviouslymobile,buthegivestheexample
withoutcommentaboutthesuppositionalstatusoftheterm.
14.TranslationsfromPeterofSpainareallfromDinneen1990.
15.ThesecontextsarecommoninLatin,whichhasnodefiniteorindefinite
articles.TheexamplesPeterhasinmindareonesthatwouldmostnaturally
betranslatedintoEnglishusingtheindefinitearticle,and,ifheisright,
givenanexistentialinterpretation.
89
16.IhavereplacedDinneen=s`Diffuse=with`Confused=topreservecontinuitywith
themajorityofothertranslators.
17.Hegivestworeasons;thefirstreasonisnotrelevanttothepointatissue;it
isalsoratherunpersuasive.Hesays:ifnegationcoulddistribute,thensince
`EverySocratesruns'isincongruous,sowouldbe`NotSocratesruns';butthelatter
isnotincongruous;sonegationdoesnotdistribute.Spadesuggests(personal
communication)that`incongruous=heremeansAungrammatical@.
18.XII.24Dinneen1990translatestheLatinexampleas`non-manisjust=,but
thereisnothingintheoriginalthatsuggeststhatthenegationshouldbeterm
negation.
19.QuotesarefromSpade1997.
20.Herepeatstheexplanationofimmobileconfusedanddistributiveas:
(45)Thus...whenonecannotdescendtothesuppositaunderaterm
thathassupposita,andneitheristhetermthathassuppositaimplied
by[its]supposita,thenthetermsuppositsconfusedanddistributively
immobilely.
21.FromtranslationinSpade[forthcoming].
90
22.IamignoringthefactthatBurleycitesthefactthatthetermhasdeterminate
suppositiontojustifythedescent,insteadofcitingthevalidityofthedescentas
ajustificationforsayingthatthetermhasdeterminatesupposition.Allthatis
neededformypointisthatthekindofsuppositionislinkedwiththekindsof
globaldescentsthatarepossible;itislessclearwhetherthekindofsupposition
orthepossibilityofdescent/ascentisprior.
Thefactthataterminonecategoricalpropositioncannotconfuseatermin
anothercategoricalwaswell-entrenchedatleastacenturybeforeBurleywrote;it
wouldbenaturalforhimtotakethisforgranted.
23.AllfromChapter70ofSummaLogicaeI,fromanunpublishedtranslationby
GarethMatthews.
24.AllquotationsattributedtoBuridanarefromKing1985.
25.TranslationsfromPartsIIandIIIofSummaLogicaebyAlbertusdeSaxonia;they
arefromanunpublisheddraftbyNormanKretzmann.
26.LogicaParvaII.4.AllcitationsfromPaulofVenicearebasedonPerreiah
1984,withoccasionalsmallvariations;Itakeresponsibilityforanyinaccuracy
introducedbythesevariations..
27.IamindebtedheretoconversationwithStephenRead.
91
28.Thetwoexceptivesareawkwardasexamplesformypoint,sincetheypresumethat
e.g.`EverymanexceptSocratesruns'isformedfrom`Everymanruns'byadding
`exceptSocrates'.ItisnotclearthatPaulhadanyopinionaboutthis.
29.AnexceptionisMates1972.
30.Hereisanotherparallelbetweenopacityandsupposition.Bothnotions
typicallygetappealedtobothinthediscussionofcontextsforwhichwealready
haveagoodsemantics,andindiscussingcontextsforwhichwesofarlackagood
account,suchas`JoanbelievesthatAgathahasahorse'inopacitytheoryor`I
promiseyouahorse'insuppositiontheory.
31.Actually,Frege'sindirectcontextsdivergeslightlyfromQuine'sopaque
contexts;thisisbecausetheformerfollowfaithfullytherecursivestructureof
languageandthelatteraregloballydefined.Thesimplestillustrationofthe
differenceisthat`itistruethatS'containsanindirectcontext(becauseofthe
`that'clause)butnoopaquecontext.
32.Spadepointsout(personalcommunication)thatthiscouldnothavebeenBurley=s
purpose,sinceBurleywasnotanominalist.
33.AllcitationstoWilliamarefromKretzmann1966unlessotherwisespecified.
92
34.Itisoddthatthefirstquotesaysthatthewordsuppositsforsomesingle
thing,sincethewordinquestion(`man')suppositsformanythings.Thekeytothis
isprobablyinthesecondquote:thewordsuppositsforonethingbyvirtueofthe
expression.Thatis,theexpressionforcessuppositionforatleastonething,but
doesnotforcesuppositionformorethanone.
35.Theaccountsketchedaboveseemstofitwellwiththeexamplesonwhich
Williamgaveanopinion,butitisnotclearhowtoapplyittocertain
others.Forexample,howdowetestforthesuppositionof`donkey'in`Every
manwhoseesadonkeyisrunning'?Atwentiethcenturyapproachwouldbeto
construethisas`Everymanxsuchthatxseesadonkeyisrunning';thenwe
couldtestforthesuppositionof`donkey'in`xseesadonkey',andgetthe
answer,"determinate".Butitisnotatallobvioushowanyoftheearly
medievalswouldapproachthisquestion.(Ihaven'tfoundacaseinwhich
Williamselectsamodeofsuppositionforsuchanexample.)Thisisprobably
agapinthetheory.
36.Somecommentators(e.g.Priest&Read1980)seethisasaflawinthe
theory;theywouldsaythatWilliamshouldhaveintendedabiconditional,
becausethepredicateofaparticularnegativepropositionshouldnothave
93
distributivesupposition.Mygoalhereistoexplainthetheory,notto
correctit.Forbetterorforworse,thiswasWilliam'saccount.
37.Allauthorsassumethattermscanbeusedintwoorthreedifferentways.When
atermisusedAnormally@ithaspersonalsupposition;thetheoryofmodesofcommon
suppositionisaclassificationofthiskindofuse.Atermcanalsohavematerial
suppositionwhenitstandsforitself(oragrammaticallyrelatedword);anexample
is`horse=in`Horsehasfiveletters=.Thenon-nominalists(includingPeter)
thoughtthatatermcanalsobeusedtostandfortheassociateduniversal;an
exampleis`man=in`Manisaspecies=.Thisiscalledsimplesupposition.Peter
thoughtthatallpredicatetermstendtohavesimplesupposition;heneedn=t
determinewhichmodeofpersonalsuppositiontheyhave,becausetheydon=thave
personalsuppositionatall.
38.ThisappearstobewhathearguesinVI.10-12andinXII.24.
39.Thefullquote('3g(v),Kretzmann&Stump1988,112)is"Strongmobile
suppositioniswhatacommontermhaswhenitisinterpretedforallofitssupposita
necessarilyanda[logical]descentcanbemadeunderit."Lambertusesthe
terminology`strong'whereothersuse`distributive'.Inthefullquoteheis
simultaneouslydefiningbothstrongsuppositionandmobility.
94
40.AtVI.10itappearsthathemightconsiderdefiningmerelyconfusedas
immobilelyconfused,butthisisinthecontextofaspeculationthathegoesonto
reject.
41.Thefullquote('3g(v),Kretzmann&Stump1988,112)is"Weakimmobile
suppositioniswhatacommontermhaswhenitisinterpretednecessarilyformore
thanonesuppositumcontainedunderitbutnotforall,andadescentcannotbemade
underit."Heuses`weak'whereothersuse`merelyconfused',andhedefines
`immobile'inthesamesentence.Lambertholdsthatthereisnosuchthingasmobile
weakconfusion.
42.Actually,itagreeswithPeterofSpainvacuouslyinthecaseofmerelyconfused
supposition,sincePeterapparentlyholdsthatnothingfallsintothiscategory;
termsthatappeartodosoactuallyhavesimplesupposition.
43.TheemendationistoreplaceSherwood'suseofthenecessityofaconditional
withthemoremodernnotionofformalentailment.Iamnotsurewhetherthisiswhat
Whatelyintendsby`invirtueoftheformoftheexpression'.
44.InGeach1956,1962,1972,1976.
45.ThisdoesnotvindicateanotherofGeach'sculprits,thedoctrinethat
95
distributionisthekeytoallofinference.Thisviewseemstoappearfirstinthe
PortRoyalLogic;itisclearlyinaccuratethereevenforstandardAristotelian
syllogistic.Thisdoctrineisquiteseparatefromanythingdiscussedinthispaper.