Supposition as Quant - philosophy.ucla.edu · again: ` x!(Px " G)'. If you do this...

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

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

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

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

Wecouldalsogiveadifferentreply,consistentwiththefirst.Wecould

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

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

Aquantifierisgloballyweaklyexistentialinaformulaifitbecomes

anexistentialquantifierin(oneof)theprenexnormalform(s)ofthat

formula,butithasscopeinsideauniversalquantifierinanysuch

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

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

theterm`man'losesitsdistributivesuppositionbecauseofthenegationon

thefront.

Inthelatertheory,determinatesuppositionisanalogoustoglobalstrongly

existentialeffect,merelyconfusedsuppositionisanalogoustoglobalweakly

existentialeffect,anddistributivesuppositionisanalogoustoglobal

universaleffect(lumpingtogetherstrongandweak).

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

`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

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

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

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:

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.

Theserules(intheearlytheory)giveanalgorithmthatisnodifferentin

principlethanamodernaccountthatreads:

Ifaquantifiercontainsavariableallbyitselforprecededby`�'it

isuniversal;ifitcontainsavariableprecededby`�'itis

existential.

Theaboverulesthusgivesyntactictestsfordeterminingmodeofsupposition.

Theuniformaccountofthesemanticsofthesetermsthengoessomethinglike

this(thisisa"generic"version):

Atermhasdeterminatesuppositioninacategoricalpropositionwhenthe

locutioncontainingitcanbeexpoundedbymeansofitsbeingtruefor

somesinglething.

Atermhasdistributivesuppositioninacategoricalpropositionwhenit

suppositsthereforallofitssupposita.

Atermhasmerelyconfusedsuppositioninacategoricalpropositionwhen

itcanbetakenthereforseveralofitssupposita,notnecessarilyfor

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

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

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

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

`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

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

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'

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):

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:

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.

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

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

`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

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

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

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

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

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

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

(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

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.

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

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

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

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,

`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

theother[terms]unchangedinthegivensentence,

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.

(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

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.

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

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

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

`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

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.

[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

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

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:

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

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

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

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.

TerenceParsons

DepartmentofPhilosophy

UniversityofCalifornia,Irvine

tparsons@uci.edu

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.

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

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".

Itisclearfrombothcommentsandapplicationsthatthisthingmustbeone

ofthesuppositaoftheterm.Itisalsoclearfrombothcommentsand

applicationsthatselectionofanyparticularthingtoplaythisrolewouldbe

incorrect.(Recallthatin`Amanisrunning'itcanbetrueforanyone

running.)Sowearelookingforananalysisofthisform:

TermAhasdeterminatesuppositionin`...A...'when:Necessarily,

...A...ifandonlyifforsomexwhichisA:`...A...'istrue

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.

WAY#1:Wecanmostsimply"limitthesuppositaof`A'tox"by

consideringtheoriginalpropositionwiththerelevantoccurrenceoftheterm

À'replacedbyÀthatisx'.Forexample,toaskwhetherÈveryanimalis

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.

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:

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

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

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...'

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

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):

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

acommontermthathasthatsortofsuppositionisused,itisenough

thatthecommontermisinterpretednecessarilyforsomesuppositum,and

itisnotrequiredthatitbeinterpretednecessarilyformorethanone,

althoughinsuppositionofthissortitcanbeinterpretedformorethan

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

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

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

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.

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

"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

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

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firsttwo-thirdsofATractatusdeProprietatibusSermonum,@indeRijk

1967,703-30.

Buridan,John.14thcentury.TractatusdeSuppositionibus.InReina,Maria

Elena,"GiovanniBuridano:TractatusdeSuppositionibus,"Rivista

criticadistoriadellafilosofia(1957),175-208.TranslatedinKing

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,

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:

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.

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.

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.

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.

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`not=canAconfuse@thesuppositionofaterm.Thishappensintwoways.

Insomecasesthesignconfusesthetermbydistributingit;thusAdistributive@

supposition(frequentlycalledAconfusedanddistributed@supposition).But

sometimesthesuppositionofthetermisconfusedwithoutdistributingit,sothat

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.

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

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.

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].

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.

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.

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

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.

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

distributionisthekeytoallofinference.Thisviewseemstoappearfirstinthe

PortRoyalLogic;itisclearlyinaccuratethereevenforstandardAristotelian

syllogistic.Thisdoctrineisquiteseparatefromanythingdiscussedinthispaper.

Supposition as Quant - philosophy.ucla.edu · again: ` x!(Px " G)'. If you do this...

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