GENERICSASPLURALPREDICATION
EinarDuengerBohn
[Draft]
Abstract:inthispaperIdevelopanaccountofthelogicalformofgenericsin
terms of plural logic, and argue that it avoids the costs and preserves the
virtuesoftheothermainaccountsonthemarket.
Considerso-calledbarepluralgenericssuchas‘Catsmeow’,‘Duckslayeggs’and
‘Sharksattackbathers’.Whydotheystrikeusastrue?Therearecatsthatdon’t
meow,roughlyhalftheducksdon’tlayeggs,andinfactmostsharksdon’tattack
bathers,soexactlywhytheyaresupposedtobetrueishardtotell.Inordertobe
true,apluralgenericcanbeneitherauniversalgeneralization,whichwouldbe
toostrong,noranexistentialgeneralization,whichwouldbetooweak.So,ifthey
aretruegeneralizationsofakindatall,theymustbeofsomekindinbetweena
universalandanexistentialgeneralization,butnonethelesstheymustbeakind
ofgeneralizationthatallowsinstancesthatvariesinitsforceofgeneralization:as
wesawabove,somearetrueofonlyafewinstances,othersaretrueofroughly
half, and yet others are true of most instances. Can there be such a kind of
generalization?
Thestandardkindofaccountofgenericssaysyes,bypostulatingaspecial
kind of operator in the “deeper”, hidden logical form of the generic sentences.1
1Seee.g.Cohen(1999)andLeslie(2007,2008,2012).Foranotherinteresting
suchaccount,whichinspiredthepresentpaper,seeSterken(2013).
1
ThisspecialoperatoriscalledGen.Simplifyingtheirpredicationalstructure,the
threeinitialexamplesthenhavethefollowingtripartitelogicalform:
1. Gen(x)[Cat(x)][Meow(x)]
2. Gen(x)[Duck(x)][Lay-eggs(x)]
3. Gen(x)[Shark(x)][Attack-bathers(x)]
In general: Gen(x)[R(x)][M(x)], where R is a restriction and M is what’s
sometimescalledthematrix,whichisthepropertyattributedtothethingsinR
picked out by Gen.2Gen is thus supposed to represent a kind of generalization
thatallowstherightkindofvariationintheforceofthatgeneralization,making
allthreesentencestrue.
Analternativeaccountofgenerics,calledTheTheoryofSimpleGenerics,3
saysno,byinsteadpostulatingthatallsuchbarepluralgenericshavethelogical
formofakindpredication.Byagainsimplifyingtheirpredicationalstructure,the
threeinitialexamplesthengetthefollowingbipartitelogicalform:
1. Meow(CATS)
2. Layeggs(DUCKS)
3. Attackbathers(SHARKS)
In general: P(k), where P is a (possibly complex) predicate and k is a kind. As
opposed to the above standard kind of account, this alternative account thus
2Thematrixisalsosometimescalledthescope.
3SeeLiebesman(2011).Leslie(2013)callsitTheSimpleView.SeealsoCarlson
(1977).
2
denies that there is any kind of generalization involved at all. There is just a
subject,namelyakind,andapredicate,holdingofthatkind.
Clearly, the alternative kind predication account is logically simpler than
the standard account. But, equally clearly, logical simplicity is not always a
virtue.Forexample,AristotelianlogicislogicallysimplerthanFregeanlogic,but
whattheformergainsinsimplicity,thelattergainsinexpressivepowers.What
we really want, of course, is an account that is both simple and sufficiently
powerful.
Inwhatfollows,Iproposesuchanaccountofbarepluralgenericsbased
onresourcesfromplurallogic:arguably,inonesense(whichwe’llbrieflycome
back to), it is as simple as the kind predication account, and it has the same
expressive powers as the standard account. In general, it seems to avoid the
vicesandpreservethevirtuesfromeachoneofthesetwotypesofaccounts.
Here is the plan: in section 1, I sketch my account; in section 2, I show
how it preserves the main virtues and avoids the main vices of the other two
accounts; and, finally, in section 3, I briefly compare my account to Koslicki
(1999), reply to some anticipated objections, and point to some potential
problemsforpurposesoffutureresearch.
1.ThePluralPredicationAccount
LetmestartbypointingoutthatitiswithagreatdealofhumilitythatIpropose
myaccountofgenerics.Iproposeitnotsomuchinvirtueofaconvictionthatitis
true as in virtue of puzzlement as to why it hasn’t been more discussed in the
literature.AsfarasIknow,apartfromKoslicki(1999),Nickel(2010),afootnote
in Liebesman (2011: fn.8), and a brief objection to Koslicki (1999) in
3
KleinschmidtandRoss(2013),4thiskindofviewisnotverywelldiscussedinthe
literature.Ihopemygeneralformulationanddiscussionofitinwhatfollowswill
helpgeneratemorediscussionofit.Afterall,itseemstohavealotofthevirtues
and few vices from the other accounts, so, clearly, it deserves more discussion
thanithasalreadygotten.
Forwhatwillsoonbecomeobviousreasons,IcalltheaccountIamabout
topropose,thePluralPredicationAccount(PPA).PPArestson(whatshouldbe)
the uncontroversial logical machinery of generalized quantification, standard
plural logic and plural lambda abstraction. The resources of generalized
quantificationaswellasplurallogichasbecomemainstream,so,tosavespace,I
here simply refer the reader to the great literature on this already out there.5
Plural lambda abstraction is simply a pluralized version of mainstream
(singular) lambda abstraction, all wrapped up into the following axiom:
λxx[Φ(xx)]aa↔Φ(aa), where ‘xx’ is a plural variable and ‘aa’ is a plural term.
(Read:aahavethepropertyΦifandonlyifaahavethepropertyofbeingxxsuch
thatΦ(xx).)Note,importantly,thatΦcanherebeeitheracollectivepredication
oradistributivepredication.6
4We’llgetbacktothesementioningsoftheviewinsection3below.
5Ongeneralizedquantification,andforfurtherreferencesonthematter,seein
particularHeim&Kratzer(1998),Portner(2005)andWesterståhl(2007).
GeneralizedquantificationgrewoutofFrege’swork(e.g.1892).Forplurallogic,
andfurtherreferencesonthematter,seeinparticularYi(2005,2006),McKay
(2006),andOliverandSmiley(2013).WhatIherecallstandardplurallogicgrew
outofBoolos(1985,1986).Themodifier’standard’ismeanttoindicatethatthe
plurallogiciscommittedtogenuinepluralquantification,referenceand
predication,i.e.quantificationover,referencetoandpredicationofpluralities,
pluralitiesnottobereducedtosets,orsomeotherkindofsingularobjects
diguisedasbeingsomethingplural.
6Roughly,Φ(xx)iscollectiveiffΦholdsofxx,butnotofeachoneofthem;Φis
distributiveiffΦholdsofxxanditholdsofeachoneofthem.So,forexample,
while‘thepoliceofficerssurroundtheprisoner’iscollective,sincenooneofthe
4
With such standard machinery on board, and as before simplifying the
predicational structure a bit, PPA gives the following analysis of the three
sentenceswestartedoutwith:
1. λxx[Q(y)[yisoneofxx][Meows(y)]]Cats
2. λxx[Q(y)[yisoneofxx][Layseggs(y)]]Ducks
3. λxx[Q(y)[yisoneofxx][Attacksbathers(y)]]Sharks
whereQistheappropriategeneralizedquantifier,i.e.thegeneralizedquantifier
providing the right amount of cats, ducks and sharks in question, for each
respective sentence. In general, we have: λxx[Φ(xx)]aa, where Φ is any plural
wff, collective or distributive, possibly including a generalized quantifier. Thus,
barepluralgenericsarejustbipartitepluralpredications.
Theintuitiveideabehindthisanalysisisthatabarepluralgenericisjusta
(possiblycomplex)one-placepredicationofapluralityofthings.So,‘Catsmeow’
isjustapluralpredicationofcats(ofthecatsthemselves,notthekindCATS,if
thatkindissomethingelsefromthecatsthemselves),sayingsomethinglikethat
they–allofthemcollectively–havethepropertysuchthatmostofthemmeow.
Likewise,‘Duckslayeggs’isonthisaccountsimplyapluralpredicationofducks
saying of them all that a proper amount of them, namely the females, lay eggs;
and‘Sharksattackbathers’isapluralpredicationofallsharkssayingthatsome
few of them attack bathers. The right amount of individuals in question is
policeofficerssurroundstheprisonerbyherself,‘theapplesareonthetable’is
distributive,sinceeachoneoftheapplesisonthetable.
5
handledbyordinarygeneralizedquantificationbuiltintothe(possiblycomplex)
pluralpredicate,notbysomespecialoperatorGen.
NotethatthequantifierQin1-3is,unliketheoperatorGen,notoneand
the same (generalized) quantifier in all cases, but rather a different one from
casetocase.7
Notealsothat,forexample,thepredicate‘meow’inthegenericcase‘Cats
meow’andintheparticularcase‘Possummeows’havedifferentsemanticvalues,
namelyacomplexlambda-propertyintheformerandtheordinarymeowingin
thelatter.Onlytheformerishereclaimedtocontainquantificationalstructure,
notthelatter.(Insentence1,thelatteroccursinsidetheformer.)Consideralso
the case ‘Possum and Magpie meow’. This latter is a case of ordinary plural
predication, and there is here no claim as to such cases containing
quantificational structure a la the generic case ‘Cats meow’. There are thus at
leastthreedifferentcasesofpredicatingmeowing:singular,ordinarypluraland
generic. PPA claims only that there is quantificational structure in the generic
case,notinthesingularortheordinarypluralcases.
It might also prove instructive to compare the cases of ‘Dinosaurs are
extinct’and‘Mosquitosarewidespread’.Bothareoftenseenaskindpredication
because it is the kind that is extinct or widespread, not any individuals of that
kind.AccordingtoPPA,bothcasesarejustcasesofpluralcollectivepredication.
They are both analyzed in the same way, namely the former as
‘λxx[Extinct(xx)]Dinosaurs’, and the latter as ‘‘λxx[Widespread(xx)]Mosquitos’,
where ‘Extinct’ and ‘Widespread’ are collective predicates. PPA thus handles
7Whencethedifferencefromcasetocase?Isayinvirtueofcontext,butsee
section3below.
6
bothcaseswithoutanyappealtokindsassomethingotherthantheindividuals
themselves.8
In the next section, I will further explicate PPA by showing (in no
particular order) how it preserves all the main virtues and avoids all the main
vicesoftheothertwokindsofaccountsonthetable;andifthat’sright,atleast
PPAdeservestobeonthatverysametablenexttotheothertwo.
2.Keepingthevirtuesandavoidingthevices
A first virtue of PPA is that it, like the kind predication account, unlike the
standardaccount,onlypostulatesabipartitestructureofsubjectandpredicate,
not a tripartite structure involving a special operator Gen.9As such, its logical
form is simpler than the standard account. For example, according to PPA, the
barepluralgeneric‘Catsmeow’issimplyaone-placepredicationofapluralityof
cats:thepluralityofcats–allofthemcollectively–aresuchthatQ-many-of-them
meow,whereQistheappropriategeneralizedquantifier.Acorollaryofthisfirst
virtueisthatPPA,likethekindpredicationaccount,unlikethestandardaccount,
8Onemighthereworryabouthow‘extinct’canapplytoapluralitythatdoesn’t
exist(afterall,therearenodinosaurs!).Thisworryisfurtherdiscussedin
section3below.Onecouldofcoursetrythisasananalysis:
‘λxx[∼∃yy(xx=yy)]Dinosaurs’(andmaybeevenaddatemporalmodifierasper
Koslicki,1999).ButIbelievethisisaninstanceofamuchmoregeneral
metaphysicalworryfacedbyeveryone,raisingmoregeneral(evenMeinongian)
worries,notaspecificworryfacedonlybyouranalysisofgenericsinparticular.
Letmeherejustaddthatsemanticsandmetaphysicsshouldrideindependently
ofeachother.
9Though,ofcourse,maybethatsimplicityiscounterbalancedbythecomplicated
structureofthelambda-abstractinvolved.
7
has a nice explanation of why no known language actually pronounces Gen: it
doesn’texist.10
AsecondvirtueofPPAisthatit,likethestandardaccount,unlikethekind
predicationaccount,keepsthestrongintuitionthatgenericsinvolvesomekind
ofgeneralization.But,unlikethestandardaccount,thiskindofgeneralizationis
not a special kind of generalization with respect to generics in particular. It is
just a good old-fashioned generalization best handled by good old-fashioned
generalizedquantification,whichdiffersfromcasetocase.
A third virtue of PPA is that it, like kind predication, easily handles
conjunctivecaseslikethefollowing:
4. Mosquitosarewidespread
5. Mosquitosareirritating
6. So,Mosquitosarewidespreadandirritating
Sentence4saysthatmosquitos–allofthemcollectively–arewidespread,while
sentence5saysthatmosquitos–butnotnecessarilyallofthemcollectively–are
irritating.Sentence6followsfrom4and5,butwhile4isakindpredication(it’s
thekindthatiswidespread),5isabarepluralgeneric,so,unlesssomethinglike
the kind predication account is true, 6 is a mixture of a kind predication and a
generic.Thatseemslessthanideallyclean-cut.Thatthekindpredicationaccount
10ThoughseeLeslie(2007,2008,2012,2013)foraninterestingexplanationof
why,accordingtoherversionofthestandardaccount,noknownlanguage
pronouncesGen.Seesection3belowfortheworrythatQisnotpronounced
either.
8
ismoreclean-cutwithrespecttosuchconjunctivecasesistakentobeoneofits
mainvirtues(cf.Liebesman,2011;Leslie,2013).
ButPPAisequallyclean-cutwithrespecttosuchcases,soitservesasa
main virtue of PPA as well: both 4 and 5 are plural predications of a plurality,
andsois6.Theonlydifferencebetween4and5isthattheforceofthegenerality
involved differs, but that is precisely as it should be; after all, mosquitos are
collectively widespread, but not equally collectively irritating; after all, some
mosquitos are not irritating at all. PPA thus gives something like the following
analysisof4-6:
7. λxx[Widespread(xx)]Mosquitos
8. λxx[Qy[yisoneofxx][yisirritating]]Mosquitos
9. λxx[Widespread(xx)&Qy[yisoneofxx][yisirritating]]Mosquitos
Where ‘Widespread’ is a collective predicate, and Q is the right kind of
generalizedquantifier;i.e.givingtherightamountofmosquitosbeingirritating.
As far as I can tell, this is a very plausible analysis of what is going on in 4-6
above,atleastasplausibleasthatoftheothertwoaccounts.
Now, the standard account can also handle such conjunctive cases by
postulatingastandardkindoftype-shiftbetween4and5(Leslie,2013).While4
involves the kind mosquitos, 5 involves the mosquitos themselves, and hence 6
can simply involve a mixture of the two, with the first conjunct being a kind
predication and the second conjunct analyzed in terms of Gen. So, as Leslie
(2013:19)putsit,suchacase“doesnotposeanespeciallydauntingproblemfor
those who would posit a Gen operator.” I agree; but nonetheless, allelsebeing
9
equal,itseemstomebetternottoproposeatype-shiftthantoproposeone.PPA,
likethekindpredicationaccount,doesnotneedtoproposeone.
A fourth kind of virtue of PPA is that it, unlike the kind predication
account, like the standard account, need not postulate kinds as anything other
than their instances. Consider ‘Cats meow’ again. According to PPA, there is no
kindCATSoverandabovethecatsthemselves.Likewisewith4and5:thereisno
kind MOSQUITOS over and above the mosquitos themselves; that’s partly why
PPAhassuchaniceexplanationof4-6,andwhythereneedbenotype-shifting.
Hence,PPA,unlikethekindpredicationaccount,likethestandardaccount,thus
needs provide no awkward explanation of how a kind can inherit properties
from its instances. Cats – that is, most of the cats themselves – meow; the kind
CATS(ifthereissuchathing),doesnotmeow(asfarasweknow).AsLiebesman
(2011)pointsout,talkaboutkinds,andhowkindsinheritpropertiesfromtheir
instancesshouldbelefttometaphysicians.Iagree;but,allelsebeingequal,italso
seemstomethatitisbetterforatheoryofgenerics,oranysemantictheoryfor
that matter, to not be committed to such kinds at all, not to mention to be
committed to the fact that the kinds need to inherit properties from their
instances. PPA, unlike the kind predication account, is free of all such
metaphysicalcommitments.11Thatisofcoursenottosaythattherearenokinds,
period; there might be for independent metaphysical reasons. It’s only to say
thatgenericsassuchdon’tgivenusagoodreasontopostulatethem.
11Liebesman(2011:fn8)claimsthathiskindpredicationaccountisfinewith
treatingthekindsaspluralities,butinsection3ofhispaper,henonethelessputs
forthaprettyloadednotionofkinds.Healso(fn.8)provideswhathetakestobe
twoworrieswithapluralaccount,whichwe’llcomebacktoinsection3below.
10
AfifthkindofvirtueofPPAisthatit,likethestandardaccount,unlikethe
kind predication account, can handle complex cases of pronouns and variable
bindings(Carlson,1977;Sterken,2012;Leslie,2013).Considerthesentence:
10. Catslickthemselves
Accordingtothestandardaccount,10hasthelogicalform:
11. Gen(x)[Cat(x)][xlicksx]
BypostulatingGen,thestandardaccountthushasnoproblemswithaccounting
for such cases of pronouns and variable bindings. But how is the kind
predication account supposed to handle 10? It seems the best it can do is this
(Leslie,2013):
12. λx[xlicksx]Cats
Butthatisaveryawkwardanalysis,ifnotjustwrong.Itwouldinanycaseneed
tobesupplementedwithastoryabouthowthekindCATSinheritthepropertyof
lickingitselffromhowmostofthecatsthemselveslickthemselves(though,for
the most part, not each other!). The kind predication account can here either
appeal to a metaphysical story about how that is (though I have no idea how
suchastorycouldgo),or,perhaps,appealtosomekindoftype-shifting,likethe
11
standardaccountdoeswithrespecttoconjunctivecasessuchas4-6above,but
supplementedwiththelogicalresourcesthatPPArelieson.12
AccordingtoPPAontheotherhand,10hasthelogicalform:
13. λxx[Q(y)[yisoneofxx][ylicksy]]Cats
Hence,likethestandardaccount,thereisnoproblem.Thestructuregeneralizes.
Consider the following slightly more complicated case from Leslie (2013:9),
whichthestandardaccountcaneasilyhandle,butthekindpredicationaccount
cannoteasilyhandle:
14. Politiciansithinktheyicanoutsmarttheiriopponents
AccordingtoPPA,simplifyingthepredicationalstructureabit,14hasthelogical
form:
15. λxx[Q(y)[y
is
one
of
xx][y
thinks
y
can
outsmart
y’s
opponents]]Politicians
whereQistherightkindofgeneralizedquantifier.
AsixthkindofvirtueofPPAisthatit,likethestandardaccount,unlikethe
kindpredicationaccount,caneasilyhandlecasesofso-called“donkeyanaphora”
12Leslie(2013)putsforththiscriticismofLiebesman’s(2011)kindpredication
account,butseemstonotrecognizethatLiebesmancanappealtotype-shifting,
justlikeshedoeswithrespecttoconjunctivecasessuchas4-6above,provided
headdsmorelogicalresourcesthanwhatheactuallydoes.
12
(Leslie, 2013:9-12). But since such cases are similar to the above cases of
pronouns and variable bindings, and it should be pretty obvious how PPA
handles them in a similar way, I’ll for purposes of space leave this case as an
exercise. (Hint: all the relevant structure is built into the quantificational
structureoftheplurallambdaabstract.)
AseventhkindofvirtueofPPAisthatit,likethestandardaccount,unlike
the kind predication account, can handle weak crossover effects. Consider the
following test to reveal whether there is a variable-binding operator in the
logicalformofasentence(adoptedfromLeslie,2013:12-14):
16. Johniislovedbyhisimother
17. HisimotherlovesJohni
Sentence 17 can be understood as a paraphrase of 16, but this kind of
paraphrase is only acceptable when the noun phrase that binds the possessive
pronoun does not involve a variable binding operator. This can be seen by
consideringthecontrastingcase:
18. Everyiboyiislovedbyhisimother
19. *Hisimotherloveseveryboyi
Clearly19isanunacceptableparaphraseof18.While18is(hopefully)true,19is
bad.Butthen,asLeslie(2013:13-14)nicelypointsout,wehaveatestbywhich
we can use the kind predication account to make a prediction, and thus see
whetheritholdsupagainsttheevidence.Considerthefollowingtwosentences:
13
20. Mostly,boysiarelovedbytheirimothers
21. *Mostly,theirimothersloveboysi
Likeinthecaseof18-19,sentence21isclearlynotanacceptableparaphraseof
20 (indicating that there is a variable-binding operator involved in the logical
form).While20is(hopefully)true,21isbad.Butbysimplyremovingtheadverb
ofquantificationin20,wehaveabarepluralgeneric:
22. Boysiarelovedbytheirimothers
So, by the kind predication account, there is no quantifier (or variable-binding
operator)involvedin22,andhenceitpredictsthatthereshouldbeaparaphrase
ofitinthesamekindofway17isaparaphraseof16.Butthisisnotborneout,as
canbeseenbythefollowing(bad)paraphraseof22:
23. *Theirimothersloveboysi
So,wehaveareasontothinkthatthekindpredicationaccountisfalse,byvirtue
of it making false predictions. The above test indicates that there is a variablebindingoperatorinvolvedin22,butthekindpredicationaccountpredictsthat
thereisnot.
PPAontheotherhand,likethestandardaccount,isfreeofthisproblem.
According to PPA, there are variable-binding operators involved in 22, it’s just
14
thattheyarebuiltintothepluralpredicate‘lovedbytheirimothers’.According
toPPA,simplifyingthepredicationalstructureabit,thelogicalformof22isthis:
24. λxx[Q(y)[yisoneofxx][yislovedbyy’smother]]Boys
So, PPA, like the standard account, unlike the kind predication account, is in
compliance with the above test, and faces no problems with the above weak
crossovereffects.
Finally, an eighth kind of virtue of PPA is that it can handle certain
ambiguously read bare plural generics (Liebesman, 2011; Sterken, 2012:3.2.13.2.1.1) better than the kind predication account, and perhaps as well as the
standardaccount(thoughI’mnotsureitfaresbetterthanthestandardaccount
on this one). The classic example is the following sentence 25, with its two
possiblegenericparaphrases26and27:
25. Typhoonsariseinthispartofthepacific
26. Typhoonsaresuchthattheyariseinthispartofthepacific
27. Thispartofthepacificissuchthattyphoonsariseinit
Sentence25isambiguousbetween(atleast)thetwodifferentgenericreadings
26and27.In26,somethinggeneralissaidabouttyphoons,butin27something
general is supposedly said about this part of the pacific. According to the
standardaccount,26-27thenhavethefollowinglogicalforms,respectively:
28. Gen(x)[Typhoon(x)][(Ariseinthispartofthepacific(x)]
15
29. Gen(x)[Thispartofthepacific(x)][Typhoonsarisein(x)]
Can PPA do as well? According to PPA, 26-27 might have something like the
followinglogicalforms,respectively:
30. λxx[Qy[yisoneofxx][Ariseinthispartofthepacific(y)]]Typhoons
31. λx[∃xx(Typhoons(xx)&xxariseinx)]Thispartofthepacific.
withQbeingtherightkindofgeneralizedquantifier.(Therearealsootherminor
variations on 31 possible.13) But it might be objected that 31 does not capture
thedesiredreadingof27aswellas29doesbecausewhereas29sayssomething
generalaboutthispartofthepacific,31seemsnotto.Sentence31,asopposedto
27and29,justsaysthatthispartofthepacifichasthepropertyofhavingsome
typhoons arise in it; it doesn’t say that it’s a general feature of this part of the
pacificthattyphoonsariseinit.Butthenagain,I’mnotsurehowbigofaproblem
thisisforPPA,orwhetheritisaproblematall.First,justhavingthepropertyof
havingsometyphoonsariseinitisbyitselfageneralfeatureofthispartofthe
pacific, as long as we’re talking about several typhoons; and that sense is
captured by 31. Second, the supposed missing generality might be a generality
due to several typhoons arising in this part of the pacific over time; and that
generality over time can easily be added into the plural predicate of 31. Third,
13 For example (31*): λx[∃zz(Typhoons(zz) & Qy[y is one of zz][y arise in
x])]Thispartofthepacific;orperhaps(31**):λx[λxx[Qy[yisoneofxx][yarisein
x]]Typhoons]Thispartofthepacific.Notethat(31**)isinterestingtotheextent
that27(also)indicatesageneralitywithrespecttotyphoons(inthepredicate)
ratherthan(just)thispartofthepacific(whichisitssubject).
16
I’m not sure I hear a generality of this part of the pacific beyond whatever is
captured by my first and second points just mentioned. Fourth, to the extent
therestillisamissinggeneralitytothispartofthepacific,andnotjustduetothe
abovegeneralityovertime,butrathersomenon-accidentalkindofgeneralityto
this part of the pacific, it might be captured by adding an independent modal
operatorintothepluralpredicatein31(thoughpresumablynotGen!).Thisthird
routetakesusovertothesixthproblemdiscussedinsection3below.
So,thoughI’mnotsurePPAdoesbetterthanthestandardaccount with
respectto27,itisalsonotcleartomethatitdoesworse.Inanycase,PPAseems
tohandle27betterthanthekindpredicationaccount.Liebesman(2011:section
4) contains an extensive discussion of how the kind predication account is to
handle 25-27. His solution basically comes down to a defense of the following
existentialreadingof27:
32. ∃x(Typhoon(x)&Ariseinthispartofthepacific(x))
ApartfromSterken’s(2012:3.2.1.1)convincingcriticaldiscussionofLiebesman’s
existentialreading,Ionlyhavetwothingstoaddinresponseto32.First,ifone
insists on keeping 32, it seems much better to formulate it in terms of a plural
existential reading: ∃xx(Typhoon(xx) & Arise in this part of the pacific(xx))
(Read: there are some typhoons arising in this part of the pacific.)14Second, all
elsebeingequal,itseemstomethataccepting31(orsomethingsufficientlyclose
14Liebesman’s(2011:427)informalformulationofmy32sometimesoccursina
pluralform,buthisformalformulation(hissentence(37))isintermsofa
singularexistentialquantifier;soisSterken’s(2013:3.2.1.1)discussionofit.
17
to it; or even accepting 29) is better than accepting 32, even given the plural
existentialreadingofitjustmentioned.
So, with respect to 27, whether or not PPA does better or worse
compared to the standard account, PPA does seem to handle it better than the
kindpredicationaccount.So,itmightthenintheendbeajudgmentastowhich
theorydoesbetteroverall,notjustwithrespectto27inparticular.
Summingup,itseemsPPAprettyclearlydeservesbeingonthetableasaviable
candidateanalysisofbarepluralgenerics,nexttothestandardkindofaccount
andthekindpredicationaccount.Afterall,ithasmostofthemainvirtueandfew
ofthemainvicesoftheothertwoaccounts;atleastsoitseemssofar.
But,ofcourse,Ianticipatesomeobjections,whichisthetopicofthenext
andlastsection.
3.Someobjections,replies,andproblems
We have so far focused on how PPA avoids the main vices and preserves the
main virtues of the standard kind of account and the kind predication account.
But,ofcourse,nothing’sperfect,sointhissection,Ianticipatesomeobjections,
andpointtosomepotentiallyseriousproblemsforpurposesoffutureresearch.I
proceedinwhatItaketobearoughlyincreasingorderofimportance.
Butfirst,letmebrieflycomparePPAtoanother(theonly?)placeintheliterature
where a fully general analysis of generics in terms of plural logic has been
suggested, namely that of Koslicki (1999). The two accounts are of a kind, but
18
they also differ in some important ways.15Unlike Koslicki’s account, PPA is not
motivated by nominalism; in fact, I don’t see any good reason to motivate
semanticsintermsofnominalism,oranyothermetaphysicalworldviewforthat
matter.Arguably,semanticsandmetaphysicsshouldrideindependentlyofeach
other. Also, due to recent developments of plural logic, PPA, unlike Koslicki’s
account,isfreedfromanyconnectionstohigher-orderquantification.16Butmore
importantly, Koslicki never suggests the presence of ordinary generalized
quantificationinsidethepluralpredicatesinthewayPPAdoes,andassuchlacks
the needed resources for empirical adequacy (though it seems her account is
compatiblewithit).Alsoimportantly,Koslicki’saccountappealstoDavidsonian
paraphrases in terms of events, and to two different levels of analysis, one
dealingwithlogicalformandanotherdealingwithlexicalknowledge/meaning.
PPAstaysneutralonboththesepoints.
For purposes of comparison, it is worth noting that Kleinschmidt and
Ross’(2013)objectiontoKoslicki(1999)isnotaproblemforPPA.Considerthe
followingkindofsentences(fromKleinschmidtandRoss,2013):
33. Thepolarbearhasfourpaws,andsodoesChompy
34. TheMoonlightSonataisroughlyfifteenminuteslong,andsoisthetimeoutIjustreceived
15Koslicki’s(1999)paperisoriginalandveryinteresting;Ifinditoddthatithas
notgottentheattentionitdeservesintheliterature.Isitbecauseitwastooearly
foritstime?By1999,plurallogicwasstillnew,andhadnotyetfullymatured.
16Therearealsoterminologicaldifferencesbetweenthetwoaccounts,alsodue
torecentdevelopmentsofplurallogic.
19
TheproblemforKoslicki(1999),accordingtoKleinschmidtandRoss(2013),is
that(inboth33and34)sheconsidersthepredicateinthefirstconjunct,butnot
in the second conjunct, to be higher-order, and the predicate in the second
conjunct,butnotinthefirstconjunct,tobefirst-order.Andassuch,accordingto
Kleinschmidt and Ross (2013): “it is very hard to make sense of the anaphoric
predication in (33). And the same applies to (34)”. They might be right about
Koslicki(1999)(thoughI’mnotsureaboutthat),butitisnotaproblemforPPA,
partly because PPA is not committed to there being a difference between firstorder and higher-order predicates here. Here is one suggestion for the correct
logicalformof33(areadingKleinschmidt&Ross(2013)shouldaccept):
35. λxx[Qy[y is one of xx][Four paws(y)]]The polar bears & Four
paws(Chompy)
Sentence 35 says simply that (most of) the polar bears have four paws andso
does Chompy (i.e. have four paws). That is, the first conjunct says something
aboutthepolarbears,whilethesecondconjunctattributesthesametoChompy.
Havingfourpawsisnotsomethingattributedtothepolarbearscollectivelyhere,
butrathertomostofthemindividually,aswellastoChompy.Whatispredicated
to the polar bears collectively, i.e. of all and only the polar bears, is the plural
property of being such that Q-many of them have four paws. So, one and the
same property of having four paws occurs in both conjuncts, but the generic
predicationisapluralpredicationofadifferentcollectiveproperty.So,asfarasI
cansee,sentence33isnotaproblemforPPAassuch,andcertainlynotbecause
20
of some difference in first-order and higher-order predicates. And the same
appliesto34.
It is perhaps worth noting that there is an alternative to 35, also
compatiblewithPPA.In33,theclause‘andsodoes’changesthefocusfromthe
polar bears being the subject to the property of having four paws, a property
which it then in turn ascribes to Chompy. So, if we focus on the property of
havingfourpawsasthesubject,perhapswecanthinkof33asfollows:
36.λX[λxx[Qy[yisoneofxx][X(y)]]Thepolarbears&X(Chompy)]Fourpaws
where ‘X’ ranges over properties. Recall, PPA, unlike Koslicki (1999), is not
motivated by nominalism.17And the same applies to 34. So, as far as I can see,
whetherornot33and34areproblematicforKoslicki(1999),theyarenotsofor
PPA,atleastnotinawaythatmeritsrejectingitasagenerallyviableaccountof
generics.18
A more detailed comparison of the two accounts must be left for another
time;letitsufficetohereonlypointoutthattheyaretwoaccountsofakind,but
with some important differences; perhaps, PPA can be seen as a further
17LikeLewis(1991),unlikeBoolos(1984,1985),Itreatplurallogicas
independentfromsecond-orderlogic.Cf.Oliver&Smiley(2013).
18NotealsothatKleinschmidt&Ross(2013)seemstothinkofplural
predication,oratleastthewaytheyinterpretKoslicki’s(1999)useofit,
differentlyfrommyunderstandinginthepresentpaper(andwhatItaketobea
standardunderstandingofittoday).Theysayofapluralpredicate,whatthey
callahigher-orderpredicate,thatitis”apredicatethatappliesplurally:itisthe
sortofthingthatcanbetruenot,e.g.ofsomeparticularpolarbear,butratherof
polarbears.”But,accordingtostandardplurallogic,apluralpredicateisafirstorderpredicate,andcanbepredicatedofasingleindividualtoo.SeeagainYi
(2005,2006)orOliver&Smiley(2013).
21
development, or updating of Koslicki’s account. We now move on to some
objectionsandproblemswithrespecttoPPAinparticular.19
First, like Gen, the generalized quantifier Q is unpronounced and hidden in a
“deeper”logicalformofthesentencesinquestion(cf.sentences1-3fromsection
1).So,whatmakesQsoimportantlydifferentfromGen?Reply:thereareatleast
two important differences. First, while Gen is the name for one and the same
variable-bindingoperatorinallcases,Qis justaplaceholderforwhat’softena
different(generalized)quantifierfromcasetocase.Assuch,allproblemsofthe
correctsemanticstoryofGendisappear,inparticulartheproblem(ormystery)
of how it is supposed to be the same kind of generalization in cases with such
differentforceofgeneralityasourinitialsentences1-3fromsection1.Second,
whileGenisasfarasweknowunpronouncedinallknownlanguages,Qisinfact
oftenpronounced;incaseswhereitisnotpronounced,it’sjustageneralization
ofakindofquantifierthatis.Assuch,Qseemslessofaradicalpostulate;it’sjust
ageneralizedquantifierthatweallalreadyknowandlove.
Second, what’s the compositional story behind PPA? Reply: the compositional
story one gets from unpacking the (possibly) complex lambda-abstract. For
example,thesimple(non-generic)caseof‘Mosquitosarewidespread’istrueiff
19Nickel(2010)alsosuggestsananalysisintermsofpluralpredications,but
onlywithrespecttoso-calledcomparativegenerics(e.g.’Girlsdobetterthan
boysinelementaryschool’).It’suncleartowhatextenttheanalysisissupposed
togeneralizebeyondsuchcomparatives.Nickel(ms)extendstheanalysisto
conjunctivecasesala4-6above,butstill,fromwhatIhaveseen,it’sunclearhow
generaltheanalysisissupposedtobe.Iamnotatpresentinapositiontogive
theaccountinNickel(ms)fulljustice,but,inanycase,myaccountisintendedto
befullygeneral.
22
thepluralityofallandonlythemosquitoshavetheplural(collective)propertyof
beingwidespread.But,foramorecomplex(generic)case,‘Catsmeow’istrueiff
thepluralityofallandonlythecatshavethepropertyofbeingsuchthatmostof
them meow, where the latter property is expressed by the lambda-abstract
λxx[Q(y)[yisoneofxx][Meows(y)]],whosesemanticvalueiscomputedfromthe
semanticvaluesofQ(i.e.whichevergeneralizedquantifiertakesitsplaceinthis
case)and‘meows’(i.e.themeowingofasingularcat).That’sadmittedlyafairly
complex story, and the gain in bipartite simplicity over the tripartite standard
kind of account is perhaps counterbalanced by this added internal complexity;
but, on the other hand, nothing novel or surprising is involved. Overall, the
complexityinternaltotheplurallambda-abstractisworththetrade.20
Third,whyuselambda-abstractionatall?Whynotjustdropit,andanalyzethe
bare plural generics directly in terms of generalized quantification? Reply: the
plural lambda-abstraction represents what’s common among all bare plural
generics,whatmakesthemallbeofakind.Barepluralgenericssayofsomekind
of things (i.e. all and only the things themselves!) that they have a certain
distinctiveproperty.Thatlogicalandsemanticcommonalityislostiftheplural
lambda-abstractionisdropped.(Consideralsodroppingthelambda-abstraction
insentence9;it’sbetternotto.)
Fourth,considerwhat’susuallytakentobekindpredications,suchas‘Mosquitos
arewidespread’and‘Dinosaursareextinct’.Theformercaneasilybeseenasan
20SeeNickel(2010)forasuggestionofacompositionalstory,thoughwith
respecttocomparativegenerics.
23
ordinarycollectivepluralpredicationofallandonlythemosquitos,butthelatter
cannot as easily be seen as a collective plural predication of all and only the
dinosaurs because if it is true, there are no dinosaurs. It is therefore usually
takentobeakindpredication;it’ssaidofthekindDINOSAURthatitisextinct;
whichisbestunderstoodassayingthatithasnoinstancesanymore.Forwantof
auniformaccount,onemightthinkthisposesaproblemforPPA:itcanhandle
‘Mosquitos are widespread’, but not ‘Dinosaurs are extinct’. Reply: there are at
least two possible directions in which to look for a solution. First, as said in
footnote 8 above, one could try this: ‘λxx[∼∃yy(xx=yy)]Dinosaurs’ (and maybe
addatemporalmodifierasperKoslicki,1999),andthenwaitandhopeforthe
best solution to the more general problem of empty terms to work out in this
case too (appeal to free plural logic?). Second, one might appeal to standard
type-shifting as discussed in section 2 above. In the case of ‘Dinosaurs are
extinct’, one might then have a type-shift up to the level of the concept of a
dinosaur, and hence analyze the sentence as saying that the concept of a
dinosaurhasnoinstances.Thisisinthespiritofthegeneralizedquantification
already in play, and it avoids postulating kinds as anything beyond pluralities
andconcepts(whichwearguablyarecommittedtoonindependentgroundsin
anycase).Notethatanappealtotype-shiftinginthecaseofemptytermsisnota
move away from PPA, towards to the standard account, which also appeals to
type-shifting(andinmorecasesthanjustinthecaseofemptyterms).Thecase
of truths involving empty terms is a general problem, and type-shifting is a
standardmove,soIdon’tseethisasaspecialproblemforPPA.
24
Fifth, Liebesman (2011:fn.8) proposes two worries with transforming his kind
predicationaccountintosomethinglikePPA.First,therearegenericsinvolving
massnouns(e.g.‘Waterdrenchesthirst’),whichare,accordingtoLiebesman,not
easily analyzed as plural predication. Second, consider this case: ‘Dogs aren’t
extinct,andtheymighthavebeenmorenumerousthantheyare’.Insuchcases,
the noun ‘Dogs’ cannot be a plural term referring to all the dogs because that
plurality cannot have been more numerous than it is. Reply to first worry: the
topic of mass nouns, in both metaphysics and semantics, is a thriving research
areathesedays,soonlythefuturecantellwhethertherewillbeafullyuniform
understandingofgenericsincorporatingboththosewithpluraltermsaswellas
thosewithmassnouns.Butnotethatthereisalsoacompanionsinguiltreplyin
the vicinity here: to the extent that PPA has problems with generics involving
massnouns,astandardaccountinvolvingGenhasthoseverysameproblemstoo.
Thefactthatthekindpredicationaccountseemstohaveaneasierwaywithitis
of no help: it is empirically inadequate on other grounds. So, overall, PPA is no
worse off than the others.Butwithallthatsaid,PPAandthestandardaccount
mighthaveawayofhandlinggenericsinvolvingmassnouns,thoughwecannot
go into much detail here. They can both treat cases such as ‘Water drenches
thirst’assayingofportionsofwaterthatarightamountofthoseportionsdrench
thirst. 21 For PPA, this gets the form: λxx[Qx[x is one of xx][Drenchesthirst(x)]]Portions-of-water, where Q is the generalized quantifier giving the
rightamountofsuchportions.Replytosecondworry:suchcaseshavenothingto
dowithbarepluralgenericsinparticular.PPA(oreventhestandardaccount)is
notmakingtheclaimthatnosentenceisbetterconstruedasakindpredication
21ThisisalsobrieflysuggestedinKoslicki(1999:455).
25
thanapluralpredication.Ratheritismakingtheclaimthatbarepluralgenerics
arebestconstruedasbeingpluralpredications.Butitisworthnotingthateven
inthecaseathand,namely‘Dogsaren’textinct,andtheycouldhavebeenmore
numerousthantheyare’,itisnotobviousthat‘Dogs’cannotfunctionasaplural
termreferringtoalltheactualdogs.Onacontext-sensitivecounterpart-theoretic
interpretation of ‘could’ (cf. Lewis, 1986), there are contexts in which it is true
that all and only the dogs could have been more numerous than they are; i.e.
there are contexts in which the counterpart of all and only the actual dogs
includemoredogs.
Sixth,howdoesPPAfarewithrespecttovariousissuesinvolvingintensionality
and modality? While pluralities are extensionally individuated (i.e. two
pluralitiesareidenticalifftheyhaveallandonlythesamemembers),kindsare
not. So, as opposed to a kind predication account, PPA seems to face the
followingproblem:supposeitturnsoutthatallandonlycatsareanimals;then
from‘Catsmeow’itfollowsthat‘Animalsmeow’,whichseemsfalse.Thesource
of the problem is mixed with the fact that generics are non-accidental
generalizations;i.e.thereisamodalaspecttothem.Forexample,‘Mosquitosare
widespread’isnotagenericlike‘Catsmeow’(atleastpartly)becausethelatter
ismuchlessaccidental(moreessential?)thantheformer.Aslongaspluralities
are purely extensionally individuated it seems PPA cannot handle such
intensionalandmodalaspectsofgenerics.Reply:thereareatleasttwodirections
inwhichtolookforasolutiontothisproblem.First,onemightbuildinamodal
operator into the lambda-abstract. So, for example, ‘Cats meow’ might then be
analyzed as: λxx[Q(y)[y is one of xx][Non-Accidentally-Meows(y)]]Cats, where
26
‘Non-Accidentally’istheappropriatemodaloperator,whateveritis.Second,one
mightinsistonthepluraltermina(bareplural)genericreferringtoallandonly
somepossiblethings.So,forexample,in‘Catsmeow’,thepluralterm‘Cats’refers
to all and only possible cats (including the actual ones, of course). In other
words, we might insist on individuating the pluralities in generics in terms of
possibilia(aswellasactuality).Thenwehaveaplausiblestoryastowhyitdoes
notfollowfromthesupposedaccidentaltruth‘Allandonlycatsareanimals’and
the generic ‘Cats meow’ that ‘Animals meow’. This solution goes well with
(thoughnotcommittedto)counterparttheory,asalsomentionedinasolutionto
thefifthobjectionabove.
Seventh,unlikeGen(whostaysconstant,butmightdifferinitsforcefromcaseto
case),thequantifierQitselfdiffersfromcasetocase.Butthatimmediatelyraises
what might be the hardest question faced by PPA: whence the difference from
case to case? That is, what selects a generalized quantifier from one case to
another?Reply:Iputmymoneyonsomekindofcontext-sensitivity,butIalsosay
thatthisisoneofthesoftspotsofPPAinneedofmoreresearchbeforePPAisto
be trusted.22Let it here suffice to say that Q deals with the force of generality
involvedina(bareplural)genericsentence,and,intuitively,thereissomedegree
of context sensitivity in that respect. Consider ‘Sharks attack bathers’ (3). In a
scientific context, the sentence is false due to the weak force of the generality,
22Sterken(2013)suggeststhatGeniscontext-sensitive(infact,evenindexical),
butstill,onheraccount,thereistheoneandonlyGeninallcases,it’sjustthatits
semanticinterpretationiscontext-sensitive.(SeealsoSterken,ms.)Accordingto
PPA,thereisnooneandonlyQinallcases,onlydifferinginitssemantic
interpretation.Rather,therearedifferentQ’sacrossdifferentcases,having
nothingmoreincommonthananytwoarbitrarygeneralizedquantifiersdo,if
thereisaQatall.
27
butinthecontextofseeingasharkonthebeachthesentenceistrueduetothe
propertyofattackingbathersbeingasalientpropertyofsharksduetosomefew
of them actually attacking bathers. Now, there is of course also a noticeable
stability in the force of the generalization of many generics across contexts
(that’spartlywhatmakesthemseemtobeofakind),butitisalsonotinsensitive
to contexts. Whether there is a satisfactory contextual story here to be told,
especially whether it can handle potential problems of overgeneration, I must
leaveforfutureresearchtosettle.ButnotethatPPAdoesnotnecessarilystand
or fall with some such contextual story being told; it might be that some other
non-contextualstoryfitsbetter.Forexample,itwouldbeinterestingtoconsider
a possible connection between the selection mechanism for Q and data from
cognitive science (cf. Leslie, 2007, 2008, 2012). In any case, I consider this an
avenueopenforfutureresearch.
Eighth,sofaronlybarepluralgenericshavebeendiscussed,butcanPPAhandle
other kinds of generics, e.g. indefinite and definite generics such as ‘A tiger is
striped’and‘Thecatmeows’(respectively)?Reply:Imusthereleavethispointto
future work, but note that, at least on the face of it, it seems the answer is yes.
Consider‘Atigerisstriped’.Itseemstobesayingsomethinglikethattypicallyan
arbitrarytigerisstriped.Assuch,wecanperhapsthinkof‘Atigerisstriped’as
havingthelogicalformofalltigershavingthepluralpropertyofbeingsuchthat
typicallyanarbitraryoneofthemisstriped.Butexactlyhowtocashthisout,and
howtoextendittothecaseofthedefinitegenerics,Imusthereleaveasanother
openavenueforfutureresearch.
28
All in all, I conclude: if we take plural logic for granted (which we should on
independent grounds anyway), it seems we can use it to provide a
straightforward and general interpretation of generics, namely PPA; an
interpretationthatfaresprettywellcomparedtoothers.Ofcourse,muchmore
workonPPAneedstobedone.Forexample,amoresophisticatedconsideration
ofPPAshouldseparateatleastfourissuesthatwerenotclearlyseparatedabove:
First: what, if any, is the quantificational force in various generic sentences?
Second: is there a special generic operator Genin the logical form of generics?
Third:whatisthesemanticvalueofabarepluralingenericsentences?Fourth:
what is the compositional semantics of various generic sentences? Logically
speaking,thesefourquestionsraisefourseparateissues,andassuchtheymight
(thoughnotnecessarily)demandseparatetreatment.Thecorrectaccountmight
thereforebemuchmoreofamixturethanwhatIhavegiventheimpressionofin
thispaper.ButIhopeatleastthatwhatIhavesaidsufficetoshowthatPPAisa
viablecandidateforprovidingthelogicalformofgenerics,andquitegenerallyso,
worthyoffurtherconsiderationsanddiscussions,nextto,orbetter,inbetween
thestandardaccountandthekindpredicationaccount.23
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