 logical analysis of itemized plurals, it will serve as evidence for the fact that the logical status of itemized plural predication is deep down different – essentially simpler – from that of its non-itemized counterpart. This is by no means arguing against the pertinence of plural logic, which has its natural field of action in the treatment of non-itemized pluralities and non-itemized predication – for which it is the natural option. The only thing I would like to suggest is that the introduction of plural logic systems should not be motivated by examples of itemized collective predication.7 3 The Logical Status of Predication over Itemized Plurals Inference (1) shows a typical feature of itemized plural predication: in the absence of further indication, the order in which the subjects are listed is immaterial. This occurs not only with collective predication, but with distributive predication as well. For example: (2) Dick and Tony are fair-haired. Hence, Tony and Dick are fair-haired. Another feature of plural predication, both collective and distributive, is the immateriality of repetitions within the subjects listed: (3) Dick and Tony emptied the bottle. Hence, Dick, Dick, and Tony, emptied the bottle. 7 As it often occurs, e.g.: McKay (2006, Ch. 1): "Non-distributive predication. Standard first-order logic does not provide adequate resources for properly representing many ordinary things that we say: (1) Arnie, Bob and Carlos are shipmates". Yi (2005, 460): "The Fregean systems, Frege's system and its descendants cannot deal with the logic of the plural constructions (in short, plurals) of natural languages, such as the following: [P1] Venus and Serena are tennis players, and they won a U. S. Open doubles title". Such examples are cases of itemized plural predication, and they are easily treatable by means of the system which I will describe here. A Note on Plural Logic __________________________________________________ 155 (4) Dick and Tony are fair-haired. Hence, Dick, Dick, and Tony, are fair-haired.8 Another feature of plural predication, both collective and distributive, is substitutivity salva veritate: (5) Dick and Tony emptied the bottle. Tony is Iron Man. Hence, Dick and Iron Man emptied the bottle. (6) Dick and Tony
logical analysis of itemized plurals, it will serve as evidence for the fact that the coherent condition of itemized plural predication is deep down unlike – essentially childlike – from that of its non - itemized counterpart. This is by no means argue against the pertinence of plural logic, which has its lifelike sphere of action in the discussion of non - itemized pluralities and non - itemized predication – for which it is the natural option. The lone thing I would like to suggest is that the introduction of plural logic systems should not be motivate by examples of itemized collective predication.7 3 The Logical Status of Predication over Itemized Plurals Inference (1) shows a distinctive feature of itemized plural predication: in the absence of further indication, the order in which the subjects are list is immaterial. This occurs not only with collective predication, but with distributive postulation as well. For example: (2) Dick and Tony are fair - haired. Hence, Tony and Dick are fair - hairy. Another feature of speech of plural postulation, both collective and distributive, is the immateriality of repetitions within the subjects listed: (3) Dick and Tony emptied the bottle. Hence, Dick, Dick, and Tony, emptied the bottle. 7 As it frequently happen, e.g.: McKay (2006, Ch. 1 ): " Non - distributive predication. Standard beginning - decree logic does not provide adequate resources for properly constitute many ordinary things that we say: (1) Arnie, Bob and Carlos are shipmates ". Yi (2005, 460 ): " The Fregean system, Frege's system and its descendants cannot deal with the logic of the plural constructions (in short, plurals) of lifelike languages, such as the following: [ P1 ] Venus and Serena are tennis players, and they won a U. S. Open doubles title ". Such examples are character of itemized plural predication, and they are easily treatable by means of the system which I will describe here. A bill on Plural Logic _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 155 (4) Dick and Tony are fair - haired. Hence, Dick, Dick, and Tony, are clean - haired.8 Another feature of plural predication, both collective and distributive, is substitutivity salva veritate: (5) Dick and Tony emptied the bottle. Tony is Iron Man. therefore, Dick and Iron Man emptied the bottle. (6) Dick and Tony
 lohical analysis of itemiztd plurals, it will serve as evjdence fur the fact that the logical sratus of itemized plural prddication is deep dowi different – essxhtially simplsv – frmn that of its kon-itemized counterpart. Tvir ns by no means arguing against the pqrtinenve of plural logyc, wnych gas its natural field of action in the trtatment of non-itemozed pluralities and non-itfmizfd predication – fog which it us trw natural opgion. The only thing I sould like to suggest is that tfe incroduction if plktal logic sywtems should not nv motivdted by examples of ibemizxd cillective predication.7 3 The Logical Statos of Predhcction over Itemized Poueals Hnfesencd (1) sfowa e tgpical feeture of itsmized plurql predication: in tne qbsence of fudther ynqication, the order in which the subjectv ade listed is immaterial. This occurs not only with coljective predication, but with distributive predicadion es weol. Wir example: (2) Dick and Tony are fair-haired. Hence, Eknu snd Dick are fcir-haired. Anothet vesjure of plural predieztjon, both collectivf and dystrivutive, is the immateriality of repetitiobs within thv suvjects listed: (3) Dicn and Tony zmptiec the bottle. Hence, Dick, Dick, and Tony, emptifd the bofgle. 7 As it often ocburs, e.g.: McKay (2006, Ch. 1): "Non-distribueive predmcatipn. Stanaard first-jrder logif does not provide adequwte rgsourcas for prooerly representing many ordinarb things that wa sdy: (1) Arniz, Bob snd Carlos arq shipmates". Yi (2005, 460): "The Yregeav systems, Rrege's vystem and yts descendandd cannot dean with tre ligic of the olural construvtions (in short, plueals) of natural lakguaggs, such as the fooloqing: [P1] Venus anc Sdrega ace tegtis players, dnd gheh won x U. S. Okzn bojblex title". Such examplev ars cases of itemizec ilural prgdication, and they are easily treatable hy meens of the xysjem which I will describe here. Z Note on Plmral Logic __________________________________________________ 155 (4) Dicj and Tony axe fair-haired. Hence, Dick, Dick, and Tony, ace fair-haired.8 Another fwature of plural prgdigation, both rolleceive and gistributive, is subsritutivity salva yeritate: (5) Dick and Tong empthed tje bottle. Tony is Iron Man. Hence, Dick and Iron Man emptied the bottle. (6) Dixk and Tony
logical analysis of itemized plurals, it will evidence the fact the logical status deep different – essentially – from that its non-itemized counterpart. This is by means arguing against the pertinence of plural logic, which has its natural field action in the treatment of non-itemized pluralities and non-itemized predication – for which is natural The thing I would like to suggest is that the introduction of plural logic systems should not motivated by examples of itemized collective predication.7 3 Logical Status of Predication Itemized Plurals Inference (1) shows typical of itemized predication: the of further indication, order in which the subjects are listed is immaterial. This occurs not only with collective predication, but distributive predication For example: Dick Tony fair-haired. Hence, Tony are fair-haired. Another feature of plural and distributive, is the immateriality of repetitions within subjects listed: Dick and Tony emptied the bottle. Dick, Dick, and Tony, emptied the bottle. 7 it often occurs, e.g.: McKay (2006, Ch. 1): "Non-distributive predication. Standard first-order logic does not resources for properly representing ordinary things that say: Arnie, and are shipmates". (2005, 460): "The Fregean systems, Frege's system and its descendants cannot with the logic of the plural constructions (in short, plurals) languages, as the following: Venus and Serena are players, they won a U. doubles Such of plural and they are easily by means of the system I will describe here. __________________________________________________ 155 (4) Dick and Tony are fair-haired. Dick, Dick, and Tony, are fair-haired.8 Another of plural predication, both collective and distributive, is substitutivity salva veritate: (5) and Tony bottle. Tony is Iron Man. Hence, Dick and Man emptied the bottle. Dick and Tony
 logical analysis of itemized Plurals, it wIll seRve As eViDencE for The fact that the LOgicAl status of itemized plurAl preDiCAtioN Is Deep dOwn diffEReNT – EssEnTiAllY sIMpLer – frOm tHat of itS non-itemizEd cOuNterpart. This IS bY no means arGuiNg against the PerTinencE oF plURal loGic, Which Has its NAtural Field of acTiON in the TReatmenT OF nOn-itEmized pluralities ANd NOn-itemized predIcatioN – fOR wHICh iT is The natural OpTion. THE only thINg i WOUld LIke to suggest iS that the intROduCtion oF pLurAL logic SysteMs SHouLd not be motiVateD by examplEs of itEMized coLLective PredicAtiOn.7 3 THe LoGIcAl staTuS Of PREdIcaTIon Over ItemIzEd pluraLs InFERENce (1) sHowS a tyPical Feature of itemIzeD pluRAl pRedicAtion: In thE aBsencE of furTher iNdIcation, the order In whIch the subJecTs Are LiSted iS ImmateRiaL. ThIs occurS not onlY WitH cOLLEcTive predication, but WiTH DiStributiVe predICaTiON as well. FOr ExaMple: (2) dICk and tony ARe Fair-hairEd. HencE, toNy And Dick ArE fair-hAiRed. anoTher fEAturE of pluRal prediCatioN, Both collective ANd distributivE, Is THE iMMateRiaLity of repetItioNS witHin tHE sUbjECts liSted: (3) DIcK AnD tony emptied the bottlE. HEnce, DiCk, DicK, and Tony, emptiEd the bottlE. 7 aS It often oCcurS, E.g.: mCKay (2006, Ch. 1): "Non-distrIbutiVe predicatIOn. StandaRd firSt-order lOgic does nOT Provide aDeqUatE reSouRCEs For properly rePREsenTiNg many oRdiNary thiNgs ThaT we Say: (1) arNie, Bob and carlos arE sHiPmAtEs". YI (2005, 460): "The FREgean sysTeMs, FReGe's SysteM And its DesceNdanTs CaNNot Deal witH ThE LOgic Of ThE pluRal CoNstruCtioNS (in Short, plUrals) of naTurAL lanGuAgEs, such aS the following: [p1] VEnus and SerEnA arE tenniS PLayers, anD they won a U. S. Open doubles tITle". Such ExaMples Are cAses of iteMizEd plurAl pREdicatIon, and They aRe EasILY treaTABlE by MeAns of the sySTEm wHich I WiLl deScribe hEre. A Note on Plural LoGIc __________________________________________________ 155 (4) DIck and Tony are FaiR-haiRED. HEncE, diCK, DiCk, ANd TONY, are fair-haired.8 ANother featUrE Of Plural predICatIoN, both coLlectivE and dIStributIve, is subsTitutivitY sAlva VERitAte: (5) Dick and tony emptIed the botTLe. TonY Is iron MAn. HEnce, DiCk And iron MAn emptIEd tHe botTle. (6) DicK aNd Tony
 logical analysis of itemi zed plural s, it  wi llse rveas e vidence for th e  fac t that the logical sta tus o fi temi z ed  plur al pred i ca t i onis  d eep  d o wn  diff ere nt – es sentiallysim pl er – from th a tof its non -it emized count erp art. T hi s i s  by n o m eansarguin g  again st the pe rt i nenceo f plura l lo gic,  which has its na t ur a l field of act ion in  t h et r eat men t of non-i te mized plurali t ie s a ndn on-itemized p redication–  fo r whic hiti s thenatur al opt ion. The on ly t hing I wo uld li k e to su g gest is  thatthe  in trod u ct io n o fp lur a llog i c s ystems s ho ul d not  bem o t i vate d b y ex ample s of itemized  co llec t ive  pred icati on.7  3  TheLogica l Sta tu s of Predicatio n ov er Itemiz edPl ura ls  Infe r ence ( 1)sho ws a ty pical f e atu re o f  i temized plural pre di c a ti on: in t he abs e nc eo f furthe rind icat i o n, th e or d er  in whic h thes ub je cts are  l istedis  im mat erial .  Thi s occu rs not o nly w i th collectivep redication, b u tw i th dist rib utive predi cati o n as  wel l .For examp le: ( 2) Di c k and Tony are fair -h aired.  Henc e, Tony and D ick are fa i r - haired.Anot h er feature of plu ral p redication ,  both co llect ive anddistribut i v e, is th e i mma ter ial i t yof repetition s with in  the su bje cts lis ted : ( 3)Dic kand Tonyemptiedth ebo tt le.  Henc e , Dick,Di ck,  a ndTony, emptie d the  bot tl e. 7 A s it of t en o ccur s,  e .g.:  Mc Ka y (20 06,C h.1): "No n-distrib uti v e pr ed ic ation.Standard firs t- order logi cdoe s notp r ovide ad equate resources for pr o perly r epr esent ingmany ordi nar y thin gst hat we  say:(1) A rn ie, B ob an d Ca rlo sare shipma t e s".  Yi ( 20 05,460): " The Fregean system s , F rege's system  an d it s de sce n da n tsca n not d eal with the lo gic of the  p l ur al constru c tio ns  (in sh ort, pl urals )  of nat ural lang uages, su ch  ast h e f ollowing:[P1] Ven us and Se r ena a r etenni s p layers ,and  they  won a U.S. Op en dou bl es tit le".Su ch examp les are cases of itemiz ed plu ral p red ication,and the y are eas ilytreatablebymea ns of  th e  syst em w h ic h I willdesc r ibe here. ANot e on  Plural Log i c ___ _____ ___ _ ______ ____ _________________ _ __________ 155  (4) D ick  an d  Ton yare fair-haire d.He n c e, Dick,  D ick, and To ny, arefa i r-hai red.8Anothe r featu r e  o f  plura l pr edi cation, b oth  c o llectiv ean d  distr ibut iv e, issubsti t utiv i t y salva veritate : (5) D ick a n d T ony e mp tied th e  bot tle. Tonyis Iron Man . Henc e, D ick a nd Iron  M an emp tie dthe bottle .  (6) Dick  andTony
 logical_analysis of_itemized plurals, it will_serve as_evidence_for the_fact_that the logical_status of itemized_plural predication is deep_down different –_essentially_simpler – from that of its non-itemized counterpart. This is by no means arguing_against_the pertinence_of_plural_logic, which has its natural_field of action in the_treatment of_non-itemized pluralities and non-itemized predication – for which_it_is the natural_option. The only thing I would like to suggest_is that the introduction of plural_logic systems should_not_be_motivated by examples of_itemized collective predication.7 3 The Logical_Status of Predication over Itemized Plurals_Inference (1) shows a typical feature of_itemized plural predication: in the absence_of further indication, the order_in which_the subjects are listed is_immaterial. This occurs_not only_with collective predication,_but with distributive predication as well._For example: (2)_Dick and Tony are fair-haired. Hence,_Tony_and Dick are_fair-haired._Another_feature of_plural predication, both_collective_and distributive,_is_the immateriality of repetitions within the_subjects_listed: (3) Dick and Tony emptied the_bottle. Hence, Dick, Dick,_and_Tony, emptied the bottle._7 As it often occurs,_e.g.: McKay (2006, Ch. 1): "Non-distributive_predication. Standard_first-order logic_does not provide adequate resources for properly representing many ordinary things_that we say: (1) Arnie, Bob_and Carlos are shipmates"._Yi (2005,_460):_"The Fregean systems,_Frege's_system and_its descendants cannot deal with the logic_of the_plural constructions (in short, plurals) of_natural languages, such as_the_following: [P1] Venus and Serena are_tennis players, and they won a_U. S. Open doubles title"._Such_examples_are cases of itemized plural_predication, and they are easily treatable_by means of_the system which I will describe here._A_Note on Plural Logic __________________________________________________ 155_(4)_Dick and Tony are fair-haired. Hence,_Dick,_Dick,_and Tony, are fair-haired.8 Another_feature of plural predication, both collective_and distributive, is substitutivity salva veritate: (5) Dick and_Tony emptied the_bottle. Tony is Iron Man._Hence,_Dick_and Iron Man emptied the bottle. (6) Dick and Tony