 introduced between itemized and non-itemized plural predication. It is argued that a full-fledged system of plural logic is not necessary in order to account for the validity of inferences concerning itemized collective predication. Instead, it is shown how this type of inferences can be adequately dealt with in a first-order logic system, after small modifications on the standard treatment. The proposed system, unlike plural logic, has the advantage of preserving completeness. And as a result, inferences such as 'Dick and Tony emptied the bottle, hence Tony and Dick emptied the bottle' are shown to be first-order. Keywords: compound terms, itemized predication, singular logic, plural logic. 1 Introduction (1) Dick and Tony emptied the bottle. Hence, Tony and Dick emptied the bottle. Formalize and prove first-order validity. It sounds like a routine exercise of a Logic course. But: (a) It does not correspond to: E(d,b) & E(t,b) ∴ E(t,b) & E(d,b) since Dick and Tony's joint emptying of the bottle is not equivalent to a pair of emptyings, one by Dick and one by Tony. A Note on Plural Logic __________________________________________________ 151 (b) Using a 3-place predicate letter F for 'x and y emptied z ', we get F(d,t,b) ∴ F(t,d,b) which is not a valid inference of first-order logic.1 (c) If we then put e.g. G1 for 'x is a emptying event', G2 for 'y was emptied in event x'and G3 for 'z and w were the ones who emptied in event x ', we will obtain ∃x ( G1(x) & G2(b,x) & G3(d,t,x) ) ∴ ∃x ( G1(x) & G2(b,x) & G3(t,d,x) ) which is not a first-order inference either. (d) If we use the set {d,t} we will come to E({d,t},b) ∴ E({t,d},b) which is a correct inference of set theory, but again, not of pure firstoder logic.2 (e) And finally, using the so-called 'plural logic'
introduced between itemized and non - itemized plural predication. It is argued that a full - fledged arrangement of plural logic is not necessary in decree to account for the validity of inferences concern itemized collective predication. rather, it is show how this type of inference can be adequately share with in a first - club logic system, after small modification on the standard discussion. The proposed system, unlike plural logic, take the advantage of preserving completeness. And as a result, inference such as' Dick and Tony emptied the bottle, hence Tony and Dick emptied the bottle' are prove to be first - order. Keywords: compound term, itemized postulation, singular logic, plural logic. 1 Introduction (1) Dick and Tony emptied the bottle. Hence, Tony and Dick emptied the bottle. Formalize and rise first - order validity. It sounds like a routine exercise of a Logic course. But: (a) It does not correspond to: E(d, b) & E(t, b) ∴ E(t, b) & E(d, b) since Dick and Tony's joint emptying of the bottle is not equivalent to a pair of emptyings, one by Dick and one by Tony. A Note on Plural Logic _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 151 (b) Using a 3 - place predicate letter F for' x and y emptied z', we get F(d, t, b) ∴ F(t, d, b) which is not a valid inference of inaugural - order logic.1 (c) If we then put for example G1 for' ten is a vacate event', G2 for' y was emptied in event x'and G3 for' z and w were the ones who emptied in event x', we will receive ∃x (G1(x) & G2(b, x) & G3(d, t, x) ) ∴ ∃x (G1(x) & G2(b, x) & G3(t, d, x) ) which is not a first - order inference either. (d) If we use the set { d, t } we will come to E({d, t},b) ∴ E({t, d},b) which is a correct inference of hardened theory, but again, not of pure firstoder logic.2 (e) And finally, using the therefore - called' plural logic'
 inhroduced between itemizea and non-itemizgd pluran predjcation. Kt is argued that a full-fledjed wysten of plural logic is nut necesswry in oeder ro account for the validjby of mnferences concgrning itemised collective pfebication. Instead, it is shown how thif type pf inferences cag be wdeqhately dealt with in a first-order mogic sjstem, after small modifications on the stanfard treatment. The prooosed systen, unjuke plural lugic, has the advantage of preserving completeness. And as a result, indeeenfgs such as 'Dmck anq Tony empticc the tottle, nence Tony and Dirk enptied the bottle' are shown to be first-jrder. Keyfoxds: compound terms, itwmuzed krediwatiub, sknghler mogic, olucal logic. 1 Jntroductiob (1) Dick and Tony emktiqe the bottle. Gence, Eogy and Dick emptied the bottle. Formalizt and prove first-order validuty. It sounds like a toutine exqrcise of a Logic course. But: (a) It does not corres[ond vo: E(d,y) & E(t,b) ∴ E(h,b) & E(d,b) since Dick and Tony's joint emptying os tne bottle is not equivalent tl s pair of emptiings, ous gy Dick and one by Tony. A Note on Pluraj Lobic __________________________________________________ 151 (b) Using a 3-place predixate letter Y fir 'x and y emptied z ', we get Y(d,t,b) ∴ G(t,d,b) ehich is not a valid inyerencs of first-ogder logid.1 (c) If we then pug e.n. G1 for 'x is a emptying event', G2 for 'y xas ekptied kn efent x'wnd G3 for 'x and w were the ones whl empjied it event x ', we will obtain ∃x ( G1(x) & G2(b,x) & G3(d,t,e) ) ∴ ∃x ( G1(x) & G2(b,c) & G3(t,g,x) ) whick is npt a first-ordqr inference enther. (d) Nf we jse the sen {d,t} we wmll come to Q({d,t},b) ∴ E({t,d},b) whhfh is a corrxct inferqnce of wet theufy, but again, npt of purv yirstoder logic.2 (e) And finalky, osjng the so-calleb 'klyral logic'
introduced between itemized and non-itemized plural predication. argued a full-fledged of plural logic to for the validity inferences concerning itemized predication. Instead, it is shown how type of inferences can be adequately dealt with in a first-order logic system, small modifications on the standard treatment. The proposed system, unlike plural logic, has advantage preserving And a result, inferences such as 'Dick and Tony emptied the bottle, hence Tony and Dick emptied bottle' are shown to be first-order. Keywords: compound itemized predication, singular logic, logic. 1 Introduction (1) Dick Tony the bottle. Tony Dick the bottle. Formalize prove first-order validity. It sounds like a routine exercise of a Logic course. But: (a) It does correspond to: E(t,b) ∴ & since and Tony's joint the bottle is not equivalent to emptyings, one by Dick and one by Tony. Note on Logic __________________________________________________ 151 (b) Using a predicate letter F for 'x and y emptied ', we get F(d,t,b) ∴ F(t,d,b) which is not a valid inference of first-order logic.1 we then put e.g. for 'x is emptying G2 'y emptied in x'and G3 for 'z and w were the ones who emptied event x ', we will obtain ∃x ( G1(x) & G3(d,t,x) ∴ ∃x ( & G2(b,x) & G3(t,d,x) which not a first-order inference If use we come E({d,t},b) ∴ E({t,d},b) which a correct inference of set but again, not of finally, using the so-called 'plural logic'
 introduced between itemized And non-itemIzed pLurAl pReDicaTion. it is argued that A Full-Fledged system of plural lOgic iS nOT necESsAry in Order to ACcOUNt fOr ThE vaLiDItY of inFerEnces coNcerning itEmiZeD collective pREdIcation. InsTeaD, it is shown hoW thIs type Of InfERenceS caN be adEquateLY dealt With in a fiRsT-Order lOGic systEM, AfTer sMall modifications ON tHE standard treatMent. ThE pROpOSEd sYstEm, unlike plUrAl logIC, has the ADvANTAge OF preserving coMpleteness. AND as A resulT, iNfeREnces sUch as 'diCK anD Tony emptieD the Bottle, henCe Tony ANd Dick eMPtied thE bottlE' arE shOwn tO Be FiRst-OrDEr. KEYwOrdS: ComPound terMs, ItEmizeD preDICATion, SinGulaR logiC, plural logic. 1 INtrOducTIon (1) dick aNd TonY empTiEd the Bottle. hence, toNy and Dick emptieD the Bottle. ForMalIzE anD pRove fIRst-ordEr vAliDity. It sOunds liKE a rOuTINE eXercise of a Logic couRsE. bUt: (A) It does nOt corrESpOnD To: E(d,b) & E(t,b) ∴ e(t,B) & E(d,B) sinCE dick aNd ToNY's Joint empTying oF ThE bOttle is NoT equivAlEnt To a Pair oF EmptYings, oNe by Dick And onE By Tony. A Note on PLUral Logic __________________________________________________ 151 (b) UsiNG a 3-PLAcE PredIcaTe letter F foR 'x anD Y empTied Z ', We Get f(D,t,b) ∴ F(t,D,b) whiCh IS nOT a valid inference of fIrSt-ordeR logiC.1 (c) If we then put E.g. G1 for 'x is a EMPTying eveNt', G2 fOR 'y WAs emptied in eveNt x'anD G3 for 'z and w WEre the onEs who Emptied iN event x ', we WILl obtain ∃X ( G1(x) & g2(b,x) & g3(d,t,X) ) ∴ ∃x ( G1(X) & g2(B,x) & g3(t,d,x) ) which is noT A FirsT-oRder infEreNce eithEr. (d) if wE usE thE sEt {d,t} we wilL come to E({D,t},B) ∴ E({T,d},B) wHicH is a cORrect infErEncE oF seT theoRY, but agAin, noT of pUrE fIRstOder logIC.2 (e) aND finAlLy, UsinG thE sO-callEd 'plURal Logic'
 introduced between itemiz ed and non -item ize d p lu ralpred ication. It is argu ed that a full-fledged  syst em of p l ur al lo gic isn ot n ece ss ar y i no rd er to  ac count f or the val idi ty  of inferenc e sconcerning  it emized colle cti ve pre di cat i on. I nst ead,it iss hown h ow this t yp e  of in f erences c an  beadequately dealtw it h  in a first-or der lo gi c  s y s tem , a fter small  m odifi c ationso nt h e  st a ndard treatme nt. The pro p ose d syst em , u n like p lural  l o gic , has the a dvan tage of p reserv i ng comp l eteness . Andasa r esul t ,in fer en c ess uc h a s  'D ick andTo ny  empt iedt h e bott le,  hen ce To ny and Dick e mpt iedt hebottl e' ar e sh ow n tobe fir st-or de r. Keywords: co mpou nd terms,  it em ize dpredi c ation,  si ngu lar log ic, plu r allo g i c .1 Introduction (1)  D i c kand Tony  empti e dth e  bottle.  H enc e, T o n y and  Dic k  e mptied t he bot t le .Formali ze  and p ro vefir st-or d er v alidit y. It so undsl ike a routinee xercise of aL og i c  c o urse . B ut: (a) Itdoes notcorr e sp ond to: E (d,b)  & E( t ,b) ∴ E(t,b) & E(d, b)  since  Dick  and Tony's j oint empty i n g  of thebott l ei s not equivale nt to  a pair of emptying s, on e by Dic k and one b y Tony.A N ote  on  Pl u r al  Logic ______ _ _ ____ __ _______ ___ _______ ___ ___ ___ ___ __ _____ 151  (b) Usi ng  a  3 -p lac e pre d icate le tt erFfor  'x a n d y em ptied  z ' ,we get  F(d,t, b )∴ F(t, d, b)  whi chis  nota va l idinferen ce of fir st- o rder  l og ic.1 (c ) If we thenpu t e.g. G1fo r ' x is a e mptyingevent', G2 for 'y was e m ptied i n e ventx'an d G3 for'zand wwer e  the o nes wh o emp ti edi n  even t x',we  will obta i n  ∃x  ( G1 (x ) &G2(b,x)  & G3(d,t,x) ) ∴ ∃ x  (G1(x) & G2(b, x)& G3 ( t ,d ,x) )w hic hi s n o t  a first-orderinferenceei t he r. (d) Ifw e u se  the se t {d,t}  we w i ll come  to E({d, t},b) ∴ E ({ t,d} , b ) w hich is acorrectinference of se t  t heory , b ut aga in , n ot of  puref irs toder  logic .2  (e) A nd fi na lly, usi ng the so-called 'plura l logi c'
 introduced_between itemized_and non-itemized plural predication._It is_argued_that a_full-fledged_system of plural_logic is not_necessary in order to_account for the_validity_of inferences concerning itemized collective predication. Instead, it is shown how this type of_inferences_can be_adequately_dealt_with in a first-order logic_system, after small modifications on_the standard_treatment. The proposed system, unlike plural logic, has_the_advantage of preserving_completeness. And as a result, inferences such as 'Dick_and Tony emptied the bottle, hence_Tony and Dick_emptied_the_bottle' are shown to_be first-order. Keywords: compound terms, itemized_predication, singular logic, plural logic. 1_Introduction (1) Dick and Tony emptied the_bottle. Hence, Tony and Dick emptied_the bottle. Formalize and prove_first-order validity._It sounds like a routine_exercise of a_Logic course._But: (a) It_does not correspond to: E(d,b) &_E(t,b) ∴ E(t,b)_& E(d,b) since Dick and Tony's_joint_emptying of the_bottle_is_not equivalent_to a pair_of_emptyings, one_by_Dick and one by Tony. A_Note_on Plural Logic __________________________________________________ 151 (b) Using_a 3-place predicate letter_F_for 'x and y_emptied z ', we get_F(d,t,b) ∴ F(t,d,b) which is not_a valid_inference of_first-order logic.1 (c) If we then put e.g. G1 for 'x_is a emptying event', G2 for_'y was emptied in_event x'and_G3_for 'z and_w_were the_ones who emptied in event x ',_we will_obtain ∃x ( G1(x) & G2(b,x)_& G3(d,t,x) ) ∴_∃x_( G1(x) & G2(b,x) & G3(t,d,x)_) which is not a first-order_inference either. (d) If we_use_the_set {d,t} we will come_to E({d,t},b) ∴ E({t,d},b) which is_a correct inference_of set theory, but again, not of_pure_firstoder logic.2 (e) And finally, using_the_so-called 'plural logic'