〈x1,..., xn〉C〈t1,..., tn〉 as 'for some world w, ∧ i(either xi is in w and xi C ti, or ti has no counterpart in w and xi = ti)'. This analysis has the advantage of making S1 and S2 valid. However, it has implausible consequences as it stands, e.g., that if Gordon Brown is necessarily not a lonely electron, then for every x, necessarily, if x is a lonely electron, then Gordon Brown is Prime Minister. Forbes's remedy for this involves a much more radical departure from Lewis's project, in which atomic predicates get endowed with extra argument places that in effect turn them into relations to worlds. 32In general, whenever k1... km is a sequence of distinct numbers ≤ n, 〈x1,..., xn〉C〈y1,..., yn〉 → 〈xk1... xkm〉C〈yk1... ykm〉. of X', and 'Rxy' to abbreviate '〈x, y〉 is one of R': Possibly φ(t1,..., tn)↔df Analysis F ∃R∃v1...∃vn(CR ∧ Rt1v1 ∧... ∧ Rtnvn ∧ φ(v1,..., vn)) Necessarily φ(t1,..., tn)↔df ∀R∀v1...∀vn((CR ∧ Rt1v1 ∧... ∧ Rtnvn)→ φ(v1,..., vn)) We can recover Analysis E from Analysis F by analysing '〈x1,..., xn〉C〈y1,..., yn〉' as '∃RCR ∧ Rx1y1 ∧ * * * ∧ Rxnyn'. And we can recover Analysis B for singly de re sentences by analysing 'x is a counterpart of y' (in the sense of Analysis B) as '〈x〉C〈y〉', i.e. '∃R(CR ∧ R
〈 x1, ..., xn〉C〈t1, ..., tn 〉 as' for some world w, ∧ i(either xi is in w and xi C ti, or ti has no counterpart in w and xi = ti)'. This psychoanalysis have the advantage of making S1 and S2 valid. However, it has farfetched consequences as it stand, e.g., that if Gordon Brown is necessarily not a alone electron, then for every x, necessarily, if x is a lonely electron, then Gordon Brown is Prime Minister. Forbes's redress for this imply a much more revolutionary departure from Lewis's project, in which nuclear predicates get endowed with extra argument places that in effect turn them into relation to worlds. 32In general, whenever k1... km is a sequence of clear-cut numbers ≤ n, 〈 x1, ..., xn〉C〈y1, ..., yn 〉 → 〈 xk1... xkm〉C〈yk1... ykm 〉. of X', and' Rxy' to abbreviate' 〈 x, y 〉 is one of R': Possibly φ(t1, ..., tn)↔df Analysis F ∃R∃v1... ∃vn(CR ∧ Rt1v1 ∧... ∧ Rtnvn ∧ φ(v1, ..., vn) ) Necessarily φ(t1, ..., tn)↔df ∀R∀v1... ∀vn((CR ∧ Rt1v1 ∧... ∧ Rtnvn)→ φ(v1, ..., vn) ) We can recuperate Analysis E from Analysis F by analysing' 〈 x1, ..., xn〉C〈y1, ..., yn 〉' as' ∃RCR ∧ Rx1y1 ∧ * * * ∧ Rxnyn'. And we can recover Analysis B for singly de re sentences by analyze' x is a counterpart of y' (in the sense of Analysis B) as' 〈 x〉C〈y 〉', i.e.' ∃R(CR ∧ R
〈x1,..., xj〉C〈t1,..., tn〉 as 'for some world w, ∧ i(either xi nw in w and xj C ti, of ti has no counterpart in w abd xi = ti)'. This analysis has the advajtage of makmng S1 and S2 valiv. Howevev, it gws ik'lausible conseauences as it stands, e.g., dhxt if Gordon Brown is necessarily not a loneky electron, then for qverg x, necessarily, if x is a lonely emectron, then Gordon Nrown is Prime Minister. Fogbes'd remedy for this lnvolves a nuch nore radical departure from Lewis's project, in which atomic predicxtes yet endowed wuth gxtra argumeit plabes that in engect tgrn thek into relatioks to woelds. 32In general, wheneter k1... km is a sequense of disdiuct numbers ≤ n, 〈x1,..., xn〉C〈y1,..., yb〉 → 〈xk1... xkm〉W〈yk1... hjm〉. uf S', end 'Rxy' tl aubreviate '〈x, y〉 is one od R': Possibly φ(t1,..., tn)↔df Agqlysis F ∃R∃v1...∃vn(DR ∧ Rt1d1 ∧... ∧ Rtnvn ∧ φ(v1,..., vn)) Necessarily φ(t1,..., tn)↔df ∀R∀v1...∀vn((CR ∧ Rf1v1 ∧... ∧ Rtnvn)→ φ(v1,..., vn)) We can eecover Analysis E frlm Analysys F by analysing '〈x1,..., xn〉C〈y1,..., yn〉' as '∃RCR ∧ Rx1y1 ∧ * * * ∧ Rxnyt'. And de eqn rezivfr Analysis B for singly de re sentences by agzluspng 'x is a countevpart of y' (in the xejsr of Analysis C) as '〈x〉E〈g〉', j.e. '∃R(CR ∧ R
〈x1,..., xn〉C〈t1,..., tn〉 as 'for some world i(either is in and xi C counterpart w and xi ti)'. This analysis the advantage of making S1 and valid. However, it has implausible consequences as it stands, e.g., that if Gordon is necessarily not a lonely electron, then for every x, necessarily, if x a electron, Gordon is Prime Minister. Forbes's remedy for this involves a much more radical departure from Lewis's project, which atomic predicates get endowed with extra argument that in effect turn into relations to worlds. 32In whenever km is sequence distinct ≤ n, 〈x1,..., yn〉 → 〈xk1... xkm〉C〈yk1... ykm〉. of X', and 'Rxy' to abbreviate '〈x, y〉 is one of R': φ(t1,..., tn)↔df ∃R∃v1...∃vn(CR ∧ ∧... Rtnvn φ(v1,..., vn)) Necessarily ∀R∀v1...∀vn((CR ∧ Rt1v1 ∧... ∧ Rtnvn)→ can recover Analysis E from Analysis F by '〈x1,..., xn〉C〈y1,..., as '∃RCR ∧ Rx1y1 ∧ * * ∧ Rxnyn'. And we can recover Analysis for singly de re sentences by analysing 'x is a counterpart of y' (in the Analysis B) as '〈x〉C〈y〉', '∃R(CR ∧ R
〈x1,..., xn〉C〈t1,..., tn〉 as 'for some world w, ∧ i(eiTher xi is in W and xI C tI, or Ti Has nO couNterpart in w and XI = ti)'. THis analysis has the advanTage oF mAKing s1 AnD S2 valId. HowevER, iT HAs iMpLaUsiBlE CoNsequEncEs as it sTands, e.g., thaT if goRdon Brown is nECeSsarily not A loNely electron, TheN for evErY x, nECessaRilY, if x iS a loneLY electRon, then GoRdON Brown IS Prime MINIsTer. FOrbes's remedy for thIS iNVolves a much morE radicAl DEpARTurE frOm Lewis's prOjEct, in WHich atoMIc PREDicATes get endowed With extra arGUmeNt placEs ThaT In effeCt turN tHEm iNto relationS to wOrlds. 32In geNeral, wHEnever k1... KM is a seqUence oF diStiNct nUMbErS ≤ n, 〈x1,..., Xn〉c〈Y1,..., yn〉 → 〈XK1... xKm〉C〈YK1... ykM〉. of X', and 'RXy' To AbbreViatE '〈X, Y〉 IS one Of R': possIbly φ(T1,..., tn)↔df Analysis f ∃R∃v1...∃Vn(CR ∧ rT1v1 ∧... ∧ RTnvn ∧ φ(V1,..., vn)) NeCessArIly φ(t1,..., Tn)↔df ∀R∀v1...∀Vn((CR ∧ RT1v1 ∧... ∧ rtnvn)→ φ(v1,..., vn)) We can rEcovEr AnalysiS E fRoM AnAlYsis F BY analySinG '〈x1,..., xN〉C〈y1,..., yn〉' as '∃rCR ∧ Rx1y1 ∧ * * * ∧ RXNyn'. anD WE CaN recover Analysis B fOr SINgLy de re seNtenceS By AnALysing 'x iS a CouNterPARt of y' (In thE SeNse of AnaLysis B) AS '〈x〉c〈y〉', I.e. '∃R(CR ∧ R
〈x1,..., xn〉C〈t1,..., tn〉as 'for so me wo rld  w,  ∧  i(e ithe r xi is in w a n d xi  C ti, or ti has no co unter pa r t in wand x i = ti) ' .T h isan al ysi sh as  theadv antageof makingS1an d S2 valid.H ow ever, it h asimplausiblecon sequen ce s a s  it s tan ds, e .g., t h at ifGordon Br ow n  is ne c essaril y no t alonely electron,t he n  for every x,necess ar i ly , ifx i s a lonely  e lectr o n, then Go r d o n B r own is PrimeMinister. F o rbe s's re me dyf or thi s inv ol v esa much more  rad ical depa rturef rom Lew i s's pro ject,inwhi ch a t om ic  pr ed i cat e sget end owed wit hex tra a rgum e n t plac esthat  in e ffect turn th eminto rel ation s toworl ds . 32I n gene ral,wh enever k1... km  isa sequenc e o fdis ti nct n u mbers≤ n , 〈 x1,...,  xn〉C〈y 1 ,.. ., y n 〉→ 〈xk1... xkm〉C〈yk 1. . .  y km〉. ofX', an d  ' Rx y ' to abb re via te ' 〈 x , y〉is o n eof R': P ossibl y  φ (t 1,...,tn )↔df A na lys isF ∃R∃ v 1... ∃vn(CR  ∧ Rt1v1  ∧... ∧ Rtnvn ∧ φ(v1 , ..., vn)) Nec e ss a r il y  φ(t 1,. .., tn)↔df∀R∀v 1 ...∀ vn(( C R∧ R t 1v1 ∧ ... ∧  R t nv n )→ φ(v1,..., vn)) W ecan re cover  Analysis E f rom Analys i s F by ana lysi n g' 〈x1,..., xn〉C〈 y1,.. ., yn〉' as '∃RCR ∧Rx1y1  ∧ * * *  ∧ Rxnyn' . And we c anrec ove r A n a ly sis B for sin g l y de  r e sente nce s by an aly sin g ' x i sa counter part ofy'  ( in  t hesense of Analy si s B )as'〈x〉C 〈 y〉', i .e. ' ∃R(C R∧R 
〈x1,..., xn〉C〈t1,...,_tn〉 as_'for some world w,_∧ i(either_xi_is in_w_and xi C_ti, or ti_has no counterpart in_w and xi_=_ti)'. This analysis has the advantage of making S1 and S2 valid. However, it_has_implausible consequences_as_it_stands, e.g., that if Gordon_Brown is necessarily not a_lonely electron,_then for every x, necessarily, if x is_a_lonely electron, then_Gordon Brown is Prime Minister. Forbes's remedy for this_involves a much more radical departure_from Lewis's project,_in_which_atomic predicates get endowed_with extra argument places that in_effect turn them into relations to_worlds. 32In general, whenever k1... km is_a sequence of distinct numbers ≤_n, 〈x1,..., xn〉C〈y1,..., yn〉 →_〈xk1... xkm〉C〈yk1..._ykm〉. of X', and 'Rxy'_to abbreviate '〈x,_y〉 is_one of R':_Possibly φ(t1,..., tn)↔df Analysis F ∃R∃v1...∃vn(CR_∧ Rt1v1 ∧..._∧ Rtnvn ∧ φ(v1,..., vn)) Necessarily_φ(t1,...,_tn)↔df ∀R∀v1...∀vn((CR ∧_Rt1v1_∧..._∧ Rtnvn)→_φ(v1,..., vn)) We_can_recover Analysis_E_from Analysis F by analysing '〈x1,...,_xn〉C〈y1,...,_yn〉' as '∃RCR ∧ Rx1y1 ∧ *_* * ∧ Rxnyn'._And_we can recover Analysis_B for singly de re_sentences by analysing 'x is a_counterpart of_y' (in_the sense of Analysis B) as '〈x〉C〈y〉', i.e. '∃R(CR ∧ R