emporal in character; this hypothesis entails that our Lewis-world is strongly isolated. claiming that every object has at least one counterpart in every Lewisworld. (The same is easily seen to be true for S2.) But such a requirement would generate wildly implausible assignments of truth values to other sentences. For example, consider a tiny Lewis-world w with no proper parts: w is in w, but nothing else is. The requirement would force w to be a counterpart of absolutely everything; and that would make it true that everything could have been a spatiotemporally isolated mereological atom. While this may be true in some exotic contexts, it is surely not true across all legitimate contexts, unlike S1. In the 1983 postscripts to Lewis 1968 and in OPW, Lewis proposed an elegant solution to some of the problems with Analysis C. According to this proposal, the analysis of multiply de re modal claims involves a relation of counterparthood holding between sequences.30 Here is a statement of this analysis, incorporating the insight that there is no need to include any special-purpose machinery for restricting quantifiers: Possibly φ(t1,..., tn)↔df Analysis E ∃v1...∃vn(〈v1,..., vn〉C〈t1,..., tn〉 ∧ φ(v1,..., vn)) Necessarily φ(t1,..., tn)↔df ∀v1...∀vn(〈v1,..., vn〉C〈t1,..., tn〉 → φ(v1,..., vn)) Analysis E is strictly more general than Analysis C. If we wanted to recover the effect of Analysis C in some context, we could do so by analysing the counterpart relation on sequences in terms of a counterpart relation on objects: 30In postscript D to the reprint of Lewis 1968, Lewis presents the "counterparts of sequences" account not as a modification of the original 1968 translation from the formal modal language to the language of counterpart theory, but as an alternative to the obvious translation from English into the formal modal language. His idea is that the English sentence 'It is possible that Dee and Dum are unrelated' should be rendered formally as something like '∃z(z = 〈Dee,Dum�
emporal in character; this hypothesis entails that our Lewis - world is powerfully apart. claiming that every object experience at least one counterpart in every Lewisworld. (The like is easily seen to be true for S2 .) But such a necessity would generate wildly implausible assignment of truth values to early sentences. For example, consider a tiny Lewis - populace w with no proper parts: w is in w, but nothing else is. The requirement would force w to be a counterpart of absolutely everything; and that would make it truthful that everything could have been a spatiotemporally isolated mereological atom. While this may be true in some exotic context, it is surely not true across all legitimate contexts, unlike S1. In the 1983 postscripts to Lewis 1968 and in OPW, Lewis propose an elegant solution to some of the problems with Analysis C. According to this proposal, the analysis of multiply de re modal claims involve a relation of counterparthood holding between sequences.30 Here is a statement of this analysis, incorporating the insight that there is no need to include any special - purpose machinery for restricting quantifiers: Possibly φ(t1, ..., tn)↔df Analysis E ∃v1... ∃vn(〈v1, ..., vn〉C〈t1, ..., tn 〉 ∧ φ(v1, ..., vn) ) Necessarily φ(t1, ..., tn)↔df ∀v1... ∀vn(〈v1, ..., vn〉C〈t1, ..., tn 〉 → φ(v1, ..., vn) ) Analysis E is strictly more cosmopolitan than Analysis C. If we desire to recover the impression of Analysis C in some context, we could cause so by analysing the counterpart relation on sequence in term of a counterpart relation on objects: 30In addendum D to the reprint of Lewis 1968, Lewis presents the " counterparts of sequences " account not as a modification of the original 1968 translation from the formal modal language to the language of counterpart theory, but as an option to the obvious translation from English into the courtly modal linguistic process. His idea is that the English sentence' It is possible that Dee and Dum are unrelated' should be rendered formally as something like' ∃z(z = 〈 Dee, Dum �
emplral in character; this hnpothesis entails that mur Lesis-world is strongly isolated. claimiig tyat ecery object has at leart one colnterpart in tvery Lewisworld. (Vge same is eaally szei to be true fot S2.) But such a requirement wuupd generate wildly implausible assidnments ov truth values to peher sentences. For example, consider a finy Lexis-world w with no proper parts: w is in w, but nothing else is. Tje requiremght riuld force w to be a counterpart or absolutely everything; and thag woukd make it teue jhat everythmng colld have been a spatimtemporslly isolated kerxolotical atom. While this may be true in soie exotic ckntexts, it is surwlt not trua acfiss alm kefitimahe rontexts, unmike S1. In tye 1983 postscripts to Kerpx 1968 and in OPS, Lewif [roposed an elegant solution to some of ths problems with Analysiw C. According to this proposal, the analysis of multiply de re modal claims invonves e felcblon ud founterparthood holding between sequences.30 Herq ix s statement of this analyxid, ogcorporating jhe insnfhf that there is no need tj incoude any fpecoal-purpose machinery for rewtricting qucntufiers: Possibly φ(t1,..., cn)↔df Analysir E ∃f1...∃vn(〈v1,..., fn〉C〈t1,..., tn〉 ∧ φ(v1,..., vn)) Necessariuy φ(t1,..., tn)↔df ∀v1...∀vn(〈v1,..., gn〉C〈t1,..., tn〉 → φ(b1,..., vn)) Analysis E ir snricdly more general than Analrsis C. If we canted tu revover ehe effect of Akdlysis C in some clntexj, we cmuld do so by analysing the counterpart rxkation on seauancvs in teris of a counterpare relation on pbjects: 30In pustscript S to thx reprint of Lewis 1968, Lewis kresents the "rounterpawts if swquencer" account not ax a modifpcction of rhe original 1968 tranxlajikn from the fornal modal language to thq paiguagq of counterpdrt gheuty, bug as an altcrnxtivr to the obvious tratslafion from English onbo the fotmal modaj language. Hix idea is that the Englmsh seitence 'It is possible that Dee and Dum zre unrelwteq' should be wendcred formally cs something like '∃z(z = 〈Dee,Dum�
emporal in character; this hypothesis entails that is isolated. claiming every object has every (The same is seen to be for S2.) But such a requirement generate wildly implausible assignments of truth values to other sentences. For example, consider tiny Lewis-world w with no proper parts: w is in w, but nothing is. requirement force to be a counterpart of absolutely everything; and that would make it true that everything could been a spatiotemporally isolated mereological atom. While this be true in some contexts, it is surely not across legitimate contexts, S1. the postscripts to Lewis and in OPW, Lewis proposed an elegant solution to some of the problems with Analysis C. According this proposal, of multiply re claims a relation of between sequences.30 Here is a statement incorporating the insight that there is no need include any machinery for restricting quantifiers: Possibly φ(t1,..., Analysis E ∃v1...∃vn(〈v1,..., vn〉C〈t1,..., tn〉 ∧ φ(v1,..., vn)) φ(t1,..., tn)↔df ∀v1...∀vn(〈v1,..., vn〉C〈t1,..., tn〉 → φ(v1,..., vn)) Analysis E is strictly more general than If we wanted to the effect of C some we do so analysing the counterpart relation on sequences in terms of a counterpart on objects: 30In postscript D to the reprint of Lewis presents "counterparts of sequences" not as a modification the 1968 translation from the language the theory, as alternative to the obvious from English into the formal language. His idea is is possible that Dee and Dum are unrelated' be rendered formally as something like '∃z(z 〈Dee,Dum�
emporal in character; this hypOthesis entAils tHat Our leWis-wOrld Is strongly isolATed. cLaiming that every object Has at LeASt onE CoUnterPart in eVErY lEwiSwOrLd. (THe SAmE is eaSilY seen to Be true for S2.) but SuCh a requiremeNT wOuld generaTe wIldly implausIblE assigNmEntS Of truTh vAlues To otheR SentenCes. For exaMpLE, consiDEr a tiny lEWiS-worLd w with no proper paRTs: W Is in w, but nothinG else iS. THE rEQUirEmeNt would forCe W to be A CounterPArT OF AbsOLutely everythIng; and that wOUld Make it TrUe tHAt everYthinG cOUld Have been a spAtioTemporallY isolaTEd mereoLOgical aTom. WhiLe tHis May bE TrUe In sOmE ExoTIc ConTExtS, it is surElY nOt truE acrOSS ALl leGitImatE contExts, unlike S1. In The 1983 PostSCriPts to lewis 1968 And iN OpW, LewIs propOsed aN eLegant solution tO somE of the proBleMs WitH ANalysIS C. AccoRdiNg tO this prOposal, tHE anAlYSIS oF multiply de re modal ClAIMs Involves A relatIOn Of COunterpaRtHooD holDINg betWeen SEqUences.30 HeRe is a sTAtEmEnt of thIs AnalysIs, IncOrpOratiNG the InsighT that theRe is nO Need to include aNY special-purpoSE mACHiNEry fOr rEstricting qUantIFierS: PosSIbLy φ(T1,..., Tn)↔df ANalysIs e ∃V1...∃vN(〈V1,..., vn〉C〈t1,..., tn〉 ∧ φ(v1,..., vn)) NecessarIlY φ(t1,..., tn)↔dF ∀v1...∀vn(〈v1,..., Vn〉C〈t1,..., tn〉 → φ(v1,..., vn)) AnaLysis E is stRICTly more gEnerAL tHAn Analysis C. If wE wantEd to recoveR The effecT of AnAlysis C iN some contEXT, we could Do sO by AnaLysING tHe counterpart RELatiOn On sequeNceS in termS of A coUntErpArT relation On objectS: 30IN pOsTsCriPt D to THe reprinT oF LeWiS 1968, LeWis prESents tHe "couNterPaRtS Of sEquenceS" AcCOUnt nOt As A modIfiCaTion oF the ORigInal 1968 traNslation fRom THe foRmAl Modal laNguage to the laNgUage of counTeRpaRt theoRY, But as an aLternative to the obvious tRAnslatiOn fRom EnGlisH into the fOrmAl modaL laNGuage. HIs idea Is thaT tHe ENGLish sENTeNce 'it Is possible THAt DEe and duM are UnrelatEd' should be rendered FOrmAlly as somethiNg lIke '∃z(Z = 〈dEe,dum�
emporal in character; this  hypothesi s ent ail s t ha t ou r Le wis-world is s t rong ly isolated. claimingthatev e ry o b je ct ha s at le a st o neco un ter pa r tin ev ery  Lewisw orld. (The  sa me  is easily s e en  to be tru e f or S2.) Butsuc h a re qu ire m ent w oul d gen eratew ildlyimplausib le assign m ents of t ru th v alues to other se n te n ces. For examp le, co ns i de r a t iny  Lewis-wor ld  w wi t h no pr o pe r p art s : w is in w,but nothing els e is.Th e r e quirem ent w ou l d f orce w to b e acounterpa rt ofa bsolute l y every thing;  an d t hatw ou ld  ma ke itt ru e t h ateverythi ng  c ouldhave b e e n aspa tiot empor ally isolated  me reol o gic al at om. W hile  t his m ay betruein  some exotic co ntex ts, it is  su re lyno t tru e  acros s a lllegitim ate con t ext s, u n li ke S1. In the 1983  p o s ts cripts t o Lewi s  1 96 8  and inOP W,Lewi s propo seda nelegantsoluti o nto  some o fthe pr ob lem s w ith A n alys is C.Accordin g tot his proposal,t he analysis o f  m u l ti p ly d e r e modal cla imsi nvol vesa  r ela t ion o f cou nt e rp a rthood holding betw ee n sequ ences .30 Here is a  statement o f  this an alys i s, incorporatingthe i nsight tha t  there i s noneed toinclude a n y  special -pu rpo semac h i ne ry for restri c t ingqu antifie rs:  Possib lyφ(t 1,. ..,  t n)↔df Ana lysis E∃v 1. .. ∃v n(〈 v1,.. . , vn〉C〈t 1, ... ,tn〉  ∧ φ( v 1,...,  vn))  Nec es sa r ily  φ(t1,. . ., t n)↔d f∀v 1... ∀vn (〈 v1,.. ., v n 〉C〈 t1,...,  tn〉 → φ( v1, . ..,vn ))  Analys is E is stric tl y more gen er althan A n a lysis C.  If we wanted to recove r  the ef fec t ofAnal ysis C in  so me con tex t , we c ould d o soby  an a l ysing t he  co un terpart re l a tio n onse quen ces interms of a counter p art  relation onobj ects : 30 Inp os t scr ip t  Dt o  the reprint of  Lewis 196 8, Le wis presen t s t he  "count erparts  of s e quences " account  not as a  m odif i c ati on of theoriginal  1968 tra n slati o nfromthe  forma lmod al la nguage tothe l anguag eof cou nterp ar t theory , but as an alternative  to th e obv iou s transla tio n  fr om Englis h in to the for mal  mo dal l ang u age.Hisi de a i s  that  the English s e nt enc e 'I t is possib l e tha t Dee  an d  Dum a re u nrelated' shouldb e rendered for mall y assom e thin glike '∃z(z = 〈 Dee ,D u m �
emporal in_character; this_hypothesis entails that our_Lewis-world is_strongly_isolated. claiming_that_every object has_at least one_counterpart in every Lewisworld._(The same is_easily_seen to be true for S2.) But such a requirement would generate wildly implausible_assignments_of truth_values_to_other sentences. For example, consider_a tiny Lewis-world w with_no proper_parts: w is in w, but nothing else_is._The requirement would_force w to be a counterpart of absolutely everything;_and that would make it true_that everything could_have_been_a spatiotemporally isolated mereological_atom. While this may be true_in some exotic contexts, it is_surely not true across all legitimate contexts,_unlike S1. In the 1983 postscripts_to Lewis 1968 and in_OPW, Lewis_proposed an elegant solution to_some of the_problems with_Analysis C. According_to this proposal, the analysis of_multiply de re_modal claims involves a relation of_counterparthood_holding between sequences.30_Here_is_a statement_of this analysis,_incorporating_the insight_that_there is no need to include_any_special-purpose machinery for restricting quantifiers: Possibly φ(t1,...,_tn)↔df Analysis E ∃v1...∃vn(〈v1,...,_vn〉C〈t1,...,_tn〉 ∧ φ(v1,..., vn))_Necessarily φ(t1,..., tn)↔df ∀v1...∀vn(〈v1,..., vn〉C〈t1,...,_tn〉 → φ(v1,..., vn)) Analysis E_is strictly_more general_than Analysis C. If we wanted to recover the effect of_Analysis C in some context, we_could do so by_analysing the_counterpart_relation on sequences_in_terms of_a counterpart relation on objects: 30In postscript_D to_the reprint of Lewis 1968, Lewis_presents the "counterparts of_sequences"_account not as a modification of_the original 1968 translation from the_formal modal language to the_language_of_counterpart theory, but as an_alternative to the obvious translation from_English into the_formal modal language. His idea is that_the_English sentence 'It is possible that_Dee_and Dum are unrelated' should be_rendered_formally_as something like '∃z(z =_〈Dee,Dum�