. 28It wouldn't really matter to this argument if we considered non-qualitative counterpart relations: for all of the objects which might plausibly figure as de re elements of the analysis of possibility claims made by us are spatiotemporally related to us, and thus qualitative relations between them, us, and objects in other, symmetric, strongly isolated Lewis-worlds are still invariant under the symmetries of those Lewis-worlds. 15 your right hand just now, while things remained the same in other respects. But for this to be true, you may have to have counterparts in other symmetric, strongly isolated Lewis-worlds: there may not be anyone in this Lewis-world who is like you except for a raised right hand.29 The trouble for Analysis C is deeper than this. The sentences that require draconian and implausible constraints on the counterpart relation to make true include not just intuitive claims like (10), but sentences that express obviously valid principles of modal logic. Consider for example the following modal schemas: (S1) ^Fa→ ^(Fa ∨ Fb) (S2) (Fa ∧ Fb)→ Fa These seem as manifestly valid as anything could in the realm of modal logic: they are especially trivial instances of the closure of possibility and necessity under logical consequence, as ensured in standard modal logic by the rule of necessitation and axiom K. But look at the analysis of S1 given by Analysis C: If some Lewis-world contains a counterpart of a that is F, then some Lewis-world contains both a counterpart of a and a counterpart of b, such that either the former or the latter is F. This is false if a has counterparts that are F, but all of them are in Lewis-worlds that contain no counterparts of b. Thus, given Analysis C, guaranteeing the truth of all instances of S1 would require 29Biting the bullet here might be less implausible for someone who thought of counterparthood in general as involving some external relation of the sort that cannot hold between strongly isolated objects. On such a view, it is much harder for ordinary possibility claims to be true: for an object to be possibly F, there needs to be a chain of perfectly natural relations connecting it to something that is F. Lewis's doctrine of Humean Supervenience, however, commits him to thinking that ordinary modal judgments are consistent with the hypothesis that the only perfectly natural relations instantiated in our Lewis-world are spatiot
. 28It wouldn't really matter to this argument if we considered non - qualitative counterpart relative: for all of the object which might plausibly figure as de re elements of the psychoanalysis of possibility claims made by us are spatiotemporally relate to us, and thus qualitative relations between them, us, and object in other, symmetric, powerfully isolated Lewis - worlds are still invariant under the isotropy of those Lewis - worlds. 15 your right hand just now, while thing remained the same in other deference. But for this to be true, you may have to have counterparts in early symmetric, powerfully isolated Lewis - worlds: there may not be anyone in this Lewis - world who is like you except for a raised right hand.29 The worry for Analysis C is deeper than this. The sentences that require draconian and implausible constraints on the counterpart relation back to make true include not just intuitive claims like (10), but sentences that express obviously valid principles of modal logic. Consider for example the follow modal schemas: (S1) ^Fa→ ^(Fa ∨ Fb) (S2) (Fa ∧ Fb)→ Fa These seem as obviously valid as anything could in the region of modal logic: they are especially trivial instances of the closure of possibility and necessity under logical consequence, as ensured in standard modal logic by the dominion of necessitation and axiom K. But look at the analysis of S1 given by Analysis C: If some Lewis - world contains a counterpart of a that is F, then some Lewis - world check both a counterpart of a and a counterpart of b, such that either the former or the latter is F. This is false if a has counterpart that are F, but all of them are in Lewis - worlds that incorporate no counterparts of b. Thus, given Analysis C, guaranteeing the truth of all instances of S1 would command 29Biting the bullet here might be less implausible for someone who thought of counterparthood in cosmopolitan as involving some external relative of the sort that cannot hold between powerfully isolated objects. On such a view, it is much harder for average possibility claims to be true: for an object to be possibly F, there necessitate to be a chain of absolutely natural relations connecting it to something that is F. Lewis's doctrine of Humean Supervenience, however, entrust him to thinking that average modal judgments are consistent with the hypothesis that the alone perfectly natural relations instantiated in our Lewis - world are spatiot
. 28It wouldn't really matter tu this argument if we ronsideded non-qjalitative counterpart relatmons: for qll of the objects whizh might ilausibly fignre as de re elements of the ahwlysns of possibiliti claims mada by us are spdtkocemporally related to us, and thus quwlitatife relations betreen ehem, ls, and objects in other, symmetrjc, stroigly isolated Lrwis-worlds are still invarlant under the symmetrles of thosg Lerus-worlds. 15 yojr right hand just now, while things remained the same in ocher respecjs. Bkj for this ti be nrue, you may msve to have cpunterparts in otier wymmetric, strongly ismlated Lewis-worlds: there maf uot be anyone in this Lwwis-wmrld who us uikt ypu exceph fkr a raises right hane.29 The trouble for Amajjxis C is deeler thwn this. The sentences that require draconpan znd implausible constraunts on the counterpatt relatiog to make true include not just intuitive claims nike (10), cut scntevxed that express obviously valid principles of ikdsl logic. Considev for example the goplpring modal scfemas: (S1) ^Fz→ ^(Fa ∨ Fb) (S2) (Fa ∧ Fb)→ Va Thesg seem as maniftstly valid as anything could in the realm oy midal logic: they arz especially trifial onstances of the closurz of pkssibility wnd necesakty under logicau cpnvequence, as ensured in stagdard model loyic by tfe role of gecessitatlon akg axiom K. But look at tke andlysis of D1 given by Analysis C: If some Lxxis-world contsits d countexpart pf a that is S, then some Lecis-world contxins both z countxrpart of a wnd a counter[wrt of b, suci that eieher the former ur the latter os F. This is false uf a has counterpavts tfzt are F, but alo od them are in Lrwir-wowlfs trdt contain nm cojntdtpartr of b. Ukus, eivem Analysis C, guarantaeinf the truth of all ikstances if S1 woujd require 29Biying the bullet hege mijht be less imklausible for someone who thouggt of coujtevparthood in deneval ws involviug some external relation of the sort thet cannot hold between wtrongly isolated oyjtcts. On such e view, it is muwh harder for ordinaey possibility clsims to be true: for ah objewt to be possibly F, there needs to be a chain of perfectly natural relations cinnectmnd it to somsthimg thdt ns F. Leris's voctrine of Humeam Supervenience, however, commits him to dhnnking that ordinary modal jucgoents are conristent with the hypotheais that the only perfectly natural relstions instantiated in omr Lewis-wirld zre spatiov
. 28It wouldn't really matter to this we non-qualitative counterpart for all of figure de re elements the analysis of claims made by us are spatiotemporally to us, and thus qualitative relations between them, us, and objects in other, strongly isolated Lewis-worlds are still invariant under the symmetries of those Lewis-worlds. 15 right just while remained the same in other respects. But for this to be true, you may have to counterparts in other symmetric, strongly isolated Lewis-worlds: there not be anyone in Lewis-world who is like you for raised right The for C is deeper this. The sentences that require draconian and implausible constraints on the counterpart relation to make true include just intuitive (10), but that obviously principles of modal for example the following modal schemas: ∨ Fb) (S2) (Fa ∧ Fb)→ Fa These as manifestly as anything could in the realm modal logic: they are especially trivial instances of closure of possibility and necessity under logical consequence, as ensured in standard modal logic by of necessitation and axiom But look at analysis S1 by C: If Lewis-world contains a counterpart of a that is F, then some contains both a counterpart of a and a counterpart of that the former or latter is F. This false a has counterparts that but of Lewis-worlds contain counterparts of b. Thus, Analysis C, guaranteeing the truth all instances of S1 here might be less implausible for someone who of counterparthood in general as involving some relation of the sort that cannot hold between strongly isolated objects. On a view, much harder for ordinary possibility claims to be for an object to possibly F, there needs to be a chain of natural connecting it something that is Lewis's doctrine of Supervenience, however, commits thinking that modal are hypothesis that the only perfectly natural instantiated our Lewis-world are spatiot
. 28It wouldn't really matter to thIs argument If we cOnsIdeReD non-QualItative counterPArt rElations: for all of the objEcts wHiCH migHT pLausiBly figuRE aS DE re ElEmEntS oF ThE analYsiS of possIbility claIms MaDe by us are spaTIoTemporally RelAted to us, and tHus QualitAtIve RElatiOns BetweEn them, US, and obJects in otHeR, SymmetRIc, stronGLY iSolaTed Lewis-worlds are STiLL invariant undeR the syMmETrIES of ThoSe Lewis-worLdS. 15 your RIght hanD JuST NOw, wHIle things remaIned the same IN otHer resPeCts. bUt for tHis to Be TRue, You may have tO havE counterpArts in OTher symMEtric, stRongly IsoLatEd LeWIs-WoRldS: tHEre MAy Not BE anYone in thIs leWis-woRld wHO IS Like You ExcePt for A raised right hAnd.29 the tROubLe for analySis C Is DeepeR than tHis. ThE sEntences that reqUire Draconian And ImPlaUsIble cONstraiNts On tHe countErpart rELatIoN TO MaKe true include not juSt INTuItive claIms likE (10), BuT sENtences tHaT exPresS OBviouSly vALiD principLes of mODaL lOgic. ConSiDer for ExAmpLe tHe folLOwinG modal Schemas: (S1) ^fa→ ^(Fa ∨ FB) (s2) (Fa ∧ Fb)→ Fa These seEM as manifestly VAlID As ANythIng Could in the rEalm OF modAl loGIc: TheY Are esPeciaLlY TrIVial instances of the cLoSure of PossiBility and neceSsity under LOGIcal consEqueNCe, AS ensured in stanDard mOdal logic bY The rule oF neceSsitatioN and axiom k. bUt look at The AnaLysIs oF s1 GiVen by Analysis c: iF somE LEwis-worLd cOntains A coUntErpArt Of A that is F, tHen some LEwIs-WoRlD coNtainS Both a couNtErpArT of A and a COunterPart oF b, suCh ThAT eiTher the FOrMER or tHe LaTter Is F. thIs is fAlse IF a hAs countErparts thAt aRE F, buT aLl Of them aRe in Lewis-worlDs That contaiN nO coUnterpARTs of b. ThuS, given Analysis C, guaranteEIng the tRutH of alL insTances of S1 WouLd requIre 29bIting tHe bullEt herE mIghT BE less IMPlAusIbLe for someoNE Who ThougHt Of coUnterpaRthood in general as iNVolVing some exterNal RelaTIOn Of tHE sORt tHaT CanNOT hold between strOngly isolaTeD ObJects. On sucH A viEw, It is mucH harder For orDInary poSsibility Claims to bE tRue: fOR An oBject to be pOssibly F, There needS To be a CHaIn of pErfEctly nAtUraL relaTions cONneCting It to soMeThing tHat is f. LEwis's docTrine of Humean SupervenieNce, howEver, cOmmIts him to tHinKIng That ordinAry mOdal judgmeNts Are ConsiSteNT with The hYPoTheSIs thaT the ONly perfecTLy NatURAl Relations inSTANtiAted iN ouR lewis-wOrld Are spatiot
. 28It wouldn't really mat ter to thi s arg ume ntif  wecons idered non-qua l itat ive counterpart relati ons:fo r  all of  theobjects wh i c h m ig ht  pl au s ib ly fi gur e as de  re elemen tsof  the analysi s  o f possibil ity  claims made  by  us ar espa t iotem por allyrelate d  to us , and thu sq ualita t ive rel a t io ns b etween them, us,a nd objects in oth er, sy mm e tr i c , s tro ngly isola te d Lew i s-world s  a r e sti l l invariant u nder the sy m met ries o ftho s e Lewi s-wor ld s . 1 5 your righ t ha nd just n ow, wh i le thin g s remai ned th e s ame  ino th er  re sp e cts .  B utf orthis tobe  t rue,youm a y have  to  hav e cou nterparts inoth er s y mme tric,  stro ngly  i solat ed Lew is-wo rl ds: there may n ot b e anyoneinth isLe wis-w o rld wh o i s l ike you  except for  a r a is ed right hand.29 T he t ro uble for  Analy s is  C is deepe rtha n th i s . The  sen t en ces that  requi r edr aconian  a nd imp la usi ble  cons t rain ts onthe coun terpa r t relation tom ake true incl u de n ot just  in tuitive cla imsl ike(10) ,  b uts enten ces t ha t  e x press obviously val id  princ iples  of modal log ic. Consid e r for exam plet he following moda l sch emas: (S1) ^Fa→ ^(F a ∨ F b) (S2)(Fa ∧ Fb ) →  Fa The sesee m a s m a n if estly valid a s anyt hi ng coul d i n the r eal m o f m oda llogic: th ey are e sp ec ia ll y t rivia l  instanc es  of  t heclosu r e of p ossib ilit yan d  ne cessity un d e r lo gi ca l co nse qu ence,  ase nsu red instandardmod a l lo gi cby therule of neces si tation and  a xio m K. B u t  look at  the analysis of S1 giv e n by An aly sis C : If  some Lew is- worldcon t ains a  count erpar tofa thati s  F , t he n some Lew i s -wo rld c on tain s botha counterpart of a and  a counterpar t o f b, s uc h t h at eit he r  th e former or the l atter is F .T hi s is false ifahas cou nterpar ts th a t are F , but all  of themar e in L ewi s-worlds t hat cont ain no co u nterp a rt s ofb.Thus,gi ven  Anal ysis C ,  gu arant eeingth e trut h ofal l instan ces of S1 would require  29Bit ing t hebullet he rem igh t be less  imp lausible f orsom eonewho thoug ht o f  c oun t erpar thoo d  in gener a lasi n vo lving somee x t ern al re lat i on ofthesort that cannoth old between st rong l y  is ola t ed o bj ects. On sucha v ie w ,  it is m uc h harder fo r ordina ry possi bility  claim s to be t ru e : foran o bje ct to bepos si b ly F, t he re needsto b ea chai n of p e rfec t l y natural relati ons c o n necti n g i t toso mething that  is F. Lew is's doctri ne ofHume an Su perveni en ce, ho wev er , commitsh im to thi nking  that o rd inar y m odal j udgm e n ts ar e co ns ist ent witht h eh yp ot h esi s th at th eonly  perfectl y  natural  re l ationsin sta n t iatedi no u r Lewis-wo rld  ares p atiot
. 28It_wouldn't really_matter to this argument_if we_considered_non-qualitative counterpart_relations:_for all of_the objects which_might plausibly figure as_de re elements_of_the analysis of possibility claims made by us are spatiotemporally related to us, and_thus_qualitative relations_between_them,_us, and objects in other,_symmetric, strongly isolated Lewis-worlds are_still invariant_under the symmetries of those Lewis-worlds. 15 your_right_hand just now,_while things remained the same in other respects. But_for this to be true, you_may have to_have_counterparts_in other symmetric, strongly_isolated Lewis-worlds: there may not be_anyone in this Lewis-world who is_like you except for a raised right_hand.29 The trouble for Analysis C_is deeper than this. The_sentences that_require draconian and implausible constraints_on the counterpart_relation to_make true include_not just intuitive claims like (10),_but sentences that_express obviously valid principles of modal_logic._Consider for example_the_following_modal schemas:_(S1) ^Fa→ ^(Fa_∨_Fb) (S2)_(Fa_∧ Fb)→ Fa These seem as_manifestly_valid as anything could in the realm_of modal logic: they_are_especially trivial instances of_the closure of possibility and_necessity under logical consequence, as ensured_in standard_modal logic_by the rule of necessitation and axiom K. But look at_the analysis of S1 given by_Analysis C: If some_Lewis-world contains_a_counterpart of a_that_is F,_then some Lewis-world contains both a counterpart_of a_and a counterpart of b, such_that either the former_or_the latter is F. This is_false if a has counterparts that_are F, but all of_them_are_in Lewis-worlds that contain no_counterparts of b. Thus, given Analysis_C, guaranteeing the_truth of all instances of S1 would_require_29Biting the bullet here might be_less_implausible for someone who thought of_counterparthood_in_general as involving some external_relation of the sort that cannot_hold between strongly isolated objects. On such a view,_it is much_harder for ordinary possibility claims_to_be_true: for an object to be possibly F, there needs_to be_a chain of_perfectly natural relations connecting it to something that is F._Lewis's doctrine of Humean Supervenience, however, commits_him to thinking that ordinary modal judgments are consistent with the_hypothesis that the only perfectly natural relations instantiated_in our Lewis-world are spatiot