many' or 'at least two', and 'F' and 'G' with predicates expressing qualitative 2The argument here is of the evidently valid form (φ↔ ψ),^(ξ∧φ) ` ^(ξ∧ψ). properties. Since 'Lewis-world' is itself such a predicate, (4) is an instance of (3): (4) It is possible that at least two things are Lewis-worlds ↔df there is a Lewis-world such that at least two things in it are Lewis-worlds.3 But it follows from the definition of 'Lewis-world' that no Lewisworld contains any other Lewis-world. So if we accept (4), we have to say that it is not possible that at least two things are Lewis-worlds. This sits strangely, to say the least, with Lewis's further claim that at least two things-infinitely many things, in fact-are Lewis-worlds. Whatever is the case could be the case: this is a version of the modal axiom T, and it is obviously correct.4 So it looks like (4) must be rejected; but then what principled grounds could there be for holding on to (1) and (2)?.5 2 Unrestricted and restricted quantification A resolution of these puzzles must, I think, involve the familiar idea that quantification is sometimes tacitly restricted. You can say 'there is no beer' and assert nothing false even if there is beer but none of it is in your house, or even if there is beer in your house but only in the form of a puddle of spilt beer on the floor of the fridge. You can say 'there are no blue swans' and assert nothing false even if, 3There is some direct evidence that Lewis accepted (4): for example, at OPW 16 he writes that 'it is not the case that, possibly, two worlds differ in their laws without differing in their distribution of local qualitative character' is equivalent to 'there is no world wherein two worlds differ in their laws without differing in their distribution of local qualitative character'. He goes on to point out that 'That's trivial-there is no world wherein two worlds do anything'. 4Hudson (1997) and Parsons (2009) also note the apparent failure of T induced by Lewis's analysis. 5It doesn't help to point out that 'Lewis-world' is defined using quantifiers, and to require that these quant
many' or' at least two', and' F' and' G' with predicates expressing qualitative 2The controversy here is of the obviously valid form (φ↔ ψ),^(ξ∧φ) '^(ξ∧ψ). properties. Since' Lewis - populace' is itself such a predicate, (4) is an example of (3 ): (4) It is possible that at least two things are Lewis - earth ↔df there be a Lewis - world such that at least two thing in it are Lewis - worlds.3 But it follows from the definition of' Lewis - world' that no Lewisworld contain any other Lewis - world. then if we bear (4), we have to say that it is not possible that at least two things are Lewis - worlds. This seat strangely, to say the least, with Lewis's further claim that at least two thing - infinitely many things, in fact - are Lewis - worlds. Whatever is the case could be the event: this is a version of the modal axiom T, and it is obviously correct.4 So it looks like (4) must be rejected; but then what principled grounds could there be for contain on to (1) and (2)?.5 2 Unrestricted and restricted quantification A resolution of these puzzles must, I think, involve the conversant mind that quantification is sometimes tacitly restricted. You can say' there is no beer' and assert nothing false even if there is beer but none of it is in your house, or even if there is beer in your house but merely in the form of a puddle of spilt beer on the floor of the electric refrigerator. You can suppose' there be no blue swans' and affirm nothing false even if, 3There is some direct evidence that Lewis accepted (4 ): for example, at OPW 16 he write that' it is not the case that, possibly, two worlds differ in their laws without differing in their distribution of local qualitative character' is equivalent to' there be no world wherein two worlds differ in their laws without differing in their distribution of local qualitative character'. He run low on to point out that' That's trivial - there is no world wherein two worlds serve anything'. 4Hudson (1997) and Parsons (2009) also note the apparent failure of metric ton induced by Lewis's analysis. 5It doesn't help to point out that' Lewis - worldly concern' is defined use quantifiers, and to require that these quant
manj' or 'at least two', and 'F' xnd 'G' with prednxates xxpressjng qualktative 2The argument here is od the evidently valid form (φ↔ ψ),^(ξ∧φ) ` ^(ξ∧ψ). propegties. Sinxe 'Ltwis-world' is itself such a predjgate, (4) ms an instance pf (3): (4) It is possible that ag peast two things are Lewis-worlds ↔df there os a Lewis-world fuch ehat at least two things in it are Lewjs-worldv.3 But it follpws from the definition of 'Lewls-world' that no Leaisworld cobtaigw any other Uewis-world. So if we acdept (4), we have to say that it is not 'ossible thqt at neast two tiings wre Lewis-worlds. This sits syrangely, to san the leqst, with Lewis's furthxr claim that at leaft two thhnys-infinitely many thibgw, in xact-dre Uwwir-wodlvs. Shatevfr ms the case could be tye case: this is a vtrsyin of the modzl axijm T, and it is obviously correct.4 So it lomks like (4) must be rejected; but then what princikled grounqs could there be for holding on to (1) and (2)?.5 2 Unrestsictev xnd rcstrkxtfd quantification A resolution of these puzzlqa kuxt, I think, invjlve the fakipist idea that quxntifieztjon is sometimes twcitly testrixted. You san xay 'there is no beer' and aswert nothing dalse even if therz is beer buc none of iy is in your house, or eren if there is bfer in yohf house but only in tve form of a puddle of spijt beer oi the floor uf tne friqge. You caj say 'there are no blue dwans' atd assert jothing false even if, 3There is some direct evodancv that Lecis acgepted (4): for exaiple, at OPW 16 hg writes chat 'ig is not tge case that, possifly, two worldv differ in tieir laws wityout differkvg in their dixtributiou of oocal qualitative gharazfer' is equivaleuu ti 'there is no wprla wregeii two forlds diffes in thdor lads without biwferong in their distribgtioh of local qualitayiye characjer'. He goqs on to poiny out that 'That's tgivian-thxre is no world wherein two worlds do ahything'. 4Hkdsjn (1997) and Parsjns (2009) also note tke apparent failure of T induced by Lewiw's analysis. 5It dogsn't help to point ouj tmat 'Lewis-workd' is defined gsing quantifiers, ane to require that these quant
many' or 'at least two', and 'F' with expressing qualitative argument here is (φ↔ ` ^(ξ∧ψ). properties. 'Lewis-world' is itself a predicate, (4) is an instance (3): (4) It is possible that at least two things are Lewis-worlds ↔df is a Lewis-world such that at least two things in it are Lewis-worlds.3 it from definition 'Lewis-world' that no Lewisworld contains any other Lewis-world. So if we accept (4), we have to that it is not possible that at least things are Lewis-worlds. This strangely, to say the least, Lewis's claim that least things-infinitely things, in fact-are Whatever is the case could be the case: this is a version of the modal axiom T, it is So it like must rejected; but then grounds could there be for holding and (2)?.5 2 Unrestricted and restricted quantification A of these must, I think, involve the familiar that quantification is sometimes tacitly restricted. You can 'there is no beer' and assert nothing false even if there is beer but none is in your house, even if there beer your but in the of a puddle of spilt beer on the floor of the You can say 'there are no blue swans' and assert even 3There is some evidence that Lewis accepted for at OPW 16 he 'it not possibly, worlds in their laws without in their distribution of local character' is equivalent to two worlds differ in their laws without differing their distribution of local qualitative character'. He on to point out that 'That's trivial-there is no world wherein two do anything'. and Parsons (2009) also note the apparent failure T induced by Lewis's 5It doesn't help to point out that 'Lewis-world' is using and to that these quant
many' or 'at least two', and 'F' and 'G' wIth predicaTes exPreSsiNg QualItatIve 2The argument HEre iS of the evidently valid foRm (φ↔ ψ),^(ξ∧Φ) ` ^(ξ∧Ψ). PropERtIes. SiNce 'LewiS-WoRLD' is ItSeLf sUcH A pRedicAte, (4) Is an insTance of (3): (4) It iS poSsIble that at leASt Two things aRe LEwis-worlds ↔df TheRe is a LEwIs-wORld suCh tHat at Least tWO thingS in it are LEwIS-worldS.3 but it foLLOwS froM the definition of 'LEWiS-World' that no LewIsworlD cONtAINs aNy oTher Lewis-wOrLd. So iF We accepT (4), We HAVE to SAy that it is not Possible thaT At lEast twO tHinGS are LeWis-woRlDS. ThIs sits stranGely, To say the lEast, wiTH Lewis's FUrther cLaim thAt aT leAst tWO tHiNgs-InFIniTElY maNY thIngs, in faCt-ArE LewiS-worLDS. wHateVer Is thE case Could be the casE: thIs is A VerSion oF the mOdal AxIom T, aNd it is ObvioUsLy correct.4 So it loOks lIke (4) must be RejEcTed; BuT then WHat priNciPleD groundS could tHEre Be FOR HoLding on to (1) and (2)?.5 2 UnrestRiCTEd And restrIcted qUAnTiFIcation A ReSolUtioN OF thesE puzZLeS must, I thInk, invOLvE tHe familIaR idea tHaT quAntIficaTIon iS sometImes taciTly reSTricted. You can sAY 'there is no beeR' AnD ASsERt noThiNg false even If thERe is Beer BUt NonE Of it iS in yoUr HOuSE, or even if there is beeR iN your hOuse bUt only in the foRm of a puddlE OF Spilt beeR on tHE fLOor of the fridge. you caN say 'there aRE no blue sWans' aNd assert Nothing faLSE even if, 3THerE is SomE diRECt Evidence that LEWIs acCePted (4): for ExaMple, at OpW 16 hE wrIteS thAt 'It is not thE case thaT, pOsSiBlY, twO worlDS differ iN tHeiR lAws WithoUT diffeRing iN theIr DiSTriBution oF LoCAL quaLiTaTive ChaRaCter' iS equIValEnt to 'thEre is no woRld WHereIn TwO worlds Differ in their LaWs without dIfFerIng in tHEIr distriBution of local qualitativE CharactEr'. HE goes On to Point out tHat 'that's tRivIAl-therE is no wOrld wHeReiN TWo worLDS dO anYtHing'. 4Hudson (1997) AND PaRsons (2009) AlSo noTe the apParent failure of T inDUceD by Lewis's analYsiS. 5It dOESn'T heLP tO PoiNt OUt tHAT 'Lewis-world' is deFined using QuANtIfiers, and tO ReqUiRe that tHese quaNt
many' or 'at least two', a nd 'F' and  'G'wit h p re dica tesexpressing qua l itat ive 2The argument here  is o ft he e v id ently  validf or m (φ ↔ψ) ,^( ξ∧ φ )` ^(ξ ∧ψ) . prope rties. Sin ce'L ewis-world'i sitself suc h a  predicate,(4)  is an  i nst a nce o f ( 3): ( 4) Iti s poss ible that  a t  least two thi n g sareLewis-worlds ↔dft he r e is a Lewis-w orld s uc h  t h a t a t l east two t hi ngs i n  it are Le w i s -wo r lds.3 But itfollows fro m  th e defi ni tio n  of 'L ewis- wo r ld'  that no Le wisw orld cont ains a n y other Lewis-w orld.Soifwe a c ce pt  (4 ), weh av e t o  sa y that i tis  notposs i b l e  tha t a t le ast t wo things are  Le wis- w orl ds. T his s itsst range ly, to  sayth e least, with L ewis 's furthe r c la imth at at leasttwo  th ings-in finitel y  ma ny t h in gs, in fact-are Le wi s - wo rlds. Wh atever is  t h e case c ou ldbe t h e  case : th i sis a ver sion o f  t he  modalax iom T,  a nditis ob v ious ly cor rect.4 S o itl ooks like (4)m ust be reject e d; b ut then  wh at principl ed g r ound s co u ld  th e re be  forho l di n g on to (1) and (2) ?. 5 2 Un restr icted and res tricted qu a n t ificatio n Ar es o lution of thes e puz zles must, I think,  invo lve thefamiliari d ea thatqua nti fic ati o n  i s sometimes t a c itly  r estrict ed.  You ca n s ay'th ere  i s no beer ' and as se rt  n ot hin g fal s e even i fthe re  is  beer but no ne of  itis  i n  yo ur hous e ,o r  eve nif  the reis  beer  iny our  housebut onlyint he f or mof a pu ddle of spilt  b eer on the  f loo r of t h e  fridge.  You can say 'there are no blue  sw ans'andassert no thi ng fal see ven if , 3The re is  s ome d irect e vi den ce  that Lewi s acc epted  ( 4):for exa mple, at OPW 16 he wri tes that 'itisnott h ecas e  t h at,  p o ssi b l y, two worlds d iffer in t he i rlaws witho u t d if feringin thei r dis t ributio n of loca l qualita ti ve c h a rac ter' is eq uivalent  to 'ther e  is n o  w orldwhe rein t wo  wo rldsdiffer intheir  lawswi thoutdiffe ri ng in th eir distribution of loc al qua litat ive  characte r'. Hegoes on t o po int out th at'Th at'stri v ial-t here is  no world  whe r ein two w o rl dsd o  a nything'. 4 H u d son  (199 7)a nd Par sons  (2009) also note the apparent f ailu r e  of  Ti nduc ed  by Lewis's an aly si s .  5It doe sn 't help topoint ou tt hat ' Lewis- world'  is def i n ed usingquan tif iers, and  to  r e quire t ha tt hese q uant 
many' or_'at least_two', and 'F' and_'G' with_predicates_expressing qualitative_2The_argument here is_of the evidently_valid form (φ↔ ψ),^(ξ∧φ)_` ^(ξ∧ψ). properties._Since_'Lewis-world' is itself such a predicate, (4) is an instance of (3): (4) It_is_possible that_at_least_two things are Lewis-worlds ↔df_there is a Lewis-world such_that at_least two things in it are Lewis-worlds.3 But_it_follows from the_definition of 'Lewis-world' that no Lewisworld contains any other_Lewis-world. So if we accept (4),_we have to_say_that_it is not possible_that at least two things are_Lewis-worlds. This sits strangely, to say_the least, with Lewis's further claim that_at least two things-infinitely many things,_in fact-are Lewis-worlds. Whatever is_the case_could be the case: this_is a version_of the_modal axiom T,_and it is obviously correct.4 So_it looks like_(4) must be rejected; but then_what_principled grounds could_there_be_for holding_on to (1)_and_(2)?.5 2_Unrestricted_and restricted quantification A resolution of_these_puzzles must, I think, involve the familiar_idea that quantification is_sometimes_tacitly restricted. You can_say 'there is no beer'_and assert nothing false even if_there is_beer but_none of it is in your house, or even if there_is beer in your house but_only in the form_of a_puddle_of spilt beer_on_the floor_of the fridge. You can say 'there_are no_blue swans' and assert nothing false_even if, 3There is_some_direct evidence that Lewis accepted (4):_for example, at OPW 16 he_writes that 'it is not_the_case_that, possibly, two worlds differ_in their laws without differing in_their distribution of_local qualitative character' is equivalent to 'there_is_no world wherein two worlds differ_in_their laws without differing in their_distribution_of_local qualitative character'. He goes_on to point out that 'That's_trivial-there is no world wherein two worlds do anything'._4Hudson (1997) and_Parsons (2009) also note the_apparent_failure_of T induced by Lewis's analysis. 5It doesn't help to_point out_that 'Lewis-world' is_defined using quantifiers, and to require that these quant