! There is no point in having a semantic debate about whether this counts as an genuine instance of Leibniz's Law. If one denies the validity of the Kripkean argument while accepting the validity of 'a is red; b = a; so b is red', one will of course want to find a meaning for 'Leibniz's Law' on which the latter argument is, and the former argument is not, among its instances. It is not technically challenging for a counterpart theorist to do this. But this terminological achievement does nothing at all to undermine the impression that the argument is, in fact, obviously valid. Endorsing a counterpart-theoretic analysis of modal claims does not mean one has to throw away one's prior intuitions about the validity of arguments involving modal operators! Rather, as we have seen, such intuitions are a crucial guide in determining what it takes for the counterpart relation to hold, or for a relation to be a counterpairing.34 33Sider (2009: p. 28) makes a similar point. 34One further point. There is no problem making sense of a sense of 'counterpairing' under which it applies to non-functions, or of sentences pschmossibly φq stipulated to be analysed in terms of such a notion. But'schmossibly', so understood, is semantically anomalous, in that the stipulated meaning of pschmossibly φq depends on merely orthographic features of φ. In general, we are free to introduce new words by stipulating them to be semantically equivalent to old words, and we expect the new words so introduced to be intersubstitutable salva veritate with the old words they were stipulated to be equivalent to, with the exception of quotation-like contexts. For example, I can stipulate that 'Lavid Dewis' is to be semantically equivalent to the name 'David Lewis'. If we hold on to Analysis F as our analysis of pschmossibly φq, however, we find that 'Schmossibly David 19 Requiring counterpairings to be functions also validates a further principle of plural modal logic which captures one half of the idea that plurals are rigid: when a thing is one of some things, it is so necessarily. (NO) Xx→ Xx. If x is one of X, and there is only one object y such that Rxy, then it follows from our definition of 'RXY'
! There is no point in having a semantic debate about whether this consider as an actual instance of Leibniz's Law. If one denies the cogency of the Kripkean argumentation while accepting the validity of' a is crimson; b = a; indeed b is red', one will of path want to find a meaning for' Leibniz's police' on which the latter argument is, and the former argumentation is not, among its case. It is not technically challenging for a counterpart theorist to do this. But this terminological achievement does nothing at all to sabotage the impression that the argument is, in fact, obviously valid. Endorsing a counterpart - theoretical analysis of modal claims does not entail one has to shed away one's prior intuitions about the validity of arguments involve modal operators! Rather, as we have seen, such intuitions are a crucial guide in determining what it takes for the counterpart relation to hold, or for a relation to be a counterpairing.34 33Sider (2009: p. 28) makes a similar point. 34One further point. There is no problem make sense of a sense of' counterpairing' under which it enforce to non - function, or of sentences pschmossibly φq stipulated to be analysed in term of such a notion. But'schmossibly', so understood, is semantically anomalous, in that the stipulated meaning of pschmossibly φq depend on merely orthographic features of φ. In general, we are free to introduce new words by stipulate them to be semantically equivalent to old words, and we expect the new word thus introduced to be intersubstitutable salva veritate with the old words they were stipulated to be equivalent to, with the exception of quotation - alike contexts. For example, I can stipulate that' Lavid Dewis' is to be semantically equivalent to the name' David Lewis'. If we hold on to Analysis F as our psychoanalysis of pschmossibly φq, however, we find that' Schmossibly David 19 ask counterpairings to be functions also validate a further principle of plural modal auxiliary verb logic which captures one half of the idea that plurals are rigid: when a matter is one of some things, it is so necessarily. (NO) Xx→ Xx. If x is one of X, and there be only one object y such that Rxy, then it follows from our definition of' RXY'
! Thfre is no point in havinn a semantic debcre abont whetger this counts as an genuine instanre od Leivniz's Law. If one denier the valpdity of rhe Jeipkean arjhment wmnle adgeptiug the validity pf 'a is reg; b = a; so b is rdd', one will of course want to find a ieaning flr 'Leibniz's Lar' on rhicg the latter argument is, and the fkrmer aggument is not, ampng its instances. It is noh tefhnically challenglng for a ciuntqepart theorirt to do this. But this terminological achievement doer notking at all ti ujgermine the imprvssion that tmv argumant is, on fact, obviouxly vaoid. Endorsing a countxrpart-theoretic analisis of mogam claims does not mwan ote hds tu thfow axay one's orikr intuitikns about tye validity of argukegnx involving jodal jpqrators! Rather, as we have seen, such intlitikns are a crucial guide in determining what lt takes sor the counterpart relation to hold, or for a reldtion go yc x clunterpairing.34 33Sider (2009: p. 28) makes a similar point. 34Knt flrther point. Therc is no problem malijg fense of a sevse of 'cohnterpairing' under which yt applies to gon-finctions, or of sentences psxhmossibly φq wtipulated to be aualysed in tzrms og sucn a notion. But'schmossibuy', sk understoof, is semahgically anomalour, ik tvat the stipulated meaning of pschmissiyly φq deoendx on mqrely orthlgrapmhc features of φ. In genetal, we are free ho introduce new words by stipulating them to ba svmanticaljy eqmivalent to old words, and we gxpect thz new dords so ihtroducxd to be intqrsubstitutabng salva veritete with ehe ild qords tfdy were stipulsted to bv tquivalent to, with the excepbion ur quotation-like cobtexts. For examlle, I saj xty[ulate that 'Navia Ddeis' ir to be semcngicakly equivalent to tha naje 'David Lewis'. If ee hold on to Analrsis F as our analysis of pschmlssibny φd, howrvet, we find that 'Schmossibly Davis 19 Requirlng counterpairyngs to be functnons also validates a further principle if plural modal lotic which captures pke half of tie idew that plgrals are rigid: when a thing is one on some things, it is so necesvarilj. (NO) Xx→ Xx. If x is one of X, and there is only one object y such that Rxy, rhen iv sollows froj out defpniciou of 'RXR'
! There is no point in having debate whether this as an genuine one the validity of Kripkean argument while the validity of 'a is red; = a; so b is red', one will of course want to find meaning for 'Leibniz's Law' on which the latter argument is, and the former is among instances. is not technically challenging for a counterpart theorist to do this. But this terminological achievement does at all to undermine the impression that the is, in fact, obviously Endorsing a counterpart-theoretic analysis of claims not mean has throw one's prior intuitions the validity of arguments involving modal operators! Rather, as we have seen, such intuitions are a crucial in determining takes for counterpart to or for a be a counterpairing.34 33Sider (2009: p. similar point. 34One further point. There is no making sense a sense of 'counterpairing' under which applies to non-functions, or of sentences pschmossibly φq to be analysed in terms of such a notion. But'schmossibly', so understood, is semantically anomalous, the stipulated meaning of φq depends on orthographic of In we are to introduce new words by stipulating them to be semantically equivalent old words, and we expect the new words so introduced intersubstitutable veritate with the words they were stipulated be to, with the exception contexts. example, that Dewis' to be semantically equivalent the name 'David Lewis'. If hold on to Analysis pschmossibly φq, however, we find that 'Schmossibly David Requiring counterpairings to be functions also validates further principle of plural modal logic which captures one half of the that plurals when a thing is one of some things, is so necessarily. (NO) Xx. If x is one of X, and there only object y that Rxy, then follows from our of 'RXY'
! There is no point in having a seMantic debaTe aboUt wHetHeR thiS couNts as an genuine INstaNce of Leibniz's Law. If one dEnies ThE ValiDItY of thE KripkeAN aRGUmeNt WhIle AcCEpTing tHe vAlidity Of 'a is red; b = a; So b Is Red', one will of COuRse want to fInd A meaning for 'LEibNiz's LaW' oN whICh the LatTer arGument IS, and thE former arGuMEnt is nOT, among iTS InStanCes. It is not technicALlY Challenging for A countErPArT THeoRisT to do this. BUt This tERminoloGIcAL AChiEVement does notHing at all to UNdeRmine tHe ImpREssion That tHe ARguMent is, in facT, obvIously valId. EndoRSing a coUNterparT-theorEtiC anAlysIS oF mOdaL cLAimS DoEs nOT meAn one has To ThRow awAy onE'S PRIor iNtuItioNs aboUt the validity Of aRgumENts InvolVing mOdal OpEratoRs! RathEr, as wE hAve seen, such intuItioNs are a cruCiaL gUidE iN deteRMining WhaT it Takes foR the couNTerPaRT RElAtion to hold, or for a rElATIoN to be a coUnterpAIrInG.34 33sider (2009: p. 28) maKeS a sImilAR Point. 34one fURtHer point. there iS No PrOblem maKiNg sensE oF a sEnsE of 'coUNterPairinG' under whIch it APplies to non-funCTions, or of sentENcES PsCHmosSibLy φq stipulaTed tO Be anAlysED iN teRMs of sUch a nOtIOn. bUt'schmossibly', so undeRsTood, is SemanTically anomalOus, in that tHE STipulateD meaNInG Of pschmossibly Φq depEnds on mereLY orthogrAphic Features Of φ. In geneRAL, we are frEe tO inTroDucE NEw Words by stipulATIng tHeM to be seManTically EquIvaLenT to OlD words, and We expect ThE nEw WoRds So intROduced to Be IntErSubStituTAble saLva veRitaTe WiTH thE old worDS tHEY werE sTiPulaTed To Be equIvalENt tO, with thE exceptioN of QUotaTiOn-Like conTexts. For exampLe, i can stipulAtE thAt 'LaviD dEwis' is to Be semantically equivalenT To the naMe 'DAvid LEwis'. if we hold oN to analysIs F AS our anAlysis Of pscHmOssIBLy φq, hOWEvEr, wE fInd that 'SchMOSsiBly DaViD 19 ReqUiring cOunterpairings to be FUncTions also valiDatEs a fURThEr pRInCIplE oF PluRAL modal logic whicH captures oNe HAlF of the idea THat PlUrals arE rigid: wHen a tHIng is onE of some thIngs, it is sO nEcesSARilY. (NO) Xx→ Xx. If x Is one of X, And there iS Only oNE oBject Y suCh that rxY, thEn it fOllows FRom Our deFinitiOn Of 'RXY'
! There is no point in hav ing a sema nticdeb ate  a bout  whe ther this coun t s as  an genuine instance o f Lei bn i z'sL aw . Ifone den i es t heva li dit yo fthe K rip kean ar gument whi leac cepting thev al idity of ' a i s red; b = a ; s o b is  r ed' ,  onewil l ofcourse want t o find ame a ning f o r 'Leib n i z' s La w' on which the l a tt e r argument is,  and t he fo r m erarg ument is n ot , amo n g its i n st a n c es. It is not tec hnically ch a lle ngingfo r a counte rpart  t h eor ist to do t his.  But this  termi n ologica l  achiev ementdoe s n othi n gat  al lt o u n de rmi n e t he impre ss io n tha t th e a r gume ntis,in fa ct, obviously  va lid. End orsin g a c ount er part- theore tic a na lysis of modalclai ms does n otme anon e has to thr owawa y one's  priori ntu it i o n sabout the validity  o f ar gumentsinvolv i ng  m o dal oper at ors ! Ra t h er, a s we ha ve seen,  suchi nt ui tions a re  a cru ci algui de in dete rminin g what i t tak e s for the coun t erpart relati o nt o  h o ld,orfor a relat iont o be  a c o un ter p airin g.3433 S id e r (2009: p. 28) mak es  a sim ilarpoint. 34Onefurther po i n t . Thereis n o  p r oblem making s enseof a sense of 'coun terpa iring' u nder whic h it appli estonon -fu n c ti ons, or of se n t ence spschmos sib ly φq s tip ula ted  to  b e analyse d in ter ms  o fsu cha not i on. But' sc hmo ss ibl y', s o  under stood , is  s em a nti cally a n om a l ous,  i nthat  th estipu late d  me aning o f pschmos sib l y φq  d ep ends on  merely ortho gr aphic feat ur esof φ.I n  general , we are free to introd u ce newwor ds by  sti pulatingthe m to b e s e mantic ally e quiva le ntt o  oldw o rd s,an d we expec t the  newwo rdsso intr oduced to be inter s ubs titutable sal vaveri t a te  wi t ht heol d  wo r d s they were sti pulated to  b e  e quivalentt o,wi th theexcepti on of quotati on-like c ontexts.Fo r ex a m ple , I can st ipulatethat 'Lav i d Dew i s'  is t o b e sema nt ica lly e quival e ntto th e name  ' DavidLewis '.  If we h old on to Analysis F as  our a nalys isof pschmo ssi b lyφq, howev er,we find th at'Sc hmoss ibl y  Davi d 19 Re qui r ing c ount e rpairings to  be f un ctions also v a lid atesa f u rtherprin ciple of plural m o dal logic whic h ca p t ure s o n e ha lf  of the idea t hat  p l u rals are  r igid: whena thingis one o f some  thing s, it i s so necess aril y.(NO) Xx→Xx .I f x ison eo f X, a nd t he re isonly o n e ob j e ct y such that R xy, t h e n itf oll ows f ro m our d e fini tion of 'R XY'
! There_is no_point in having a_semantic debate_about_whether this_counts_as an genuine_instance of Leibniz's_Law. If one denies_the validity of_the_Kripkean argument while accepting the validity of 'a is red; b = a; so_b_is red',_one_will_of course want to find_a meaning for 'Leibniz's Law'_on which_the latter argument is, and the former argument_is_not, among its_instances. It is not technically challenging for a counterpart_theorist to do this. But this_terminological achievement does_nothing_at_all to undermine the_impression that the argument is, in_fact, obviously valid. Endorsing a counterpart-theoretic_analysis of modal claims does not mean_one has to throw away one's_prior intuitions about the validity_of arguments_involving modal operators! Rather, as_we have seen,_such intuitions_are a crucial_guide in determining what it takes_for the counterpart_relation to hold, or for a_relation_to be a_counterpairing.34_33Sider_(2009: p._28) makes a_similar_point. 34One_further_point. There is no problem making_sense_of a sense of 'counterpairing' under which_it applies to non-functions,_or_of sentences pschmossibly φq_stipulated to be analysed in_terms of such a notion. But'schmossibly',_so understood,_is semantically_anomalous, in that the stipulated meaning of pschmossibly φq depends on_merely orthographic features of φ. In_general, we are free_to introduce_new_words by stipulating_them_to be_semantically equivalent to old words, and we_expect the_new words so introduced to be_intersubstitutable salva veritate with_the_old words they were stipulated to_be equivalent to, with the exception_of quotation-like contexts. For example,_I_can_stipulate that 'Lavid Dewis' is_to be semantically equivalent to the_name 'David Lewis'._If we hold on to Analysis F_as_our analysis of pschmossibly φq, however,_we_find that 'Schmossibly David 19 Requiring_counterpairings_to_be functions also validates a_further principle of plural modal logic_which captures one half of the idea that plurals_are rigid: when_a thing is one of_some_things,_it is so necessarily. (NO) Xx→ Xx. If x is_one of_X, and there_is only one object y such that Rxy, then it_follows from our definition of 'RXY'