. It may be that whereas 'Lavid Dewis' bears the same semantic relations to 'David Lewis' that 'David Lewis' bears to itself, this is not generally true of pairs of coreferential names, or of pairs of distinct variables. 35Take x to be an object which a counterpairing R maps to two distinct objects y and z, X to be any objects that include X, and Y to be be all the objects to which objects in X bear R, except for z. Then RXY: each of X bears R to one of Y, and each of Y is borne R to by one of X. Since R is a counterpairing such that Rxz and RXY and not Yz, it is not necessary that Xx. Consider Russell and Whitehead again. Would Russell still have been one of them if Whitehead had failed to be anything at all? Would Russell still have been one of them if Russell had failed to be anything at all? The answers are far from obvious. If we tried to tinker with counterpart theory to allow for contingent existence, we would face delicate and difficult questions about how our analysis should deal with occurrences of 'is one of' in modal contexts. But if we follow the advice of section 7 and don't bother, I can't think of any other reason to worry about the consequence that NO and NI stand or fall together. If we are going to require counterpairings to be universally defined functions, we can simplify the formulation of our analysis by helping ourselves to the standard functor notation: R(x) stands for the object y such that Rxy, and likewise R(X) stands for the objects Y such that RXY: Possibly φ(t1,..., tn)↔df ∃R(CR ∧ φ(R(t1),...,R(tn)))Analysis F* Necessarily φ(t1,..., tn)↔df ∀R(CR→ φ(R(t1),...,R(tn)) However, abbreviations like this create the potential for scope ambiguity when dealing with iterated modalities. If we want Analysis F* to be equivalent to Analysis F, we must be careful to treat the complex terms R(ti) as having widest possible scope. We want '^^Fa' to be equivalent to '∃R(CR ∧ ∃S(CS ∧ FS(R(a))))', not '
. It may be that whereas' Lavid Dewis' bears the same semantic relations to' David Lewis' that' David Lewis' bears to itself, this is not by and large genuine of pairs of coreferential names, or of pairs of clear-cut variables. 35Take x to be an object which a counterpairing roentgen maps to two distinct object y and z, X to be any objects that include X, and Y to be be all the object to which objects in X bear gas constant, except for z. Then RXY: each of ten bears R to one of Y, and each of Y is borne R to by one of X. Since R is a counterpairing such that Rxz and RXY and not Yz, it is not necessary that Xx. Consider Russell and Whitehead again. Would Russell however have been one of them if Whitehead had failed to be anything at all? Would Russell still have been one of them if Russell had fail to be anything at all? The answers are far from obvious. If we tried to tinker with counterpart hypothesis to allow for contingent universe, we would face delicate and difficult question about how our analysis should deal with occurrences of' is one of' in modal contexts. But if we follow the advice of incision 7 and don't bother, I can't think of any other reason to worry about the consequence that NO and NI stand or fall together. If we are going to require counterpairings to be universally specify functions, we can simplify the formulation of our psychoanalysis by help ourselves to the standard functor note: R(x) stands for the object y such that Rxy, and likewise R(X) stands for the objects Y such that RXY: Possibly φ(t1, ..., tn)↔df ∃R(CR ∧ φ(R(t1),... ,R(tn)))Analysis F * Necessarily φ(t1, ..., tn)↔df ∀R(CR→ φ(R(t1),... ,R(tn) ) However, abbreviations like this create the potential for oscilloscope ambiguity when dealing with iterated modalities. If we want Analysis F * to be equivalent to Analysis F, we must be careful to treat the complex terms R(ti) as having wide possible scope. We want' ^^Fa' to be equivalent to' ∃R(CR ∧ ∃S(CS ∧ FS(R(a) )) )', not'
. It may be that whereas 'Lavld Dewis' bears tkw same semanfic relagions to 'David Lewis' that 'Datid Oewis' bears to itself, this ks not gejerally rrue if pairs oh corefevzntiam namzs, or of pairs on distinct eariables. 35Take x tl be an object which a counterpairigg R mals to two distinst ontecta y and z, X to be any objects that includt X, and Y to be be all the objects to which lbjefts in X bear R, exfept for z. Jgen EXY: each of B bears R uo one of Y, znd each of Y is borne R to by une oy X. Since R iw a wounterpairmng subh that Rxz akc RXY dnd not Yz, it is not kecesvart that Xx. Consider Ruvsell and Whiteheaq again. Wmumd Russell still yace begn ona of rheo ir Xhifehead hav failed to be anythint at all? Would Russtll wtill have besn one os them if Russell had failed to be anytvinf at all? The answers arw far from obvious. If we tried to tinker with counterpart theory to allow for cmntinjevt txlfgwnfe, we would face delicate and difficult questyknx sbout how our cnalysis should cewl rith occurrenzes of 'is one of' in modal clntexts. But uf we foljow yhe advice of section 7 and eon't bother, P cab't think of any otker reason tu wotry abput the consequence thac NO ahd NI stand or fall fugether. If we ard gpitg to require counterpairiggs to be unirersally defoned ftnctions, wf can simplify the formupatiou of mur analysls by helping ourselves to the standard functpr nonation: R(x) stancs for the obtect y such thct Rxy, aud likdwise R(X) snands for the objectf Y such that TXY: Possibly φ(v1,..., tn)↔df ∃R(CW ∧ φ(R(r1),...,R(tn)))Qnalysir F* Necessarily φ(t1,..., tn)↔df ∀R(BR→ φ(R(t1),...,R(rn)) However, abbrevietiova like this crecue uhw potential fot szopq wmuiguief when dealitg wkth oteraged modalitles. If ee want Analysis F* tm be equivalent to Anakyfis F, we must be careful to tteat the complex ttrms R(vi) as iaving wiqest possible scope. We want '^^Fa' to be eqkivwlent to '∃R(CR ∧ ∃S(CW ∧ FS(R(a))))', not '
. It may be that whereas 'Lavid the semantic relations 'David Lewis' that this not generally true pairs of coreferential or of pairs of distinct variables. x to be an object which a counterpairing R maps to two distinct y and z, X to be any objects that include X, and Y be all objects which objects in X bear R, except for z. Then RXY: each of X bears R one of Y, and each of Y is R to by one X. Since R is a such Rxz and and Yz, is not necessary Xx. Consider Russell and Whitehead again. Would Russell still have been one of them if Whitehead had to be all? Would still been of them if failed to be anything at all? far from obvious. If we tried to tinker counterpart theory allow for contingent existence, we would delicate and difficult questions about how our analysis deal with occurrences of 'is one of' in modal contexts. But if we follow the section 7 and don't I can't think any reason worry the consequence NO and NI stand or fall together. If we are going require counterpairings to be universally defined functions, we can simplify of analysis by helping to the standard functor R(x) for the object y Rxy, likewise the Y that RXY: Possibly φ(t1,..., ∃R(CR ∧ φ(R(t1),...,R(tn)))Analysis F* Necessarily tn)↔df ∀R(CR→ φ(R(t1),...,R(tn)) However, potential for scope ambiguity when dealing with iterated If we want Analysis F* to be to Analysis F, we must be careful to treat the complex terms as having scope. We want '^^Fa' to be equivalent to ∧ ∃S(CS ∧ FS(R(a))))', '
. It may be that whereas 'Lavid DeWis' bears thE same SemAntIc RelaTionS to 'David Lewis' tHAt 'DaVid Lewis' bears to itself, tHis is NoT GeneRAlLy truE of pairS Of CORefErEnTiaL nAMeS, or of PaiRs of disTinct variaBleS. 35TAke x to be an obJEcT which a couNteRpairing R mapS to Two disTiNct OBjectS y aNd z, X tO be any OBjects That incluDe x, And Y to BE be all tHE ObJectS to which objects in x BeAR R, except for z. ThEn RXY: eAcH Of x BEarS R tO one of Y, and EaCh of Y IS borne R TO bY ONE of x. since R is a counTerpairing sUCh tHat Rxz AnD RXy And not yz, it iS nOT neCessary that xx. CoNsider RusSell anD whiteheAD again. WOuld RuSseLl sTill HAvE bEen OnE Of tHEm If WHIteHead had fAiLeD to be AnytHING At alL? WoUld RUsselL still have beeN onE of tHEm iF RussEll haD faiLeD to be AnythiNg at aLl? the answers are faR froM obvious. IF we TrIed To TinkeR With coUntErpArt theoRy to allOW foR cONTInGent existence, we wouLd FACe Delicate And difFIcUlT QuestionS aBouT how OUR analYsis SHoUld deal wIth occURrEnCes of 'is OnE of' in mOdAl cOntExts. BUT if wE folloW the adviCe of sECtion 7 and don't boTHer, I can't think OF aNY OtHEr reAsoN to worry aboUt thE ConsEqueNCe ThaT nO and nI staNd OR fALl together. If we are goInG to reqUire cOunterpairingS to be univeRSALly definEd fuNCtIOns, we can simpliFy the FormulatioN Of our anaLysis By helpinG ourselveS TO the stanDarD fuNctOr nOTAtIon: R(x) stands foR THe obJeCt y such ThaT Rxy, and LikEwiSe R(x) stAnDs for the oBjects Y sUcH tHaT RxY: POssibLY φ(t1,..., tn)↔df ∃R(cR ∧ Φ(R(t1),...,r(tN)))AnAlysiS f* NecesSarilY φ(t1,..., tN)↔dF ∀R(cr→ φ(R(T1),...,R(tn)) HowEVeR, ABbreViAtIons LikE tHis crEate THe pOtentiaL for scope AmbIGuitY wHeN dealinG with iterated MoDalities. If We WanT AnalySIS F* to be eqUivalent to Analysis F, we muST be careFul To treAt thE complex tErmS R(ti) as HavINg wideSt possIble sCoPe. WE WAnt '^^Fa' TO Be EquIvAlent to '∃R(CR ∧ ∃s(cs ∧ FS(r(a))))', not '
. It may be that whereas ' Lavid Dewi s' be ars  th esame  sem antic relation s  to'David Lewis' that 'Da vid L ew i s' b e ar s toitself, th i s  is  n ot  ge ne r al ly tr ueof pair s of coref ere nt ial names, o r  o f pairs of  di stinct varia ble s. 35T ak e x to be  an  obje ct whi c h a co unterpair in g  R map s  to two d is tinc t objects y and z ,  X to be any obje cts th at in c l ude  X,  and Y tobe  be a l l the o b je c t s  to which objects  in X bearR , e xceptfo r z .  ThenRXY:ea c h o f X bears R  toone of Y,  and e a ch of Y is born e R to  by  on e of X.  S inc eR  is acou n ter pairingsu ch  that  Rxz a n d  RXY  an d no t Yz,  it is not ne ces sary tha t Xx.  Cons ider  R ussel l andWhite he ad again. Would  Rus sell stil l h av e b ee n one of the m i f W hitehea d had f a ile dt o be  anything at all?Wo u l dRussellstillh av eb een oneof  th em i f Russe ll h a dfailed t o be a n yt hi ng at a ll ? Thean swe rsare f a r fr om obv ious. If  we t r ied to tinkerw ith counterpa r tt h eo r y to  al low for con ting e nt e xist e nc e,w e wou ld fa ce de l icate and difficult  q uestio ns ab out how our a nalysis sh o u l d deal w itho cc u rrences of 'is  oneof' in mod a l contex ts. B ut if we  follow t h e  adviceofsec tio n 7 a nd  don't bother , I ca n' t think  of  any ot her  re aso n t oworry abo ut the c on se qu en cethatN O and NI  s tan dorfallt ogethe r. If  wear eg oin g to re q ui r e  cou nt er pair ing sto be  uni v ers ally de fined fun cti o ns,we  c an simp lify the form ul ation of o ur  an alysis b y helpin g ourselves to the stan d ard fun cto r not atio n: R(x) s tan ds for  th e  objec t y su ch th at  Rx y ,  andl i ke wis eR(X) stand s for  theob ject s Y suc h that RXY: Possib l y φ (t1,..., tn)↔ df∃R(C R ∧φ(R ( t1 ) ,.. ., R (tn ) ) )Analysis F* Ne cessarilyφ( t 1, ..., tn)↔d f  ∀R (C R→ φ(R( t1),... ,R(tn ) ) Howev er, abbre viationsli ke t h i s c reate thepotentia l for sco p e amb i gu ity w hen  deali ng  wi th it erated mod aliti es. If  w e want  Anal ys is F* to  be equivalent to Analy sis F,  we m ust  be caref ult o t reat thecomp lex termsR(t i)as ha vin g  wide st p o ss ibl e  scop e. W e  want '^^ F a'  to b eequivalentt o '∃R (CR ∧  ∃S ( CS ∧ F S(R( a))))', not '
. It_may be_that whereas 'Lavid Dewis'_bears the_same_semantic relations_to_'David Lewis' that_'David Lewis' bears_to itself, this is_not generally true_of_pairs of coreferential names, or of pairs of distinct variables. 35Take x to be_an_object which_a_counterpairing_R maps to two distinct_objects y and z, X_to be_any objects that include X, and Y to_be_be all the_objects to which objects in X bear R, except_for z. Then RXY: each of_X bears R_to_one_of Y, and each_of Y is borne R to_by one of X. Since R_is a counterpairing such that Rxz and_RXY and not Yz, it is_not necessary that Xx. Consider_Russell and_Whitehead again. Would Russell still_have been one_of them_if Whitehead had_failed to be anything at all?_Would Russell still_have been one of them if_Russell_had failed to_be_anything_at all?_The answers are_far_from obvious._If_we tried to tinker with counterpart_theory_to allow for contingent existence, we would_face delicate and difficult_questions_about how our analysis_should deal with occurrences of_'is one of' in modal contexts._But if_we follow_the advice of section 7 and don't bother, I can't think_of any other reason to worry_about the consequence that_NO and_NI_stand or fall_together._If we_are going to require counterpairings to be_universally defined_functions, we can simplify the formulation_of our analysis by_helping_ourselves to the standard functor notation:_R(x) stands for the object y_such that Rxy, and likewise_R(X)_stands_for the objects Y such_that RXY: Possibly φ(t1,..., tn)↔df ∃R(CR_∧ φ(R(t1),...,R(tn)))Analysis F*_Necessarily φ(t1,..., tn)↔df ∀R(CR→ φ(R(t1),...,R(tn)) However, abbreviations_like_this create the potential for scope_ambiguity_when dealing with iterated modalities. If_we_want_Analysis F* to be equivalent_to Analysis F, we must be_careful to treat the complex terms R(ti) as having_widest possible scope._We want '^^Fa' to be_equivalent_to_'∃R(CR ∧ ∃S(CS ∧ FS(R(a))))', not '