Necessarily, I is the identity relation' is also true in our current context, and so is 'Necessarily, Mars is red iff I(Mars) is red'. But even in this context, 'Necessarily, Mars is red iff Mars is actually red' is false. So in this context at least, we can't accept the analysis 'For Mars to be actually red is for I(Mars) to be red'. We could accept this analysis if we understood it not as a sentence of English but as a sentence of a three-sorted language standing to English as LW stands to LACT. But then again, while the three-sorted language can in some sense be translated into English, these translations don't seem to work like analyses. Does this mean that modal realists are after all are forced to accept "primitive modality" in the form of the 'actually' operator? I think not. It is a familiar point that the philosopher's 'actually' is impoverished by comparison with comparable devices in natural language. Actual sentences using 'actually' seem to exhibit something akin to scope ambiguity: it can locally undo some but not all of the modal operators in whose scope it occurs. For example, 'Necessarily, everyone could have had a child he doesn't actually have' is naturally read as inconsistent with the claim that possibly, some parent x has a child 28 y and could not have had any child other than y. It is easy to devise formal languages with 'actually'-like operators that exhibit this flexible behaviour. For example, we can have a modal language L↑↓ with a pair of operators ↑ and ↓, each taking a numerical subscript: ↑i functions like a label for a world which occurrences of ↓i within its scope can refer back to.50 The sentence above can then be symbolised as follows: ↑1∀x^∃y(y is a child of x ∧ ↓1¬(y is a child of x)). It is a straightforward matter to extend our translation scheme for 'actually' to this more flexible language. We use a stock of world variables W1,W2,W3.... In going from L↑↓ to LW, we replace '↓i...' with 'at Wi (...)', and we replace '↑i...' with ∃Wi(Wi are the identity pairs ∧...
Necessarily, I is the identity relation' is also true in our current context, and therefore is' inevitably, Mars is red iff I(Mars) is red'. But even in this context,' inevitably, Mars is red iff Mars is actually crimson' is false. So in this context at least, we can't bear the analysis' For Mars to be actually red is for I(Mars) to be crimson'. We could accept this analysis if we understand it not as a sentence of English but as a sentence of a three - grouped language standing to English as LW stands to LACT. But then again, while the three - sorted language can in some sense be translated into English, these translation don't seem to work like analyses. Does this think of that modal realists are after all are coerce to accept " primitive modality " in the form of the' actually' operator? I remember not. It is a familiar point that the philosopher's' actually' is impoverished by comparison with comparable devices in natural language. Actual sentences using' actually' seem to exhibit something akin to scope ambiguity: it can locally undo some but not all of the modal operators in whose scope it occurs. For example,' Necessarily, everyone could have have a child he doesn't actually have' is naturally read as inconsistent with the title that possibly, some parent x has a child 28 y and could not have had any child other than y. It is comfortable to devise conventional languages with' actually'-like operators that parade this flexible behaviour. For example, we can have a modal language L↑↓ with a pair of operator ↑ and ↓, each taking a numerical subscript: ↑i functions like a label for a world which occurrences of ↓i within its scope can refer back to.50 The conviction above can then be symbolised as follows: ↑1∀x^∃y(y is a child of x ∧ ↓1¬(y is a child of x) ). It is a straightforward matter to extend our transformation scheme for' actually' to this more flexible language. We use a stock of world variables W1,W2,W3.... In going from L↑↓ to LW, we replace' ↓i...' with' at Wi (...)', and we substitute' ↑i...' with ∃Wi(Wi are the identity pairs ∧...
Necfssarily, I is the identiuy relation' is also true in oud curreng context, and so is 'Necessarmly, Nars us red iff I(Mars) is rea'. But evej in thiw coitext, 'Necessarilb, Mars is red jnf Maxs is actually rgd' is false. Vo in this condebt at least, we can't accept the analysys 'For Kags to be actuajly geq is for I(Mars) to be red'. We could accelt this analysis if ee understood it not as a dentfnce of English buh as a sentghce if a three-softed language standing to English as LW stands to LACG. But then agaib, qhipg the three-sirted language cak in soke sensr be translatec iito Wnglish, these translavions don't seem to wjrk like dnclyses. Does this mean tyat mmdal reauustr ade arter apl ere forced fo accept "peimitive modality" im eye form of ths 'actuwljy' operator? I think not. It is a familiag pojnt that the philosophee's 'actually' is impovetished by somparison with comparable devices in natural lancuage. Xctbql sevrejces using 'actually' seem to exhibit something zkon to scope ambinuity: it can localky umqo some but nut all of the modal operatogs in wrose wcope it jccuts. For example, 'Necessarily, wveryone couje have had a child he doesn't cctualky hafe' is naturally read as incknsistent wlth the cmxim that possiblh, spma parent x has a child 28 y wnd could not have hxd amy chijd other tjan y. It is easy to devide fotmal ldnguages wlth 'actually'-like operators that exhibit this glaxitle behariour. Nor example, we san have a modcl langucge L↑↓ dith a paig of operetors ↑ and ↓, qach taking a jumerical suuscript: ↑i funxtiobs like x label for a eorld whibh occyrrences of ↓i withln itr scope can refex vack to.50 The senyenze wblvx can dhen be symbmlisdd xx foluows: ↑1∀x^∃y(y is x chold of x ∧ ↓1¬(y is a chind or x)). It is a straigntnorward mqtter to extend our ttanslation scheme vor 'artuallb' to tnis more flexible language. We use a stock lf rorld variabjes Q1,W2,W3.... In going from L↑↓ to LW, we replace '↓i...' with 'at Wi (...)', end we replace '↑i...' with ∃Wu(Wi are the identiti psirs ∧...
Necessarily, I is the identity relation' is in current context, so is 'Necessarily, is But even in context, 'Necessarily, Mars red iff Mars is actually red' false. So in this context at least, we can't accept the analysis 'For to be actually red is for I(Mars) to be red'. We could accept analysis we it as a sentence of English but as a sentence of a three-sorted language standing to English LW stands to LACT. But then again, while three-sorted language can in sense be translated into English, translations seem to like Does mean that modal are after all are forced to accept "primitive modality" in the form of the 'actually' operator? I not. It familiar point the 'actually' impoverished by comparison devices in natural language. Actual sentences to exhibit something akin to scope ambiguity: it locally undo but not all of the modal in whose scope it occurs. For example, 'Necessarily, could have had a child he doesn't actually have' is naturally read as inconsistent with that possibly, some parent has a child y could have any child than y. It is easy to devise formal languages with 'actually'-like that exhibit this flexible behaviour. For example, we can have language with a pair operators ↑ and ↓, taking numerical subscript: ↑i functions label a of within scope can refer back The sentence above can then symbolised as follows: ↑1∀x^∃y(y ∧ ↓1¬(y is a child of x)). It a straightforward matter to extend our translation for 'actually' to this more flexible language. We use a stock of variables W1,W2,W3.... from L↑↓ to LW, we replace '↓i...' with Wi (...)', and we '↑i...' with ∃Wi(Wi are the identity pairs ∧...
Necessarily, I is the identity Relation' is Also tRue In oUr CurrEnt cOntext, and so is 'NECessArily, Mars is red iff I(Mars) Is red'. buT Even IN tHis coNtext, 'NeCEsSARilY, MArS is ReD IfF Mars Is aCtually Red' is false. so iN tHis context at LEaSt, we can't acCepT the analysis 'for mars to Be ActUAlly rEd iS for I(mars) to BE red'. We Could accePt THis anaLYsis if wE UNdErstOod it not as a sentenCE oF english but as a sEntencE oF A tHREe-sOrtEd language StAndinG To EngliSH aS lw StaNDs to LACT. But thEn again, whilE The Three-sOrTed LAnguagE can iN sOMe sEnse be transLateD into EnglIsh, theSE translATions doN't seem To wOrk Like ANaLySes. doES thIS mEan THat Modal reaLiStS are aFter ALL ARe foRceD to aCcept "Primitive modaLitY" in tHE foRm of tHe 'actUallY' oPeratOr? I thiNk not. it Is a familiar poinT thaT the philoSopHeR's 'aCtUally' IS impovEriSheD by compArison wITh cOmPARAbLe devices in natural LaNGUaGe. Actual SentenCEs UsINg 'actualLy' SeeM to eXHIbit sOmetHInG akin to sCope amBIgUiTy: it can LoCally uNdO soMe bUt not ALl of The modAl operatOrs in WHose scope it occURs. For example, 'NECeSSArILy, evEryOne could havE had A ChilD he dOEsN't aCTuallY have' Is NAtURally read as inconsisTeNt with The clAim that possibLy, some pareNT X Has a chilD 28 y anD CoULd not have had anY chilD other than Y. it is easy To devIse formaL languageS WIth 'actuaLly'-LikE opEraTORs That exhibit thIS FlexIbLe behavIouR. For exaMplE, we Can HavE a Modal langUage L↑↓ witH a PaIr Of OpeRatorS ↑ And ↓, each tAkIng A nUmeRical SUbscriPt: ↑i fuNctiOnS lIKe a Label foR A wORLd whIcH oCcurRenCeS of ↓i wIthiN Its Scope caN refer bacK to.50 tHe seNtEnCe above Can then be symbOlIsed as follOwS: ↑1∀x^∃y(Y is a chILD of x ∧ ↓1¬(y is a Child of x)). It is a straightfoRWard matTer To extEnd oUr translaTioN schemE foR 'ActualLy' to thIs morE fLexIBLe lanGUAgE. We UsE a stock of wORLd vAriabLeS W1,W2,W3.... in going From L↑↓ to LW, we replace '↓I...' WitH 'at Wi (...)', and we repLacE '↑i...' wiTH ∃wi(wi aRE tHE idEnTIty PAIrs ∧...
Necessarily, I is the iden tity relat ion'isals otrue  inour current co n text , and so is 'Necessari ly, M ar s  isr ed  iffI(Mars) is r ed' .Bu t e ve n  i n thi s c ontext,  'Necessar ily ,Mars is redi ff  Mars is a ctu ally red' is  fa lse. S oint his c ont ext a t leas t , we c an't acce pt the an a lysis ' F o rMars  to be actually r e di s for I(Mars)to bere d '. W e c oul d accept t hi s ana l ysis if we u n der s tood it not a s a sentenc e  of  Engli sh  bu t  as asente nc e  of  a three-so rted  language  stand i ng to E n glish a s LW s tan dsto L A CT .But  t h ena ga in, whi le the t hr ee -sort ed l a n g u agecan  insomesense be tran sla tedi nto  Engl ish,thes etrans lation s don 't  seem to work l ikeanalyses.  Do es  th is  mean that m oda l r ealists  are af t eral l a re  forced to accept"p r i mi tive mod ality" in  t h e form o fthe  'ac t u ally'  ope r at or? I th ink no t .It  is a f am iliarpo int  th at th e  phi losoph er's 'ac tuall y ' is impoveris h ed by compari s on w it h  com par able device s in natu rall an gua g e. Ac tualse n te n ces using 'actually 'seem t o exh ibit somethin g akin tos c o pe ambig uity :  i t  can locally u ndo s ome but no t  all ofthe m odal ope rators in w hose sco peitocc urs . Fo r example, 'N e c essa ri ly, eve ryo ne coul d h ave  ha d a  c hild he d oesn't a ct ua ll yhav e' is naturall yrea dasincon s istent  with  the  c la i m t hat pos s ib l y , so me  p aren t x  h as achil d  28  y andcould not  ha v e ha dan y child  other than y .It is easy  t o d evisef o rmal lan guages with 'actually'- l ike ope rat ors t hatexhibit t his  flexi ble behavi our. F or ex am ple , we ca n ha veamodal lang u a geL↑↓ w it h apair of  operators ↑ and ↓ ,  ea ch taking a n ume rica l su bsc r ip t : ↑ if unc t i ons like a labe l for a wo rl d  w hich occur r enc es  of ↓iwithinits s c ope can  refer ba ck to.50Th e se n t enc e above ca n then b e symboli s ed as fo llows :  ↑1∀x^∃ y( y i s a c hild o f  x∧ ↓1¬ (y isachildof x) ).  It is a  straightforward matter  to ex tendour  translat ion sch eme for ' actu ally' to t his  mo re fl exi b le la ngua g e.  We use a  sto c k of worl d  v ari a b le s W1,W2,W3. . . .  In  goin g f r om L↑↓  toLW, we replace '↓ i ...' with 'atWi ( . . .)' , a n d we  r eplace '↑i...'  wi th ∃ Wi(Wi ar ethe identit y pairs∧. . .
Necessarily, I_is the_identity relation' is also_true in_our_current context,_and_so is 'Necessarily,_Mars is red_iff I(Mars) is red'._But even in_this_context, 'Necessarily, Mars is red iff Mars is actually red' is false. So in_this_context at_least,_we_can't accept the analysis 'For_Mars to be actually red_is for_I(Mars) to be red'. We could accept this_analysis_if we understood_it not as a sentence of English but as_a sentence of a three-sorted language_standing to English_as_LW_stands to LACT. But_then again, while the three-sorted language_can in some sense be translated_into English, these translations don't seem to_work like analyses. Does this mean_that modal realists are after_all are_forced to accept "primitive modality"_in the form_of the_'actually' operator? I_think not. It is a familiar_point that the_philosopher's 'actually' is impoverished by comparison_with_comparable devices in_natural_language._Actual sentences_using 'actually' seem_to_exhibit something_akin_to scope ambiguity: it can locally_undo_some but not all of the modal_operators in whose scope_it_occurs. For example, 'Necessarily,_everyone could have had a_child he doesn't actually have' is_naturally read_as inconsistent_with the claim that possibly, some parent x has a child_28 y and could not have_had any child other_than y._It_is easy to_devise_formal languages_with 'actually'-like operators that exhibit this flexible_behaviour. For_example, we can have a modal_language L↑↓ with a_pair_of operators ↑ and ↓, each_taking a numerical subscript: ↑i functions_like a label for a_world_which_occurrences of ↓i within its_scope can refer back to.50 The_sentence above can_then be symbolised as follows: ↑1∀x^∃y(y is_a_child of x ∧ ↓1¬(y is_a_child of x)). It is a_straightforward_matter_to extend our translation scheme_for 'actually' to this more flexible_language. We use a stock of world variables W1,W2,W3...._In going from_L↑↓ to LW, we replace_'↓i...'_with_'at Wi (...)', and we replace '↑i...' with ∃Wi(Wi are_the identity_pairs ∧...