 ifw is a p world, then Simw(p) =w. (See e.g. Stalnaker 1968; the constraint is motivated by the thought that a world is more similar to itself than to any other world.) And so ifw is a p world in BelS, thenw is in ConBelS(p). 13 ConBelS(p) contains only the p worlds in BelS because of the Stalnakerian Belief Set constraint. With non-(C)FWAs, there are p worlds in BelS. The Stalnakerian Belief Set Constraint then dictates that Simw(p)-and therefore ConBelS(p)-never reaches outside of BelS, for allw in BelS. So ifw is a p world in ConBelS(p), thenw is in BelS. With (17) established, return to our domain, ConBelS(p) ∪ ConBelS(¬p). With a non-(C)FWA, there are p worlds in BelS, so ConBelS(p) contains all and only the p worlds in BelS; with a non-(C)FWA, there are ¬p worlds in BelS, so ConBelS(¬p) contains all and only the ¬p worlds in BelS. Put these two facts together and ConBelS(p) ∪ ConBelS(¬p) contains all and only the worlds in BelS; in other words, our domain for non-(C)FWAs is BelS. 5.2 (C)FWAs While non-(C)FWAs operate entirely with the agent's indicative conditional beliefs, (C)FWAs operate half with the agent's indicative conditional beliefs and half with her counterfactual conditional beliefs. Begin with CFWAs. (18) Truth conditions for CFWAs, informally If S believes ¬p, ⌜S wants p⌝ is true iff: S prefers what she believeswould happen if p were true to what she believeswill happen given that ¬p is true. Take, for instance, our CFWA from before, (2), repeated below: (2) Wu wants to be promoted (but he believes he won't be). (2) is true just if he prefers what he believes would happen if he were to be promoted (this is the counterfactual element) to what he believes will happen given that he won't
ifw is a p world, then Simw(p) = w. (See e.g. Stalnaker 1968; the restraint is motivate by the idea that a world is more similar to itself than to any early world .) And so ifw is a p universe in BelS, thenw is in ConBelS(p). 13 ConBelS(p) contains only the phosphorus world in BelS because of the Stalnakerian Belief Set constraint. With non-(C)FWAs, there be p worlds in BelS. The Stalnakerian Belief Set Constraint then dictate that Simw(p)-and consequently ConBelS(p)-never reaches outside of BelS, for allw in BelS. So ifw is a phosphorus world in ConBelS(p), thenw is in BelS. With (17) build, fall to our domain, ConBelS(p) ∪ ConBelS(¬p). With a non-(C)FWA, there are p earth in BelS, so ConBelS(p) contains all and only the p universe in BelS; with a non-(C)FWA, there are ¬p worlds in BelS, so ConBelS(¬p) contains all and only the ¬p worldly concern in BelS. Put these two facts together and ConBelS(p) ∪ ConBelS(¬p) contains all and only the worlds in BelS; in other words, our domain for non-(C)FWAs is BelS. 5.2 (C)FWAs While non-(C)FWAs operate entirely with the agent's indicative conditional beliefs, (C)FWAs operate half with the agent's indicative conditional beliefs and one-half with her counterfactual conditional belief. Begin with CFWAs. (18) accuracy condition for CFWAs, informally If S believes ¬p, ⌜ S wants p ⌝ is genuine iff: S prefers what she believeswould happen if p were true to what she believeswill find given that ¬p is true. Take, for instance, our CFWA from before, (2), repeated below: (2) Wu wants to be promoted (but he believes he won't be). (2) is true just if he prefer what he believes would find if he were to be promote (this is the counterfactual element) to what he believes will happen given that he won't
 ifa is a p world, then Simw(k) =w. (See e.g. Stalnaker 1968; thx constdaint is motivated by the thought thet a worle is more similar to igself thaj to any othtr world.) And so ihs is a i wormf in UelS, thenw is ik ConBelS(p). 13 ConBelS(p) contdivs only the p worlds in BelS because jf the Xtwlnakerian Belyef Xqt cknstraint. With non-(C)FWAs, there are l worldv in BelS. The Stalnakerian Belief Set Clnstgaint then dictated that Simw(k)-znd rherefore CovBelS(p)-neveg reaches ootside of BelS, for allw in BelS. Ro ifc is a p wotls lt ConBelS(p), vhenw ps in BelS. Wibn (17) estdblishec, return to ouv domein, XonBelS(p) ∪ ConBelS(¬p). Wivh a non-(C)FWA, there ate p worldv nn BelS, so ConBelS(p) cinrains all and inlh tge p worldd ii BelS; with a non-(C)FWA, rhere are ¬p worlds on VelS, so ConBemS(¬p) cogtwins all and only the ¬p worlds in BelS. Kut tgese two facts together and ConBelS(p) ∪ ConBelD(¬p) contaigs all and only the worlds in BelS; in other words, our vooaiu for vin-(F)FWAs is BelS. 5.2 (C)FWAs While non-(C)FWAs operate egfiteky with the agcnt's indicative comdltojnal beliefs, (Z)FWAs opedate half with the agent's indixative cogditoonal beliefs and half with her counteryacrual conditional bzliefs. Begin witn CFWSs. (18) Truth conditions fox CFWAa, informallj If S bemkeves ¬p, ⌜S wants o⌝ ix drue iff: S prefers what shq believewwoukd happdn ig p wewe true to what she believeswill hwppen ghven that ¬o is true. Take, for instance, our CFWA from befpra, (2), gepeated yelow: (2) Wu wants to fe promoted (buj he belizves hd won't be). (2) is trux just if he prefers what je believes xould hap[en uf hw were gu be promoted (yhis is tkt counterfqctual element) to xhat ge believes wilo hqppen given thay hd wjn'n
ifw is a p world, then Simw(p) e.g. 1968; the is motivated by is similar to itself to any other And so ifw is a p in BelS, thenw is in ConBelS(p). 13 ConBelS(p) contains only the p worlds BelS because of the Stalnakerian Belief Set constraint. With non-(C)FWAs, there are p in The Belief Constraint then dictates that Simw(p)-and therefore ConBelS(p)-never reaches outside of BelS, for allw in BelS. So is a p world in ConBelS(p), thenw is BelS. With (17) established, to our domain, ConBelS(p) ∪ With non-(C)FWA, there p in so ConBelS(p) contains and only the p worlds in BelS; with a non-(C)FWA, there are ¬p worlds in BelS, so contains all the ¬p in Put two facts together ∪ ConBelS(¬p) contains all and only BelS; in other words, our domain for non-(C)FWAs BelS. 5.2 While non-(C)FWAs operate entirely with the indicative conditional beliefs, (C)FWAs operate half with the indicative conditional beliefs and half with her counterfactual conditional beliefs. Begin with CFWAs. (18) Truth CFWAs, informally If S ¬p, ⌜S wants is iff: prefers she believeswould if p were true to what she believeswill happen given that is true. Take, for instance, our CFWA from before, (2), (2) wants to be (but he believes he be). is true just if what believes he to promoted (this is the element) to what he believes happen given that he
 ifw is a p world, then Simw(p) =w. (See E.g. StalnakeR 1968; the cOnsTraInT is mOtivAted by the thougHT thaT a world is more similar to ItselF tHAn to ANy Other World.) AnD So IFW is A p WoRld In bEls, thenW is In ConBeLS(p). 13 ConBelS(P) coNtAins only the p WOrLds in BelS bEcaUse of the StalNakErian BElIef sEt conStrAint. WIth non-(c)fWAs, thEre are p woRlDS in Bels. the StalNAKeRian belief Set ConstraiNT tHEn dictates that simw(p)-aNd THeREForE CoNBelS(p)-neveR rEacheS Outside OF BELs, For ALlw in BelS. So ifW is a p world iN conbelS(p), tHeNw iS In BelS. with (17) eStABliShed, return tO our Domain, ConbelS(p) ∪ CONBelS(¬p). WITh a non-(C)fWA, theRe aRe p WorlDS iN BElS, So cOnBELS(P) coNTaiNs all and OnLy The p wOrldS IN bElS; wIth A non-(c)FWA, tHere are ¬p worldS in belS, SO CoNBelS(¬P) contAins AlL and oNly the ¬P worlDs In BelS. Put these tWo faCts togethEr aNd conbeLS(p) ∪ CoNbelS(¬p) cOntAinS all and Only the WOrlDs IN bEls; in other words, our doMaIN FoR non-(C)FWAS is Bels. 5.2 (c)FwAS while non-(c)FwAs OperATE entiRely WItH the agenT's indiCAtIvE conditIoNal belIeFs, (C)fWAS operATe haLf with The agent'S indiCAtive conditionAL beliefs and haLF wITH hER couNteRfactual conDitiONal bElieFS. BEgiN With CfWAs. (18) TRuTH cONditions for CFWAs, infOrMally IF S belIeves ¬p, ⌜S wants p⌝ Is true iff: S PREFers what She bELiEVeswould happen If p weRe true to whAT she beliEveswIll happeN given thaT ¬P Is true. TaKe, fOr iNstAncE, OUr cFWA from beforE, (2), REpeaTeD below: (2) WU waNts to be ProMotEd (bUt hE bElieves he Won't be). (2) is TrUe JuSt If hE prefERs what he BeLieVeS woUld haPPen if hE were To be PrOmOTed (This is tHE cOUNterFaCtUal eLemEnT) to whAt he BEliEves wilL happen giVen THat hE wOn'T
 ifw is a p world, then Si mw(p) =w.(Seee.g . S ta lnak er 1 968; the const r aint  is motivated by the t hough tt hata  w orldis more si m i lar  t oits el f  t han t o a ny othe r world.)And  s o ifw is a p wo rld in Bel S,thenw is inCon BelS(p ).  13 ConBe lS( p) co ntains only t he p worl ds in Bel S  becaus e of  the  Stalnakerian Bel i ef Set constraint . With  n o n- ( C )FW As,  there are  p  worl d s in Be l S. T h e S t alnakerian Be lief Set Co n str aint t he n d i ctates  that  S i mw( p)-and ther efor e ConBelS (p)-ne v er reac h es outs ide of  Be lS,  for al lw  in  B e lS. So  if w  is  a p wor ld  i n Con BelS ( p ) ,  the nwis i n Bel S. With (17)est abli s hed , ret urn t o ou rdomai n, Con BelS( p)  ∪ ConBelS(¬p).  Wit h a non-( C)F WA , t he re ar e  p wor lds  in  BelS,so ConB e lS( p) c o nt ains all and onlyth e pworlds i n BelS ;  w it h  a non-( C) FWA , th e r e are  ¬pw or lds in B elS, s o  C on BelS(¬p )contai ns  al l a nd on l y th e ¬p w orlds in  BelS .  Put these two facts togethe r  a n d  C o nBel S(p ) ∪ ConBelS (¬p) cont ains al l a n d onl y the  w o rl d s in BelS; in other  w ords,our d omain for non -(C)FWAs i s B elS. 5.2  (C) F WA s  While non-(C) FWAsoperate en t irely wi th th e agent' s indicat i v e condit ion albel ief s ,  ( C)FWAs operat e half  w ith the  ag ent's i ndi cat ive  co nd itional b eliefs a nd  h al fwit h her counterf ac tua lcon ditio n al bel iefs.  Beg in  w i thCFWAs.( 18 ) Trut hco ndit ion sfor C FWAs ,  in formall y If S be lie v es ¬ p,  ⌜ S wants  p⌝ is true i ff : S prefer swha t sheb e lieveswo uld happen if p were tr u e to wh atshe b elie veswill h app en giv ent hat ¬p  is tr ue. T ak e,f o r ins t a nc e,ou r CFWA fro m bef ore,(2 ), r epeated  below: (2) Wu wan t s t o be promoted  (b ut h e be lie v es hewo n 'tb e ). (2) is truejust if he  p r ef ers what h e  be li eves wo uld hap pen i f  he wer e to be p romoted ( th is i s the  counterfa ctual el ement) to whath ebelie ves  willha ppe n giv en tha t  he  won' t
 ifw_is a_p world, then Simw(p)_=w. (See_e.g._Stalnaker 1968;_the_constraint is motivated_by the thought_that a world is_more similar to_itself_than to any other world.) And so ifw is a p world in BelS,_thenw_is in_ConBelS(p)._13_ConBelS(p) contains only the p_worlds in BelS because of_the Stalnakerian_Belief Set constraint. With non-(C)FWAs, there are p_worlds_in BelS. The_Stalnakerian Belief Set Constraint then dictates that Simw(p)-and therefore_ConBelS(p)-never reaches outside of BelS, for_allw in BelS._So_ifw_is a p world_in ConBelS(p), thenw is in BelS._With (17) established, return to our_domain, ConBelS(p) ∪ ConBelS(¬p). With a non-(C)FWA,_there are p worlds in BelS,_so ConBelS(p) contains all and_only the_p worlds in BelS; with_a non-(C)FWA, there_are ¬p_worlds in BelS,_so ConBelS(¬p) contains all and only_the ¬p worlds_in BelS. Put these two facts_together_and ConBelS(p) ∪_ConBelS(¬p)_contains_all and_only the worlds_in_BelS; in_other_words, our domain for non-(C)FWAs is_BelS._5.2 (C)FWAs While non-(C)FWAs operate entirely with_the agent's indicative conditional_beliefs,_(C)FWAs operate half with_the agent's indicative conditional beliefs_and half with her counterfactual conditional_beliefs. Begin_with CFWAs._(18) Truth conditions for CFWAs, informally If S believes ¬p, ⌜S_wants p⌝ is true iff: S_prefers what she believeswould_happen if_p_were true to_what_she believeswill_happen given that ¬p is true. Take,_for instance,_our CFWA from before, (2), repeated_below: (2) Wu wants_to_be promoted (but he believes he_won't be). (2) is true just_if he prefers what he_believes_would_happen if he were to_be promoted (this is the counterfactual_element) to what_he believes will happen given that he_won't