 when E1 _ p is certain. And of course E1 _ p may be certain, even when neither E1 nor p is. This undercuts their \triviality" claim, and as it turns out EEE3 is not trivial at all. In fact, it's false. MORE TROUBLES FOR COMESÃNA AND TAL 3 We'll assume in establishing this that there is a largest proposition algebra A on which the \background prior" is dened. We will consider a case in which S1's total evidence proposition (i.e. the maximally specic proposition in A known by S1 to be true) is some probabilistically non-trivial E0. Now take E1 to be any non-trivial proposition in A that is entailed by, but not probabilistically equivalent to, E0. Next put E2 = E1 ^:E0. Finally, let p = :E0. Since E0 entails E1, E1 is evidence that S1 has. Since E2 entails E1 and E1 is non-trivial, E1 is evidence for E2. And of course E2 entails p and so is evidence for it. The antecedent of EEE3 is therefore satised, but we claim that the consequent is not. Indeed, any evidence E3 2 A possessed by S1 must be entailed by E0 and so cannot conrm p = :E0. It is meanwhile unclear that any E3 62 A can constitute evidence for p, given that Prob(pjE3) will not exist. We see one plausible attempt. If S1's total evidence proposition were E1 rather than E0 then one might try to claim that E3 = my current credence in E2 is = Prob(E2jE1) is evidence for p on the grounds that a bystander accepting it would be justied in adopting S1's credence in E2 as their own and updating (by Jerey conditionalization, Jerey 1965) their credence in p to + (1  )Prob(pj:E2) > Prob(p). Given that S1's total evidence proposition is E0 = :p, however, this move is unavailable. One may sacrice realism for concreteness by setting A equal to some xed nite algebra of propositions. For example, if A consists just in the 252 propositions constraining Card
when E1 _ p is certain. And of course E1 _ p may be certain, even when neither E1 nor p is. This undercut their \triviality " title, and as it turns out EEE3 is not trivial at all. In fact, it's fake. MORE TROUBLES FOR COMESÃNA AND TAL 3 We'll assume in lay down this that there be a largest suggestion algebra A on which the \background prior " is de  ned. We will consider a character in which S1's total evidence proposition (i.e. the maximally speci  vitamin c proposition in A known by S1 to be true) is some probabilistically non - trivial E0. Now take E1 to be any non - fiddling proposition in A that is entailed by, but not probabilistically equivalent to, E0. Next put E2 = E1 ^:E0. last, let p =: E0. Since E0 entails E1, E1 is evidence that S1 has. Since E2 entails E1 and E1 is non - fiddling, E1 is evidence for E2. And of course E2 entails p and so is evidence for it. The antecedent of EEE3 is consequently satis  ed, but we claim that the consequent is not. Indeed, any evidence E3 2 A possessed by S1 must be entailed by E0 and so cannot con  rm p =: E0. It is meanwhile ill-defined that any E3 62 A can constitute evidence for p, given that Prob(pjE3) will not exist. We see one plausible attempt. If S1's total evidence proposition were E1 rather than E0 then one might try to claim that E3 = my current credence in E2 is = Prob(E2jE1) is evidence for phosphorus on the background that a bystander accepting it would be justi  ed in espouse S1's credence in E2 as their own and updating (by Je  rey conditionalization, Je  rey 1965) their credence in p to + (1 ) Prob(pj: E2) > Prob(p). give that S1's total evidence proposition is E0 = :p, however, this move is unavailable. One may sacri  ce realism for concreteness by adjust A equal to some xed nite algebra of propositions. For example, if A consists just in the 252 propositions stiffen Card
 whfn E1 _ p is certain. And on course E1 _ p mai ve cervain, evsn when veither E1 nor p is. This undeccutw theur \triviality" claim, ana as it tlrns out WEE3 ms not trivial av all. In fact, jb's fanwe. MORE TROUBLGS FOR COMESÃTA AND TAL 3 We'nl adsume in establishing this that thewe is a lwrgest proposijion sjgebda A on which the \background prior" is dentd. We will considet a case in which S1's total evifence proposition (l.e. the maxinallr specic propusition in A known by A1 to be true) is some probabilisgicalky non-trivuao E0. Tow take E1 vo be wny non-trivial propovition on A that is ektailxd bt, but not probabilistmcally equivalent to, E0. Next pgt E2 = E1 ^:E0. Finally, lwt p = :E0. Sinwe E0 wntxila X1, E1 is evldeice that S1 gas. Since E2 entails E1 and E1 is njb-trivial, E1 is evidegcq for E2. And of course E2 entails p and sm ia evidence for it. The abtecedent of EEE3 is tjerefore fatised, but we claim that the consequent is not. Itdeed, xny eyidevxe E3 2 A possessed by S1 must be entailed by E0 anq sp bannot conrm p = :E0. It is meanehllr unclear that any E3 62 A can constitute evldence sor p, given thwt Ptob(pjE3) will not exist. We sew one plausiyle attempt. If S1's totcl evidence 'roposotion were E1 rather than E0 tken ons might try to claim ghat E3 = my currevt bredance in T2 is = Prob(E2jE1) is edidence fir p on the groonds thwt a bystajder accepting it would he judthed in adooting S1's credence in E2 as their own and updatonc (bj Jerey cjnditlonalization, Jewey 1965) their crebence in p to + (1  )Prob(pj:V2) > Prob(p). Jiven that S1'f total evidetfe propositimn is E0 = :p, hiwevwr, this oove is unavaikable. One may sacrixe realism for congretevsss by setting C tqyal to some xec nkte apgxbra jx propositiots. Fur dcampld, if A conslstr juxt in the 252 propositimns donstraining Card
when E1 _ p is certain. And E1 p may certain, even when This their \triviality" claim, as it turns EEE3 is not trivial at all. fact, it's false. MORE TROUBLES FOR COMESÃNA AND TAL 3 We'll assume in this that there is a largest proposition algebra A on which the \background is ned. will a case in which S1's total evidence proposition (i.e. the maximally speci c proposition in A by S1 to be true) is some probabilistically E0. Now take E1 be any non-trivial proposition in that entailed by, not equivalent E0. Next put = E1 ^:E0. Finally, let p = :E0. Since E0 entails E1, E1 is evidence that S1 Since E2 and E1 non-trivial, is for E2. And E2 entails p and so is The antecedent of EEE3 is therefore satis ed, we claim the consequent is not. Indeed, any E3 2 A possessed by S1 must be by E0 and so cannot con rm p = :E0. It is meanwhile unclear that 62 A can constitute for p, given Prob(pjE3) not We one plausible If S1's total evidence proposition were E1 rather than E0 then might try to claim that E3 = my current credence is Prob(E2jE1) is evidence p on the grounds a accepting it would be in S1's as own updating (by Je rey Je rey 1965) their credence p to + (1 that S1's total evidence proposition is E0 = however, this move is unavailable. One may ce realism for concreteness by setting A equal to some xed nite of propositions. if A consists just in the 252 propositions Card
 when E1 _ p is certain. And of coursE E1 _ p may be ceRtain, EveN whEn NeitHer E1 Nor p is. This undeRCuts Their \triviality" claim, anD as it TuRNs ouT eEe3 is noT triviaL At ALL. In FaCt, It's FaLSe. mORE TrOUbLES FOR cOMESÃNA ANd TAl 3 WE'll assume in eSTaBlishing thIs tHat there is a lArgEst proPoSitIOn algEbrA A on wHich thE \BackgrOund prior" Is DEned. We WIll consIDEr A casE in which S1's total evIDeNCe proposition (i.E. the maXiMAlLY SpeCic PropositioN iN A knoWN by S1 to bE TrUE) IS soME probabilistiCally non-triVIal e0. Now taKe e1 to BE any noN-trivIaL ProPosition in A That Is entaileD by, but NOt probaBIlisticAlly eqUivAleNt to, e0. neXt Put e2 = E1 ^:e0. finALlY, leT P = :E0. SInce E0 entAiLs e1, E1 is eVideNCE THat S1 Has. sincE E2 entAils E1 and E1 is noN-trIviaL, e1 is EvideNce foR E2. AnD oF courSe E2 entAils p AnD so is evidence foR it. THe antecedEnt Of eEE3 Is ThereFOre satIseD, buT we claiM that thE ConSeQUENt Is not. Indeed, any evidEnCE e3 2 A PossesseD by S1 muST bE eNTailed by e0 aNd sO canNOT conrM p = :E0. IT Is MeanwhilE uncleAR tHaT any E3 62 A cAn ConstiTuTe eVidEnce fOR p, giVen thaT Prob(pjE3) Will nOT exist. We see one PLausible attemPT. IF s1'S tOTal eVidEnce proposiTion WEre E1 RathER tHan e0 Then oNe migHt TRy TO claim that E3 = my currenT cRedencE in E2 iS = Prob(E2jE1) is eviDence for p oN THE grounds That A BySTander acceptinG it woUld be justiED in adoptIng S1's Credence In E2 as theiR OWn and updAtiNg (bY JeRey CONdItionalizatioN, jErey 1965) ThEir credEncE in p to + (1  )PRob(Pj:E2) > proB(p). GIvEn that S1's tOtal evidEnCe PrOpOsiTion iS e0 = :p, howeveR, tHis MoVe iS unavAIlable. one maY sacRiCe REalIsm for cONcRETeneSs By SettIng a eQual tO somE Xed Nite algEbra of proPosITionS. FOr Example, If A consists juSt In the 252 propoSiTioNs consTRAining CaRd
 when E1 _ p is certain. A nd of cour se E1  _p m ay  becert ain, even when neit her E1 nor p is. Thisunder cu t s th e ir  \tri viality "  c l a im,  a nd  as  i t  t urnsout  EEE3 i s not triv ial  a t all. In fa c t,  it's fals e.MORE TROUBLE S F OR COM ES ÃNA AND T AL3 We' ll ass u me inestablish in g  thist hat the r e  i s alargest propositi o na lgebra A on wh ich th e\ ba c k gro und  prior" is  d ened .  We wil l  c o n s ide r  a case in wh ich S1's to t aleviden ce  pr o positi on (i .e .  th e maximally  spe cic prop ositio n  in A k n own byS1 tobetru e) i s  s om e p ro b abi l is tic a lly  non-tri vi al  E0.Nowt a k e  E1tobe a ny no n-trivial pro pos itio n  in  A th at is  ent ai led b y, but  notpr obabilistically  equ ivalent t o,E0 . N ex t put E2 = E 1 ^ :E0 . Final ly, let p =  : E 0 .  S ince E0 entails E1 ,E 1  i s eviden ce tha t  S 1h as. Sinc eE2enta i l s E1andE 1is non-t rivial ,  E 1is evid en ce for  E 2.And  of c o urse  E2 en tails pand s o  is evidence f o r it. The ant e ce d e nt of E EE3  is therefo re s a tised,b ut  we claim  that  t h ec onsequent is not. I nd eed, a ny ev idence E3 2 A  possessed b y  S1 must  bee nt a iled by E0 and  so c annot conr m p = :E 0. It  is mean while unc l e ar thatany  E3  62  Ac a nconstitute ev i d ence  f or p, g ive n thatPro b(p jE3 ) w il l not exi st. We s ee  o ne  p lau sible attempt.  I f S 1' s t otale videnc e pro posi ti on wer e E1 ra t he r than  E 0then  on emight  try toclaim t hat E3 =myc urre nt  c redence  in E2 is = P ro b(E2jE1) i sevi dencef o r p on t he grounds that a bysta n der acc ept ing i t wo uld be ju sti ed in  ad o ptingS1's c reden ce  in E 2 ast h ei r o wn  and updat i n g ( by Je r ey c onditio nalization, Jerey 196 5) their cred enc e in p  t o + (1  ) Pr o b(p j : E2) > Prob(p).Given that  S 1 's  total evi d enc eproposi tion is  E0 = :p, how ever, thi s move is  u nava i l abl e. One may  sacric e realism for c o nc reten ess  by se tt ing  A eq ual to som e xed  niteal gebraof pr op ositions . For example, if A con sistsjustinthe 252 p rop o sit ions cons trai ning Card
 when_E1 __p is certain. And_of course_E1__ p_may_be certain, even_when neither E1_nor p is. This_undercuts their \triviality"_claim,_and as it turns out EEE3 is not trivial at all. In fact, it's_false._MORE TROUBLES_FOR_COMESÃNA_AND TAL 3 We'll assume_in establishing this that there_is a_largest proposition algebra A on which the \background_prior"_is dened. We_will consider a case in which S1's total evidence_proposition (i.e. the maximally specic proposition_in A known_by_S1_to be true) is_some probabilistically non-trivial E0. Now take_E1 to be any non-trivial proposition_in A that is entailed by, but_not probabilistically equivalent to, E0. Next_put E2 = E1 ^:E0._Finally, let_p = :E0. Since E0_entails E1, E1_is evidence_that S1 has._Since E2 entails E1 and E1_is non-trivial, E1_is evidence for E2. And of_course_E2 entails p_and_so_is evidence_for it. The_antecedent_of EEE3_is_therefore satised, but we claim that_the_consequent is not. Indeed, any evidence E3_2 A possessed by_S1_must be entailed by_E0 and so cannot conrm_p = :E0. It is meanwhile_unclear that_any E3_62 A can constitute evidence for p, given that Prob(pjE3) will_not exist. We see one plausible_attempt. If S1's total_evidence proposition_were_E1 rather than_E0_then one_might try to claim that E3 =_my current_credence in E2 is = Prob(E2jE1)_is evidence for p_on_the grounds that a bystander accepting_it would be justied in adopting_S1's credence in E2 as_their_own_and updating (by Jerey conditionalization,_Jerey 1965) their credence in p_to + (1_ )Prob(pj:E2) > Prob(p). Given that S1's_total_evidence proposition is E0 = :p,_however,_this move is unavailable. One may_sacrice_realism_for concreteness by setting A_equal to some xed nite algebra_of propositions. For example, if A consists just in_the 252 propositions_constraining Card