 agent's degree of belief in the hypothesis given the background assumptions is measured by F (H,¬E,B) = [ Pr (¬E | H ∩B)− Pr (¬E | ¬H ∩B) Pr (¬E | H ∩B) + Pr (¬E | ¬H ∩B) ] For an agent with degree of belief function Pr the expected epistemic value of an experiment E with possible experimental outcomes E and ¬E for hypothesis H relative to background assumptions B can then be defined in the standard decision-theoretic way as F (H, E, B) = F (H,E,B) Pr (E | B) + F (H,¬E,B) Pr (¬E | B) There are other measures of incremental confirmation besides F, and it is an interesting question which one is best suited for measuring an agent's epistemic value of an experimental outcome for a hypothesis relative to some background assumptions. Importantly, though, Bayesian confirmation theorists rule out that any measure of incremental confirmation be used for this purpose. For instance, Christensen ([1999]) wants to capture the support an agent's confidence in H already receives from E (in contrast to the potential further support that might be gotten from raising Pr(E)). (Christensen [1999], p. 449, notation adapted) He thus explicitly rules out that confirmation be used to measure the epistemic value of experimental outcomes. 13 Other philosophers follow Christensen in aiming at an explication of "actualized support" (Christensen [1999], p. 449) as opposed to potential further support. More specifically, many Bayesian confirmation theorists are committed to denying that a measure of confirmation quantifies potential further support, even if they do not deny this explicitly. This can be seen from the fact that they take the following to be a problem for their accounts of incremental confirmation. Recall that evidence E incrementally confirms hypothesis H relative to background assumption B and probability measure Pr just in case Pr (H | E ∩B) > Pr (H | B). On this account, evidence E which receives probability one relative to background assumptions B cannot confirm or disconfirm any hypothesis H. The reason is that the conditional probability of the hypothesis given the evidence and the background assumptions, Pr (H | E ∩B), equals the probability of the hypothesis given merely the background assumptions, Pr (H | B), if the probability of the evidence given the background assumptions equals one, Pr (E | B)
agent's degree of belief in the hypothesis give the setting assumptions is measured by F (H,¬E, B) = [ Pr (¬E | H ∩B)− Pr (¬E | ¬H ∩B) Pr (¬E | H ∩B) + Pr (¬E | ¬H ∩B) ] For an agentive role with degree of belief function Pr the expect epistemic value of an experiment E with possible experimental result E and ¬E for hypothesis heat content relative to background presumption B can then be define in the standard decision - theoretical way as F (H, E, B) = F (H, E, B) Pr (east | B) + F (H,¬E, B) Pr (¬E | B) There embody other measures of incremental confirmation besides F, and it is an interesting motion which one is best suited for measuring an agent's epistemic value of an experimental result for a hypothesis relative to some background assumptions. Importantly, though, Bayesian confirmation theorist rule out that any measure of incremental confirmation be used for this purpose. For instance, Christensen ([ 1999 ]) want to appropriate the support an agent's confidence in H already receives from E (in contrast to the potential further support that might be gotten from raise Pr(E) ). (Christensen [ 1999 ], p. 449, notation adapted) He therefore explicitly predominate out that ratification be used to measure the epistemic value of experimental outcomes. 13 Other philosophers follow Christensen in aiming at an explication of " actualized support " (Christensen [ 1999 ], p. 449) as oppose to potential further support. More specifically, many Bayesian confirmation theorists are committed to traverse that a measure of confirmation quantifies potential further support, even if they do not deny this explicitly. This can be see from the fact that they take the pursuit to be a trouble for their account of incremental confirmation. Recall that evidence E incrementally confirms guess H relative to background assumption B and probability measure Pr just in case Pr (H | E ∩B) > Pr (H | B). On this score, evidence E which get probability one relative to setting assumptions bacillus cannot confirm or disconfirm any hypothesis H. The rationality is that the conditional probability of the hypothesis give the evidence and the background assumptions, Pr (H | E ∩B), equals the probability of the hypothesis give merely the background assumptions, Pr (H | B), if the probability of the evidence given the background assumptions equals one, Pr (E | B )
 agfnt's degree of belief in the hypothesis given vhe baciground xssumptions is measured by F (H,¬W,B) = [ Kg (¬E | H ∩B)− Pr (¬E | ¬H ∩B) Pr (¬E | H ∩B) + Ir (¬E | ¬H ∩B) ] Foc an agent with vsgree on beljcf fuucvion Pr the expgcted epistekic value of at dx'eriment E with possible experimentaj outcoked E and ¬E for rypouhefis G relative to background assumptiohs B cai then be definrd in the standard decisioj-thelretic way as F (H, F, B) = F (H,E,B) Kd (E | B) + F (H,¬E,B) Pr (¬E | B) Thert cre other mgasures of incremental confirmatkon bzsides F, ane ut lv an interewting question whlbh one hs best suited for messucing an agent's epistemic talue of an experimegtal outcmmz for a hypothesis reoarive jo soke bxxkgfouhd aasumptlona. Importanfly, though, Vayesian confirmatipn nneorists ruls out ehwt any measure of incremental confirmatpon ge used for this purposw. For instance, Christgnsen ([1999]) wanes to capture the support an agent's confidence in H alcexdy rcceixws from E (in contrast to the potential further fhpkorn that might be gjtten from talsogg Pr(E)). (Christgnsen [1999], '. 449, hotation adapted) Hf thus gxplicutly rulef ouy that confirmation be used to measure nhe wpistemic value of experimentcl outvomes. 13 Other philosophers foulow Christensej in aimihe at an explicatkon ox "actualized support" (Chriseensen [1999], p. 449) as opposea to poteneial furthfr sui[ort. More specificwlly, laty Bayesiaj confirmation theorists are committed to deniinc tvat a mecsure pf confirmatijn quantifies kotential furtfer supporn, even if they do noe deny this efklicitly. This can be feen fron the fxzt that they tske the following ti be a problem for thgid accounts of iuertmwntal confirmayiov. Rqcwlk evat evidence E ivcrdkentauly confirmw hyppthesis H relative tm badkground assumptiom N and provability measure Pr jist in case Pr (H | T ∩B) > Pc (H | B). On tnis account, evidence E which recejves probwbijity one relwtivc to backgrounb assumptions B cannot confirm or disconhirm any hypothesis H. Jhe reason is that thg cpnditional 'robabylity of dhe hypothesis given the evidence and the background assumltions, Pr (H | E ∩B), equals the probability of the hypothesis given merely the backgroune assumptions, Pr (H | B), of thv pxobcbility of vhx evidence given nhe background assumptions equalr one, Pr (E | B)
agent's degree of belief in the hypothesis background is measured F (H,¬E,B) = ∩B)− (¬E | ¬H Pr (¬E | ∩B) + Pr (¬E | ¬H ] For an agent with degree of belief function Pr the expected epistemic of an experiment E with possible experimental outcomes E and ¬E for hypothesis relative background B then be defined in the standard decision-theoretic way as F (H, E, B) = F (H,E,B) (E | B) + F (H,¬E,B) Pr (¬E B) There are other of incremental confirmation besides F, it an interesting which is suited for measuring agent's epistemic value of an experimental outcome for a hypothesis relative to some background assumptions. Importantly, though, confirmation theorists that any of confirmation used for this instance, Christensen ([1999]) wants to capture agent's confidence in H already receives from E contrast to potential further support that might be from raising Pr(E)). (Christensen [1999], p. 449, notation He thus explicitly rules out that confirmation be used to measure the epistemic value of 13 Other philosophers follow in aiming at explication "actualized (Christensen p. 449) opposed to potential further support. More specifically, many Bayesian confirmation theorists committed to denying that a measure of confirmation quantifies potential even they do not this explicitly. This can seen the fact that they following be their of confirmation. Recall that evidence incrementally confirms hypothesis H relative background assumption B and case Pr (H | E ∩B) > Pr | B). On this account, evidence E receives probability one relative to background assumptions B cannot confirm or disconfirm hypothesis H. is that the conditional probability of the hypothesis the evidence and the assumptions, Pr (H | E ∩B), equals the probability the given merely background assumptions, Pr | B), if probability of the the background equals Pr
 agent's degree of belief in the Hypothesis Given The BacKgRounD assUmptions is measURed bY F (H,¬E,B) = [ Pr (¬E | H ∩B)− Pr (¬E | ¬H ∩B) Pr (¬E | H ∩B) + Pr (¬e | ¬H ∩B) ] FoR aN AgenT WiTh degRee of beLIeF FUncTiOn pr tHe EXpEcted EpiStemic vAlue of an exPerImEnt E with possIBlE experimenTal Outcomes E and ¬e foR hypotHeSis h RelatIve To bacKgrounD AssumpTions B can ThEN be defINed in thE STaNdarD decision-theoretiC WaY As F (H, E, B) = F (H,E,B) Pr (E | B) + f (H,¬E,B) Pr (¬e | B) tHeRE Are OthEr measures Of IncreMEntal coNFiRMATioN Besides F, and it Is an interesTIng QuestiOn WhiCH one is Best sUiTEd fOr measuring An agEnt's epistEmic vaLUe of an eXPerimenTal outComE foR a hyPOtHeSis ReLAtiVE tO soME baCkground AsSuMptioNs. ImPORTAntlY, thOugh, bayesIan confirmatiOn tHeorISts Rule oUt thaT any MeAsure Of incrEmentAl Confirmation be uSed fOr this purPosE. FOr iNsTance, cHristeNseN ([1999]) waNts to caPture thE SupPoRT AN aGent's confidence in H AlREAdY receiveS from E (IN cOnTRast to thE pOteNtiaL FUrtheR supPOrT that migHt be goTTeN fRom raisInG Pr(E)). (ChRiSteNseN [1999], p. 449, notATion AdapteD) He thus eXplicITly rules out thaT Confirmation bE UsED To MEasuRe tHe epistemic ValuE Of exPeriMEnTal OUtcomEs. 13 OthEr PHiLOsophers follow ChrisTeNsen in AiminG at an explicatIon of "actuaLIZEd supporT" (ChrIStENsen [1999], p. 449) as opposed To potEntial furtHEr supporT. More SpecificAlly, many BAYEsian conFirMatIon TheORIsTs are committeD TO denYiNg that a MeaSure of cOnfIrmAtiOn qUaNtifies poTential fUrThEr SuPpoRt, eveN If they do NoT deNy ThiS explICitly. THis caN be sEeN fROm tHe fact tHAt THEy taKe ThE folLowInG to be A proBLem For theiR accounts Of iNCremEnTaL confirMation. Recall tHaT evidence E InCreMentalLY Confirms Hypothesis H relative to baCKground AssUmptiOn B aNd probabiLitY measuRe PR Just in Case Pr (h | E ∩B) > Pr (h | B). on tHIS accoUNT, eVidEnCe E which reCEIveS probAbIlitY one relAtive to background aSSumPtions B cannot ConFirm OR DiScoNFiRM anY hYPotHESis H. The reason is That the conDiTIoNal probabiLIty Of The hypoThesis gIven tHE evidenCe and the bAckground AsSumpTIOns, pr (H | E ∩B), equalS the probAbility of THe hypOThEsis gIveN merelY tHe bAckgrOund asSUmpTions, pr (H | B), if ThE probaBilitY oF the evidEnce given the background aSsumptIons eQuaLs one, Pr (E | B)
 agent's degree of beliefin the hyp othes isgiv en  the  bac kground assump t ions  is measured by F (H,¬ E,B)=[  Pr( ¬E  | H∩B)− Pr (¬ E | ¬ H∩B ) P r( ¬E  | H∩B)  + Pr ( ¬E | ¬H ∩B ) ]  F or an agentw it h degree o f b elief functi onPr the  e xpe c ted e pis temic  value of anexperimen tE  withp ossible e xp erim ental outcomes Ea nd ¬E for hypothe sis Hre l at i v e t o b ackgroundas sumpt i ons B c a nt h e n b e  defined in t he standard dec ision- th eor e tic wa y asF( H,E, B) = F ( H,E, B) Pr (E| B) + F (H,¬E , B) Pr ( ¬E | B ) T her e ar e  o th erme a sur e sofi ncr ementalco nf irmat ionb e s i desF,andit is  an interesti ngques t ion  whic h one  isbe st su ited f or me as uring an agent' s ep istemic v alu eofan  expe r imenta l o utc ome for  a hypo t hes is r e la tive to some backg ro u n dassumpti ons. I m po rt a ntly, th ou gh,  Bay e s ian c onfi r ma tion the orists ru le  out th at  any m ea sur e o f inc r emen tal co nfirmati on be used for thisp urpose. For i n st a n ce ,  Chr ist ensen ([199 9])w ants  toc ap tur e  thesuppo rt an agent's confidencein  H alr eadyreceives from  E (in con t r a st to th e po t en t ial further su pport  that migh t  be gott en fr om raisi ng Pr(E)) . (Christe nse n [ 199 9], p .449, notation a dapt ed ) He th usexplici tly  ru les  ou tthat conf irmation  b eus ed  to  meas u re the e pi ste mi c v alueo f expe rimen talou tc o mes . 13 Ot h er p hilo so ph ersfol lo w Chr iste n sen  in aim ing at an  ex p lica ti on  of "ac tualized supp or t" (Christ en sen  [1999 ] ,  p. 449)  as opposed to potentia l  furthe r s uppor t. M ore speci fic ally,man y  Bayes ian co nfirm at ion t heori s t sare  c ommitted t o den yingth at a  measur e of confirmationq uan tifies potent ial  fur t h er  su p po r t,ev e n i f they do not den y this exp li c it ly. This c a n b eseen fr om thefactt hat the y take th e followi ng  tob e  aproblem fo r theiraccountso f inc r em ental  co nfirma ti on.  Reca ll tha t  ev idenc e E in cr ementa lly c on firms hy pothesis H relative tobackgr oundass umption B  an d  pr obability  mea sure Pr ju stincasePr( H | E  ∩B) >Pr( H | B ). O n  this acc o un t,e v id ence E whic h r ece ivespro b abilit y on e relative to bac k ground assumpt ions B  ca nno t  con fi rm or disconfi rman y hypothes is  H. The rea son is t ha t  thecondit ionalprobabi l i ty of the  hyp oth esis give n t he evidenc ean d  the b ackg ro und as sumpti o ns,P r  (H | E ∩B), equ als t h e  prob a bil ity o fthe hyp o thes is given m erely the b ackgro undassum ptions,  P r (H |  B) ,if the pro b ability o f the  eviden ce  giv enthe ba ckgr o u nd as sump ti ons  equals o n e ,P r(E | B )
 agent's_degree of_belief in the hypothesis_given the_background_assumptions is_measured_by F (H,¬E,B)_= [ Pr_(¬E | H ∩B)−_Pr (¬E |_¬H_∩B) Pr (¬E | H ∩B) + Pr (¬E | ¬H ∩B) ] For_an_agent with_degree_of_belief function Pr the expected_epistemic value of an experiment_E with_possible experimental outcomes E and ¬E for hypothesis_H_relative to background_assumptions B can then be defined in the standard_decision-theoretic way as F (H, E,_B) = F_(H,E,B)_Pr_(E | B) +_F (H,¬E,B) Pr (¬E | B)_There are other measures of incremental_confirmation besides F, and it is an_interesting question which one is best_suited for measuring an agent's_epistemic value_of an experimental outcome for_a hypothesis relative_to some_background assumptions. Importantly,_though, Bayesian confirmation theorists rule out_that any measure_of incremental confirmation be used for_this_purpose. For instance,_Christensen_([1999])_wants to_capture the support_an_agent's confidence_in_H already receives from E (in_contrast_to the potential further support that might_be gotten from raising_Pr(E))._(Christensen [1999], p. 449,_notation adapted) He thus explicitly_rules out that confirmation be used_to measure_the epistemic_value of experimental outcomes. 13 Other philosophers follow Christensen in aiming_at an explication of "actualized support"_(Christensen [1999], p. 449)_as opposed_to_potential further support._More_specifically, many_Bayesian confirmation theorists are committed to denying_that a_measure of confirmation quantifies potential further_support, even if they_do_not deny this explicitly. This can_be seen from the fact that_they take the following to_be_a_problem for their accounts of_incremental confirmation. Recall that evidence E_incrementally confirms hypothesis_H relative to background assumption B and_probability_measure Pr just in case Pr_(H_| E ∩B) > Pr (H_|_B)._On this account, evidence E_which receives probability one relative to_background assumptions B cannot confirm or disconfirm any hypothesis_H. The reason_is that the conditional probability_of_the_hypothesis given the evidence and the background assumptions, Pr (H_| E_∩B), equals the_probability of the hypothesis given merely the background assumptions, Pr_(H | B), if the probability of_the evidence given the background assumptions equals one, Pr (E |_B)