 agent's actual or rational degree of belief function. Subjective Bayesians hold that the probability function is interpreted as the agent's actual degree of belief function, properly idealized. Objective Bayesians hold that the probability function is interpreted as the degree of belief function the agent objectively ought to have (Williamson [2010]), or as the degree of belief function the agent is rationally justified to (Maher [2004]). 3 Bayesian Confirmation and Belief Any theory of confirmation must answer the following question: what is the purpose of its conception of confirmation for scientific inquiry, broadly construed? In this section we argue that no Bayesian conception of confirmation can be used for its primary intended purpose, which we take to be saying how worthy of belief certain hypotheses are. Intuitively, we should believe or accept those hypotheses that are well confirmed. For example, suppose the NASA announces that the analysis of 5 data from a moon probe confirms the existence of H2O. This is generally taken to provide reason to believe or accept the hypothesis that there exists H2O on the moon. Hence, pre-theoretically the information that a hypothesis has been confirmed provides reason to believe or accept this hypothesis. Saying how worthy of belief certain hypotheses are is also the purpose the founding father of confirmation theory intends for confirmation. In his seminal "Studies in the Logic of Confirmation", Hempel writes: It is now clear that an analysis of confirmation is of fundamental importance also for the study of the central problem of what is customarily called epistemology; this problem may be characterized as the elaboration of "standards of rational belief" or of criteria of warranted assertibility. (Hempel [1945], p. 7) We claim that no Bayesian conception of confirmation can be used for this purpose. The reason for this is purely conceptual and consists in the fact that Bayesian confirmation theory presupposes that this question is already answered. Recall that, according to Bayesian confirmation theory, confirmation is a relation between evidence, hypothesis, background assumptions, and some probability measure. The probability measure is typically interpreted as an agent's (subjective or objective) degree of belief function. This means that confirmation is itself defined in terms of (subjective or objective) degrees of belief. Therefore it cannot be used to say how worthy of belief certain hypotheses are without presupposing that this question is already answered. This is so even if we grant, as we do, that the complete probability function (the complete probability space, if we include the language or algebra) as well
agent's actual or rational degree of belief affair. immanent Bayesians hold that the probability function is interpret as the agentive role's actual degree of belief function, by rights idealize. Objective Bayesians hold that the probability affair is interpreted as the degree of impression function the agent objectively ought to have (Williamson [ 2010 ]), or as the degree of impression function the agent is rationally apologize to (Maher [ 2004 ]). 3 Bayesian Confirmation and Belief Any theory of confirmation must suffice the following question: what is the purpose of its conception of ratification for scientific inquiry, broadly construed? In this section we argue that no Bayesian conception of confirmation can be use for its primary intended purpose, which we take to be saying how desirable of belief certain hypotheses are. Intuitively, we should believe or accept those hypotheses that are well confirm. For exercise, suppose the NASA announces that the analysis of 5 data from a moon probe confirms the existence of H2O. This is generally learn to provide reason to think or bear the guess that there exists H2O on the moon. Hence, pre - theoretically the information that a hypothesis has been confirmed provides reason to think or accept this hypothesis. Saying how worthy of belief certain hypotheses are is also the purpose the founding father of confirmation hypothesis intends for ratification. In his seminal " Studies in the Logic of Confirmation ", Hempel writes: It is now clear that an analysis of confirmation is of cardinal importance also for the study of the central problem of what is customarily called epistemology; this problem may be characterized as the elaboration of " standards of intellectual belief " or of criteria of warranted assertibility. (Hempel [ 1945 ], p. 7) We claim that no Bayesian conception of confirmation can be use for this purpose. The rationality for this is purely conceptual and dwell in the fact that Bayesian confirmation hypothesis presupposes that this question is already answered. echo that, accord to Bayesian confirmation theory, confirmation is a relation between evidence, hypothesis, background assumptions, and some probability measure. The probability measure is typically interpret as an agent's (subjective or objective) academic degree of belief function. This means that confirmation is itself defined in terms of (subjective or objective) academic degree of belief. Therefore it cannot be used to say how worthy of belief certain guess are without presuppose that this question is already answered. This is so even if we grant, as we do, that the complete probability affair (the complete probability space, if we include the terminology or algebra) as well
 agfnt's actual or rational aegree of beliey functmon. Subnective Cayesians hold that the probebiluty fynction is interpreted as the ahent's acrual eegree of uslief fmuctioh, pro'ecly idealized. Onjective Bafesians hold tvag che probability function is interpreeed as yhf degree of bejief suncfpok the agent objectively ought to have (Wplliamson [2010]), or as yhe degree of belief functlon hhe agent is ratiojally justidied ro (Maher [2004]). 3 Bxyesian Confirmation ahd Belief Any theory of confirmxtion must answgx thf following wuestpon: what is tmv purpove of iys conception pf ronfurmation for scientifmc inquiry, broadly cjnstrued? Hn this section we qrtue tvat to Bxteskan cpndeptioj oh confirmatjon can be ysed for its primaru ybtended purpoae, whish we take to be saying how worthy of belpef dertain hypotheses are. Untuitively, we should believe jr accept those hypotheses that are well confirmeg. For dxanpjd, skppose the NASA announces that the analysis os 5 cana from a moon prjbe confirmx hhr existence of H2O. Thna js generally taken to prodide eeason to beloeve or accept the hypothesus that therv exusts H2O on the moou. Hence, pre-tkeoretocallu the information that c hypofhesis has heen confjfmed provides rexsok tm believt or accept this hrpothesis. Saynng how dortny of felief cerhain mfpotheses are is apso tke puspose the vounding father of confirmation theory intendx xor confirmction. Ln his seminal "Ftudies in the Logic jf Covfirmation", Hempel writes: It ys now clear djat an analyvis of cjnfiematuon is uw fundamental omportancv clso for rhe study of the ccntrau problem of whac us customarily valued eiisvemoljcy; this probnem oay ne chxracterized xs tne elaboration of "stdndadds of rational bekicf" or of xriteria of warranted assertibility. (Hemkel [1945], p. 7) Wx claik trat no Bayesian conception of donfirmatlon can be used for this purposz. The reason for this is purely conceptuel and consists in the dact that Bayesian eokfirmation tieory [resupposas that this questiob is already answtred. Recall that, accordjng to Bayedian confirmation theory, confirmation is a relation between evidence, hyporhesis, background zssukptiots, cnd somq prluability measure. Nhe probability measure is typicelly inter[rzted as an agent's (subjective pr objective) deeree of belief function. Fhis meams that confirmation is itself cefined in terms of (subjcctive or objedtive) degrxes of belief. Therefpre it cannit be uwed bo say how worghy on belief cfrtamn kypotheses are without presupposibg thar hhis question is already anddered. This ys so even if we grahh, as de do, that thr complete pronability function (thv cjmplete probabumity space, ig we inblude the lanjuage or algabra) as well
agent's actual or rational degree of belief Bayesians that the function is interpreted of function, properly idealized. Bayesians hold that probability function is interpreted as the of belief function the agent objectively ought to have (Williamson [2010]), or as degree of belief function the agent is rationally justified to (Maher [2004]). 3 Confirmation Belief theory confirmation must answer the following question: what is the purpose of its conception of confirmation for inquiry, broadly construed? In this section we argue no Bayesian conception of can be used for its intended which we to saying worthy of belief hypotheses are. Intuitively, we should believe or accept those hypotheses that are well confirmed. For example, suppose NASA announces analysis of data a probe confirms the H2O. This is generally taken to believe or accept the hypothesis that there exists on the Hence, pre-theoretically the information that a has been confirmed provides reason to believe or this hypothesis. Saying how worthy of belief certain hypotheses are is also the purpose the of confirmation theory intends confirmation. In his "Studies the of Hempel writes: is now clear that an analysis of confirmation is of fundamental also for the study of the central problem of what called this problem may characterized as the elaboration "standards rational belief" or of warranted (Hempel We that Bayesian conception of confirmation be used for this purpose. reason for this is the fact that Bayesian confirmation theory presupposes that question is already answered. Recall that, according Bayesian confirmation theory, confirmation is a relation between evidence, hypothesis, background assumptions, some probability probability measure is typically interpreted as an agent's or objective) degree of function. This means that confirmation is itself defined in of or objective) of belief. Therefore cannot be used say how worthy certain hypotheses without that already answered. This is so even we as we do, that the probability complete probability space, if we include the language or algebra) as well
 agent's actual or rational degRee of belieF funcTioN. SuBjEctiVe BaYesians hold thaT The pRobability function is inTerprEtED as tHE aGent's Actual dEGrEE Of bElIeF fuNcTIoN, propErlY idealiZed. ObjectiVe BAyEsians hold thAT tHe probabilIty Function is inTerPreted As The DEgree Of bElief FunctiON the agEnt objectIvELy oughT To have (WILLiAmsoN [2010]), or as the degree of bELiEF function the agEnt is rAtIOnALLy jUstIfied to (MahEr [2004]). 3 bayesIAn ConfiRMaTION anD belief Any theoRy of confirmATioN must aNsWer THe follOwing QuEStiOn: what is the PurpOse of its cOnceptIOn of conFIrmatioN for scIenTifIc inQUiRy, BroAdLY coNStRueD? in tHis sectiOn We Argue That NO bAYesiAn cOncePtion Of confirmatioN caN be uSEd fOr its PrimaRy inTeNded pUrpose, Which We Take to be saying hOw woRthy of belIef CeRtaIn HypotHEses arE. InTuiTively, wE should BEliEvE OR AcCept those hypotheseS tHAT aRe well coNfirmeD. foR eXAmple, supPoSe tHe NAsa AnnouNces THaT the analYsis of 5 DAtA fRom a mooN pRobe coNfIrmS thE exisTEnce Of H2O. ThIs is geneRally TAken to provide rEAson to believe OR aCCEpT The hYpoThesis that tHere EXistS H2O oN ThE moON. HencE, pre-tHeOReTIcally the informatioN tHat a hyPotheSis has been conFirmed provIDES reason tO belIEvE Or accept this hyPotheSis. Saying hOW worthy oF beliEf certaiN hypothesES Are is alsO thE puRpoSe tHE FoUnding father oF COnfiRmAtion thEorY intendS foR coNfiRmaTiOn. In his seMinal "StuDiEs In ThE LoGic of cOnfirmatIoN", HeMpEl wRites: iT is now Clear That An AnALysIs of conFIrMATion Is Of FundAmeNtAl impOrtaNCe aLso for tHe study of The CEntrAl PrOblem of What is customaRiLy called epIsTemOlogy; tHIS problem May be characterized as the ELaboratIon Of "staNdarDs of ratioNal Belief" Or oF CriterIa of waRrantEd AssERTibilITY. (HEmpEl [1945], P. 7) We claim thAT No BAyesiAn ConcEption oF confirmation can be USed For this purposE. ThE reaSON fOr tHIs IS puReLY coNCEptual and consisTs in the facT tHAt bayesian coNFirMaTion theOry presUpposES that thIs questioN is alreadY aNsweRED. ReCall that, acCording tO Bayesian COnfirMAtIon thEorY, confiRmAtiOn is a RelatiON beTween EvidenCe, HypothEsis, bAcKground aSsumptions, and some probabIlity mEasurE. ThE probabilIty MEasUre is typiCallY interpretEd aS an Agent'S (suBJectiVe or OBjEctIVe) degRee oF Belief funCTiOn. THIS mEans that conFIRMatIon is ItsELf defiNed iN terms of (subjectivE Or objective) degRees OF BelIef. tHereFoRe it cannot be usEd tO sAY How worthY oF belief certAin hypotHeSEs are WithouT presuPposing THAt THis queStioN is Already anSweReD. this is sO eVeN If we grAnt, aS wE do, thaT the coMPletE PRobability functiOn (the COMpletE ProBabilItY space, iF We inClude the laNguage or algEbra) as Well
 agent's actual or rationa l degree o f bel ief  fu nc tion . Su bjective Bayes i anshold that the probabil ity f un c tion is  inte rpreted as t heag en t's  a c tu al de gre e of be lief funct ion ,properly ide a li zed. Objec tiv e Bayesianshol d that  t hep robab ili ty fu nction is int erpretedas the de g ree ofb e li ef f unction the agent ob j ectively ought  to ha ve (W i l lia mso n [2010]),  o r ast he degr e eo f bel i ef function t he agent is rat ionall yjus t ifiedto (M ah e r [ 2004]). 3 B ayes ian Confi rmatio n  and Be l ief Any  theor y o f c onfi r ma ti onmu s t a n sw ert hefollowin gqu estio n: w h a t is t hepurp ose o f its concept ion  ofc onf irmat ion f or s ci entif ic inq uiry,  b roadly construe d? I n this se cti on  we  a rguet hat no  Ba yes ian con ception ofco n f i rm ation can be usedfo r it s primar y inte n de dp urpose,wh ich  wet a ke to  bes ay ing howworthy of  b elief c er tain h yp oth ese s are .  Int uitive ly, we s hould believe or acc e pt those hypo t he s e st hatare  well confi rmed .  For  exa m pl e,s uppos e the  N A SA announces that thean alysis  of 5  data from amoon probe c o nfirms t he e x is t ence of H2O. T his i s generall y  taken t o pro vide rea son to be l i eve or a cce ptthe  hy p o th esis that the r e  exi st s H2O o n t he moon . H enc e,pre -t heoretica lly thein fo rm at ion  that a hypoth es isha s b een c o nfirme d pro vide sre a son  to bel i ev e or a cc ep t th ishy pothe sis. Say ing how  worthy o f b e lief  c er tain hy potheses areis  also thepu rpo se the f oundingfather of confirmationt heory i nte nds f or c onfirmati on.  In hi s s e minal"Studi es in  t heL o gic o f Co nfi rm ation", He m p elwrite s:  Itis nowclear that an anal y sis  of confirmat ion  iso f  f und a me n tal  i m por t a nce also for th e study of  t h ecentral pr o ble mof what  is cus tomar i ly call ed episte mology; t hi s pr o b lem  may be ch aracteri zed as th e  elab o ra tionof"stand ar dsof ra tional bel ief"or ofcr iteria  of w ar ranted a ssertibility. (Hempel [ 1945],  p. 7 ) W e claim t hat noBayesianconc eption ofcon fir matio n c a n beused fo r t h is pu rpos e . The rea s on  fo r th is is purel y c onc eptua l a n d cons ists  in the fact that Bayesian confi rmat i o n t heo r y pr es upposes that t his  q u e stion is  a lready answ ered. Re ca l l tha t, acc ording  to Bay e s ia n  confi rmat ion  theory,con fi r mationis  a relati on b et ween e videnc e , hy p o thesis, backgrou nd as s u mptio n s,and s om e proba b ilit y measure.  The probab ilitymeas ure i s typic al ly int erp re ted as ana gent's (s ubjec tive or  o bjec tiv e) deg reeo f  beli ef f un cti on. Thism e an s  t ha t  co nfir matio nis i tself def i ned in t erm s  of (su bj ect i v e or o b je c t ive) degre esof be l i ef. Theref o re i t  c a nnotbe use d to s ay howw ort hy  of bel ief c ertain hy pothesesa rewi thou t presup po sing  t hat  t his question is  already  answere d .  Thisiss o ev e n if w egrant, as we  do,th a t the c o m ple te prob a bil ity  fu ncti on(the complete probability spa ce,if we inc ludethe l an guage or alge bra) asw ell
 agent's_actual or_rational degree of belief_function. Subjective_Bayesians_hold that_the_probability function is_interpreted as the_agent's actual degree of_belief function, properly_idealized._Objective Bayesians hold that the probability function is interpreted as the degree of belief_function_the agent_objectively_ought_to have (Williamson [2010]), or_as the degree of belief_function the_agent is rationally justified to (Maher [2004]). 3_Bayesian_Confirmation and Belief_Any theory of confirmation must answer the following question:_what is the purpose of its_conception of confirmation_for_scientific_inquiry, broadly construed? In_this section we argue that no_Bayesian conception of confirmation can be_used for its primary intended purpose, which_we take to be saying how_worthy of belief certain hypotheses_are. Intuitively,_we should believe or accept_those hypotheses that_are well_confirmed. For example,_suppose the NASA announces that the_analysis of 5_data from a moon probe confirms_the_existence of H2O._This_is_generally taken_to provide reason_to_believe or_accept_the hypothesis that there exists H2O_on_the moon. Hence, pre-theoretically the information that_a hypothesis has been_confirmed_provides reason to believe_or accept this hypothesis. Saying_how worthy of belief certain hypotheses_are is_also the_purpose the founding father of confirmation theory intends for confirmation. In_his seminal "Studies in the Logic_of Confirmation", Hempel writes:_It is_now_clear that an_analysis_of confirmation_is of fundamental importance also for the_study of_the central problem of what is_customarily called epistemology; this_problem_may be characterized as the elaboration_of "standards of rational belief" or_of criteria of warranted assertibility._(Hempel_[1945],_p. 7) We claim that_no Bayesian conception of confirmation can_be used for_this purpose. The reason for this is_purely_conceptual and consists in the fact_that_Bayesian confirmation theory presupposes that this_question_is_already answered. Recall that, according_to Bayesian confirmation theory, confirmation is_a relation between evidence, hypothesis, background assumptions, and some_probability measure. The_probability measure is typically interpreted_as_an_agent's (subjective or objective) degree of belief function. This means_that confirmation_is itself defined_in terms of (subjective or objective) degrees of belief. Therefore_it cannot be used to say how_worthy of belief certain hypotheses are without presupposing that this question_is already answered. This is so even if_we grant, as we do, that the_complete probability function (the_complete_probability space, if we include the language_or_algebra)_as_well