icitly, in others implicitly – by proponents of Bayesian confirmation theory. We conclude in section 5. 2 Bayesian Confirmation Theory Bayesian confirmation theory is defined within the general Bayesian framework. The latter consists of the synchronic norm that an agent's degrees of belief should obey the probability calculus and the diachronic norm that, depending on the format of the new information received, the agent's degrees of belief should be updated by strict conditionalization or Jeffrey conditionalization (Jeffrey [1983a]) or Field conditionalization (Field [1978]). Bayesian confirmation theory adds two notions of confirmation to this general Bayesian framework: absolute confirmation and incremental confirmation. According to both notions confirmation is a relation between evidence E, hypothesis H, background assumptions B, and some probability measure Pr (and some formal language of sentences or algebra of propositions, which may be ignored for present purposes). Evidence E is said to absolutely confirm hypothesis H relative to background assumptions B and probability function Pr if and only if the conditional probability of the hypothesis given the evidence and the background assumptions is sufficiently high, Pr(H | E ∩B) > r, where r is a number not smaller than 1/2, but smaller than 1. The degree of absolute confirmation of hypothesis H by evidence E relative to background assumptions B is defined as the conditional probability of the hypothesis given the evidence and the background assumptions, Pr(H | E ∩B). Evidence E is said to incrementally confirm hypothesis H relative to background assumptions B and probability function Pr if and only if the conditional probability of the hypothesis given the evidence and the background assumptions is greater than the probability of the hypothesis given 4 merely the background assumptions, Pr(H | E ∩ B) > Pr(H | B). The degree of incremental confirmation of hypothesis H by evidence E relative to background assumptions B is defined as the distance between the conditional probability of the hypothesis given the evidence and the background assumptions, Pr (H | E ∩B), and the probability of the hypothesis given merely the background assumptions, Pr (H | B). There are several ways to measure distance (Earman [1992], ch. 5), and there are other quantities the distance between which can be measured (Joyce [2003]). The way distance is measured, and the quantities between which it is measured, affect the validity of various arguments in Bayesian confirmation theory (Brössel [2013]; Fitelson [1999]). However, these differences do not matter for present purposes. The probability measure figuring in these definitions of confirmation is typically interpreted as an
icitly, in others implicitly – by proponents of Bayesian confirmation theory. We conclude in incision 5. 2 Bayesian Confirmation Theory Bayesian ratification theory is defined within the cosmopolitan Bayesian framework. The latter consist of the synchronic norm that an agentive role's degree of belief should obey the probability tartar and the diachronic average that, depending on the format of the new data received, the agent's degree of impression should be updated by strict conditionalization or Jeffrey conditionalization (Jeffrey [ 1983a ]) or Field conditionalization (Field [ 1978 ]). Bayesian ratification theory add two notions of confirmation to this general Bayesian framework: absolute ratification and incremental confirmation. According to both impression confirmation is a sexual intercourse between evidence E, hypothesis H, background assumptions B, and some probability measure Pr (and some formal linguistic process of sentences or algebra of propositions, which may be ignored for present purposes). Evidence E is said to absolutely confirm hypothesis H relative to background assumptions B and probability function Pr if and only if the conditional probability of the hypothesis given the evidence and the background assumptions is sufficiently eminent, Pr(H | E ∩B) > r, where r is a issue not little than 1/2, but smaller than 1. The degree of absolute confirmation of guess H by evidence east relative to background assumption B is defined as the conditional probability of the hypothesis given the evidence and the background assumptions, Pr(H | E ∩B). Evidence E is suppose to incrementally confirm hypothesis H relative to background assumptions B and probability affair Pr if and only if the conditional probability of the hypothesis given the evidence and the background assumptions is capital than the probability of the hypothesis given 4 merely the background assumptions, Pr(H | E ∩ B) > Pr(H | B). The degree of incremental confirmation of hypothesis H by evidence einsteinium relative to background premise B is defined as the distance between the conditional probability of the guess given the evidence and the background assumptions, Pr (H | E ∩B), and the probability of the guess given merely the background assumptions, Pr (H | B). There be several room to measure distance (Earman [ 1992 ], ch. 5), and there are other quantities the distance between which can be measured (Joyce [ 2003 ]). The way distance is measured, and the quantities between which it is measure, affect the validity of versatile arguments in Bayesian confirmation hypothesis (Brössel [ 2013 ]; Fitelson [ 1999 ]). However, these differences do not matter for present purposes. The probability measure figuring in these definitions of confirmation is typically interpreted as an
icihly, in others implicitly – by proponents of Bayxsian cknfirmatkon theory. We conclude in sertiob 5. 2 Bqyesian Confirmation Tfeory Bayvsian condirmetion theory is vsfined within bhe gznxral Bayesian ftamework. The latter consisds oy the synchronic norm that an agent's degreex lf belief shoujd onqy tgv krobability calculus and the diacgronic iorm that, depencing on the format of the jew lnformation receivfd, the agenj'a dqtrees of belkef should be updated gy strict conditionalization or Jeffxey conditiinqlixdtion (Jeffrxy [1983a]) og Field condibponalizdtion (Foeld [1978]). Bayesian coifirnation theory adds twm notions of confitmation to tkis general Bayesian drqmewotk: abvolugw cunfjrkafion ajd mncremental confirmatiin. According to botn gitions confirjation if a relation between evidence E, hypothevis H, background assumptiobs B, and some probabipity meastre Pr (and some formal language of sentences or angebre uf kriposiguojs, which may be ignored for present purposes). Qbicekce E is said to absolutely clngyrm hypothesir H relatjve to background wssumptyons V and profabikity function Pr if and onlt if the conbituonal probability lf the hypochesis givem the evidence and the yackgrkund assumphions is ajfficiently high, Pr(M | A ∩B) > r, where r is a number not smaloer chan 1/2, bug smsller ehan 1. The fegrec of absolute configmatiln of hypothfsis H by evidence E relative to background axsgmpnions B if deflned as the conqitional probayility oy the fypothesis given vhe evidence and the backctound assumptmons, Pr(H | E ∩B). Evieence E ks said to inctementallj eonfirm htpothesis H relatiye to gackground assunptuons B and probsbiuitr vuictiog Pr if and otly kf gne covditional pvobxbiloty of the hypothesiv giben the evidence amd the bacjground wssumptions ix greater than the probebilitb of tne rypothesis given 4 merely the bzckground asfumptions, Pr(R | E ∩ B) > Pr(H | B). Che degree of incremental confirmation oh hypothesis H by evidgnce E relative to baeknround assum'tions B is defhned as the distance between the condltional probability of the hfpothfsis given the evidence and the background assumptions, Pr (H | E ∩B), and the probabmlyty of the gypoyhesiv yivzn merejy tie background assukptions, Pr (H | B). There are severel ways to mzasure distance (Earman [1992], ch. 5), amd there are otfer quantities the distahce betwren which can be measured (Joyce [2003]). The way distance is messured, abd ths quannjtmes between which it is mecsured, affect the validity of xarooms argumenhs ii Bcyesian confirmation theory (Brösseo [2013]; Fitwldon [1999]). However, theve differenger do hot majter for present lurpkdes. Tfe probabilitu measure figuting in these defininiogs of confirmauion is typicalky injzgpreted as an
icitly, in others implicitly – by proponents confirmation We conclude section 5. 2 theory defined within the Bayesian framework. The consists of the synchronic norm that agent's degrees of belief should obey the probability calculus and the diachronic norm depending on the format of the new information received, the agent's degrees of should updated strict or Jeffrey conditionalization (Jeffrey [1983a]) or Field conditionalization (Field [1978]). Bayesian confirmation theory adds two notions confirmation to this general Bayesian framework: absolute confirmation incremental confirmation. According to notions confirmation is a relation evidence hypothesis H, assumptions and probability measure Pr some formal language of sentences or algebra of propositions, which may be ignored for present purposes). Evidence is said confirm hypothesis relative background B and probability if and only if the conditional hypothesis given the evidence and the background assumptions sufficiently high, | E ∩B) > r, where is a number not smaller than 1/2, but than 1. The degree of absolute confirmation of hypothesis H by evidence E relative to B is defined as conditional probability of hypothesis the and background assumptions, | E ∩B). Evidence E is said to incrementally confirm hypothesis relative to background assumptions B and probability function Pr if if conditional probability of hypothesis given the evidence the assumptions is greater than of hypothesis the assumptions, | E ∩ B) Pr(H | B). The degree incremental confirmation of hypothesis to background assumptions B is defined as the between the conditional probability of the hypothesis the evidence and the background assumptions, Pr (H | E ∩B), and probability of given merely the background assumptions, Pr (H | There are several ways measure distance (Earman [1992], ch. 5), and there are quantities distance between can be measured [2003]). The way is measured, and between which is affect various arguments in Bayesian confirmation theory [2013]; [1999]). However, these differences do matter purposes. The probability measure figuring in these definitions of confirmation is typically interpreted as an
icitly, in others implicitly – bY proponentS of BaYesIan CoNfirMatiOn theory. We concLUde iN section 5. 2 Bayesian ConfirMatioN THEory bAyEsian ConfirmATiON TheOrY iS deFiNEd WithiN thE generaL Bayesian fRamEwOrk. The latter COnSists of the SynChronic norm tHat An agenT's DegREes of BelIef shOuld obEY the prObability CaLCulus aND the diaCHRoNic nOrm that, depending oN ThE Format of the new InformAtIOn RECeiVed, The agent's dEgRees oF Belief sHOuLD BE upDAted by strict cOnditionaliZAtiOn or JeFfRey COnditiOnaliZaTIon (jeffrey [1983a]) or FIeld ConditionAlizatIOn (Field [1978]). bAyesian ConfirMatIon TheoRY aDdS twO nOTioNS oF coNFirMation to ThIs GenerAl BaYESIAn frAmeWork: AbsolUte confirmatiOn aNd inCRemEntal ConfiRmatIoN. AccoRding tO both NoTions confirmatiOn is A relation BetWeEn eViDence e, HypothEsiS H, bAckgrouNd assumPTioNs b, AND sOme probability measUrE pR (aNd some foRmal laNGuAgE Of sentenCeS or AlgeBRA of prOposITiOns, which May be iGNoReD for preSeNt purpOsEs). EVidEnce E IS saiD to absOlutely cOnfirM Hypothesis H relATive to backgroUNd ASSuMPtioNs B And probabilIty fUNctiOn Pr IF aNd oNLy if tHe conDiTIoNAl probability of the hYpOthesiS giveN the evidence aNd the backgROUNd assumpTionS Is SUfficiently higH, Pr(H | E ∩b) > r, where r is A Number noT smalLer than 1/2, bUt smaller THAn 1. The degRee Of aBsoLutE COnFirmation of hyPOThesIs h by evidEncE E relatIve To bAckGroUnD assumptiOns B is deFiNeD aS tHe cOnditIOnal probAbIliTy Of tHe hypOThesis Given The eViDeNCe aNd the baCKgROUnd aSsUmPtioNs, PR(H | e ∩B). EviDencE e is Said to iNcrementaLly COnfiRm HyPothesiS H relative to bAcKground assUmPtiOns B anD PRobabiliTy function Pr if and only if THe condiTioNal prObabIlity of thE hyPothesIs gIVen the EvidenCe and ThE baCKGrounD ASsUmpTiOns is greatER ThaN the pRoBabiLity of tHe hypothesis given 4 mERelY the backgrounD asSumpTIOnS, Pr(h | e ∩ B) > pR(H | B). thE DegREE of incremental cOnfirmatioN oF HyPothesis H bY EviDeNce E relAtive to BackgROund assUmptions B Is defined As The dISTanCe between tHe conditIonal probABilitY Of The hyPotHesis gIvEn tHe eviDence aND thE backGround AsSumptiOns, Pr (h | E ∩b), and the pRobability of the hypothesIs giveN mereLy tHe backgroUnd ASsuMptions, Pr (h | B). ThEre are seveRal WayS to meAsuRE distAnce (eArMan [1992], CH. 5), and tHere ARe other quANtItiES ThE distance beTWEEn wHich cAn bE MeasurEd (JoYce [2003]). The way distance IS measured, and thE quaNTItiEs bETweeN wHich it is measurEd, aFfECT the valiDiTy of various ArgumentS iN bayesIan conFirmatIon theoRY (brÖSsel [2013]; FiTelsOn [1999]). HOwever, theSe dIfFErences Do NoT Matter For pReSent puRposes. tHe prOBAbility measure fiGurinG IN thesE DefInitiOnS of confIRmatIon is typicAlly interprEted as An
icitly, in others implicit ly – by pr opone nts  of  B ayes ianconfirmation t h eory . We conclude in secti on 5.  2 Baye s ia n Con firmati o nT h eor yBa yes ia n  c onfir mat ion the ory is def ine dwithin the g e ne ral Bayesi anframework. T helatter  c ons i sts o f t he sy nchron i c norm  that anag e nt's d e grees o f be lief  should obey thep ro b ability calcul us and  t h ed i ach ron ic norm th at , dep e nding o n  t h e for m at of the new  informatio n  re ceived ,the agent' s deg re e s o f belief sh ould  be updat ed bys trict c o ndition alizat ion  or  Jef f re ycon di t ion a li zat i on(Jeffrey  [ 19 83a])  orF i e l d co ndi tion aliza tion (Field [ 197 8]). Bay esian  conf irma ti on th eory a dds t wo  notions of con firm ation tothi sgen er al Ba y esianfra mew ork: ab solutec onf ir m a t io n and incrementalco n f ir mation.Accord i ng  t o  both no ti ons  con f i rmati on i s  a  relatio n betw e en  e vidence  E , hypo th esi s H , bac k grou nd ass umptions  B, a n d some probabi l ity measure P r  ( a n ds omefor mal languag e of sent ence s  o r a l gebra  of p ro p os i tions, which may be  i gnored  forpresent purpo ses). Evid e n c e E is s aidt oa bsolutely conf irm h ypothesisH  relativ e tobackgrou nd assump t i ons B an d p rob abi lit y fu nction Pr ifa n d on ly  if the  co ndition alpro bab ili ty  of the h ypothesi sgi ve nthe  evid e nce andth e b ac kgr ounda ssumpt ionsis s uf fi c ien tly hig h ,P r (H |  E  ∩ B) >  r,  w herer is a n umber n ot smalle r t h an 1 /2 ,but sma ller than 1.Th e degree o fabs olutec o nfirmati on of hypothesis H by e v idenceE r elati ve t o backgro und  assum pti o ns B i s defi ned a sthe c ondit i o na l p ro bability o f the  hypo th esis  giventhe evidence and t h e b ackground ass ump tion s ,  P r(H |E  ∩B ). Evi d e nce E is said t o incremen ta l ly  confirm h y pot he sis H r elative  to b a ckgroun d assumpt ions B an dprob a b ili ty functio n Pr ifand onlyi f the co nditi ona l prob ab ili ty of  the h y pot hesis  given  t he evi dence  a nd the b ackground assumptions i s grea ter t han  the prob abi l ity  of the h ypot hesis give n 4  me relythe backg roun d  a ssu m ption s, P r (H | E ∩B )> P r ( H| B). The d e g r eeof in cre m entalconf irmation of hypot h esis H by evid ence E  re lat i ve t obackground ass ump ti o n s B is d ef ined as the  distanc eb etwee n thecondit ional p r o ba b ilityof t hehypothesi s g iv e n the e vi de n ce and  the  b ackgro und as s umpt i o ns, Pr (H | E ∩B ), an d the p r oba bilit yof theh ypot hesis give n merely th e back grou nd as sumptio ns , Pr ( H |  B ). There a r e several  ways  to mea su re d ist ance ( Earm a n  [199 2],ch . 5 ), and th e r ea re  o t her  qua ntiti es  the  distance betweenwhi c h can b emea s u red (J o yc e [2003]). T heway d i s tance is m e asur e d, and t he qua ntitie s betwe e n w hi ch it i s m e a sured, af fect thev ali di ty o f variou sargu me nts  i n Bayesian conf irmation  theory( B rössel  [2 0 13]; Fitels on  [1999]). Ho wever ,t hese di f f ere nces do not  ma tte r fo r p rese n t purposes. The probabil itymeasu r e f iguri ng in  t hese def i niti ons of c o nfirmation is  typically inte r pre t ed a s a n 
icitly, in_others implicitly_– by proponents of_Bayesian confirmation_theory._We conclude_in_section 5. 2_Bayesian Confirmation Theory_Bayesian confirmation theory is_defined within the_general_Bayesian framework. The latter consists of the synchronic norm that an agent's degrees of_belief_should obey_the_probability_calculus and the diachronic norm_that, depending on the format_of the_new information received, the agent's degrees of belief_should_be updated by_strict conditionalization or Jeffrey conditionalization (Jeffrey [1983a]) or Field_conditionalization (Field [1978]). Bayesian confirmation theory_adds two notions_of_confirmation_to this general Bayesian_framework: absolute confirmation and incremental confirmation._According to both notions confirmation is_a relation between evidence E, hypothesis H,_background assumptions B, and some probability_measure Pr (and some formal_language of_sentences or algebra of propositions,_which may be_ignored for_present purposes). Evidence_E is said to absolutely confirm_hypothesis H relative_to background assumptions B and probability_function_Pr if and_only_if_the conditional_probability of the_hypothesis_given the_evidence_and the background assumptions is sufficiently_high,_Pr(H | E ∩B) > r, where_r is a number_not_smaller than 1/2, but_smaller than 1. The degree_of absolute confirmation of hypothesis H_by evidence_E relative_to background assumptions B is defined as the conditional probability of_the hypothesis given the evidence and_the background assumptions, Pr(H_| E_∩B)._Evidence E is_said_to incrementally_confirm hypothesis H relative to background assumptions_B and_probability function Pr if and only_if the conditional probability_of_the hypothesis given the evidence and_the background assumptions is greater than_the probability of the hypothesis_given_4_merely the background assumptions, Pr(H_| E ∩ B) > Pr(H_| B). The_degree of incremental confirmation of hypothesis H_by_evidence E relative to background assumptions_B_is defined as the distance between_the_conditional_probability of the hypothesis given_the evidence and the background assumptions,_Pr (H | E ∩B), and the probability of_the hypothesis given_merely the background assumptions, Pr_(H_|_B). There are several ways to measure distance (Earman [1992],_ch. 5),_and there are_other quantities the distance between which can be measured (Joyce_[2003]). The way distance is measured, and_the quantities between which it is measured, affect the validity of_various arguments in Bayesian confirmation theory (Brössel [2013];_Fitelson [1999]). However, these differences do not_matter for present purposes._The_probability measure figuring in these definitions of_confirmation_is_typically_interpreted as an