 of green cheese, even though this disjunction is a consequence of your belief and distinct from it. But perhaps this is because, once again, you do not need a reason to believe the disjunction, since perhaps in some way you already believe it by believing one of the disjuncts. However, if you believe the earth is flat, then surely in some sense that gives you a reason to believe the very distinct consequence that there is no horizon. In response to this contrary thought, I am willing to agree that in some sense or other your belief that the earth is flat gives you a reason to believe there is no horizon. In general, if you 6 believe P, in some sense or other this gives you a reason to believe the consequence Q, if Q is significantly different from P itself. But this sense is an unsatisfactory one. Expressed more precisely, the position is that a particular relation holds between your believing P and your believing Q: one rationally requires the other, as I shall put it. In symbols: B(P) O6 B(Q), (D) where O6 is this relation of rationally requiring. The formula (D) attaches rationality to the relation between the beliefs. In belief reasoning, the relation of rationally requiring mirrors the relation of entailment that holds between propositions. If one proposition entails another, believing the first rationally requires believing the second. 6. Rational requirement If we needed to formalize a rational requirement, we could adopt the notion of a 'conditional obligation' from deontic logic. (See the survey in Åqvist (1984).) The analysis of conditional obligations is by no means settled. (For a recent analysis, see Makinson (1998).) It might turn out, for instance, that (D) is best understood as: O(B(P) 6 B(Q)) where 'O' stands for 'ought' and '6' is the material conditional. But the important question for our purposes is whether (D) implies B(P) 6 R(B(Q)), (E) where '6' is the material conditional, and 'R' stands for 'have a reason to'. In (E), the rationality is attached to the consequent rather than the connective, as it is in (D). This means the consequent can be detached by modus ponens. From B(P) and (E), we can infer R(B(P)). If you believe P, then (E) says you have
of green cheese, even though this disjunction is a consequence of your belief and discrete from it. But possibly this is because, once again, you do not need a reason to think the disjunction, since possibly in some way you already believe it by believe one of the disjuncts. However, if you think the earth is flat, then surely in some sense that gives you a reason to think the very distinct consequence that there is no horizon. In response to this contrary opinion, I am willing to agree that in some sense or other your belief that the land is flat gives you a reason to think there is no horizon. In general, if you 6 think P, in some common sense or other this gives you a reason to believe the consequence Q, if Q is significantly different from phosphorus itself. But this sense is an unsatisfactory one. Expressed more precisely, the position is that a particular relation holds between your believe phosphorus and your believing Q: one rationally requires the other, as I shall put it. In symbols: B(P) O6 B(Q), (D) where O6 is this relation of rationally requiring. The rule (vitamin d) attaches rationality to the relation between the impression. In impression reasoning, the relation back of rationally requiring mirrors the relation of entailment that holds between propositions. If one proposition fee-tail another, believing the first rationally requires believing the second. 6. Rational requirement If we want to formalize a rational requirement, we could adopt the impression of a' conditional obligation' from deontic logic. (experience the sketch in Åqvist (1984) .) The analysis of conditional obligations is by no means settled. (For a late analysis, see Makinson (1998) .) It might turn out, for instance, that (D) is best understood as: O(B(P) 6 B(Q) ) where' O' stands for' ought' and' 6' is the material conditional. But the important motion for our purposes is whether (five hundred) implies B(P) 6 R(B(Q) ), (E) where' 6' is the fabric conditional, and' R' stands for' have a reason to'. In (E), the rationality is impound to the consequent rather than the connective, as it is in (five hundred). This means the consequent can be detached by modus ponens. From B(P) and (E), we can infer R(B(P) ). If you believe P, then (vitamin e) says you give birth
 of green cheese, even thougm this disjunction is a consesuence ow your belief and distinct fcom ut. Buu perhaps this is bdcause, onbe again, tou vo not need a reeaon to nzlievs the visjunction, singe perhaps hn some way yog xlxeady believe it by believing one of the dixjkncts. However, yf ypt bempeye the earth is flat, then surely in somt sense that gives you a reason to believe tje vfry distinct conseeuence that theww is no horixon. In reskouse to this contrary thought, I am willing go agxee that in sime vense or otier yolr belief thab the edrth is flat gives yom a rxasob to believe there is no horizon. In gengral, if yog 6 believe P, in somw wense or mthef thks fites you a reeson to beljeve the cobsequence Q, if Q is sytnificantly djfferegt from P itself. But this sense is an unsdtiafactory one. Expressed nore precisely, the podition is that a particular relation holds between your benieviig P ckq tokr believing Q: one rationally requires the otrsr, ax I shall put lt. In symbols: B(P) O6 B(E), (C) where O6 is tfis relatjon of rationally gequirigg. Thw formula (D) aytaches rationality to the eelation betceeb the beliefs. In bzlief reasonnng, thg relayion of rationally requnring jirrors the relation uf entailment thxt molgs betwetv propositions. If one propisitnon entakls snothew, believinh the first rationally rfquirgs belheving the second. 6. Rational requirement Ih we needed tp xorkalize a ratipnal requiremqnt, we could abopt the notiun of a 'cohditionel obligatiog' from deontiw logic. (See tie survey in Åwvisr (1984).) The xvalysis of concitional obligationw is by no means scttlea. (For a recent aucliwis, see Makinspn (1998).) It mpghv turg out, for insdancd, tfst (D) ks best undcrsgood as: O(B(P) 6 B(Q)) where 'O' vtanss for 'ought' and '6' os the matgrial conqitional. But yhe important quesuion fmr uur pirpjses is whether (D) implies B(P) 6 D(B(Q)), (E) whege '6' is the matewial conditional, and 'R' stands for 'have a reason to'. In (E), the rationality iw attached to the cpksequent ratier thwn the cotnective, as it is in (D). This means the consequent can be defached by mldus ponens. From B(P) and (E), we can infer R(B(P)). If you believe P, then (E) says yiu havx
of green cheese, even though this disjunction consequence your belief distinct from it. once you do not a reason to the disjunction, since perhaps in some you already believe it by believing one of the disjuncts. However, if you the earth is flat, then surely in some sense that gives you a to the distinct that there is no horizon. In response to this contrary thought, I am willing to agree in some sense or other your belief that earth is flat gives a reason to believe there no In general, you believe in some sense other this gives you a reason to believe the consequence Q, if Q is significantly different from itself. But is an one. more the position is particular relation holds between your believing believing Q: one rationally requires the other, as shall put In symbols: B(P) O6 B(Q), (D) O6 is this relation of rationally requiring. The (D) attaches rationality to the relation between the beliefs. In belief reasoning, the relation of mirrors the relation of that holds between If proposition another, the first requires believing the second. 6. Rational requirement If we needed to a rational requirement, we could adopt the notion of a from logic. (See the in Åqvist (1984).) The of obligations is by no (For recent (1998).) might out, for instance, that is best understood as: O(B(P) B(Q)) where 'O' stands the material conditional. But the important question for purposes is whether (D) implies B(P) 6 (E) where '6' is the material conditional, and 'R' stands for 'have reason to'. the rationality is attached to the consequent rather the connective, as it in (D). This means the consequent can be detached modus From B(P) (E), we can R(B(P)). If you P, then (E) have
 of green cheese, even though thIs disjunctIon is A coNseQuEnce Of yoUr belief and disTInct From it. But perhaps this is BecauSe, ONce aGAiN, you dO not neeD A rEASon To BeLieVe THe DisjuNctIon, sincE perhaps in SomE wAy you already BElIeve it by beLieVing one of the DisJuncts. hoWevER, if yoU beLieve The earTH is flaT, then sureLy IN some sENse that GIVeS you A reason to believe tHE vERy distinct consEquencE tHAt THEre Is nO horizon. In ReSponsE To this cONtRARY thOUght, I am willinG to agree thaT In sOme senSe Or oTHer youR beliEf THat The earth is fLat gIves you a rEason tO Believe THere is nO horizOn. IN geNeraL, If YoU 6 beLiEVe P, IN sOme SEnsE or other ThIs Gives You a REASOn to BelIeve The coNsequence Q, if Q Is sIgniFIcaNtly dIfferEnt fRoM P itsElf. But This sEnSe is an unsatisfaCtorY one. ExpreSseD mOre PrEciseLY, the poSitIon Is that a ParticuLAr rElATIOn Holds between your beLiEVInG P and youR belieVInG Q: ONe rationAlLy rEquiRES the oTher, AS I Shall put It. In syMBoLs: b(P) O6 B(Q), (D) wHeRe O6 is tHiS reLatIon of RAtioNally rEquiring. the foRMula (D) attaches rATionality to thE ReLATiON betWeeN the beliefs. in beLIef rEasoNInG, thE RelatIon of RaTIoNAlly requiring mirrorS tHe relaTion oF entailment thAt holds betWEEN proposiTionS. if ONe proposition eNtailS another, beLIeving thE firsT rationaLly requirES BelievinG thE seConD. 6. RaTIOnAl requirement iF We neEdEd to forMalIze a ratIonAl rEquIreMeNt, we could Adopt the NoTiOn Of A 'coNditiONal obligAtIon' FrOm dEontiC Logic. (SEe the SurvEy In åQviSt (1984).) The anALySIS of cOnDiTionAl oBlIgatiOns iS By nO means sEttled. (For A reCEnt aNaLySis, see MAkinson (1998).) It mighT tUrn out, for iNsTanCe, that (d) IS best undErstood as: O(B(P) 6 B(Q)) where 'O' staNDs for 'ouGht' And '6' is The mAterial coNdiTional. but THe impoRtant qUestiOn For OUR purpOSEs Is wHeTher (D) impliES b(P) 6 R(b(Q)), (E) whErE '6' is tHe materIal conditional, and 'R' STanDs for 'have a reaSon To'. In (e), THe RatIOnALitY iS AttACHed to the consequEnt rather tHaN ThE connectivE, As iT iS in (D). ThiS means tHe conSEquent cAn be detacHed by moduS pOnenS. fRom b(P) and (E), we caN infer R(B(p)). If you belIEve P, tHEn (e) says You Have
 of green cheese, even tho ugh this d isjun cti onis  a c onse quence of your beli ef and distinct from i t. Bu tp erha p sthisis beca u se , onc eag ain ,y ou  do n otneed areason tobel ie ve the disju n ct ion, since  pe rhaps in som e w ay you  a lre a dy be lie ve it  by be l ieving  one of t he disjun c ts. How e v er , if  you believe thee ar t h is flat, the n sure ly in s ome  se nse that g iv es yo u  a reas o nt o bel i eve the verydistinct co n seq uenceth att here i s noho r izo n. In respo nseto this c ontrar y  though t , I amwillin g t o a gree th at  in  s o mes en seo r o ther you rbe liefthat t h e  ear this f lat g ives you a re aso n to bel ievethere  isno  hori zon. I n gen er al, if you 6 be liev e P, in s ome  s ens eor ot h er thi s g ive s you a  reason tobe l i e ve  the consequence Q ,i f  Q  is sign ifican t ly  d i fferentfr omP it s e lf. B ut t h is  sense i s an u n sa ti sfactor yone. E xp res sed  more prec isely,  the pos ition is that a part i cular relatio n  h o l ds betw een  your belie ving P an d yo u rbel i eving  Q: o ne ra t ionally requires th eother,  as I  shall put it . In symbo l s :  B(P) O6  B(Q ) ,( D) where O6 is  this  relationo f ration allyrequirin g. The fo r m ula (D)att ach esrat i o na lity to the r e l atio nbetween  th e belie fs.  In  be lie freasoning , the re la ti on  o f r ation a lly requ ir ing  m irr ors t h e rela tionof e nt ai l men t thath ol d s  bet we en  pro pos it ions.  Ifo neproposi tion enta ils anot he r,  believ ing the first  r ationallyre qui res be l i eving th e second. 6. Rational r e quireme ntIf we  nee ded to fo rma lize a  ra t ionalrequir ement ,wec o uld a d o pt  th enotion ofa 'co nditi on al o bligati on' from deontic l o gic . (See the su rve y in Å qv ist (1 9 84) .) The a nalysis of cond itional ob li g at ions is by nome ans set tled. ( For a recentanalysis,  see Maki ns on ( 1 9 98) .) It migh t turn o ut, for i n stanc e ,that(D)  is be st  un derst ood as :  O( B(P)6 B(Q) )where'O' s ta nds for'ought' and '6' is themateri al co ndi tional. B utt heimportant  que stion forour  pu rpose s i s  whet her( D)  im p liesB(P) 6 R(B(Q)) ,  ( E)w h er e '6' is th e m ate rialcon d itiona l, a nd 'R' stands for 'have a reason  to' . In(E) ,  the  r ationality isatt ac h e d to the  c onsequent r ather th an the c onnect ive, a s it is i n( D). Th is m ean s the con seq ue n t can b ede t achedby m od us pon ens. F r om B ( P ) and (E), we ca n inf e r  R(B( P )).  If y ou  believ e  P,then (E) s ays you hav e
 of_green cheese,_even though this disjunction_is a_consequence_of your_belief_and distinct from_it. But perhaps_this is because, once_again, you do_not_need a reason to believe the disjunction, since perhaps in some way you already_believe_it by_believing_one_of the disjuncts. However, if_you believe the earth is_flat, then_surely in some sense that gives you a_reason_to believe the_very distinct consequence that there is no horizon. In_response to this contrary thought, I_am willing to_agree_that_in some sense or_other your belief that the earth_is flat gives you a reason_to believe there is no horizon. In_general, if you 6 believe P,_in some sense or other_this gives_you a reason to believe_the consequence Q,_if Q_is significantly different_from P itself. But this sense_is an unsatisfactory_one. Expressed more precisely, the position_is_that a particular_relation_holds_between your_believing P and_your_believing Q:_one_rationally requires the other, as I_shall_put it. In symbols: B(P) O6 B(Q),_(D) where O6 is_this_relation of rationally requiring._The formula (D) attaches rationality_to the relation between the beliefs._In belief_reasoning, the_relation of rationally requiring mirrors the relation of entailment that holds_between propositions. If one proposition entails_another, believing the first_rationally requires_believing_the second. 6._Rational_requirement If_we needed to formalize a rational requirement,_we could_adopt the notion of a 'conditional_obligation' from deontic logic._(See_the survey in Åqvist (1984).) The_analysis of conditional obligations is by_no means settled. (For a_recent_analysis,_see Makinson (1998).) It might_turn out, for instance, that (D)_is best understood_as: O(B(P) 6 B(Q)) where 'O' stands_for_'ought' and '6' is the material_conditional._But the important question for our_purposes_is_whether (D) implies B(P) 6_R(B(Q)), (E) where '6' is the_material conditional, and 'R' stands for 'have a reason_to'. In (E),_the rationality is attached to_the_consequent_rather than the connective, as it is in (D). This_means the_consequent can be_detached by modus ponens. From B(P) and (E), we can_infer R(B(P)). If you believe P, then_(E) says you have