Two Concepts of Causation Ned Hall

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1 Two Conpts of Custion N Hll 1 Introution Custion, unrstoo s rltion btwn vnts, oms in t lst two bsi n funmntlly iffrnt vritis. On of ths, whih I ll pnn, is simply tht: ountrftul pnn btwn wholly istint vnts. In this sns, vnt is us of (istint) vnt just in s pns on ; tht is, just in s, h not ourr, woul not hv ourr. Th son vrity is rthr mor iffiult to hrtriz, but w vok it whn w sy of n vnt tht it hlps to gnrt or bring bout or prou nothr vnt, n for tht rson I ll it proution. Hr I will rtiult, fn, n bgin to xplor th onsquns of this istintion btwn pnn n proution. A synopsis: Aftr tking r of som prliminris ( 2), I will rgu for th istintion in slightly vious mnnr, by strting with bro-stroks ritiqu of ountrftul nlyss of ustion ( 3). Th rson for this pproh is plin: Sin I n up norsing th simplst kin of ountrftul nlysis lbit only s n nlysis of on kin of vnt-ustion it mks sns to py som ttntion to th prospts for this n kinr nlyss, n to xmin why thr is no hop of turning thm into nlyss of univol onpt of vnt-ustion. Spifilly, my ritiqu will im to show tht th bst ttmpts to shor up ountrftul nlyss in th f of wll-known n stubborn ountrxmpls (involving rtin kins of ovrtrmintion) rly on thr gnrl thss bout ustion: Trnsitivity: If vnt is us of, n is us of, thn is us of. Lolity: Cuss r onnt to thir ffts vi sptiotmporlly ontinuous squns of usl intrmits. Intrinsinss: Th usl strutur of pross is trmin by its intrinsi, non-usl hrtr (togthr with th lws). Ths thss prtiulrly th son n thir will rquir mor isussion n lbortion, whih will om in u tim. For now, ontrst thm with th thsis tht lis t th hrt of ll ountrftul nlyss of ustion: Dpnn: Countrftul pnn btwn wholly istint vnts is suffiint for ustion. Th simplst ountrftul nlysis s tht pnn is nssry for ustion. As gnrl nlysis of ustion, it fils for wll-known rsons, whih w will rviw shortly. Consquntly, no ountrftul nlyst tht I m wr of norss this nssry onition. But to my knowlg, ll nors th suffiint onition oifi in th thsis of Dpnn. In, it is probbly sf to sy tht Dpnn is th ornrston of vry ountrftul nlysis. Wht is th troubl? Simply this: A hithrto ignor lss of xmpls involving wht I ll oublprvntion rvls p n intrtbl tnsions btwn th thss of Trnsitivity, Lolity, n Intrinsinss, on th on hn, n Dpnn, on th othr ( 4). In 5, I ll to my s by rguing tht xtly prlll tnsions ivi th first thr thss from th thsis of Omissions: Omissions filurs of vnts to our n both us n b us. This thsis will lso n furthr lbortion n isussion. On immit rsult is tht ountrftul nlyss r oom to filur (unlss, s I think, thy r unrstoo to b nrrowly trgt t just on kin of vnt-ustion): for thy n th first thr thss if thy r to op with th wll-known ountrxmpls involving ovrtrmintion, but thy nnot bi ths thss if thy r to op with th ountrxmpls involving oubl-prvntion (or, for tht mttr, if thy mit omissions s uss n ffts). Although importnt, this rsult is lips by mor signifint lsson tht I will vlop in 6. For th fiv thss I hv mntion r, I lim, ll tru. Givn th p n intrtbl tnsions btwn thm, tht n only b bus thy hrtriz istint onpts of ustion. Evnts n stn in on kin of usl rltion pnn for th xplition of whih th ountrftul nlysis is prftly suit (n for whih omissions n b prftly suitbl rlt). An thy n stn in n ntirly iffrnt kin of usl rltion proution whih rquirs n ntirly iffrnt kin of nlysis (n for whih omissions r not suitbl rlt). Dpnn n Omissions r tru of th first of ths usl rltions; Trnsitivity, Lolity, n Intrinsinss r tru of th son. I ll los 6 by fning this lim ginst som of th most obvious objtions. How r proution n pnn to b nlyz? Dpnn, I think, is sy; it is ountrftul pnn, nothing mor nor lss (with, prhps, th proviso tht ountrftul pnn itslf n om in iffrnt vritis; s 7 for brif isussion). Proution is trikir, n in 7 I ll offr spultiv proposl bout its nlysis, onfin to th spil s of trministi lws tht prmit no

2 Two onpts of ustion 2 tion t tmporl istn or bkwrs ustion. But I ll sy t on tht I m muh mor onfint of th proprity of th istintion thn I m of this prtiulr gloss on th proution hlf of it. I ll los, in 8, by suggsting som wys in whih th istintion btwn proution n pnn might b put to work, n by highlighting wht I think r th most importnt bits of unfinish businss. 2 Prliminris, n brif mthoologil srmon Thr r, in th litrtur, t lst ozn vrsions of ountrftul nlysis of ustion tht I m wr of. To ttk thm ll, in til, woul rquir (to borrow n pt trm from Tim Mulin) kin of philosophil trnh wrfr tht only ply ommitt prtisns oul fin ngging. I ll onfss to tst for trnh wrfr, but I won t inulg it hr. Inst, I will follow iffrnt strtgy, fousing my ritiqu on th simplst ountrftul nlysis, oring to whih ustion is ountrftul pnn btwn wholly istint vnts. It will b fr mor illuminting to xplor th most bsi problms for this nlysis long with th lrst n most plusibl strtgis for onfronting thm thn it woul b to win through th onvolutions built into th multitu of mor sophistit vrints. In orr to vlop this ritiqu s onstrutivly s possibl, w must voi vrious mthoologil pitflls. For tht rson, it will b importnt to hrtriz, if only in rough wy, th usl rltion whih is th trgt of th ountrftul nlysis. I tk th nlysis to onrn th onpt of ustion s trnsitiv, glitrin rltion btwn loliz, tbl vnts. Lt s look t th prts of this hrtriztion in turn. Bgin with th rlt. In unrstning thm to b vnts, I m tking sis on n issu tht hs sn muh rnt ontrovrsy. 1 I grnt tht thr my b snss in whih non-vnts fts, proprtis, myb vn things n us n b us; rtinly w spk of vnt typs s oing so, s whn w sy tht lightning uss firs. All th sm, I ssum tht thr is lr n ntrl sns of us th on t issu hr in whih uss n ffts r lwys vnts. (In 6, I ll qulify this ssumption slightly, suggsting tht pnn, t lst, n mit mor kins of rlt.) I will, furthrmor, follow ommon prti by strthing orinry usg of th trm vnt to ovr suh things s, for xmpl, th prsn, t th pproprit tim, of th oxygn n ry timbr tht ombin with th lightning bolt to prou th forst fir. I will lso tk it for grnt tht w n qutly isrn whn two vnts fil to b wholly istint tht is, whn thy stn in som sort of logil or mrologil rltionship tht rnrs thm unsuit to stn in usl rltionships n tht w n tll whn sription is too isjuntiv or xtrinsi to su in piking out n vnt. Without suh ssumptions, it is fr too sy to mk hsh of th simpl nlysis, n th nlyss tht buil on it, by wy of llg ountrxmpls to th lim tht ountrftul pnn is suffiint for ustion (f. Kim, 1973). Exmpls: Suppos tht I shut th oor, n in ft slm it. W my hv two vnts hr shutting n slmming istinguish bus th first oul hv hppn without th son (if, for xmpl, I h shut th oor softly). But if I hn t shut th oor, I ouln t (n so wouln t) hv slmm it so it sms tht th nlysis wrongly tlls us tht th shutting is us of th slmming. Anothr s: Suzy xprtly throws rok t glss bottl, shttring it. Th shttring onsists t lst in prt of mny smllr n mor loliz vnts: first th glss frturs, thn on shr gos flying off this wy, nothr tht wy, n so on. If th shttring hn t hppn thn non of its onstitunt vnts woul hv hppn so it sms tht th nlysis wrongly tlls us tht th shttring is us of thm ll. A thir s: Fr wy, Billy throws nothr rok, shttring iffrnt glss bottl. Suppos thr is isjuntiv vnt whih, nssrily, ours iff ithr Suzy s throw or Billy s throw ours. If hn t ourr, nithr bottl woul hv shttr so it sms tht, oring to th nlysis, w hv isovr firly immit ommon us of ths wily sprt vnts. A finl s: Suppos thr is typ of xtrinsilly spifi vnt tht, nssrily, hs n instn ourring t tim t iff I snt n mil mssg xtly 2 ys bfor t. Lt b suh n instn, n lt b th rply, ourring t, sy, tim on y ftr I snt th givn mil (n so y bfor ). Sin woul not hv hppn if hn t, it sms tht, oring to th nlysis, w hv bkwrs ustion vry muh on th hp. Eh s srvs iffrnt ignosis. In th first s, w shoul sy tht th vnts fil to b istint bus of thir logil rltionship. In th son s, w shoul sy tht th shttring is not istint from its onstitunts, bus of thir mrologil rltionship. In th thir s, w shoul sy tht th isjuntiv vnt is not n vnt t ll, hn not pt to us (or b us). In th finl s, w

3 Two onpts of ustion 3 shoul sy tht thr r no suh xtrinsilly spifi vnt typs. W shoul sy ll ths things, n it s up to philosophil thory of vnts to tll us why w r justifi in oing so. 2 Of ours, I o not t ll mn to suggst tht it is n sy mttr to provi n qut philosophil ount of vnts tht mts ths ritri. I rtinly won t try to provi ny suh ount hr. Wht I will o is voi hoosing xmpls whr ny of th ontrovrsis surrouning th ntur of vnts mks iffrn. 3 Turn nxt to th hrtriztion of th rltion. Trnsitivity is strightforwr nough: if vnt is us of vnt b, n b us of, thn is thrby us of. Wht I mn by glitrin n bst b m lr by ontrst with our usul prti. Whn linting th uss of som givn vnt, w typilly mk wht r, from th prsnt prsptiv, inviious istintions, ignoring prftly goo uss bus thy r not suffiintly slint. W sy tht th lightning bolt us th forst fir, filing to mntion th ontribution of th oxygn in th ir, or th prsn of suffiint quntity of flmmbl mtril. But in th glitrin sns of us, omplt invntory of th fir s uss must inlu th prsn of oxygn n of ry woo. (Not tht trnsitivity hlps mk for n glitrin rltion: vnts uslly rmot from givn vnt will typilly not b slint but will still b mong its uss, for ll tht.) Now for brif mthoologil srmon: If you wnt to mk troubl for n nlysis of ustion but wnt to o so on th hp thn it s onvnint to ignor th glitrin hrtr of th nlysnum. Gt your uin to o th sm, n you n pro to liit jugmnts tht will ppr to unrmin th nlysis, but whih r in ft irrlvnt to it. Suppos tht my fvorit nlysis ounts th Big Bng s mong th uss of toy s snowfll ( likly rsult, givn trnsitivity). How sy it is to rfut m, by obsrving tht if sk wht us th snowfll (bttr still: wht ws th us of it), w woul nvr it th Big Bng! Of ours, th right rspons to this rfuttion is obvious: It onflts th trnsitiv, glitrin sns of us with muh mor rstritiv sns (no oubt grtly inft with prgmtis) tht pls hvy wight on slin. A simpl mistk, it woul sm. But th sm sort of mistk shows up, in mor subtl forms, in xmpls rwn from th litrtur. It will b hlpful to work through fw illustrtiv ss ons tht show, inintlly, how vn first-rt uthors n somtims go stry. First, Bnntt (1987, pp ; itlis in th originl), who is hr onrn with Lombr s thsis tht n vnt s tim is ssntil to it: Tk s whr this is tru: Thr ws hvy rin in April n ltril storms in th following two months; n in Jun th lightning took hol n strt forst fir. If it hn t bn for th hvy rin in April, th forst woul hv ught fir in My. A Lombr s thsis to tht, n you gt If th April rin hn t ourr th forst fir wouln t hv ourr. Intrprt tht in trms of th ountrftul nlysis n you gt Th April rins us th forst fir. Tht is unptbl. A goo nough thory of vnts n of ustion might giv us rson to pt som things tht sm intuitivly to b fls, but no thory shoul prsu us tht lying forst s burning for month (or in for minut) is using forst fir. Lombr grs tht Bnntt s rsult is unptbl. It is bit of goo ommon sns tht hvy rins n put out firs, thy on t strt thm; it is fls to sy tht th rins us th fir. (Lombr 1990, p. 197; itlis in th originl) Lombr isusss son xmpl whih shows tht th ssntility of n vnt s tim is not t issu (ibi., pp ): Suppos tht Jons livs in vry ngrous nighborhoo, n tht on vning Smith ttmpts to stb him to th. Jons is sv bus of th tion of Brown who frightns Smith off. Howvr, yr ltr, Jons is shot to th by th prsistnt Smith. So, if Brown s tion h not ourr, Jons s th u to th shooting woul not hv ourr, sin h woul hv i of stb wouns yr rlir. But, I fin it intuitivly quit unptbl to suppos tht Brown s tion ws us of Jons s ying s rsult of gunshot yr ltr. Finlly, Lwis isusss vry similr xmpl (Lwis 1986b, p. 250):

4 Two onpts of ustion 4 It is on thing to postpon n vnt, nothr to nl it. A us without whih it woul hv ourr ltr, or soonr, is not us without whih it woul not hv ourr t ll. Who woul r b otor, if th hypothsis unr onsirtion [tht n vnt s tim is ssntil to it] wr right? You might mng to kp your ptint liv until 4:12, whn othrwis h woul hv i t 4:08. You woul thn hv us his th. For his th ws, in ft, his th t 4:12. If tht tim is ssntil, his th is n vnt tht woul not hv ourr h h i t 4:08, s h woul hv on without your tion. Tht will not o. If ths xmpls r mnt to provi rok-soli t upon whih th ountrftul nlysis (n prhps othrs) founrs, thn thy uniformly fil for in h s, w n fin inpnntly plusibl prmiss tht ntil th llgly unptbl onsquns. Of ours tht osn t show tht th onsquns r tru. But it os show tht w mk srious mthoologil mistk if w trt thos of our intuitions tht run ountr to thm s non-ngotibl t. First w must isntngl irrlvnt but onfusing issus. It is probbly right tht n vnt s tim is not in vry s ssntil to it; but (p Lwis) tht osn t hlp in ny of th thr ss. This is mor or lss obvious in th first two ss (th Jun fir is not th sm s th fir tht woul hv hppn in My; th th by shooting is not th sm s th th by stbbing tht woul hv hppn yr rlir). So onsir Lwis s s. Supposly, it will not o to ssrt tht th otor s tion is mong th uss of th ptint s th. But wht os this hv to o with th proximity of th tul tim of th to th tim t whih th ptint woul hv i? Suppos you mng to kp your ptint liv until Jun of 1999, whn othrwis h woul hv i in Jun of Woul you thn hv us his th, sin without your tion th th h in ft i woul not hv ourr? It is no lss (n no mor) unptbl to sy ys in this s thn it is to sy ys in Lwis s s. But if, following Lwis, w onlu tht th tul th is th sm s th th whih woul hv ourr yr rlir, thn w r tking th nil of th ssntility of tims to riiulous xtrm. Suh nil, howvr wrrnt, os not giv th ountrftul nlyst th mns to rspon fftivly vn to Lwis s problm. Th nlyst n, howvr, rw on our brif mthoologil srmon to point to two sorts of jugmnts bout ustion whih th thr xmpls impliitly tr on but illgitimtly, sin ths jugmnts onrn typs of ustion whih r not t issu. W n ll gr tht hvy rins n put out firs, thy on t strt thm, just s w n gr tht smoking uss lung nr, but rgulr xris osn t. So wht? Th intuitions ll upon hr o not onrn th onpt of ustion s trnsitiv, glitrin rltion btwn vnts, but rthr som othr onpt of ustion s n inglitrin rltion btwn vnt-typs. (Nvr min tht strting fir is not th only wy to b on of its uss!) Similrly, w n ll gr tht it is th lightning tht uss th forst fir, n nothing ls inluing th hvy rins. Agin, so wht? Hr w sm to hv in min rstrit, inglitrin onpt of vnt-ustion oring to whih vnts tht r to ount s uss must b prtiulrly slint in som rspt; but jugmnts involving this onpt mttr not t ll to th ountrftul nlysis, sin it onrns th wkr n mor inlusiv trnsitiv, glitrin onpt. Unfortuntly, Bnntt, Lombr n Lwis hv ll mui th qustion of whthr th ountrftul nlysis is qut by hoosing xmpls whr intuitions of th two typs just isuss r prtiulrly strong n smingly slint: It s not th rinfll tht uss th Jun fir, but rthr th lightning; morovr, it s just goo ommon sns tht hvy rins on t us firs! 4 Of ours, whil rognizing ths points you might still jug ths ss to hv som intuitiv for s ountrxmpls. Fir nough; thy o. But mor rful xmintion shows how hsty it woul b to tk ny suh intuitions s isiv. I ll mk th s ginst Bnntt, ftr whih it will b lr nough how to pro ginst Lombr n Lwis tht w n lv thos ss si. Th i is to fin n vnt intrmit btwn th us n its llg fft whih is lrly us of th son, n t lst plusibly n fft of th first. So obsrv tht mong th uss of th Jun fir is not just th lightning but lso th vry prsn of th forst, fill with flmmbl mtril. Th prsn of th forst in th hours bfor th lightning striks is itslf n vnt, or prhps olltion of vnts. This vnt is us of th Jun fir (lbit not slint us). Wht r its uss? A typil ountrftul nlysis will lim tht on of its uss is th April rinfll, sin without th rinfll th forst woul hv bn stroy in My. But w n rgu for th plusibility of this lim inpnntly, by noting tht th following jugmnts sm, intuitivly, to b orrt: it is in prt bus of th April rins tht th forst is prsnt in Jun; ny omplt usl xplntion of th forst s prsn must it th rol of th April rins in prvnting its strution; th April rins r t lst in prt rsponsibl for th prsn of th forst in Jun. 5

5 Two onpts of ustion 5 On oul ny th truth of ths jugmnts, or ny tht thy show tht th April rinfll is us of th forst s prsn in Jun, or ny tht ustion is trnsitiv in th wy tht is n to omplt th infrn to th lim tht th April rinfll is mong th uss of th Jun forst fir. But unlss on n fin som grouns for supporting suh nils grouns inpnnt of th mr intuitiv implusibility of th lim in qustion thn this implusibility will fil to provi prtiulrly omplling rson for giving up th ountrftul nlysis. (Extly prlll points pply to th othr two xmpls.) Hppily, I think th onlusions rwn in 6 lr up wht is going on in th rinfll s (n th othr ss), prisly by showing tht ountrftul nlyss uttrly fil to ptur on importnt sns of us proution n tht in this sns th April rins r not mong th uss of th Jun fir. But it will tk som work to gt thr, n long th wy w must not b istrt by th tmpttions of suh bogus rfuttions s thos w hv just xmin. Intuitions bout ss must b h, to b sur. But not blinly. Onwr. It will hlp to hv mns of rprsnting simpl usl struturs; oringly, I will opt th nuron igrms us by Lwis. 6 Th igrm blow pits pttrn of nuron firings. Gry irls rprsnt firing nurons, whil rrows rprsnt stimultory onntions btwn nurons. Th orr of vnts is lft to right: In figur 1 nuron firs, sning stimultory signl to nuron b, using it to fir; b s firing in turn sns stimultory signl to nuron, using it to fir. b Figur 1 W will lso n wy to rprsnt prvntion of on vnt by nothr. So lt us inhibitory onntions to th nuron igrms, rprsnt by lin ning in soli ot: b b firs Figur 2 if hn t fir In th lft-hn igrm, nurons n fir simultnously; s firing uss to fir, whih in turn uss to fir. Howvr, thnks to th inhibitory signl from, s firing os not us b to fir; b s filur to fir is rprsnt by lving its irl unsh. Th right-hn igrm shows wht woul hv hppn if h not fir. Clling ths igrms nuron igrms is mrly pitursqu; wht is importnt bout thm is tht thy n provi, in rily igstibl form, prtil rprsnttions of mny usl struturs. 3 Th simpl ountrftul nlysis, n two kins of ovrtrmintion 3.1 Th simpl nlysis Both for simpliity n to voi nlss ontrovrsis, I will fous only on th ountrftul nlysis s it pplis to worls with trministi lws tht prmit nithr bkwrs ustion nor tion t tmporl istn (lthough th lssons of th ppr pply muh mor gnrlly, s fr s I n s). I will lso lv si ss, if suh thr b, whr us is simultnous with on of its ffts. Hr n throughout I will not vnts by lowr-s bol-f lttrs, b,, n so forth; th proposition tht n vnt ours by O ; n th ountrftul or subjuntiv onitionl by (r: wr it th s tht thn it woul b th s tht ). 7 Th simpl nlysis is s follows: Evnt is us of vnt iff (i) n r wholly istint vnts;

6 Two onpts of ustion 6 (ii) O, O, n ~O ~O r ll tru. An immit problm riss, whos solution rquirs th ountrftul onitionl to b unrstoo in rthr spifi wy. In figur 1, it is rtinly orrt to sy tht if hn t fir, wouln t hv; but it my lso b orrt to sy tht if hn t fir, wouln t hv. (If you on t lik th soun of tht, try th hppir loution: If hn t fir, it woul hv to hv bn tht in t fir.) If so, th nlysis wrongly sys tht is us of. (Not th hrmlss but onvnint mbiguity: lttrs somtims rfr to vnts, somtims to nurons.) Two rsponss sm possibl. W oul ugmnt th nlysis by ing som thir onition to gurnt th symmtry of ustion (for xmpl: uss must pr thir ffts). Or w oul ny th truth of th offning ountrftul, ppling to n ount of th onitionl whih sur th flshoo of ll suh bktrkrs (to us Lwis s pt trm). 8 Swin (1978), for xmpl, opts for th first ltrntiv, Lwis (1979 n 1986) (n most othr ountrftul nlysts) for th son. 9 Th first rspons osn t work, prtly for rsons tht hv bn wll-xplor n tht I won t rhrs in til hr (.g., mrly ing th rquirmnt tht uss pr thir ffts won t hlp if, sy, n r joint ffts of som vnt, with ourring bfor ; for w oul still rson tht if hn t hppn, it woul hv to hv bn tht in t hppn, n thrfor tht in t hppn). A iffrnt, oftn unnoti rson for rjting th first rspons srvs som isussion, howvr: Th problm is tht this rspons impliitly supposs tht bktrkrs thrtn only th suffiiny of th bov nlysis. If tht wr tru, it woul mk sns to furthr onitions, so s to mk th nlysis lss librl. But bktrkrs lso unrmin its nssity, s figur 2 shows. In figur 2, is, lrly, us of. But if, in vluting ountrftuls with th ntnt os not our, w pro by mking miniml ltrtions to th pst vnts tht l to, thn w will rh ountrftul sitution in whih os not our, but still os tht is, ountrftul sitution in whih ours. Tht is, if w llow s tru th bktrkr ~O ~O, thn th right-hn igrm lso sribs wht woul hv hppn if hn t fir, n so th onitionl ~O ~O is fls. Thn how n it b tht turns out to b us of? Aing xtr onitions to (i) n (ii) provis no nswr. 10 (Nor will it hlp to librliz th nlysis in th stnr wy, by tking ustion to b th nstrl of ountrftul pnn. For th problm tht thrtns th onntion btwn n will qully thrtn th onntion btwn n ny vnt tht mits btwn n.) In short, ring th ountrftul in bktrking mnnr stroys th pnn of on. Tht s not only troubl for th simpl nlysis: it s just wrong, sin it mnifstly is th s tht if hn t fir, wouln t hv. Or, mor utiously, thr mnifstly is n ptbl ring of th ountrftul onitionl oring to whih this is tru. I will hnforth tk it for grnt tht both th simpl nlysis n its mor lbort kin mploy suh non-bktrking ring of th onitionl. Not ruil ftur of this ring, howvr. Spifilly, w on t voi th problm ris by figur 2 mrly by nying th bktrking onitionl ~O ~O. For to ny ountrftul X Y is not to ssrt th ontrry onitionl X ~Y, but rthr to ssrt th wkr might onitionl, symboliz s X ~Y n r h X bn tru, Y might hv bn fls. 11 This might onitionl is wkr bus, unlik X ~Y, it is onsistnt with th might onitionl X Y. In th s t hn, th flshoo of ~O ~O is onsistnt with th truth of ~O ~O in othr wors, onsistnt with th lim tht if h not fir, thn ours of vnts whih might hv ourr is tht srib by th right-hn igrm. But in tht s, if h not fir, thn might hv fir nywy; in symbols, ~O O. An this might onitionl is th nil of th onitionl ~O ~O. So, not only must th onitionl ~O ~O b fls, but th onitionl ~O O must b tru. If hn t fir, woul hv fir just th sm. It is mttr of som ontrovrsy wht is th propr smntis for this kin of onitionl. Rll th stnr possibl worls smntis: Th onitionl X Y is tru iff som possibl worl whr X n Y r both tru is losr to tulity thn ny worl whr X is tru but Y fls. Without trying to fin th losr thn rltion, w n still stblish this muh bout it: Som worl w whr firs but os not is losr to tulity (th lft-hn igrm) thn ny worl whr nithr nor firs (for if h not fir, still woul hv). How n this b? Don t th lws gurnt tht if firs, thn firs? Vrious rsponss r possibl. On might point out tht lon is not lwfully suffiint for : othr onitions must onspir with th firing of to bring bout th firing of, n in w (so this story gos) som of thos othr onitions rn t mt. Or on might ny tht th lws of our worl hol without xption in w. Of ours, thy h bttr hol lmost without xption in prtiulr, thy h bttr hol from th tim of s (non)ourrn forwr (ls th vlution of th onitionl ~O ~O gos hywir). But tht is no problm: w n only mit just nough of violtion to brk th

7 Two onpts of ustion 7 onntion btwn n. 12 Or on might ny tht uniform smntis is rquir for onitionls X Y tht r forwr trking (in th sns tht X onrns tims bfor thos tht Y onrns) n thos tht r bktrking. 13 Fortuntly, w n only om up with rul for vluting ountrftuls of th form ~O ~O, whr n both our, n prs n on suh rul, th thr forgoing pprohs n rtinly gr. Following Mulin (2000), I suggst th following: Ltting t b th tim of ourrn of th givn vnt, w vlut th onitionl ~O ~O by ltring th stt of th worl t t just nough to mk th ntnt tru (without rgr to wht th pst woul hv to hv bn lik in orr to giv ris to tht ountrftul t-stt), volving tht stt forwr in tim in orn with th (tul) lws, n sing whthr th onsqunt oms out tru. 14 So, in figur 2, if hn t fir, irumstns ontmpornous with its firing suh s th non-firing of b woul hv bn unhng, n so woul not hv fir. W n lv it uni wht th pst woul hv bn lik, or vn whthr th smntis for our onitionl ns to nswr tht qustion. 3.2 Erly pr-mption Th simpl nlysis my ppr quit bl to stv off hllngs to its suffiiny. But obvious problms bst its lim to nssity. Consir s of orinry pr-mption, s in figur 2. Th firing of is ovrtrmin by th simultnous firings of n. But not in wy tht lvs us t ll unrtin s to wht uss wht: Without qustion, is us of, vn though if hn t ourr, woul hv ourr nywy, thnks to n ltrntiv pross, bginning with, whih pr-mpts. Thr is n obvious strtgy for hnling this kin of s. First, w librliz our nlysis, by tking ustion to b th nstrl of ountrftul pnn: is us of iff thr r vnts 1,, n suh tht 1 ountrftully pns on, 2 pns on 1,, n pns on n. Nxt, w look for n vnt (or squn of vnts) intrmit btwn th prvnting us n th fft, suh tht pns on n likwis on. Th strtgy works hnily in th s bfor us (provi, on gin, tht w r rful not to intrprt th ountrftul in bktrking sns, oring to whih, h not fir, it woul hv to hv bn th s tht in t fir, n so b woul hv fir, n so woul still hv fir). Obsrv how nturl this mbllishmnt to th simpl nlysis is n obsrv tht it givs ntrl rol to th Trnsitivity thsis. 3.3 Lt pr-mption Othr, quit orinry ss of ovrtrmintion rquir iffrnt trtmnt. Consir s of soll lt pr-mption, s in figur 3: b b firs if hn t fir Figur 3 (nurons n fir simultnously) Nurons n fir simultnously, so tht firs t th sm tim s b; th inhibitory signl from thrfor prvnts from firing. If hn t fir, still woul hv; for in tht s woul not hv bn prvnt from firing n so woul hv stimult to fir. Likwis for vry vnt in th usl hin ling from to : if tht vnt h not ourr, woul nvrthlss hv fir. So th strtgy of fining suitbl intrmits brks own; for it to su, woul hv to pn on t lst on vnt in th hin ling bk to, n it os not. Hr is nothr xmpl with slightly iffrnt strutur; it illustrts how bsolutly munn ths ss r. Suzy n Billy, our xprt rok-throwrs, r ngg in omptition to s who n shttr trgt bottl first. Thy both pik up roks n throw thm t th bottl, but Suzy throws hrs split son bfor Billy. Consquntly Suzy s rok gts thr first, shttring th bottl. Sin both throws r prftly urt, Billy s woul hv shttr th bottl if Suzy s h not ourr, so th

8 Two onpts of ustion 8 shttring is ovrtrmin. On th bottl hs shttr, howvr, it nnot o so gin; thus th shttring of th bottl prvnts th pross initit by Billy s throw from itslf rsulting in shttring. Suzy s throw is us of th shttring, but Billy s is not. In, vry on of th vnts whih onstitut th trjtory of Suzy s rok on its wy to th bottl is us of th shttring. But th shttring pns on non of ths vnts, sin h ny of thm not ourr th bottl woul hv shttr nywy, thnks to Billy s xprt throw. So th trnsitivity strtgy fils. Thr ltrntiv strtgis for ling with this kin of s suggst thmslvs. Th first rsts on th obsrvtion tht Suzy s throw mks iffrn to th tim n mnnr of th shttring, whrs Billy s os not. Th son rsts on th obsrvtion tht Suzy s throw is onnt to th shttring by sptiotmporlly ontinuous hin of usl intrmits, whrs Billy s is not. An th thir rsts on th obsrvtion tht thr is squn of vnts onnting Suzy s throw to th shttring tht hs th right sort of intrinsi hrtr to ount s usl squn, whrs no suh squn onnts Billy s throw to th shttring. Lt us onsir ths strtgis in turn. Thr r vrious wys to implmnt th first strtgy. For xmpl, w oul ny tht th fft whih os th prvnting is numrilly th sm s th fft whih woul hv ourr vi th ltrntiv pross; if so, thn our two xmpls o xhibit th n pttrn of ountrftul pnn, sin th fft whih tully ourr woul not hv ourr without its us (lthough vry similr vnt woul hv ourr in its pl). In figur 3, th firing of whih woul hv ourr, h not fir, is not th sm vnt s th firing whih tully ours. Likwis, if Suzy h not thrown hr rok thn th bottl woul still hv shttr but ltr thn it tully i, so it woul not hv bn th sm shttring. Altrntivly, w oul rmin silnt bout th iniviution of vnts, n simply mploy slightly iffrnt ountrftul in th nlysis sy, by ounting us of iff, h not ourr, woul not hv ourr t th tim it tully i (Pul 1998). In rnt work, Lwis (2000) hs rgu tht w shoul ount us of if thr is suitbl pttrn of ountrftul pnn btwn vrious iffrnt wys or somthing lik it might hv ourr n orrsponingly iffrnt wys in whih or somthing lik it might hv ourr. (Lwis proposs tking ustion itslf to b th nstrl of this rltion.) Ths pprohs r uniformly non-strtrs. Nvr min th wll-known problms (.g., tht nonuss n sily mk iffrn to th tim n mnnr of n vnt s ourrn gust of win tht ltrs th ours of Suzy s rok vr so slightly, for xmpl). Wht sms to hv gon unnoti is tht it is not t ll ssntil to xmpls of lt pr-mption tht th gnuin us mk ny iffrn to th tim or mnnr of th fft. As Stv Yblo point out to m, it s sy nough to onstrut ss in whih is lrly us of, but in whih nithr nor ny vnt uslly intrmit btwn it n mks th slightst iffrn to th wy ours. Yblo points out tht w n simply ltr th story of Billy n Suzy. This tim, Billy throws Smrt Rok, quipp with n on-bor omputr, xquisitly sign snsors, lightning-fst propulsion systm n instrutions to mk sur tht th bottl shttrs in xtly th wy it os, t xtly th tim it os. In ft, th Smrt Rok osn t n to intrvn, sin Suzy s throw is just right. But h it bn ny iffrnt in, h hr rok s trjtory iffr in th slightst, t ny point th Smrt Rok woul hv swoop in to mk sur th job ws on proprly. Sur, th xmpl is bizrr. But not in wy tht mttrs in th slightst to th vlution of th usl sttus of Suzy s throw: Smrt Rok notwithstning, hr throw is still us of th shttring vn though nithr it nor ny vnt tht mits btwn it n th shttring mks iffrn to th tim or mnnr of tht shttring. I won t onsir ths pprohs furthr. It will b fr mor instrutiv for us to fous on th two ltrntiv strtgis. Suzy s throw is sptiotmporlly onnt to th shttring in th right wy, but Billy s is not. So prhps w shoul th Lolity thsis s onstrint on th nlysis: Cuss hv to b onnt to thir ffts vi sptiotmporlly ontinuous squns of usl intrmits. Now, on th f of it this is stp in ntirly th wrong irtion, sin it mks th nlysns mor stringnt. But if w simultnously librliz th nlysis in othr rspts, this strtgy might work. For xmpl, w might sy tht is us of just in s thr is sptiotmporlly ontinuous squn of vnts onnting with n (possibly mpty) st S of vnts ontmpornous with suh tht h ltr vnt in th squn (inluing ) pns on h rlir vnt or t lstwoul hv, h th vnts in S not ourr. Tht will istinguish Suzy s throw s us, n Billy s s non-us. Of ours, sin tion t istn is surly possibl, n so Lolity t bst highly intrsting ontingnt truth, this mn ountrftul nlysis lks gnrlity. But it is ptntly gnrl nough to b of vlu. At ny rt, it is not so importnt for our purposs whthr this strtgy, or som vrint,

9 Two onpts of ustion 9 n hnl ll ss of lt pr-mption. Wht is importnt is tht it is plusibl n nturl strtgy to pursu n it givs ntrl rol to th Lolity thsis. Lwis hs propos thir, iffrnt strtgy. H bgins with th intuition tht th usl strutur of pross is intrinsi to it (givn th lws). As h puts it: Suppos w hv prosss ourss of vnts, whih my or my not b uslly onnt going on in two istint sptiotmporl rgions, rgions of th sm or of iffrnt possibl worls. Disrgring th surrounings of th two rgions, n isrgring ny irrlvnt vnts tht my b ourring in ithr rgion without bing prt of th pross in qustion, wht gos on in th two rgions is xtly lik. Suppos furthr tht th lws of ntur tht govrn th two rgions r xtly th sm. Thn n it b tht w hv usl pross in on of th rgions but not th othr? It sms not. Intuitivly, whthr th pross going on in rgion is usl pns only on th intrinsi hrtr of th pross itslf, n on th rlvnt lws. Th surrounings, n vn othr vnts in th rgion, r irrlvnt. In ss of lt pr-mption, th pross onnting us to fft os not xhibit th right pttrn of pnn but only bus of intl fturs of its surrounings. Th pross tht bgins with Suzy s throw n ns with shttr bottl os not xhibit th right pttrn of pnn (thnks to Billy s throw), but it is intrinsilly just lik othr possibl prosss tht o (nmly, prosss tking pl in surrounings tht lk Billy, or ountrprt of him). Lwis suggsts, in fft, tht for tht rson Suzy s throw shoul ount s us. Clrly, Lwis is trying to prly somthing lik th Intrinsinss thsis into n mn ountrftul nlysis, on qut to hnl ss of lt pr-mption. Now, I think thr r srious problms with th tils of Lwis s own pproh (spll out in th pssg following tht just quot), but sin tht wy lis trnh wrfr, I won t go into thm. I o, howvr, wnt to tk issu with his sttmnt of th Intrinsinss thsis, whih is too vgu to b of rl us. Wht, ftr ll, is pross or ours of vnts? If it is just ny ol squn of vnts, thn wht h sys is obviously fls: W might hv squn onsisting of th lighting of fus, n n xplosion but whthr th on is us of th othr is not trmin by th intrinsi hrtr of this two-vnt pross, sin it obviously mttrs whthr this fus ws onnt to tht xploing bomb. I will simply giv wht I think is th right sttmnt of th Intrinsinss thsis, on whih shws unfin tlk of prosss. 15 Suppos n vnt ours t som tim t. Thn onsir th strutur of vnts whih onsists of, togthr with ll of its uss bk to som rbitrry rlir tim t. Tht strutur hs rtin intrinsi hrtr, trmin by th wy th onstitunt vnts hppn, togthr with thir sptiotmporl rltions to on nothr. It lso hs rtin usl hrtr: in prtiulr, h of th onstitunt vnts is us of (xpt itslf, of ours). Thn th Intrinsinss thsis stts tht ny possibl strutur of vnts tht xists in worl with th sm lws, n tht hs th sm intrinsi hrtr s our givn strutur, lso uplits this spt of its usl hrtr tht is, h uplit of on of s uss is itslf us of th -uplit. 16 Thr obsrvtions: First, sm intrinsi hrtr n b r in vry strit sns, oring to whih th two struturs of vnts must b prft uplits. R this wy, I think th Intrinsinss thsis is inontrovrtibl. But it n lso b r in lss strit sns, oring to whih th two struturs must b, in som sns, suffiintly similr in thir intrinsi hrtrs. R this wy, th thsis is strongr but still highly plusibl. Consir gin th s of Billy n Suzy, n ompr th sitution in whih Billy throws his rok with th sitution in whih h osn t. Clrly, thr is strong intuition tht th usl fturs of th squn of vnts bginning with Suzy s throw n ning in th shttring shoul b th sm in h s, prisly bus Billy s throw is xtrinsi to this squn. But it is too muh to hop for tht th orrsponing squns, in h sitution, b prft uplits; ftr ll, th grvittionl ffts of Billy s rok, in th sitution whr h throws, will mk minut iffrns to th xt trjtory of Suzy s rok, t. So if it is th Intrinsinss thsis tht givs voi to our onvition tht, from th stnpoint of Suzy s throw, th two situtions must b trt lik, thn w shoul r th sm intrinsi hrtr lus in tht thsis in th lss stringnt wy. Doing so quit obviously lvs us with th burn of xplining wht nr-but-not-quit-prft uplition of intrinsi hrtr onsists in. I won t try to unlo tht burn hr. It will mrg tht for my min purposs, tht osn t mttr, sin in orr to us th Intrinsinss thsis to rgu tht pnn n proution r two istint kins of ustion, I n r sm intrinsi hrtr in th mor stringnt sns. (Als, w will lso s tht my own prfrr nlysis of proution will rquir th lss stringnt ring.)

10 Two onpts of ustion 10 Th son obsrvtion to mk bout th Intrinsinss thsis is tht it is somwht limit in sop: it os not pply, in gnrl, to situtions in whih thr is ustion t tmporl istn, or to situtions in whih thr is bkwrs ustion. Roughly, th problm is tht th rlvnt strutur of vnts must b omplt in rtin rspt, onsisting in omplt st of joint uss of th givn fft, togthr with ll of thos vnts tht mit btwn ths uss n. I won t go into th rsons why it must xhibit this kin of ompltnss (but s my 2000). But onsir s whr th fft tks pl t 1 o lok, n w hv ollt togthr ll of its uss tht our t noon, s wll s thos tht our btwn noon n 1. If thr is tion t tmporl istn, thn som of th othr uss with whih th noon uss ombin to bring bout th fft might hv ourr bfor noon, in whih s our strutur won t b suffiintly omplt. If thr is bkwrs ustion, thn som of th vnts tht mit btwn th noon uss n th fft might our outsi th givn intrvl, in whih s our strutur won t b suffiintly omplt. Eithr wy, thr is troubl. It is prtly in orr to finss this troubl tht I hv limit my fous by ignoring both bkwrs ustion n ustion t tmporl istn. Th thir obsrvtion to mk bout th Intrinsinss thsis is tht w must ssum on pin of rnring th thsis trivilly fls tht th strutur of vnts ginst whih w ompr givn strutur inlus no omissions. Lt th strutur S onsist of, togthr with ll of its uss bk to som rbitrry rlir tim t.. An lt th strutur S simply onsist of S, togthr with som rbitrry omission tht ours t som point in th rlvnt intrvl. Plusibly, this omission will ontribut nothing to th intrinsi hrtr of S for it simply onsists in th filur of som typ of gnuin vnt to our. So S will prftly mth S. If w pply th Intrinsinss thsis unritilly, w immitly gt th bsur rsult tht th omission whtvr it is! ounts s us of. Now, it ws lry firly lr tht whtvr th guiing intuition is bhin th Intrinsinss thsis, it os not onrn omissions. This rsult onfirms th suspiion. So th finl lus of th Intrinsinss thsis shoul r: ny possibl strutur of gnuin vnts (not inluing ny omissions) tht xists in worl with th sm lws, n tht hs th sm intrinsi hrtr s our givn strutur, lso uplits. (It osn t follow tht S th strutur pik out s onsisting of, togthr with ll of its uss bk to som rlir tim t must inlu no omissions. W ll tk up th qustion of whthr it n in 5, blow.) Prhps th ountrftul nlyst n us th Intrinsinss thsis to hnl th problm of Billy n Suzy. Aftr ll, in th ltrntiv irumstns in whih Billy s throw is bsnt, it sms orrt to sy tht th usl history of th shttring (bk to th tim of Suzy s throw) onsists xtly of thos vnts on whih it pns. Wht s mor, this strutur mths strutur tht tks pl in th tul irumstns, whr Billy s throw onfouns th ountrftul rltions; Suzy s throw, bing prt of this strutur, will thrfor ount s us of th shttring, thnks to th Intrinsinss thsis. To b sur, this is no mor thn suggstion of rvis nlysis. But gin, wht is importnt is tht it is plusibl n nturl suggstion to pursu n it givs ntrl rol to th Intrinsinss thsis. 4 Doubl-prvntion Now for somthing ompltly iffrnt: kin of xmpl tht splls troubl for th suffiiny of th simpl nlysis, by showing tht th ornrston thsis of Dpnn runs hlong into onflit with h of Trnsitivity, Lolity, n Intrinsinss. 4.1 Exmpl Suzy n Billy hv grown up, just in tim to gt involv in Worl Wr III. Suzy is piloting bombr on mission to blow up n nmy trgt, n Billy is piloting fightr s hr lon sort. Along oms n nmy fightr pln, pilot by Enmy. Shrp-y Billy spots Enmy, zooms in, pulls th triggr, n Enmy s pln gos own in flms. Suzy s mission is unisturb, n th bombing tks pl s plnn. If Billy hn t pull th triggr, Enmy woul hv lu him n shot own Suzy, n th bombing woul not hv hppn. This is s of wht I ll oubl prvntion : on vnt (Billy s pulling th triggr) prvnts nothr (Enmy s shooting own Suzy), whih h it ourr woul hv prvnt yt nothr (th bombing). Th slint usl strutur is pit in figur 4:

11 Two onpts of ustion 11 g g b f b f firs Figur 4 if hn t fir Nurons, b, n ll fir simultnously. s firing prvnts from firing; if h fir, it woul hv us f to fir, whih in turn woul hv prvnt g from firing. Thus, if h not fir, g woul not hv. So is us of g: Billy s pulling th triggr is us of th bombing. This onsqun of th ountrftul nlysis might sm nturl nough. Aftr ll, wouln t w giv Billy prt of th rit for th suss of th mission? Isn t Billy s tion prt of th xplntion for tht suss? An so on. On th othr hn, it might sm quit unnturl for th suffl btwn Billy n Enmy tks pl, lt us suppos, hunrs of mils wy from Suzy, in suh wy tht not only is sh ompltly oblivious to it, but it hs bsolutly no fft on hr whtsovr. Hr sh is, in on rgion, flying hr pln on th wy to hr bombing mission. Hr Billy n Enmy r, in n ntirly sprt rgion, ting out thir ftful rm. Intuitivly, it sms ntirly unxptionbl to lim tht th vnts in th son rgion hv no impt t ll on th vnts in th first for isn t it plin tht no physil onntion units thm? So fr, it might sm tht w hv stlmt: two ontrry intuitions bout th s, with no wy to i btwn thm. (In, my informl polling suggsts tht intuitiv jugmnts vry quit lot.) Not so: Both th jugmnt tht w hv s of ustion hr, n th thsis of Dpnn whih norss this jugmnt, run into troubl with h of th thss of Lolity, Intrinsinss, n Trnsitivity. 4.2 Problms with Lolity W ll know wht tion t istn is: w hv s of it if w hv us, t lst on of whos ffts is not onnt to it vi ny sptiotmporlly ontinuous usl hin. 17 I tk it tht tion t istn is possibl, but tht its mnifsttion in worl is nvrthlss highly non-trivil ft bout tht worl. Yt if Billy s tion ounts s us of th bombing, thn th quit orinry n munn rltionship it brs to th bombing lso ounts s s of tion t istn. Is this ll it tks to hiv non-lolity? (An to think tht philosophrs hv bn fussing ovr Bll s Inqulitis!) If so, w woul b hr-prss to srib lws tht in t prmit tion t istn. For xmpl, vn th lssil lws tht srib prftly lsti ollisions woul hv to b jug non-lol, sin thy prmit situtions in whih on ollision prvnts son, whih, h it hppn, woul hv prvnt thir so tht w hv pnn of th thir ollision on th first, but no onnting squn of usl intrmits. In short, it pprs tht whil Dpnn osn t quit ontrit Lolity, it rnrs it stisfibl only by th most trivil lws (.g., lws whih sy tht nothing vr hngs). Tht s wrong: Th istintion btwn lws whih o n lws whih on t prmit tion t istn is intrsting; to ssimilt it to th ll-but-vuous istintion btwn lws whih o n lws whih on t prmit oubl-prvntion is mistk. A rmrkbly frqunt but ntirly unstisftory rspons is th following: Billy s tion is onnt to th bombing vi sptiotmporlly ontinuous usl hin it s just tht this hin onsists, in prt, of omissions (nmly, th vrious filurs of Enmy to o wht h woul hv on, h Billy not fir). Now, it s not just tht suh rlin on ustion by omission is sprt on its f (though in it is). It s tht vn if w grnt tht ths omissions xist, n r lot whr th vnts omitt woul hv ourr ( non-trivil supposition: right now I m t hom, n hn fil to b in my offi; is this omission lot thr or hr?), it osn t hlp. For thr is no rson to bliv tht th rgion of sptim ths omissions oupy intrsts th rgion of sptim tht Suzy n hr bombr tully oupy; to hol othrwis is just to mistk this rgion with th rgion sh woul hv oupi, h Billy not fir. W n gr tht h Billy not fir, thn th Enmy-rgion woul hv intrst th Suzy-rgion; but if, sy, Suzy woul hv swrv unr thos irumstns, thn it s

12 Two onpts of ustion 12 just fls to suppos tht this ountrftul Enmy-rgion (= th tul omission-of-enmy-rgion) intrsts th tul Suzy-rgion. Of ours, th bt n tk vrious twists n turns from hr: thr r furthr strtgms on might rsort to in n ffort to intrpolt squn of omissions btwn Billy n th bombing; ltrntivly, on might ny tht ustion without onnting squn of usl intrmits rlly is suffiint for tion t istn. It won t profit us to pursu ths twists n turns (but s my 2000b); suffi it to sy tht th strtgms fil, n th prospts for rplmnt for th suffiint onition sm hoplss. 4.3 Problms with Intrinsinss Lt s first rll wht th Intrinsinss thsis sys, in its rful formultion: Suppos n vnt ours t som tim t. Consir th strutur of vnts S tht onsists of, togthr with ll of its uss bk to som rbitrry rlir tim t. Thn ny possibl strutur of vnts tht xists in worl with th sm lws, n tht hs th sm intrinsi hrtr s S, lso hs th sm usl hrtr, t lst with rspt to th usl gnrtion of. For th purposs of this stion, w n r hs th sm intrinsi hrtr s s prftly uplits w won t n to ompr struturs of vnts tht xhibit nr-but-not-quit-prft mth of intrinsi hrtr. Now for som mor til. Whn Billy shot him own, Enmy ws witing for his hom bs hunrs of mils wy to rio him instrutions. At tht momnt, Enmy h no prtiulr intntion of going ftr Suzy; h ws just mining his own businss. Still, if Billy hn t pull th triggr, thn Enmy woul hv lu him, n momnts ltr woul hv riv instrutions to shoot own th nrst suitbl trgt (Suzy, s it hppns). H woul thn hv on so. But Billy os shoot him own, so h nvr rivs th instrutions. In ft, th hom bs osn t vn bothr to sn thm, sin it hs bn monitoring Enmy s trnsmissions n knows tht h hs bn shot own. Fous on th usl history of th bombing, bk to th tim of Billy s tion. Thr is, of ours, th pross onsisting of Suzy flying hr pln, t. (n, lss onspiuously, th pross onsisting in th prsistn of th trgt). If Dpnn is tru, thn th usl history must lso inlu Billy s tion n its immit ffts: th bullts flying out of his gun, thir impt with Enmy s fuslg, th subsqunt xplosion. (Prhps w shoul lso throw in som omissions: th filur of Enmy to o wht h woul hv on, h h somhow lu Billy. It mks no iffrn, sin thir ontribution to th intrinsi hrtr of th rsulting usl history is nil.) Lt this strutur of vnts b S. Two problms now mrg. In th first pl, th intrinsi hrtr of S fils to trmin, togthr with th lws, tht thr r no othr ftors tht woul (i) stop Enmy, if Billy somhow fil to; (ii) o so in wy whih woul rvrs th intuitiv vrit (suh s it is) tht Billy s tion is us of th bombing. Suppos, for instn, tht w hng th xmpl by ing bomb unr Enmy s st, whih woul hv gon off sons ftr th tim t whih Billy fir. An suppos tht within this hng xmpl, w n fin uplit of S in whih s th spifition of th intrinsi hrtr of S must lv out th prsn of th bomb. Tht shows (wht ws, prhps, pprnt lry) tht th pnn of th bombing on Billy s tion is ft xtrinsi to S. If w i tht in this hng xmpl, Billy s tion is not us of th bombing (sin, thnks to th bomb unr Enmy s st, h in ft poss no thrt to Suzy), thn w must ithr giv up th Intrinsinss thsis, or grnt tht th usl history of th bombing (bk to th tim of Billy s tion) wsn t srib ompltly by S. Nithr option is ttrtiv. Lt us ll this th problm of th xtrinsi bsn of isbling ftors (isbling in th sns tht if thy wr prsnt, thr woul b no pnn of th bombing on Billy s tion). Muh mor srious is th problm of th xtrinsi prsn of nbling ftors (nbling in th sns tht if thy wr bsnt, thr woul b no pnn of th bombing on Billy s tion). For onsir thir s, xtly lik th first xpt in th following ritil rspt: Th hom bs hs no intntions of sning Enmy orrs to shoot nyon own. In ft, if Billy hn t pull th triggr, thn th instrutions from th hom bs woul hv bn for Enmy to rturn immitly. So Enmy poss no thrt whtsovr to Suzy. Hn Billy s tion is not us of th bombing. Yt th strutur of vnts S is uplit xtly in this snrio. So if th Intrinsinss thsis is right, thn tht usl history S must not in ft hv bn omplt; w must hv mistknly xlu som vnts for whih th thir snrio ontins no uplits. Prsumbly, ths vnts will b th ons tht onstitut th monitoring of Enmy by his hom bs, togthr with th intntions of his supriors to orr him to shoot own th nrst pproprit trgt. But now w r for to sy tht ths vnts ount s uss of th bombing. Tht is riiulous. It is not tht thy hv no onntion to th bombing, it s just tht thir onntion is muh mor obliqu:

13 Two onpts of ustion 13 ll w n sy is tht if thy hn t hppn, thn th bombing woul not hv pn on Billy s tion. An noti, finlly, tht it is xtly th inlusion of Billy s tion s prt of th usl history S tht is th ulprit: On w inlu it, w must lso inlu (on pin of nying Intrinsinss) ll thos vnts whos ourrn is rquir to sur th ountrftul pnn of th bombing on this tion. To s this problm mor vivily, ompr th vnts pit in figurs 5 n 6: g g b f b f h h firs if hn t fir Figur 5 g g b f b f h h firs if hn t fir Figur 6 Hr, f is stubborn nuron, ning two stimultory signls in orr to fir. Nuron h, in figur 5, firs shortly ftr th tim t whih nurons, b, n ll fir (so I hv bus th usul lft-to-right onvntions slightly). In th lft-hn igrm of figur 5, g pns on, but in figur 6 it os not; in, it woul b quit riiulous to lim, bout th lft-hn igrm of figur 6, tht ws in ny sns us of g. But now onsir th usl history of g, in th lft-hn igrm of figur 5, n suppos tht in kping with Dpnn w ount s prt of this usl history. Thn it woul sm tht this usl history is uplit xtly in th lft-hn igrm of figur 6 in whih s ithr Intrinsinss is fls, or in figur 6 is, ftr ll, us of g. Th only wy out of this ilmm is to ny Dpnn or ls to insist, ginst ll goo sns, tht th usl history of g, in figur 5, lso inlus th firing of h (whih is not uplit in figur 6). But of ours it os not: in figur 5, th firing of h is nssry, in orr for g to pn on ; but tht os not mk it on of g s uss. 4.4 Problms with trnsitivity A mor striking problm pprs whn w fous on th trnsitivity of ustion. I bgin by ing yt mor til to th xmpl. Erly in th morning on th y of th bombing, Enmy s lrm lok gos off. A goo thing, too: if it hn t, h nvr woul hv wokn up in tim to go on his ptrolling mission. In, if his lrm lok hn t gon off, Enmy woul hv bn nowhr nr th sn t whih h ws shot own. It follows tht if Enmy s lrm lok hn t gon off, thn Billy woul not hv pull th triggr. But it is lso tru tht if Billy hn t pull th triggr, thn th bombing woul nvr hv tkn pl. By trnsitivity, this ringing is on of th uss of th bombing.

14 Two onpts of ustion 14 Figur 7 hlps to rinfor th bsurity of this onlusion: f f b b firs Figur 7 if hn t fir Nuron n nvr fir. If os not fir, thn won t gt stimult by, whrs if os fir, thn th stimultion from will b blok by th inhibitory signl from b. So poss no thrt whtsovr to th firing of f. Th littl four-nuron ntwork whih ulmints in is, from th stnpoint of f, totlly inrt. Clrly, s firing nnot b us of f s firing. At most, w might hrtriz s firing s somthing whih thrtns to prvnt f s firing, by wy of th -- onntion with th thrt blok by th -b- onntion. Yt if both Dpnn n Trnsitivity r orrt, thn s firing is us of f s firing. For if hn t fir, thn b woul not hv fir. Likwis, if b h not fir, thn f woul not hv fir (rll hr tht bktrking is forbin: w nnot sy tht if b h not fir, thn it woul hv bn tht in t fir, n so f woul hv fir ll th sm). Sin f pns on b, n b pns on, it follows from Dpnn n Trnsitivity tht s firing is us of f s firing. Tht onsqun is unptbl. Crtin xmpls with this strutur borr on th omi. Billy spis Suzy bout to throw rok t winow. H rushs to stop hr, knowing tht s usul h s going to tk th blm for hr t of vnlism. Unfortuntly for him, trips ovr tr-root, n Suzy, quit oblivious to his prsn, gos h n brks th winow. If h hn t tripp, h woul hv stopp hr so th brking pns on th tripping. But if h hn t st out to stop hr, h wouln t hv tripp so, by th ombintion of Trnsitivity n Dpnn, h hs hlp us th brking ftr ll, mrly by stting out to stop it! Tht onlusion is, of ours, just silly. 18 Conlusion: If th thsis of Dpnn is tru, thn h of Lolity, Intrinsinss, n Trnsitivity is fls. Mor prisly, if Dpnn is tru t worl, n th vnts in tht worl xhibit usl strutur rih nough to provi vn on s of oubl-prvntion lik h of th ons w hv bn xmining, thn h of Lolity, Intrinsinss, n Trnsitivity is fls t tht worl. In th nxt stion, w ll s tht n xtly prlll onlusion n b rwn with rspt to th thsis tht omissions n b uss n fft. 5 Omissions Th thsis of Omissions brings in its wk numbr of iffiult qustions of ontology: Dos it imply ommitmnt to pulir kin of vnt whos ourrn onitions ssntilly involv th filur of som orinry typ of vnt to our? Dos it mk sns to spk of th filur of to our, whr is suppos to rfr to som orinry vnt? (For prhps suh singulr rfrn to non-tul vnts is impossibl; ltrntivly, prhps it is possibl, but th irumstns in whih w wnt to it som omission s us or fft typilly unrtrmin whih orinry vnt is omitt.) Do omissions hv lotions in sp n tim? If so, wht trmins ths lotions? (Rll th rmrks in 4.2: right now I m t hom, n hn fil to b in my offi; is this omission lot thr or hr?) An so on. I m simply going to gloss ovr ll of ths issus, n ssum tht ountrftul supposition of th form omission o os not our is quivlnt to th supposition tht som orinry vnt of givn typ C os our (t, prhps, spifi pl n tim) whr th typ in qustion will b fix, somhow, by th spifition of o (or prhps by ontxt, or prhps by both). At ny rt, howvr justifi omplints bout th ontologil sttus of omissions might b, thy r mphtilly not wht is t issu, s w r bout to s.

15 Two onpts of ustion 15 In wht follows, I ll mk th s tht xmpls of ustion by omission routinly violt h of Lolity n Intrinsinss. Th thniqus I mploy n b pt so strightforwrly to mk th sm points bout prvntion (i.., ustion of omission) tht w n sfly lv thos ss si. Displying th onflit btwn Omissions n Trnsitivity will rquir s in whih w trt n omission s n fft of on vnt n s us of nothr. Finlly, I m lso going to gloss ovr th rmrkbly triky qustion of whn, xtly, w hv s of ustion by or of omission qustion to whih th thsis of Omissions only givs th vgu nswr, somtims. For xmpl, is it nough to hv ustion of by th filur of n vnt of typ C to our for to ountrftully pn on this omission? Or must furthr onstrints b stisfi? If not if pnn is ll tht is rquir w gt suh unwlom rsults s tht my t of typing hs mong its uss quit stonishing multitu of omissions: th filur of mtorit to strik our hous momnts go, th filur of th Prsint to wlk in n intrrupt m, t. If, on th othr hn, w insist tht mr pnn is not nough for ustion by omission, thn w f th unnvibl tsk of trying to hrtriz th furthr onstrints. I m going to sistp ths issus by piking ss tht r unontrovrsil xmpls of ustion by omission unontrovrsil, tht is, on th ssumption tht thr r ny suh ss. 5.1 Problms with Lolity W n rw on th story of Suzy, Billy, n Enmy to show tht, vn if w wiv worris bout whthr omissions hv trmint lotions, Lolity fils for typil ss of ustion by omission. Fous on tim t t whih Enmy woul hv bn pprohing Suzy to shoot hr own, h h not bn shot own himslf. H Enmy not bn bsnt, Suzy s mission woul hv fil; so th bombing pns on, s w might put it, th omission of Enmy s ttk. Mor thn this: Th omission of Enmy s ttk is mong th uss of th bombing t lst, if thr is to b ustion by omission t ll, this s shoul rtinly b n xmpl. But on gin, it pprs tht th onntion btwn this omission n th bombing must lso qulify s s of tion t istn, for no sptiotmporlly ontinuous squn of usl intrmits onnts th two vnts. As bfor, th problm is not with fining suitbl lotion for th omission; it is rthr tht nothing gurnts tht th squn of omissions tht pros from it (Enmy s filur to pproh, pull th triggr, t.) will intrst Suzy s tul flight. W n grnt tht th rgion of sptim in whih ths omissions tk pl intrsts th rgion sh woul hv oupi, h Enmy not bn bsnt. But it ommits th sm mistk s bfor to suppos tht this rgion is th sm s th rgion sh tully oupis. 5.2 Problms with Intrinsinss Whtvr omissions r, thy r notbly lking in intrinsi hrtr. W lry sw tht for this rson, th Intrinsinss thsis n to b phrs rthr rfully: Whn w hv pik out n vnt n strutur of vnts S omprising n ll uss of bk to som rlir tim, it is to b unrstoo tht ny strutur ginst whih w ompr S is ompos solly of gnuin vnts, not omissions. (On th othr hn, no hrm oms of ltting S inlu omissions, t lst on th ssumption tht thy ontribut nothing to its intrinsi hrtr.) Still, it is for ll tht onsistnt to hol tht Intrinsinss pplis to ustion by omission, s follows: Suppos tht ours t tim t, n tht S onsists of n ll uss of bk to som rlir tim t. Suppos furthr tht w ount th omission o s on of s uss, n tht o ours (in whtvr sns is pproprit for omissions) in th intrvl btwn t n t. Thn if strutur S intrinsilly mths S, thr must b som omission o orrsponing to o tht uss th vnt in S tht orrspons to in S (nvr min tht o is not prt of S ). In short, w might think tht ustion of n vnt by omission suprvns on th intrinsi hrtr of tht vnt s positiv usl history. This onjtur is fls. To show why, I ll rgu tht both of th problms w sw in 4.3 th problm of th xtrinsi lk of isbling ftors n th problm of th xtrinsi prsn of nbling ftors rur in this ontxt. A simpl nuron igrm will srv to illustrt h:

16 Two onpts of ustion 16 f f b b b osn t fir if b h fir Figur 8 In figur 8, is ull nuron tht ns two stimultory signls in orr to fir. Thus, fils to fir vn though stimult by ; still, sin firs, s firing pns on th filur of b to fir (t, sy, tim t, whih w will tk to b th tim of s firing). Not finlly tht if b h fir n f h s wll (t t), thn woul hv fir ll th sm. Lt us suppos, in kping with th Omissions thsis, tht th filur of b to fir t t is mong th uss of s firing. Lt S onsist of, togthr with ll of its (positiv) uss bk to tim t. Thn if Intrinsinss pplis to ustion by omission in th wy w hv suggst, ny nomologilly possibl strutur tht uplits S will xhibit th sm usl rltionships: in prtiulr, thr will b n omission tht uplits b s filur to fir n tht will b us of th vnt tht uplits s firing. Hr is on suh possibl strutur, mb in slightly iffrnt surrounings: f b An hr is nothr, gin in iffrnt surrounings: Figur 9

17 Two onpts of ustion 17 f b Figur 10 Th problm is tht in h s, b s filur to fir is no longr us of s firing, ontr th rquirmnts of our onjtur bout how Intrinsinss ovrs ustion by omission. In figur 9, th firing of f rnrs b s filur to fir quit irrlvnt to whthr firs, showing tht whn b s filur to fir is us of s firing, this is u in prt to th xtrinsi bsn of isbling ftors. Likwis, in figur 10, s filur to fir rnrs th bhvior of b irrlvnt, showing tht whn b s filur to fir is us of s firing, this is u in prt to th xtrinsi prsn of nbling ftors. So th ling i bhin th Intrinsinss thsis nmly, tht it is th intrinsi hrtr of som vnt s usl history tht (togthr with th lws) mks it th s tht this is its usl history oms irtly into onflit with th Omissions thsis. 5.3 Problms with Trnsitivity As bfor, mor striking problms mrg whn w ombin th thss of Omissions n Trnsitivity. To s how sy it is to onot n bsurity from ths two ingrints, onsir th following vrint on our story: This tim, Enmy s supriors on th groun h no intntion of going ftr Suzy until, tht is, Billy shoots Enmy own. Outrg by this unprovok t of ggrssion, thy sn out n ll-points-bulltin, instruting ny vilbl fightr to go ftr Suzy ( muh mor vlubl trgt thn Billy). Als, Enmy ws th only fightr in th r. H h somhow bn prsnt t th tim of th brost, h woul hv riv it, n promptly trgt n shot own Suzy; his bsn is thrby us of th bombing. But, of ours, his bsn is itslf us by Billy s tion. So by Trnsitivity, w gt th rsult tht Billy s tion is us of th bombing. Lst th tils of th s b istrting, lt s b lr: ll Billy os it to provok thrt to th bombing; lukily for him, th vry tion tht provoks th thrt lso mngs to ountrt it. Not th similrity to our rlir ountrxmpl to Trnsitivity: Enmy s tion (tking off in th morning) both uss thrt to th bombing (by putting Enmy within striking rng of Suzy) n ountrts tht thrt (by likwis putting Enmy within Billy s striking rng). Conlusion: If th thsis of Omissions is tru, thn h of Lolity, Intrinsinss, n Trnsitivity is fls. Mor prisly, if Omissions is tru t worl, n th vnts in tht worl xhibit usl strutur rih nough to provi ss of th kins w hv just onsir, thn h of Lolity, Intrinsinss, n Trnsitivity is fls t tht worl. 6 Dignosis: two onpts of ustion Hr r two oppos rtions on might hv to th isussion so fr: Countrftul pnn is not ustion. In th first pl, it s not (s vryon rognizs) nssry for ustion. In th son pl, th bst ttmpts to trt it up in suh wy s to yil fullblown nlysis of ustion rly on th thr thss of Lolity, Intrinsinss, n Trnsitivity n th lsson of oubl prvntion ( lsson lso support by onsiring th usl sttus of omissions) is tht ths thss ontrit th lim tht pnn is suffiint for ustion. Th thss r too importnt; this lttr lim must b givn up. But giv up Dpnn, n you v torn th hrt out of ountrftul nlyss of ustion. Nonsns; ountrftul pnn is too ustion. Hr w hv two wholly istint vnts; morovr, if th first h not hppn, thn th son woul not hv hppn. So w n sy noti

18 Two onpts of ustion 18 how smoothly th wors gli off th tongu! tht it is in prt bus th first hppn tht th son hppn, tht th first vnt is prtly rsponsibl for th son vnt, tht th ourrn of th first vnt hlps to xplin why th son vnt hppn, t. Nor o w rvrs ths vrits whn w isovr tht th pnn riss by wy of oubl prvntion; tht sms quit irrlvnt. All of ths loutions r usl loutions, n thir ppropritnss n, quit lrly, b justifi by th lim tht th son vnt ountrftully pns on th first vnt. So how oul this rltion fil to b usl? To b sur, it s nothr qustion whthr w n us it to onstrut full-blown nlysis of ustion, but t th vry lst w hv th rsult tht ountrftul pnn (btwn wholly istint vnts) is suffiint for ustion whih is just to sy tht Dpnn is tru. Th lims of both of th forgoing prgrphs r orrt. But not by mking ontrition tru: rthr, wht is mnt by ustion in h s is iffrnt. Countrftul pnn is ustion in on sns: but in tht sns of us, Trnsitivity, Lolity, n Intrinsinss r ll fls. Still, thy r not fls simpliitr; for thr is iffrnt onpt of ustion th on I ll proution whih rnrs thm tru. Thus, wht w hv in th stnr ss of ovrtrmintion w rviw in 3 r not mrly ountrxmpls to som hoplss ttmpt t n nlysis of ustion, but ss tht rvl on wy th onpts of pnn n proution n om prt: Ths ss uniformly xhibit proution without pnn. Wht w hv in th ss of oubl-prvntion n ustion by omission w xmin in 4-5 r not mrly mor nils in th offin of th ountrftul nlysis, but ss tht rvl th othr wy th two usl onpts n om prt: For ths ss uniformly xhibit pnn without proution. Similrly, w n now ignos th intuitions Bnntt is pumping in his April rins/jun forst fir s. For whil thr is sns in whih th rins o us th fir th fir lrly pns on th rins thr is n qully goo sns in whih thy on t th rins o not hlp to prou th fir. Tht is bus (surpris!) w hv hr s of oubl-prvntion: Th rins prvnt n vnt (fir in My) whih, h it ourr, woul hv prvnt th Jun firs (by stroying th flmmbl mtril). Th prinipl virtus of my lim r thus lr: It llows us to mintin h of th fiv thss. It provis us with nturl n omplling ignosis of th most importnt problm ss for nlyss of ustion. An it shoul om s no surpris tht th istintion btwn proution n pnn hs gon unnoti, for typilly th two rltions oini (mor xtly, I think, proution typilly oinis with th nstrl of pnn; mor on this in 7.4, blow). An itionl virtu of th position, prhps lss obvious thn th forgoing ons, onrns th ontologil sttus of omissions. Thos who nors th Omissions thsis might worry tht thy r thrby ommitt to th xistn of spil sort of vnt s if th truth of th filur of n vnt of typ C to our us to our rquir th xistn of somthing tht nswr to th sription, filur of n vnt of typ C to our. But if th only sns in whih omissions n us n b us is tht thy n ntr into rltions of ountrftul pnn, thn this worry is quit mispl. For tlk of ustion by n of omissions turns out to b nothing mor thn wy of tlking bout lims of th form, if n vnt of typ C h ourr, thn... n if..., thn n vnt of typ C woul hv ourr. Mnifstly, nithr loution rris n ontologil ommitmnt to strng sort of ngtiv vnt. So, if I m right, nxitis bout whthr w n fin pl for omissions in th usl orr rst on bsi onfusion bout wht it mns to ttribut usl sttus to omissions. This obsrvtion onnts to bror point, whih is tht pnn, unrstoo s rltion btwn vnts, is unuly rstritiv. For quit gnrlly thr n b ountrftul pnn btwn fts (tru propositions), whr ths n b positiv, ngtiv, isjuntiv, or whtvr n whr only rrly n w shohorn th fts so rlt into th form, suh-n-suh n vnt ourr. Whn w n whn w n sy tht th ft tht ourr pns on th ft tht ourr thn w n go h n ll this kin of vnt-ustion. But to s it s nything but spil s of usl rltion with muh bror omin woul b, I think, mistk. 19 W n bring my thsis into still shrpr fous by onsiring th som of th mor obvious objtions to it. It sms wis to bgin by irtly onfronting wht mny will s s th most mning objtion whih is simply tht it posits two onpts of vnt-ustion! This might strik som s n xtrvgntly high pri to py: Aftr ll, whn possibl w shoul b onsrvtiv, n onsrvtism rgus for tking our onpt of vnt-ustion to b univol. At th vry lst, shouln t w viw th bifurtion of our onpt of vnt-ustion s vry srious ost of my proposl? No, w shoul not n not bus w shouln t b onsrvtiv. It s rthr tht this objtion mistks prftly snsibl mthoologil mxim with rson to bliv. Th mthoologil mxim gos: Whn trying to om up with n nlysis of onpt, strt out by oprting unr th ssumption tht th onpt is univol. I think tht s soun. But it osn t t ll follow tht it is somhow

19 Two onpts of ustion 19 ntntly mor probbl tht th onpt in qustion is univol lt lon so probbl tht ny nlysis tht sys othrwis pys high pri. In th f of th right sorts of rsons to prfr nonunivol nlysis, w shoul giv up our oprtiv ssumption n w shouln t xpt thos rsons to hv to rry n xtr hvy burn of proof bus of th intrinsi plusibility of th hypothsis of univolity. To think othrwis mnifsts bsi onfusion. It s rthr s if I h lost my kys somwhr in this room; I hv no i whr. Thy might b ovr thr, whr it s rk n lot of bris obsurs things; or thy might b ovr hr, whr it s sunny n unluttr. It mks xingly goo sns for m to strt by looking in th sunny n unluttr prt of th room to t s if I bliv my kys wr thr. But tht is not bus I o bliv thy r thr, or vn bus I onsir it mor likly thn th ltrntiv (s if th hypothsis tht lif is sy hs som intrinsi plusibility to it!). It s rthr tht if my kys r in th unluttr r, thn I will soon fin thm n if thy r not, I will quikly fin tht out s wll. In th sm wy, whn w go to nlyz som onpt of philosophil intrst, it mks xingly goo sns to strt by looking for univol nlysis. For vn if w r wrong, n som hin mbiguity lurks in our orinry pplitions of th onpt, th vry problms w will nountr in trying to om up with univol nlysis will (if w r rful n ttntiv) b ignosti of this mbiguity. (Th ritiqu of th ountrftul nlysis rri out in 3-5 ws prtly sign to b s in point.) But it is foolishnss to mistk this vi for rson to bliv tht th onpt is univol. In, if I onsir th hypothsis tht our onpt of vnt-ustion is univol, I s no rson whtsovr to jug it to b highly probbl, ntntly to ny invstigtion. An ftr suffiint invstigtion in prtiulr, ftr vry bsi prinipls govrning our pplition of us hv bn shown to om into onflit I think its plusibility is just bout nil. A mor subtl objtion is th following: Wht I hv rlly shown is not tht thr r two onpts of ustion, but rthr tht thr r two kins of ustion, two iffrnt wys in whih on vnt n b us of nothr. Tht my wll b right; rtinly, I ws hppy to bgin this ppr by nnouning tht vnt-ustion oms in two vritis. I o not know how to jug th mttr, bus I m not suffiintly lr on wht unrlis this istintion btwn onpts n kins. Compr ni xmpl borrow from Tim Mulin: Thr r t lst thr iffrnt wys of bing mothr. W might ll thm DNA-mothr, womb-mothr, n nurturing mothr. Dos tht mn w hv thr iffrnt onpts of mothr n mbiguity lrgly unnoti only bus thos w ll mothrs r typilly ll thr? I on t know. At ny rt, in th s t hn it osn t mttr in th slightst. I m quit ontnt to gr tht I hv (mrly) shown tht thr r two kins of ustion s long s thos who insist on this rnring of my thsis gr tht th two kins nswr to vry iffrnt ritri, n onsquntly rquir vry iffrnt nlyss. Tht lim lon is nough to show how unwis it woul b, whn ttmpting to provi philosophil ount of vnt-ustion, mrly to forg blinly h, trying to om up with n nlysis whih n sussfully run th guntlt of known problm ss. If I m right, ny suh singl nlysis is oom to filur. A thir, mor ongnil objtion bgins by grnting th istintion btwn proution n pnn, but nying tht pnn srvs to b ount kin of ustion t ll. Now, I think thr is somthing right bout this objtion, in tht proution os sm, in som sns, to b th mor ntrl usl notion. As vin, onsir tht whn prsnt with prigm s of proution without pnn s in, sy, th story of Suzy, Billy, n th brokn bottl w unhsittingly lssify th prour s us; whrs whn prsnt with prigm s of pnn without proution s in, sy, th story of Suzy, Billy, n Enmy our intuitions (wll, thos of som of us, nywy) bout whthr gnuin usl rltion is mnifst r shkir. Fir nough. But I think it gos too fr to ny tht ountrftul pnn btwn wholly istint vnts is not kin of usl rltion. Prtly this is bus pnn plys th pproprit sort of rols in, for xmpl, xplntion n ision. (S 8, blow, for mor isussion of this point.) An prtly it is bus I o not s how to ommot ustion of n by omissions (s w shoul) s spis of proution; ountrftul pnn sms th only pproprit usl rltion for suh ngtiv vnts to stn in. This lst point brings up fourth possibl objtion, whih is tht in liming tht thr r two kins of ustion, h hrtriz by iffrnt subst of th fiv thss, I hv ovrstpp my bouns. Aftr ll, vn if th rgumnts of 4-5 su, ll thy stblish is, roughly, (i) tht Dpnn ontrits h of Lolity, Intrinsinss, n Trnsitivity; n (ii) tht Omissions likwis ontrits h of Lolity, Intrinsinss, n Trnsitivity. It obviously osn t follow tht Dpnn n Omissions shoul b bunl togthr n tkn to hrtriz on kin of ustion, nor tht Lolity,

20 Two onpts of ustion 20 Intrinsinss, n Trnsitivity shoul b bunl togthr n tkn to hrtriz nothr. Prhps th mbiguity in our orinry usl tlk is mor multifrious n mssy thn this lim llows. D right. An vn though I think tht furthr invstigtion oul unrth mor positiv rsons for iviing th fiv thss into th two groups I hv hosn, I o not hv suh rsons to offr hr. For wht it s worth, I o hv strong hunh tht, s not bov, thr ouln t b nything mor to ustion of n by omissions thn ountrftul pnn; hn th piring of Omissions with Dpnn. An in th nxt stion I ll propos n nlysis of proution tht givs ntrl rols to both Intrinsinss n Trnsitivity, s wll s to slightly wkn vrsion of Lolity. But tht s hrly nough to wrrnt onvition. Rthr, wht s wnt r mor probing rgumnts s to why our orinry notion of vnt-ustion shoul frtur lnly long th lins I hv rwn. Lking suh rgumnts, I will fll bk on th mthoologil mxim isuss bov: Givn tht w n no longr tk it s working hypothsis tht th onpt of ustion is univol, lt us nvrthlss opt th most onsrvtiv working hypothsis vilbl to us. Sin w hv yt to fin ny rson to think tht Dpnn onflits with Omissions, or tht onptul tnsions thrtn th hppy union of Lolity, Intrinsinss, n Trnsitivity, lt us ssum gin, s working hypothsis tht th first two thss hrtriz on usl notion, th lst thr nothr. An lt us now onsir how th two usl notions r to b nlyz. 7 Th two onpts nlyz Prt of th tsk nlyzing pnn is sy: it is simply ountrftul pnn btwn istint vnts. Mor utiously, w might wnt to mit nothr kin of ountrftul pnn s wll. Prhps ountrftul ovrition mnifst whn th tim n mnnr of on vnt s ourrn systmtilly ountrftully pn on th tim n mnnr of nothr s shoul ount s kin of ustion s wll, to b lssifi s los rltiv of pnn. (It s lrly possibl to hv pnn without ovrition, s in typil ss of oubl-prvntion; Shffr (2000) provis omplling xmpls of ovrition without pnn, s wll.) No mttr; givn tht ths ountrftul loutions r thmslvs wll-unrstoo, our work hr is bsilly lry on for us. (But s 8.2 for som tnttiv rsrvtions.) Proution is hrr. In this stion I will put forth my own proposl spultiv, n, s w ll s, somwht limit in sop for rutiv nlysis of this rltion. I will st it out in two prts. Th first, lss spultiv prt outlins rtin strtgy for vloping n nlysis, whih I ll th bluprint strtgy. Th son, mor spultiv prt sribs my (urrntly) prfrr wy of implmnting this strtgy. 7.1 Th bluprint strtgy Suppos w hv n nlysis tht sus whn irumstns r ni in singling out portion of th usl history of som trgt vnt, whr this is unrstoo to b th history of s prours. (Whn irumstns r not ni, lt th nlysis fll silnt.) It might b simpl ountrftul nlysis: Whn irumstns r ni (whn thr is no oubl-prvntion, or ovrtrmintion ), th usl history of bk to som rlir tim t onsists of ll thos vnts ourring in tht intrvl upon whih pns. Or it might b Mki-styl nlysis: th usl history onsists of ll thos vnts (gin, ourring in tht intrvl) whih r nssry prts of som suffiint onition for. Or it might b som othr kin of nlysis. Thn provi w n sy with nough prision wht it tks for irumstns to b ni w n us th Intrinsinss n Trnsitivity thss to xtn th rh of this nlysis, s follows: First, suppos w xmin som vnts n, n fin tht our nlysis is silnt s to whthr is us of. Still, w fin tht n blong to strutur of vnts S suh tht (i) S intrinsilly mths som othr strutur of vnts S (ourring in worl with th sm lws s th worl of S); n (ii) our nlysis ounts S s sgmnt of th usl history of (whr is th vnt in S whih orrspons to in S). Tht is, our nlysis ounts S s rih nough st of uss of for th Intrinsinss thsis to pply. It follows tht S hs th sm usl strutur s S (t lst, with rspt to th trgt vnt ), hn tht is us of. For onvnin, lt us sy tht whn th onjuntion of our nlysis with th Intrinsinss thsis ounts s us of, is proximt us of. Thn, son, w prly proximt ustion into ustion simpliitr by mns of th Trnsitivity thsis: ustion is simply th nstrl of proximt ustion. In short, w us our originl nlysis to fin st of bluprints for usl struturs, whih w n thn us to mp out (if w r luky) th usl strutur of ny st of vnts, in ny irumstns, by mns of th Intrinsinss n Trnsitivity thss.

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