on the semantics of ought to do

8/12/2019 On the Semantics of Ought to Do

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HECTOR-NERI CASTAI~IEDA

O N T H E S E M A N T I C S O F T H E O U G H T - T O - D O

D eo n t i c co n cep t s l i k e oug ht r ight obl igat ion forbidden a n d permissiblehave benef i t ed f rom the ph i losoph ica l ly exc i t i ng work in t he seman t i cs o fm o d a l co n cep t s d o n e b y K an g e r 1, H i n t i k k a 2, K r i p k e 3, M o n t ag u e 4 an do ther s . Thei r seman t i cs i l l umina tes bo th the t op i c and the con t r ibu t iono f t h e s t an d a r d ax i o ma t i c ap p r o ac h t o d eo n t i c lo g i c : t h e t o p i c is w h a tp h i l o s o p h e r s u s ed t o ca l l t h e O u g h t - t o - b e . O n t h e o t h e r h an d , t h e n o n -s t an d a r d ap p r o ach r ep r e s en t ed b y ea r l y ax i o ma t i c d eo n t i c s y s t ems o fo u r s d ea l s w i t h t h e O u g h t - t o - d o . Th u s , r a t h e r t h an co mp e t i n g w i t h t h es t an d a r d ap p r o ach t o d eo n t ic l og ic , o u r n o n - s t an d a r d ap p r o ac h co m -p l emen t s i t . Th i s can , h o w ev e r , b e s een o n l y b y p r o v i d i n g o u r n o n -s t an d a r d ap p r o ach w i t h a mi n i m u m o f s eman t i ca l f o u n d a t i o n s . Th i s isp rec i se ly w hat t h i s essay a t t emp t s t o do . W e sha l l a l so p rov ide a r a t i ona l ef o r o u r n o n - s t an d a r d s eman t i ca l s y s t em b y f o rmu l a t i n g s o m e p r o t o -p h i l o s o p h ica l d a t a t h a t b o t h g u i d e t h e d ev e l o p m en t o f th e s y s t em an dserve as t es t s o f adequ acy fo r it . In f ac t , ou r conc ern i s p r imar i ly ph i lo -soph ica l , no t t echn ica l .

Th e r e a r e , o f co u rs e , i mp o r t an t g en e r a l p h il o s o p h i ca l r ea s o n s f o rdeve lop ing d ivergen t sys t ems: ( i) ou r app rec i a t i on o f s t andard sys t ems i sen h an ced b y co n t ra s t i n g t h em w i th n o n - s t an d a r d o n es , an d (ii) o u r u n d e r -s t and ing o f a se t o f concep t s im prove s by see ing them in d i ff e ren t l igh t s .1. Ought-To-Be and Ought-To-DoTh e s t an d a r d ap p r o ach t o d e o n t i c l o g ic co n ce iv es o f d eo n t i c ex p r e ss i o ns( i t is ob l iga to ry tha t , i t is permiss ib le t ha t , i t is fo rb idden th a t , i t isw rong tha t , i t is ri gh t t ha t , i t ough t t o be t he case t ha t , e t c .) as ex -p r e s s i n g o p e r a t o r s t h a t h av e t h e s ame d o ma i n an d r an g e : t h e d o ma i n o fp rop os i t i ons (o r s t a t es o f a f fa ir s ) and p roper t i es . L ingu i s t ica l ly , deon t i cex p r e s si o n s a r e , i n th e s t an d a r d ap p r o ach , o p e r a t o r s w h o s e d o m a i n an drange a re b o th the dom ain o f sen t en t i a l fo rm s and sen tences , i. e., t he t o t a lSyn these 21 1970) 449--468. Al l R igh ts ReservedCopyright 1970 by D. Reidel Publishing Company Do rdrech t- t to l land


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450 HECTOR NERI CASTA~EDAset of all well-formed formulas (wffs). Thus, on the standard approach ifD is a deontic expression a ndfis a wff, fis a wff of the same general kindf i s . Semantically, the beautiful idea is that fis true in a given possibleworld w if and only iff is true (or false, depending on D) in some (orevery) possible world which is ideal with respect to W. Here a possibleworld W' is ideal with respect to Wif and only if all obligations belongingto W both are also obligations belonging to W' and are fulfilled in W'.This idea has been both explained in detail and put to important uses byHint ikka in 'Deont ic Logic and Its Philosophical Morals' (presented in asymposium on deontic logic at the meeting of the Western Division of theAmerican Philosophical Association in Cleveland, Ohio, in May, 1969).A tremendously valuable distinction Hintikka makes is that betweenlogical consequence and deontic consequence.

The intuitive idea behind this standard semantical analysis of the truth-conditions for 'It ought to be the case that f ' is straightforward and in-sightful: what makes our world have genuine, non-empty obligations isnothing but its failing short of an ideal in some respects, i.e., its havingsomething false which is (or would be) true in an ideal world; since therealization of certain ideals may prevent others from being realized, wemust consider not only one ideal world but a set of them, not necessarilyarranged in a linear sequence of perfection: there may be alternative roadsto perfection.

The primary contrast in the above conception of deontic logic is thecontrast between what is and what ought to be. The idea of who is torealize the obligation is not considered, so that the approach can handlevery nicely genuinely impersonal statements like There ought to be nopain , meant merely to articulate something about the universe, which isnot conceived as an agent but simply as the totality of all existents and allfacts. This impersonal statement tells of what would be a necessary lack inevery universe, and neither attributes responsibility for any action to some-body nor demands any action from anybody: the statement is oriented tono agents: it has the structure of the statement It is (would be) desirablethat there were no pain .

Naturally, the sentence 'There ought to be no pain' may very well beused in ordinary language to formulate a personal, agential statement,e.g., Go d ought to have created no pain . Conversely, the sentence 'Godought to have created no pain' can express a non-agential statement


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ON THE SEMANTIC S OF THE OU GHT TO DO 45

a t t r i b u t i n g s o m e f o r m o f d e s ir a b il it y o r ' o u g h t n e s s ' t o t h e s t a t e o f a f f a ir so r p r o p o s i t i o n G o d c r e a te d n o p a i n . T h i s n o n - a g e n t i a l s t a t e m e n t m a y ,p e r h a p s , b e m o r e n a t u r a l l y e x p r e ss e d b y t h e s e n t e n c e ' I t o u g h t t o b e t h ec a se t h a t G o d c r e a t ed n o p a i n ' . O r d i n a r y s e n te n c es c a n e as i ly b e m a d e t oe x p r e s s d i f f e r e n t , t h o u g h r e l a t e d s t a t e m e n t s . W h a t m a t t e r s i s t h a t w ed i s t in g u i s h t h e p r e c e d in g n o n - a g e n t i a l s t a t e m e n t T h e r e o u g h t t o b e n op a i n f r o m t h e a g e n ti a l s t a t e m e n t t h a t a t t ri b u t e s t o G o d a d u t y o r o bl ig a -t i o n , a n d a r t i c u l a t e s n o t m e r e l y a n i d e a l c r e a t i o n , b u t e s t a b l i s h e s a b a s i sf o r b l a m i n g o r p r a i si n g G o d f o r h is c r e a ti o n .

I n e a r l i er p a p e r s I h a v e a d o p t e d a n o n - s t a n d a r d v i e w o f d e o n t i c lo g ic .T h a t v i e w f o c u s e s o n t h e a g e n t i a l o u g h t s t a t e m e n t s , a n d i s b a s e d o n ag e n e r a l i z a t i o n o f th e c o m m o n s t r u c t u r e u n d e r l y i n g a l l p r o c e s s e s o f le g is -l a t in g o r r u l e - m a k i n g , w h e t h e r t h e y g o o n c o n t i n u o u s l y in h i g h l e g is la ti v ec h a m b e r s o f n a t io n s , o r i n p o m p o u s m e e t i n g s o f l eg i sl at iv e bo d i e s o fi n s t it u t i o n s , o r i n p e d e s t r i a n d i s c us s i o ns o f p r o c e d u r e s b y t h e m e m b e r s o fi n f o r m a l g r o u p s o r c l ub s . A f o r m a l a n a ly s i s o f th e g e n e r a l u n d e r l y i n gs t r u c t u r e o f r u l e - m a k i n g , w h a t e v e r i ts k in d , i s t h i s : ( i) a f r a m e w o r k o ff a c t s a n d l a w s o f n a t u r e g o v e r n i n g t h e f a c t s is r e c o g n i z e d ; (ii) a s e t f l o fp r e s c r i p t i o n s , o r c o m m a n d s o r i m p e r a t i v e s a r e a d o p t e d o r e n d o r s e d(sub jec t t o ove r r id ing cons ide ra t ions in ca se s o f conf l i c t s ) ; ( i i i ) t he se t f ll i m i ts t h e f r e e d o m o f a c t i o n , i .e ., o f d e c i s io n a n d c o m m a n d , o f t h e a g e n t st h e c o m m a n d s i n fl a r e ' a d d r e s s e d ' o r d i r e c t e d t o . T h u s , a p i e c e o f r u l e -m a k i n g c o n f r o n t s t h e r e a l w o r l d , w i t h a ll it s fa c t s a n d l a w s o f n a tu r e , w i t ho t h e r p o s s i b le p r a c t ic a l w o r l d s i n w h i c h t h e s a m e f a c t s a n d l a w s o f n a t u r eh o l d , b u t d i f f e r e n t d e c is i o ns a n d o r d e r s t a k e p l a c e : t h e m a k i n g o f a s e t o fr u le s i s, a t b o t t o m , n o t h i n g m o r e ( o n t h i s a n al y s is ) t h a n t h e a d o p t i o n o f as y s t e m S 0 o f a l t e r n a t i v e pr ctic l w o r l d s w h i c h s h a r e b o t h t h e s a m e f a c t sa n d t h e s a m e s e t fl o f p re s c r ip t i o n s o r c o m m a n d s . A c o n t i n g e n t p re s cr ip -t i o n o r c o m m a n d ( w i t h r e s pe c t to S p) is o n e t h a t h o l d s i n s o m e w o r l d s b u tf a il s t o h o l d i n o t h e r w o r l d s o f S o W h a t i s o b l i g a t o r y w i t h r e s p e ct t o t h el e g i s l a ti n g o r e n a c t i n g o f f l , i .e . , w h a t i s o b l i g a t o r y 0 i s w h a t i s ' c o m m a n d e d 'i n e v e r y w o r l d o f S o : W h a t i s o b l i g a t o r y i s , t h u s , i n a s e n s e , w h a t i sn e c e ss a r il y p r e s c ri b e d o r c o m m a n d e d .

T h e p r e c e d i n g i s a c r u d e s t a t e m e n t o f th e i n t u i ti o n b e h i n d o u r a p p r o a c ht o d e o n t i c l o g i c . I t i s n o n - s t a n d a r d w i t h r e s p e c t t o t h e i d e a l - w o r l d a n a l -y s i s , y e t i t , t o o , h a s l o n g a n d r e s p e c t a b l e r o o t s i n t h e h i s t o r y o f p h i l o s -o p h y . T h e r e is n o n e e d t o r e m i n d a n y b o d y o f t h e im p e r a t i v is t a n a l y si s o f


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452 H E C T O R - N E R I C A S T A 17 1EDAought-statements or of traditional command analysis of laws. However, itmust be clear that the preceding paragraph is not concerned with theanalysis of ought-statements themselves, but only with the analysis of thetruth condit ions of ought-statements.

Now, an important feature of certain deontic statements is that theyinvolve an action and an agent and a demand that the agent do, or fail todo, the action in question. Many an ordinary statement that is apparentlyagentless demands an action; e.g., Cars ought to have plates demandsthat some agents put plates on cars; it is short for a statement to the effectthat people in a relationship R of a certain kind to a car (ownership,usership, managership, etc.) put plates on that car. The statement sup-ports imperatives of the form If you are R to that car, put plates on it .That statement contrasts very sharply with the agentless statement Thereought to be no pain discussed above. In short, deontic statements divideneatly into: (i) those that involve agents and actions and support im-peratives, and (ii) those that involve states of affairs and are agentless andhave by themselves nothing to do with imperatives. The former belong towhat used to be called the Ought to do and the latter to the Ought to be.Our non-standard approach, then, is not suited for the Ought-to-be; but,we hope, it is adequate for the Ought-to-do.2. Proto Phi losophical DataWe have just demarkated the Ought-to-do as our topic by means ofimperatives. Thus, in order to gather data for any theory of the Ought-to-do we must engage in a phenomenological analysis of imperatives, aswell, of course, as in a phenomenological analysis of normative or deonticstatements.2.1. Prescriptions. We shall call commands, orders, petitions, requests,pieces of advice, entreaties, and suggestions mandates. Clearly mandatesbelong into families. One and the same imperative sentence, e.g., 'Karl,go home at 3 p.m.', may express an order, a command, apiece of advice,a petition, a request, etc. What all these have in common is a structureconsisting of a reference to an entity named 'Karl' and the predicativeaction going-home-at-3-p.m. This structure we shall call a prescription.It is like a proposition or statement; but in this simple or atomic case itdiffers from the corresponding proposition expressed with the sentences'Karl goes home at 3 p.m.' and 'Karl will go home at 3 p.m.' in the way


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ON THE SEMANTIC S OF THE OUGHT TO DO 453sub jec t and p red i ca t e a re r e la t ed , i .e ., i n t he copu la t i on o f t he su b j ec t andpred i ca t e . The prescr i p t i ve copu l a t i on we sha l l say , m akes o f t he sub j ec tan a gen t p rescr ip t ive ly cons idered , and , l ikewi se i t m akes o f t he ac t i on anac t ion p rescr ip t i ve ly cons idered . The c ruc i a l po in t i s t ha t an agen t p re-scr ip ti ve ly cons idered has a cer t a in asym m et ry wi th r espec t t o t he o therm em bers o f a r e l a t ion . A c lue t o t h is appe ar s i n t he f ac t tha t an i nd i ca t ive( i . e . , p ropos i t i on -express ing) sen t ence fo rmula t i ng t he per fo rmance o rd o i n g o f an ac t i o n h as b o t h a p a s s iv e an d an ac t i v e co u n t e r p a r t ; b u t t h e r ei s no such coun terpar t fo r an impera t i ve ( i . e . , p rescr ip t i on -express ing)s en ten ce . F o r ex am p l e : w e can s ay e i th e r P au l h i t M ar y o r M ar y w ash i t b y P au l a s s e r ti n g th e s ame p r o p o s i ti o n . B u t w e can n o t ch o o s e t o p u tt h e p r e s c r i p t io n emb ed d e d i n P au l , h i t M ar y i n t h e p a s s iv e v e r s io n

M a r y , b e h i t b y P a u l .C o mp l ex p r e s c r i p t i o n s d i f f e r f r o m t h e i r co r r e s p o n d i n g p r o p o s i t i o n s

u l t imate ly i n t he d if f e ren t cop u la t i on o f t he i r a tom ic co ns t i t uen t p re-scr ip ti ons . P rescr ip t i ons , a re , t hen , abs t r ac t i ons f ro m fami l ies o f mand atest h a t d i s r eg a r d n o t o n l y t h e mo d a l i t y o f t h e man d a t e s , ( e .g ., c o m m an d ,o rder , sugges t i on , en t r ea ty ) , bu t a l so t he ac t o f i s su ing and the e l emen t so f th i s ac t : t he t ime , t he p l ace , and the i s suer . W e sha l l i n ou r p r o to -ph i losoph ica l examina t ion r ep resen t p rescr ip t i ons by t he c l ause r esu l t i ngf r o m i mp e r a t i v e s en t en ces b y d e l e t i n g t h e co mma a f t e r t h e ag en t n ame ;t h u s , i n t h e ab o v e ex am p l e o u r p r e s c r ip t i o n i s ex p re s s ed p u r e l y b y ' K a r lg o h o m e ' .

A n i m p o r t an t s t r u c tu r a l f ea t u r e o f p r e s c r ip t io n s a n d m an d a t e s is th a tmi x ed co m p o u n d s o f p r e s c r ip t i o n s ( o r m an d a t e s ) an d p r o p o s i t i o n s a r ep rescr ip t i ons (o r ma ndates ) . Cons ider , fo r i n s t ance :

(1) Ka r l , do t he fo l l owing : i f i t r a ins , c l ose t he wi ndow s i f an d o n l yi f t he aw nings a re n o t u p , a nd i f i t ha il s , turn c i rcula tor A on i fand on ly i f c i r cu l a to r B i s o f f.

Ev iden t ly , i n (1 ) t here a re two a tomic p rescr ip t i ons , Kar l c l ose t hew i n d o w s a n d Kar l t u rn c i r cu l a t or A on l i n k ed b y co n n ec t i v e s t o f o u rp ropo s i t i ons , and the w ho le o f (1) is a m and ate hav ing a t i ts co re a mixedcom plex p rescr ip t ion . Th i s i s an ex t r emely im por t a n t po in t . As ide f romthe im pera t i ve p ref ix o f (1 ) 'Kar l , do t he fo l l owing ' , i t i s pa t en t ly c l eartha t t he p rescr ip t i ve c l ause ' i f i t r a ins . .. o f f ' i s, t hough an i nco m ple t es en ten ce , a m i x ed co m p o u n d . P a l p ab l y , t h e co n d i t io n i n g c l au s e s o f (1 )


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454 HECTOR NERI CASTAgTEDAn e e d n o t e x p r e s s st a t e s o f t h i n g s o r o f t h e w e a t h e r : t h e y m a y e x p r e s sp e r f o r m a n c e s o f K a r l h i m s e l f , e. g .,

( 2) K a r l , d o t h e f o l l o w i n g : i f y o u c o m e l a t e , d o n ' t c l o se t h ew i n d o w s i f a n d o n l y i f y o u -r a i se - t h e- a w n i n g s , b u t do ra i s e t hea w n i n g s i f i t is r a in in g .

H e r e w e s ee b o t h t h e p r o p o s i t i o n Y o u [ K a r l ] r a is e t h e a w n i n g s a n dt h e p r e s c r ip t i o n K a r l r ai se t h e a w n i n g s a s c o n s t i t u e n t s o f t h e s a m em a n d a t e . W e a l s o s ee a g a i n t h a t o r d i n a r y E n g l i s h h a s a w i d e l y a p p l i c a b l em a n d a t e o p e r a t o r t h a t y i el d s a canon ica l no ta t i on f o r t h e e x p r e s s io n o f am a n d a t e a s a n a l y z e d i n t o t h e i m p e r a t iv e o p e r a t o r a n d a p r e s c ri p t i o n :g i v e n a n y c l a u s e C f o r m u l a t i n g a p r e s c r i p t i o n P , w h e r e ' a l ' , ' a2 ' , .. . , ' an 'a r e n a m e s o r t e r m s r e f e r r i n g to t h e a g e n t s r e f e r r e d t o i n C , t h e n t h e s e n -t e n c e ra 1 a2 . . . an d o t h e f o l l o w i n g : C q e x p re s se s a m a n d a t e w h o s e c o r ei s p r e s c r i p t i o n P . F o r e x a m p l e :

(3 ) P a u l , M a r y a n d T e d , d o t h e f o l lo w i n g : i f i t r a in s , P a u l m o wt h e l a w n , a n d T e d p u t t h e s p r i n k le r o n ; a n d i f i t d o e s n o t r a i n ,T e d o p e n t h e w i n d o w s , a n d M a r y p a i n t t h e w i n d o w sills.

2.2. T h e P a r a l l e l i s m B e t w e e n I m p e r a t i v e a n d l n d i c a t i v e L o g i c . P h i l o s o p h e r sh a v e a r g u e d a n d c o n t i n u e t o a r g u e w h e t h e r m a n d a t e s h a v e a l o gi c a t a l l,w h e t h e r t h e y h a v e a t w o - v a l u e d lo g ic , a n d w h e t h e r m a n d a t e s c a n a c t u a l lyb e i n f e r r e d f r o m o t h e r m a n d a t e s . A s f a r a s w e c a n s e e t h e s e d i sp u t e s a r e t oa l a r g e e x t e n t v e r b a l d is p u t e s. T h e f a c t is t h a t m a n d a t e s d o s t a n d t o o t h e rm a n d a t e s a n d p r o p o s i t i o n s i n f o r m a l r e la t io n s h i p s h o l d i n g b e tw e e n ( a n da m o n g ) p r o p o s i t io n s , a n d t h e s t u d y o f m a n d a t e f o r m a l r e la t io n s h i p s is o fg r e a t i m p o r t a n c e f o r t h e p h i l o s o p h y o f e t hi c s a n d o f a c t io n . H o w w e c a llt h e m i s u n i m p o r t a n t . T h u s , f o r c o n v e n i e n c e , w e s h a l l h e r e s i m p l y u s e th ec u s t o m a r y t e r m i n o l o g y o f l o g i c i a n s i n a n e x t e n d e d sense to cove r them a n d a t e a n d p r e s c r i p t i v e r e l a t i o n s h i p s .

N o w , w h e t h e r t h e l og i c o f m a n d a t e s i s t w o - v a l u e d o r n o t i s n o t a p u r e l yv e r b a l is su e . W e m u s t , h o w e v e r , r e m e m b e r t h a t i n t h e c a se o f p r o p o s i t i o n sw e f i n d c a se s w h i c h p r e s e n t tr u t h - v a l u e g a p s a n d t h a t b y s o m e p r o c e d u r e so f r e g i m e n t a t i o n w e d o m a n a g e p r e t t y w e ll w i t h a t w o - v a l u e d p ro p o s i -t i o n a l l o g ic . L i k e w i s e , t h e m e r e a p p e a r a n c e o f c e r t a in t o u g h c a s e s o fm a n d a t e s a n d p r e s c r ip t io n s i s n o t a p r o o f t h a t a p a r a ll e l tw o - v a l u e dt h e o r y o f p r es c ri p ti v e i m p l i c a ti o n s w o n ' t w o r k w e l l e n o u g h . B u t a s id ef r o m m e r e l y d e f en s iv e m o v e s , w e c a n m a r s h a l l a n i m p r e s si v e m a s s o f


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ON THE SEMAN TICS OF THE OUGHT TO DO 55

ev i d en ce t h a t s u p p o r t s t h e c l a im o f p a ra ll e li s m b e t ween p ro p o s i t i o n a l an dprescr ip t iona l log ic . T o s ta r t wi th , in fe rences o f the fo l low ing fo rm sa p p e a r s o u n d :

(F1 ) X , d o ATh ere fo re , X , d o n ' t f a il to d o A .

(F2) X, do n ' t fa i l to do AHen ce , X , d o A .

Th e v a l id i ty o f (F1 ) an d (F2 ) am o u n t s t o t h e r e j ec ti o n o f t h ree v a l u es fo rm an d a t e s ; c l ea rl y 'A ' c an r ep re s en t an y ac ti o n wh a t ev e r s im p l e o r co m p l ex .M o re ev i d en ce fo r t h e p a ra ll e li s m b e t ween p ro p o s i ti o n a l a n d p re s c ri p -t i o n a l lo g i c co m es f ro m t h e f ac t t h a t t h e fo l l owi n g i m p l ica t i o n s ch em a t as eem t o h o l d :

(F3) 'X, do A ' impl ies 'X, do A and do A '(F4 ) 'X , d o A an d B ' i m p l ie s ' 2 , d o A '(F5 ) 'X , d o n ' t b o t h d o A an d fa i l t o d o B ' i m p li e s 'X , d o n ' t d o b o t h

o f th e fo l l o wi n g : o n e , f a il to d o B an d s o m e ac t i o n C ; t wo ,d o C an d A . '

(F6 ) 'X , d o A ' an d 'X , d o n ' t d o b o t h : A an d n o t -B ' i m p l y 'X , d o B . 'Fu r t h e rm o re , t h e fo l l o wi n g co n n ec t i o n b e t ween s ch em a t a is a l s o ap p a ren t :

(F7) I f 'X , do A ' impl ies 'X, do B ' , then the co r resp ond ing p re-s c r ip t io n o f th e fo rm 'X , d o n ' t d o b o t h A a n d n o t -B ' isnece ssari ly ( logical ly) 'b ind ing ' on X .

(F1 ) - (F6 ) co n s t i tu t e s t ro n g ev i d en ce o f t h e p a ra l l e li s m b e t w een i m p e ra t i v ean d i n d ica t iv e l o g ic fo r t h e rea s o n t h a t (F3 ) - (F5 ) co r r e s p o n d t o t h e ax i o m sof , and (F6) to the ru le o f in ference o f , a c lass ica l tw o-va lued sys tem ofp ro p o s i t io n a l l o g ic p u t fo rwa rd b y J . B a rk l ey R o s se rS :

A1 p = (p p )i .e ., , - , (p , ,~(p p) )

A2 (p q ) = pi.e ., ,-~ (( p q) ,-,/7)

A 3 ~ ( p ~ q ) = ~ ( ~ ( q r ) ~ ~ ( r p ) )i.e., , , , ( , . , ( p , , , q ) ,,~ , ,~ ( , , ~ ( q r ) ,,~ ~ ( r p ) ) )M o d u s p o n e n s : f r o m p a n d ~ ( p N q ) i n fe r q .

Th e d i ff e ren ces b e t ween t h e se ax i o m s an d (F3 ) - (F5 ) a r e : ( i) t h a t ax i o m s


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456 HECTOR NERI CASTAI~IEDA( A I - A 3 ) a r e w f f s o f R o s s e r s s y s t em an d b e l o n g t o t h e o b j ec t l an gu ag e ,whereas (F3) - (F5) a re t he co r respond ing meta- l i ngu i s t i c s t a t emen t s , sotha t we shou ld con s ider t he ob j ec t -l ingu i s t ic coun terpar t s o f (F3) - (F 5) i n -s t ead o f t hese ; ( i i) t ha t t he dou b le nega t ions o f A3 are m i ssing i n (F5) . Bu tschem a (F7) e rases d i ff e rence ( i) by ma pp ing an im pl i ca t ion i n to a va l i dp rescr ip ti on . L ikewise i f we a l low the s ubs t i t u t i on o f t he equ iva l en t s es t ab -l ished by (F1) and (F2) , w e have , then , t he e rasu re o f d i f fe rence ( ii ). Hen ce(F1 ) - (F7 ) g ive us a sys t em v i rt ua l ly i somorp h ic t o R osse r s sys tem. Na tu -ra l ly , th i s i somorp h i sm ho lds on ly fo r t he va lues o f t he var i ab l es X , A ,B , an d C o f ( F 1 ) - ( F 7 ) . S in ce X can rep r e s en t an y s eq uen ce o f ag en tsre fer red t o i n t he a tom ic p rescr ip t ions c ons t i t u t ing A and B , t he r esu l t has a

go od dea l o f genera l it y . Never the l ess , we g ran t t ha t t here is no e f fec t ive w ayo f d e t e rmi n i n g t h e ran g e o f t h e v a ri ab le s A , B , an d C . A l l w e can s ay i st ha t t he va l i d i t y o f schem ata (F1 ) - (F7) does es t ab li sh tha t fo r a c lass o fac t io n s t h e l og ic o f man d a t e s is i s o mo r p h i c t o t h e t w o - v a l u ed l o g ic o fp r o p o s i t io n s . W e m u s t , o f co u r se , b e p r ep a r ed t o en co u n t e r i n t h e ca s e o fma n d a t e s p r o b l em s an a l o g o u s t o t h e t r u t h - v a lu e g ap s w e l l -s t ud i ed i n t h ecas e o f p r o p o s i ti o n s . B u t w e mu s t a l so b e r ead y t o m ee t t h o s e p ro b l em sw i t h a l l t h e w eap o n s a l r ead y av a i l ab l e i n t h e p r o p o s i t i o n a l a r mo r y - a swel l as wi th new ones t h a t i nves t iga t i on m ay de liver.

I n s h o r t , w e h av e ex ce l l en t s u p p o r t f o r a t w o - v a l u ed t r ea t men t o fimpera t i ves , and i t i s o f ph i losoph ica l im por t an ce t o deve lop the two-va lued po in t o f v i ew in de t a i l. Th i s i s so , even i f me re ly t o d i scover t heprec i se j unc tu res a t wh ich i t r ea l ly b reaks d ow n.2.3. D e o n t i c S t a t e m e n t s . O n e o f th e m o s t s t r ik i ng t h in g s a b o u t t h e O u g h t -to -do i s , as we po in t ed ou t i n Sec t ion 1 , t he f ac t t ha t de on t i c s t a t emen t sare i n timate ly l i nked to impera t i ves . To beg in wi th , wh atever is man date d( i . e . , commanded , o rdered , r eques t ed , e t c . ) i s sa id t o be ob l iga to ry , fo r -b idden , w rong , permiss ib l e , e tc . Fo r i n s t ance , t he im pera t i ve sen t ence (1 )ab o v e n a t u r a ll y y i e ld s d eo n t ic s en ten ces b y t w o g r amm at ica l t r an s f o r ma-t i ons : ( a ) r ep l ace t he impera t i ve m oo d an d p u t i n it s p l ace t he sub junc t ivep r e s c ri p ti o n a l f o r m , b y d r o p p i n g t h e co m m a b e f o r e th e m a i n v e r b ; ( b )p refix t o t he r esu l t a d eon t i c p refix , fo r e xam ple :

l d ) I t i s perm i t t ed t ha t Ka r l d o t he fo l l owing : i f i t ra ins , c lose thew i n d o w s i f and on ly i f t he aw nings a re n o t up , a nd i f i t ha i ls ,turn c i rcu la tor A on i f and only i f c i rculator B i s of f .


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O THE SEMANTI CS OF THE OUGHT TO DO 4 5 7P h e n o m e n o l o g i c a l t y , t h e s t r u c t u r a l c o n n e c t i o n r e v e a l e d h e r e i s t h i s :

D . I . D e o n t i c o p e r a t o r s o f t h e O u g h t - t o - d o t y p e ( o f c o u r se , n o tp e r h a p s t h o s e o f th e O u g h t - to - b e t y p e ) ar e o p e r a t o r s o np r e s c r i p t i o n s .

F u r t h e r m o r e , t h e p r e s c ri p ti o n s i n t h e r a n g e o f a d e o n t i c o p e r a t o r c a n b ea t o m i c o r c o m p o u n d , a s i n t h e c a se o f ( l d ) . N o w , i t s e em s t h a t d e o n t i cs t a t e m e n t s o f t h e O u g h t - t o - d o t y p e a r e t h e m s e lv e s n o t p r e s c ri p t io n s . T h ev e r b ' O u g h t ' d o e s n o t e v e n h a v e a n i m p e r a t i v e f o r m , a n d e x p r e s s io n s li k e' B e o b li g a t e d to d o A ' o r 'B e f o r b i d d e n t o d o A ' s o u n d n o n s e n s i c al . O fc o u r s e , o n e c a n p e r f o r m a c t i o n s t h a t b r i n g a b o u t o b l i g a ti o n s , s o t h a t i t iss e n se t o a d v i c e o r o r d e r " M a k e i t t h e c a s e t h a t i t is o b l i g a t o r y t h a t J o h na n d M a r y s ta y h o m e a f t e r 6 p . m . " B u t h e r e th e i m p e r a ti v e d o es n o t d e -m a n d t h e p e r f o r m a n c e o f t h e ac t o f be ing ob l iga to ry : t h e r e is n o s u c h a c t ;t h e m a n d a t e d e m a n d s t h e d o i n g o f a n a c t i o n t h a t causes a n o b l i g a t io n t oo b t a i n .

I n d e e d , d e o n t i c st a t e m e n t s a r e s t a t e m e n t s o r p r o p o s i t i o n s .T h u s :

D . 2. D e o n t i c o p e r a t o r s o f t h e O u g h t - t o - d o t y p e y i e ld p r o p o s i t i o n so r s t a t e m e n t s .

A n i m m e d i a t e c o n s e q u e n c e o f D . I a n d D . 2 i sD . 3 . D e o n t i c o p e r a t o r s o f t h e O u g h t - t o - d o t y p e a r e n o t i te r a ti v e .

T h i s c o n s e q u e n c e p r o v i d e s a p a r t i a l c o n f i r m a t i o n o f D . 1 a n d D . 2 s in c ei t e r a t i o n s o f d e o n t i c p r e f i x e s a r e : e i t h e r ( i) n o n s e n s i c a l , o r ( ii ) s t u t t e r i n gr e p e t i t i o n s , o r ( i i i ) t h e i t e r a t e d p r e f i x e s a r e n o t m e a n t i n t h e s a m e s e n s e ,a s ' I t i s o b l i g a t o r y t h a t i t i s o b l i g a t o r y t h a t e v e r y b o d y p a y h i s i n c o m e t a x 'c l e a r l y s h o w s , n

D . 3 d o e s n o t , h o w e v e r , p r e c l u d e a d e o n t i c o p e r a t o r f r o m a p p l y i n g t o ap r e s c r i p t i o n h a v i n g a d e o n t i c s t a t e m e n t a s a c o n s t i t u e n t a s i n " I t i so b l i g a t o r y th a t P a u d o t h e f o l lo w i n g : d o A , i f i t is o b l i g a t o r y t h a t h e d o A . "2 .4 . Overriding O ugh t and Pr im a Fac ie O ugh t s I t is a c o m m o n p l a c e t h a tt h e r e a r e m a n y t y p e s o f d e o n t i c s t a te m e n t s , t h a t t h e r e a r e c o n f li c ts o fd u t ie s , s o t h a t w h a t w e o u g h t t o d o e v e r y t h i n g b e i n g c o n s i d e r e d is n o tw h a t w e o u g h t t o d o g i v e n c e rt a i n c o n s i d e ra t i o n s . 7 T h u s , w h a t w e a d v i ses o m e b o d y t o d o i s n o t a n a c t i o n th a t w e b el ie v e h e o u g h t t o d o , b u t o n e


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458 HECTOR NERI CASTAI~IEDAt ha t we be l i eve he o ugh t t o d o a bov e else, every th ing be ing cons idered .That i s ,

D .4 . W h i le t h e o v e r r id i n g o u g h t i n X o u g h t t o d o A m ay b e s a idt o imp l y o r f u ll y s u p p o r t th e imp e r a t i v e X , d o A , t h e p r i ma-fac i e ough t s i n conf l i c t do no t imply o r fu l l y suppor t t he i rco r respond ing impera t i ve .

N o w , w h a t ev e r t h e co n s id e r a t io n s m ay b e w h i ch d e te r mi n e o b l i g a ti o n s , iti s pheno me no log ica l l y c l ear t ha t t hose cons idera t i ons , by de t e rmin ing a se to f d eo n t i c s ta t emen t s o f t h e f o r m I t i s o b l i g a t o r y t h a t A , d e t e r mi n e a l s oa se t o f p rescr ip ti ons , na me ly , t he va lues o f 'A ' i n t ha t fo rm . Likewise ,t hey a l so de t e rmine a se t o f m andates , t o wi t , t hose which have t hepreced ing p rescr ip t i ons a t t he i r co re . Thus , fo rmal ly we can r ep resen t ase t o f deon t i ca ll y r e l evan t cons idera t i ons by t he se t o f p rescr ip t ions t heydet ermine . Form al ly , w e sha l l i den t i fy d i f fe ren t se ts o f cons idera t i ons i ft hey necessar i l y de t e rmine t he sa m e se t o f p rescr ip t ions .2.5. Ought to do and Can. Philosophers continue to debate whether Oughtimpl i es Ca n o r no t . The t ru th o f t he mat t e r seem s to be t ha t t here a res ev e ra l u s e s o f th e d eo n t ic w o r d s i n s o m e o f w h i ch O u g h t d o es , an d i no ther s O ugh t does no t , imply Can , espec i a ll y wh en the Ca n in ques t i on isn o t a l o g ica l C an . H e r e w e ch o o s e t o b e co n ce r n ed j u s t w i t h t h o s e d eo n t i cs t a temen t s o f t h e O u g h t - t o - d o s u b t y p e t h a t i mp l y C an . I n p a r ti cu la r , w ea d o p t :

D .5 . I t i s ob l iga to ry t ha t X do A impl i es t ha t t he p rescr ip t i onX to do A i s cons i s t en t.

D .5 . is a na tu ra l e luc ida t ion o f t he i dea tha t O ugh t impl i es Can , wh ichis o f t en pu t t hus : I t is ob l iga to ry t ha t X do A impl ies i t is poss ib l e fo rX t o d o A .

Th ere i s one case that deserves Special analysis . W e all agree that I t i so b l i g a t o r y th a t ev e r y b o d y w h o h as a w i fe b ri n g h e r t o t h e m ee t i n gi mp li es n e i th e r Ev e r y b o d y h as a w i f e n o r S o m eo n e h as a w i f e . B u tcons ider

(4) I t i s ob l iga to ry t ha t som eone (o r o ther ) w ho has a wi fe b r ingher t o t he meet ing .

D oe s (4 ) imply (The re i s) someo ne [ in t he un iver se o f agen t s in ques t i on ]


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ON THE SEMANTICS OF THE OUG HT TO DO 59

( w h o ) h a s a w i f e ? T h e a n s w e r s r u n i n b o t h d i r ec t io n s . A n d , a g a i n , t h et r u t h o f t h e m a t t e r i s t h a t t h e d e o n t i c w o r d s h a v e m a n y d i f f e r e n t s e ns e so r u s e s , s o t h a t f o r s o m e s t a t e m e n t s e x p r e s s e d w i t h t h e s e n t e n c e ( 4 ) t h ei m p l i c a t i o n h o l d s , a n d f o r o t h e r s i t d o e s n o t . H o w e v e r , w e c a n p r o v i d e ac r i t e r i o n f o r d i s t i n g u i s h i n g t w o s u c h s e t s o f s e n s es o r u s e s . I n t h e s e n s eso r u s es i n w h i c h O u g h t i m p l ie s C a n , (4 ) d o e s i m p l y S o m e o n e h a s a w i f e ,f o r i f n o b o d y a m o n g t h e a g e n t s i n q u e s t i o n h a s a w i f e n o b o d y c a n f u lf il lt h e o b l i g a t i o n e s t a b l i s h e d b y ( 4 ) . N a t u r a l l y , t h e p h i l o s o p h e r s ' j o b i s , i nf a c t , t o e l u c i d a te t h e s t r u c t u r e o f o u r c o n c e p t u a l f r a m e w o r k s w i t h o u tp r e j u d i c e : t h u s , w e m u s t n o t e t h a t

D .6 . F o r s o m e f a m i li e s o f d e o n t i c c o n c e p t s, s t a t e m e n t s o f t h e f o r mI t i s o b l i g a t o r y t h a t p a n d A , i m p l y t h e c o r r e s p o n d i n g

s t a t e m e n t t h a t p , w h e r e ' p ' s t a n d s f o r a p r o p o s i t i o n a n d ' A 'f o r a p r e s c r i p t i o n .

2.6. The Good-Samaritan Paradox'. s I t i s n o r m a l l y h e l d t h a t a p r i n c i p l el ik e t h e f o l l o w i n g g o v e r n s d e o n t i c s t a t e m e n t s :

( P ) I f X ' s d o i n g A i m p l ie s Y ' s d o i n g B , t h e n( 1) t h a t i t is o b l i g a t o r y , f o r X t o d o A i m p l i es t h a t i t is

o b l ig a t o ry ~ f o r Y t o d o B , a n d( 2) t h a t i t is w r o n g , f o r Y t o d o B i m p l i e s t h a t i t is w r o n g l f o r

X t o d o A .N o w , i n a s t a n d a r d a p p r o a c h t o d e o n t i c lo g i c t h a t a l l o w s m i x t u r e s o fd e o n t i c a n d n o n - d e o n t i c s ta t e m e n t s , t h e a n t e c e d e n t o f ( P ) i s i n t e r p r e te da s t h e m e t a - s t a t e m e n t t h a t ' X d o e s ( p e r fo r m ) A i m p l ie s Y d o e s ( p er -f o r m ) B . A n d t h is h a s g i v en ri se t o t h e s o -c a ll ed g o o d - s a m a r i t a n p a r a d o x .C o n s i d e r t h e c a se o f A r t h u r , w h o s e d u t y i s t o b a n d a g e a m a n , h i s e m -p l o y e r , w h o m h e w il l k i ll a w e e k h e n c e . S i nc e A r t h u r b a n d a g e s a m a nw h o m h e w il l k i ll a w e e k h e n c e d o e s im p l y 'A r t h u r w i l l k i ll a m a n a w e e kh e n c e , i t i s t a k e n t h a t b y ( P ) i t f o l lo w s t h a t A r t h u r h a s a d u t y t o k i ll am a n . I f t h e r e is a p a r a d o x h e r e , t h e n s o l u t i o n s b a s e d o n d i f fe r e n c e s o fa g e n t s a n d t i m e s a r e b e s i d e t h e m a r k : h e r e A r t h u r i s b o t h t h e b a n d a g e ra n d t h e k il l er , a n d t h e t im e o f t h e k i l li n g i s l a t e r t h a n t h a t o f t h e b a n d a g i n g ,b u t , o b v i o u s l y , it c a n b e e a r l i e r t h a n t h e l a t t e r .

H o w e v e r , i n t h e p r e s e n t c a s e t h e r e i s r e a l l y n o p a r a d o x , e v e n i f ( P ) i si n t e r p r e t e d t o h a v e a n a n t e c e d e n t a b o u t t h e i m p l i c a t i o n b e t w e e n t w o


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460 HECTOR NERI CASTAI~IEDAperformance statements: Keeping scope distinctions suffices to dispel theparadox here. The sentence 'Arthur has a duty to bandage a man he willkill' really means:

(Sa) (3x) (a will kill x & a has a duty to bandage x),and not

(5b) (3x) (a has a duty to bandage x & kill x).Thus, it does not follow from (5a) by (P) (1) that Arthur has a duty to kill,since the part a has a duty to bandage x of (5a) implies nothing aboutkilling.In general, several of the cases that have been proposed as variants ofthe good-samaritan 'paradox' can be analyzed as involving confusions onthe scope of the deontic operators at issue, or of a definite description:but not all. A beautiful case that cannot be analyzed away by scopedistinctions is Aqvist's 'paradox' of the Knower, in Good Samaritans,Contrary-to-Duty Imperatives, and Epistemic Obligations , pages 366ff. sConsider the case of a man, say Jones, whose job is to know what is donewrong by other people in a certain office. Suppose that Smith did A, whichis wrong by the rules of the office. Thus, It is wrongj that Smith do Aand Jones oughtj to know that Smith (does) did A are true. SinceJones knows tha t Smith (does) did A implies Smith (does) did A ,

by (P)( i ) interpreted as we have been doing, we have, then, Smithoughtj to do (have done) A , which contradicts the hypothesis that itis wrongj for Smith to do A. Here the scope distinction does not help.

For one thing, there is apparently no satisfactory analysis of knowledgeso that we can take, in the model of (5a), some conjuncts of the analysisoutside the scope of the deontic operator o u g h t j But suppose that we cananalyze Jones knows that p as p and Jones believes that p and Joneshas evidence for that p . Then the scope analysis patterned after (5a), ofJones oughtj to know that Smith did A yields Smith did A and Jones

ought i to both believe tha t Smith did A and have evidence for this . Butthe fact is that a duty to know is not the same as the duty to believe andhave evidence: surely one can have the latter without having the former.

In general, there are psychological attitudes that one must acquire, orpsychological acts that one must perform that imply that something thathappens to be wrong has occurred. Such cases give rise to troubles for (P).The trouble is compounded in those cases in which there is no purely


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ON THE SE MANTICS OF THE OUGH T TO DO 46

psycho log ica l con ten t , t ha t can be ex t r ac t ed , i n t he way be l i ev ing i s t hep u r e p s y ch o l o g i ca l co r e o f k n o w i n g . F o r i n s tan ce , t h e r e i s n o p u r e l ypsycho log ica l co re t ha t can be r ea l l y ob l iga to ry when one i s , a l l eged lyincor rec t ly , sa id t o be ob l iga t ed t o r epen t , t o l am en t , o r t o apo log ize fo r ,h av i n g d o n e s o m e ac t io n A w h i ch it is w r o n g i to d o .

Aq v i s t ' s p rop ose d so lu t i on cons i s t ed o f d i s ti ngu i sh ing d i f f e ren t t ypes o fd u t i e s . B u t h i s p r o p o s a l w as s h o w n b y Law r en ce P o w er s , i n ' S o meD eo n t i c Lo g i c i an s ', p p . 3 8 4 - 38 8 , n o t t o b e a t a l l ad eq u a te . O f co u r s e , w ed o n o t o b j ec t t o d i s ti n g ui sh i n g t y p es o f d u t ie s : w e h av e d o n e s o in o u rp h en o m en o l o g i ca l e x ami n a t i o n o f co nf li c ts o f du t ie s . B u t w e d o n o t h av et o r e s o r t t o t h is t o s o lv e t h e K n o w er p a r ad o x . I n f ac t , w e h av e a l r ead yf o u n d , i n d ep en d en t l y o f P) , t h a t d eo n t i c o p e r a t o r s ap p l y t o p r e s c r i p -t ions . Thus , we ca n r ecogn ize i n (P ) a p rescr ip ti ve p r inc ip l e , no t a p rop -os i t i ona l one , namely :

D .7 . I f p rescr ip t i on A impl i es p rescr ip t i on B , t hen(1) I t is obl igatory~ tha t A impl ies I t i s obligatory~ that B ,

a n d(2) I t i s wro ng , t ha t B impl i es I t is wro ng , t ha t A .

N ow , D .7 p rov ides an imm edia t e , sharp and un i f ied so lu t i on t o a l lt h e fo r ms o f t h e g o o d - s amar i t an ' p a r ad o x ' . I n A q v i s t 's f o r m w e h av e :

( 6) I t is o b l i g a t o r y j t h a t J o n es k n o w t h a t S mi t h d i d A ,w h i ch co n t a i n s t h e p r e s c r ip t i o n J o n es k n o w t h a t S mi t h d i d A . Th i sp r e s c r ip t i o n i mp l ie s n e i th e r th e p r o p o s i t io n J o n es k n o w s t h a t S m i th d i dA n o r th e p r e s c r ip t io n J o n es d o A . H en ce , f r o m (6 ) b y D .7 w e can n o tder ive t ha t i t i s ob l iga to ry j [o r wrong ] fo r S mi th t o do (have done) A.Th u s , w e may p r o p e r l y an d co n s i s t en t l y accep t t h a t t h e s y s t em o f r u l e sgovern ing the t asks o f a l l t he peo p le i n Jone s ' o ff ice , i nc lud ing Jon es , a redu t i es in exac t ly t he sam e sense , and eve n o f t he sam e type .3. A Basic Language fo r the Ought-To-Do.W e p as s n o w t o d e s c r i b e t h e s y n t ac t i ca l s t r u c t u r e o f a p u r e d eo n t i cl an g u ag e f o r t h e O u g h t - t o - d o . A c t u a l l y w e s t a r t b y co n s t r u c t i n g a l a r g enum ber o f such syn tac t i ca l s t ruc tu res , one fo r each p r ima fac i e ob l iga-to r iness and one fo r t he over r id ing ough t . These l anguages wi l l be ca l l edDi . , fo r i = 1 , 2 , 3 . . . , wh ere D~. i s t he l anguage o f t he pure over r id ingo u g h t . W e s h a ll c a ll th e u n i o n o f th e s e lan g u ag es D * .


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4 6 2 HECTOR NERI CASTAI~EDAP r i m i t i v e s i g n s : i n d i v i d u a l c o n s t a n t s ; i n d i v i d u a l v a r i a b l e s , p r e d i c a t ec o n s t a n t s ; t h e c o n n e c t i v e s ', -~ ' a n d ' & ' ; t h e u n d e r l y i n g s ig n ' _ ' t o i n d i -

c a t e p r e s c r i p t i v i t y ; t h e s i g n 'O i ' o f o u g h tn e s s ~ o r o b l i g a t o r i n e s s i , a n d' ( ' a n d ' ) ' .

R u l e s o f f o r m a t i o n : W e u s e Q u i n e ' s c o r n e r s i m p l i ci tl y t h r o u g h o u t . L e tt h e s m a l l l e t te r s ' p ' , ' q ' , ' r ' , r a n g e o v e r in d i c a t i v e s (i .e ., e x p r e s s i o n s o fp r o p o s i t i o n s o r p r o p o s i t i o n a l f u n c t i o n s ) ; l e t t h e c a p i t a l l e t te r s 'A ' , ' B ' , ' C 'r a n g e o v e r p r e s c r i p t iv e s ( i. e. , e x p r e s s i o n s o f p r e s c r i p t i o n s o r p r e s c r i p -t i o n a l f u n c t i o n s ); l e t ' p * ' a n d ' q * ' r a n g e o v e r b o t h i n d i c at i v e s a n d p r e -s c r i p t iv e s ; l e t ' Z ' r a n g e o v e r p r e d i c a t e s a n d ' x ' o v e r i n d i v i d u a l v a r i a b l e s ,u n l e s s o t h e r w i s e s p e c i f i e d .

( a ) I n d i c a t i v e s a r e s e q u e n c e s h a v i n g o n e o f t h e f o r m :(1) Z ( x i . . . . x ~ . . . . . x . ) , w h e r e Z i s an . n - a d i c p r e d i c a t e a n d e a c h

x ~ i s a n i n d i v i d u a l c o n s t a n t o r v a r i a b l e , a n d n o x i is u n d e r l i n e d ;( 2 ) ( ~ p ) ;( 3 ) ( p & q ) ;( 4 ) ( x ) p ;(5) O A;( b ) P r e s c r i p t i v e s a r e s e q u e n c e s o f si g ns h a v i n g o n e o f t h e f o ll o w i n g f o r m s :(1 ) Z ( x l , . .. , x i , . . . , x . ) , w h e r e Z i s a n n - a d i c p r e d i c a t e , e a c h x , i f

a n i n d i v i d u a l v a r i a b l e o r c o n s t a n t , a n d a t l e a s t o n e x ~ i su n d e r l i n e d ( t o i n d i c a t e t h e a g e n c y o f x ~ );

(2 ) ( - .~A) ;( 3) ( p a ) ;( 4 ) ( A & p ) ;(5) (x ) A .T h e i n d i c a t i v e s a n d t h e p r e s c r i p t i v e s a r e a l l t h e w f f s o f O ~ . . W e w r i t e' A x ' a n d ' A x ' , i n th e c a s e o f a m o n a d i c p r e d i c a t e , f o r ' A ( x )' a n d ' A ~ ) ' ,

r e s pe c t iv e l y . W e a d o p t t h e c u s t o m a r y c o n v e n t i o n s o n p a r e n t h e s e s a n du s u a l d e fi n it io n s o f ' v ', ' = ' , a n d ' = ' .

W e i n t r o d u c e t h e o t h e r d e o n t i c t e rm s b y m e a n s o f t h e f o l lo w i n g d e fi n i-t i o n s :

D D 1 .D D 2 .D D 3 .

R ~ A = ..~ O i . . ~ A ( I t i s r i g h t s t h a t A )W i A = O i . . . A ( I t i s w r o n g i t h a t A )F i A = ~ O i A ~ O i ~ A ( I t i s c o m p l e t e l y f r e e o r o p t i o n a lt h a t A )


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ON THE SEMANTICS OF THE OUGHT TO DO 463W e can a l r eady see t ha t each D 7 sat is fies som e o f t he p ro to -p h i lo -soph ica l d a t a o f S ec t ion 2 abov e: ( i) t he d i f f e rence be tw een an a tomic

prescr ip t ive and i t s corresponding indicat ive l ies in the copula; ( i i ) theprescr ip t i ve copu la ass igns t o some s ingu lar express ions t he ro l e o f ex -p ress ing agency ; ( i i i ) mixed ind i ca t i ve-p rescr ip t i ve compounds a re im-pera t i ve ; ( i v ) deon t i c opera to r s map p rescr ip t i ves i n to i nd i ca t i ves ; (v )there a re no i t e ra t i ons o f deon t i c opera to r s .

W e s h a l l c al l t h e n o n - q u an t if i ed s u b s y s t em o f D * an d o f each D,,,D c* an d D~* resp ect ively ; i .e ., D~* i s D~, w i tho ut the ru les o f fo rm at io n(a) (4) an d (b) (5), an d sim ilarly fo r D ~*.4. The Axiomatic Systems 0 ~,O u r n o n - s t an d a r d ap p r o ach h as s o f a r b een ma i n ly s y n tac t ica l, i t s l a te s tr ep rese n t a t i on s cons i s t s o f t he ex t ens ion o f each syn tac t ica l s t ruc tu reD~, t o an ax iom at i c sys t em O~,, by a d junc t ion o f t he fo ll owing ax ioms andru l es o f i n ference .

A x i o m s : as ide f rom the ax iom s fo r quan t i f ica t i on , a l l wiTs hav ing a t/ e a s t o n e o f t h e f o l lo w i n g f o r ms a r e ax i o ms :

p * , i f p * h a s t h e f o r m o f a t r u th - t ab l e t au t o l o g y .1.02a. O iA ~ ,-.O~,,,A02b . 0 1 A ~ A03. (O~A OiB ) ~ Oi (A B )04. (p O~A) ~ O~ (p A)

Rules of inference:M . P . ( m o d u s p o n e n s ) :

N o te : t he over r id ing ough tt ak es a s ax i o m s ch ema 0 2 bins t ead o f 02a , wh i l e t he p r i -ma fac i e ough t s t ake 02a i n -s t ead o f 0 2 b ; a l l o th e r ax i o mschemata ho ld fo r a l l Ough t s -to -do tha t imply Can , as d i s -cussed in Sect ion 2 .5 .

I f k i p * an d k i p * ~ q * , t h en k i q * .D R 1 . I f ~ -c iA = B , t h en I - iOiA ~ O~B.D R 2 . I f b c i p D A , t h e n l -~p ~ OiA .U G . I f b ~p* , b ~ x)p* .W e ad op t t he usua l def in i ti ons o f ' p ro of ' , ' t heo rem ' , e t c . as wel l as the

cu s t o m ar y co n v e n t i o n s o n b r ack e t s . H e r e q - ~ p * ' mean s t h a t p * i s a t h eo -rem of t he ca l cu lus O ~,. The non-quan t i f ied pa r t o f O i , wi ll be ca l l ed


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4 6 4 HECTOR-NERI CASTA ~EDA0 7 * ; m o r e p r e c is e ly , O 7 i s O ~ , w i t h o u t t h e a x i o m s o f q u a n t i f i c a ti o n a n dw i t h o u t r u l e s U G , ( a ) ( 4 ) a n d (b ) ( 4 ). W e s h a l l w r i t e ' * '~ c p t o m e a n t h a tp * i s a t h e o r e m o f 0 7 * .

T h e p r e c e d i n g a x i o m a t i z a t io n o f p r o p o s i t i o n a l d e o n t i c l o g i c i s c o n -s i st e n t a n d a d m i t s o f d e c is i o n p r o c e d u r e s , e . g ., a t r a n s li t e ra t i o n o f Q u i n e ' sp r o c e d u r e f o r u n i f o r m q u a n t i f ic a t i o n c u m p r o p o s i t i o n a l v a r i ab l e s . 1 I ta d e q u a t e l y r e p r e s e n t s t h e f o l l o w i n g p r i n c i p l e s .

T h l . ] - icO~(A B ) ~ O~A OiBT h 2 . [ - ~ O i ( p & A ) ~ p O ~ AM T . 1 . I f a p r e s c r ip t i v e A x i s l o g i c a ll y v a l id , t h e n t h e c o r r e s p o n d i n gA x i s l og i c a l l y va l i d .M T . 2 . ,-~ O ~ ( A x & ~ A x ) i s l o g i c a l l y v a l i d .M T . 3 . N e i t h e r O~ ( Ax ) n o r , ,~Oi(Ax_) e n t a i l s t h e i n d i c a t i v e A x .M T . 4 . N e i t h e r O i ( A x ) n o r ~ Oi ( Ax _) e n t a i l s t h e i n d i c a t i v e ~ A x .

5. M odels fo r the System s Di, .A s i n S e c t i o n 3 w e c o n t i n u e t o r e f e r : ( i) to a r b i t r a r y w f f s o f D ~ ,, w h e t h e ri n d i c a t i v e o r p r e s c r i p t i v e w i t h th e a s t e r i s k e d le t t e rs ' p * ' , ' q * ' , a n d ' r * ' ; ( ii )t o a r b i t r a r y i n d i c a ti v e s o f D ~ , w i t h t h e p l a i n l e t te r s ' p ' , ' q ' a n d ' r ' , a n d( iii) t o a r b i t r a r y p r e s c r i p t i v e s o f D ~ . w i t h t h e c a p i t a l l e tt e r s 'A ' , ' B ' , a n d ' C ' .~. .5 .1 . O ~ . A m o d e l M f o r a sy s t e m D i i s a n o r d e r t r ip l e < W o , P c ' , / > , w h e r e____W s a n o n em p ty se t o f en t i t i e s ca l l e d possible deontic worlds, o r j u s tw o r l d s , f o r s h o r t, W o is a m e m b er of___.Wa n d i s c a l l e d t h e real o r designatedworld, a n d / is a t w o - a r g u m e n t f u n c t i o n t h a t a s s ig n s t o e a c h p a i r o f aw o r l d a n d a w f f o f D~* j u s t o n e e l e m e n t o f t h e s e t { 1 , 2 } , i n a c c o r d a n c e w i t ht h e f o l l o w i n g r u l e s , w h e r e W j a n d W h a r e m e m b e r s o f __W .

R 1 . / ( p * , W ~ )= 1 o r 2 , i f p * i s a t o m i c , i .e ., p * i s a w f f o f Di. b yf o r m a t i o n r u l e ( a ) ( 1 ) o r ( b ) ( 1 ) .R 2 . / ( ~ p * , W j ) = I , i f a n d o n l y i f / ( p * , W ~ ) = 2 ; o t h er w i se

~a ~_ e , w j = 2 .R 3 . I ( ( p * & q * ) , W j) = 1 , i f a n d o n l y i f b o t h _ ./( p* , W j ) = 1 a n dI_(q*, W j)= 1 ; o t h e r w i s e , f ( (p* q*) , W j)=2.R 4 . I f t h e r e i s a w o r l d W j s u c h t h a t I ( p , W j )= 1 , t h e n f o r e v e r y

w o r l d Wh: l_ (p, W h)= 1.R 5 a . l ( O i A , W o ) = 1 , i f a n d o n l y i f f o r e v e r y w o r l d W j in _ _ W d if fe re nt

f r o m W o : I (A , Wj) = 1.


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ON THE SEMANTI CS OF THE OUGHT TO DO 465R 5 b . l _ . OiA ,W o ) = l , i f a n d o n l y i f f o r e v er y w o r l d W j i n W :w j = 1.W e d e f i n e : p* is valid in D~*, ~ ic P* , i f a n d o n l y i f f o r e v e ry m o d e lM , I p * , Wo) = 1, fo r / an d Wo in M . A nd p* h a s a m o d e l i f a n d o n l y i f

f o r s o m e m o d e l M , I p * , W o)= 1 , fo r _ /, an d Wo i n M .I t i s a s i m p l e t h i n g t o s h o w t h a tM T 1 . I f k i c p * , t h e n ~ ~ cP *.

A n d t h e p r o o f o f t h e f o l l o w i n g p r o c e e d s a l o n g t h e l i n es o f a ll p r o o f s o fH e n k i n c o m p l e t e n e s s :M T 2 . I f p * i s c o n s i s t en t , p * h a s a m o d e l .Ou tline o f proof. B y s t a n d a r d p r o c e d u r e s i t c a n b e s h o w n t h a t t h e s e t o f

w f f s o f D~* i s d e n u m e r a b l e a n d t h a t e v e r y c o n s i s t e n t s e t c a n b e e x t e n d e dt o a m a x i m a l c o n s i s t e n t s et . T a k e a n y m a x i m a l c o n s i s te n t s e t o f w i t s o fD~.* th a t i nc lude s p* , an d ca l l i t Wo. T ak e a s __W he se t o f m ax im a l co n-s i s t e n t s e ts W j g e n e r a t e d f r o m W o a s f o l l o w s : e v e r y i n d i c a ti v e p o f Wo isi n W j , a n d f o r e v e r y i n d i c a ti v e o f t h e f o r m OiA in Wo, A is in Wj; in thel a t t e r c a s e A i s a l s o i n W o i f w e a r e d e a l i n g w i t h 0 1 A . W e l e t _ / b e t h ef u n c t i o n I s u c h t h a t : i) I p* , W j ) = 1 i f a n d o n l y i f p * b e l o n g s t o W j , a n dii) I p*, Wj)=2 i f a n d o n l y i f p * d o e s n o t b e l o n g t o W j. I t is c l e ar f r o m

t h e c o n s t r u c t i o n t h a t < W o , __W, / > i s a m o d e l f o r p * .W e h a v e , t h e re f o re , f r o m M T 1 a n d M T 2 , b y s t a n d a r d r e a s o n i n g , t h a t :M T3 . t- ,c p* , i f an d o n ly i f ~ ic P* .

5 . 2 . O i , . T h e m o d e l s f o r t h e f u l l s y s t e m s O i , a r e o r d e r e d q u i n t u p l e s< W 0, __W,D, ~ , _ . /) , wh e re Wo an d __W a re a s ab ove , D i s a do m a in o f ob -j e c t s , ~p a f u n c t i o n a s s i g n i n g s u b s e ts o f D t o t h e w o r l d s i n W , a n d / i s a sb e f o r e e x c e p t f o r c o n d i t i o n s a s s i g n i n g I o r 2 t o q u a n t i f i e d f o r m u l a s . H e r ew e i n t r o d u c e i n p r i n c ip l e a l l t h e p r o b l e m s o f e x is te n c e a n d m o d a l i t y ;b u t i t i s w o r t h e m p h a s i z i n g t h a t t h o s e p r o b l e m s p r e s e n t n o p e c u l i a ra s p e c t f o r d e o n t i c lo g i c. I n f a c t , t h e y a r e s o m e w h a t l es s p r e s s in g . C l e a r l y ,i n m o d a l p r o p o s i t i o n a l l o g i c i t is o f g re a t i m p o r t a n c e n o t t o a s s u m e t h a tt h e o b j e c ts i n t h e u n i v e r s e a r e n e c e s s a r i l y f i x e d o n c e a n d f o r a l l , i .e . ,r e g a rd l e ss o f t h e o b j e ct s i t h a s w e m u s t a l l o w t h a t t h e u n i v e r s e m a y h a v eh a d m o r e , o r f e w e r , o b j e c ts . O n t h e o t h e r h a n d , f o r p u r e d e o n t i c lo g i c w e


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4 6 6 HECTOR NERI CASTANEDAm a y a s s u m e w i t h o u t d a m a g e t h a t t h e a g e n ts a n d o b j e c t s a r e c o n s t a n t - i fw e a r e d e a l i n g w i t h a s y s t e m o f d u t ie s a n d i n t e r d i c t i o n s a t a g i v e n t im e .T h u s , t h e r e is n o g r e a t d i s t o r t io n e v e n i f w e a d o p t d e o n t i c s y st e m s t h a tc o n t a i n t h e B a r c a n f o r m u l a a n d i t s c o n v e r s e a s t h e o r e m s .

F u r t h e r m o r e , d e o n t i c c o n t e x t s a r e w h o l l y n o t r e f e r e n t ia l ly o p a q u e i nQ u i n e ' s s e n se , o r t h e y a r e n e a r l y s o . I t is p a l p a b l y c l e a r t h a t i f a = b a n d xo u g h t i t o d o t o a s o m e a c t i o n A ( t h a t i n v o l v e s n o r e f e r e n t i a l o p a c i t y ) ,t h e n x o u g h t o d o A t o b . A n d t h i s i s, o f c o u r s e , a s i t s h o u l d b e. D i f f e r e n tp r o p e r t i e s o f o b j e c t s o r p e r s o n s m a y , c e r t a i n l y , y ie l d d if f e r e n t p r i m a f a c i ed u t i e s t h a t c o n f l ic t . B u t s i n ce e a c h p r i m a f a c i e d u t y i s re l a t iv e t o a g r o u n d ,o t h e r c o n s i d e r a t i o n s a r e i r r e l e v a n t t o it . I n t h e c a s e o f th e o v e r r i d i n go u g h t w e a r e , s o t o s p e a k , f a c e t o f a c e w i t h b r u t e f a c t s a n d e v e n t s , a f t e rt h e c a n c e l l a ti o n o f a ll i n t e n t io n a l a n d i n t e n s io n a l c o n s i d e r a t io n s , a n d o n e ' sd u t y i s s im p l y t o a l t e r a p o s s i b l e t r a i n o f e v e n t s, r e g a r d l e s s o f h o w t h e s ea r e n o w c o n s i d e r e d o r r e f e r r e d t o .

S i n c e w e a r e p r i m a r i l y i n te r e s t e d in p r e s e n t i n g a s e m a n t i c a l f o u n d a t i o nf o r o u r n o n - s t a n d a r d a p p r o a c h t o d e o n t i c lo g ic , w e n e e d n o t g o i n t o t h es t a n d a r d p r o b l e m s o f q u a n t i f i c a ti o n a n d m o d a l i t y .

W e m u s t n o t e , h o w e v e r , t h a t o u r n o n - s t a n d a r d m o d e l s f o r o u r n o n -s t a n d a r d a x i o m s y s te m d o s a ti s fy th e p r o t o - p h i l o s o p h i c a l d a t a g a t h e r e d i nS e c t i o n 2 a b o v e .6 Prescr i p t ive or I m pera t i ve Va l uesI n S e c t i o n 2 .2 w e a r g u e d t h a t p r e s c r i p t i v e ( a n d i m p e r a t i v e ) l o g i c i s t w o -v a l u e d , a n d t h e a r g u m e n t w e g a v e d o e s j u s t i fy o u r a x i o m 0 1. B u t w e s til lo w e a n a c c o u n t o f t h e s e m a n t ic a l v a l u e s o f p r e s c r ip t i o n s . T h e c r u c i a lt h i n g is th e i n t e r p r e t a t i o n o f th e m e m b e r s h i p o f a p r e s c r i p t io n i n a p o s -s ib le d e o n t i c w o r l d W j. (W e a r e , p r e s u m a b l y , q u i t e c l e a r o n w h a t i t m e a n st o s a y t h a t a n i n d i c a t i v e o r a p r o p o s i t i o n b e l o n g s t o a p o s s i b l e w o r l d ) .O u r v i e w is e s se n t i a ll y t h a t a p r e s c r i p t i o n b e l o n g s t o a w o r l d i f it ise n d o r s e d a t l e a s t p a r t i a l l y i n t h a t w o r l d . A n d t h e p r o b l e m i s t o e x p l a i nw h a t e n d o r s e m e n t is . T h i s p r o b l e m , h o w e v e r , is n o t a l o g i c a l p r o b l e m ;i t is th e a n a l o g u e o f th e p r o b l e m o f d e t e r m i n i n g w h a t i s t r u e , w h i c h t a k e sw i d e l y d i f f e r e n t f o r m s i n d i f f e r e n t c a s e s : c r i t e r i a f o r v e r i d i c a l p e r c e p t i o n ,s c ie n t if ic m e t h o d o l o g y , e tc . F o r o u r p r e s e n t p u r p o s e s i t su f fi ce s t h a t w ed i sc u s s t h e m o r e g e n e r a l c h a r a c te r is t ic s o f e n d o r s e m e n t .

N a t u r a l l y , s o m e p r e s c r i p t i o n s a r e e s p e c i a l l y a n d d e l i b e r a t e l y e n d o r s e d .


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ON THE SEMANTI CS OF THE OUGHT TO DO 4 6 7

T h i s i s s o w h e n , f o r i n s t a n c e , w e i s s u e i m p e r a t i v e s t h a t w e i n t e n d t o b ef u l fi ll e d , a s w h e n a t a d i n n e r t a b l e w e r e q u e s t J o h n , p a s s th e s a lt ,p l e a s e ; w e a l s o e n d o r s e p r e s c r i p t i o n s w h e n w e f o r m u l a t e r u le s o r s et s o fD o ' s a n d D o n ' t ' s . W e a l so e n d o r s e t h e p r e s c r ip t i o n s w h i c h a r e e n a c t e d b yt h e r u l e - m a k i n g b o d i e s o f th e i n s t it u t io n s w e b e l o n g . I t m a y b e a l so s a i dt h a t w e e n d o r s e th e p r e s c r i p t io n s w h i c h d e m a n d t h e d o i n g o f a c ti o n st h a t a r e n e c e s s a r y f o r t h e a t t a i n m e n t o f th e g o a l s o r e n d s w e p u r s u e. B u ta l l o f th e s e k i n d s o f e n d o r s e m e n t s a r e s u c h t h a t f o r a g i v e n p r e s c r i p t io n

X d o A w e m a y v e r y w e l l n e i t h e r e n d o r s e i t n o r e n d o r s e i ts d e n i a l Xd o n o t d o A . T h u s , i n o r d e r t o s e c u re a t w o - v a l u e d l og i c o f p r e s c r i p t io n sw e m u s t i n c l u d e a c l o s i n g p r i n c i p l e t h a t p u t s e i t h e r A o r ,-, A t o g e t h e r w i t ht h e e n d o r s e d p r e s c r i p t i o n s . S u c h p r i n c i p l e i s , d o u b t l e s s l y , b e h i n d t h ep h e n o m e n o l o g i c a l a r g u m e n t d e v e l o p e d in S e c t i o n 2 .2 . O u r v i e w is th a tt h e p r i n c i p l e i n q u e s t i o n i s t h i s :

J ) I f n e i t h e r a p r e s c r i p t i o n A n o r i t s d e n i a l ~ A i s e n d o r s e d i n ap o s s ib l e d e o n t i c w o r l d W j, g i v e n al l o f t h e m e t h o d s o f e n -d o r s e m e n t t h a t d e t e r m i n e W j, th e n : A b e lo n g s to W j i f a n do n l y i f A i s f u l fi ll e d , i .e . , t h e p r o p o s i t i o n c o r r e s p o n d i n g t o Ai s t r ue i n Wj ; o t he r w i s e , ~ A be l on gs t o Wj .

7. Alternative Deontic Syatems for the Ought-To-DoS o m e p h i l o s o p h e r s h a v e a r g u e d t h a t d e o n t i c lo g i c d i ff e rs f r o m p r o p o s i -t i o n a l m o d a l l o g i c i n t h a t s o m e o f th e p r i n c ip l e s t h a t h o l d i n t h e l a t te rd o n o t h a v e v a l i d d e o n t i c c o u n t e r p a r t s . F o r i n s t a n c e , m a n y p h i l o s o p h e r so b j e c t t o OiA ~ Oi Avb). O t h e r p h i l o s o p h e r s i n s i s t t h a t t h e r e i s as t r o n g s e n s e o f ' r i g h t ' i n w h i c h t h e r i g h t n e s s o f a n a c t i o n i s n o t i d e n t i c a lw i t h t h e n o n - o b l i g a t o r i n e s s o f th e o m i s s i o n o f t h e a c t i o n .

N o w w e s h a ll n o t e x a m i n e th e s e o r r e l a te d cl ai m s . W e w a n t t o p o i n to u t o n l y t h a t o u r n o n - s t a n d a r d s e m a n ti c al a p p r o a c h t o d e o n t i c lo g ic c a np r o v i d e a f o u n d a t i o n f o r o t h e r s y s t e m s . W e c a n , f o r o n e t h i n g , r e j e c tp r i n c i p le ( J ) a n d h a v e p o s s i b le d e o n t i c w o r l d s i n w h i c h s o m e p r e s c r i p ti o n sa r e m i s s in g t o g e t h e r w i t h t h e i r n e g a t i o n s . W e c a n , f o r a n o t h e r t h i n g , l im i tt h e p r o p o s i t i o n s t h a t b e l o n g t o a l l t h e p o s s i b l e w o r l d s , t h i s p r o v i d i n g ad i s t i n c t i o n b e t w e e n f u n d a m e n t a l l y r e l e v a n t a n d f u n d a m e n t a l l y i r r e l e v a n tc i r c u m s t a n c e s . W e c a n , t h i r d l y , c o n s i d e r d e o n t i c s y s t e m s i n w h i c h t h ew o r l d s i n W a r e n o t o n e q u a l f o o t in g , b u t r e l a t e d b y w e a k e r r e la t io n s . I n


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468 HECTOR-NERI CASTA/~IEDAs h o rt o u r n o n - s t an d a r d ap p r o a ch t o d eo n t i c lo g ic i s am en ab l e t o d ev e l o p -m en t b y mean s o f t h e f e rt il e me t h o d s d i s co v e red b y H i n t i k k a K an g e rK r i p k e an d M o n t ag u e . A n d o n ce ag a in o u r p h i lo s o p h i ca l u n d e r s t an d in gi s bound to g row by the con templa t ion o f severa l a l t e rna t ives i n fu l ldep loym ent . T h i s is par t icu l a r ly so in v i ew o f an in it ia l ad equ acy o f theapp roach tha t fu l ly sa tis fi es a l l t he p ro to -ph i losop h ica l d a t a exh ib i tedab o v e .lndiana niversity

REFERENCES1 Stig Kanger, Provability in Logic Almquist Wiksell, Stockholm, 1957; 'A Noteon Quantification and Modalities' and 'On the Characterization of Modalities', bothin Theoria 23 (1957).Jaakko Hintikka, 'Modality and Quantification',Theoria 27 (1961), and 'The Modesof Modality', Ac ta Philosophica Fennica 16 (1963).3 Saul Kripke, 'A Completeness Theorem in Modal Logic', The Journal o f Symbol icLogic 24 (1959), and 'Semantical Analysis of Modal Logic I' , Zet tschr i f t f i i r mathema-t ische Logik und Grundlagen der Ma them at ik 9 (1963).4 Richard Montague, 'Logical Necessity, Physical Necessity, Ethics, and Quantifiers',Inquiry 3 (1960).5 j. Barkley Rosser, Logic for Mathematicians McGraw-Hill, New York, 1953,Chapter IV, pp. 55-76.6 For a detailed examination of the overall connections between imperatives anddeontic statements see H.-N. CastaSeda's 'Imperatives, Decisions and Oughts' inM oral i ty and the Language o f Conduct (ed. by H.-N. Castafeda and G. Nakhnikian),Wayne State University Press, Detroit, Mich., 1963; paperback edition, 1967.7 On conflicts of duties and pr ima fac i e oughts see H.-N. CastaSeda's 'Imperatives,Oughts and Moral Oughts', The Australasian Journal o f Philosophy 44 (1966).8 For a discussion of proposals to solve the Good Samaritan paradox, see H.-N.Castafieda, 'Acts, the Logic of Obligation, and Deontic Calculi' ,Philosophical Studies19 (1968); W. Sellars, 'Reflections on Contrary-to-Duty Imperatives', N o a s 1 (1967);L./~qvist, 'Good Samaritans, Contrary-to-Duty Imperatives, and Epistemie Obliga-tions', N o a s 1 (1967); and L. Powers, 'Some Deontic Logicians', Notes 1 (1967).9 H.-N. CastaSeda, 'Actions, Imperatives, and Obligations' , Proceedings o f the Aris-totelian Society 67 (1967-1968) 45 ft.10 See W. V. Quine, Methods o f Log ic Holt, Rinehart and Winston, New York, revisededition, 1959, pp. 107-117.

on the semantics of ought to do

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