University of Southern California Dissertations and Theses

The Logic Of Obligation

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The Logic Of Obligation

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Content T H E L O G IC O F O B L IG A T IO N by M a lh a m M . W akin A D i s s e r t a t i o n P r e s e n t e d to th e F A C U L T Y O F T H E G R A D U A TE SC H O O L U N IV ER SITY O F SO U T H E R N C A L IFO R N IA In P a r t i a l F u lfillm e n t of the R e q u ir e m e n ts fo r th e D e g re e D O C T O R O F PH IL O SO P H Y ( P h ilo s o p h y ) Ju n e 1959 UNIVERSITY O F S O U T H E R N CALIFORNIA G R A D U A T E S C H O O L U N I V E R S I T Y P A R K L O S A N G E L E S 7. C A L I F O R N I A This dissertation, written by M ALH AM M. WAKIN under the direction of hi&....Dissertation C om mittee, and approved by all its members, has been presented to and accepted by the Graduate School, in partial fulfillment of requirements for the degree of D O C T O R O F P H I L O S O P H Y Dean D ate. M ay 195 9 DISSERTATION C O M M IT TE E C hairm an C O N T E N T S C h a p te r P a g e I. IS THERE A LOGIC OF O B L IG A T IO N ?.............................. 1 n . IM PERATIVE LO G ICS...................................................................... 28 1. A lf R o s s a n d th e " P r a c t i c a l I n f e r e n c e " ................... 30 2. A C l o s e r L o o k a t th e S a tis f a c tio n - f u n c tio n I n t e r p r e t a ti o n of I m p e r a t i v e s ................................... 49 3. I m p e r a ti v e s I n t e r p r e t e d a s D is ju n c tiv e I n d i c a t i v e s ........................................................................... 54 4. A T h r e e - v a l u e d L o g ic of I m p e r a t i v e s ....................... 65 HI. NORMATIVE L O G IC S ....................................................................... 75 1. Von W rig h t's " D e o n tic L o g i c " ......................................... 77 2. P r i o r 's D e v e lo p m e n t of th e v o n W rig h t S y s t e m ................................................................................... 97 3. F u r t h e r C o n s id e r a tio n s of th e C o m m itm e n t a n d D is s o lu tio n L a w s ..................................................... 105 4. S y s te m s of C o n d itio n a l P e r m i s s i o n a n d O b l i g a t i o n ............................................................................... 114 C h a p te r P a g e 5. T h e R e d u c tio n of D e o n tic L o g ic to A le th ic M o d a l L o g i c .............................................................. 131 6. S u m m a r y ................................................................................ 143 IV. T H E C O N C E P T O F O B L IG A T IO N A N D T H E P R O P E R F O R M U L A T IO N O F O B L IG A T IO N S E N T E N C E S ...................... 146 1. T h e C o n c e p t of O b l i g a t i o n ......................................... 147 2. O b lig a tio n S e n te n c e s a s N o r m a tiv e s . . . . 167 3. O b lig a tio n S e n te n c e s a n d I m p e r a ti v e s . . . 182 V. S C H E M A T A F O R T H E " V E R T IC A L " A N D "H O R IZ O N T A L " R E L A T IO N S H IP S O F O B L IG A T IO N S E N T E N C E S ........................................................................................ 190 1. A V e r tic a l S y s te m f o r O b lig a tio n S e n te n c e s . 192 2. A n A x io m S y s te m f o r th e H o r iz o n ta l R e la tio n s h ip s of O b lig a tio n S e n te n c e s ................................... 200 L i s t o f S y m b o ls of H a n d T h e ir In te n d e d I n t e r p r e t a t i o n ..................................................... 200 R u le s of F o r m a t i o n ................................................ 202 C h a p te r P a g e A xiom s of H ....................................................... 204 T h e o re m s of H .................................................. 206 3. C o m bin ed O p e ra tio n s of the V e r tic a l and H o riz o n ta l S y s t e m s .......................................... 212 VI. CONCLUDING S U M M A R Y ................................................... 214 L IST O F WORKS C I T E D .................................................................... 219 iv C H A P T E R I IS T H E R E A L O G IC O F O B L IG A T IO N ? T h e p r o b l e m u n d e r i n v e s tig a tio n is w h e th e r o r n o t t h e r e is s o m e lo g ic a l p r o c e s s of r e a s o n i n g by w h ic h we d e t e r m i n e w h e th e r a n a c t s h o u ld o r s h o u ld not b e d o n e. F o r th e p r e s e n t , 'o b l i g a t io n 1 s h a l l be ta k e n in i t s v e r y b r o a d s e n s e to m e a n a n y ty p e o f o b lig a tio n a t a ll. A ny s e n te n c e w h ic h e x p r e s s e s a m o r a l o b lig a tio n , a le g a l o b lig a tio n , o r a n y o th e r ty p e of o b lig a tio n w ill be c a l le d a n o b lig a tio n s e n t e n c e . L a t e r on it w ill be m o r e c o n v e n ie n t to n a r r o w o u r p r o b l e m dow n to p a r t i c u l a r ty p e s of o b lig a tio n . In C h a p te r IV th e v a r i o u s c o n c e p ts of o b lig a tio n w ill be c r i t i c a l l y a n a ly z e d , but it w ill s e r v e o u r p r e s e n t p u r p o s e s to c o n s i d e r a s a n o b lig a tio n s e n t e n c e a n y s e n t e n c e w h ich s a y s of a p o s s ib le h u m a n a c tio n th a t it o u g h t ( o r o u g h t n o t) to be d o n e, s h o u ld ( o r s h o u ld n o t ) be d o n e , b y a h u m a n a g e n t. T h e q u e s tio n o f th e lo g ic a l s t a t u s o f o b lig a tio n s e n t e n c e s h a s b e c o m e a n i m p o r t a n t i s s u e in r e c e n t p h ilo s o p h ic a l l i t e r a t u r e . T h e a tte n tio n th is i s s u e is r e c e i v i n g m a y be due in p a r t to th e c u r r e n t e m p h a s i s on lo g ic a n d th e i n c r e a s i n g p o p u la r ity of la n g u a g e a n a l y s i s a s a n a p p r o a c h to p h ilo s o p h ic p r o b l e m s . A n o th e r a n d p e r h a p s e v e n 2 m o r e in f lu e n tia l f a c t o r c o n tr ib u tin g to th e p r o m in e n c e o f th is i s s u e is th e r e a c t i o n to th e s c h o o l o f th o u g h t w h ic h h a s s e g r e g a t e d a ll m o r a l s e n t e n c e s ( o r v a lu e ju d g m e n ts ) f r o m th e r e a l m o f o b je c tiv e ly v e r i f i a b le s e n t e n c e s . H e n r i P o i n c a r £ , f o r e x a m p le , s u g g e s t e d th a t a ll m o r a l s e n t e n c e s a r e in th e i m p e r a t i v e , a s d is tin g u is h e d f r o m th e in d ic a tiv e , m o o d . * R u d o lf C a r n a p , in th e p e r i o d of P h ilo s o p h y an d n 3 L o g ic a l S y n ta x a n d T h e L o g ic a l S y n ta x of L a n g u a g e , s u g g e s t e d t h a t th e p r o p e r t a s k of p h ilo s o p h y w a s th e lo g ic a l a n a l y s i s of th e s y n ta x of th e la n g u a g e o f s c i e n c e . O n h is v ie w , h o w e v e r, s c i e n c e c o n ta in s no v a lu e s t a t e m e n t s . A ll v a lu e s t a t e m e n t s a r e d is g u is e d i m p e r a t i v e s , a n d i m p e r a t i v e s a p p a r e n t l y do n o t r a t e th e s t a t u s o f s c i e n t i f i c s t a t e m e n t s . B u t a c tu a lly a v a lu e s t a t e m e n t is n o th in g e ls e th a n a c o m m a n d in a m is le a d i n g g r a m m a t i c a l f o r m . It m a y h a v e e f f e c ts u p on th e a c tio n s of m e n , a n d t h e s e e f f e c ts m a y e i t h e r b e in a c c o r d a n c e w ith o u r w is h e s o r n o t; b ut it is n e i t h e r t r u e n o r f a l s e . It d o e s n o t a s s e r t a n y th in g a n d c a n n e i t h e r be p r o v e d n o r d is p r o v e d . F r o m th e s t a t e m e n t ,K illin g is e v i l 1 we c a n n o t d e d u c e a n y p r o p o s i t io n a b o u t f u tu r e e x p e r i e n c e s . T h u s t h is s t a t e m e n t is not v e r i f i a b l e a n d h a s n o t h e o r e t i c a l s e n s e , a n d th e s a m e th in g is t r u e of a ll o t h e r v a lu e s t a t e m e n t s . ^ * P e r n if e r e s P e n s £ e s ( P a r i s , 1 9 1 3 ) , pp. 2 2 4 - 2 2 5 . ^ L o n d o n , 1 9 3 5 . 3 N ew Y o rk , 1 9 3 7 . ^ R . C a r n a p , P h ilo s o p h y a n d L o g ic a l S y n ta x (L o n d o n , 1935 ) , p p . 2 4 -2 5 . 3 A. J . A y e r h o ld s th a t the e th ic a l t e r m s in m o r a l ju d g m e n ts h av e a p u r e ly e m o tiv e fu n ctio n . We c a n now s e e why it is im p o s s ib le to fin d a c r i t e r i o n f o r d e te r m in in g th e v a lid ity of e th ic a l ju d g e m e n ts . It is not b e c a u s e th e y h av e a n " a b s o lu te " v a lid ity w hich is m y s te r io u s ly in d e p e n d en t of o r d in a r y s e n s e - e x p e r ie n c e , b ut b e c a u s e th e y have no o b je c tiv e v a lid ity w h a ts o e v e r. . . . s e n te n c e s w hich s im p ly e x p r e s s m o r a l ju d g e m e n ts do not s a y an y th in g . T h ey a r e p u r e e x p r e s s i o n s of fe e lin g an d a s su c h do not co m e u n d e r th e c a te g o ry of t r u th an d fa ls e h o o d . . . . th e y do not e x p r e s s g en u in e p r o p o s itio n s . ® S ta te m e n ts lik e th o s e c ite d f r o m C a rn a p an d A y e r a p p e a r to h a lt o u r in v e s tig a tio n im m e d ia te ly . If o b lig a tio n s e n te n c e s have "n o th e o r e tic a l s e n s e , " if th ey "d o not s a y a n y th in g , " th e n a tte m p ts to d is c o v e r th e lo g ic a l r e la tio n s h ip s b e tw e e n o b lig a tio n s e n te n c e s w ould s e e m to s e r v e no p u rp o s e . C h a r le s L . S te v e n so n h a s s u g g e s te d th a t e th ic a l s e n te n c e s h a v e m u ch in c o m m o n w ith i m p e r a tiv e s . T h ey a r e s i m i l a r in th a t th ey a r e u se d to e n c o u ra g e o r a l t e r p e o p le 's a im s and c o n d u ct, r a t h e r th an f o r s im p ly d e s c r ib in g th e m , a s the s e n te n c e s of s c ie n c e do. ® S te v e n so n s t r e s s e s a n i n te r p r e ta tio n of e th ic a l t e r m s as e x p r e s s in g a ttitu d e s of a p p ro v a l o r d is a p p ro v a l. T h is e m p h a s is le a d s h im to s u g g e s t th e fo llo w in g a s a " w o rk in g m o d el" f o r in te r p r e tin g 5 A lf re d J . A y e r, L a n g u a g e, T r u th an d L o g ic , 1st ed. (L o n d o n , 1 9 3 6 ), p. 161 . ®C. L . S te v en so n , E th ic s a n d L an g u a g e (N e w H aven, 1 9 4 4 ), p. 21 . 4 ( m o r a l ) o b lig a tio n s e n t e n c e s : " 'H e o u g h t to do t h i s 1 m e a n s _I d is a p p r o v e of h is le a v in g th is u n d o n e ; do s o a s w e ll" ( E th ic s a n d L a n g u a g e , p . 2 1 ) . O n S te v e n s o n 's v ie w , o b lig a tio n s e n t e n c e s a r e n o t m e a n in g l e s s ; th e y s i m p ly h a v e a d i f f e r e n t k in d of m e a n in g f r o m s c i e n t i f i c o r d e s c r i p t i v e s e n t e n c e s . S te v e n s o n a l s o s t r e s s e s th e p e r s u a s i v e u s e of e th i c a l t e r m s . T h e q u e s tio n w h ic h m o s t c o n c e r n s u s w ith t h is i n t e r p r e t a t i o n is w h e th e r S te v e n s o n ’s s u g g e s tio n s o f f e r a n y a id in c la r if y in g th e lo g ic a l s t r u c t u r e o f o b lig a tio n s e n t e n c e s . P r o f e s s o r R. M . H a r e s u g g e s t s th a t S te v e n s o n 's i n t e r p r e t a t i o n u n n e c e s s a r i l y c o m p l i c a te s o u r ta s k : S e n te n c e s c o n ta in in g th e w o rd 'a p p r o v e ' a r e s o d iffic u lt of a n a l y s i s th a t i t s e e m s p e r v e r s e to u s e th is n o tio n to e x p la in th e m e a n in g of m o r a l ju d g e m e n ts w h ic h w e l e a r n to m a k e y e a r s b e f o r e w e l e a r n th e w o rd 'a p p r o v e ' ; a n d s i m i l a r l y , it w ould be p e r v e r s e to e x p la in th e m e a n in g of th e i m p e r a t i v e m o o d in t e r m s of w is h in g o r a n y o t h e r f e e lin g o r a ttitu d e ; f o r we l e a r n how to r e s p o n d to a n d u s e c o m m a n d s lo n g b e f o r e w e l e a r n th e c o m p a r a t i v e l y c o m p le x n o tio n s of 'w is h ' , 'd e s i r e ' , 'a v e r s i o n ' , & c. 7 If o b lig a tio n s e n t e n c e s a r e r e d u c e d to i m p e r a t i v e s , o r m a d e to fu n c tio n in a s i m i l a r m a n n e r to i m p e r a t i v e s , it w o u ld s e e m th a t o b lig a tio n s e n t e n c e s c o u ld n o t o c c u r a s e le m e n t s in a lo g ic a l i n f e r e n c e o r s y l l o g i s m . If o b lig a tio n s e n t e n c e s a r e n o t t r u e o r f a l s e , th e y c o u ld n o t o c c u r a s o n e of th e p r e m i s e s o r a s a c o n c lu s io n of a lo g ic a l in f e r e n c e . H e n c e , if t h e r e i s to be a lo g ic of o b lig a tio n , w e a r e le ft 7 R . M . H a r e , T h e L a n g u a g e of M o r a ls ( O x fo rd , 1952 ) , p. 12 . 5 w ith a t l e a s t th e s e tw o a lte r n a tiv e s : 1) o b lig a tio n s e n te n c e s m a y be s o e x p r e s s e d a s to be c o n s id e r e d a s e i t h e r t r u e o r f a l s e an d m a y th e n o c c u r as e le m e n ts in th e o r e ti c a l in f e r e n c e s ; o r 2) o b lig a tio n s e n te n c e s , w h e th e r c o n s id e r e d t r u e o r f a ls e o r not, m a y o c c u r a s e le m e n ts in in f e r e n c e s of a type d if fe r e n t f r o m t h e o r e ti c a l in f e r e n c e s b u t w hich a r e , n e v e r t h e l e s s , lo g ic a l in f e r e n c e s in so m e s e n s e . T h is s e c o n d a lte r n a tiv e s e e m s th e m o s t p r o m is in g , an d it w ill be p a r t of th e m a j o r p u rp o s e of th is d i s s e r t a t io n to e x a m in e its p la u s ib ility . T he p o s s ib ility of h av in g m o r e th a n one ty p e of lo g ic a l i n f e r e n ce is not a new notion; its h i s t o r ic a l r o o ts c a n be t r a c e d a t le a s t a s f a r b a c k a s th e w o rk s of A r is to tle . In th e N ic o m a c h e a n E th ic s A r is to tle d is tin g u is h e d b e tw e e n th e th e o r e ti c a l an d th e p r a c t ic a l s y llo g is m . P r a c t i c a l w isd o m in v o lv e s c a lc u la tin g ab o u t th in g s w hich co n d u ce to th e good life in g e n e r a l a n d s u c h d e lib e r a tio n s a r e d i f f e r e n t f r o m the d e m o n s tr a tio n s of t h e o r e tic a l o r s c ie n tif ic k n o w led g e. Now no one d e lib e r a te s ab o u t th in g s th a t a r e in v a r ia b le , n o r a b o u t th in g s th a t it is im p o s s ib le f o r h im to do. T h e r e f o r e , s in c e s c ie n tif ic k n ow ledg e in v o lv e s d e m o n s tr a tio n of th in g s w hose f i r s t p r in c ip le s a r e v a r ia b le ( f o r a ll s u c h th in g s m ig h t a c tu a lly be o t h e r w i s e ) , an d s in c e it is im p o s s ib le to d e lib e r a te about th in g s th a t a r e of n e c e s s ity , p r a c t i c a l w isd o m c a n n o t be s c ie n tif ic kn ow ledge n o r a r t ; not s c ie n c e b e c a u s e th a t w hich c a n be done is c a p a b le of b ein g o th e r w is e , n o t a r t b e c a u s e a c tio n a n d m ak in g a r e d iffe re n t k in d s of th in g . T he r e m a in in g a lte r n a tiv e , th en , is th a t it is a t r u e a n d r e a s o n e d s t a te of c a p a c ity to a c t w ith r e g a r d to the th in g s th a t a r e good o r b a d f o r m a n . ( N ic o m a c h e a n E th ic s , 1140a 3 1 -3 6 , 1140b 1 - 6 ) 6 T h e p r a c t i c a l s y llo g is m , f o r A r i s t o t le , in v o lv e s d e lib e r a tio n , but a p e c u l i a r kind of d e lib e r a tio n . E x c e lle n c e in d e lib e r a tio n " is c l e a r l y a k in d of c o r r e c t n e s s , b u t n e it h e r of k n o w le d g e n o r o p in io n " D ( 1142b 10 ) . B u t e x c e lle n c e in d e lib e r a tio n d o e s in v o lv e r e a s o n in g . T h e r e f o r e A r i s t o t le c o n c lu d e s th a t e x c e lle n c e in d e lib e r a tio n is " c o r r e c t n e s s of th in k in g " (1 1 4 2 b 1 3 ) . T h is " c o r r e c t n e s s " d o e s n ot a lo n e c o n s is t in a r r i v i n g a t th e r ig h t c o n c lu s io n c o n c e rn in g w hat o u g h t to be d one; the s y llo g is tic r e a s o n i n g p r o c e s s m u s t i ts e l f be c o r r e c t : it is p o s s ib le to a tta in e v e n good by a f a ls e s y llo g is m , an d to a tt a i n w h a t one o u g h t to do b u t not by the r i g h t m e a n s , th e m id d le t e r m b e in g f a l s e ; s o th a t th is to o is not y e t e x c e lle n c e in d e lib e r a tio n . (1 1 4 2 b 2 2 -2 5 ) We c a n c o n c lu d e th a t th o s e s y llo g is m s w h ich a r e r e f e r r e d to a s p r a c t ic a l in v o lv e c o r r e c t r e a s o n in g p r o c e s s e s a n d a r e c o r r e c t l y r e f e r r e d to a s lo g ic a l s y l l o g is m s . T h e r u l e s of lo g ic w hich g o v e rn p r a c t i c a l s y llo g is m s a r e not d i s c u s s e d by A r i s t o t le . It is n e t c l e a r w h e th e r he w o u ld r e q u i r e c e r t a i n s p e c i a l lo g ic a l r u le s f o r p r a c t i c a l s y llo g is m s o r n o t. T h e m a jo r d iff e re n c e b e tw e e n th e p r a c t i c a l and t h e o r e ti c a l s y llo g is m s is th a t th e f o r m e r a r e " th e s y llo g is m s w h ich d e a l w ith p °A11 f u r t h e r r e f e r e n c e s to A r i s t o t le w ill be to p a s s a g e s of th e N ic o m a c h e a n E t h i c s , h e n c e o n ly th e p a g in a tio n a n d lin e w ill be c ite d . T h e t r a n s l a t i o n u s e d is th a t of W. D. R o s s a s in c lu d e d in R ic h a r d M cK eon, e d . , T h e B a s ic W o rk s of A r i s t o t l e (N e w Y o rk , 1 9 4 1 ) . 7 a c ts to be done" ( 1144a 3 1 ) . R. M. H a re s t a t e s th a t s in c e A r i s t o t l e 's p r a c t i c a l s y llo g is m m u s t c o n c lu d e in an a c tio n , it m u s t r e f e r to c o n tin g e n t p a r t i c u l a r s , w h ich t h e o r e ti c a l s y llo g is m s a r e n o t 9 (b y A r i s t o t l e ) a llo w e d to do. An im p o r ta n t p o in t to n o tic e is th a t the p r a c t i c a l s y llo g is m r e s u l t s in a c tio n . A r is to tle , in d is tin g u is h in g s c ie n tif ic f r o m p r a c t i c a l r e a s o n in g s t a t e s th a t; th e s o u l m u s t in one ty p e of c a s e a f f ir m th e c o n c lu sio n , w hile in th e c a s e of o p in io n s c o n c e rn e d w ith p ro d u c tio n it m u s t i m m e d ia te ly a c t ( e . g . if E v e r y th in g s w e e t ought to be t a s t e d 1 , a n d 'th is is s w e e t', in the s e n s e of b e in g one of th e p a r t i c u l a r s w e e t th in g s , the m a n who c a n a c t an d is not p r e v e n te d m u s t at th e s a m e tim e a c tu a lly a c t a c c o rd in g ly ) . ( 1147a 2 7 -3 2 ) T he m a j o r p r e m i s e of a p r a c t i c a l s y llo g is m is r e p r e s e n t e d by A r i s t o t le ( a s in the e x a m p le c ite d a b o v e ) a s a u n iv e r s a l s ta te m e n t c o n ta in in g an 'o u g h t1 o r 's h o u ld ' t e r m . H a re c o m m e n ts th a t A r is to tle " n e v e r s e e m s to h av e r e a liz e d how d if fe r e n t th e s e f o r m s a r e f r o m n o r m a l in d ic a tiv e s " ( L a n g u a g e of M o ra ls , p. 26 , n ote 1 ) . T h e f a c t th a t A r is to tle r e s e r v e d th e s e u n iv e r s a l o u g h t- s e n te n c e s f o r ^ T h e L an g u a g e of M o ra ls , p . 26 , note 1 . ^ H a re ( p . 26, note 1) s a y s of A r i s t o t le th a t " h e s a y s th a t th e c o n c lu s io n is an a c tio n (n o t an im p e r a tiv e e n jo in in g an a c t i o n ) ." A r i s t o t le is not c l e a r on th is p o in t but H a r e 's in te r p r e t a t i o n is m i s le a d in g . A r is to tle s u r e l y did not m e a n th a t th e lo g ic a l c o n c lu s io n of a s y llo g is m c o u ld be a n y th in g o th e r th a n a ju d g m e n t of s o m e ty p e . H a re is q u ite c o r r e c t , h o w e v e r, in h o ld in g th a t A r is to tle did not p e r m it th e p r a c t i c a l s y llo g is m s to c o n clu d e w ith an im p e r a tiv e . th e m a jo r p r e m i s e s of p r a c t i c a l s y llo g is m s in d ic a te s th a t he did d is tin g u is h th e m f r o m " n o r m a l in d ic a tiv e s , " a lth o u g h it is tr u e th a t he did not e m p h a s iz e th is d iff e re n c e . The c u r r e n t tr e n d in p h ilo s o phy to w a rd s lan g u a g e a n a ly s is m ig h t a c c o u n t f o r th e s t r e s s w hich the p r e s e n t - d a y p h ilo s o p h e r p la c e s on d iff e re n t s e n te n c e f o r m s , but it s e e m s u n ju s t to c r i t ic i z e A r is to tle fo r fa ilin g to e m p h a s iz e th e s e d if f e r e n c e s . In deed, it is a m a z in g th at, w hile fa ilin g to r e a liz e "h o w d iffe re n t th e s e f o r m s a r e f r o m n o r m a l in d ic a tiv e s , " A r is to tle w as a b le to s u g g e s t a m eth o d { w h a te v e r its d ra w b a c k s m ig h t b e ) fo r h a n d lin g the lo g ic of su c h f o r m s . The fa c t th a t A r is to tle does not s t r e s s th e d iffe re n c e b e tw e e n in d ic a tiv e c o n te x ts an d w hat H a re c a lls the " i m p e r a tiv e f o r m " a c tu a lly is q u ite f o r tu n a te f o r H a r e ’s p u r p o s e s . He fin d s s o m e ju s tif ic a tio n fo r th e p o s s ib ility of an im p e r a tiv e logic in A r i s t o t l e ’s g e n e r a l d e fin itio n of a s y llo g is m : " S y llo g is m c o n s is ts in sa y in g , g iv en c e r t a i n th in g s , so m e th in g f u r t h e r w hich fo llow s n e c e s s a r i l y f r o m th e m . " T h is d e fin itio n c o u ld a p p ly to im p e r a tiv e s a s w ell a s in d ic a tiv e s . ^ G. E . M. A n s c o m b e p o in ts out th a t the u s e of u n iv e r s a l o b lig a - T he L an g u a g e of M o ra ls , p. 26, note 1 . T h e r e f e r e n c e s to A r is to tle w hich H a re g iv e s f o r th e d e fin itio n of s y llo g is m w hich w as q u o te d a r e : S o p h is tic a l R e fu ta tio n s, 151a 1 ; T o p ic s , 100a 25 ; P r i o r A n a ly tic s , 24b 18 . 9 tio n s e n te n c e s a s m a j o r p r e m i s e s f o r p r a c t i c a l s y l l o g is m s " h a s no doubt h e lp e d th e v ie w th a t th e p r a c t i c a l s y l l o g is m is e s s e n t ia ll y e t h i c a l, but th e v ie w h a s n o p la u s ib ility . A n s c o m b e 's r e m a r k is c o r r e c t p ro v id e d h e m e a n s by it th a t th e p r a c t i c a l s y l l o g is m is not e s s e n t i a l l y " e th ic a l" in the n a r r o w m o d e r n s e n s e of th e w o rd 'e t h i c a l . 1 H is f u r t h e r r e m a r k s a r e a ls o q u ite p e r tin e n t : In th in k in g of th e w o rd f o r ’s h o u ld 1, 'o u g h t1, e tc . ( & t z ) a s it o c c u r s in A r i s t o t le , we s h o u ld th in k of it a s it o c c u r s in o r d i n a r y la n g u a g e ( e . g . a s it h a s j u s t o c c u r r e d in th is s e n te n c e ) a n d n o t j u s t a s it o c c u r s in th e e x a m p le s of ’m o r a l d i s c o u r s e 1 g iv en by m o r a l p h ilo s o p h e r s . . . . A ny f a i r s e le c tio n of e x a m p le s , if we c a r e to s u m m o n th e m up, s h o u ld c o n v in c e us th a t 's h o u ld 1 is a r a t h e r lig h t w o rd w ith u n lim ite d c o n te x ts of a p p l i c a tio n , a n d it c a n be p r e s u m e d th a t it is b e c a u s e of th is f e a t u r e th a t A r i s t o t le c h o s e a ro u g h ly c o r r e s p o n d in g G r e e k w o rd a s th e w o rd to p u t into th e u n i v e r s a l p r e m i s e of h is s c h e m a ti c p r a c t i c a l s y llo g is m . (In te n tio n , p . 6 3 ) A n s c o m b e 'a o b s e r v a tio n s le a d u s to c o n c lu d e th a t th e u s e of 'o u g h t' in s e n te n c e s e x p r e s s in g th e n a r r o w m o d e r n s e n s e of m o r a l o b lig a tio n , g iv e s s im p ly one of m a n y ty p e s of o b lig a tio n s e n te n c e s w h ich m ig h t o c c u r in th e A r i s t o t e l i a n p r a c t i c a l s y llo g is m . T h is c o n c lu s io n is f u r t h e r s u p p o r te d by R ex W a r n e r , who s t a t e s t h a t : " T h e r e is a s e n s e in w h ich A r i s t o t le d o e s n o t e m p lo y a t a ll o u r c o n c e p t of 1 ^ 'm o r a l i t y '. " T r a n s l a t i o n d if fic u ltie s m ig h t a c c o u n t f o r s o m e of In te n tio n ( I th a c a , N. Y . , 1 9 5 7 ) , p. 6 3 . The G r e e k P h ilo s o p h e r s (N e w Y o rk , 1 9 5 8 ) , p. 1 1 4 . 10 the co n fu sio n s w hich hav e a r i s e n . As W a rn e r p o in ts o u t ( p . 1 1 4 ), th e G r e e k w o rd a r e t e is u su a lly r e n d e r e d a s " v ir tu e , " and the m o d e rn c o n ce p t of v ir tu e is u s u a lly th a t of " m o r a l v i r t u e ." But the v ir tu e s of A r is to tle in clu d e w hat we w ould g e n e r a lly c a ll good c h a r a c t e r t r a i t s - - e . g . , good m a n n e rs , wit, b r a v e r y - - a s w ell as h o n esty , tru th f u ln e s s , and th e o th e r t r a i t s w hich we r e f e r to as s p e c ific a lly m o r a l. It is not, of c o u rs e , th a t A r is to tle d o es not d is c u s s w hat we sh o u ld r e g a r d as m o r a l q u e stio n s ; it is only th a t he does not s p e c ia lly d istin g u is h th e m f r o m o th e r q u e stio n s of w hat is good in conduct an d c h a r a c te r , an d in d e e d he has not the lin g u is tic m ea n s of doing s o . T h is a b s e n c e of o u r m o d e rn , l i m ite d c o n ce p t of m o r a lity s e e m s c h a r a c t e r i s t i c of the a n c ie n t w o rld in g e n e r a l. In C ic e ro fo r in s ta n c e , w ritin g th r e e c e n t u r ie s la t e r , we a g a in find no d istin c tio n d ra w n b e tw ee n m o r a l and n o n m o ra l q u e stio n s about h u m a n c h a r a c t e r , no s h a r p d is tin c tio n b etw een good m a n n e r s , "good fo rm , " and good m o r a ls . ( W a r n e r , pp. 1 1 4 -1 1 5 ) Since the m o d e rn c o n ce p t of m o r a l o b lig a tio n is not to be found in A ris to tle , we can n o t e x p e c t the p r a c tic a l s y llo g is m to p r o vide a c o m p le te lo g ic a l s c h e m a tis m fo r th is c o n c e p t. T h e re is a s e n s e , h o w e v er, in w hich the m o d e rn m o r a l v ir tu e s a re in clu d ed w ithin th e b r o a d e r sc o p e of the A r is to te lia n " M o r a l V irtu e s . " If t h e r e is any v a lid ity to be found in th e a p p lic a tio n of the p r a c tic a l s y llo g is m to h u m an a c ts in g e n e r a l, we m ay be able to adapt th is s c h e m a tis m to d e a l w ith th o se a c ts w hich a r e to d ay c o n s id e re d o b lig a to ry f r o m a m o ra l, leg a l, o r so m e o th e r point of view . 11 T he p r a c t i c a l s y llo g is m h a s not b e e n c o m p le te ly n e g le c te d s in c e th e tim e of A r i s t o t le , St. T h o m a s A q u in as h a s m a d e s e v e r a l r e f e r e n c e s to th e p r a c t i c a l s y llo g is m , an d in h is w o rk s we o b ta in an e la b o r a tio n of th e s o m e tim e s v a g u e r e f e r e n c e s w h ic h A r is to tle m a d e to th e p r o c e s s of p r a c t i c a l re a s o n in g . St. T h o m a s c o m e s to a d i s c u s s io n of o u r p a r t i c u l a r p r o b le m w hen he e x p la in s th e te c h n ic a l o p e ra tio n of c o n s c ie n c e . C o n s c ie n c e h a s to do w ith the a p p lic a tio n of know ledg e to a c ts , b u t : c o n s c ie n c e c an n o t d en o te a s p e c ia l h a b it o r p o w e r, but d e s ig n a te s th e a c t its e lf, w hich is the a p p lic a tio n of an y h a b it o r of an y know ledge to so m e p a r t i c u l a r a c t. ( De V e r it a te , Q . 17, a r t . 1) T h u s 'c o n sc ie n c e * is th e n a m e of th e a c t of a p p ly in g know ledg e to p a r t i c u l a r a c ts and is , a s it w e re , a ls o th e n a m e of the a c t of p r a c t i c a l re a s o n in g . St. T h o m a s e x p lic itly s t a te s th a t the p r o c e s s of d e te r m in in g w hat ought to be done is a lo g ic a l one. He r e f e r s to th is p r o c e s s of r e a s o n in g w hich d e te r m in e s w h e th e r a p a r t i c u l a r a c t ought to be done a s a p r a c t i c a l s y llo g is m , a s d is tin g u is h e d f r o m th e s p e c u la tiv e s y llo g is m s of ju d g m e n ts not d ir e c te d to w a rd w hat ought to be d one. In th e c o n s tr u c tio n of p r a c t i c a l s y llo g is m s th e r e a r e tw o w ays in w h ich e r r o r m a y o c c u r . O ne is th e u s e of fa ls e p r e m i s e s ; th e o th e r is a p u r e ly lo g ic a l m is ta k e (f a u lty c o n s tr u c tio n o f th e s y l l o g is m ) . St. T h o m a s , like A r is to tle , s t a te s th a t th e m a jo r p r e m i s e of the 12 p r a c t i c a l s y llo g is m is a u n iv e r s a l ju d g m e n t, b ut St. T h o m a s f u r t h e r s tip u la te s th a t it is a u n i v e r s a l ju d g m e n t of s y n d e r e s i s . T h e k n o w l edge g a in e d by th e h a b it of s y n d e r e s is is s e l f - e v i d e n t know ledge ab o u t a c ts in g e n e r a l w ith r e s p e c t to a b s o lu te ly n e c e s s a r y e n d s. S in ce th e a c t to w hich c o n s c ie n c e a p p lie s th e kno w led ge of s y n d e r e s is is p a r t i c u l a r , a n d th e ju d g m e n t of s y n d e r e s is is u n i v e r s a l, " th e ju d g m e n t of s y n d e r e s is c a n be a p p lie d to th e a c t o nly if s o m e p a r t i c u l a r ju d g m e n t is u s e d as th e m in o r p r e m i s e " ( De V e rita te , Q. 17, a r t . 2 ) . T h e s e p a r t i c u l a r ju d g m e n ts f o r th e m in o r p r e m i s e a r e s u p p lie d by e i t h e r th e h ig h e r r e a s o n ( w i s d o m ) o r by the lo w e r r e a s o n ( s c i e n t if i c k n o w le d g e ) . " T h u s , th e a c t of c o n s c ie n c e is th e r e s u l t of a kind of p a r t i c u l a r s y llo g is m " ( De V e r ita te , Q . 17, a r t . 2 ) . St. T h o m a s f u r n is h e s th e fo llo w in g ill u s t r a ti o n of w hat he m e a n s by th is p r a c t i c a l o r p a r t i c u l a r s y llo g is m : If th e ju d g m e n t of s y n d e r e s is e x p r e s s e s th is s ta te m e n t: " I m u s t n ot do a n y th in g w h ich is fo rb id d e n by th e law of G od, " an d if th e k n ow led ge of h ig h e r r e a s o n p r e s e n t s th is m in o r p r e m i s e : " S e x u a l in te r c o u r s e w ith th is w o m an is fo rb id d e n by th e law of G od, " the a p p lic a tio n of c o n s c ie n c e w ill be m a d e by c o n clu d in g : " I m u s t a b s ta in f r o m th is i n t e r c o u r s e . " ( De V e r it a te , Q. 17, a r t . 2) T he m a j o r p r e m i s e of th e p r a c t i c a l s y llo g is m , b ein g u n i v e r s a l and s e lf -e v id e n t, c an n o t be m is ta k e n . T he m in o r p r e m i s e , h o w e v e r , b e in g p a r t i c u l a r , c a n be in e r r o r . If it is a ju d g m e n t of h ig h e r r e a s o n , it m a y be m i s t a k e n - - " a s h a p p e n s w hen one ju d g e s s o m e th in g 13 to be lic it o r illic it w hich is not" ( De V e r ita te , Q. 17 , a r t . 2 ) . If th e m in o r p r e m i s e is a ju d g m e n t of th e lo w e r p a r t of r e a s o n , it m ay be in e r r o r - - " a s h a p p e n s w hen one is m is ta k e n ab o u t c iv il n o rm s of w hat is j u s t o r u n ju st, good o r b a d . " T h u s, if a p r a c t ic a l s y llo g is m is in v alid b e c a u s e a f a ls e p r e m i s e has b e e n u se d , it m u s t be th e m in o r p r e m i s e w hich is fa ls e . T h e o th e r p o s s ib le r e a s o n f o r in v a lid ity of th e p r a c t ic a l s y llo g is m is th a t c o n s c ie n c e m ay m a k e a fa u lty a p p lic a tio n of know ledge to a c ts : F o r , a s in c o n s tru c tin g s p e c u la tiv e s y llo g is m s one m ay n e g le c t the p r o p e r f o r m of a rg u m e n ta tio n , and thus a r r i v e a t a f a ls e c o n c lu sio n , so h e can do the s a m e in p r a c tic a l s y llo g is m s . ( De V e rita te , Q. 1 7, a r t . 2) E tie n n e G ilso n , in c o m m e n tin g upon St. T h o m a s 's d is c u s s io n of p r a c t ic a l re a s o n in g , e m p h a s iz e s the c o n tin g e n c y of h u m a n a c tio n s an d th e u n c e rta in ty in v o lv ed in know ing w hich a c tio n s a r e o b lig a to ry . Now, w hen we p a s s f r o m the u n iv e r s a l to th e p a r tic u la r , we leav e behind the im m o v a b le and c e r ta in to e n te r the r e a lm of th e v a ria b le and u n c e rta in . H ence th e know ledge of w hat ought to be done is in e v ita b ly fille d w ith u n c e rta in ty . ^ It is p r e c is e ly b e c a u s e of th e u n c e rta in ty of o u r know ledge with r e s p e c t to the p a r t i c u l a r a c t th a t we r e f e r to a p r o c e s s of d e l i b e r a tio n s u c h a s th a t d e s c r ib e d a s a p r a c t i c a l s y llo g is m . E tie n n e GilBon, T h e C h r is tia n P h ilo so p h y of St. T h o m a s A q u in as ( New Y ork, 1956 ) , p. 2 5 3 . 14 D elib eratio n , o r the p ra c tic a l sy llo g ism , m u st conclude with a jud gm en t. "If we a r e to be alw ays d e lib e ra tin g , we sh a ll have to go on to infinity" ( N icom achean E th ic s , 1113a 2 ) . "T h u s d e lib e r a tio n concludes with a judgm ent of the p r a c tic a l re a so n " (G ilso n , p. 2 5 4 ) . In the light of th e se o b se rv atio n s we m ight c la rify o u r e a r l i e r r e m a r k th at A risto tle held th a t a p r a c tic a l sy llo g ism t e r m i n a te s in an action and not in an im p e ra tiv e . It s e e m s m o re c o r r e c t to s a y th at A risto tle m e a n t th at the con clu sio n of a p r a c tic a l s y llo g ism is a judgm ent th at an actio n should o r should not be done, and th at he did not c o n s id e r th is judgm ent to be an im p e ra tiv e . Although we have no c le a r s ta te m e n t of th is position, it se e m s e sse n tia l; for how e ls e can we account fo r A r is to tle ’s su b seq u en t r e fe re n c e s to choice, e . g . , " it is th at which has been decided upon a s a r e s u lt of d e lib e ra tio n th at is the object of choice" ( 1113a 5) . St. T hom as m o re ex p licitly s ta te s that; choice re s u lts fro m the d e cisio n o r judgm ent which is, as it w ere, the co nclusion of a p ra c tic a l sy llo g ism . H ence, that which is the co nclusio n of a p r a c tic a l sy llo g ism , is the m a tte r of choice. ( Sum m a T heologica, I - I I , 13, 3) Both A risto tle and St. T hom as A quinas, in th e ir re fe re n c e s to the p ra c tic a l sy llo g ism , have in d icated a s ta r tin g point in the s e a r c h fo r a logic of obligation. O bligation s e n te n c e s o c cu r as e le m e n ts of a p r a c tic a l sy llo g ism , and the p ra c tic a l sy llo g ism is e n title d to be called lo g ical in so fa r as the co n clusio n follows 15 im m e d ia te ly f r o m th e p r e m i s e s . T he s tr o n g e s t r e a s o n c u r r e n tly a d v a n c e d f o r not p e r m ittin g o b lig atio n s e n te n c e s to o c c u r a s e le m e n ts in a lo g ic a l in fe re n c e is th a t o b lig a tio n s e n te n c e s can n o t be s a id to be tr u e o r fa ls e . But th is o b je c tio n did not c o n s titu te a p r o b le m fo r A r is to tle o r St. T h o m a s, s in c e th e ir c o n c e p tio n s of o b lig a tio n w e re c lo s e ly r e la te d to ju d g m e n ts r e g a rd in g the n e c e s s a r y ends of a c tio n a n d th in g s. W hen St. T h o m a s s a y s th at u n iv e r s a l ju d g m e n ts of s y n d e r e s is can n o t be m is ta k e n , he undoubtedly c o n s id e rs su c h ju d g m e n ts to be tr u e s ta te m e n ts in the s a m e s e n s e in w hich any o th e r u n iv e r s a l ju d g m e n ts m ay be s a id to be tr u e . T he m o d e rn p r o b le m of a c c o u n tin g fo r the lo g ic a l re la tio n s of o b lig a tio n s e n te n c e s h a s o c c u r r e d b e c a u s e of a d eep ly ro o te d , fu n d a m e n ta l s h ift in m o r a l p h ilo so p h y . T h is " s h ift" is a ls o re s p o n s ib le fo r the c o n c e rn of m o d e rn e th ic a l th e o r is ts w ith d e fin itio n s of th e e th ic a l t e r m s - - i t now h a s becom e n e c e s s a r y to e x p la in the re la tio n s h ip s of 'good, 1 • r i g h t ,' and 'o u g h t' to one a n o th e r an d to a s s ig n to e ach t e r m a sp e c ific ro le in e th ic s . T h is fu n d a m e n ta l s h ift m ay a ls o ex p lain why it is now fe a s ib le ( o r e v en n e c e s s a r y ) to d is tin g u is h b etw een v a lu e th e o ry and m o r a l p h ilo so p h y a s p h ilo s o p h ic a l d is c ip lin e s . T h e r e is no obvious s in g le e x p la n a tio n fo r th is m a jo r s h ift in m o r a l p h ilo so p h y . A s is th e c a s e w ith m an y p h ilo s o p h ic a l tr e n d s , th e c o n trib u tin g fa c to rs a r e n u m e ro u s and c o m p le x . A m ong th e m we 16 w o u ld in c lu d e th e t e m p o r a r y p o p u la r ity of th e a u t h o r i t a r i a n i s m o f W illia m o f O c k h a m , *5 th e f a r r e a c h i n g e f f e c ts of th e P r o t e s t a n t R e f o r m a tio n , a n d th e e m p h a s i s p la c e d o n th e le g a l a p p r o a c h by e a r l y s e v e n t e e n t h c e n t u r y p h ilo s o p h e r - t h e o l o g i a n s , s u c h a s F r a n c i s 1 fi S u d r e z . T h e in f lu e n c e o f th e a n c i e n t J u d a ic c o n c e p t of s t r i c t o b e d ie n c e to th e L a w is a l s o n o t to be o v e r lo o k e d . T h e m o s t c o n c r e t e a n d u n d o u b te d ly th e m o s t i m p o r t a n t in f lu e n c e u p o n th e m o d e r n c o n c e p tio n of o b lig a tio n , h o w e v e r , h a s b e e n th e m o r a l p h ilo s o p h y of I m m a n u e l K a n t. O n K a n t's v ie w , th e n o tio n of o b lig a tio n ( a s a l s o in th e c a s e of f r e e d o m ) b e c o m e s m e a n in g f u l o n ly if we r e g a r d m a n a s a c it i z e n of tw o w o r ld s : th e w o rld of s e n s e ( a p p e a r a n c e s o r p h e n o m e n a ) , a n d th e in te llig ib le w o rld ( t h e n o u m e n a l w o r l d ) . F r e d e r i c k C o p le s to n r e p o r t s of O c k h a m 's e th i c a l v ie w s th a t h e h a d h e ld t h a t " G o d 's w ill c o n s t it u t e s th e w h o le b a s i s of g o o d a n d e v il. A c tio n s a r e g o o d o r e v il s i m p ly a n d s o l e l y in s o f a r a s th e y a r e o r d e r e d o r p r o h i b it e d by G o d " ( A H i s t o r y of P h ilo s o p h y , I I I , W e s t m in s t e r , M a r y la n d , 1953, p. 3 8 4 ) . 1^ De L e g ib u s a c D eo l e g i a l a t o r e ( 1 6 1 2 ) . C o p le s to n s u g g e s t s t h a t S u d r e z fo llo w s St. T h o m a s in m a n y b a s i c p o in ts in v o lv in g th e n a t u r a l la w , e t e r n a l la w , a n d p o s itiv e h u m a n la w ( H i s t o r y of P h ilo s o p h y , I I I , 3 8 4 -3 8 5 , 3 9 2 - 3 9 5 ) . T h e e m p h a s i s in S u fire z , h o w e v e r , is o n th e n o tio n of o b lig a tio n a s im p o s e d by la w . C e r t a i n a c tio n s a r e s p o k e n of a s c o m m a n d e d by o r p r o h ib ite d b y n a t u r a l law , e t e r n a l la w , e tc . T h e e m p h a s is in St. T h o m a s , a s in A r i s t o t l e , w a s p l a c e d u p o n th e g o o d n e s s o f th o s e a c tio n s w h ic h a c c o r d w ith r i g h t r e a s o n a n d th e r o l e o f c o n s c ie n c e in m a k in g p r a c t i c a l ju d g m e n ts a b o u t in d iv id u a l a c t s . 17 the id e a of fre e d o m m a k e s m e a m e m b e r of an in te llig ib le w orld, in c o n seq u e n ce of w hich, if I w e re nothing e ls e , a ll m y a ctio n s would alw ays c o n fo rm to th e autono m y of the w ill; but a s I a t the s a m e tim e in tu ite m y se lf a s a m e m b e r of the w o rld of s e n s e , th ey ought so to c o n fo rm , and th is c a te g o r i c a l 'o u g h t1 im p lie s a sy n th e tic a p r i o r i p ro p o sitio n , . . . . ( F u n d a m e n ta l P r in c ip le s of the M etap h y sic s of M o ra ls, p. 8 8 ) 17 In th e C ritiq u e of P u re R e aso n K ant te lls us th at, "W hen we have the c o u rs e of n a tu re alone in view , ' ought' has no m ea n in g w h a tso e v e r" 1ft (A 547= B 575) . F o r Kant, a ll of m o ra lity c e n te rs a ro u n d the 'o u g h t ': "T he philosophy of n a tu re deals w ith a ll th a t is , the philosophy of m o ra ls with th a t w hich ought to be" (C r itiq u e of P u re R e a s o n , A 84 0= B 868 ). The " n e c e s s ity " im p o s e d by the ought has im p e r a tiv a l fo rc e . It is fro m Kant, m o re than fro m any o th e r s o u rc e , th a t we d e riv e o u r m o d e rn s t r e s s on im p e ra tiv e s in m o r a l philosophy. In the C ritiq u e of P u re R easo n , when he is in te r e s te d in d e m o n s tra tin g a s e n s e in w hich o u r re a s o n can be c o n s id e re d a c a u s a l fo rc e , he r e f e r s to the im p e r a tiv e s of re a s o n w hich apply to h um an actio n s: 17 R e fe re n c e s to th e F u n d a m e n ta l P r in c ip le s a r e ta k e n fr o m the T h o m as K ings m ill A bbott tra n s la tio n e n title d K a n t's T h e o ry of E th ic s , 6th ed. (L ondon, 1 9 0 9 ), and the p a g in a tio n is th at of vol. 8 of th e R o se n k ra n z and S c h u b e rt ed itio n of K a n t's whole w o rk s. 1 ft R e fe re n c e s to th e C ritiq u e of P u r e R e a so n a re f r o m the N o rm a n K em p Sm ith tr a n s la tio n and the p ag in a tio n is th at of K a n t's f i r s t and se c o n d ed itio n s (A and B , r e s p e c tiv e ly ) . 18 T h a t o u r r e a s o n h a s c a u s a lity , o r th a t w e a t l e a s t r e p r e s e n t it to o u r s e l v e s a s h a v in g c a u s a lity , is e v id e n t f r o m th e i m p e r a t i v e s w h ic h in a ll m a t t e r s of c o n d u c t we im p o s e a s r u l e s upon o u r a c tiv e p o w e r s . ’O u g h t1 e x p r e s s e s a kind of n e c e s s i t y a n d o f c o n n e c tio n w ith g ro u n d s w h ich is fo u n d n o w h e r e e ls e in th e w h o le of n a tu r e . (A 5 4 7 = B 5 7 5 ) A g a in , in th e F u n d a m e n ta l P r i n c i p l e s ( G ru n d le g u n g ) , K ant s t a t e s ; T h e c o n c e p tio n o f a n o b je c tiv e p r in c ip le , in s o f a r a s it i s o b lig a to ry f o r a w ill, is c a lle d a c o m m a n d ( o f r e a s o n ) , a n d th e f o r m u la o f th e c o m m a n d is c a lle d a n I m p e r a tiv e . A ll i m p e r a t i v e s a r e e x p r e s s e d by th e w o rd o u g h t ( o r s h a l l ) , a n d t h e r e b y in d ic a te th e r e l a t i o n o f a n o b je c tiv e la w of r e a s o n to a w ill, . . . . ( p p . 3 6 - 3 7 ) In th e I n tr o d u c tio n to th e M e ta p h y s ic s of M o r a ls , K an t g iv e s th e f o l lo w in g d e fin itio n of o b lig a tio n : " O b lig a tio n is th e n e c e s s i t y of a f r e e 19 a c tio n , f a llin g u n d e r a c a t e g o r i c a l i m p e r a t i v e of r e a s o n ( p . 2 2 ). T h e d is tin c tio n b e tw e e n c a t e g o r i c a l a n d h y p o th e tic a l i m p e r a t i v e s r e s t s upon th e n a tu r e of th e a c tio n w hich is c o m m a n d e d . H y p o th e tic a l i m p e r a t i v e s c o m m a n d a p o s s ib le a c tio n c o n s id e r e d a s a m e a n s to s o m e th in g e ls e , w hile a c a t e g o r i c a l i m p e r a t i v e c o m m a n d s a n a c tio n c o n c e iv e d a s good in its e lf , i . e . , a s n e c e s s a r y of i t s e l f (o b je c tiv e ly R e f e r e n c e s to th e M e ta p h y s ic s o f M o r a ls a r e f r o m th e J . W. S e m p le t r a n s l a t i o n of I. K an t, T h e M e ta p h y s ic s of E th ic s (E d in b u rg h , 1 8 3 6 ). U n fo rtu n a te ly , th e o r i g in a l p a g in a tio n is n o t p r e s e r v e d in th is t r a n s l a t i o n but by c o o r d in a tin g w ith th e A b b o tt t r a n s l a t i o n (w h ich d o e s not in c lu d e th e w hole o f th e M e ta p h y s ic s of M o r a l s ) , th e p a g in a tio n of th e R o s e n k r a n z e d itio n h a s b e e n d e te r m in e d . T h u s th e p a g in a tio n of b o th th e G ru n d le g u n g a n d th e M e ta p h y s ic s of M o ra ls a p p e a r h e r e in a c c o r d a n c e w ith th a t of th e R o s e n k r a n z e d itio n . 19 n e c e s s a r y ) w ithout r e f e r e n c e to a n o th e r e n d ( G ru n d le g u n g , p . 3 8 ) . T h e r e a r e no c o n d itio n s, no p u r p o s e s , a tta c h e d to th e c a te g o r ic a l i m p e r a tiv e . It is th e f o r m an d p r in c ip le of th e a c tio n , not th e c o n s e q u e n c e of th e a c tio n , w ith w hich the c a t e g o r i c a l im p e r a tiv e is c o n c e rn e d ; " w h a t is e s s e n t ia ll y good in it c o n s is ts in th e m e n ta l d is p o s itio n " ( G ru n d le g u n g , p . 4 1 ) . It is p r e c i s e ly th is m e n ta l d is p o s itio n w hich s e t s a m o r a l o b lig a tio n a p a r t f r o m a r u le of s k i l l o r c o u n s e l of p ru d e n c e . "D uty, done f o r th e s a k e of duty" e x p r e s s e s th e f o r m a lity r e q u i r e d of th is d is p o s itio n w hich a lo n e d is tin g u is h e s th e r e a l m of m o r a lity . T he m e r e c o n c e p tio n of the c a te g o r ic a l im p e r a tiv e as an a b s o lu te c o m m a n d ( i . e . , a s a law c o n ta in in g no r e s t r i c t i n g c o n d itio n s ) , le a d s 20 K ant to c o n clu d e th a t t h e r e is only one s u c h im p e r a tiv e , n a m e ly : " A c t only on th a t m a x im w h e re b y th o u c a n s t a t th e s a m e tim e w ill th a t it s h o u ld b e c o m e a u n iv e r s a l la w " ( G ru n d le g u n g , p . 47 ) . T h e m o r a l a g e n t is one who a c ts f r o m a n a u to n o m o u s w ill; a n a g e n t c o n c e iv e d a s a la w g iv e r unto h im s e lf . M o ra l d u tie s o r o b lig a tio n s a r e d e te r m in e d a s m o r a l only in s o f a r a s th e y c o n fo r m to, a n d a r e done ^ K an t a c tu a lly g iv es th r e e fo r m u la tio n s of th e c a te g o r ic a l i m p e r a tiv e know n a s th e f o r m u la of th e a u to n o m y of th e w ill, th e f o r m u la of a u n iv e r s a l law of n a tu r e , a n d th e f o r m u la of th e k in g d o m of e n d s . T h e f o r m u la of the a u to n o m o u s w ill c a n be c o n s id e r e d th e p r in c ip a l f o r m of the c a t e g o r i c a l im p e r a tiv e f o r th e p u r p o s e s of th is d is c u s s io n . 20 f r o m th e in te n tio n of, th e c a te g o r ic a l im p e r a tiv e . F u r t h e r e la b o r a tio n s of K a n t’s f o r m u la s f o r the c a te g o r ic a l im p e r a tiv e a n d d is c u s s io n of th e d u tie s to w a rd s s e l f a n d o th e r s w ould ta k e us p e r h a p s to o f a r a fie ld f r o m th e p o in t a t h a n d . K ant h a s th ro w n th e r e a l m of m o r a lity , an d in p a r t i c u l a r th e c o n c e p t of m o r a l o b lig a tio n , in to th e f r a m e w o r k of s t r i c t im p e r a t i v e s . T h e m o r a l ought im p o s e s a n e c e s s a r y o b lig a tio n a n d its lin g u is tic f o r m is s t r i c t l y im p e r a tiv a l. T h e r e h a s b e e n a d is tin c t s h if t in e m p h a s is f r o m th e A r is to te lia n c o n c e p tio n of v ir tu e a s a s t a te of c h a r a c t e r d i s p o s e d to c h o o se the m e a n , to th e K a n tia n p o s itio n th a t 1 1 V irtu e is th e s tr e n g th of th e m a n ’s m a x im in h is o b e d ie n c e to duty" ( M e ta p h y s ic s of M o r a l s , p . 2 4 1 ) . F o llo w e r s of K ant h a v e o fte n e m p h a s iz e d to o m u ch th e f o r m a l is m w hich p e r v a d e s th e G ru n d le g u n g an d h av e fa ile d to p a y s u ffic ie n t a tte n tio n to th e c o n te n t of the m a x im s of a c tio n w hich K ant e la b o r a te s in th e M e ta p h y s ic s of M o r a l s . It is th is n o tio n of f o r m a l is m , h o w e v e r, w hich h as m o s t in flu e n c e d th e p o s t- K a n tia n 21 d e o n to lo g ic a l e th ic a l th e o r i e s . ^ A " d e o n to lo g ic a l e th ic a l th e o r y " m a y be c o n s id e r e d in one s e n s e to be a d o c tr in e of m o r a l d u tie s . D e o n to lo g y is u s u a lly c o n s id e r e d a s o p p o se d to te le o lo g y in e th ic s ; th e d e o n to lo g ic a l p o in t of v iew b e in g th a t th e " o u g h t- to - b e - d o n e " o r " m o r a l ly rig h t" a c tio n c a n be d e te r m in e d w ithou t r e f e r e n c e to v a lu e th e o r y (the "g o o d , " e n d s, o r c o n s e q u e n c e s of th e a c tio n ). E x a m p le s of e th ic a l t h e o r i e s w hich c o n te n d th a t we d ir e c tly in tu ite o u r duty a r e to b e found in th e d e o n to lo g ic a l 21 Som e of th e p r in c ip le s w ith r e s p e c t to o b lig a tio n w hich K ant m e n tio n e d h a v e o c c u r r e d a g a in an d a g a in a s c e n t r a l i s s u e s in a tte m p ts to f o r m a liz e th e la n g u a g e of m o r a l s . K ant s ta te d in th e C ritiq u e of P u r e R e a s o n th a t, " N o th in g is m o r e r e p r e h e n s ib l e th a n to d e riv e th e la w s p r e s c r i b i n g w hat ou g h t to be done f r o m w hat is done" (A 319= B375 ) . H um e h a d a ls o m a d e m u c h of th e fa lla c y of s h iftin g f r o m " i s " to "o u g h t" p r o p o s itio n s in a lo g ic a l a r g u m e n t ( T r e a t i s e , Bk. 3 ) . O u r in v e s tig a tio n of th e r e c e n t a tte m p ts to a c c o u n t fo r o b lig a tio n s e n te n c e s w ill r e v e a l th e m a jo r im p o r ta n c e of th is p r in c ip le to a n y f o r m a l lo g ic of o b lig a tio n . In th e C ritiq u e of P r a c t i c a l R e a s o n K ant g iv e s a ta b le of th e c a te g o r ie s of F r e e d o m a n a lo g o u s to th e ta b le of c a t e g o r i e s of the p u r e u n d e rs ta n d in g g iv en in th e C r itiq u e of P u r e R e a s o n . T he c a t e g o r ie s o f F r e e d o m lis te d u n d e r M o d a lity a r e th e follow ing: T he p e r m i tt e d a n d th e fo rb id d e n . D uty a n d th e c o n tr a r y to d u ty . P e r f e c t an d i m p e r f e c t d u ty . ( C r itiq u e of P r a c t i c a l R e a s o n , p . 188) R e c e n t f o r m a l s y s te m s of " D e o n tic L o g ic " h a v e ta k e n a s t h e i r p r im itiv e s y m b o ls th e c o n c e p ts of th e p e r m itte d , th e fo rb id d e n , and in tu itio n is m of H. A. P ric h a rd * 8 M o r a l O b lig a tio n (O x fo rd , 1 959); S ir D av id R o s s 's T h e R ight a n d th e G ood ( OxforcT, 1930), and F o u n d a tio n s of E th ic s ( O x fo rd , 1939 ); an d E . F . C a r r i t t 's T he T h e o r y of M o ra ls ( L ondon, 1928 ) . 22 22 th e o b lig a to ry . T he c o n n e c tio n b e tw e e n th e s e p r i m i t iv e s a n d th e K a n tia n m o d a l c a te g o r ie s of f r e e d o m is e it h e r n ot n o tic e d o r s im p ly n o t m e n tio n e d by th e a u th o rs of th e s e s y s te m s . It is i n te r e s tin g to n o te th a t the p e r m i tt e d a n d the fo rb id d e n , a s m o d a l c a te g o r ie s of f r e e d o m , a r e a n a lo g o u s to p o s s ib ility an d im p o s s ib ility , th e m o d a l c a te g o r ie s of the u n d e rs ta n d in g a s g iv en in the T ab le of C a te g o r ie s ( C ritiq u e of P u r e R e a s o n , A80=B106 ) . T h is a n a lo g y p la y s a s ig n if ic a n t r o le in f o r m a l d e o n tic lo g ic . Von W rig h t’s f o r m a l s y s te m 23 b r in g s out the u s e fu ln e s s and lim ita tio n s of th is an alo g y , w hile A n d e r s o n e s ta b lis h e s a f o r m a liz e d r e la tio n s h ip b e tw e e n th e s e p r a c t i - 24 c a l a n d t h e o r e ti c a l m o d a litie s . In th e C r itiq u e of P r a c t i c a l R e a s o n K ant s t a t e d th a t " it is a l w ays in e v e r y o n e ’s p o w e r to s a tis f y th e c a te g o r ic a l c o m m a n d of m o r a lity " ( p . 150). A nd "w e c a n b e c a u s e o u r own r e a s o n r e c o g n iz e s th is a s its c o m m a n d and s a y s th a t we ought to do it" ( p . 309 ) . A. N. P r i o r e s ta b lis h e s th e K a n tia n p r in c ip le th a t ’th e ou g h t im p lie s c a n 1 22 g ee th e d is c u s s io n of th e s y s te m s of von W rig h t, R e s c h e r , P r i o r , an d A n d e r s o n in C h a p te r H I . 23 G e o rg H e n rik von W rig h t, "D e o n tic L o g ic ," M ind, 60;1-15, 1951. ^ A . R . A n d e rs o n , "A R e d u c tio n of D eo n tic L o g ic to A le th ic M o d al L o g i c ," M ind, 6 7 :1 0 0 -1 0 3 , 1958. 23 25 a s a p ro v a b le th e o r e m in a f o r m a l s y s t e m of d e o n tic lo g ic . P r o p o s itio n s of th is ty p e e s t a b l is h a r e la tio n s h ip b e tw e e n th e m o d a litie s of P r a c t i c a l R e a s o n (the d e o n tic m o d a litie s ) a n d th e m o d a litie s w h ich a r e c a te g o r ie s of th e u n d e rs ta n d in g . In c u r r e n t te r m in o lo g y th is m e a n s a r e la tio n s h ip b e tw e e n th e d e o n tic m o d a lity an d a le th ic m o d a l lo g ic . It fo llo w s, t h e r e f o r e , th a t an y f o r m a l s y s te m in w hich s u c h p ro p o s itio n s m a y o c c u r m u s t c o n ta in both d e o n tic an d th e a le th ic m o d a l c o n c e p ts p lu s th e r e q u i r e d r u le s of f o r m a tio n an d r u l e s of p ro o f. K ant a ls o m a k e s r e f e r e n c e to a s y llo g is m a s th e lo g ic a l f o r m of p r a c t i c a l r e a s o n i n g : th e d iv is io n of the a n a ly tic of p u r e p r a c t i c a l r e a s o n m u s t r e s e m b l e th a t of a s y llo g is m , n a m e ly , p ro c e e d in g f r o m th e u n i v e r s a l in th e m a jo r p r e m i s s (the m o r a l p r in c ip le ) , th ro u g h a m in o r p r e m i s s c o n ta in in g a s u b s u m p tio n of p o s s ib le a c tio n s ( a s good o r e v i l ) u n d e r th e f o r m e r , to th e c o n c lu s io n , n a m e ly th e s u b je c tiv e d e te r m in a tio n of th e w ill ( a n i n t e r e s t in th e p o s s ib le p r a c t i c a l good, and in th e m a x im fo u n d ed on i t ) . ( C ritiq u e of P r a c t i c a l R e a s o n , p . 219) It is d iffic u lt to d e te r m in e how c lo s e ly K an t in te n d e d th e p r a c t i c a l r e a s o n in g p r o c e s s to " r e s e m b l e " th e s y llo g is m . It is p e rtin e n t to n o te , h o w e v e r, th a t th e " m a j o r p r e m i s s " he s p e a k s of f a lls w ith in A pp en d ix D to T im e a n d M o d a lity (O x fo rd , 1957), p . 142. T h e t h e o r e m p ro v e n , in s y m b o ls is : O (p ) —> M (p ), i . e . , if an a c t is o b lig a to ry th e n it is p o s s ib le . 24 th e s c o p e of o u r c l a s s o f o b lig a tio n s e n t e n c e s . O b lig a tio n s e n t e n c e s , h o w e v e r d if f e r e n tly th e y m a y h a v e b e e n i n t e r p r e t e d , h a v e b e e n a d m itte d by A r i s t o t l e , S t. T h o m a s , a n d K a n t a s e l e m e n t s of i n f e r e n c e s w h ic h a r e in s o m e s e n s e lo g ic a l. T h e s e m a n t i c a l v a lu e s o f o b lig a tio n s e n t e n c e s p r e s e n t e d no d iffic u lty to A r i s t o t l e a n d S t. T h o m a s s i n c e th e y t r e a t e d o b lig a tio n s e n t e n c e s lik e o t h e r s e n t e n c e s in th e in d ic a tiv e m o o d { i.e . , a s c a p a b le of b e in g t r u e o r f a l s e ) . A r i s t o t l e a n d St. T h o m a s h a d a b r o a d c o n c e p tio n o f o b lig a tio n a n d of v i r t u e . W ith K a n t we g e t a c l e a r a n d f in a l d is t in c t io n b e tw e e n o b lig a tio n s w h ic h a r e s t r i c t l y m o r a l a n d o b lig a tio n s of a n y o t h e r ty p e . ’L a w , ’ 'd u ty , 1 a n d 'im p e r a tiv e * b e c o m e t h e k e y w o r d s of th e K a n tia n m o r a l f r a m e w o r k . A c tio n s c a n be c o n c e iv e d a s m o r a l l y o b lig a to r y o n ly i n s o f a r a s th e y a r e in a c c o r d a n c e w ith th e c a t e g o r i c a l i m p e r a t i v e , w ith th e on e u n c o n d itio n a l la w o f a w ill w h ic h a c t s a s la w g iv e r u n to i t s e l f , a n d a r e p e r f o r m e d w ith th e in te n tio n of d u ty f o r th e s a k e of d u ty . T h e f a c t th a t th e c a t e g o r i c a l i m p e r a t i v e is a c o m m a n d of r e a s o n , h o w e v e r, d o e s n ot d e s t r o y th e p o s s i b i l i t y o f s o m e lo g ic a l s t r u c t u r e in th e c o n s i d e r a t i o n of th e o b l i g a t o r i n e s s of a p a r t i c u l a r a c t. K a n t s u g g e s t s th a t th e p r a c t i c a l r e a s o n i n g p r o c e s s " r e s e m b l e s ” th a t of a s y l l o g i s m . T h e m o d a l c a t e g o r i e s o f th e p r a c t i c a l r e a s o n s u g g e s t a n a n a lo g y w ith th e m o d a l c a t e g o r i e s o f s p e c u la tiv e r e a s o n . In a n a tt e m p t to g iv e th e 25 lo g ic a l s t r u c t u r e of th e d e o n tic c a te g o r ie s it s e e m s r e a s o n a b le to in v e s tig a te th e p o s s ib ility of d e v e lo p in g a s y s te m w h ich is a n a lo g o u s to th e s y s te m s of c l a s s i c a l m o d a l lo g ic . P r o f e s s o r s v on W rig h t, P r i o r , an d A n d e rs o n a r e a m o n g th o s e who h a v e p u r s u e d th is a n a lo g y an d t h e i r w o rk th e r e f o r e m e r i t s e x te n s iv e c o n s id e r a tio n . K a n t's e m p h a s is upon th e im p e r a tiv e fu n c tio n of o b lig a tio n s e n te n c e s h a s te n d e d to d is c o u r a g e a tte n tio n to th e p r a c t ic a l s y l l o g is m o r o th e r p o s s ib le lo g ic a l s t r u c t u r e s o f p r a c t i c a l r e a s o n in g . M o ra l c o m m a n d s , no le s s th a n c o m m a n d s in g e n e r a l, c a n n o t be r e a d ily c o n c e iv e d to be e i t h e r t r u e o r f a ls e in th e s a m e s e n s e th a t in d ic a tiv e s e n te n c e s a r e s a id to be tr u e o r f a l s e . K an t, h im s e lf, d id n o t fin d th is a s tu m b lin g b lo c k to th e o p e ra tio n of p r a c t i c a l r e a s o n s in c e h e w as m o re c o n c e rn e d w ith th e p r in c ip le s of o b lig a tio n th a n w ith a r ig o r o u s lo g ic o f o b lig a tio n . H is c a te g o r ic a l im p e r a tiv e e x p r e s s e s th e c o n d itio n n e c e s s a r y fo r th e v e r y p o s s ib ility of m o r a l a c tio n , an d th e s u b s u m p tio n of p a r t i c u l a r a c tio n s u n d e r th is g e n e r a l r u le c e r ta in ly r e s e m b l e s th e s y llo g is tic a rg u m e n t e v e n th o u g h th e C h a p te r H I of th is d i s s e r t a t i o n is c o n c e rn e d w ith th o s e f o r m a l s y s te m s w h ich a tte m p t to a c c o u n t f o r th e lo g ic a l r e la tio n s in v o lv e d in th e d e o n tic m o d a litie s . V on W rig h t's s y s te m (" D e o n tic L o g ic " ) in p a r t i c u l a r , a p p e a r s a s a la n d m a r k in th e stu d y of th e lo g ic of o b lig a tio n s in c e h e is a p p a r e n tly th e f i r s t to a tte m p t to f o r m a liz e th e r e la tio n s b e tw e e n th e d e o n tic m o d a litie s of th e p e r m itte d , th e fo rb id d e n , a n d th e o b lig a to ry . 26 m a j o r p r e m i s e a n d th e c o n c lu s io n a r e in th e im p e r a tiv e m o o d . In th e A r i s t o t e l i a n a n d T h o m is tic f r a m e w o r k , o b lig a tio n s e n te n c e s w e r e c o n s id e r e d to b e d e s c r i p t iv e o f f a c t . T h a t a n a c tio n o u g h t to b e d o n e i s a ju d g m e n t o f th e i n te l le c t , d if f e r in g f r o m s p e c u la tiv e ju d g m e n ts o n ly in th a t i t is c o n c e r n e d w ith a c tio n s to be d o n e . T h e r e r e m a in s a m e a n in g fu l d is tin c tio n b e tw e e n ’’T h is o u g h t to b e d o n e " a n d "D o t h i s ! " In a d d itio n , n e i t h e r th e A r i s t o t e l i a n n o r T h o m is tic f r a m e w o r k r e q u i r e s o r r e c o g n iz e s a s h a r p d is tin c tio n b e tw e e n a r e a l m o f v a lu e th e o r y a n d a r e a l m o f m o r a l p h ilo s o p h y . V ir tu e c o n s i s t s in a c tin g in a c c o r d a n c e w ith th e n a tu r a l la w a s d i s c e r n e d b y th e n a tu r a l lig h t of r e a s o n . T h u s th e p r o b le m w h ic h w e f a c e in a c c o u n tin g f o r th e lo g ic a l r e l a t i o n s of o b lig a tio n s e n te n c e s i s s e e n to b e p e c u l ia r to m o d e r n ( p e r h a p s p o s t - K a n t i a n ) p h ilo s o p h y . If th e p r a c t i c a l s y llo g is m w a s in s o m e s e n s e a d e q u a te a s a lo g ic a l s c h e m a ti s m f o r a b r o a d e r c o n c e p tio n of o b lig a tio n , h o w e v e r, it m a y b e a d a p ta b le , w ith p r o p e r m o d if ic a tio n s , to th e m o d e r n c o n c e p tio n of o b lig a tio n . T h e c h ie f o b s tr u c tio n , f r o m th e m o d e r n p o in t o f v ie w , is th e la c k of a m e th o d f o r c o p in g w ith th e im p e r a tiv e m o o d . R e le v a n t b e g in n in g s of a lo g ic of o b lig a tio n h a v e b e e n fo u n d in th e w o rk s o f A r i s t o t le , S t. T h o m a s , a n d K a n t. T h e s e a r e n p t th e o n ly p h ilo s o p h e r s w ho h a v e c o n c e r n e d th e m s e lv e s w ith th e lo g ic a l a s p e c ts of p r a c t i c a l r e a s o n in g , b u t we c a n d i s c e r n in t h e i r w o rk s th e 27 m a j o r t r e n d s w h ic h h a v e b r o u g h t a b o u t th e s e a r c h f o r a lo g ic of o b lig a tio n . In th e tw e n tie th c e n tu r y t h e r e h a s b e e n a r e v i v a l of i n t e r e s t in th e n a tu r e of p r a c t i c a l i n f e r e n c e s . T h e c o m p le x ity o f th e m o d e r n p r o b le m h a s b e e n s e e n to b e , in p a r t , d u e to th e K a n tia n f o r m u la tio n o f o b lig a tio n s e n t e n c e s a s i m p e r a t i v e s . It is n o t s u r p r i s i n g th a t o b lig a tio n s e n t e n c e s h a v e b e e n s u b s u m e d u n d e r th e c l a s s o f i m p e r a tiv e s e n t e n c e s , a n d th e s e a r c h f o r a lo g ic o f o b lig a tio n h a s s o m e t im e s b e e n a s u b o r d in a te p a r t o f th e s e a r c h f o r a lo g ic o f i m p e r a t i v e s . T h o s e f o r m a l i z e d s y s t e m s w h ic h h a v e b e e n p r o p o s e d to s e r v e a s a lo g ic of o b lig a tio n w ill be e x a m in e d in th e fo llo w in g tw o c h a p t e r s . T h is i n v e s tig a tio n w ill r e v e a l th e a d d itio n a l p r o b le m s in v o lv e d in th e d e v e lo p m e n t o f a lo g ic of o b lig a tio n . T h e m e a s u r e of s u c c e s s to b e m e t w ith in r e s o l v in g t h e s e p r o b le m s w ill c o n s titu te a n e f f e c tiv e a n s w e r to th e q u e s tio n : " is t h e r e a lo g ic o f o b lig a tio n ? " C H A P T E R H IM P E R A T IV E L O G IC S A tte m p ts to p r e s e n t f o r m a l i z e d s y s te m s f o r th e h a n d lin g of th e lo g ic o f o b lig a tio n h a v e b e e n fe w e n o u g h to p e r m i t a n a l y s i s o f th e m a j o r o f f e r in g s w ith in th e s c o p e of th e p r e s e n t in v e s tig a tio n . T h e s y s te m s a v a ila b le in th e e x is tin g l i t e r a t u r e m a y b e d iv id e d in to tw o g e n e r a l ty p e s , e a c h b e in g d e fin e d in t e r m s of i t s b a s i c a p p r o a c h to th e p r o b le m s in v o lv e d . T h e f i r s t ty p e a tt e m p t s to in c lu d e th e lo g ic of o b lig a tio n a s a p a r t o f a g e n e r a l lo g ic of i m p e r a t i v e s o r d e m a n d s . T h e s e c o n d ty p e d e a ls m o r e e x c lu s iv e ly w ith th e c o n c e p t of o b lig a tio n a n d w ith th e r e l a t e d c o n c e p ts o f p r o h ib itio n a n d p e r m i s s i o n . It w ill b e c a lle d th e lo g ic of n o r m a t iv e s o r d e o n tic l o g i c . T h e b a s ic d iv is io n h e r e in d ic a te d f i t s in w e ll w ith a c h r o n o lo g ic a l s u r v e y s in c e th e s y s te m s p r i o r to 1951 ( w ith a fe w e x c e p tio n s ) a r e g e n e r a l l y of th e f i r s t ty p e , w h e r e a s th o s e fo llo w in g ( a n d in c lu d in g ) G e o r g H e n r ik v o n W r i g h t s " D e o n tic L o g ic " 1 a r e g e n e r a l l y o f th e s e c o n d ty p e . 1 M in d , 6 0 :1 -1 5 , 1951; r e p r i n t e d in G . H. v o n W rig h t, L o g ic a l S tu d ie s ( L o n d o n , 1 9 5 7 ), p p . 5 8 -7 4 . 28 29 P e r h a p s th e f i r s t of th e m o d e r n f o r m a l iz e d s y s te m s in te n d e d 2 to s e r v e a s a lo g ic o f o b lig a tio n is th a t d e v e lo p e d by E r n s t M a lly . J u r g e n J ^ r g e n s e n ^ r e f e r s to M a l ly ^ " L o g ik d e s W ille n s " a s a " lo g ic o f i m p e r a t i v e s , " 4 th u s p la c in g it u n d e r th e f i r s t of th e tw o g e n e r a l ty p e s of s y s te m s d is tin g u is h e d a b o v e . M a lly h im s e lf a ls o u s e d th e t e r m * D e o n tik l in c o n n e c tio n w ith h is s y s te m . T h is t e r m w ill r e c e iv e f u r t h e r c o n s id e r a tio n in th e d i s c u s s io n of n o r m a tiv e lo g ic s b u t m a y s e r v e now a s in d ic a tin g th a t th e d is tin c tio n b e tw e e n im p e r a tiv e a n d n o r m a tiv e lo g ic s is b a s e d o n th e a p p ro a c h fo llo w e d . F o r b o th , h o w e v e r, a n i n t e r p r e t a t i o n a s a lo g ic of o b lig a tio n ( in te n d e d o r n o t) m a y b e g iv e n . T h e b a la n c e of th e p r e s e n t c h a p te r w ill be d e v o te d to a d i s c u s s i o n o f th o s e s y s t e m s w h ic h m a y b e c h a r a c t e r i z e d a s im p e r a t i v e lo g ic s . T h e c a s e of th e lo g ic o f n o r m a tiv e s ( d e o n tic lo g ic ) w ill be c o n s id e r e d in d e ta il in th e n e x t c h a p te r . ^ G r u n d g e s e tz e d e s S o lle n s , E le m e n te d e r L o g ik d e s W ille n s ( G r a z , 1926 ) . ^ " I m p e r a ti v e s a n d L o g ic , " E r k e n n tn is , 7 :2 8 8 -2 9 6 , 1 9 3 8 . 4 J o r g e n s e n , p . 290 . 30 1. A lf R o s s a n d th e u P r a c t i c a l I n f e r e n c e '1 5 T h e in v e s tig a tio n s of A lf R o s s p ro v id e a n e x c e lle n t s t a r t i n g p o in t f o r th e s tu d y o f im p e r a tiv e lo g ic s b e c a u s e R o ss a n a ly z e s th e r e s u l t s of th e im p o r ta n t s y s te m s p r i o r to h is own and b a s e s h is c o n c lu s io n s on th is a n a ly s is . S u b s e q u e n t d e v e lo p m e n ts in th e lo g ic of im p e r a tiv e s a ls o r e f e r b a c k to R o s s ’s w o rk . We m a y , th e r e f o r e , u se h is a r t i c l e a s a p o in t of r e f e r e n c e f o r o u r c o m p a r is o n of th e p r o p o s e d lo g ic s of im p e r a tiv e s . R o ss c o n c e iv e s im p e r a tiv e s e n te n c e s to be n o n d e s c r ip tiv e b u t, n e v e r th e le s s , m e a n in g fu l. T h e fu n c tio n o f a n im p e r a tiv e s e n te n c e is to c o n v e y a d e m a n d f o r a c tio n : " ’im p e r a tiv e , 1 a s u s e d h e r e , m e a n s a s e n te n c e , th e o b je c t of w hich is to e x p r e s s a n im m e d ia te d e m a n d f o r a c tio n , but n o t to d e s c r ib e a fa c t" ( R o s s , p . 3 1 ) . T h is c o n c e p t of im p e r a tiv e s is e x p a n d e d to in c lu d e a ll s e n te n c e s w h ich c o n ta in a n im m e d ia te d e m a n d f o r a c tio n , w h e th e r th e y a r e lin g u is tic a lly in th e im p e r a tiv e m o o d o r n o t. F o r a ls o lin g u is tic a lly in d ic a tiv e s e n te n c e s o f " d u ty " an d o th e r f o r m s of " r i g h tn e s s " w ith r e g a r d to a c tio n , c o n ta in , a c c o rd in g to t h e i r m e a n in g , an im m e d ia te d e m a n d fo r a c tio n . T h e y s h o u ld be in c lu d e d in th e d e fin itio n , b e c a u s e in s p ite of " im p e r a tiv e s an d L o g ic ," P h ilo s o p h y of S c ie n c e , 1 1 :3 0 -4 6 , J a n u a r y 1944. 31 t h e i r lin g u is tic a lly in d ic a tiv e m o o d , th e y a p p e a r e p is te m o lo g i- c a lly to c o n ta in n o d e s c r ip tio n of a f a c t, a n d c o n s e q u e n tly g iv e r i s e to th e s a m e p r o b le m of t h e i r r e l a ti o n to lo g ic . ( R o s s , p p . 3 1 -3 2 ) S in c e th is d e fin itio n in t e r m s of " d e m a n d f o r a c tio n " in c lu d e s b o th im p e r a tiv e s in t h e i r n o r m a l lin g u is tic f o r m a n d im p e r a tiv e s in th e in d ic a tiv e f o r m , t h e r e c a n b e n o c l e a r d is tin c tio n f o r R o s s b e tw e e n n o r m a tiv e s a n d im p e r a tiv e s s o f a r a s an y s y s te m of lo g ic a l in f e r e n c e m a y be r e la te d to th e m . H e n c e , th e s y s te m s w h ic h h e d i s c u s s e s ( th e lo g ic of s a tis f a c tio n an d th e lo g ic of v a lid ity ) in c lu d e w ith o u t d is c r im in a tio n b o th n o r m a tiv e s an d im p e r a tiv e s u n d e r th e one g e n e r a l h e a d in g of a lo g ic o f im p e r a tiv e s . T h e p r o b le m of d e v e lo p in g a lo g ic f o r i m p e r a tiv e s is s e e n b y R o s s to a r i s e f r o m a d ile m m a s ta te d by J o r g e n s e n . ® T h e f i r s t h o rn of th e d ile m m a is fo u n d in th e f a c t th a t in o r d in a r y lo g ic a l in f e r e n c e s th e c o n c lu s io n h a s th e s a m e ty p e of s e m a n tic a l v a lu e r e f e r e n t a s th e p r e m i s e s f r o m w h ich i t is d e riv e d . F o r e x a m p le , if ( s t a t e m e n t ) S„ a ® J o r g e n s e n d e v e lo p s th e f i r s t h o rn of h is d ile m m a f r o m an a rg u m e n t of H e n ri P o i n c a r e ’s ( D e rn lfe re s P e n a t e s , p p . 2 2 4 - 2 2 5 ) . J o r g e n s e n ’s s u m m a r y of P o i n c a r e 's a rg u m e n t is a s fo llo w s: " A ll s c ie n tif ic s e n te n c e s a r e in th e in d ic a tiv e m o o d , w h e r e a s a ll m o r a l s e n te n c e s a r e in th e im p e r a tiv e m o o d . But f r o m s e n te n c e s in th e in d ic a tiv e m o o d o n ly s e n te n c e s w h ich a r e a ls o in th e in d ic a tiv e m o o d c a n be d e r iv e d by lo g ic a l in f e r e n c e . T h e r e f o r e it is im p o s s ib le to in f e r a m o r a l s e n te n c e f r o m a s c ie n tif ic s e n te n c e , h o w e v e r m u c h th e c o n c e p ts in v o lv e d m a y be m a n ip u la te d ." ( " I m p e r a t i v e s a n d L o g ic ," E r k e n n tn is , 7 :2 8 8 . ) 32 is lo g ic a lly i n f e r r e d f r o m ( s t a t e m e n t ) , th e n S 2 is t r u e if S j n is t r u e . T h u s a l l th e p a r t s ( p r e m i s e s a n d c o n c lu s io n s ) of a lo g ic a l in f e r e n c e m u s t b e c a p a b le of b e in g t r u e o r f a l s e . B u t i t i s o b v io u s t h a t im p e r a t i v e s c a n b e n e it h e r t r u e n o r f a l s e . T h e q u e s tio n a s to w h e th e r " C lo s e th e d o o r ! " o r " B e q u i e t ! " a r e t r u e o r f a ls e h a s no m e a n in g . T h e r e f o r e i t is q u ite im p o s s ib le f o r a n im p e r a tiv e to be e i t h e r a p r e m i s e o r a c o n c lu s io n of a lo g ic a l in f e r e n c e . T h e s e c o n d h o r n of th e d ile m m a a r i s e s w hen we r e c o g n iz e th a t c e r t a i n im m e d ia te ly e v id e n t in f e r e n c e s c a n b e d ra w n in c a s e s w h e re s o m e o r a ll o f th e c o m p o n e n ts a r e i m p e r a t i v e s . A s a n e x a m p le of th is c o n s id e r th e fo llo w in g : K e e p y o u r p r o m is e s T h is is a p r o m is e of y o u r s T h e r e f o r e : K e ep th is p r o m is e .® R o s s m a in ta in s th a t in f e r e n c e s o f th is f o r m " m u s t be c o n s id e r e d ty p ic a l of th e w ay in w h ic h r e a s o n in g ta k e s p la c e in p r a c t i c a l life a n d in th e s c i e n c e s o p e r a tin g w ith n o r m a tiv e e x p r e s s io n s , e s p e c ia lly th e s c ie n c e o f la w " ( p . 3 2 ) . H e c a lls a n y in f e r e n c e w h ic h h a s a m o n g i t s ^ R e f e r e n c e h e r e i s to o r d i n a r y in d ic a tiv e lo g ic a l s y s te m s b a s e d o n th e la w o f c o n tr a d ic tio n a n d n o t to m o d a l o r m u lti- v a lu e d l o g i c s . ® B o th R o s s ( p . 32 ) a n d J o r g e n s e n ( " i m p e r a t i v e s a n d L o g ic , " E r k e n n tn is , 7 :2 9 0 ) u s e th is e x a m p le a n d b o th c o n s id e r it a s v a lid a s a n y in d ic a tiv e lo g ic a l s y llo g is m . 33 g c o m p o n e n ts o n e o r m o r e i m p e r a t i v e s a p r a c t i c a l i n f e r e n c e . T h e c h ie f p r o b le m in d e v e lo p in g a lo g ic o f i m p e r a t i v e s i s to g iv e a n a d e q u a te a c c o u n t of th e c h a r a c t e r i s t i c s o f a p r a c t i c a l i n f e r e n c e . A d o p tin g a s u g g e s tio n m a d e b y W a lte r D u b is la v , 10 J o r g e n s e n p r o p o s e s a r e s o l u t i o n f o r th e d ile m m a d e s c r i b e d a b o v e . H e s u g g e s ts t h a t e v e r y i m p e r a t i v e c a n be r e l a t e d to a n in d ic a tiv e w h ic h e x p r e s s e s th e " th e m e o f d e m a n d " of th e i m p e r a t i v e . If a s e n te n c e is a n i m p e r a tiv e , th e n , b y d e fin itio n , it m u s t e x p r e s s a d e m a n d f o r a c tio n a n d m u s t c o n ta in , a t l e a s t im p lic itly , a s t a te m e n t o f th e n a tu r e of th e th in g d e m a n d e d . T h e th e m e o f d e m a n d c o n s i s t s of a c e r t a i n f a c t, o r a s t a t e o r a n a c tiv ity , w h ic h i s a s s u m e d n o t to e x i s t a t th e m o m e n t o f th e d e m a n d , b u t th e r e a l i z a t i o n of w h ic h is r e q u e s t e d by th e d e m a n d th r o u g h th e a c tio n o f th e o n e to w h o m th e d e m a n d is d i r e c t e d . ( R o s s , p . 3 3 ) T h e i m p e r a t i v e , ’P e t e r , c lo s e th e d o o r, ' w ill h a v e a s i t s th e m e of d e m a n d th e in d ic a tiv e s e n te n c e , ’P e t e r c lo s e s th e d o o r . * S im ila r ly , f o r e v e r y i m p e r a t i v e s e n te n c e , 1^ , t h e r e i s a c o r r e s p o n d in g in d ic a tiv e s e n te n c e , S j , a n d c o n v e r s e ly . T h is r e l a ti o n s h i p is e x p r e s s e d 9 R o s s ’s fo o tn o te 6 o n p . 33 . T h e s i m i l a r i t y b e tw e e n R o s s 's t e r m ’p r a c t i c a l in fe re n c e * a n d th e p r a c t i c a l s y l l o g is m of A q u in a s a n d A r i s t o t l e s h o u ld n o t p a s s u n n o tic e d . 10 In " Z u r U n b e g rf ln d b a rk e it d e r F o r d e r u n g s s a t z e , " T h e o r ia , 3 :3 3 0 -3 4 2 , 1937. R o s s r e f e r s to t h is a s th e D u b i s l a v - J o r g e n s e n s o lu tio n . 34 in th e fo rm u la : I j —><— ! ( ) . ** W ith th e e s ta b lis h m e n t of th is r e la tio n s h ip b e tw e e n im p e r a tiv e a n d in d ic a tiv e s e n te n c e s , J o r g e n s e n b e lie v e d th a t h is d ile m m a h ad b e e n r e s o lv e d . T he in d ic a tiv e s a r e s u b je c t to th e o r d in a r y lo g ic a l tr e a tm e n t, a n d by r e f e r r i n g e a c h in d ic a tiv e b a c k to its c o rr e s p o n d in g im p e r a tiv e we o b ta in a n in d ir e c t lo g ic f o r im p e r a tiv e s . T h u s he c o n c lu d e s: T h e o r d in a r y r u le s of lo g ic b e in g v a lid f o r th e in d ic a tiv e s e n te n c e s w hich c a n be d e riv e d f r o m th e im p e r a tiv e o n e s , and no s p e c ific r u le s f o r th e im p e r a tiv e s b e in g know n ( u n le s s it s h o u ld be th e ru le g o v e rn in g th e d e riv a tio n of th e in d ic a tiv e s e n te n c e f r o m th e im p e r a tiv e o n e ) th e r e s e e m s to be no r e a s o n f o r, in d e e d h a rd ly a n y p o s s ib ility of, c o n s tr u c tin g a s p e c if ic " lo g ic of im p e r a tiv e s . " ( J o r g e n s e n , p . 296 ) T o th is s o lu tio n R o ss r a i s e s tw o o b je c tio n s . F i r s t , th e p r o c e d u re d e s c r ib e d by J o r g e n s e n d o es not go f a r en o u g h . J o r g e n s e n o n ly m e n tio n s c o n c lu s io n s f r o m one im p e r a tiv e p r e m is e and y e t, f r o m th e e x a m p le s of im p e r a tiv e s y llo g is m s g iv en , it is a p p a re n t th a t th e r e m u s t be so m e in d ic a tio n of a w ay f o r h a n d lin g c o n c lu s io n s w h ich f o l low e ith e r f r o m tw o im p e r a tiv e s o r f r o m an im p e r a tiv e an d a n T he sy m b o l 1—> < — ' is to be tr a n s la te d 'i f a n d o n ly if, ' e x p re s s in g th e r e la tio n s h ip of m a te r ia l e q u iv a le n c e b e tw e e n a n te c e d e n t an d c o n se q u e n t. T h e e x c la m a tio n p o in t, 1 ! 1, w ill be u s e d a s a n im p e r a tiv e o p e r a to r an d m ay be t r a n s la te d ’it is c o m m a n d e d t h a t . ' T h u s, if S* is i n te r p r e te d a s th e in d ic a tiv e s e n te n c e ‘T h e d o o r i s c l o s e d ,1 th e n ! o r I j a r e b o th i n te r p r e t e d a s th e im p e r a tiv e ’C lo se th e d o o r! * o r ’It is c o m m a n d e d th a t th e d o o r be c lo s e d . ’ 35 in d ic a tiv e . S e c o n d ly , e v e n if J o r g e n s e n 's p r o c e d u r e w e r e c o m p le te , i t s t i l l w o u ld n o t t e l l u s w h a t i s m e a n t b y i n f e r r i n g a n i m p e r a t i v e f r o m o n e o r m o r e g iv e n i m p e r a t i v e s ; th e d ile m m a , t h e r e f o r e , r e - 12 m a in s u n r e s o lv e d . In o r d e r to u n d e r s ta n d fu lly t h is l a t t e r c r i t i c is m , w e m u s t c o n s i d e r w h a t J o r g e n s e n 's s o lu tio n a c tu a lly in v o lv e s . G iv e n a n i m p e r a t i v e s e n t e n c e , 1^ , J o r g e n s e n g iv e s u s a r u l e o f t r a n s f o r m a t i o n w h ic h e n a b le s u s to c o n s t r u c t a c o r r e s p o n d in g in d ic a tiv e s e n t e n c e , S j . B y th e o r d i n a r y r u l e s o f d e d u c tio n w e m a y i n f e r th e in d ic a tiv e s e n te n c e , S 2 , f r o m . T h e n , by o u r r u l e o f t r a n s f o r m a t i o n , we c a n c o n s t r u c t th e im p e r a t i v e , I 2 , w h ic h c o r r e s p o n d s to S 2 . T h u s w e h a v e r u l e s w h ic h p e r m i t u s to m a k e a t r a n s i t i o n f r o m Ij, to I 2 ; b u t R o s s a s k s f o r th e m e a n in g o f th is t r a n s i t i o n . W e h a v e a m e th o d f o r d e te r m in in g w h e th e r Ig fo llo w s f r o m I j b u t we h a v e n o t c l a r i f i e d a t a ll w h a t it m e a n s to s a y th a t I 2 fo llo w s f r o m I j . R o s s in d ic a te s tw o p o s s ib le w a y s in w h ic h th e d ile m m a in q u e s tio n m a y b e m e a n in g f u lly r e s o lv e d : (1) by e x te n d in g th e c o n c e p t o f lo g ic a l i n f e r e n c e to in c lu d e th e p r a c t i c a l i n f e r e n c e s ( t h o s e i n v o lv in g a t l e a s t o n e i m p e r a t i v e ); o r (2) b y s h o w in g th a t th e p r a c t i c a l s y l l o g is m s a r e o n ly a p p a r e n t l y lo g ic a l ( i. e . , th a t th e y a r e p s e u d o - * ^ R o s s , p . 34 . 36 lo g ic a l) . In c o n n e c tio n w ith ( 1 ), R o s s o b s e r v e s th a t th e c o n c e p t o f lo g ic a l in f e r e n c e is a tta c h e d to th e d e d u c tiv e lo g ic a l s y s te m a s s u c h , a n d n o t to an y s p e c ia l in te r p r e t a t i o n of th e s y s te m . T h e lo g ic a l e le m e n t, t h e r e f o r e , i s n o t n e c e s s a r i l y c o n n e c te d w ith th e v a lu e s t r u th an d f a ls ity ; a n d it is not o n th is a c c o u n t th a t im p e r a tiv e s a r e to be e x c lu d e d f r o m b e in g p a r t s of lo g ic a l in f e r e n c e s . If a n a n a lo g o u s s e t o f v a lu e s c a n be d e te r m in e d f o r im p e r a tiv e s e n te n c e s ( R o ss s u g g e s ts v a lid ity a n d in v a lid ity in p la c e of t r u t h a n d f a ls ity ) , a n d if th e s e v a lu e s a r e o b je c tiv e in th e s a m e s e n s e a s th e v a lu e s of t r u th a n d f a ls ity a r e o b je c tiv e , th e n p o s s ib ility (1) is f e a s ib le . . . . if t h e r e b e a n y s e n s e in a s c r ib in g o b je c tiv e v a lid ity and in v a lid ity to im p e r a tiv e s o r to a c e r t a i n g ro u p of im p e r a t i v e s , th e n it i s p o s s ib le to i n t e r p r e t th e lo g ic a l d e d u c tiv e s y s te m a s b e in g a p p lic a b le to th e s e im p e ra tiv e s T T h e lo g ic a l d e d u c tio n o f I 2 f r o m I* th e n m e a n s th a t I 2 h a s o b je c tiv e v a lid ity in c a s e I i h a s o b je c tiv e v a lid ity . ( R o s s , p . 3 5 ) T h e n e c e s s a r y c o n d itio n f o r p o s s ib ility (1) to be a c c e p ta b le a s a s o lu tio n is , t h e r e f o r e , th e d e te r m in a tio n of s o m e p r o c e s s of " le g itim a tio n " f o r im p e r a tiv e s , a n a lo g o u s to th e p r o c e s s o f v e r i f i c a tio n f o r th e tr u th - v a lu e of in d ic a tiv e s . B u t "N o b o d y h a s e v e r s u c c e e d e d in d e m o n s tr a tin g i r r e f u ta b ly a p r o c e s s of le g itim a tio n f o r th e o b je c tiv e a s c e r ta in m e n t o f th e v a lid ity of a n im p e r a tiv e " ( R o s s , p . 36 ) . T h e n e c e s s a r y c o n d itio n h a s not b e e n fu lfille d . F o r th e p r e s e n t, t h e r e f o r e , R o ss g iv e s up th e n o tio n of in c lu d in g th e p r a c t ic a l 37 in f e r e n c e u n d e r a n e x te n d e d c o n c e p t of lo g ic a l in f e r e n c e . O th e r p h ilo s o p h e r s , h o w e v e r, in d e v e lo p in g lo g ic a l s y s te m s f o r i m p e r a tiv e s , do a tte m p t to e s t a b l is h a le g itim a tio n p r o c e s s f o r o b ta in in g o b je c tiv e ly v a lid i m p e r a tiv e s . T h o m a s S to r e r , fo r e x a m p le , in " T h e L o g ic of V alu e I m p e r a t i v e s ,1 1 s u g g e s ts 0 , 1 , an d 2 a s th e v a lu e c o u n te r s in a th r e e - v a lu e d d e d u c tiv e s y s te m f o r i m p e r a tiv e s . T h e in te r p r e t a t i o n w h ich S to r e r h a s in m in d f o r h is v a lu e c o u n te r s is th a t th e y s h o u ld r e p r e s e n t m o r a l, a m o r a l, and im m o r a l, r e s p e c tiv e ly . B ut th o s e a u th o r s w ho h a v e a p p ro a c h e d th e p r o b le m f r o m th e p o in t of v ie w o f a lo g ic of n o r m a tiv e s a ls o s u g g e s t o b je c tiv e le g itim a tio n p r o c e s s e s a n d a r e a b le to r e t a in a tw o -v a lu e d ( t r u t h and f a l s it y ) lo g ic s in c e th e lin g u is tic a lly in d ic a tiv e n o r m a tiv e s c a n be c o n s id e r e d a s b e in g e it h e r tr u e o r f a ls e . P o s s ib ility ( 1 ), h o w e v e r, h a s b e e n s e t a s id e by R o s s , who m u s t now d e a l w ith p o s s ib ility ( 2 ) - - th a t of i n te r p r e t i n g p r a c t i c a l i n f e r e n c e s a s b e in g p s e u d o - lo g ic a l. He d is c u s s e s tw o w ay s in w hich th is s e c o n d p o s s ib ility m ig h t be r e a liz e d , n a m e ly , a lo g ic o f s a tis f a c tio n a n d a lo g ic o f s u b je c tiv e v a lid ity . A n in te r p r e t a t i o n of im p e r a tiv e s ^ P h ilo s o p h y of S c ie n c e , 1 3 :2 5 -4 0 , 1946. S t o r e r 's s y s te m w ill be g iv e n m o re d e ta ile d c o n s id e r a tio n in th e fin a l p o r tio n of th is c h a p te r . 14 T h e n o r m a tiv e a p p ro a c h w ill be d is c u s s e d a t le n g th in C h a p te r I I I . 38 in t e r m s o f a lo g ic o f s a t i s f a c t i o n h a s b e e n e x p lo r e d by H o f s ta d te r a n d M c K in s e y in t h e i r p a p e r , " O n th e L o g ic o f I m p e r a t i v e s . In a c c o r d a n c e w ith th is i n t e r p r e t a t i o n , a n i m p e r a t i v e is s a i d to be " s a t i s f i e d " w h e n th e c o r r e s p o n d in g in d ic a tiv e s e n te n c e , d e s c r i b i n g th e th e m e of d e m a n d o f th e i m p e r a t i v e , is t r u e . A n i m p e r a t i v e is s a i d to be " n o n s a t is f ie d " w h e n th e c o r r e s p o n d in g in d ic a tiv e s e n te n c e i s f a l s e . R o u g h ly , w e u n d e r s ta n d a n i m p e r a t i v e to be s a t i s f i e d i f w h a t is c o m m a n d e d i s th e c a s e . T h u s th e f i a t " L e t th e d o o r b e c l o s e d ! " is s a t i s f i e d i f th e d o o r is c lo s e d . It w ill be s e e n th a t th e s a t i s f a c t i o n of a n i m p e r a t i v e is a n a lo g o u s to th e t r u t h o f a s e n t e n c e . T h e c o n n e c tiv e s y m b o ls w h ic h w e in tr o d u c e l a t e r m a y , o n t h e i r a n a lo g y w ith th e t r u t h - f u n c tio n s of th e c a lc u lu s o f s e n t e n c e s , b e th o u g h t of a s s a t i s - f a c tio n - f u n c tio n s o f i m p e r a t i v e s . ( H o f s t a d t e r a n d M c K in s e y , p . 4 4 7 ) U s in g th is n o tio n o f s a t i s f a c t i o n it is p o s s ib le to c o n s t r u c t c o r r e s p o n d in g in d ic a tiv e s e n te n c e s f o r a n y g iv e n i m p e r a t i v e s a n d , f u r t h e r , to c o n s t r u c t n e g a tio n s , c o n ju n c tio n s , d is ju n c tio n s , a n d i m p l i c a ti o n - s e n t e n c e s f r o m t h e s e i n d ic a t i v e s . T h e l a t t e r m a y b e c o m b in e d w ith a n y in d ic a tiv e s e n t e n c e s ( w h e th e r d e r iv e d f r o m i m p e r a t i v e s o r n o t ) to o b ta in lo g ic a l i n f e r e n c e s . T h e c o n c lu s io n s th u s d e r i v e d m a y th e n be t r a n s f o r m e d b a c k in to i m p e r a t i v e s e n t e n c e s . ^ A . H o f s ta d te r a n d J . C . C . M c K in s e y , " O n th e L o g ic of I m p e r a t i v e s , " P h ilo s o p h y o f S c ie n c e , 6 :4 4 6 -4 5 7 , 1 9 3 9 . 39 16 T h e fo llo w in g e x a m p le d e m o n s tr a te s th is p r o c e d u r e . G iv e n 1^ : C lo s e th e d o o r! C o r r e s p o n d in g S j : T h e d o o r i s c lo s e d . N e g a tin g S j w e o b ta in S 2 : T h e d o o r is n o t c lo s e d . C o r r e s p o n d in g I 2 : D o n o t c lo s e th e d o o r! O u r r u l e s t e l l us th a t 1^ is s a t i s f i e d if i s t r u e . B ut if is t r u e , th e n Sg m u s t be f a ls e ( b y th e o r d i n a r y p r in c ip le of n o n c o n tr a d ic tio n f o r in d ic a tiv e s e n te n c e s ) a n d , h e n c e X 2 w o u ld be n o n s a t i s fie d . T h e p r o c e d u r e of r e la tin g i m p e r a t i v e s to c o r r e s p o n d in g in d ic a tiv e s , a s d e r iv e d f r o m th e D u b is la v - J o r g e n s e n p a p e r s , h a s th u s b e e n i n t e r p r e t e d by H o f s ta d te r a n d M c K in se y a s a lo g ic o f s a t i s f a c t i o n - fu n c tio n s . R o s s c a u tio n s , h o w e v e r, th a t th is i n t e r p r e t a t i o n " i s n o t th e o n ly a n d p r e s u m a b ly n o t e v e n th e m o s t 'n a t u r a l 1 a n a lo g y to th e t r u th of th e in d ic a tiv e " ( R o s s , p . 37, fo o tn o te 1 0 ) . T h e p r i n c i p a l o b je c tio n w h ic h R o s s b r in g s a g a in s t th e H o f s ta d te r - M c K in s e y i n t e r p r e t a t i o n is th a t it c o m p le te ly i s o l a t e s th e im p e r a tiv e e le m e n t. T h e lo g ic a l e le m e n t is a tta c h e d s o le ly to th e in d ic a tiv e s e n te n c e s e x p r e s s in g th e th e m e of d e m a n d . T o o v e rc o m e th is c o m p le te is o la tio n of th e im p e r a tiv e e le m e n t, H o f s ta d te r a n d M c K in s e y c o n c lu d e th a t th e in d ic a tiv e , , s t r i c t l y im p lie s its c o r - 1 fi T h e e x a m p le g iv e n is a n a d a p ta tio n o f th e one g iv e n by R o s s o n p . 37 . 40 17 r e s p o n d in g im p e r a t i v e , I j . T h is , h o w e v e r, m a k e s a n y s p e c i a l i m p e r a t i v e - s e n s e c o m p le te ly s u p e r f lu o u s . T h u s , in th e e x a m p le g iv e n a b o v e , to s a y th a t th e d o o r i s c lo s e d is e q u iv a le n t to s a y in g t h a t th e im p e r a tiv e , " C lo s e th e d o o r ! " h a s b e e n s a t i s f i e d . B u t th is i n t e r p r e t a t i o n d e p r iv e s a n y d i r e c t p r a c t i c a l in f e r e n c e o f e v e n a p s e u d o - lo g ic a l s t a t u s . T h e fo llo w in g is a n a d a p ta tio n of a n e x a m p le g iv e n by R o s s ( p . 38 ) , w h ic h p o in ts up th e in a d e q u a c y of th e H o f s ta d te r - M c K in s e y i n t e r p r e t a t i o n of s a t is f a c ti o n - f u n c t i o n s . G iv e n 1^ : S lip th e l e t t e r in to th e l e t t e r - b o x ! C o r r e s p o n d in g S j : T h e l e t t e r is s lip p e d in to th e l e t t e r - b o x . F r o m w e v a lid ly i n f e r S 2 : E i t h e r th e l e t t e r is s lip p e d in to th e l e t t e r - b o x o r it is b u r n e d . C o r r e s p o n d in g I g : E it h e r s l i p th e l e t t e r in to th e l e t t e r - b o x o r b u r n it! F o llo w in g th e s a tis f a c tio n - f u n c tio n i n t e r p r e t a t i o n , I 2 is v a lid ly i n f e r r e d f r o m . If I i is s a t i s f i e d , th e n S j is t r u e ; if is t r u e , th e n S 2 is t r u e ; b u t if S 2 i s t r u e , th e n I 2 is s a t i s f i e d . B u t i t is o b v io u s ( a p a r t f r o m th e s a tis f a c tio n - f u n c tio n i n t e r p r e t a t i o n ) th a t I * ^ R o s s , p . 38 . K a r l M e n g e r s h o w s t h a t M a lly 's s y s t e m le d to th e s a m e c o n c lu s io n ( p —> ! p ) a n d th a t " I t in d ic a te s th a t th e i n t r o d u c tio n o f th e s ig n I is s u p e r f lu o u s in th e s e n s e th a t it m a y be c a n c e lle d o r i n s e r t e d in a n y f o r m u la a t a n y p la c e w e p le a s e " ( " A L o g ic of th e D o u b tfu l. O n O p ta tiv e a n d I m p e r a tiv e L o g ic , " R e p o r ts o f a M a th e m a tic a l C o llo q u iu m , N o tre D a m e , 1939, s e c o n d s e r i e s , i s s u e 1 , p . 58 ) . 41 c a n n o t v a li d l y b e i n f e r r e d f r o m 1^ . W e c a n a d d o t h e r e x a m p le s to t h i s o n e b y u s i n g d i f f e r e n t t r u t h - f u n c t i o n a l c o n n e c t i v e s . R o s s p o in ts o u t t h a t D u b is la v , w h e n h e f i r s t p r o p o s e d h is t r a n s f o r m a t i o n m e th o d , e m p h a s i z e d t h a t th e i n f e r e n c e i s v a lid o n ly i f th e s a m e d e m a n d in g 18 s u b j e c t ( i m p e r a t o r ) i s p r e s u p p o s e d . T h e v a l i d i t y in v o lv e d m u s t , in s o m e s e n s e o r o t h e r , b e d i r e c t l y r e l a t e d to th e i m p e r a t i v e s t h e m s e l v e s . T h is l e a d s R o s s to c o n s i d e r th e p o s s i b i l i t y o f h a v in g th e l o g i c a l e l e m e n t r e f e r to t h e " s u b j e c t i v e v a li d i ty " of th e i m p e r a t i v e . T h e s u b j e c t i v e - v a l i d i t y a p p r o a c h s u g g e s t s t h a t th e v a li d i ty ( o r n o n v a li d i ty ) o f a n i m p e r a t i v e d e p e n d s u p o n th e p s y c h o l o g ic a l s t a t e o f e i t h e r th e i m p e r a t o r o r th e r e c e i v e r o f a d e m a n d . A n i m p e r a t i v e w o u ld b e v a li d if a s t a t e of d e m a n d c o r r e s p o n d i n g to th e i m p e r a t i v e e x i s t s in th e i m p e r a t o r , o r i f a s t a t e of a c c e p t a n c e c o r r e s p o n d i n g to th e i m p e r a t i v e e x i s t s in a c e r t a i n p e r s o n . B u t a p r o b l e m i m m e d i a t e l y a r i s e s w ith r e s p e c t to th e n e g a t io n - f u n c ti o n o f s u c h a n i n t e r p r e t a t i o n . If, f o r e x a m p le , th e s t a t e o f d e m a n d c o r r e s p o n d i n g to th e i m p e r a t i v e d o e s n o t e x i s t in th e i m p e r a t o r , t h e n th e i m p e r a t i v e i s in v a lid ; b u t t h i s d o e s n o t m e a n t h a t a n i m p e r a t i v e w ith a n e g a t iv e th e m e o f d e m a n d i s i n v a lid . If w e r e p r e s e n t th e i m p e r a t i v e e l e m e n t b y I a n d th e th e m e of d e m a n d b y x , th e p o in t * ® R o s s , p . 38 a n d D u b is la v , p . 341 42 1Q a t i s s u e c a n b e m a d e c l e a r b y th e fo llo w in g s ta te m e n ts : (a) I ( x ) : C lo s e th e d o o r! (b) M x ) : Do n o t c lo s e th e d o o r! = L e a v e i t o p en! (c) ~ I ( x ) : Do n o t c lo s e th e d o o r! = T h e im p e r a tiv e I(x) is n o t v a lid . (d) *>'I~(x) : Do n o t n o t c lo s e th e d o o r! = T h e im p e r a tiv e H x ) is n o t v a lid . T r a n s la tio n s in th e lin g u is tic a lly im p e r a tiv e m o o d do n o t r e f l e c t th e v e r y im p o r ta n t d if f e r e n c e b e tw e e n (b) an d ( c ) . T h is d if f e r e n c e m a y be m a d e a p p a r e n t, h o w e v e r, by s h iftin g to th e lin g u is tic a lly in d ic a tiv e m o o d a s f o llo w s : (b 1) I— ( x ) : It is y o u r duty n o t to c lo s e th e d o o r. ( c 1) ^ -I(x ): It is n o t y o u r d u ty to c lo s e th e d o o r. T h is a m b ig u ity w ith r e s p e c t to n e g a tio n w as u n d o u b te d ly a ls o 20 o b s e r v e d by T h o m a s S to r e r an d m a y e x p la in in p a r t h is c h o ic e o f a th r e e - v a lu e d , r a t h e r th a n a tw o -v a lu e d , lo g ic f o r v a lu e i m p e r a tiv e s . E v e r e tt W. H a ll is a ls o v e ry c o n c e rn e d w ith th is p r o b le m an d s u g g e s ts th a t a t h r e e - v a l u e d lo g ic is n e c e s s a r y to a v o id th e a m b ig u ity of 21 th e n e g a tio n -fu n c tio n . R o s s 's r e m a r k s c o n c e rn in g a s h if t to th e *® R o ss u s e s a b a r a b o v e th e l e t t e r to s y m b o liz e n e g a tio n , e . g . , (b) a b o v e a p p e a r s a s I(x) in R o s s . T h e c u r l, ,~ I , is u s e d h e r e a n d th ro u g h o u t th e d i s s e r t a t io n in th e i n t e r e s t of u n ifo rm ity a n d to s p a r e th e n o n te c h n ic a l r e a d e r th e t a s k of i n te r p r e t i n g a n u n n e c e s s a r i l y la r g e n u m b e r of s y m b o ls . 20 " T h e L o g ic of V alu e I m p e r a tiv e s , " P h ilo s o p h y of S c ie n c e , 1 3 :2 6 -4 0 , 1946. C a te g o r ia l A n a ly s is of V alu e, " P h ilo s o p h y of S c ie n c e , 14:341, 1947; a n d W hat is V a lu e ? (N ew Y o rk , 1952), p p . 121, 2 3 9 ^2 4 0 . 43 lin g u is tic a lly in d ic a tiv e m o o d of im p e r a tiv e s ( i. e . , to n o r m a tiv e s ) , a s in (b 1) an d ( c 1) a b o v e , a r e w e ll ta k e n . H ad he d e v e lo p e d th is n o tio n , h is v e r s io n of th e lo g ic o f o b lig a tio n w ould m o r e c lo s e ly r e s e m b le th e n o r m a tiv e lo g ic s w h ich w ill be d is c u s s e d in th e n e x t c h a p te r . O ne d is tin c t a d v a n ta g e of th e n o r m a tiv e a p p ro a c h is th a t it a v o id s th e a m b ig u ity of th e n e g a tio n -fu n c tio n w ith o u t r e c o u r s e to th e th r e e - v a l u e d s y s te m s of S to r e r a n d H a ll. H o w e v e r, f u r t h e r c o n s i d e r a tio n of th e th ir d o r " e x t r a " v a lu e t e r m s in th r e e - v a lu e d s y s te m s ( S t o r e r 's 'a m o r a l ' an d H a ll's 'n o n - l e g i t im a te 1) is n e e d e d . T h e c o n c lu s io n w h ich R o ss d ra w s f r o m h is c o n s id e r a tio n of th e a m b ig u ity of th e n e g a tio n -fu n c tio n is th a t v a lid ity an d non v a lid ity a p p ly to th e c o n n e c tio n s b e tw e e n im p e r a tiv e s a n d n o t to a c o n n e c tio n b e tw e e n t h e i r th e m e s of d e m a n d . If I(x) is v a lid an d I(y) is v a lid , th e n it fo llo w s th a t I(x)&.I(y) is v a lid , but n o t th a t I(x& y) is v a li d .^2 T h is is n o t an a d e q u a te c h a r a c t e r i z a t io n of th e im m e d ia te ly e v id e n t in f e r e n c e s w ith w h ic h R o s s is c o n c e rn e d , b e c a u s e th e o n ly lo g ic a l c o m b in a tio n s it p e r m i ts a r e th o s e b e tw e e n im p e r a tiv e s and not b e tw e e n th e m e s o f d e m a n d . " B u t t h e r e c a n be no d o u b t th a t th e The a m p e r s a n d , , w ill be u s e d a s th e sy m b o l f o r c o n ju n c tio n th ro u g h o u t th e d i s s e r t a t io n . I(x)&I{y) is t r a n s la te d ‘B o th I(x) a n d I ( y ) , ’ i . e . , 'B o th x is c o m m a n d e d an d y is c o m m a n d e d , ' I(x& y) is t r a n s la te d 'I t is c o m m a n d e d th a t b o th x an d y .‘ 44 im p e r a tiv e in f e r e n c e s in p r a c t i c a l life a r e m a in ly s u c h a s e x p r e s s a c o n n e c tio n b e tw e e n th e m e s of d e m a n d " ( R o s s , p . 3 9 ) . T h e lo g ic of s a tis f a c tio n , w h en ta k e n b y its e l f , f a lls s h o r t in i t s a tte m p t to f o r m a l iz e th e p r a c t i c a l i n f e r e n c e . T h e s a m e is t r u e of th e lo g ic o f v a lid ity a s d e s c r ib e d by R o s s w ho i s , t h e r e f o r e , le d to s u g g e s t th a t a c o m b in a tio n of th e tw o s y s te m s m ig h t y ie ld a m o re a d e q u a te lo g ic a l p r o c e d u r e f o r h a n d lin g p r a c t i c a l in f e r e n c e s . I now a d v a n c e th e h y p o th e s is th a t th e c h a r a c t e r i s t i c f e a t u r e of th e e x is tin g p r a c t i c a l in f e r e n c e s is th a t th e y p u r p o r t to b r in g a b o u t a c o m b in a tio n of th e r e s u l t s to w h ic h th e lo g ic of s a t is f a c ti o n a n d th e lo g ic o f v a lid ity m a y le a d r e s p e c tiv e ly , n a m e ly s o th a t th e tr a n s f o r m a ti o n r u l e s of th e lo g ic of s a t i s f a c - tio n a r e c o m p lie d w ith , b u t th a t r e le v a n c e w ith r e g a r d to th e v a lid ity of th e im p e r a tiv e is a s c r i b e d to th e t r a n s f o r m a ti o n . ( p . 4 0 ) H o w e v e r, w h en h e a c tu a lly c o m b in e s th e tw o s y s te m s , R o s s fin d s th a t t h e i r r e s u l t s , ta k e n to g e th e r , a r e a p p lic a b le to th e n e g a tio n - f u n c tio n but not to th e fu n c tio n s of th e o th e r lo g ic a l c o n n e c tiv e s . T h e a p p lic a tio n o f th e c o m b in e d r e s u l t s to th e n e g a tio n o f im p e r a tiv e s is e a s i l y d e m o n s tr a te d . In th e lo g ic of s a t is f a c ti o n , th e n e g a tio n of I(x) is I-«(x) : I ( x ) : Y ou a r e to c lo s e th e d o o r . I - ^ x ) : Y ou a r e ( n o t to c lo s e th e d o o r ) . = ( L e a v e it o p e n ) . I(x) is s a t i s f i e d if a n d o n ly if H x ) is n o n s a tis f ie d . In th e lo g ic of v a lid ity , th e n e g a tio n o f I(x) is ~ I ( x ) : I ( x ) : Y ou a r e to c lo s e th e d o o r. ~ I(x ) : Y ou ( a r e n o t t o ) c lo s e th e d o o r. = It is n o t y o u r d u ty to c lo s e th e d o o r. I(x) is v a lid if a n d o n ly if "-I(x) is n o n v a lid . 45 C o m b in in g t h e s e r e s u l t s , w e o b ta in a s a d e f in itio n f o r : I(x ) is v a lid if a n d o n ly if I"~<x) i s n o n v a lid , o r 23 I ( x ) —> < — ~ I ^ x ) . T h e fo llo w in g e x a m p le m a y h e lp to c l a r i f y t h is d e fin itio n . L e t I(x ) b e th e i m p e r a t i v e , "Y o u a r e to c lo s e th e d o o r , " a n d s u p p o s e , f u r t h e r , th a t I(x) is v a lid b e c a u s e it h a s b e e n c o m m a n d e d by N ; th e n th e i m p e r a t i v e I*^<x) r e a d s : 'Y o u a r e (n o t to c lo s e th e d o o r )* = 'Y o u a r e to le a v e th e d o o r o p e n , 1 a n d H x ) is n o n v a lid , i . e . , it i s n o t c o m m a n d e d b y N . T h e p r a c t i c a l i n f e r e n c e in th is e x a m p le ( f r o m th e v a lid ity o f I(x ) w e i n f e r r e d th e n o n v a lid ity of I'-K x )) i s c o n c e iv e d a s lo g ic a lly e v id e n t; y e t,o n ly e x p e r i e n c e c o u ld c o n f ir m o r d i s c o n f ir m i t s v a lid ity . It is v a lid o n ly o n th e c o n d itio n th a t w ith in th e s y s t e m in q u e s tio n t h e r e a r e n o d u tie s te l l in g u s to p e r f o r m in c o m p a tib le a c tio n s . A s th is i s s e l f - e v i d e n t to a p r a c t i c a l a ttitu d e o f m in d , th is p r e m i s e is o v e rlo o k e d , a n d th e in f e r e n c e a s s u m e s th e c h a r a c t e r of u n c o n d itio n a l lo g ic a l v a lid ity . ( R o s s , p p . 4 0 -4 1 ) T h e p r a c t i c a l in f e r e n c e o f f r o m I(x) i s , t h e r e f o r e , of a p s e u d o - l o g ic a l c h a r a c t e r a n d is v a lid o n ly o n th e a s s u m p tio n o f w h a t R o s s c a l l s th e p r e m i s e o f p r a c t i c a l c o n s e q u e n c e : " e x p e d ie n t f r e e d o m f r o m c o n tr a d ic t io n o r r a t h e r f r e e d o m f r o m c o u n te r a c tio n b e tw e e n th e i m p e r a t i v e s th a t a r e v a lid w ith in th e s a m e s y s te m " ( p . 43 ) . W ith r e s p e c t to d is ju n c tio n , c o n ju n c tio n , a n d im p lic a tio n , 23 A d a p te d f r o m th e e x a m p le g iv e n by R o s s o n p . 40 . 46 R o s s s t a te s th a t no c o m b in a tio n of th e lo g ic s o f s a tis f a c tio n an d v a lid ity c a n a c c o u n t f o r th e lo g ic a l a ttr ib u te s o f th e im p e r a tiv e s 24 I ( x v y ) , I(x & y ), o r I(x —> y ) . H is a n a ly s is of th e s e fu n c tio n s le a d s R o s s to th e c o n c lu s io n th a t it is im p o s s ib le to a r r i v e a t a n y of th e fo llo w in g f o r m u la s : I(x )—> I(x v y ) I(x&y>—> I(x ) (I(x)& I(x—> y ) ) —>I<y) T h e d e o n tic lo g ic s , l a t e r d e v e lo p e d by vo n W rig h t an d o t h e r s , u s in g th e n o r m a tiv e a p p ro a c h , a r e m u c h c o n c e rn e d w ith f o r m u la s of th e ty p e ju s t m e n tio n e d . Von W rig h t’s f i r s t s y s te m , w hich w ill be d i s c u s s e d in d e ta il, d e p e n d s upon th e p o s s ib ility of r e ta in in g c e r t a i n f o r m u la s of th is ty p e a s r u l e s of th e s y s te m . We sa w e a r l i e r th a t R o s s r e g a r d s n o r m a tiv e s a s th e lin g u is tic a lly in d ic a tiv e f o r m of / im p e r a tiv e s . In v iew of th e r e le v a n c e of a c o m p a r is o n b e tw e e n th e im p e r a tiv e a n d n o r m a tiv e a p p ro a c h e s , th e p r o c e d u r e s f o r h a n d lin g " c o m b in e d " p r o p o s itio n s a d o p te d b y v on W rig h t an d s u c c e e d in g a u th o r s w ill be of m a jo r i n t e r e s t in c la r if y in g th e p r o b le m of th e p r a c t i c a l in f e r e n c e a s th is p r o b le m is fo r m u la te d by R o s s . R o s s h a s p o in te d o u t th a t th e lo g ic of s a tis f a c tio n a lo n e is not ^ T h e s y m b o l, ’v 1 , is u s e d fo r d is ju n c tio n . In g e n e r a l, ’A v B ’ is t r a n s l a t e d ’E it h e r A o r B o r b o t h .' T he sy m b o l ’—> ' is u s e d a s th e c o n d itio n a l s ig n an d 'A —> B ’ is t r a n s la te d ’if A th e n B. ' 47 a n a d e q u a te s o lu tio n to th e d ile m m a s t a t e d by J o r g e n s e n . H e h a s a l s o e s t a b l is h e d th a t th e lo g ic o f s u b je c tiv e v a lid ity , a s h e p r e s e n t s i t, is n o t a d e q u a te to th e t a s k . T h e id e a l c h o ic e o f a lo g ic in v o lv e s a c o m b in a tio n o f th e c o n c e p ts of s a t i s f a c t i o n a n d v a lid ity ; b u t s u c h a c o m b in a tio n i s p o s s ib le o n ly f o r th e n e g a tio n - f u n c tio n , a n d e v e n th e n th e r e s u l t is s t i l l o n ly p s e u d o - lo g ic a l, b e c a u s e i t is v a lid o n ly o n a s s u m in g th e " p r e m i s e o f p r a c t i c a l c o n s e q u e n c e " r e f e r r e d to e a r l i e r . T h e r e is o n e o th e r c a s e in w h ic h i m p e r a t i v e s p la y a r o l e in p r a c t i c a l in f e r e n c e s , a s R o s s c o n c e iv e s th e m . T h is is th e c a s e of s u b s u m p tio n u n d e r a g e n e r a l i m p e r a t i v e o f w h ic h th e fo llo w in g a r e e x a m p le s ; (A) Y o u a r e to k e e p y o u r p r o m i s e s . T h is is o n e o f y o u r p r o m i s e s . Y ou a r e to k e e p t h is p r o m is e . (B ) Do w h a t H c o m a n d s . H c o m m a n d s : c lo s e th e d o o r! C lo s e th e d o o r! B o th (A) a n d (B ) a r e s e e n to be v a lid in th e s e n s e r e l e v a n t to th e lo g ic o f v a lid ity , b u t t h e i r v a lid ity c a n n o t b e e s t a b l i s h e d w ith o u t r e f e r e n c e to th e t r a n s f o r m a t i o n r u l e s o f th e lo g ic of s a t i s f a c t i o n . T h is , h o w e v e r , is n o t s t r i c t l y lo g ic a l v a lid ity , a c c o r d in g to R o s s , s in c e c e r t a i n p s y c h o lo g ic a l f a c t s a r e in v o lv e d : " i t is n o t lo g ic a lly n e c e s s a r y th a t a p e r s o n d e m a n d in g a g e n e r a l r u l e s h o u ld a ls o d e m a n d th e s p e c i a l a p p lic a tio n o f t h is r u le " ( p . 4 4 ) . We th u s h a v e a s e c o n d c a s e o f p s e u d o - lo g ic a l i n f e r e n c e s w h ic h p r e s u m e th e " p r e m i s e of p r a c t i c a l c o n s e q u e n c e " m e n tio n e d in c o n n e c tio n w ith th e p s e u d o - lo g ic a l c h a r a c t e r o f th e n e g a tio n - f u n c tio n . R o s s c o n s i d e r s e x a m p le (B ) v e r y i m p o r t a n t s in c e it i l l u s t r a t e s th e d e le g a tio n of th e a u th o r i ty of c o m m a n d . A s a n a p p lic a tio n o f t h is ty p e o f a r g u m e n t, h e s u g g e s t s th e p r o v i s i o n s o f th e c o n s t i t u tio n r e l a t i n g to l e g i s l a t i o n ( p . 4 4 ) . T h e f o r m of s u b s u m p tio n u n d e r a g e n e r a l i m p e r a t i v e , a s e x e m p lif ie d by b o th (A ) a n d ( B ) , is p a r t i c u l a r l y i m p o r t a n t w h e n it is a p p lie d to o r d i n a r y lif e a n d to 25 la w . B u t w e s h a l l d e a l l a t e r w ith a p p lic a tio n s o f th e lo g ic o f o b lig a tio n a n d w ith R o s s 's r e m a r k s o n i t s a p p lic a tio n to la w . W h a t, s p e c i f i c a l l y , d o e s R o s s c o n c lu d e w ith r e s p e c t t o th e a p p e a r a n c e o f i m p e r a t i v e s in lo g ic a l i n f e r e n c e s ? F i r s t , i m p e r a t i v e s m a y b e c o n s t it u e n t p a r t s o f a g e n u in e lo g ic a l i n f e r e n c e . T h is is in d i r e c t o p p o s itio n to th e p o s itio n th a t i m p e r a t i v e s , b e in g n e i t h e r t r u e n o r f a l s e , c a n n o t a p p e a r in a lo g ic a l s y l l o g is m . R o s s q u a lif ie s h is p o s itio n , h o w e v e r , by s a y in g th a t w h en i m p e r a t i v e s do o c c u r in s u c h s y l l o g i s m s , " i t is s i m p ly a c a s e of a 't r a n s l a t i o n 1 o f lo g ic a l i n f e r - 25 R o s s 's s u b s u m p tio n u n d e r a g e n e r a l i m p e r a t i v e is s i m i l a r to th e c h a r a c t e r i z a t i o n of th e p r a c t i c a l s y l l o g i s m in S t. T h o m a s A q u in a s . T h e m in o r p r e m i s e o f A q u in a s ' p r a c t i c a l s y l l o g is m is a p a r t i c u l a r ju d g m e n t ( o f w is d o m o r s c i e n t if i c k n o w le d g e ) w h ic h is s u b s u m e d u n d e r a u n i v e r s a l ju d g m e n t of s y n d e r e s i s ( t h e m a j o r p r e m i s e ) to a r r i v e a t a ju d g m e n t o f c o n s c ie n c e c o n c e r n in g a p a r t i c u l a r a c t . 49 en ceB c o n c e rn in g in d ic a tiv e s e n te n c e s a b o u t th e p s y c h o lo g ic a l f a c t s w h ic h d e fin e th e V a lid ity * of a n i m p e r a t i v e " ( p . 45 ) . B u t th is t r a n s l a t i o n in to in d ic a tiv e f o r m r e d u c e s th e s y l l o g is m to a n o r d i n a r y lo g ic a l in f e r e n c e a n d th e s p e c if ic p r a c t i c a l c h a r a c t e r is n o t a t a ll in v o lv e d . S e c o n d ly , t h e r e a r e c e r t a i n c a s e s ( n e g a tio n -f u n c tio n a n d s u b s u m p tio n u n d e r a g e n e r a l i m p e r a t i v e ) in w h ic h i m p e r a t i v e s m a y a p p e a r a s c o n s titu e n t p a r t s of p s e u d o - lo g ic a l i n f e r e n c e s : In th o s e c a s e s th e in f e r e n c e a s s u m e s th e c h a r a c t e r of a s p e c if ic p r a c t i c a l in f e r e n c e , b u t a c tu a lly it w ill b e o n ly p s e u d o - lo g ic a l. If th e t a c i t l y a s s u m e d p r e m i s e is in c lu d e d , th e i n f e r - e n c e b e c o m e s r e a l l y lo g ic a l, b u t th e in f e r e n c e th e n lo s e s its c h a r a c t e r of b e in g s p e c i f i c a ll y p r a c t i c a l . < R o s s , p . 45 ) 2. A C l o s e r L o o k a t th e S a tis f a c tio n - f u n c tio n I n t e r p r e t a t i o n of I m p e r a ti v e s R o s s 's c r i t i c i s m o f th e H o f s ta d te r - M c K in s e y lo g ic of s a t i s f a c tio n m a k e s t h e i r s y s t e m a p p e a r w h o lly in a d e q u a te a s a b a s i s f o r p r a c t i c a l s y l l o g is m s . H o w e v e r, th e s y s t e m d e v e lo p e d b y H o f s ta d te r a n d M c K in s e y h a d n o t b e e n in te n d e d to d e a l w ith a l l of th e i m p e r a tiv e s c o v e r e d by R o s s 's b r o a d d e fin itio n o f th e t e r m . O n th e c o n tr a r y , 9 fi in t h e i r p a r t i a l s y n t a c t i c a l a n a l y s i s of i m p e r a t i v e s , H o f s ta d te r a n d M c K in s e y sh o w th a t tw o f o r m s o f i m p e r a t i v e s m a y be d is tin g u is h e d . " O n th e L o g ic o f I m p e r a ti v e s , " P h ilo s o p h y of S c ie n c e , 6 :4 4 6 -4 4 7 , 1939. 50 T h u s , a fia t ia a n im p e r a tiv e w h ic h in c lu d e s no r e f e r e n c e to a n a g e n t w ho is to c a r r y it o u t, w h e re a s a d ir e c tiv e is a n im p e r a tiv e w h ich d o e s in d ic a te s u c h a n a g e n t. T h e s y s te m r e f e r r e d to by R o s s a s th e lo g ic of s a tis f a c tio n is d e v e lo p e d by H o fs ta d te r a n d M c K in se y to h a n d le f ia ts o n ly . M o re o v e r, H o f s ta d te r a n d M c K in se y d is tin g u is h b e tw e e n th e s a tis f a c tio n a n d th e c o r r e c t n e s s of im p e r a t i v e s . A n i m p e r a tiv e is s a tis f ie d if i ts c o r r e s p o n d in g in d ic a tiv e ( d e s c r i b i n g th e th e m e of d e m a n d ) is tr u e ; it is c o r r e c t , if th e th e m e of d e m a n d o u g h t to be th e c a s e . C o r r e c t n e s s i s , th u s , not a lo g ic a l a ttr ib u te of im p e r a tiv e s b u t i s to be d e te r m in e d by m o r a l p h ilo s o p h y . T h e la n g u a g e f o r w h ich H o f s ta d te r a n d M c K in se y g iv e a c a l c u lu s is c a lle d L an g u a g e Ic . T h e y f o r m th is la n g u a g e f r o m R u d o lf 27 C a r n a p ’s L a n g u a g e I by a d d in g to th e p r im itiv e s y m b o ls a n d p r im itiv e s e n te n c e s s o th a t Ic c o n ta in s b o th in d ic a tiv e s e n te n c e s a n d 28 im p e r a tiv e s . T h e b a s ic th e o r e m of t h e i r c a lc u lu s p e r m its th e e lim in a tio n of a ll im p e r a tiv e c o n n e c tiv e s in a n im p e r a t i v e - - w i t h th e e x c e p tio n of one sy m b o l, th e e x c la m a tio n p o in t ( ! ) . F o r m a lly th is p o r tio n of th e th e o r e m s ta te s ; I I 1 i ^ C a rn a p d e v e lo p s th is la n g u a g e in T h e L o g ic a l S y n tax of ! L a n g u a g e ( New Y o rk , 1 9 3 7 ), P a r t s I a n d I I , p p . 1 1 -8 2 . 28 H o fs ta d te r a n d M c K in se y do n o t s p e a k of im p e r a tiv e s e n - te n c e s . T h ey c a ll I c a " c o m b in e d la n g u a g e of s e n te n c e s a n d i m p e r a t iv e s " ( p . 4 4 7 ) . 51 If C j i s a n y im p e r a tiv e o f L a n g u a g e I , th e n t h e r e e x is ts a s e n te n c e S j , o f L a n g u a g e I , s u c h th a t C j = ! is p r o v a b le in L a n g u a g e I c . ( p . 4 5 2 ) It fo llo w s f r o m th is th e o r e m th a t, if is p ro v a b le , a n d C 2 = ! S 2 is p r o v a b le , th e n C 2 is d e r iv a b le f r o m if S 2 is d e r iv a b le f r o m . In th is s a m e w ay a ll th e s y n ta c tic a l c o n c e p ts d e fin e d f o r s e n te n c e s ( in d ic a tiv e s ) a r e e x te n d e d to c o v e r i m p e r a t i v e s . R o s s h a s p o in te d o u t th a t th is p r o c e d u r e s im p ly r e m o v e s a n y p o s s ib le lo g ic a l e le m e n t f r o m th e im p e r a tiv e a n d a v o id s g iv in g O Q e v e n a p s e u d o - lo g ic a l s ig n if ic a n c e to th e p r a c t i c a l in f e r e n c e . I n d e e d , H o f s ta d te r a n d M c K in se y do c o n c lu d e th a t t h e i r im p e r a tiv e s ig n , 1 I 1, is s u p e r f lu o u s , a n d th a t an y r e s u l t s in v o lv in g th e i m p e r a tiv e c o n n e c tiv e s a r e t r i v i a l . In p a r t i c u l a r , it m a y p e r h a p s be f e lt th a t th e a b o v e th e o r e m , s in c e i t m a k e s e v e r y s e n te n c e in v o lv in g th e m a r k " ! " e q u ip o l le n t to a s e n te n c e n o t in v o lv in g th is m a r k , sh o w s th a t th e i n t r o d u c tio n o f th e " I " is s u p e r f lu o u s . ( H o f s ta d te r a n d M c K in se y , p . 4 5 3 ) W hat H o f s ta d te r a n d M c K in se y do n o t n o te is th a t, in a d d itio n to m a k in g th e im p e r a tiv e s ig n s u p e r f lu o u s , t h e i r c a lc u lu s a llo w s m a n y d e r iv a tio n s w h ic h a r e im m e d ia te ly s e e n to be in v a lid . F o r e x a m p le , f r o m " S lip th e l e t t e r in to th e b o x ! " one c a n p r o p e r l y ( i n a c c o r d a n c e j w ith th e lo g ic o f s a t i s f a c t i o n ) i n f e r " S lip th e l e t t e r in to th e b ox o r | | 29 R o s s , p . 38 . b u r n itf " 52 T h e a u t h o r s in te n d t h a t t h e i r a n a l y s i s o f i m p e r a t i v e s s h o u ld a p p ly to v a lu e j u d g m e n t s w h e n e v e r s u c h ju d g m e n ts a r e c o n s i d e r e d to b e in th e i m p e r a t i v e m o o d . In t h i s c a s e th e p r o b l e m b e c o m e s o n e o f d e t e r m i n i n g th e " c o r r e c t n e s s " o f e a c h i m p e r a t i v e a s d i s t i n g u i s h e d f r o m th e " c r i t e r i o n o f s a t i s f a c t i o n . " T o e s t a b l i s h th e c o r r e c t n e s s o f i m p e r a t i v e s " s c i e n t i f i c a l l y , " H o f s t a d t e r a n d M c K in s e y s u g g e s t a m e th o d c l o s e l y c o r r e s p o n d i n g to th e s c i e n t i f i c p r o c e d u r e o f f o r m i n g a n d t e s t i n g h y p o t h e s e s . C o r r e s p o n d i n g to p r o b l e m s a s to w h a t i s th e c a s e , p r o b l e m s a n s w e r a b l e b y i n d i c a t i v e s e n t e n c e s , t h e r e w o u ld b e p r o b l e m s a s to w h a t o u g h t to b e th e c a s e , w h a t o u g h t to b e d o n e , a n s w e r a b l e b y i m p e r a t i v e s . ( H o f s t a d t e r a n d M c K in s e y , p . 4 5 6 ) T h e d e d u c tiv e p r o c e s s in v o lv e d in d e v e lo p in g i m p e r a t i v e h y p o t h e s e s f o llo w s th e p r o c e d u r e o f th e lo g ic o f s a t i s f a c t i o n ( o u t l i n e d a b o v e ) . T h e p r o b l e m o f f i n a l c o n f i r m a t i o n , h o w e v e r , d i f f e r s f r o m c u s t o m a r y s c i e n t i f i c p r o c e d u r e in t h a t n o b a s i c i n t e r - s u b j e c t i v e a g r e e m e n t c o n c e r n i n g i m p e r a t i v e s is in e v id e n c e : t h e r e i s n o r e a s o n to b e li e v e t h a t i n t e r s u b j e c t i v e l y c o n f i r m a b l e 1 c o n c l u s i o n s w ill r e s u l t , u n l e s s a t s o m e tim e w e a n d o u r s o c i e t y ; s h o u l d a l l b e s o c o n s t it u t e d , t h a t w e s h o u ld f in d o u r s e l v e s in s u b j e c t i v e a g r e e m e n t o n t h e s e m a t t e r s , ( p . 4 5 7 ) * I | H o f s t a d t e r a n d M c K in s e y h a v e r e a l i z e d c o r r e c t l y t h a t t h e i r p r o p o s e d i n t e r p r e t a t i o n in t e r m s o f s a t i s f a c t i o n - f u n c t i o n s c a n n o t, in i t s e l f , g iv e u s a s c i e n t i f i c p r o c e d u r e f o r e s t a b l i s h i n g v a lu e j u d g m e n t s . 53 T h e la c k of i n t e r s u b j e c t i v e a g r e e m e n t, h o w e v e r , is n o t th e s o le s tu m b lin g b lo c k to f i n a l c o n f ir m a tio n a s th e y w o u ld h a v e u s b e lie v e . E v e n if w e s u p p o s e th a t c o m p le te i n t e r s u b je c tiv e a g r e e m e n t d id e x is t w ith r e s p e c t to c e r t a i n v a lu e ju d g m e n ts , w e c a n s t i l l n o t a p p ly th e H o f s ta d te r - M c K in s e y c a lc u lu s to v a lu e i m p e r a t i v e s u n le s s w e a r e w illin g to a c c e p t a s v a lid th e i n f e r r i n g o f w h a t o u g h t to b e f r o m w h a t i s . N ot m a n y m o r a l p h ilo s o p h e r s a r e p r e p a r e d to ta k e th is f in a l s t e p . T h e b a s i c p r o b le m w h ic h c o n c e r n s u s h e r e is n o t th a t of e s t a b l is h i n g th e c o r r e c t n e s s o f e a c h i m p e r a t i v e . W e a r e c o n c e r n e d , r a t h e r , w ith d i s c o v e r i n g w h a t ty p e of lo g ic a l o r p s e u d o - l o g ic a l e l e m e n ts a r e in v o lv e d in th e i m m e d ia te l y - e v i d e n t p r a c t i c a l s y l l o g is m s . T h e H o f s ta d te r - M c K in s e y c a l c u l u s , b a s e d o n s a t is f a c t i o n - f u n c t i o n s , is n o t a s o lu tio n to t h is p r o b le m , f o r , a s R o s s p o in ts o u t, it a v o id s th e p r o b le m a lt o g e t h e r by m a k in g th e i m p e r a t i v e e le m fe n t s u p e r f lu o u s . T h e 1 1 c o r r e c t n e s s " w h ic h w e a r e s e e k in g is th a t of c o r r e c t l y p r o c e e d in g , d e d u c tiv e ly , f r o m o n e i m p e r a t i v e ( o r n o r m a tiv e ) to a n o th e r , a n d th e c o r r e c t n e s s of t h is p r o c e s s m u s t p o s s e s s a t l e a s t j i a p s e u d o - l o g ic a l c h a r a c t e r . T h e lo g ic o f s a t i s f a c t i o n n o t o n ly f a i l s i to d e a l w ith t h is ty p e of c o r r e c t n e s s , i t p e r m i t s th e d e d u c in g of one i m p e r a t i v e f r o m a n o th e r in w h a t is i m m e d ia te ly s e e n to be in ! ! " i n c o r r e c t " ( i n v a l i d ) i n f e r e n c e . 54 3. I m p e r a ti v e s I n t e r p r e t e d a s D is ju n c tiv e In d ic a tiv e s 30 H. G. B o h n e rt, in " T h e S e m io tic S ta tu s of C o m m a n d s ," s u g g e s t s a n i n t e r p r e t a t i o n of i m p e r a t i v e s w h ic h is in te n d e d to a v o id R o s s 's c r i t i c i s m s of th e H o f s ta d te r - M c K in s e y c a lc u lu s . B o h n e r t d is c la im s an y a b s o lu te in d e p e n d e n c e of i m p e r a t i v e f r o m d e c l a r a ti v e s e n te n c e s . H e a r g u e s th a t: a ll s e n t e n c e s a r e a t l e a s t p o te n tia lly m o tiv a tio n a l an d th a t a l th o u g h m o tiv a tio n a l s itu a tio n s c a u s a lly g ive r i s e to th e c o m m a n d f o r m , the c o m m a n d n e e d n ot s a y o r a s s u m e a n y th in g a b o u t th e d e s i r e s o r f e a r s of the h e a r e r o r s p e a k e r ; th a t m o tiv a tio n by its e l f d o e s not j e o p a r d iz e t r u t h v a lu e ; th a t in a b e h a v io r a l s e n s e c o m m a n d s fu n c tio n a s , i . e . , a r e , d e c la r a tiv e s e n te n c e s ; th a t th e i m p e r a t i v e f a c t o r c a n a l s o p la y a r o l e in d e riv a tio n ; th a t s u c h d e r iv a tio n s a r e g e n u in e d e r iv a tio n s , ( n o t m e r e l y p s e u d o - lo g ic a l) . ( " T h e S e m io tic S ta tu s of C o m m a n d s ," p. 3 0 3 ) So i n t e r p r e t e d , a ll c o m m a n d s a r e sh o w n to h av e a fu n c tio n a l o r ig in in d e c l a r a ti v e s e n te n c e s . F o r e x a m p le , B o h n e r t h o ld s th a t 'K e e p th is c a r p r o p e r l y lu b r ic a te d ! ' is a n e ll i p s i s f o r 'E i t h e r th is c a r is p r o p e r l y lu b r ic a te d o r it w ill s o o n b r e a k dow n. ' So lo ng a s th e e ll i p s i s is u n d e rs to o d f o r w h at it is , it c a n p la y a r o l e in im p e r a t i v e d e r iv a tio n s su c h a s th e fo llo w in g : K eep th is c a r p r o p e r l y lu b r ic a te d ! I w ill n o t l u b r ic a te th is c a r . Q 1 T h e n th e c a r w ill s o o n b r e a k dow n. P h ilo s o p h y of S c ie n c e , 1 2 :3 0 2 -3 1 5 , 1945. 3* T h e e x a m p le g iv e n is d i r e c tl y q u o te d f r o m B o h n e rt (p. 306). A s s o o n a s th e m i s s i n g p a r t s of th e m a j o r p r e m i s e a r e u n d e rs to o d ( a s in th e e ll i p s i s m e n tio n e d a b o v e ) , th is s y llo g is m ta k e s on a t r u l y lo g ic a l c h a r a c t e r , w ith th e im p e r a t i v e r e t a in i n g th e t r u t h v a lu e • > of th e d e c l a r a ti v e f o r w h ic h it is a n e llip s e . B o h n e r t s u g g e s ts a b a s ic d e c la r a tiv e d is ju n c tiv e a s an a p p r o p r i a t e i n t e r p r e t a t i o n f o r a ll im p e r a tiv e s e n te n c e s , w ith th e s e c o n d p a r t of th e d is ju n c tiv e e x p r e s s in g th e p e n a lty f o r f a i l u r e to o b e y th e c o m m a n d . ^ F o r e x a m p le , 'S t o p ! 1 m a y b e i n t e r p r e t e d a s 'E i t h e r you w ill sto p o r you w ill b e s h o t. ' If P r e p r e s e n t s a c e r t a i n g iv en p e n a lty , th e n a f o r m a l im p e r a tiv e s y s t e m c a n b e e s ta b lis h e d w ith r e f e r e n c e to P . U sin g th e d is ju n c tiv e i n t e r p r e t a t i o n o f c o m m a n d s , B o h n e r t b e lie v e s th a t, f o r a ll c o m m a n d s in v o lv in g th e s a m e p e n a lty P, it is p o s s ib le to g iv e a n i n t e r p r e t a t i o n to th e H o f s ta d te r an d M c K in se y s y s t e m w h ich w ill r e n d e r it a n a ly tic , i . e . , w ill m a k e t h e i r la n g u a g e I id e n tic a l w ith I , w ith o u t in v o lv in g th e t r i v i a li t y th a t A lf R o sk c h a r g e s th is s y s t e m w ith, an d w ith o u t r e q u ir in g t h e i r own s a t is f a c ti o n f u n c tio n a l i n t e r p r e t a t i o n of it. ( p p . 3 1 1 -3 1 2 ) T h e s y s t e m w hich B o h n e rt s u g g e s ts , g ro w s out of th e H o f s ta d te r a n d M c K in se y s y s t e m by re d e fin in g in b a s ic d is ju n c tiv e ^ A. R . A n d e rs o n , in d e v e lo p in g a m o d a l v e r s i o n of d e o n tic lo g ic w h ich w ill be d i s c u s s e d in th e n e x t c h a p te r , c r e d i t s B o h n e rt w ith h a v in g b e e n the f i r s t to in tro d u c e th e n o tio n of r e w a r d o r p u n is h m e n t in to a f o r m a l iz e d s y s t e m f o r i m p e r a t i v e s o r n o r m a tiv e s ( s e e p a r t i c u l a r l y p p . 1 4 -1 5 of A. R. A n d e rs o n a n d O. K. M o o re , " T h e F o r m a l A n a ly s is of N o r m a tiv e C o n c e p ts ," A m e r i c a n S o c io lo g ic a l R e v ie w , 2 2 :9 -1 7 , 1 9 5 7 ) . 56 f o r m e a c h i m p e r a tiv e p r im itiv e s y m b o l o f th e l a t t e r s y s te m . F o r e x a m p le , M S * is d e fin e d a s ’S v P * , a n d 1 is d e fin e d a s '-'-SvP* { P b e in g a p r o p o s itio n a l c o n s t a n t ) . F o llo w in g h is r e i n t e r p r e ta tio n of th e s e s y m b o ls , B o h n e rt s u g g e s ts th a t th e o p e r a t o r 1 ! 1 b e c o m e s s u p e rflu o u s in h is s y s te m a ls o but not fo r th e s a m e r e a s o n th a t it w as s u p e r flu o u s in th e H o f s ta d te r - M c K in s e y s y s t e m s . A l though —> ! S j is p ro v a b le in B o h n e r t's s y s te m , ! S j —> S j is not p r o v a b le in h is s y s te m , f o r th e l a t t e r is e q u iv a le n t to ( S j v P ) —> S j . ^ T he b a s ic H o f s ta d te r - M c K in s e y t h e o r e m h a d m a d e e v e r y im p e r a tiv e s e n te n c e " e q u ip o lle n t" to an in d ic a tiv e ( C j = ! S j ), th u s m a k in g th e in tro d u c tio n of th e im p e r a tiv e s ig n 1 ! 1 s u p e r f lu o u s . B o h n e rt d o e s not s p e c if ic a lly t e ll us in w hat w ay th e im p e r a tiv e s y m b o l h a s b e c o m e s u p e rflu o u s in h is s y s te m . It s e e m s c o n s is te n t w ith h is a p p ro a c h , h o w e v e r, to a s s u m e th a t th e im p e r a tiv e s y m b o l is s u p e rf lu o u s b e c a u s e B o h n e r t’s i n te r p r e t a t i o n a llo w s it to be r e p la c e d in e v e r y c a s e by a d is ju n c tiv e . Som e of th e h ig h ly o b je c tio n a b le r e s u l t s w h ich w e re o b ta in a b le in th e lo g ic of s a tis f a c tio n a r e a ls o o b ta in a b le in B o h n e r t’s s y s te m . He c a n s t i l l d e riv e ! f r o m , b u t he a p p a r e n tly r e g a r d s ^ B o h n e rt u s e s th e " h o r s e s h o e " a s th e c o n d itio n a l s ig n but it h a s b e e n r e p la c e d h e r e an d e ls e w h e r e by the a r r o w ( —> ) in the i n t e r e s t of u n ifo rm ity . 57 th is a s p ro p e r: The fa c t th a t 1 1 The d o o r is c lo se d " im p lies " C lo se the d o o r! " so u n d s s tra n g e is due to th e fa c t th a t su c h a d e riv a tio n is h a rd ly e v e r u sed , ju s t a s it is th e c a s e th a t if one knows th at the d o o r is c lo s e d he does not announce the p e rfe c tly c o r r e c t in fe re n c e " E it h e r the d o o r is c lo se d o r a u n ic o rn is ju s t o u tsid e . " ( p. 312 ) T he r e a s o n why the " s tra n g e " d e riv a tio n ’S ^—> ! S^1 is " h a rd ly e v e r u se d " is th a t su c h a d e riv a tio n is sim p ly not v a lid . The m ea n in g of th e im p e ra tiv e e le m e n t, even B o h n e rt’s "m o tiv a tio n a l" m eaning, s e e m s to have b een s e t a sid e . The in te rp r e ta tio n of the p re s e n t ex am p le in t e r m s of s a tis fa c tio n would be le s s o b jectio n ab le th an is B o h n e rt’s, fo r th en one could sa y th a t the d e c la ra tiv e , 'T h e d o o r is clo sed , 1 im p lie s th at the im p e ra tiv e , ’C lo se th e d o o r ! 1 has been s a tis fie d . But the sh o rtc o m in g s of the logic of s a tis fa c tio n have a l re a d y b een d is c u s s e d . So f a r o u r in tu itiv e re je c tio n of B o h n e rt’s d i s ju n ctiv e in te r p re ta tio n of im p e ra tiv e s h a s been b a s e d upon his c o n ten tio n th a t a tru e in d ic ativ e like ’T he d o o r is closed* im p lie s its c o rre s p o n d in g im p e ra tiv e ’C lo se the d o o r ! 1 The " im p lie s " which o c c u rs in B o h n e rt’s s y s te m h as the p r o p e r tie s of m a te r ia l im p lic a tion. By re d u c in g e a c h im p e ra tiv e to its c o rre s p o n d in g in d icativ e d isju n ctiv e, we th e r e f o r e obtain the follow ing: (1) I S j - t S i V P ) by definition, th e o re m . ( 2 ) (3) e (4) Suppose S e S j —> { S jv P ) (1), su b stitu tio n . Suppose S^ to be fa ls e . 58 (5) T h e n S j —> ( S 2 v P ) is a v a lid in f e r e n c e , p —> q h o ld s w h e n e v e r q is t r u e o r p is f a ls e . (6) T h e r e f o r e S j —'> 1 3 2 i s a v a lid in f e r e n c e . (5 ), s u b s titu tio n . T h is r e s u l t is p e r h a p s e v e n m o r e " s t r a n g e " th a n th a t in d i c a te d by B o h n e rt, f o r we now h a v e d e m o n s tr a te d th a t a p p a r e n tly , a f a ls e in d ic a tiv e s e n te n c e im p lie s an y im p e r a t i v e a t a ll. T h is i m p l i c a tio n , i n t e r p r e t e d w ith in a n in d ic a tiv e s y s t e m o f m a t e r i a l im p lic a tio n , is u n d e r s to o d to b e a r e l a ti o n s h i p b e tw e e n th e t r u t h a n d f a l s it y of in d ic a tiv e p r o p o s itio n s a n d d o e s n ot a t a ll in v o lv e a n y c o n n e c tio n b e tw e e n th e m e a n in g s of the t e r m s o f th e p r o p o s itio n s . It m a y be th e c a s e , h o w e v e r, th a t, if s ig n if ic a n c e is to b e a tta c h e d to th e p r a c t i c a l i n f e r e n c e a t a ll, th e n th e in f e r e n c e in v o lv e s th e ( i n t e n s i o n a l ) m e a n in g s of th e t e r m s , i. e. , p r a c t i c a l in f e r e n c e s h a v e th e c h a r a c t e r i s t i c s o f s t r i c t o r n e c e s s a r y i m p lic a tio n . A nd if th is is s o , th e n an im p e r a t i v e ! c a n n o t be v a lid ly d e r iv e d f r o m an in d ic a tiv e S j w ithout r e f e r e n c e to a m e a n in g - c o n n e c tio n . If we a g r e e w ith S t o r e r th a t " th e c o n te n t o r m e a n in g of an im p e r a t i v e lie s in its c o m m a n d n a tu r e o r d ir e c tiv e 34 fu n c tio n , " th e n we m u s t c o n c lu d e th a t no in f e r e n c e a t a ll c a n be d ra w n d i r e c tl y f r o m an is o la te d in d ic a tiv e s e n te n c e to a n i m p e r a t i v e . T h is c o n c lu s io n , a lth o u g h p h r a s e d d iff e r e n tly by d if f e r e n t ip h ilo s o p h e r s , h a s a long t r a d i ti o n in th e h i s t o r y of m o r a l p h ilo s o p h y . 34 " T h e L o g ic of V alue I m p e r a ti v e s , " p. 27 . 59 I n t e r p r e t i n g a n im p e r a t i v e a s c o m m a n d in g w hat o u g h t to be d o n e, a n d a d e c l a r a ti v e a s d e s c r i b i n g w h a t is th e c a s e , o u r c o n c lu s io n , r e p h r a s e d , is th a t w h at o u g h t to b e done c a n n o t v a lid ly be d e r iv e d f r o m w h a t i s th e c a s e . P . H . N o w e ll-S m ith , who a r r i v e s a t a s i m i l a r c o n c lu s io n , q u o te s th e fo llo w in g p a s s a g e f r o m H u m e a s a s u p p o r tin g a r g u m e n t: In e v e r y s y s t e m of m o r a l it y w h ic h I h a v e h ith e r to m e t w ith I h a v e a lw a y s r e m a r k e d th a t th e a u th o r p r o c e e d s f o r s o m e tim e in th e o r d i n a r y w ay of r e a s o n in g , a n d e s t a b l is h e s th e b e in g of a G od, o r m a k e s o b s e r v a tio n s c o n c e rn in g h u m a n a f f a i r s ; w hen of a s u d d e n I a m s u r p r i s e d to find, th a t i n s t e a d of th e u s u a l c o p u la tio n s of p r o p o s itio n s an d is not, I m e e t w ith no p r o p o s itio n th a t is n ot c o n n e c te d w ith an o u g h t, o r a n o u g h t n o t. T h is c h a n g e is i m p e r c e p tib le ; b u t is , h o w e v e r, of the l a s t c o n s e q u e n c e . F o r a s th is ou g h t o r o u g h t n o t e x p r e s s e s s o m e new r e l a ti o n o r a f f i r m a tio n , i t is n e c e s s a r y t h a t it s h o u ld be o b s e r v e d and e x p la in e d ; a n d a t th e s a m e tim e th a t a r e a s o n s h o u ld be g iv e n f o r w hat s e e m s a l t o g e t h e r in c o n c e iv a b le , how th is new r e l a ti o n c a n be a d e d u c tio n f r o m o th e r s th a t a r e e n ti r e l y d if f e r e n t f r o m it. ^ N o w e ll-S m ith g o e s on to p o in t o ut th a t s t a t e m e n t s c o m m a n d in g th a t a n a c t ought to b e done a ls o c a n n o t be d e d u c e d f r o m s t a te m e n t s a b o u t w h at i s th e c a s e : T h is m u s t be ille g itim a te r e a s o n in g , s in c e th e c o n c lu s io n of a n a r g u m e n t c a n c o n ta in n o th in g w h ic h is n o t in th e p r e m i s e s , a n d t h e r e a r e no 'o u g h ts ' in th e p r e m i s e s . (N o w e ll- S m ith , p. 3 7 ) T h is c o n c lu s io n a p p e a r s a ls o a s a r u l e of s y llo g is m s in 35 H u m e , T r e a t i s e , B k. m , P a r t I , S e c tio n i; q u o te d in N o w e ll-S m ith , E th ic s (L o n d o n , 1 9 5 4 ), pp. 3 6 - 3 7 . 60 36 R . M . H a r e 's T h e L a n g u a g e of M o r a l s . H e r e i t is s t a t e d th a t: " N o i m p e r a t i v e c o n c lu s io n c a n b e v a lid ly d r a w n f r o m a s e t of 37 p r e m i s s e s w h ic h d o e s n o t c o n ta in a t l e a s t o n e i m p e r a t i v e . " H a r e a l s o s u g g e s t s th a t A r i s t o t l e , K a n t, G . E . M o o re , a n d P r i c h a r d s u b - 38 s c r i b e d to t h i s r u l e , a n d w e h a v e , in a d d itio n , a l r e a d y c o n s i d e r e d s i m i l a r s t a t e m e n t s by P o i n c a r £ ( t h r o u g h J o r g e n s e n ) , A lf R o s s , a n d S t o r e r . T o m a i n t a i n t h is r u l e is to d e s t r o y t h e v e r y b a s i s of b o th th e H o f s t a d t e r - M c K i n s e y s y s t e m a n d t h a t p r o p o s e d by B o h n e r t, a n d it is o n t h is g r o u n d t h a t w e j u s t if y t e r m i n g t h e s e s y s t e m s i n a d e q u a te . T h e r e a r e o t h e r c o n s i d e r a t i o n s w h ic h f u r t h e r s t r e n g t h e n t h is d e c i s i o n to r e j e c t th e H o f s t a d t e r - M c K i n s e y lo g ic of s a t i s f a c t i o n a n d t h e B o h n e r t r e d u c t i o n of i m p e r a t i v e s to d i s j u n c t i v e i n d i c a t i v e s . In c r i t i c i z i n g th e lo g ic of s a t i s f a c t i o n , R o s s p o in te d o u t th a t c e r t a i n of i t s r e s u l t s a r e i n a d m i s s i b l e a s r e p r e s e n t a t i o n s of p r a c t i c a l i n f e r e n c e s . F o r e x a m p le , th e d is ju n c tiv e f o r m u la , p —> ( p v q ) , is a lw a y s v a lid in th e o r d i n a r y lo g ic o f i n d ic a t i v e s ( e . g . , in th e s e n t e n t i a l ^ O x fo rd , 1 9 5 2 . 37 T h e L a n g u a g e o f M o r a l s , p . 2 8 . 38 H a r e , p p . 2 9 -3 0 . K a n t's e m p h a ti c s t a t e m e n t w a s th a t " N o th in g is m o r e r e p r e h e n s i b l e t h a n to d e r i v e th e la w s p r e s c r i b i n g w h a t o u g h t to be d o n e f r o m w h a t is d o n e " ( C r i t i q u e of P u r e R e a s o n , A 3 19 K 61 c a lc u lu s ) . H o f s ta d te r an d M c K in se y c a n i m m e d ia te ly o b ta in the s a m e f o r m u la b y t h e i r t r a n s f o r m a t i o n r u l e s , a n d it m ig h t th e n be w r itte n ! p —> ( ! p v ! q ) . T h u s , 'M a il th is l e t t e r ! 1 im p lie s ( m a t e r i a l l y ) 'M a il th is l e t t e r o r b u r n i t ! ' R o s s h o ld s th a t s u c h an 39 i n f e r e n c e is im m e d ia te ly s e e n to be in v a lid ; th e s y s t e m in w h ich s u c h f o r m u la s a r e p e r m i t t e d f a ils to r e p r e s e n t p r o p e r l y th e n a tu r e of p r a c t i c a l i n f e r e n c e s . B o h n e rt, in a n s w e r in g R o s s ’s o b je c tio n on th is p o in t, a p p a r e n tly a g r e e s th a t d is ju n c tiv e in f e r e n c e s of th e ty p e m e n tio n e d do n ot p r o p e r l y c a p tu r e th e i m p e r a t i v e m e a n in g : T o a d d an a l t e r n a t i v e w h ich h a s p e r h a p s no o r n e g a tiv e c a u s a l r e l a t i o n to th e a v o id a n c e of th e r e p r i m a n d a p p e a r s to p e r v e r t i m p e r a tiv e m e a n in g . ( B o h n e r t, p. 3 1 3 ) T h e fa c t r e m a i n s , h o w e v e r, th a t in B o h n e r t1 s p r o p o s e d i n t e r p r e t a t i o n 40 ! S j —> ( ! S^v ! S 2 ) is p r o v a b le . B o h n e rt, r e a l iz i n g th a t th is is the c a s e , a tte m p ts to m e e t th e o b je c tio n by a p p e a lin g to a p s y c h o lo g ic a l a rg u m e n t, n a m e ly , th a t, n o r m a lly , p e o p le a r e n o t m o tiv a te d to a c tio n in th is w ay. T h is o b je c tio n c an , h o w e v e r, be m e t by n o tic in g th a t j u s t a s p e o p le who know A s e ld o m d e r iv e f r o m it A v B , w h ich h a s l e s s lo g ic a l c o n te n t th a n A , s o a p e r s o n who is in f o r m e d of a i I 1 **9 " I m p e r a ti v e s a n d L o g i c ," p . 38 . T h e f o r m u la in q u e s tio n , by B o h n e r t's d e fin itio n s , is | id e n tic a l w ith ( S j^ v P ) —> ( ( S ^ v P ) v ( S 2v P ) ) . 62 d isju n ctio n in the c o m m an d fo r m is not going to behave on le s s th an th e to ta l in fo rm a tio n a v a ila b le by d e riv in g f ro m it a s e n ten c e w ith an a d d itio n al a lte rn a tiv e and actin g on th at. (p . 313) Now, if o u r a c tu a l p r a c tic a l in fe re n c e s a r e not of th is type ( a s B o h n e rt a d m its ) , th en it does not s e e m re a s o n a b le th at th ey should be v alid ly ob tain ed w ithin a lo g ical s y s te m d esig n ed to handle p r a c tic a l in fe re n c e s . M o re o v e r, it is s u r e ly not re a s o n a b le to r e ta in u n d e sira b le fo rm u la s ( a s lo g ically v a l i d ) on th e g ro u n d th at, sin c e people do not think th a t way, su c h fo rm u la s m ay n e v e r o c c u r. S to r e r a g re e s with o u r g e n e ra l contention th a t a c o m p lete re d u c tio n of im p e ra tiv e logic to in d ic ativ e logic c a u s e s a lo ss in the p e c u lia r sig n ific a n c e of im p e ra tiv e in fe re n c e s . He also , in a g r e e m ent with R o ss, c o n s id e rs fo rm u la s of the type p —> { p v q ) as in v alid in im p e ra tiv e logic. T hat th is notion of deduction b a sed on sc o p e is v e ry r e s tr ic tiv e , a n d not sim p ly a m a tte r of in d ic ativ e logic r e w r i t ten, m ay be s e e n by c o n sid e rin g d e riv a tio n s , v alid in s e n te n tia l c a lc u lu s, but n e c e s s a r ily in v alid in an im p e ra tiv e logic. F o r ex am p le , in th e s e n te n tia l calcu lu s p —> (p v q ) is a fo rm u la . In an im p e ra tiv e logic th is would le a d to the a b s u rd ity th at to te ll so m e o n e to 'm a il the l e t t e r 1 would be to te ll h im to ‘m a il the le tte r o r b u rn the l e t t e r 1. T he g e n e ra l use of th e im p lic a tio n -fu n c tio n with r e s p e c t to S to re r, footnote 2 on p. 27. S to re r u se s the " h o rs e s h o e ” fo r m a te r ia l im p lic a tio n in th e fo rm u la m en tio n ed . I have re p la c e d th e h o rs e s h o e by the a rr o w ( —>). 63 i m p e r a t i v e s i s a n o t h e r c o n t r o v e r s i a l i s s u e b e tw e e n B o h n e r t a n d R o s s . R o s s h a d p o in te d o u t t h a t a n i n f e r e n c e in v o lv in g I ( x —> y ) c a n b e m e a n in g f u l i n t h e lo g ic of s a t i s f a c t i o n , a n d t h a t a n i n f e r e n c e in v o lv in g I(x )—> I ( y ) c a n be m e a n in g f u l i n th e lo g ic of v a l i d i t y . H o w e v e r , a c o m b i n a t i o n o f t h e tw o , g iv in g m e a n i n g in th e lo g ic of v a l i d i t y to a n i n f e r e n c e in v o lv in g I ( x —> y ) , i s n o t p o s s i b l e . T o d e m o n s t r a t e t h i s , R o s s u s e s th e f o llo w in g e x a m p l e ( p . 4 2 ) : I ( x ) : L o v e y o u r s e l f ! I ( x —> y ) : L o v e y o u r n e i g h b o r a s y o u r s e l f ! I ( y ) : L o v e y o u r n e i g h b o r ! If e a c h o f th e p r e m i s e s i s s a t i s f i e d , t h e n t h e c o n c l u s i o n is s a t i s f i e d . R o s s a r g u e s , h o w e v e r , t h a t f r o m th e p o in t o f v ie w o f v a l i d i t y , th e i n f e r e n c e in q u e s t i o n i s f a l s e ( p . 4 2 ) . T h e s e c o n d p r e m i s e s a y s t h a t o n e 's n e ig h b o r is to b e lo v e d a s o n e a c t u a l l y lo v e s o n e s e l f . B u t w e c a n n o t p r e s u p p o s e th a t th e f i r s t p r e m i s e is s a t i s f i e d ; a n d if i t is n o t s a t i s f i e d , t h e n th e c o n c l u s i o n d o e s n o t fo llo w . A t r a n s l a t i o n of t h i s i n f e r e n c e in to t h e l i n g u i s t i c a l l y i n d i c a t i v e f o r m of e a c h i m p e r a t i v e m a y h e lp s u p p o r t R o s s 's c r i t i c i s m : I ( x ) : Y o u o u g h t to lo v e y o u r s e l f . I ( x —> y ) : Y o u o u g h t to lo v e y o u r n e i g h b o r a s y o u lo v e y o u r s e l f . I ( y ) : Y o u o u g h t to lo v e y o u r n e i g h b o r . T h is v e r s i o n of t h e i n f e r e n c e s h o w s q u ite c l e a r l y th a t t h e c o n c l u s i o n f o llo w s o n ly if y o u a c t u a l l y do lo v e y o u r s e l f ; b u t n e i t h e r p r e m i s e s a y s 64 th a t th is is the c a s e . In th e lig h t of th e s e c o n s id e r a tio n s , R o s s n o te s th a t: It is s tr a n g e th a t th is a n d s i m i l a r e x a m p le s r e c u r in J u r g e n J o r g e n s e n , G r e llin g , G r u e - S o r e n s e n , an d R o se R an d w ithout th e s e a u th o r s b e in g a w a r e of th e f a c t th a t, n a tu r a lly u n d e rs to o d , i. e. , u n d e rs to o d w ith a v ie w to th e v a lid ity of th e im p e r a tiv e s , th e c o n c lu s io n is f a ls e . ( R o s s , p. 4 2 ) T he in f e r e n c e in q u e s tio n is p ro v a b le in B o h n e r t's s y s te m , and, a s m ig h t be e x p e c te d , he s id e s w ith J o r g e n s e n , G re llin g , and o th e r s in h o ld in g th a t th e c o n c lu s io n fo llo w s v a lid ly f r o m th e p r e m i s e s . B o h n e rt s u g g e s ts th a t h is d i s a g r e e m e n t w ith R o ss m u s t be a d iffe re n c e in p e r s o n a l in tu itio n s : "T h e a u th o r c a n only b lu n tly s a y th a t he fe e ls th e c o n c lu d in g c o m m a n d to follow f r o m th e c o n ju n c tio n of th e two p r e c e d in g c o m m a n d s " ( B o h n e rt, p. 313 ) . It s e e m s e v id e n t, h o w e v e r, th a t R o s s 's c o n s id e r a tio n s , a id e d by o u r t r a n s la ti o n of h is e x a m p le , m a k e a s t r o n g e r c a s e th a n B o h n e r t's " f e e l in g s ." N e ith e r th e lo g ic of s a t is f a c ti o n a lo n e n o r th e lo g ic of v a lid ity a lo n e , a s d e v e lo p e d th u s far, is c a p a b le of a c c o u n tin g f o r th e im p lic a tio n - fu n c tio n of p r a c t i c a l in f e r e n c e s . R o s s h a s h e ld th a t no c o m b in a tio n of th e tw o s y s te m s c a n be f o r m u la te d to r e s o lv e th e d iffic u lty . We s h a l l s e e , in o u r d is c u s s io n s of the s y s t e m s d e v e lo p e d by von W rig h t a n d o th e r s , th a t th e im p lic a tio n - fu n c tio n f o r d e o n tic c o n c e p ts is not e a s i l y a c c o u n te d f o r an d y e t is too im p o r ta n t to be ig n o re d . 65 4. A T h r e e - v a l u e d L o g ic of I m p e r a ti v e s T h o m a s S t o r e r 's a r t i c l e , " T h e L o g ic of V alue I m p e r a t i v e s , " ^ h a s b e e n r e f e r r e d to in c o n n e c tio n w ith th e p r o b le m s of th e a m b ig u ity of th e n e g a tio n - f u n c tio n in im p e r a t i v e lo g ic a n d th e p e c u l i a r i t i e s of th e im p lic a tio n - f u n c tio n . T h e s y s t e m f o r i m p e r a t i v e lo g ic w h ich S t o r e r p r o p o s e s is a p u r e ly s y n t a c t ic a l s y s t e m d e s ig n e d to a c c o m m o d a te a n y n u m b e r of s e m a n t ic a l i n t e r p r e t a t i o n s in t e r m s of a x io lo g y : B e c a u s e of i ts e th ic a lly n e u tr a l n a tu r e , I b e lie v e th e c a l c u lu s to be e q u a lly u s e fu l fo r th e a n a l y s i s of a ll a x io lo g ic a l s y s t e m s , i . e . , of a ll s y s t e m s w h o se b a s ic s t a t e m e n t s c a n be s c a l e d by r e l a ti o n s a n a lo g o u s , in t h e i r f o r m a l p r o p e r t i e s , to th e t e r m 'b e t t e r th a n ' a n d ’a s g o o d a s '. T he m a in p o in ts of d if f e r e n c e b e tw e e n v a r i o u s a x io lo g ic a l p o s itio n s c o u ld o n ly be b ro u g h t o u t by a c o n s id e r a tio n of th e s e m a n t ic s y s te m n e c e s s a r y to m a k e u s e of th is c a lc u lu s , ( p . 2 8 ) S t o r e r s u g g e s ts th a t a s y s t e m of c o u n te r s o r a v a lu e s y s t e m m ig h t be d e v e lo p e d f o r i m p e r a t i v e s on th e b a s i s o f t h e i r d e g r e e , t h e i r f o r c e , o r t h e i r s c o p e . T h e m e th o d of s u b s u m in g u n d e r a g e n e r a l i m p e r a t i v e s u g g e s te d b y R o s s w ould b e a n e x a m p le of w h at S t o r e r m e a n s b y a v a lu e s y s t e m b a s e d on th e s c o p e of i m p e r a t i v e s . S c a lin g a c c o r d in g to f o r c e in v o lv e s d is tin g u is h in g th e u r g e n c y w ith w h ic h an a c tio n is c o m m a n d e d . Such a s c a lin g m ig h t be m a d e of the i m p e r a - P h ilo s o p h y of S c ie n c e , 1 3 :2 5 -4 0 , 1946 . 66 t iv e s : 'd o n ot k ill, 1 'y o u o u g h t not to k ill, ' a n d 'i t is y o u r d u ty n ot to k i l l . ' S t o r e r 's s u g g e s tio n h e r e in d ic a te s th a t th e d if f e r e n c e b e tw e e n w h at we h a v e c a lle d i m p e r a t i v e s a n d n o r m a t iv e s , r e s p e c t iv e ly is not on e of k in d b u t of r e l a t i v e p o s itio n on a g e n e r a l s c a l e of i m p e r a t iv e s . S t o r e r h i m s e l f c h o o s e s the d e v e lo p m e n t of v a lu e c o u n te r s f o r i m p e r a t i v e s in t e r m s of d e g r e e a s th e m o s t s a t i s f a c t o r y o n e of th e t h r e e a p p r o a c h e s m e n tio n e d . T h is k ind of v a lu e c o u n te r m a y be in tu itiv e ly th o u g h t of a s e x p r e s s in g th e " g o o d n e s s " o r " e th ic a l r i g h tn e s s " of c o m m a n d s - - h e n c e th e u s e of th e t e r m 'v a lu e i m p e r a t i v e s ' in th e title of S t o r e r 's a r t i c l e . T h e p r i m i t iv e s y m b o ls of h is c a lc u lu s in c lu d e b o th in d ic a tiv e s e n t e n t ia l v a r i a b l e s ( p . q, r , . . . ) a n d im p e r a t i v e s e n te n tia l v a r i a b le s ( a, b, c, . . . ) . In g e n e r a l, p is an in d ic a tiv e s e n t e n t ia l v a r ia b le , w h e r e a s p j r e p r e s e n t s a c o n s ta n t in d ic a tiv e s e n te n c e ; c r e p r e s e n t s a n im p e r a t i v e s e n t e n t ia l v a r i a b le , w h e r e a s c j r e p r e s e n t s a n im p e r a t i v e s e n t e n c e . C o m b in in g th e p a n d c e le m e n ts in a ll p o s s ib le w a y s, we o b ta in a n u m b e r of c o m p o s itio n m a t r i c e s , d e s ig n a te d by th e p r e f ix M . T h e r e a r e e ig h t p o s s ib i l i ti e s f o r th e s e r e s u l t a n t c o m p o u n d s w h ich S t o r e r g ro u p s in th e fo llo w in g w ay ( p . 2 8 ) : la ; M ( p p ) is a p Ilia : M ( p c ) is a p b; M ( p p ) is a c b; M ( p c ) is a c Ila: M ( c c ) is a p IV a: M ( c p ) is a p b; M ( c c ) is a c b; M ( c p ) is a c 67 In h is c a lc u lu s S t o r e r d o e s n o t d is tin g u is h b e tw e e n g r o u p s III a n d IV . T h e n u m b e r o f c o m b in a tio n s f o r w h ich m a t r i c e s n e e d to be g iv e n is t h e r e f o r e r e d u c e d to s ix . S t o r e r f u r t h e r e x c lu d e s m a t r i c e s of th e ty p e I b ^ a n d H la , i. e . , n o m a t r i c e s of th e ty p e ' M ( p p ) is a c ’ or lM ( p c ) is a p 1 w ill be a llo w e d . T h is w ill m e a n th a t to g e n e r a t e a n i m p e r a t i v e fro m tw o s e n te n c e s o r a s e n te n c e f r o m a n i m p e r a t i v e a n d a s e n te n c e is i m p o s s ib le . T h is I b e lie v e to b e a b a s ic f e a t u r e of a n y c a lc u lu s w h ic h h o p e s to r e f l e c t th e p r o p e r t i e s i m p e r a t i v e s p o s s e s s in th e s p o k e n la n g u a g e , (pp. 28-29) T h is s t a t e m e n t is a v a r i a n t of th e c o n c lu s io n w e h a d r e a c h e d e a r l i e r , n a m e ly , th a t a n i m p e r a t i v e c a n n o t be d e r iv e d f r o m in d ic a tiv e s a lo n e . S t o r e r 's a d d e d s tip u la tio n t h a t we s h o u ld n o t d e r i v e a n in d ic a tiv e s e n te n c e f r o m a n i m p e r a t i v e an d a n in d ic a tiv e s e e m s a ls o to be in tu itiv e ly c o r r e c t . O f th e e ig h t c o m b in a tio n s fo u r now r e m a i n f o r w hich m a t r i c e s a r e g iv e n in S t o r e r 's c a lc u lu s . H o w e v e r, one m a y q u e s tio n th e f e a s i b i li t y of r e t a in i n g on e of th e fo u r c o m b in a tio n s , n a m e ly , H a, w h ich c o m b in e s tw o i m p e r a t i v e s to f o r m a n in d ic a tiv e . It is not e v id e n t th a t, in g e n e r a l, s u c h c o m b in a tio n s c a n be c o r r e c t l y m a d e . ^ T h e r e is a n o b v io u s m i s s t a t e m e n t on p. 29 of S t o r e r 's p a p e r w h e re h e r e f e r s to tw o of th e r e m a in in g ty p e s a s M Ib and H a . " Ib is d e fin ite ly e x c lu d e d , a n d the te x t s h o u ld r e a d H Ib and H a . T h is is b o rn e out l a t e r in th e p a p e r w hen he a c tu a lly u tiliz e s m a t r i c e s of ty p e H Ib but n e v e r g iv e s a m a t r i x of ty p e I b . 68 H o w e v e r, the only u s e s w hich S t o r e r m a k e s of th is c l a s s of m a t r ic e s do n o t, in th e m s e lv e s , s e e m o b je c tio n a b le . H e c o m b in e s tw o i m p e r a t iv e s by a s y m b o l f o r " in c lu s io n " s o th a t one c o m m a n d is s a id to in c lu d e a n o th e r w hen it is m o r e m o r a l th a n the o th e r . The e q u iv a le n c e r e la tio n of im p e r a tiv e s is th e n defin ed a s h o ld in g w hen e a c h im p e r a tiv e " in c lu d e s " th e o th e r: 'c = d ' is tru e if and only if th e im p e r a tiv e s 'c ' an d 'd ' a r e of th e s a m e d e g re e . The e q u iv a le n c e - s e n te n c e is i ts e l f a n in d ic a tiv e an d m ay b e tr u e o r f a ls e , a lth o u g h it e x p r e s s e s a r e la tio n s h ip b e tw ee n tw o im p e r a tiv e s . T he s a m e m a y be s a id of th e in c l u s i o n - s e n te n c e s . T h e v a lu e c o u n te r s f o r th e p ( in d ic a tiv e ) s e n te n c e s in S t o r e r 's s y s te m a r e T an d F (for 't r u e ' an d 'f a ls e ') . T he v a lu e c o u n te rs fo r c ( i m p e r a t i v e ) s e n te n c e s a r e 0, 1, and 2, w hich " m a y be c o n c e iv e d a s r e p r e s e n ti n g p s e u d o - s e m a n tic a l te r m s 'm o r a l , ' 'a m o r a l,' and 'i m m o r a l,' r e s p e c tiv e ly " ( p . 29). The d e te r m in a tio n of th e m o r a l im p e r a tiv e s m a y be b a s e d upon a p a r t i c u l a r a x io m s e t, e . g . , the T e n C o m m a n d m e n ts . T hen, if Cj is th e v a lu e im p e r a tiv e 'h o n o r th y f a th e r a n d thy m o th e r, ' it is a m o r a l s e n te n c e and has th e d e g re e 0 . T h e n e g a tio n of any m o r a l s e n te n c e y ie ld s an i m m o r a l s e n te n c e (o f d e g r e e 2) . H o w ev er, an a x io m s e t, s u c h as th e T e n C o m m a n d m e n ts , le a v e s a n u m b e r of h u m a n s itu a tio n s u n e x p la in e d . F o r e x a m p le , 'e a t c e l e r y ' is an im p e r a tiv e w hich is 69 n e i t h e r m o r a l n o r i m m o r a l u n d e r th is s y s te m ; it is t h e r e f o r e of d e g r e e 1 { a m o r a l ) - T h e n e g a tio n of a n a m o r a l s e n te n c e is s t i l l a n a m o r a l s e n te n c e . T h e s e c o n s i d e r a ti o n s ju s tif y S t o r e r 's c h o ic e o f a t h r e e - v a l u e d lo g ic f o r i m p e r a t i v e s . B u t th e c h o ic e of th e t h r e e v a lu e s d o e s n o t, in its e lf , r e l i e v e th e a m b ig u ity of th e n e g a tio n - fu n c tio n ; f o r c o n s i d e r the fo llo w in g : (1) ‘Do n o t k i ll 1 is m o r a l ( of d e g re e 0 ) . (2) 'D o n o t not k i l l 1 = ‘D o k ill' is i m m o r a l ( of d e g r e e 2 ) . (3) ‘not ( d o not k i l l ) 1 is th e n e g a tio n o f th e e n t i r e c o m m a n d b ut is n e ith e r m o r a l n o r i m m o r a l . T o h a n d le th e l a s t o f th e s e i m p e r a tiv e f o r m s , S t o r e r in tr o d u c e s a c a n c e lla tio n o p e r a t o r w h ich h a s th e p r o p e r t y o f n u llify in g an y g iv e n m o r a l c o m m a n d . T h e o r d i n a r y n e g a tio n o f m o r a l s e n te n c e (1) y ie ld s i m m o r a l s e n te n c e (2) ; th e c a n c e lla tio n of (1) y ie ld s (3) . S t o r e r m ig h t h a v e p o in te d out th a t (1) a n d (2) a r e c o n t r a r i e s w hile (1) a n d (3) a r e c o n t r a d i c t o r i e s . A c tu a lly a t h r e e - v a l u e d lo g ic is n o t a n e c e s s a r y p r e r e q u i s i t e f o r r e s o l v in g th e a m b ig u ity of th e n e g a tio n - fu n c tio n . E a c h of the s y s te m s to b e d i s c u s s e d in th e n e x t c h a p te r is a b le to a v o id th is d iffic u lty w ith in a tw o - v a lu e d lo g ic by u sin g s p e c if ic o p e r a t o r s f o r th e c o n c e p ts of o b lig a tio n a n d p e r m i s s i o n . T h e o r d i n a r y n e g a tio n s ig n p r e c e d in g one of t h e s e " d e o n tic " o p e r a t o r s a c h ie v e s th e s a m e r e s u l t ( o f n u llify in g th e d e o n tic p r o p o s i t io n ) as S t o r e r 's c a n c e lla tio n o p e r a t o r . T he p r o b l e m of h a n d lin g a m o r a l a c t s 70 is a l s o a d e q u a te ly r e s o l v e d b y c h a r a c t e r i z i n g s u c h a c t s a s th o s e 44 w h ic h o n e i s b o th p e r m i t t e d to d o a n d p e r m i t t e d to o m it. S t o r e r 's s e l e c t i o n o f th e d e g r e e of a n d - c o m b in a tio n s a n d o r - c o m b i n a t i o n s i s g u id e d by th e s e m a n t i c a l i n t e r p r e t a t i o n h e h a s in m in d f o r h is s y n t a c t i c a l s y s t e m . A n a n d - c o m b in a t io n ta k e s th e l e s s e r o f th e tw o d e g r e e s of its c o m p o n e n ts . T h e c o m b in a tio n 'h o n o r th y f a t h e r a n d m o th e r , a n d e a t c e l e r y ' h a s v a lu e s o f th e f o r m '0 a n d 1* . T h u s , in a c c o r d a n c e w ith S t o r e r 's r u l e , th is c o m b in a tio n w ill be of d e g r e e 0 , a n d th is s e e m s q u ite c o r r e c t s in c e th e s t a t e m e n t a c t u a l l y d o e s c o m m a n d a m o r a l a c t. S t o r e r 's r u l e f o r o r - c o m b i n a t i o n s is th a t th e y ta k e th e g r e a t e r of th e tw o d e g r e e s of t h e i r c o m p o n e n ts ; th e d e g r e e o f o u r e x a m p le ( '0 o r 1' ) is , t h e r e f o r e , 1 . S t o r e r a d m i t s th a t s u c h a n i n t e r p r e t a t i o n p r e s u p p o s e s : a p e o p le w ho a r e by n a tu r e m o r a l l y v ic io u s , and who w ould a lw a y s c o m m it i m m o r a l a c t s w e re th e y n o t k e p t in c h e c k b y th e i m p e r a t i v e la w s w h ic h g o v e r n th e m . ( p . 3 3 ) F a c e d w ith a '1 o r 2' s itu a tio n , we a r e im p u te d b y th e d e fin itio n a lw a y s to c h o o s e th e 2 ( the i m m o r a l a c t i o n ) . S u ch a n i n t e r p r e t a tio n of h u m a n n a t u r e m a y o r m a y n o t b e c o r r e c t , b u t it o b v io u s ly le a d s u s f a r a f ie ld f r o m o u r s p e c i f i c p r o b l e m . P h i l o s o p h e r s la c k in g th is C a lv i n i s t ic v ie w o f h u m a n n a tu r e w o u ld r e q u i r e a d if f e r e n t S e e the d i s c u s s i o n of v o n W r ig h t's f i r s t s y s t e m in C h a p te r I I I . 71 i n t e r p r e t a t i o n o r , w hat s e e m s m o r e p r o b a b le , a d if f e r e n t s y n t a c t ic a l s y s t e m . T h e c o n n e c tiv e w h ic h s e e m s a t f i r s t g la n c e to b e a r th e m o s t p r o m i s e is th e a r r o w , ' —>' , w h ich is i n t e r p r e t e d a s 'i f . . . th e n . . . A n i n t e r e s t i n g a p p lic a tio n of th is c o n n e c tiv e o c c u r s in th e c o m b in a tio n m a t r i x Illb ( M ( p c ) is a c ) . In th is c a s e the a r r o w c o m b in e s a n in d ic a tiv e w ith an i m p e r a t i v e to y ie ld a n i m p e r a tiv e , s y m b o lic a lly : ’p —> c ’ ( ’if p th e n c ' ). A s a n i ll u s t r a t i o n S t o r e r g iv e s th e s e n te n c e ’if he is a foe, th e n s h o o t h im . 1 T he d e fin in g m a t r i x fo r the —> m a k e s th e r e s u l t a n t i m p e r a t i v e h a v e th e d e g r e e of c w h e n e v e r p is t r u e , a n d th e d e g re e 1 ( a m o r a l ) w h e n e v e r p is f a l s e . T h u s, if 'h e is a fo e ' is t r u e , the w hole i m p e r a tiv e h a s th e d e g re e of 's h o o t h i m . ' If ’he is a fo e ' is f a l s e , th e n th e d e fin itio n s a y s th a t th e w hole c o m m a n d is a m o r a l. Now, S t o r e r s a y s th a t if 'h e is a fo e ' is f a l s e , th e c o m m a n d is n e it h e r to s h o o t, n o r not to s h o o t. No c o m m a n d h a s b e e n m a d e , s o th e i m p e r a tiv e is a m o r a l, a n d o f d e g re e 1 . ( p. 34 ) T h is s e e m s lik e a p r o m is in g w ay out of th e a n a lo g u e to tw o - v a lu e d lo g ic s in w h ich a f a ls e s e n te n c e m a t e r i a l l y im p lie s a n y th in g . U n f o r tu n a te ly , it d o e s n o t s e e m p o s s ib le to h o ld c o n s is te n tly th a t " n o c o m m a n d h a s b e e n m a d e " and, a t th e s a m e tim e , th a t " th e i m p e r a tiv e is a m o r a l . " A n a m o r a l c o m m a n d ( e .g . , ’e a t c e l e r y ' ) is no l e s s a c o m m a n d th a n a m o r a l c o m m a n d ( e . g . , ’do n o t k ill' ) . A p e r s o n 72 who is sh o t on an a m o r a l c o m m a n d is o s te n s ib ly ju s t a s dead a s one who is sh o t on a m o r a l c o m m a n d . The re la tio n s h ip p —> c m u s t, by defin itio n , c h a r a c t e r i z e a c o m m a n d , and, in c a s e p is fa ls e , th e to ta l c o m m a n d is a m o r a l. S t o r e r 's o b s e rv a tio n th a t, w hen p is fa ls e , no c o m m a n d is m a d e , is c o r r e c t . In th e e x a m p le given, th e c o m m a n d is to sh o o t if the ta r g e t is a foe. H ence, if th e t a r g e t is not a foe, no c o m m a n d h a s b e en g iven a n d th e r e is no im p e r a tiv e of d e g re e 1 o r o f any o th e r d e g re e . H o w ev er, it would be a m o re s a t is f a c to r y c h a r a c te r iz a tio n to m a in ta in p —>c a s a v a lid fo rm u la only if p is t r u e . W here p is fa ls e , no c o m m a n d is given , and p —>c h a s no im p e r a tiv e m ea n in g . B ut th is is q u ite d iffe re n t f r o m sa y in g th a t p—>c is a m o r a l. The a n alo g u e in th is c a s e is to the c o n ce p t of s t r i c t im p lic a tio n in tw o v a lu e d lo g ic s, r a t h e r th an to m a t e r i a l im p lic a tio n . S to r e r d ev elo p s an a x io m s e t fo r h is s y s te m , but e v a lu a tio n of the a x io m s would only le a d us b a ck to a c o n s id e ra tio n of h is b a s ic d e fin itio n s, w hich we h av e a lr e a d y d is c u s s e d . T he a d v a n ta g e s of S t o r e r ’s th r e e - v a lu e d logic of im p e r a tiv e s in avo iding the a m b ig u ity of th e n e g a tio n -fu n c tio n do not outw eigh th e d is a d v a n ta g e s . T he a s s u m p tio n of a c o rr u p t h u m a n n a tu re , n e c e s s a r y f o r a ju s tif ic a tio n of h is c h o ice of v alu e c o u n te r s , is its e lf in n e ed of ju s tific a tio n . H is g e n e r a l a p p ro a c h of a tte m p tin g to c la s s if y im p e r a tiv e s a c c o rd in g to 73 their degree of ethical rightness does not appear to be ai from a logical point of view as the approach involving th« scope of imperatives. The approach to the logic of obligation which we the imperative approach has not given us a completely s £ answer to our problem. N o one of the systems discusse « has adequately characterized the "practical syllogism" ' the key to the logic of obligation. W e have, however, ar— several major conclusions concerning the nature of imps- ferences. It is not possible to arrive at an imperative cm unless at least one of the premises in the reasoning invoH imperative. Ross's characterization of the practical in f« one containing at least one imperative, thus must be furt: stricted to inferences containing at least one imperative The logic of satisfaction, and in general any system whic imperatives to indicative sentences, has been deemed vfi~~ adequate since it makes superfluous the very imperative which w e attempt to account. The most straightforward practical inference appears to be the subsumption under imperative. The relevant passages in Aristotle and St. seem to refer to this type of practical syllogism, and thx. fruitful deductive .ave called * ~tisfactory „ -1 thus far holds » ’ stive in- ^ nr.lnsinn, E_ "ved is an rence as ler re- » remise, l i reduces oily in- content for ty p e of general "homas i fact, plus Ross's observations, suggests the need for further inves— ;i gat ion 74 along these lines. The authors of the s y s t e m s we h a v e d i s c u s s e d a ll s e e m to a ssu m e that norm atives ( s e n t e n c e s e x p r e s s i n g " o u g h t s , " d u tie s, o r obligations ) a re types o f i m p e r a t i v e s to w h ic h t h e i r p ro p o se d lo g ics should apply. Ross a n d S t o r e r a c tu a lly m a k e e x p lic it s t a t e m en ts to this effect. In the n e x t c h a p te r we s h a l l c o n s i d e r s y s te m s w hich deal directly with n o r m a t i v e s . A c o m p a r i s o n of the i m p e r a tiv e and norm ative a p p ro a c h e s sh o u ld r e v e a l w h ic h h o ld s th e m o st p ro m is e as an adequate c h a r a c t e r i z a t i o n of th e l o g i c of oblig atio n . If R oss and S torer are c o r r e c t , th en th e r e s u l t s o f th e two a p p ro a c h e s should apply e q u a lly to o b lig a tio n s e n t e n c e s , w h e th er they a r e ex p re ssed as im p e ra tiv e s o r a s n o r m a t i v e s . CHAPTER III N O RM A TIV E LOGICS T he s y s te m s d is c u s s e d in C h a p te r II a tte m p te d to a cc o u n t fo r the lo g ic a l in te r r e la tio n s of o b lig a tio n s e n te n c e s w ithin a g e n e r a l logic f o r im p e r a tiv e s . In th e p r e s e n t c h a p te r we s h a ll d is c u s s th e s y s te m s w hich have re c e n tly been d ev elo p ed in o r d e r to d e a l w ith o b lig a tio n s e n te n c e s m o re e x c lu siv e ly . T h is a p p ro a c h to the logic of o b lig a tio n w ill be c a lle d th e n o rm a tiv e a p p ro a c h , and to e a c h s y s te m w hich ev o lv e s f r o m it we s h a ll apply e ith e r the t e r m ’n o rm a tiv e lo g ic ' o r th e t e r m ’deo ntic lo g ic. ’ G e o rg H e n rik von W right, the a u th o r of th e f i r s t of the n o rm a tiv e s y s te m s w hich w ill be d is c u s s e d , ^ a p p lie s the term ’D eontic L o g ic 1 to h is s y s te m , c re d itin g C. D. B ro a d w ith the s u g g e stio n of the n a m e . H o w ev er, the u se of the te r m ’D eontic L o g ic ’ in c o n n ec tio n with w hat we have c a lle d the p r a c t ic a l s y llo g is m w as 1 T h e " p io n e e r" n o rm a tiv e logic is the s y s te m d ev elo p ed by von W right in "D eo n tic L ogic, " M ind, 60 :1 -1 5 , 1951; re p r in te d in von W right, L o g ic a l S tu dies ( London, 1957), pp. 58-74. T h is s a m e s y s te m is d e s c r ib e d by von W right in An E s s a y in M odal L ogic ( A m s te rd a m , 1951), pp. 36-41. 75 76 know n as e a r ly a s 1926, w hen E r n s t M ally p u b lish ed h is G ru n d g e s e tz e d es S o llen s; E le m e n te d e r L ogik des W ille n s. A c c o rd in g to Alf R o ss, M ally a p p lie d the t e r m rD eontik' to h is "L o g ik des W ille n s" and " M a lly , s way of re a s o n in g le a d s in a w ell known m a n n e r, to w a rd s the c o n s tru c tio n of a f o r m a lis tic e t h i c s ." ^ T he m a jo r p ro b le m of the im p e r a tiv e a p p ro a c h w as to: e lu c id a te w h e th e r s e n te n c e s w hich a re not d e s c r ip tiv e , but w hich e x p r e s s a d em an d , a w ish, o r the like, m ay be m ad e o b je c ts of lo g ic a l tr e a tm e n t in the s a m e o r a s i m i l a r m a n n e r a s th e in d ic a tiv e s ta te m e n ts . (Ross, p. 31) T he m a jo r p ro b le m of the n o rm a tiv e a p p ro a c h is to p r e s e n t a lo g ic a l s y s te m fo r h an d lin g s e n te n c e s w hich e x p re s s o b lig a tio n s, p e r m i s s io n s , an d p ro h ib itio n s . T h a t th e r e m ay be a d v an tag e s in th is n o r m a tiv e a p p ro a c h h a s a lre a d y been fo re sh a d o w e d by R o s s 's d is c u s s io n of th e n e g a tio n -fu n c tio n fo r im p e r a tiv e s . An in te r p r e ta tio n fo r the n e g a - tio n -s y m b o l as ap p lied to im p e ra tiv e s w as seen to be a m b ig u o u s ; but w hen R o ss tr a n s la te d th e im p e r a tiv e s in to n o rm a tiv e s , the a m b ig u ity d is a p p e a r e d . ^ B oth a p p r o a c h e s - - th e im p e ra tiv e and the n o r m a tiv e - - a g re e upon the p r a c tic a l n a tu re of th e re s p e c tiv e s e n te n c e s u n d e r in v e s tig a tio n . T he a u th o rs of the im p e r a tiv e s y s te m s g e n e ra lly c o n s i d e r im p e r a tiv e s a s m a k in g a d em an d fo r a c tio n and h av e m uch to 2 A lf R o ss , " I m p e ra tiv e s and L o g ic ," P h ilo so p h y of S cien ce, 11:30. ^ See R o ss , p. 3 9. 77 s a y ab o u t the " th e m e of d em an d " of the im p e r a tiv e . T he a u th o rs of n o rm a tiv e s y s te m s t r e a t n o rm a tiv e s a s s a y in g so m e th in g about a c tio n s , i. e . , a n o rm a tiv e s a y s of an a c t th a t it is o b lig a to ry , p e rm itte d , o r fo rb id d en . Von W rig h t's v e rs io n of deo ntic logic p ro v id e s s o u r c e m a te - 4 r i a l to w hich su c c e e d in g s y s te m s refer. A. N. P r i o r , A. R. 5 0 A n d e rso n , and von W right h im s e lf, use von W rig h t's o rig in a l s y s te m a s a b a s is fo r d eveloping o th e r v e r s io n s of d eo n tic lo g ic. In view of the im p o rta n t ro le w hich it thus p lay s in the d ev elo p m en t of deo n tic logic, von W rig h t's o rig in a l s y s te m m e r i ts d e ta ile d c o n s id e r a tio n in o u r s e a r c h fo r an a d eq u ate logic of oblig atio n . 1. Von W rig h t's "D eo n tic L ogic " Von W right sp e a k s of th e deontic m o d a litie s as being "ab o u t th e m ode o r way in w hich we a r e p e r m itte d o r not to p e r f o r m an act."^ ^ "M odal and D eontic L o gic, " A ppendix D to T im e and M odality ( O xford, 1957), pp. 1 4 0 -1 4 5 . "A R ed u ctio n of D eontic L o g ic to A leth ic M odal L ogic, " M ind, 67 :1 00-103, 1958. "A Note on D eontic L ogic an d D e riv e d O bligation, " M ind, 65:507-509, 1956. n An E s s a y in M odal L ogic, p. 3 6 . 78 In o r d in a r y language th e w o rd 'a c t ' is s o m e tim e s u s e d fo r a c t- q u alify in g p r o p e r tie s ( e . g . , theft), and s o m e tim e s fo r an in d iv id u a l c a s e w hich fa lls u n d e r th is p r o p e r ty ( e .g . , th is t h e f t ) . The g e n e r a l a c t of s te a lin g m ay be c o n s id e r e d a s a p ro p e r ty , w hile the a c t of s te a lin g a c e r ta in th in g , c o m m itte d by a c e r ta in in d iv id u al, on a c e r ta in o c c a sio n , is an in d iv id u a l o c c u r r e n c e of th a t p r o p e rty . Von W rig h t's p ro p o s a l is to c o n s id e r the d eo n tic c o n c e p ts a s a ttr ib u te s of a c t - p r o p e r t ie s and not of a c t- in d iv id u a ls . Such a r e s t r i c ti o n n e c e s s a r il y le a d s to an " a b s o lu te " lo g ic a l s y s te m in the s e n s e th a t only g e n e r a l c a s e s of o b lig a to ry , p e rm itte d , o r fo rb id d e n a c ts m ay be d e a lt w ith. T he p ro b le m of s u b s u m in g a s p e c ific o c c u r r e n c e of an a c t u n d e r a g e n e ra l a c t - p r o p e r t y is not c o n s id e r e d in th is s y s te m a t a ll. The notion of " p r e s e n c e - f u n c tio n s " fo r p r o p e r tie s is in tro d u c e d by von W right in s t r i c t analogy to the c o n ce p t of tr u th -f u n c tio n s fo r p ro p o s itio n s . A c e r ta in p r o p e r ty is s a id to be p r e s e n t in a c e r ta in thing w hen th e s ta te m e n t th a t th a t thing h as th a t p r o p e r ty is true. S im ila rly , a p r o p e r ty is s a id to be a b s e n t in the th in g if the s t a t e m en t th a t the th in g h a s th a t p r o p e r ty is fa ls e . S u b stitu tin g 'a c t' f o r 'p r o p e r t y 1 an d 'p e r f o r m e d ' fo r 'p r e s e n t ' we obtain: a c e r ta in a c t is s a id to be p e rf o r m e d by an ag en t w hen th e s ta te m e n t th a t th a t a g e n t h as p e r f o r m e d th a t a c t is true; th e a c t is s a id to be o m itte d 79 < " n o t- p e r f o r m e d " ) by an a g e n t w hen the s ta te m e n t th a t th a t ag en t h a s p e r f o r m e d th a t a c t is fa ls e . A p r o p e r ty is a p r e s e n c e - fu n c tio n of so m e o th e r p r o p e r t i e s , we m ay sa y , if th e p r e s e n c e - v a lu e of th e f o r m e r in a th in g is u n iq u ely d e te r m in e d by the p r e s e n c e - v a lu e s of the l a t t e r in the s a m e th in g . (A n E s s a y in M odal L ogic, p p . 6-7) S im ila rly : An a c t w ill be c a lle d a p e rfo r m a n c e -f u n c tio n of c e r ta in o th e r a c ts , if its p e r f o r m a n c e -v a lu e fo r any g iven ag en t uniquely d ep en d s upon th e p e r f o r m a n c e - v a lu e s of th o se o th e r a c ts fo r the s a m e a g e n t. (" D e o n tic L o g ic ," p. 2 ) Von W rig h t d ev elo p s th e c o n cep t of a p e rfo rm a n c e -fu n c tio n in s t r i c t a n alo g y to th e c o n c e p t of a tru th -fu n c tio n in o r d in a r y pro- p o s itio n a l lo g ic. F o r e x a m p le the n e g atio n ( - act) of a given a c t is th e a c t p e rf o r m e d if, and only if, th e ag en t does not perform the g iv en a c t. If A d e n o te s ( i s the n a m e o f) an a c t, ~ A w ill denote its n e g atio n ( - a c t ) . T h u s, if A d en o tes the act of re p a y in g a loan, ~~A d e n o te s the a c t of not re p a y in g it (" D e o n tic L o g ic, " p. 2 ) . If A and B denote a c ts , A&.B d en o tes th e ir co n ju n ctio n . T he c o n ju n c tio n -a c t d en o ted by A&B is p e r f o r m e d by an ag en t if and only if, the a c t d en o ted by A and the a c t den oted by B a r e both p e rf o r m e d . If A an d B d en o te a c ts , AvB d e n o te s th e ir d is ju n c - tio n -a c t, A —>B d en o tes th e ir im p lic a tio n -a c t, and A < > B d e n o te s th e ir e q u iv a le n c e a c t. A d isju n c tio n a c t of two g iv en a c ts 80 is p e r f o r m e d if, and only if, a t l e a s t one of th e two g iven a c ts is p e r f o r m e d . An im p lic a tio n - a c t of tw o g iv en a c ts is p e r f o r m e d if, an d only if, it is not th e c a s e th a t th e f i r s t a c t is p e r f o r m e d an d the s e c o n d a c t is not p e rf o r m e d . An e q u iv a le n c e - a c t of tw o g iven a c ts is p e r f o r m e d if, an d only if, th e se c o n d a c t is p e r f o r m e d w h e n e v e r th e f i r s t a c t is p e r f o r m e d and th e f i r s t a c t is p e r f o r m e d w h e n e v e r th e s e c o n d a c t is p e r f o r m e d . T he p e c u lia r n a tu re of p e r f o r m a n c e -f u n c tio n s of a c ts sh o u ld be c a r e fu lly a p p r a is e d in o r d e r to a v o id c o n fu sio n . Von W rig h t e x p lic itly s t a te s th a t ->-A , A&B , AvB , A —> B , and A < >B are g n a m e s of a c ts ( i . e . , th ey d en o te a c ts ) . "-A , f o r in s ta n c e , d e n o te s th e n e g a tio n -a c t of th e a c t d e n o te d by A . ~A is not a s e n te n c e ; it d o e s n ot d en o te a t r u th - v a lu e n o r d o e s it co n n o te a p ro p o s itio n . W hen fu n c to rs ( ~ , & , v , —> , <-------■>) a r e co n jo in ed to a n a m e o r n a m e s of a c ts , th e r e s u l t s a r e a lw a y s n a m e s of acts. C o m p lic a tio n s a r i s e w hen th e n a m e s of a c ts o c c u r in s e n te n c e s b e c a u s e von W rig h t u s e s th e s a m e f u n c to rs f o r the tru th - f u n c tio n s of s e n te n c e s a s he d o e s f o r the p e r f o r m a n c e fu n c tio n s of a c ts . C o n fu sio n c a n be a v o id e d by 8 In the e x p o s itio n of von W rig h t's s y s te m and th e s y s te m s of o th e r w r i t e r s , sy m b o ls w ill be u s e d b oth n o r m a lly a n d a u to n y m o u sly . T h u s, f o r e x a m p le , the sy m b o l ~ A is s o m e tim e s a v a r ia b le ra n g in g o v e r a c ts ( the d u m m y n a m e of an a c t ) and s o m e tim e s is th e m e t a lin g u is tic n a m e of th e s y m b o l. 81 b e a rin g in m in d th a t w hen fu n c to rs a r e c o n jo in ed to n a m e s of a c ts , the r e s u l ts a r e a lw ay s n a m e s of a c ts ; w hile the r e s u l ts o b ta in e d by co n jo in in g fu n c to rs to s e n te n c e s a re alw ays s e n te n c e s . The th re e d eo n tic c a te g o r ie s of von W rig h t‘s s y s te m a r e the p e rm itte d , th e fo rb id d e n , and th e o b lig a to ry . T he only undefined p r im itiv e t e r m of the s y s te m is ‘p e rm itte d . 1 W ith the help of th is te r m , the t e r m s ‘fo rb id d e n 1 and ‘o b lig a to ry 1 a r e d e fin itio n a lly in tro d u c e d . If an a c t is not p e rm itte d , the t e r m ‘fo rb id d e n 1 is a p p lied to it. If the n eg atio n (om ission) of an a c t is fo rb id d e n , the te r m ‘o b lig a to ry 1 is a p p lie d to the a c t. T h u s, an o b lig a to ry a c t is one w hich we a re not p e r m itte d to o m it. "W e ought to do th a t w hich we a r e not allo w ed not to do" (" D e o n tic L o g ic ," p. 3 ) . If an a c t and its n e g atio n a r e both p e rm itte d , the te r m ‘m o ra lly in d iff e r e n t1 is a p p lie d to it. N otice th a t the p o ss ib le fo rm u la tio n of the n a m e s of m o r a lly in d iffe re n t a c ts in th is s y s te m , co m b in ed with a n o n a m b ig u - ous n e g a tio n -fu n c tio n w hich w ill be e x p la in e d la te r , e lim in a te s th e n e c e s s ity of a th r e e - v a lu e d s y s te m . Von W rig h t's in te r p r e ta tio n of o b lig a tio n a s a d eo n tic co n cep t, h is r e f e r e n c e to m o r a lly in d iffe re n t a c ts , and h is l a t e r fo rm u la tio n s of m o r a l c o m m itm e n t m ak e it ev id en t th at he is d e a lin g only w ith th e co n cep t of m o r a l o b lig a tio n . In a l a t e r 82 a r tic le , ® in w hich he a n s w e rs an o b je c tio n to h is s y s te m m ade by R. N. M cL augh lin, von W right s u g g e s ts th a t p a r t of M c L a u g h lin 's o b je c tio n a r i s e s b e c a u s e he u se s an e x am p le involving a c ts w hich a r e not s t r i c t l y m o r a l a c ts . T h e s e r e m a r k s a r e m ad e h e re in o r d e r to e s ta b lis h the fa c t th a t von W rig h t's s y s te m is in te n d ed to d e a l w ith m o ra lly o b lig a to ry a c ts . Now we w ish to m a in ta in th a t any a c t w hich an a g e n t is m o ra lly oblig ed to p e r f o r m is a v o lu n ta ry a c t, i. e . , it m u s t be in the a g e n t's p o w e r to e ith e r do o r not do the a c t. If we m a in ta in th a t only v o lu n ta ry a c ts c an be s a id to be o b lig a to ry , th en we m u s t a ls o hold th a t only v o lu n ta ry a c ts can be s a id to be p e r m itte d o r fo rb id d e n . H ence, the n a m e s of in v o lu n ta ry a c ts cannot o c c u r in the lis t of sy m b o ls in a d e o n tic s y s te m . T h is r e s t r i c t i o n is im p lic it in von W rig h t's s y s te m an d is m ad e e x p lic it h e re to p ro v id e a b a s is fo r in te r p r e tin g th e undefined deontic term 'p e r m is s io n . 1 The deontic s e n te n c e s of von W rig h t's s y s te m a r e o b tain ed by conjoinin g one of the d eontic o p e r a to r s to th e n am e of an a c t. P is th e d e o n tic o p e r a to r r e p r e s e n tin g the concept of p e r m is s io n . T he p ro p o s itio n th a t the a c t n a m e d by A is p e rm itte d is e x p r e s s e d in ® "A Note on D eontic L ogic and D e riv e d O bligation, " M ind, 64:400-4 02, 1955. In M c L a u g h lin 's " F u r t h e r P r o b le m s of D e riv e d O b lig atio n ," M ind, 64 :40 0-402, 1955 . 83 sy m b o ls by PA ; th e p ro p o s itio n th a t the a c t n a m e d by A is f o r bidden is sy m b o liz e d by —{ P A ) ; the p ro p o s itio n th a t the a c t n a m e d by A is o b lig a to ry is sy m b o liz e d by — ( P — A ) - - w hich is s h o r te n e d to OA ; th e p ro p o sitio n th at the a c t n a m e d by A is m o ra lly in d iffe ren t is s y m b o liz e d by ( PA )&( P — A ) ; and the p r o p o s itio n th a t the a cts n a m e d by A and B a r e m o r a lly in c o m p a tib le is s y m b o liz e d by — P ( A&B ) . Som e c o m b in atio n s of th e s e n te n c e s lis te d above c an be show n to be tru e by u s e of the law s of p ro p o s itio n a l lo g ic a lo n e . A s an e x a m p le von W right m e n tio n s a v e rs io n of the f a m ilia r m odus to lle n s p rin c ip le : ( P B —> P A ) —> ( — P A —> — P B ) (" D e o n tic L o g ic ," p. 5 ) . T h is fo rm u la is in te r p r e te d a s: ‘if A is p e r m itte d if B is p e rm itte d , then B is fo rb id d en if A is f o r b id d e n .' T h e r e is a s e n s e in w hich we c a n sp e a k of this and a ll s i m il a r p ro p o s itio n s a s t r i v i a l with r e s p e c t to d eo n tic logic, sin c e th e tr u th value c an be d e te r m in e d w hether th e s e n te n c e s a re d e o n tic o r n o t. T h e re a r e s o m e p ro v a b le fo rm u la s , h o w ev er, which a r e p e c u lia r to the d eontic c o n c e p ts . In our s u r v e y of th e lite ra tu r e p r i o r to von W right, we have s e e n th a t the e x is te n c e of such a g ro u p of p ro p o s itio n s h a s b e e n a lte r n a te ly c o n firm e d and denied. Men lik e A lf R o ss and S to r e r w e re c o n v in c ed th a t a s p e c ia l lo g ic involving d e o n tic c o n c e p ts w as fe a s ib le , 84 w h e re a s H o fs ta d te r, M cK in sey , and B o h n e rt c o m p le te ly re d u c e d any p o s s ib le deon tic in f e re n c e s to p ro p o s itio n a l ( in d ic a tiv e ) lo g ic. W ith von W rig h t's in te r p r e ta tio n we g e t a d e fin ite lo g ic of s p e c i f i c a l ly d e o n tic p ro p o s itio n s , but, a s m ig h t be e x p e c te d , th is p o rtio n of h is s y s te m is s u b je c t to c o n s id e ra b le c r i t ic i s m . The notion of m o r a l c o m m itm e n t o r d e riv e d o b lig a tio n is th e m o s t im p o rta n t c o n c e p t of von W rig h t's d e o n tic lo g ic, f o r it m o s t c le a r ly in v o lv es p ro p o s itio n s w hose tr u th - v a lu e s depend upon th e sp e c ific lo g ic a l c h a r a c t e r of th e d eo n tic c o n c e p ts . T he p ro p o s itio n th a t the p e rf o r m a n c e of the a c t n a m e d by A c o m m its us to p e r f o r m th e a c t n a m e d by B is s y m b o liz e d by 0 ( A —> B ) . By d e fin itio n OA is th e s a m e a s -'-(P '— A ) , 0 ( A —> B ) is the s a m e as ~“P ( A & ~B ) . ^ U sin g th is c o n ce p t of c o m m itm e n t, von W right e s ta b lis h e s the follow ing p ro p o sitio n : ( 0 A & 0 ( A —> B ) ) —> O B . T h is s a y s th at, if A is o b lig a to ry an d if doing A c o m m its us to do B , th e n B is a ls o o b lig a to ry (" D e o n tic L o g ic ," p. 5 ) . Von W rig h t s t a te s th at: * * T he fa c t th a t ~ P ~ ( A —> B ) is the s a m e a s ~ P ( A & ~ B ) c o m e s d ir e c tly f r o m th e d e fin itio n of A —> B . Since A —>B d e n o te s th a t a c t w hich is p e r f o r m e d by an agen t if, and only if, it is not the c a s e th a t A is p e r f o r m e d an d B not p e rf o r m e d by th e ag en t, th en ~ ( A —> B ) m u s t denote th a t a c t w hich is p e r f o r m e d w hen both A and ~ B a r e p e rf o r m e d , i . e . , ( A&~B ) . 85 It is in tu itiv e ly obvious th a t th is is a tr u th of logic, i . e . , s o m e th in g w hich is v a lid on p u re ly f o r m a l g ro u n d s. It is, h o w e v e r, n o t a n a p p lic a tio n of any s c h e m e w hich is v a lid fo r any s e n te n c e s w h e th e r d eo n tic o r not. The e x is te n c e of lo g ic a l t r u th s w hich a r e p e c u lia r to the deontic c o n ce p ts is w hat m a k e s th e stu d y of D eontic L o g ic in te re s tin g . (" D e o n tic L og ic, " p. 5 ) It s e e m s m o s t ex p ed ien t a t th is point to continue w ith the d e v elo p m e n t of von W right*s s y s te m b e fo re c o n s id e rin g the c r i t i c is m s of th is c h a r a c te r iz a tio n of d e riv e d o b lig a tio n . Von W right does not depend upon th e in tu itiv e o b v io u sn e ss of h is b a s ic c o m m it m e n t p ro p o s itio n but p ro v id e s a c o m p le te d e c is io n - p r o c e d u r e by w hich the lo g ic a l tr u th o r fa ls ity of any p ro p o s itio n c ap a b le of bein g fo rm u la te d in h is s y s te m m ay be e s ta b lis h e d . T h u s, if we w ish to d isp u te th e v a lid ity of the c o m m itm e n t fo rm u la , we w ill have to r e je c t, a t the sa m e tim e , the m a c h in e ry by m e a n s of w hich the fo r m u la is e s ta b lis h e d a s p ro v a b le . T he d e c is io n - p ro c e d u r e which von W right o u tlin e s fo r his s y s te m in v o lv es th e f a m ilia r lo g ic a l p rin c ip le s f o r th e c o n s tru c tio n of t r u th - t a b l e s and the p o s s ib ility of d e te rm in in g the p e r f e c t d i s ju n ctiv e n o rm a l form of the n a m e s of a c ts w hich o c c u r in deontic p ro p o s itio n s . G iven any c o m b in a tio n of m ( m ^ 1) n a m e s of a c ts , th e p e rf e c t d isju n c tiv e n o rm a l fo rm of th at c o m b in a tio n is a 0 - , 1- , . . . ; n - t e r m e d d isju n c tio n -n a m e of m - t e r m e d co n ju n ctio n - n a m e s , w h ere in e a c h c o n ju n c tio n -n a m e th e r e o c c u rs e ith e r one of 86 th e m o r i g in a l n a m e s o r e ls e its n e g a tio n . F o r e x a m p le , th e p e r f e c t d is ju n c tiv e n o r m a l f o r m o f ( A v B ) is ( A & B )v( Afc-^B )v( -*-AA—B ) . N ow , le t c d e n o te a n y c o m b in a tio n o f m n a m e s of a c t s . L e t c ^ , C g, , c n d e n o te th e n c o n ju n c tio n - n a m e s in th e p e r f e c t d is ju n c tiv e n o r m a l f o r m o f c . L e t P (c ) b e a n a r b i t r a r y P - s e n t e n c e ( s e n te n c e e x p r e s s i n g a p r o p o s i t io n a b o u t th e p e r m i t t e d c h a r a c t e r of a n a c t) w ith a r g u m e n t c . T h e n , th e s e n t e n c e s P(cj_ ), P ( c 2 ), . . . , P ( c n ) a r e c a l le d th e P - c o n s t i t u e n t s of P ( c ) . V on W rig h t now w is h e s to s h o w th a t P (c ) is a t r u t h - f u n c t i o n a l c o m p o u n d of its P - c o n s t i t u e n t s - - i . e . , he w is h e s to sh o w th a t th e t r u t h - v a l u e of P (c ) i s u n iq u e ly d e te r m i n e d by th e t r u t h - v a l u e s of P ( c ^ ) , P ( c 2 >, P < cn ). H is p ro o f o f t h is t h e o r e m m a k e s u s e of th e 12 l e m m a th a t c d e n o te s a d e o n tic fu n c tio n of th e a c ts n a m e d by , C2 , . . . , c n . T h is l e m m a in t u r n fo llo w s f r o m th e P r i n c i p l e of D e o n tic D is tr ib u tio n : If a n a c t is th e d is ju n c tio n o f tw o o t h e r a c t s , th e n th e p r o p o s itio n th a t t h e d is ju n c tio n is p e r m i t t e d is th e d is ju n c tio n of th e p r o p o s i t io n th a t th e f i r s t a c t is p e r m i t t e d a n d th e p r o p o s i tio n t h a t th e s e c o n d a c t is p e r m i t t e d . ( " D e o n tic L o g ic , " p . 7 ) It i s a c o n s e q u e n c e of th e P r i n c i p l e o f D e o n tic D is t r i b u ti o n 12 "A n a c t w ill b e c a lle d a d e o n tic f u n c tio n of c e r t a i n o t h e r a c t s , if th e d e o n tic v a lu e of th e f o r m e r u n iq u e ly d e p e n d s u p o n th e d e o n tic v a lu e s o f th e l a t t e r " ( " D e o n tic L o g ic , " p . 6 ) . 87 th at any d isju n ctiv e c o m p lex of n a m e s of a c ts d eno tes a deontic function of the a c ts denoted by th e t e r m s of th at d isju n ctio n . Since Cj , C2 , . . . , c n a r e the conjunction n a m e s in the p e rf e c t d isju n ctiv e n o rm a l f o r m of c it follow s im m e d ia te ly th a t c d en o tes a deontic function of the a c ts n a m e d by c^ , c g , . . . , c n . T he deontic value of c -- h e n c e , its p e r m i s s i o n - - i s a function of the p e r m is s io n of C1 , Cg, , c n , But P ( C1) is tru e ju s t in c a s e c^ is p e rm itte d , and s i m il a r ly with P ( Cg ), . .. , P ( cR) • In c o n seq u e n ce the t r u th - value of P ( c ) is uniquely d e te rm in e d by the tr u th - v a lu e of P ( c j ), P f c g ) , . . . . P ( c n )--i. e., P ( c ) e x p r e s s e s a tru th -fu n c tio n of the p ro p o sitio n s e x p r e s s e d by its P -c o n s titu e n ts . In o r d e r to d e te rm in e the tru th -v a lu e of P (c) then, we c o n s tru c t a co lu m n in the tr u th - ta b le fo r e ac h of its P -c o n s titu e n ts and c o m p a re th e s e colum ns u n d e r the e s ta b lis h e d t r u th - r u le fo r d is ju n c tio n --th e tru th value of P ( c ) is d e te rm in e d by the tr u th - v a lu e of P ( c j ) v P ( c 2 >v.. . v P ( c n ). As an e x am p le of the p ro c e d u re f o r c o n s tru c tin g tr u th - ta b le s fo r deontic s e n te n c e s , c o n s id e r the c a s e in which A and B a r e the n a m e s of a c ts w hich o c c u r in a c o m p lex deon tic s e n te n c e . L et us su p p o se th a t fo r th is se n te n c e we w ish to c o n s tru c t th e tru th -c o lu m n fo r PA . T he p e rfe c t d isju n c tiv e n o rm a l f o r m of A ( in te r m s of A and B ) is ( A&B) v ( A & ~B ) . To obtain the tr u th -c o lu m n fo r PA we m u st c o m p a re (u n d e r the e s ta b lis h e d t r u th - r u l e fo r d isju n c tio n ) 88 the tr u th - c o lu m n s of P (A & B ) and P(A & —B ) . In o r d e r to c o n s tru c t a c o m p le te tr u th - ta b le for any given d e o n tic s e n te n c e ( re d u c e d to its P - c o n s titu e n ts ) , it is n e c e ssa ry to c o n s id e r a ll th e p o s s ib ilitie s f o r co n ju n ctio n of th e nam es of the acts w hich o c c u r in the g iven s e n te n c e . F o r e x a m p le , in a sentence in w hich A an d B o c c u r, th e r e a r e fo u r con ju n ctio n po ssib ilities, n a m e ly , P ( A & B), P ( A & - B ) , P ( - A & B ) , and P ( - A & - B ) . In g e n e r a l, if n is th e n u m b e r of n a m e s of a c ts in a given proposition, t h e r e a r e 2n co n ju n ctio n p o s s ib ilitie s . The fo u r p o ssib ilities m e n tio n e d above (v o n W right c a lls th e m deontic units ) , a re logically in d e p e n d e n t of one a n o th e r. T h e re fo re , t h e i r tru th -ta b le will contain fo u r c o lu m n s of s ix te e n tr u th - v a lu e s e a c h . A p ro b le m a ris e s , how e v e r , w ith the c o m b in a tio n which h as a ll of the deontic units false to g e th e r. C o n s id e r the s im p le r c a s e w h e re the n am e of only one act, A , o c c u rs in th e s e n te n c e being e v a lu a te d . T he deontic units in this c a s e a r e P A and P — A . If we allow the co m b in atio n in our truth- ta b le w hich h a s th e s e two p ro p o s itio n s fa ls e to g e th e r, we a re really s a y in g th a t an a c t its e lf an d its n eg atio n a r e both forbidden, i . e . , ( —P A )&< - P - A ) . S ince th e a c t o r its n e g a tio n is p e r f o r m e d by any agent w h e n e v e r he a c ts , the fa lse h o o d of a ll the deontic units m eans th a t we a r e fo rb id d e n to a c t in any way w h a tso e v e r. ("D eontic L o g ic, " p . 8 ) 89 F u r t h e r , by definition, if the n eg atio n of an a c t is fo rb id d e n , the a c t its e lf is o b lig a to ry . S u b stitu tin g OA fo r — P-vA in th e f o rm u la in q u e stio n , we o b tain ( —P A )&( O A ), i . e . , the s a m e a c t is both f o r b id d en and o b lig a to ry . T h at th is can be the c a se s u r e ly c o n flic ts with o r d in a ry u se of lan g u ag e and o u r c o m m o n s e n s e in tu itio n s c o n c e rn in g o b lig a tio n c o n c e p ts . ( E s s a y in M odal L o g ic , p. 38 ) Von W right is th e r e f o r e f o r c e d to r e s t r i c t the lo g ic a l in d ep e n d en c e of th e deontic u n its; th ey cannot a ll be fa ls e to g e th e r. He fo r m u la te s th is r e s t r i c ti o n a s a " P r in c ip le of P e r m is s io n " : "A ny g iven a c t is e it h e r its e lf p e rm itte d o r its n eg atio n is p e rm itte d " (" D e o n tic L o g ic ," p. 9 ) . T h is m e a n s th at w hen a ll of th e 2n d eo n tic u n its o c c u r a s P -c o n s titu e n ts of a given s e n te n c e , th e tr u th - ta b le c o n s tr u c te d f o r th at se n te n c e w ill not includ e the c o m b in a tio n w h ere a ll 2n deontic units a r e fa ls e to g e th e r. In in v e s tig a tin g the tr u th - ta b le s fo r P (A&~A ), von W right d is c o v e r s a n o th e r d ifficu lty w hich in d u ces h im to p o s it an a d d itio n a l b a s ic p rin c ip le of deon tic logic. Since the p e rf e c t d isju n c tiv e n o rm a l f o r m of Afc-'-A is " e m p ty ," P (A & ^ A ) is a z e r o - t e r m e d d isju n c tio n of P - c o n s titu e n ts . By definition, a d isju n c tio n is tr u e if, and only if, a t le a s t one of its m e m b e ts is tr u e . T h e r e fo r e , d isju n c tio n s w ithout m e m b e r s would a p p e a r to be alw ays f a ls e . B ut if P ( A & —A) is a l w ays fa ls e , th en its negation, -* -P (A & ~ A ), sh o u ld alw ay s be tr u e . B u t ~ P ( A & ~ A ) is th e s a m e a s ^ P ^ ( A v - A ) , w hich, by d efin itio n , is 0 ( A v -^ A ). T h e q u e s tio n a r i s e s a s to w h e th e r o r not c o n tr a d ic to r y a c ts a r e a lw a y s f o rb id d e n - — P ( A & ^ A ) - -a n d a ls o w h e th e r o r n o t ta u to lo g o u s a c t s - - a r e a lw a y s o b lig a to r y - - O ( Av-*-A ) . Von W right c la im s th a t " O r d in a r y lan g u a g e and o u r c o m m o n s e n s e lo g ic a l in tu itio n s s e e m not to p ro v id e us w ith a c l e a r a n s w e r " ( "D e o n tic L o g ic ," p . 10). He a d m its th a t, a lth o u g h it a p p e a r s " a w k w a rd " to p e r m i t c o n tr a d ic to r y a c tio n s , t h e r e a r e no im m e d ia te lo g ic a l a r g u m e n ts a g a in s t su c h p e r m i s s io n . He t h e r e f o r e c o n s id e r s P ( A&—A ) a n d 0 ( A v-'-A ) a s e x p r e s s in g c o n tin g en t p ro p o s itio n s w hich m a y be e it h e r tr u e o r f a ls e . T h is is f o rm u la te d a s th e " P r i n c ip l e of D eo n tic C o n tin g e n c y " : "A ta u to lo g o u s a c t is not n e c e s s a r i l y o b lig a to ry , a n d a c o n tr a d ic to r y a c t is not n e c e s s a r i l y fo rb id d e n " (" D e o n tic L o g ic , " p. 11 ). In An E s s a y in M odal L o g ic (pp. 3 8 -3 9 ), von W right r e i t e r a t e s th a t, f r o m the p o in t of view of f o r m a l lo g ic, th e p r in c ip le of d e o n tic c o n tin g en c y s e e m s th e s a f e s t c o u rs e to c h o o se . H o w ev e r, h e c r e d i ts J . H in tik k a w ith th e o b s e r v a tio n th a t if th e r e r e a l ly e x is te d an a c t s u c h th a t P ( A & ~ A ) e x p r e s s e s a tr u e p ro p o s itio n , th e n e v e r y a c t w ould be p e r m itte d . S ince A&"-A h a s the s a m e p e r f o r m a n c e - v a lu e a s A & (-^A & B ), if P ( A & ~ A ) is tr u e , s o is P(A & ~A & B ), a n d f r o m th is P B fo llo w s. T h u s, if P ( A & —A) is 91 tr u e , th e n e v e r y a c t w ould be p e r m i tt e d and th u s we a r e f o r c e d to a c c e p t a s t a te of " m o r a l a n a r c h y " o r " m o r a l n i h i l i s m ." If von W rig h t’s s y s te m is to b e p r e v e n te d f r o m le a d in g to m o r a l n ih ilis m , P ( A & ~ A ) m u s t a lw a y s be f a ls e , i . e . , ^ P < A & -^ A ) m u s t a lw a y s be t r u e . B ut ~ P ( A & ~ A ) m e a n s th e s a m e a s O ( A v — A ) - -h e n c e if m o r a l n ih ilis m is to be a v o id e d we m u s t a s s e r t th e tr u th of the p r o p o s itio n th a t a ta u to lo g o u s a c t is o b lig a to ry . A n o b je c tio n w hich c a n b e b r o u g h t a g a in s t v on W rig h t's t r u t h - t a b l e p r o c e d u r e is s i m i l a r to th e o b je c tio n A lf R o s s r a i s e d a g a in s t th e i n t e r p r e t a t i o n of im p e r a t i v e s in t e r m s of s a t is f a c ti o n - fu n c tio n s . It w ill be r e c a l l e d th a t th e lo g ic of s a t is f a c ti o n p e r m i t s th e v a lid in f e r e n c e of th e im p e r a tiv e I ( xvy ) f r o m th e im p e r a tiv e I(x) . F r o m ’M a il th e l e t t e r ! 1 we c a n v a lid ly in f e r ’M ail th e l e t t e r o r b u r n it! r A s i m i l a r in f e r e n c e c a n be v a lid ly d ra w n in von W rig h t’s d e o n tic lo g ic by m e a n s of h is t r u t h - t a b l e p r o c e d u r e . F r o m ’P r o m i s e - k e e p i n g i s o b l ig a to r y ’ we c a n v a lid ly in f e r ’P r o m i s e - k e e p in g o r s te a lin g is o b l i g a t o r y '- - ( a n d a n y a c t a t a ll c a n be s u b s titu te d f o r " s te a lin g " ) . T h e d e m o n s tr a tio n th a t, in von W rig h t’s s y s te m , th e l a t t e r in f e r e n c e is a ta u to lo g y fo llo w s: (1) OA—> 0 ( A v B ) is th e f o r m u la to be t e s te d . (2) -vP-'-A—> -* -P ~ (A v B ) by d e fin itio n of OA and s u b s titu tio n in (1). 92 (3) —> H P ( ) by s u b s titu tio n in (2) s in c e th e p e r f o r m s n e e -fu n c tio n of -^ ( A v B ) = th e p e r f o r m a n c e - f u n c tio n of ( -vAfc—B ) . (4) T h e n o r m a l f o r m of — A is ( -vA&B )v( -*rA&"-B) . T he n o r m a l f o r m of "^A&~B is ( ~ A & ~ B ) . P ( ~ A & B ) P ( ~ A & ~ B ) OA O (A v B ) OA—> Q ( A v B ) T T F F T T F F T T F T F F T F F T T T (5) O A —> 0 < A v B ) is a ta u to lo g y s in c e th e a s s ig n m e n t of t r u th - v a lu e s to its u ltim a te P - c o n s titu e n ts y ie ld s a fin a l c o lu m n of v a lu e s w hich a r e a ll T 's . R o s s h e ld th a t th e in fe r e n c e in v o lv in g i m p e r a t i v e s - - I ( x ) —> I ( x v y ) - - i s not im m e d ia te ly c o n c e iv e d to be lo g ic a lly v a lid . T he in fe r e n c e in q u e s tio n s im p ly fa ils to e x p r e s s c o r r e c t l y th e m e a n in g in te n d e d by th e im p e r a tiv e . S im ila rly , f r o m the o b lig a tio n to k e ep o n e 's p r o m is e s it d o e s not s e e m to fo llo w th a t one is o b lig e d to k e ep o n e 's p r o m is e s o r to s te a l. Y et, th is in f e r e n c e is f ir m ly e s ta b lis h e d as a ta u to lo g y w ith in von W rig h t's s y s te m . S e v e ra l law s w hich c a n be e s ta b lis h e d a s d e o n tic ta u to lo g ie s by th e tr u th - t a b l e m e th o d a r e lis te d by von W right (" D e o n tic L o g ic , " pp. 1 3 -1 4 ) . Two law s r e l a te the c o n c e p ts of p e r m i s s i o n an d o b lig a tion: a. PA is id e n tic a l w ith ~ 0 — A . (B y " id e n tic a l w ith" von W rig h t m e a n s " th e e q u iv a le n c e - s e n te n c e of th e tw o s e n te n c e s e x p r e s s e s a tr u th of D eo n tic L o g ic, " i. e. , P A —> < — MD— A e x p r e s s e s a d e o n tic tau to lo g y ) . 93 b. OA e n ta ils P A , i . e . , O A —> P A e x p r e s s e s a d eo n tic tau to lo g y . F o u r law s g o v e rn th e " d is s o lu tio n " of d e o n tic o p e ra to r s : a. 0 ( A & B ) is id e n tic a l w ith (O A )& (O B ). b. P ( AvB ) is id e n tic a l w ith ( PA )v( P B ) . c . ( OA )v( O B ) e n ta ils O ( AvB ) . d. P ( A& B) e n ta ils ( P A )&( P B ) . Six law s of " c o m m itm e n t" a r e s ta te d from w hich th e follow ing th r e e have b e e n s e le c te d fo r c o n s id e ra tio n : a. 0 A & 0 ( A —> B ) e n ta ils O B . If doing w hat we ought to do c o m m its u s to do so m e th in g e ls e , th e n th is new a c t is a l so s o m e th in g w hich we ought to do. d. 0 ( A —> ( B v C ) ) &-'*'PB&~PC e n ta ils -~PA . An a c t which c o m m its u s to a c h o ic e b e tw ee n fo rb id d e n a lte r n a tiv e s is fo rb id d en . e. ~ { 0 ( A vB ) &~PA&"**PB) . It is lo g ic a lly im p o s s ib le to be o b lig ed to c h o o se b e tw ee n fo rb id d e n a lte r n a tiv e s . Von W right c r e d its P . G each with the o b s e rv a tio n th a t c o m m itm e n t law s d and e a r e referred to s e v e r a l tim e s by St. T h o m a s 13 A q u in a s. St. T h o m a s s ta te s th a t a p e rs o n is p e rp le x u s se c u n d u m quid if by a p re v io u s w ro n g a c t he c o m m its h im s e lf to a ch o ice b e tw e en fo rb id d e n a lte r n a tiv e s . A m a n is s a id to be p e rp le x u s s i m p lic ite r if he is o b lig ed to c h o o se b etw een fo rb id d e n a lte r n a tiv e s . 1 Q D eontic L o g ic ," p . 14, fo o tn o te 1 . The p a s s a g e s in A q u in as w hich a r e r e f e r r e d to a r e : De V e rita te , Q. 17, a r t . 4; S u m m a T h eo lo g ic a , j a j j a r , ( jajjar is an obvious m is p rin t and sh o u ld be I-II, i.e. , P a r t I of the Second P a r t ) Q . 19, a r t . 6; S u m m a T h e o lo g ic a , iiia , Q.64, a r t . 6. 94 S t. T h o m a s a g r e e s w ith v o n W rig h t* s c o m m i tm e n t la w d w h en he a f f i r m s t h a t a m a n m ig h t be p e r p l e x u s s e c u n d u m q u id . H e a g r e e s w ith v o n W rig h t* s c o m m i t m e n t la w e w h e n h e d e n ie s t h a t a m a n m ig h t b e p e r p l e x u s s i m p l i c i t e r . T h e p e r p l e x u s s i m p l i c i t e r of S t. T h o m a s to w h ic h v o n W rig h t r e f e r s i s m e n tio n e d in De V e r i t a t e in c o n n e c tio n w ith th e p r o b l e m of th e b in d in g p o w e r o f a f a l s e c o n s c i e n c e . A m a n c a n n o t be c o m p l e t e ly p e r p l e x e d ( p e r p l e x u s s i m p l i c i t e r ) w h en h is c o n s c i e n c e e r r o n e o u s l y t e l l s h im to c o m m i t f o r n i c a ti o n , f o r h e c a n c h a n g e h is f a l s e c o n s c i e n c e . A f a l s e c o n s c i e n c e , t h e r e f o r e , d o e s n o t o b lig a te , b u t s o lo n g a s it p e r s i s t s , a m a n m a y be p e r p l e x e d to s o m e d e g r e e 14 ( p e r p l e x u s s e c u n d u m q u i d ) . A n d t h e r e is no d if f ic u lty in s a y i n g t h a t, if s o m e c o n d itio n is p r e s u p p o s e d , it i s i m p o s s i b l e f o r a m a n to a v o id s in ; j u s t a s if we p r e s u p p o s e th e in te n tio n of v a in g lo r y , o n e w ho is r e q u i r e d to g iv e a lm s c a n n o t a v o id s in . F o r if h e g i v e s a l m s , b e c a u s e o f s u c h an in te n tio n h e s i n s ; but, if he d o e s n o t g iv e a l m s , h e v i o la t e s th e la w . ^ S o m e of th e la w s w h ic h v o n W rig h t m e n tio n s w ill be d i s c u s s e d 1 fi in th e lig h t of c o m m e n t s m a d e a b o u t t h e m b y A . N. P r i o r a n d 14 D e V e r i t a t e , I I , Q . 17, a r t . 4. p e V e r i t a t e , I I , Q . 17, a r t . 4, a n s w e r to d if f ic u ltie s 8. 1 fi " T h e P a r a d o x e s of D e r iv e d O b lig a tio n , " M ind, 6 3 :6 4 - 6 5 , 1954; a n d F o r m a l L o g ic ( O x f o r d , 1955 ) , p . 224 . 95 17 R . N. M c L a u g h lin . B e fo re p ro c e e d in g to th is d is c u s s io n , h o w e v e r, we w ill c o n s id e r s o m e of von W rig h t's g e n e r a l c o n c lu s io n s . He h o ld s th a t a ll of h is s u g g e s te d law s fo llo w fro m o u r in tu itiv e n o tio n s of o b lig a tio n and p e r m i s s io n , but not a ll of th e la w s a r e in tu itiv e ly o b v io u s: In th e c a s e of s o m e of th e la w s, m o r e o v e r , it is not in tu i tiv e ly c l e a r w h e th e r t h e i r t r u th is a m a t t e r of lo g ic o r a m a t t e r of m o r a l c o d e. T h is p r o v e s th a t th e d e c is io n p r o c e d u r e of D e o n tic L o g ic w hich we have o u tlin e d is n ot v o id of p h ilo s o p h ic a l i n t e r e s t . ( "D e o n tic L o g i c ,1 1 p . 1 4 ) C r i ti c s of h is s y s t e m h o ld th a t not a ll of the law s von W rig h t m e n tio n s fo llo w fro m o u r in tu itiv e n o tio n s of o b lig a tio n and p e r m i s s io n . Von W rig h t h im s e lf l a t e r r e p u d ia te s h is c h a r a c t e r i z a t io n of th e c o m m i t m e n t r e la tio n s h ip . M o r e o v e r, we have a lr e a d y m e n tio n e d a c a s e in w hich by von W rig h t's d e c is io n p r o c e d u r e , a f a ls e p r o p o s itio n O A —> 0 ( AvB ), can be show n to be a d e o n tic ta u to lo g y . P r i o r and M c L a u g h lin s u g g e s t o th e r u n d e s ir a b le o r o b v io u sly f a ls e p ro p o s itio n s w hich a r i s e in th e s y s te m . B ut a d e c is io n p r o c e d u r e w hich p e r m i ts o b v io u sly f a ls e p r o p o s itio n s to be e s ta b lis h e d a s d e o n tic ta u to lo g ie s , a lth o u g h p h ilo s o p h ic a lly in te r e s tin g , can n o t be c o n s id e r e d a d e q u a te to its in te n d e d ta s k . " F u r t h e r P r o b l e m s of D e riv e d O b lig atio n , " M ind, 6 4 :4 0 0 -4 0 2 , 1955. ^®M A N ote on D eo n tic L o g ic and D e riv e d O b lig a tio n ,1 1 M ind, 1956. 96 Von W right points out an im p o rta n t d iffe re n c e b etw een the d eo n tic m o d a litie s and the a le th ic , e p is te m ic , and e x is te n tia l m o d a l- 19 itie s . If a p ro p o sitio n is tru e , it is not fa lsifie d , and if a p ro p e rty is tr u e of a thing, the p ro p e rty e x is ts . But the p e rfo rm a n c e -v a lu e of an a c t involves no lo g ical connection with the o b lig a to ry , fo rbidden, o r p e rm itte d c h a r a c te r of the act. T h e re is thus an im p o rta n t s e n s e in which the deontic m o d a litie s unlike the a le th ic , e p is te m ic , an d e x is te n tia l ones have no lo g ical connexions with m a tte r s of fa c t ( truth and fa ls e h o o d ) . T his is a point about deon tic c a te g o rie s which h a s often been s t r e s s e d by m o ra l p h ilo s o p h e rs . ("D e o n tic L ogic, " p. 15 ) The thought re fle c te d h e re is that w h eth er an a c t is done o r not is lo g ic a lly independent of the q u e stio n a s to w h eth er th a t a c t ought to be done o r not. The law s g o v ern in g th e d isso lu tio n of deontic o p e ra to rs and the law s of c o m m itm e n t a r e the m o st in te re s tin g and the m o st c o n t r o v e r s i a l e le m e n ts of von W rig h tJs deontic s y s te m . In the d isc u ssio n w hich follow s, von W right*s c h a ra c te r iz a tio n of m o r a l c o m m itm e n t and th e v a lid ity of c e r ta in of his d isso lu tio n r u le s w ill be c a lle d into q u e stio n . B e ca u se his definition of c o m m itm e n t le a d s to so m e un- 19 T he a le th ic m o d a litie s a r e the n e c e s s a ry , p o ssib le , and co ntingen t m odes of tru th ; th e e p is te m ic a re the v e rifie d , undecided, and fa ls ifie d ; and the e x is te n tia l m o d a litie s a r e th o se of u n iv e rs a lity , e x iste n c e , and e m p tin e ss of p r o p e rtie s of c la s s e s (see "D eontic L ogic, " p. 1 ) . 97 d e s ir a b le ’’p a ra d o x e s , " von W rig h t h im s e lf , l a t e r r e v i s e d h is s y s - te rn ( see s e c tio n 4 of th is c h a p te r ) . 2. P r i o r ’s D e v e lo p m e n t of the von W rig h t S y s te m 20 A. N. P r i o r c o n s tr u c ts w ith in von W rig h t’s s y s te m the d e o n tic a n a lo g u e s of th e p a ra d o x e s of s t r i c t im p lic a tio n . He s ta te s th at: T he d eo n tic an alo g u e of s t r i c t im p lic a tio n its e lf is w hat von W rig h t c a lls b ein g ’co m m itted * by th e doing of A to the doing of B , and s y m b o liz e s as *0 ( A —> 6 ) ' . { " P a r a d o x e s ," p. 64 ) . 0 ( A —> B ) h a s b e en d e fin e d as —P ( A & —B ) , i . e . , ’it is not p e r m itte d to do A w itho ut doing B . ' It c an be e s ta b lis h e d in th e von W rig h t s y s te m th a t if a c t A is fo rb id d e n , th en th e c o n ju n c tio n -a c t of A w ith any o th e r a c t is a ls o fo rb id d e n , i.e. , —P A —> —P ( A & B ) o r —P A —> — P ( A&— B ) . B ut —P(A & —B) h a s b e en g iv en a s th e d e fin itio n of 0 ( A —> B ) . H en ce, —P A —> 0 ( A —> B ) is a d e o n tic tau to lo g y : the doing of w hat is fo rb id d e n c o m m its us to th e doing of a n y th in g w h a ts o e v e r. U sin g th e s a m e p rin c ip le , P r i o r sh o w s th at O B —> 0 ( A —> B ) c a n a ls o be e s ta b lis h e d . O B —> 0 ( A —> B ) e x - 20 In both " T h e P a r a d o x e s of D e riv e d O b lig atio n , " M ind, 6 3 :6 4 -6 5 , 1954; and F o r m a l L o gic (O x fo rd , 1955 ), p. 224. 98 p r e s s e s th e p ro p o s itio n th a t if a n a c t is o b lig a to ry , we a r e c o m m itte d to it by an y a c t w h a ts o e v e r. T he p r o v a b ility of OB—> 0 ( A —> B ) c a n be e s ta b lis h e d a s fo llo w s: (1) -■'PA—> ~ P ( A & B ) fro m th e p re c e d in g a rg u m e n t. (2) ~ P ~ B —> ~ P <'"'B&A ) fro m (1) by s u b s titu tio n . (3) ~ P ~ B —> ~ P (A & -* -B ) fro m the d e fin itio n of th e p e r f o r m a n c e - fu n c tio n of A an d B , a n d s u b s titu tio n in (2) . (4) —> 0 ( A —> B ) d e fin itio n of 0 ( A —> B ) a n d s u b s titu tio n in (3). (5) O B —> 0 ( A —> B ) d e fin itio n of OB an d s u b s titu tio n in (4) . P r i o r fin d s th e f i r s t p a ra d o x , -~PA—> 0 ( A —> B ) , th e m o s t d is tu rb in g , " it te n d s to s u g g e s t a 'm i g h t - a s - w e l l - b e - h a n g e d - f o r - a - s h e e p - a s - a - l a m b 1 m o r a lity " ( " P a r a d o x e s , " p. 64 ). He p o in ts out, h o w e v e r, th a t w hen we c o n s id e r th e m e a n in g ( s e n s e ) a s s ig n e d by 21 the d e fin itio n s of th e t e r m s in v o lv ed , the p a ra d o x d is a p p e a r s . To s a y th a t s te a lin g c o m m its us to c o m m ittin g a d u lte ry , u sin g 'c o m m its u s to ' in von W rig h t's s e n s e , m e a n s th a t s te a lin g a c c o m p a n ie d by r e f r a in in g from a d u lte r y is s t i ll s te a lin g , an d s o is s t i l l w ro n g ; and it m e a n s no m o r e th an th a t. It do es not m e a n th a t w hen we h a v e s to le n we t h e r e a f te r s ta n d u n d e r an o b lig a tio n to c o m m it a d u lte r y . ( " P a r a d o x e s , " p. 6 4 ) B ut a t th is point P r i o r a p p r o p r ia te ly r a i s e s th e q u e stio n , "O u g h t it not to m e a n t h a t ? " A nd if we a c c e p t von W rig h t's d e fin itio n s of the a r r o w ( —>) and th e c o m m itm e n t r e la tio n s h ip , we m u s t a g r e e th a t it m e a n s e x a c tly th is . 21 P r i o r n o te s th a t C. I. L e w is m a k e s a s i m i l a r c o m m e n t w ith r e s p e c t to th e p a ra d o x e s of s t r i c t im p lic a tio n . 99 2 2 In h is s u g g e stio n s fo r a s y s te m of deontic logic, P r i o r p o in ts out a c lo se analog y w ith c la s s ic a l m o d a litie s . T he th re e m o r a l o p e r a to r s , o b lig a to ry , in d iffe re n t ( p e r m i tt e d ) , an d fo rb id d e n , a r e an alo g o u s to the m o d al o p e r a to r s fo r n e c e s s ity , co n tin g en cy , and im p o s s ib ility . But he points out, as von W right did, th at the a x io m s f o r d eo n tic logic do not r e m a in c o n siste n tly an alo g o u s to th o se of c la s s ic a l ( o r d i n a r y ) m o d al lo g ic. F o r e x a m p le , p —>M p, ( *If p is tr u e th en p is p o s s ib le 1 ), is a law of o rd in a r y m o d al logic; but a —> P a , ('if A is done th en A is p e r m i s s ib l e ' ), which would be the an alo g u e in deon tic logic, is not a law of d e o n tic lo g ic. One im p ro v e m e n t o v e r von W rig h t's u se of sy m b o ls is P r i o r 's u se of the s m a ll l e t t e r a ( b , c., e tc . ) to denote an a s s e r ti o n of the form 'A n a c t of the s o r t A is d o n e .' T his change m a k e s it p o ss ib le to avoid r e f e r r i n g to th e p e rfo rm a n c e -fu n c tio n s of a c ts . The n o tatio n 'a & b ' d en o tes the co n ju n ctio n of a s s e r tio n s about A an d B r a th e r th an denoting the c o n ju n c tio n -a c t of A and B . P r i o r p ro v e s w hat we m ig h t c a ll a p rin c ip le of d eo n tic n e c e s sity , n am ely , If the a s s e r ti o n th at a c e r ta in s o r t of a c t is done e x p r e s s e s a lo g ic a l law , th en we have a m o ra l o b lig atio n to a c t in th a t m a n n e r. ( F o r m a l L ogic, p. 222) ^^In F o r m a l L o g ic, p. 220-229. 1 0 0 P r i o r 's p ro o f of th is p rin c ip le r e q u ir e s ( in ad d itio n to von W rig h t's s y s te m ) a c c e p ta n c e of th e axiom , 'N ot e v e ry th in g is p e r m i s s ib l e . ' M o re o v e r, P r i o r is able to p ro v e , an d w ithout th e u se of th e new a x io m , a r u le s i m il a r to the p rin c ip le of d eo n tic n e c e s s ity but w ith r e s p e c t to p e rm is s io n : 'If the a s s e r tio n th a t a c e r ta in s o r t of a c t is done e x p r e s s e s a lo g ic a l law , th en it is a law th at th a t a c t is p e r m i s sible.' P r i o r s u g g e s ts th e follow ing a s a f r e e tr a n s la tio n of th is ru le : 'W h at I can not but do, I a m p e rm itte d to do. 1 A pplying th is in te r p r e ta tio n to n eg ativ e a c ts , he o b tain s: 'W hat I cannot but o m it, I a m p e r m itte d to o m it, 1 and th is s ta te m e n t a m o u n ts to the ru le : 'W hat I cannot do, I a m not ob lig ed to do' ( F o r m a l L ogic, p. 224 ) . T h is fin a l r e s u lt, when p r o p e r ly tr a n s p o s e d , is r e a d by P r i o r as the K an tian p rin c ip le , 'W h at I ought, I can. 1 W hen we d is c u s s a tte m p ts to co m b in e d eo n tic o p e ra to r s w ith o r d in a r y m o d al o p e r a to r s in one 23 s y s te m , it w ill be s e e n th a t th is p rin c ip le is d ir e c tly fo rm u la b le 24 a s a th e s is ( e . g . , Oa—>M a) in su c h a s y s te m . To avoid the m o st o b je c tio n a b le of the p a ra d o x e s to w hich von 23 C om b in ed s y s te m s of th is type a r e g iv en by P r i o r in "M o d al and D eontic L o g ic ," A ppendix D to T im e an d M odality (O x fo rd , 1956 ), pp. 140-145; and by A. R. A n d e rso n in "A R ed u ctio n of D eontic L ogic to A lethic M odal L o g ic ," M ind, 6 7 :100 -103, 1958. 24 'M ' is the m o d al o p e r a to r tr a n s la te d by 'i t is p o s s ib le th a t.1 1 0 1 W rig h t's c h a r a c te r iz a tio n of th e c o m m itm e n t- r e la tio n s h ip le a d s , P r i o r s u g g e s ts an a lte r n a tiv e fo rm u la tio n fo r the c o n ce p t of c o m m it m e n t. H is " a lte r n a tiv e and p e rh a p s m o re n a tu r a l f o rm u la " is o ^ a —>O b, i . e . , 'If we do A we a r e ob lig ed to do B. 1 T h is new fo rm u la , h o w e v e r, s till d o e s not avoid th e se c o n d and le a s t o b je c tio n a b le of th e p a ra d o x e s p re v io u s ly m e n tio n e d --th e p a ra d o x Ob—> ( a —> O b ), i.e. , 'If an a c t is o b lig a to ry , we a r e c o m m itte d to it by any a c t w h a ts o e v e r. 1 But the f i r s t p a ra d o x , w hich in the a lte r e d no tation, a p p e a rs in the f o r m ~ P a —> ( a —>Ob) , c an no lo n g e r be p ro v en . T h e r e a r e c e r ta in "q u ite p la in tr u th s " about c o m m itm e n t in th e a lte r e d s e n s e w hich a r e not p ro v a b le in the von W right s y s te m . One of th e s e "q u ite p lain tr u th s " which P r i o r m e n tio n s is th is: If we a r e obliged to do A , th en if o u r doing A im p lie s th a t we a r e o blig ed to do B , we a r e obliged to do B . (F o rm a l L ogic, p. 225 ) If th is is a c c e p te d as tru e , th en th e a lte r e d form of the first p a ra d o x , ~ P a —> ( a —> O b), can a ls o be d e riv e d in P r i o r 's s y s te m . B e ca u se von W right can n o t p ro v e c e r ta in " t r u t h s " - - s u c h as the one ju s t m e n t i o n e d - - P r i o r s u g g e s ts th at th is is 25 P r i o r c r e d its G. E . H ughes w ith th e s u g g e s tio n of th is a lte r n a tiv e fo r m u la ( F o r m a l L ogic, p. 224, footnote 1 ) . 1 0 2 a f u r t h e r in d ic a tio n th at h is r u le s and a x io m s a r e not su ffic ie n t fo r the d e riv a tio n of a ll th e law s w hich a r e fo rm u la b le w ith O and P . ( F o r m a l L o g ic, p. 225 ) In F o r m a l L o g ic, P r i o r d is c u s s e s th e p o s s ib ility of c o m bin in g d eo n tic w ith o r d in a r y m o d al o p e ra to r s in a sin g le s y s te m . H ow ever, he does not th e r e give a f o r m a liz e d v e rs io n of such a lo g ic . One of the a x io m s a v a ila b le to a "co m b in e d " s y s te m is the K an tian p rin c ip le m e n tio n e d e a r l i e r , n a m e ly , J W hat I ought, I can, 1 ( Oa—>M a) . A lso fo rm u la b le in th is w id e r s y s te m a r e p rin c ip le s of th e type s u g g e ste d by G re llin g in one of the e a r l i e r p a p e r s on a 26 f o r m a l logic of o b lig atio n . F itc h g iv es the follow ing v e rs io n of G r e llin g 1 s f i r s t ru le ; " if z follow s from x and y, th en the c o n - 27 ju n ctio n of x and soll(y) im p lie s s o l l ( z ) . " P r i o r 's v e rs io n of G r e llin g 's f i r s t ru le is: If the doing of A and B jo in tly n e c e s s ita te s the doing of C , th en if we do A and a r e o b lig ed to do B , we a r e o b lig ed to do C . (F o r m a l L ogic, p. 226 ) 9 0 In sy m b o ls th is m ay be w ritte n a s: ((a& b)-L->c)—> ((a & O b )—>Oc). ^ K u rt G re llin g , " Z u r L ogik d e r S o llsa e tz e , " U nity of S cien ce F o ru m , J a n u a ry 1939, pp. 4 4 -4 7 . 27 F r e d e r i c B. F itc h (rev. of G r e llin g 's " Z u r L ogik d e r S o l l s a e t z e " ) , J o u rn a l of S y m b o lic L ogic, 5:39, 1940. F itc h a ls o g iv es th e follow ing v e rs io n of G r e llin g 's se c o n d ru le : "If s o ll( y ) follow s fro m x , th en so ll( x ) im p lie s s o l l ( y ) . " 28* -i->' r e p r e s e n ts the m ode of n e c e s s a r y o r s t r i c t im p lic a tion, and is tr a n s la te d 'if . . . , th en . . . ' . p a ->q s a y s th a t if p is 103 O Q K. R e ac h , in c r itic iz in g G r e ll i n g 's p a p e r , p o in te d out th at, by s u b s titu tin g C f o r A a n d n o t-C fo r B , we o b tain : "If doing b o th - C - a n d - n o t- C n e c e s s i t a t e s doing C , th e n if we do C but 30 ought not to do C , we oug ht to do C . " P r i o r c a lls the c o n s e q u e n c e , 'If we do C b u t ought not to do C , th e n we ought to do C, ' th e ’’p rin c ip le of f a it a c c o m p li. 1 1 If we a c c e p t th is p r in c ip le , we a r e f o r c e d to deny th a t anyone e v e r does w hat he ough t not to do o r to deny the p r in c ip le of s u b a lte r n a tio n , 'If we a r e o b lig e d not to do A we a r e not o b lig e d to do A' ( F o r m a l L o g ic, p. 227 ) . R e tu rn in g to th e o r ig in a l s ta te m e n t of G r e e lin g 's ru le , P r i o r sh o w s th at, by su b s titu tin g a f o r c , it c a n be p ro v e n th a t e it h e r n o th in g at a ll is o b lig a to ry o r w h a te v e r we a r e doing is o b lig a to ry . G r e llin g 's ru le , t h e r e f o r e , m u st be r e j e c t e d b e c a u s e of a " r e d u c tio ad a b s u r d a m . " ^ T h e fin a l s u g g e s tio n w hich P r i o r m a k e s w ith r e s p e c t to p r o p - t r u e th e n q m u s t be tr u e b e c a u s e of s o m e c o n n e c tio n of th e m e a n in g s of the t e r m s in p and q . 29 K. R each , "S o m e C o m m e n ts on G r e ll i n g ’s P a p e r 'Z u r L o g ik d e r S o lls a e tz e ', " P h ilo s o p h y of S c ie n c e F o r u m , A p r il 1939, p. 72. 30 P r i o r , F o r m a l L o g ic, p. 227. P r i o r sh o w s in d e ta il how R e a c h 's r e s u l t is lo g ic a lly d e riv a b le fr o m G r e ll i n g 's f i r s t r u le . 31 P r i o r c r e d its G. E . H ughes w ith th e use of th e p r in c ip le " e i t h e r n o th in g a t a ll is o b lig a to ry o r w h a te v e r we a r e doing is o b lig a to ry " as a r e d u c tio ad a b s u r d a m of G r e ll i n g 's r u le . ( F o r m a l L o g ic , p. 228, note 1) 104 o s itio n s e x p r e s s in g m o r a l c o m m itm e n ts is th a t a r i c h e r s y s te m m a y be d e v is e d to d is c r im in a te b e tw ee n p e r p e tu a l ( u n i v e r s a l ) o b lig a tio n s a n d o b lig a tio n s w hich a p p ly only on a p a r t i c u l a r o c c a s io n . Such a s y s t e m c an be d e v is e d by u sin g v a r ia b le s fo r in d iv id u a l a c tio n s and a ttrib u tin g a c e r t a i n c h a r a c t e r to a c tio n s , u s in g G r e e k l e t t e r s to r e p r e s e n t the c h a r a c t e r in te n d e d . P r o p o s itio n s u sin g the O - o p e r a to r w ould th e n sig n ify th a t a g iv e n a c tio n x ought to hav e s u c h an d su c h c h a r a c t e r . B rin g in g the x w ithin th e sc o p e of a u n iv e r s a l o r e x i s te n tia l q u a n tif ie r w ould d is tin g u is h b e tw ee n the p e r p e tu a l and the p a r t i c u l a r o b lig a tio n s . P r i o r s u g g e s ts th a t th e fo llo w in g e x a m p le i l l u s t r a t e s th e n e c e s s ity f o r m ak in g th is d is tin c tio n b e tw e e n ty p e s of o b lig a tio n : If lo v in g God and o u r n e ig h b o r n e c e s s i t a t e s rid in g a b ic y c le , th e n if we ought to love God and o u r n e ig h b o r we ought to rid e a b ic y c le . ( F o r m a l L o g ic , p. 228) E v e n in s itu a tio n s w h e re th e love of G od and n e ig h b o r d o es a c tu a lly n e c e s s i t a t e rid in g a b ic y c le , the o b lig a tio n to r id e the b ic y c le is of a n a tu r e d iffe re n t from th a t of the o b lig a tio n to love G od and o u r n e ig h b o r. O u r f o r m a liz e d lo g ic of o b lig a tio n ought to r e f le c t th a t d iff e re n c e , and, h e n c e , th e ju s tific a tio n fo r the in tro d u c tio n of q u a n tif ie r s in to a s y s te m of c o m b in e d d eo n tic and o r d in a r y m o d a l o p e r a t o r s . 105 3. F u r th e r C o n a id e ra tio n s of the C o m m itm e n t and D iss o lu tio n L aw s T he p ro b le m s a ris in g from von W rig h t's o rig in a l a tte m p t to c h a r a c t e r i z e lo g ic a lly the co n cep t of c o m m itm e n t a r e ta k e n up by 32 R. N. M cL au g h lin , w hose a p p ro a c h is no tab ly d iffe re n t from th a t of P r i o r . M cL au g h lin a rg u e s th a t the p ro p o s itio n e x p r e s s e d by ( 0 A & 0 ( A —> B ) ) —>OB is not in tu itiv e ly v a lid . It is not tru e th a t in e v e r y c a se , if A is o b lig a to ry and if doing A c o m m its to doing B , th en B is o b lig a to ry too. A s a c o u n te r- e x a m p le M cL au g h lin su g - t e s ts th at, if w alking in a p u b lic p la c e c o m m its us to w e a rin g c lo th e s and w alk in g in a public p la c e is o b lig a to ry , it do es not follow th a t we a r e o b lig a te d to w e a r c lo th e s ev en though we do not w alk in a public p la c e . Von W rig h t's e x a m p le sa y s nothing at a ll ab o u t the p e r f o r m - a n c e -v a lu e of A , ev en though the truth of s e n te n c e s of the type m en tio n e d depen ds upon w h e th er A is a c tu a lly p e r f o r m e d o r not ( M cL aug hlin, p. 400 ) . M cL au g h lin r a i s e s a se c o n d o b je c tio n a g a in s t the c o m m it - m e n t-p ro p o s itio n u n d e r d is c u s s io n , w hich s t r i k e s d ire c tly at the fou ndations of von W rig h t's s y s te m . M cL au g h lin po in ts out th a t in F u r t h e r P ro b le m s of D e riv e d O b lig a tio n ," Mind, 6 4:400-402, 1955. 106 th e t r u t h - t a b l e p r o o f o f th e p r o p o s i t io n a c e r t a i n d is s o l u t i o n r u le m u s t be a s s u m e d to b e t r u e . T h is r u l e i s v o n W r ig h t's d i s s o lu tio n r u l e ( d) , w h ich s t a t e s th a t P ( A&B) e n ta il s ( P A ) & ( P B ) . T h is r u l e m u s t be r e j e c t e d , h o w e v e r , b e c a u s e it is n o t a lw a y s t r u e ; a n d it is n ot a lw a y s t r u e f o r th e s a m e r e a s o n th a t th e c o m m i tm e n t p r o p o s itio n is not a lw a y s t r u e : " th e p e r f o r m a n c e v a lu e s of A a n d R m a y be such th a t, a lth o u g h P ( A&B ) is t r u e , P A i s f a l s e " ( M c L a u g h lin , p . 402) . If w a lk in g in a p u b lic p la c e a n d w e a r in g c lo th e s is p e r m i t t e d , th e n th e d is s o l u t i o n la w s t a t e s th a t we c a n i m m e d ia te ly c o n c lu d e th a t w a lk in g in a p u b lic p la c e is p e r m i t t e d . " B u t, " M c L a u g h lin a s k s , " i s w a lk in g in a p u b lic p la c e p e r m i t t e d if c lo th e s a r e n o t w o r n ? " (p. 402) M c L a u g h lin , f u r t h e r m o r e , s u g g e s t s th a t th e p a r a d o x e s w h ic h P r i o r h a s p o in te d o ut a ls o d e p e n d upon d i s s o l u t i o n - r u l e ( d ) f o r t h e i r v a lid d e r i v a ti o n . R e je c tio n of th is rule, t h e r e f o r e , m a k e s it i m p o s s i b l e to e s t a b l i s h th e p a r a d o x e s of d e r i v e d o b lig a tio n . H ow e v e r , s o m e d i s s o l u t i o n - r u l e is n e c e s s a r y to h a n d le e a c h n u c l e a r d e o n tic p r o p o s itio n of th e ty p e P ( A & B ) , 0 ( A & B ) , P ( A vB ), . . .. It m a y be r e c a l l e d a t t h is p o in t th a t A lf R o s s , in h is in v e s tig a tio n s of i m p e r a t i v e lo g ic s , h a d r e j e c t e d th e p o s s i b i l i t y of f o r m u l a t i n g d i s s o lu tio n r u l e s f o r s i m i l a r c o m b in a tio n s of i m p e r a t i v e s . S in c e , f o r R o s s , i m p e r a t i v e s in c lu d e th e d e o n tic p r o p o s i t io n s , we c a n a s s u m e th a t he would a g re e w ith M cL au g h lin th at d is s o lu tio n ru le ( d ) is in v alid , an d th a t he would add th a t, w ith the e x c e p tio n of the n e g a tio n -fu n c tio n , a ll s u c h d isso lu tio n r u le s a r e in v alid . In h is a r tic le , "A Note on D eontic L ogic and D e riv e d O b lig a- 33 tio n . " von W right ta k e s up M c L a u g h lin 's o b je c tio n s. He r e p e a ts h is co n v ictio n th a t ( 0 A & 0 ( A —> B ) ) —>OB is a v a lid law of deontic lo g ic. R e f e r r in g to M c L a u g h lin 's e x am p le (g iv e n a b o v e ) and in a n s w e r to M c L a u g h lin 's q u e ry a s to w h e th er it is o b lig a to ry to w e a r c lo th e s even though we do not w alk in a public p lac e, von W right s a y s I think the a n s w e r is y e s - - a n d that, th e p r e m i s s e s of the p ro b le m being ta k e n into due c o n sid e ra tio n , th is is in good a c c o rd w ith o u r in tu itio n s . ("N o te , " p. 507) If w alking in a public p la c e is r e a lly o b lig a to ry , th en o m ittin g ( n e g le c tin g ) th is a c t is fo rb id d en ; but the se c o n d p r e m is e , 0 ( A —> B ) , s a y s th at it is o b lig a to ry to n e g le c t w alking in a public p lac e o r be d r e s s e d . H ence, sin c e n e g le c tin g to w alk in a p ublic p lac e is f o r bidden, it is o b lig a to ry th a t we be d re s s e d . T he a s s u m p tio n w hich von W right m a k e s is th a t OA r e f e r s to a c ts th a t a r e u n co n d itio n ally im p o s e d upon people as being th e ir duty. F r o m th is point of view , th e a c t of w alking in a public p lac e is not a v e ry good e x a m p le . Von W rig h t g iv es a n e x a m p le of a d e riv e d o b lig atio n w hich do es not 33 M ind, 65:507-509, 1956. 108 in v o lv e th e u n iv e r s a lity o f th e law in q u e s tio n . He s u g g e s ts th a t we c o n s id e r w alk ing in a p u b lic p la c e a s a d e riv e d o b lig a tio n in the s e n s e th a t no one is a llo w e d to go to b ed w ithout f i r s t ta k in g a w alk in a p u b lic p la c e . A nd su p p o se th a t, a s ab o v e, w alk in g in a p u b lic p la c e c o m m its us to w e a rin g c lo th e s . T h en it w ould n ot follow th a t w e a rin g c lo th e s is o b lig a to ry e v e n though we do not w alk in a p u b lic p la c e , - - a n d th e a g e n t m a y s a f e ly u n d r e s s w hen going to bed w ithout r is k in g to b r e a k the law s of d e o n tic lo g ic. ("N o te," p. 507) T h u s, if w alking in a p u b lic p la c e is to be a d e riv e d o b lig a tio n , it m u s t be d e riv e d from th e p r i o r a c t of going to b ed , i . e . , going to bed, A , c o m m its us to w alking in a p u b lic p la c e f i r s t , B ; o r 0 ( A —> B ) . W alking in a p u b lic p la c e , B , c o m m its us to w e a rin g c lo th e s , C . H en ce we h ave only the p ro p o s itio n ' 0 ( A —> B ) & 0 ( B —> C ) * , a n d n o thing a t a ll fo llo w s a b o u t the u n i v e r s a l o b lig a to rin e s s o f C . W ith r e s p e c t to the r u le P ( A & B ) —> P A , von W rig h t c la im s th a t M c L au g h lin is g u ilty of a lo g ic a l b lu n d e r. If w alk in g in a p u b lic p la c e an d w e a rin g c lo th e s is p e r m itte d , th e n the p ro p o s itio n th a t w alk in g in a p u b lic p la c e is p e r m itte d , fo llo w s im m e d ia te ly . When M c L a u g h lin a s k s , " Is w alking in a p u b lic p la c e p e r m itte d if c lo th e s a r e not worn?" he p o s e s the c a s e of P(A & -^B ). But P ( A&~-B) d o es not follow from P ( A & B ) an d h e n c e d o e s not e n te r in to the 109 v a lid ity of th e p ro p o s itio n in q u e s tio n . Von W rig h t's a r g u m e n ts a p p e a r to r e f u te M c L a u g h lin ’s p o sitio n , but th e is s u e is m u c h m o r e in v o lv e d th a n th is b r ie f t r e a t m e n t in d ic a te s . T he p o in t w h ich M c L a u g h lin w as try in g to m ak e (th o u g h u n s u c c e s s f u lly ) is th a t a co m p o u n d d e o n tic p r o p o s itio n n e ed n o t be u n iq u e ly r e la te d to its c o m p o n e n t p a r t s in the s a m e way in w hich o r d in a r y in d ic a tiv e co m p o u n d p ro p o s itio n s a r e r e l a te d to t h e i r c o m p o n e n ts . We m a y add, e v e n m o r e fo rc e fu lly , th at, in fa c t, th ey a r e n o t so r e la te d . If a an d b r e p r e s e n t o r d in a r y in d ic a tiv e p r o p o s itio n s s ta tin g , r e s p e c tiv e ly , th a t a c t A is done and a c t B is done, th e n o u r p o s itio n m a y be m a d e c l e a r by the follow ing s t a t e m e n ts : (1) (a&b) is id e n tic a l w ith (a)&(b) but 0 { a & b ) is not id e n tic a l w ith 0 ( a ) & 0 ( b ) . (2) ( 0 ( a ) & 0 ( b ) ) e n ta ils O(b) but 0 ( a&b ) does not e n ta il O (b) . (3) O(a) e n ta ils 0(a)vO(b) but O(a) d o es not e n ta il O ( a v b ) . S ta te m e n t (1) d ir e c tly c o n tr a d ic ts von W rig h t's d is s o lu tio n law ( a ) , a c c o rd in g to w hich 0 ( A & B ) is id e n tic a l w ith (O A )& (O B ). T he t h r e e s ta te m e n ts g iv en ab o v e h o ld a ls o w hen P is s u b s titu te d f o r O . If th is is done s ta te m e n t (2) c o n tr a d ic ts (mediately) d is s o lu tio n law (d), th e law w hich a s s e r t s P ( A & B ) e n ta ils ( P A ) & ( P B ) ; and s ta te m e n t (3) c o n tr a d ic ts the p ro p o s itio n P ( A ) —> P ( A v B ) , w hich we w e re a b le to p ro v e a s a th e o r e m of 1 1 0 von W rig h t's s y s te m . A lf R o ss ho ld s a p o sitio n s i m i l a r to o u rs w ith r e s p e c t to the d is s o lu tio n of com poun d im p e r a tiv e s , i. e . , he s e e s no way f o r the im m e d ia te d isso lu tio n of I(x&y) and I ( x v y ) . K a rl M e n g er, in an e a r l i e r p a p e r, ^ s ta te s a s i m i l a r p o sitio n : A c c o rd in g to th e o r d in a r y c a lc u lu s of p ro p o s itio n s the c la s s to w hich a com pound p ro p o s itio n belongs is u n iq u ely d e te r m in e d by th e c la s s e s to w hich the co m p o n en t p r o p o s i tio n s belong, e . g ., the p ro p o s itio n p&q belo ngs to the c la s s of tr u e p ro p o s itio n s if and only if both p and q b e long to th is c la s s . But th e logic of o u r every day life do es not have th is fe a tu r e w ith r e g a r d to doubtful p ro p o s itio n s . ( M e n g er, p. 53 ) M e n g e r goes on to s u g g e s t a logic of w ish e s and c o m m a n d s (in cluding " e th ic a l p r o b le m s " ) in w hich the p ro p o s itio n s of the s y s te m a r e ta k e n to be "doubtful" p ro p o s itio n s . He s ta te s that, in g e n e ra l, T he o b je c ts of our w ish e s and co m m a n d s a r e n e ith e r n e c e s s itie s n o r im p o s s ib ilitie s . In building up a logic of w ish e s and c o m m a n d s we s h a ll d e a l m e r e ly with p ro p o s itio n s th at, in the s e n s e of the lo g ic of th e doubtful a r e n e ith e r a s s e r t e d n o r n eg ated , i. e. , w ith doubtful p ro p o s itio n s . ( M e n g e r, p. 59 ) M en g er, h o w e v er, d istin g u is h e s b etw een w ish es and c o m - ^ M A L ogic of the D oubtful. On O p tativ e and Im p e ra tiv e L ogic, " R e p o rts of a M a th e m a tic a l C o llo q u iu m ( P u b lic a tio n s of th e U n iv e rs ity of N o tre D am e ), 1939, se c o n d s e r i e s , is s u e 1, pp. 53-64 . I l l m a n d s, and, in h is s y s te m , th e d isso lu tio n of " c o m m a n d " p r o p o s i tio n s r e ta in s the s a m e form a s th at of o r d in a r y in d ic a tiv e p r o p o s i t i o n s . D enoting the c o m m a n d function by 'C 1, he o b tain s: C ( p & q ) —X — (Cp&Cq) {p. 59). T h is ru le is e x a c tly what R o ss d o es not allow fo r im p e r a tiv e s and c o rr e s p o n d s to von W rig h t's d i s so lu tio n ru le ( a ) f o r deontic p ro p o s itio n s . M e n g e r does not p e r m it an a n a lo g o u s f o rm u la fo r o p ta tiv e s ( w ish e s ) . T he re le v a n t fo r m u la fo r o p ta tiv e s w hich he does p e r m it ( 1D* r e p r e s e n tin g 'd e sire') is ( Dp&Dq )—> D ( p&q ) ( p . 59). E v e r e tt W. H all d o es not a g re e th a t M e n g e r's d is tin c tio n b e tw e en o p ta tiv e s and im p e r a tiv e s is a v a lid one. He m a in ta in s th at " th e d istin c tio n d o es not s e e m in tu itiv e ly c o r r e c t so fa r as c o m m o n u sa g e is c o n c e rn e d . H all f u r th e r a g r e e s w ith o u r p o sitio n ( a s o p p o sed to M en g er and von W rig h t) th at M e n g e r's ru le fo r the d i s so lu tio n of im p e r a tiv e s is not alw ay s v alid . He holds that: " ' ( p ) ! & ( q ) ! ' e n ta ils *( q ) !' but '( p&q ) !' does not e n ta il ' ( q ) ! 1, " ^ and th a t "'( p) !' e n ta ils '(p) I v (q ) 11 but '(p)!' O 1 7 does not e n ta il '(pvq) !'" T h u s, H all w ould r e g a r d M e n g e r's 35 w h a t is V alu e? (New Y o rk and L ondon, 1952 ), p. 134 . 36 foo tno te 2 on p. 136. 3? footnote 1 on p. 137. 112 tr e a tm e n t of the log ic of o p ta tiv e s a s h o ld ing a ls o fo r im p e r a tiv e s , o r a t le a s t as b eing m o r e n e a r ly c o r r e c t th an th e lo g ic a l tr e a tm e n t w hich M e n g e r a c tu a lly d o e s give im p e r a tiv e s . O u r p o sitio n is b a s ic a lly in a g re e m e n t w ith th a t of H all and R o ss w ith r e s p e c t to the d is s o lu tio n of com po und im p e r a tiv e p r o p o s i tio n s - - w ith the add ed a s s e r tio n , h o w e v er, th at o u r p o sitio n a p p lie s a ls o to von W rig h t's deon tic p ro p o s itio n s . F r o m the fac t th at it is c o m m a n d e d to do two a c ts to g e th e r a s a sin g le a ct, th e r e does not follow the lo g ic al e n ta ilm e n t of the c o m m an d to do one of th e s e a c ts s e p a r a te ly . S im ila rly , fr o m th e fa c t th at two a c ts , ta k e n to g e th e r as a sin g le co n ju n ctiv e act, a r e o b lig a to ry ( o r p e r m itte d ) , it does not follow th a t e ac h of th e s e a c ts , ta k e n s e p a r a te ly , is o b lig a to ry ( o r p e r m itte d ) . To d e m o n s tra te th is we need but give a sin g le 38 c o u n te r- e x a m p le . L e t us su p p o se th a t A d e n o te s the a ct of p u t tin g on a p a ra c h u te and B the a c t of ju m p in g f ro m an a i r c r a f t a t two th o u sa n d fe e t. T h en P ( A&B ) is c o n c e iv e d as a v a lid p ro p o sitio n . E v en P ( A&B ) —> P ( A ) would s e e m u n o b jectio n ab le in th is p a r t i c u l a r c a s e . But w hat of P ( A & B ) —> P ( B ) ? C an it be s a id th at, b e c a u se it is p e r m itte d to ju m p f r o m an a ir c r a f t w hile w e a rin g a 3 8 O u r e x am p le is ad ap ted fr o m one u se d by H all ( p . 142) to illu s tr a te a d iffe re n t but r e la te d point. 113 p a ra c h u te , it follow s lo g ic a lly th a t it is p e r m itte d to ju m p f r o m an a i r c r a f t ? It w ould s e e m r a t h e r , th a t the d isso lu tio n of d eo n tic m o le c u la r p ro p o s itio n s is d ep en d en t upon th e fa c tu a l situ a tio n ; f o r in so m e c a s e s a co m ponent a c t m ay not be p e r m itte d by its e lf but m ay be p e r m itte d in c o m b in a tio n w ith so m e o th e r a c t. We can th e r e f o re not a s s e r t th a t in e v e ry c a s e the re la tio n s h ip of lo g ic a l e n ta ilm e n t e x is ts b etw een com pound and s in g u la r deontic p ro p o s itio n s . The f u r th e r fa c t th a t P ( A ) —> P ( A v B ) is a ls o an u n d e s ira b le fo rm u la tio n s u g g e s ts th a t the d isju n ctiv e re la tio n s h ip s , a s w ell a s the co n ju n ctiv e, a r e not the sa m e fo r d eo n tic and in d ic ativ e p ro p o s itio n s . W ith th e se c o n s id e ra tio n s in m ind, we tak e a se c o n d look a t von W rig h t's b a sic law of m o r a l c o m m itm e n t- - th e law ( 0 A & 0 ( A —> B ) ) —> O B . 0 ( A —> B ) has b een defined to m e a n the s a m e a s ~ P ( A & ~ B ) , and hence th e re le v a n c e of o u r d is c u s s io n of the d isso lu tio n of deontic m o le c u la r c o n ju n c tio n s. The im p o rta n t q u e stio n we m u st a n s w e r is, what c o n clu sio n follow s lo g ic a lly fro m the co n ju n ctio n of th e p r e m i s e s th a t A is o b lig a to ry and th a t it is fo rb id d e n to do A w ithout a ls o doing B ? T h e re can be only one in tu itiv e ly obvious a n s w e r to th is q u e stio n , n a m e ly , th a t f ro m the s ta te d p r e m i s e s we c a n conclud e th at the conjunctive a c t (A & B ) is o b lig a to ry , and nothing e ls e . S ince the o b lig a to rin e s s of B alone cannot be d e riv e d fr o m the o b lig a to rin e s s of (A & B ) , von W rig h t's 114 c o n c lu sio n is in e r r o r . T he law of c o m m itm e n t, p r o p e r ly re w r itte n , i s : ( 0 A & 0 ( A —> B ) ) -t- > 0 ( A&B ), i . e . , 'if A is o b lig a to ry and A can n o t be done w ithout a ls o doing B , th e n it is o b lig a to ry to do A and B to g e th e r. ' T he sy m b o l fo r n e c e s s a r y im p lic a tio n ( -L ->) is u se d to e m p h a s iz e th a t th e c o n c lu sio n m u st follow f r o m the a n te c e d e n t p r e m i s e s by v irtu e of th e m e a n in g s of the d e o n tic p ro p o s itio n s i n volved. F u r th e r , th e tr u th - v a lu e of th e a n te c e d e n t is i r r e l e v a n t to its im p lic a tiv e p o w e r. T h u s, in the e x a m p le d is c u s s e d by von W right and R e s c h e r , if it is o b lig a to ry to w alk in p u b lic and w alking in p u b lic c o m m its us to w e a rin g c lo th e s , then it is o b lig a to ry to w alk in public and w e a r c lo th e s . T he q u e s tio n w hich M c L au g h lin a s k s c o n c e rn in g w h e th e r o r not it is o b lig a to ry to w e a r c lo th e s ev en though we do not w alk in p u b lic cannot be a n s w e r e d fr o m the lo g ic a l in fo rm a tio n given. 4. S y ste m s of C o n d itio n al P e r m i s s i o n and O b lig atio n Von W right ta k e s the p a ra d o x e s in tro d u c e d by P r i o r m u ch m o re s e r io u s ly th a n he does the o b je c tio n s of M c L au g h lin . He a g r e e s w ith P r i o r th a t ~ P A —> 0 ( A —> B ) is a law of d eo n tic lo g ic and th a t, w ith the in te r p r e ta tio n he has g iven it in t e r m s of m o r a l c o m m itm e n t, th is law m e a n s th a t doing a fo rb id d e n a c t c o m m its us m o ra lly to any o th e r a c t w h a ts o e v e r; "A nd th is , o b v io u sly , c o n flic ts w ith o ur 'in tu itio n s ' in the m a tte r " (" N o te , " p. 508 ) . Von W rig ht is not 115 w illing to p e rm it th e s e p a ra d o x e s to re m a in as p ro v a b le th e o re m s in h is s y s te m . It is obvious th at he is a tte m p tin g to acco u n t fo r o u r in tu itiv e co n cep ts of obligation. T h is inten d ed in te rp r e ta tio n of his s y s te m ta k e s p re c e d e n c e o v e r its m e r e dev elopm ent as a lo g istic s y s te m which m ay o r m ay not " s q u a re " with o u r in tu itio n s. He r e je c ts h is e a r l ie r c h a r a c te r iz a tio n of m o ra l c o m m itm e n t an d s u g g e sts a n o th e r as the b a s is fo r a new logic of obligation. I think th a t the p r o p e r c o n clu sio n to be draw n fr o m P r i o r 's o b jec tio n is th a t 0 ( A —> B ) is not ( c o n tr a r y to m y e a r l i e r o p in io n ) an adequate e x p re s s io n in sy m b o lic te r m s of the notion of c o m m itm e n t ( o r d e riv e d o b lig a tio n ) . My b e lief is, m o re o v e r, th at a fo rm a liz a tio n of th is notion cannot be a c c o m p lish e d at all w ithin the s y s te m develop ed in m y p a p e r. ( " N o te ," p. 5 0 8-509 ) The o rig in a l s y s te m p re s e n te d in "D eontic L o g ic" w ill be r e f e r r e d to as the von W rig ht S y ste m I ; the new s y s te m , which we sh a ll now d is c u s s , w ill be r e f e r r e d to as the von W right S y ste m II. F o r th is new s y s te m von W right in tro d u c e s the sy m b o l, P ( p / c ) , which is to m ean: 'p is p e rm itte d u n d er co n ditions c . 1 - ^ P ( p / c ) m ea n s th a t p is fo rb id d en u n d er conditions c . ~ P ( ~ p / c ) m ean s th at n e g le ctin g p is fo rb id d en u n d er conditions c , o r th a t p is o b lig a to ry un d er co n d itio n s c . In ad dition to th e s e defin itio n s, von W right stip u la te s two fu n d am en tal a x io m s : A l. P ( p / c ) v P ( ~ p / c ) A2. P ( p & q/c ) —><— P ( p / c ) &P ( q/c&p ) The f i r s t of th ese two axiom s s ta te s th at u n d e r a sp e c ific s e t of 116 conditions c , e ith e r any a c t p is p e rm itte d o r its n e g a tio n -a c t is p e rm itte d (" o n e is p e rm itte d to do o r p e rm itte d to n e g le c t any a r b i t r a r y a c t p" ) . T h is axiom , a s von W right po in ts out ( ’’Note, " p. 509), s ta te s th a t u n d er no c ir c u m s ta n c e s could both, doing p and not doing p , be fo rb id d en . T he seco n d a x io m s ta te s th at the join t p e rfo rm a n c e of a c ts p and q is p e rm itte d u n d e r conditions c , if and only if, p is p e rm itte d u n d e r c o n d itio n s c , and q is p e r m i t ted u n d e r con ditions c , a ssu m in g th a t p h as a lre a d y been done. The s y s te m developed fro m th e s e two b a sic a x io m s and the p rin c ip le s of f o rm a l logic is g e a r e d to re la tiv e c o n ce p ts of p e r m i s sion, p ro h ib itio n , and obligation, a s d istin g u ish e d f ro m the a b so lu te c o n cep ts of von W rig h t's S y stem I . S y ste m II " in c lu d e s " S y ste m I in the s e n s e th a t the law s of S y ste m I w ill a p p e a r a s law s of S y stem II which hold u n d er tautolo gous condition s, i .e ., u n d e r ( c v ^ c ) (p. 509). T he conditions c m ay th e m s e lv e s be a c ts . With th is in m ind, von W right lays down the follow ing ru le : "A n e c e s s a r y c o n d i tio n fo r sa y in g th at doing q c o m m its us to p is th a t p is o b lig a to ry u n d e r co nditions q" (p . 509) . It is a th e o re m of S y stem II th at 0 { p / q ) e n ta ils 0 ( q —> p /c v —c ) . T his is tr a n s la te d as: " if doing q c o m m its us to do p , th en e ith e r n e g le c tin g p o r doing q is 'a b s o lu te ly ' o b lig a to ry " ( p . 509) . T h is does not s e e m to be a c o r r e c t tr a n s la tio n of the th e o re m a s s ta te d in sy m b o ls, but it is p o ss ib le 117 th a t a ty p o g ra p h ic a l e r r o r h a s d i s t o r te d von W rig h t's tr a n s la tio n . If q —>p is to be i n t e r p r e t e d in a m a n n e r c o n s is te n t w ith p re v io u s in te r p r e t a t i o n s , th e n th e t h e o r e m sh o u ld be r e a d a s fo llo w s: If doing q c o m m its u s to do p , th e n e it h e r n e g le c tin g q o r doing p 39 is a b s o lu te ly o b lig a to ry . S y s te m II d o e s not c o n ta in a s th e o r e m s th e tw o p ro p o s itio n s c o rr e s p o n d in g to th o s e w hich P r i o r c a lle d d e o n tic p a r a d o x e s , i. e . , n e it h e r ( p / c v m : )—> 0 ( q / p ) , nor 0 ( q / c v ~ c ) —> 0 ( q / p ) a r e p ro v a b le in the new s y s te m . A n a b s o lu te ly fo rb id d e n a c t d o e s not c o m m it us to any a c t w h a ts o e v e r, n o r does an y a c t w h a ts o e v e r c o m m it u s to an a b s o lu te ly o b lig a to ry a c t. N ic h o la s R e s c h e r a d o p ts von W rig h P s new a p p ro a c h and 40 d e v e lo p s a n a x io m s y s te m b a s e d upon it. R e s c h e r 's s u g g e s tio n s s e e m v e ry p r o m is in g in th a t m an y th e o r e m s w hich a p p e a r to be in tu i tiv e ly e v id e n t a r e p ro v a lb e from the a x io m s w hich he e s ta b lis h e s . H o w ev e r, we can n o t im m e d ia te ly d e te r m in e th e e n tir e s e t of lo g ic a l QQ ^ I f p a n d q a r e p r o p o s itio n s , th e n ( q —> p ) —><"—<~qvp ) but ( q —> p ) is not id e n tic a l w ith ( ~-pvq). If p a n d q a r e th e n a m e s of a c ts , th e n ( q —> p ) h a s the s a m e p e r f o r m a n c e - v a lu e a s ( •"-qvp ) b ut ( q —> p ) d o e s n ot h a v e the s a m e p e r f o r m a n c e - v a lu e as ( —pvq ) . 40 "A n A x io m S y s te m f o r D eo n tic L o g ic , " P h ilo s o p h ic a l S tu d ie s , 9 :2 4 -3 0 , 1958. 118 c o n s e q u e n c e s d e r i v a b l e f r o m t h a t s e t of a x io m s a n d m u s t t h e r e f o r e d e f e r ju d g m e n t a s to th e s u i t a b i l i t y a n d c o m p l e t e n e s s of th e s e t . T h e fo llo w in g a r e th e s e v e n a x io m s of R e s e l l e r 's s y s t e m : A l . P ( p v - ~ p / c ) A 2 . P ( p v q / c )—><— ( P ( p / c ) v P ( q / c )) A3. <p—> q ) —> < P ( p / c ) —> P ( q / c ) ) A 4 . P ( p & q /c )—> P ( p / c & q ) A5. ( P ( p / c ) & P ( q / c & p ) ) —> P ( p & q / c ) A6. P (p /c v -» -c )—> P ( p / d ) A7. P ( p / d ) —> P ( p / c & - * c ) R e s c h e r c l a i m s t h a t w ith th e in te n d e d i n t e r p r e t a t i o n of P , e a c h of t h e s e a x io m s i s in tu i t iv e l y a c c e p t a b l e ( p . 2 5 ) . T h e p r o p o s i tio n s w h ic h e a c h o f th e a x io m s is i n t e r p r e t e d to a s s e r t a r e a s fo llo w s : A l . E i t h e r d o in g p o r d o in g -~p ( i . e . , r e f r a i n i n g f r o m d o in g p ) is p e r m i t t e d in a n y c i r c u m s t a n c e c . A 2 . D o in g p o r q o r b o th in c i r c u m s t a n c e s c i s p e r m i t t e d if, a n d o n ly if, e i t h e r p is p e r m i t t e d in th is c i r c u m s t a n c e , o r q is p e r m i t t e d in it, o r b o th . A 3. If p i m p l i e s q , th e n if p is p e r m i t t e d in s o m e c i r c u m s t a n c e , s o is q ( i n th a t s a m e c i r c u m s t a n c e ) . ^ A 4 . If d o in g b o th p a n d q is p e r m i t t e d in c i r c u m s t a n c e c , th e n p i s p e r m i t t e d in c i r c u m s t a n c e c w h e n q h a s b e e n o r is b e in g d o n e . 41 R e s c h e r n o te s t h a t 'i m p l i e s ' i s h e r e u s e d in th e s e n s e of s t r i c t i m p l i c a t i o n ( s e e h is n o te 3 o n p. 29 ) . P e r h a p s th e m e a n in g in te n d e d f o r p —> q is b e s t e x p r e s s e d by s a y in g t h a t th e d o in g of p in v o lv e s th e d o in g of q . T h e i n t e r p r e t a t i o n of A3 w o u ld th e n r e a d , " i f th e d o in g of p in v o lv e s t h e d o in g of q , th e n if p i s p e r m i t t e d in a g iv e n c i r c u m s t a n c e , q is a ls o p e r m i t t e d in th a t c i r c u m s t a n c e . " 119 A5. If p is p e rm itte d in c ir c u m s ta n c e c , and q is p e rm itte d in c irc u m s ta n c e c w hen p h a s been o r is b ein g done, th en doing both p and q is p e rm itte d in c irc u m s ta n c e c . A6. If an a c t is p e rm itte d in a c irc u m s ta n c e th at is alw ays r e a l ized, th en th a t a c t is p e rm itte d in any c ir c u m s ta n c e w h a tso e v e r. A7. If an act is p e rm itte d in som e c irc u m s ta n c e o r o th e r ( d ) , th en it is p e rm itte d ( t r iv i a l l y ) in u n re a liz a b le c ir c u m sta n c e s . 42 It sh o u ld be c a re fu lly n oted th a t p , q , . . . , ra n g e , not o v e r p r o p o sitio n s , but o v e r a c ts ; hence, c o n n ec tiv es o c c u rrin g b etw een the n a m e s of tw o a c ts ( e .g . , p—>q) sh o u ld not be co n fu sed with s e n te n tia l c o n n e c tiv e s. F r o m th e s e se v e n a x io m s, R e s c h e r d e riv e s ten e le m e n ta ry th e o re m s of c o n d itio n al p e rm is s io n (p . 26). The two b a sic ax io m s of von W rig h t's S y stem II o c c u r as th e o re m s T3. 1 and T3.4 in R e s c h e r 's lis t of ten t h e o r e m s . T 3. 1 has the form P( p / c)vP ( -'-p /c ) and a s s e r t s th at, in a given c irc u m s ta n c e c , e ith e r doing p is p e rm itte d o r re f ra in in g fr o m doing p is p e rm itte d . T3.4 has the f o rm P ( p & q / c ) —><— ( P ( p/c )&P ( q/c&p )) and a s s e r t s th at both p and q a re p e rm itte d in c irc u m s ta n c e c if, and only if, p is p e r m itte d in c irc u m s ta n c e c and q is p e rm itte d in c ir c u m s ta n c e c 42 The in te rp re ta tio n s of R e s e lle r's se v en axiom s given h e re a re ad opted, with m in o r a m p lific a tio n s fo r the sa k e of c la rity , fro m th o se w hich he gives on p. 25 . 1 2 0 w hen p has b e e n o r is b e in g done. The d e fin itio n of c o n d itio n al o b lig atio n in R e s c h e r 's s y s te m is th e s a m e a s th a t g iv en in von W rig h t's S y s te m II. 0 ( p / c ) is in te r p r e te d to m e a n th at th e a c t p is o b lig a to ry in c ir c u m s ta n c e c . In t e r m s of p e r m is s io n , 0 ( p / c ) is defined a s ~ P ( ~ p / c ) , i .e ., 'p is o b lig a to ry in c ir c u m s ta n c e c 1 is by d efin itio n sy n o n y m o u s w ith 'i t is fo rb id d e n to o m it p in c ir c u m s ta n c e c. 1 On the b a s is of h is d e fin itio n of c o n d itio n a l o b lig atio n , and u sin g th e a x io m s and p re v io u s th e o r e m s , R e s c h e r p ro v e s six te e n th e o r e m s of c o n d itio n a l o b lig atio n . F r o m th e point of view of c o m p a r is o n with th e o r e m s of p re v io u s s y te m s , T h e o re m s T 4. 1, T 4. 2 , T 4 . 7 , and T 4. 12 a r e am o n g th e m o st in te r e s tin g . T4.1 O ( p&q / c ) —> <— ( O ( p / c )&O ( q / c )) Doing both p an d q is o b lig a to ry in c ir c u m s ta n c e c if, and only if, doing p is o b lig a to ry in c irc u m s ta n c e c and doing q is o b lig a to r y in c ir c u m s ta n c e c . N otice th a t the c ir c u m s ta n c e c a c ts as a co n n ec tin g lin k b e tw ee n p an d q , a c o n n ec tio n w hich was a b se n t in p re v io u s d is s o lu tio n ru le s fo r deon tic c o n ju n c tio n s. N e ith e r p n o r q a re s a id to be o b lig a to ry a p a r t f r o m the c o n n ec tio n w hich c s u p p lie s . It a p p e a rs , th e r e f o re , th a t R e s c h e r h as s u c c e e d e d in o v e rc o m in g o u r p re v io u s o b je c tio n s to d is s o lu tio n r u le s f o r deontic c o n ju n c tio n s. An e x a m p le of T 4. 1 m ig h t be th at it is o b lig a to ry to 1 2 1 be h o n e st and w e a r c lo th es w hile w orking in a bank if, and only if, it is o b lig a to ry to be h o n est while w orking in a bank an d it is o b lig a to ry to w e ar clo th es w hile w o rk in g in a bank. T his s e e m s to be in tu itiv e ly c o r r e c t. T4.2 ( p —> q ) —> ( 0 ( p / c ) —> 0 ( q / c ) ) If doing p s tr ic tly im p lie s ( in volv es ) doing q , then, if p is o b lig a to ry in c ir c u m s ta n c e c , q is o b lig a to ry in c irc u m s ta n c e c . If we think of p as an a c t d ire c te d to w a rd s an end and of q as an a c t d ire c te d to w a rd the m e a n s to th at end, th e o re m T 4. 2 gains a d - 43 ditio n al m ean ing . In th is c a se , if p is o b lig a to ry in c irc u m s ta n c e c , th en the m ea n s to the end at which p is a im e d a r e o b lig a to ry in th is sa m e c irc u m s ta n c e . T h is in te rp r e ta tio n s u g g e sts a p o ssib le c o n n ectio n w ith th e a n c ie n t m ax im , "W h o e v e r w ills an end a ls o w ills the m e a n s to th at end. " T4.7 O ( p/c )—> P ( p/c ) 43 T h is is not R e s e lle r 's in te rp re ta tio n , but it s e e m s quite fe a s ib le and holds m any in te r e s tin g p o s s ib ilitie s . C o n sid e r p as d ire c te d to w a rd s an end and q a s d ire c te d to w a rd s the m e a n s to th a t end, th en ( ( p - ^ q ) & 0 ( p / c ) )-l- > 0 ( q / c ) is an in tu itiv e ly c o r r e c t fo rm u la tio n of the m o r a l-c o m m itm e n t re la tio n s h ip . We i n te r p r e t th is fo rm u la a s sa y in g that, if p in v o lv es q and p is o b lig a to ry in c irc u m s ta n c e c , then ( n e c e s s a r i l y ) q is o b lig a to ry in c irc u m s ta n c e c . T he c ir c u m s ta n c e c p re v e n ts th is fo rm u la tio n fr o m being i n t e r p r e te d as sa y in g th a t the end ju s tifie s the m e a n s, sin c e the ju d g m en t 0 { p / c ) m u st a lre a d y have ta k e n the m ea n s into c o n sid e ra tio n . 1 2 2 If doing p is o b lig a to ry in c ir c u m s ta n c e c , th e n doin g p is p e r m itte d in c ir c u m s ta n c e c . T h is is in tu itiv e ly o b v io u s. T 4 . 12 0 ( p v q / c ) —> ( P ( p /c ) v P ( q /c )) If do in g a t le a s t one of p o r q is o b lig a to ry in c ir c u m s ta n c e c , th e n a t l e a s t one of th e s e a lte r n a tiv e s m u s t be p e r m itte d in c . R e s c h e r s u g g e s ts th a t T 4. 12 e x p r e s s e s w hat St. T h o m a s m e a n t w hen he d e n ie d th a t it could be o b lig a to ry to c h o o se b e tw e e n fo rb id d e n 44 a lt e r n a t iv e s ( i. e. , a m a n c a n n o t be p e rp le x u s s i m p li c it e r ) . R e s e ll e r 's th e o r e m s a y s th a t of o b lig a to ry a lte r n a tiv e s a t l e a s t one m u s t be p e r m itte d . T he c o n c e p ts of a b s o lu te p e r m i s s io n and a b s o lu te o b lig a tio n r e c e iv e s p e c ia l f o r m u la tio n in R e s e lle r 's s y s te m . He a g r e e s w ith von W rig h t th a t, in g e n e ra l, an a c t is a b s o lu te ly o b lig a to ry o r a b s o lu te ly p e r m itte d if it is o b lig a to ry o r p e r m itte d u n d e r a ll c i r c u m s ta n c e s w h a ts o e v e r ( p . 27). R e s c h e r , h o w e v e r, so c o n s tr u c ts his d e fin itio n s th a t it is no lo n g e r p o s s ib le to d efin e a b s o lu te o b lig a tio n in t e r m s of a b s o lu te p e r m i s s io n . He in tr o d u c e s the c o n s ta n t t , w hich s a t i s f i e s th e co n d itio n t —> < — c v m :, and th e c o n s ta n t f , w hich s a t is f ie s th e c o n d itio n f —> < — c &m : . T h u s, t s ta n d s f o r th e t r i v i a l c ir c u m s ta n c e th a t is a lw ay s r e a liz e d , w h e r e a s f s ta n d s fo r ^ S e e R e s e ll e r 's n ote 7 on pp. 29-30. 123 th e im p o s s ib le c ir c u m s ta n c e th a t is n e v e r r e a liz e d . L e ttin g P * r e p r e s e n t a b so lu te p e r m is s io n and O* r e p r e s e n t a b so lu te o b lig a tion, R e s c h e r g iv es the follow ing defin itio n s: P * ( p ) is defined a s P ( p / t ) . O* ( p ) is defined a s 0 ( p / f ) . ^ F r o m th e s e d e fin itio n s two th e o r e m s follow im m e d ia te ly : T 5. 1 P * ( p ) —> P ( p / c ) T5.2 O* ( p )—> 0 ( p/c ) T 5. 1 sa y s th at, if doing p is a b so lu te ly p e rm itte d , th e n p is p e r m itte d (c o n d itio n a lly ) in any c ir c u m s ta n c e w h a ts o e v e r. T5. 2 s a y s th at, if doing p is a b so lu te ly o b lig a to ry , th en p is o b lig a to ry (c o n d itio n a lly ) in any c ir c u m s ta n c e w h a tso e v e r. T h e s e th e o r e m s , th u s, sa y p r e c is e ly w hat w as in d ic a te d as a d e s ir a b le no tio n in g e n e r a l fo r th e c o n c e p ts of a b so lu te p e r m is s io n and a b s o lu te o b lig a tion. R e s c h e r po in ts out th a t so m e stu d e n ts in te r p r e t K ant as ^ T he d e fin itio n s of P * ( p ) and O* ( p ) r e s p e c tiv e ly a r e R e s c h e r ’s D2 and D3 , given on p. 27, but slig h tly r e p h r a s e d to avoid in tro d u c in g new n o tatio n . H. N. C a s te n a d a ( ’’T he L o g ic of O b lig a tio n ," P h ilo so p h ic a l S tudies, 10:17-23, F e b r u a r y , 1959) s ta te s th at R e s e lle r 's S 3 is c le a r ly p o in tle s s . Since D3 s a y s th at an a c t is a b so lu te ly o b lig a to ry if and only if it is o b lig a to ry in im p o s s ib le c ir c u m s ta n c e s ( in no c ir c u m s ta n c e w h a ts o e v e r ), it follo w s th a t no a c t is a b s o lu te ly o b lig a to ry . But in o th e r p la c e s (p . 28 and footnote 8 ) R e s c h e r in te r p r e ts 0 * ( p ) as " a c t p is o b lig a to ry u n d e r a ll c ir c u m s ta n c e s w h a ts o e v e r ." C a s te n a d a 's point is w ell t a k e n - - R e s c h e r 's c h a r a c te r iz a tio n of O* ( p ) is co n fu sed . 124 h a v in g h e ld in h is M e ta p h y s ic s of E th ic s th a t c ir c u m s ta n c e s a r e not re le v a n t to th e m o r a l w o rth o f a c tio n s , so th a t an y o b lig a to ry a c t is a b s o lu te ly o b lig a to ry in th e s e n s e of ’a b s o lu te 1 j u s t m e n tio n e d . B ut, a c c o rd in g to R e s c h e r , th is is not a c o r r e c t i n te r p r e t a t i o n of K a n t's v iew . K an t h o ld s th a t a c ts a r e o b lig a to ry w hen th e m o d e of a c tio n in v o lv e d c o u ld be ta k e n as d e te r m in in g p r in c ip le fo r th e co n d u ct of a ll m e n in a n a lo g o u s c ir c u m s ta n c e s . He is th u s n o t a s s e r t i n g th a t a c o n d itio n a lly o b lig a to ry a c t m u s t ip s o fa c to be a b s o lu te ly o b lig a to ry , b u t m e r e ly th a t th e a c t m u s t a ls o b e o b lig a to ry in c a s e s w hich d iffe r f r o m th a t in q u e s tio n only w ith r e s p e c t to the p e r s o n a l h i s t o r y of th e in d iv id u a l a g e n ts in v o lv e d in th e s e c i r c u m s ta n c e s . T hus a c o n d itio n a lly o b lig a to ry a c t n e e d not, on K a n t’s view , be o b lig a to ry u n d e r a ll c ir c u m s ta n c e s w h a ts o e v e r ( i . e . , be a b s o lu te ly o b l ig a t o r y ) , but, r a t h e r , it m u s t a ls o be o b lig a to ry o n ly in a c e r t a i n f a m ily of s i m i l a r c a s e s . ( R e s c h e r , n ote 8, p . 3 0 ) In a d d itio n to th e f i r s t tw o th e o r e m s w hich e x p lic a te th e a b s o lu te d e o n tic c o n c e p ts , R e s c h e r l is ts e le v e n m o r e w hich in v o lv e a b s o lu te p e r m i s s i o n and a b s o lu te o b lig a tio n ( p . 27). Of th e s e e le v e n t h e o r e m s th e fo llo w in g fo u r a r e of p a r t i c u l a r i n t e r e s t b e c a u s e th ey c o r r e s p o n d to th e fo u r d is s o lu tio n r u l e s of von W rig h t's S y s te m I . In o r d e r to f a c ilita te c o m p a r is o n , th e c o rr e s p o n d in g r u le in von W rig h t's S y s te m I is h e r e lis te d belo w e a c h R e s c h e r th e o r e m ; T5.10. O* (p & q )—><— ( O* < p )& 0 * ( q ) ) a. 0 ( A & B ) is id e n tic a l w ith (OA )& (OB) T5.4. P * ( p v q ) —><-— ( P * ( p )vP * ( q )) b. P ( A v B ) is id e n tic a l w ith ( PA )v( P B ) 125 T 5 . 11. ( O * ( p ) v O * < q ) ) —> 0 * (pvq) c . ( OA ) v ( O B ) e n ta ils O ( A v B ) T5.7. P* (p & q )—> < P * (p )& P * ( q ) ) d. P ( A& B ) e n ta ils ( P A ) & ( P B ) It is e a s i l y s e e n th a t th e d is s o lu tio n la w s of v on W rig h t's S y s te m I a r e in c lu d e d a s t h e o r e m s in R e s c h e r 's s y s t e m w h e n a p p r o p r i a te d e fin itio n s fo r a b s o lu te p e r m i s s i o n an d o b lig a tio n a r e in tr o d u c e d . P e r h a p s th e m o s t im p o r ta n t p o in t c o n c e rn in g th e a b s o lu te d e o n tic c o n c e p ts w h ich R e s c h e r m a k e s is th a t a b s o lu te o b lig a tio n c a n n o t be d e fin e d in t e r m s of a b s o lu te p e r m i s s i o n . We s a w th a t c o n d itio n a l o b lig a tio n , 0 ( p / c ) , w as s o d e fin e d a s to be e q u iv a le n t t o ~ P ( ~ p / c ) , i . e . , 0 ( p / c ) —>< P ( ~ p / c ) . In v o n W rig h t's S y s te m I , in w hich O an d P a r e s y m b o ls f o r u n i v e r s a l ( a b s o lu te ) o b lig a tio n a n d p e r m i s s i o n , OA is by d e fin itio n s y n o n y m o u s w ith ~ P ~ A , i . e . , O A —> < — ~ P -vA . On th e b a s is of th is d e fin itio n , von W rig h t a ls o e s t a b l is h e s th e d e o n tic ta u to lo g y P A —><— ~ ( O ^ A ) . It c a n be sh o w n th a t none of th e s e t h r e e e q u iv a le n c e - r e l a ti o n s h i p s h o ld s f o r R e s c h e r 's O* an d P * . T h e in f o r m a l d e m o n s tr a tio n r e q u i r e s th e u s e of th e u n i v e r s a l q u a n tif ie r , ( c ), w h ich m a y be r e a d , 'f o r e v e r y c . ' O* ( p ) is in te n d e d to s ig n ify th a t th e a c t n a m e d by p is o b lig a to r y in e v e r y c i r c u m s t a n c e . T h u s, O* ( p ) is e q u iv a le n t to ( c ) 0 ( p / c ) . By d e fin itio n 0 ( p / c ) is s y n o n y m o u s w ith ~ P ( ~ p / c ) ; t h e r e f o r e , O* ( p ) is e q u iv a le n t to { c P ( ~ p / c ) . P* (p ) is 126 in te n d e d to m e a n ( c ) P ( p / c ) . H e n c e , ^ P * ( —p ) is e q u iv a le n t to " * * ( c )P( —p / c ). F r o m th e s e r e s u l t s it is s e e n th a t 0 * ( p ) —> ~ P * ( ~ p ) h o ld s ( a n d in f a c t is R e s c h e r 's t h e o r e m T 5 . 8 ) , b u t th e r e v e r s e d o e s n o t h o ld . T h a t is to s a y , ( c ) « - P ( ~ p / c ) —> ~ ( c ) P ( ~ p / c ) h o ld s , but c ) P ( —p / c ) —> ( c )— P ( '■ ^'p / c ) d o e s n o t h o ld . T h is i r r e v e r s i b i l i t y of th e r e l a ti o n im p lie s th a t " T h e d u a lity of O a n d P . . . d o e s not a n d s h o u ld n o t c a r r y o v e r to O* a n d P * " ( R e s c h e r , p . 28 ) . T h e n o n d u a lity of O* an d P * m e a n s th a t a lth o u g h f r o m th e f a c t th a t a n a c t p is a b s o lu te ly o b lig a to ry we c a n i m m e d ia te ly c o n c lu d e th a t o m ittin g p is a b s o lu te ly n ot p e r m i tt e d , th e r e v e r s e is not t r u e : f r o m th e f a c t th a t it is a b s o lu te ly n o t p e r m i t t e d to o m it p we c a n n o t c o n c lu d e th a t p is a b s o lu te ly o b lig a to ry . V on W rig h t h a d 46 s u g g e s te d th a t O* ( p ) be d e fin e d a s 0 ( p / c v ~ c ) , but th is d e fin i tio n d o e s p e r m i t the d u a lity of O* a n d P * . R e s c h e r c h o o s e s to give up th e d u a lity p r in c ip le . T h e s e c o n s id e r a tio n s m ig h t s e r v e a s j u s t if i c a t io n f o r d e fin in g O* ( p ) a s 0 ( p /c & '— c ) , w h e re (c&r~c) is th e im p o s s ib le s itu a tio n w h ich is n e v e r r e a l i z e d . T h is is a n a w k w a r d d e fin itio n an d is in n e e d of ju s tif ic a tio n . T h e o r e m T 5 . 2, w h ic h s t a t e s th a t a n a b s o lu te ly o b lig a to ry a c t is o b lig a to r y in a n y c i r c u m s ta n c e w h a t s o e v e r - - O * ( p ) —> 0 { p / c ) - - r e l i e v e s th e " a w k w a r d n e s s " of th e c h a r a c t e r i z a t i o n of O* . It s h o u ld be n o te d , h o w e v e r, th a t Von W rig h t, "N o te , " p . 509 . 127 T 5. 2 can only be e s ta b lis h e d by e m p lo y in g A 7 , w hich s ta te s th at any a c t p e rm itte d in so m e c irc u m s ta n c e o r o th e r is p e r m itte d in u n re a liz a b le c ir c u m s t a n c e s - - P ( p / d ) —> P ( p/cG r'C ) . T h is axiom is its e lf a rtif ic ia l, but th e r e is no obvious in tu itiv e a rg u m e n t a g a in st c o n s tru c tin g su c h an a x io m . F u r th e r , we do s o m e tim e s m ake m ean in g fu l s ta te m e n ts involving c ir c u m s ta n c e s th a t a re n e v e r r e a liz e d . R e s c h e r gives a s an ex am p le of the la tte r th e c o u n te r- fa c tu a l sta te m e n t, " if he had o ffe re d you a b rib e you would have been ob lig ed to re fu s e it" (n o te 6, p. 29). H ow ever, R e s c h e r ’s exam p le does not re lie v e our difficulty sin c e it d e a ls w ith c irc u m s ta n c e s w hich m ig h t- h a v e - b e e n -b u t- w e r e - n o t r e a liz e d . T he c irc u m s ta n c e (c& ^-c) is one w hich n e v e r could be re a liz e d . A7 m u s t s till be r e g a r d e d a s an a r tif ic ia l o r nonintu itive axiom , and s im ila r ly the d efinition of O* ( p ) is n o n in tu itiv e . R e s c h e r h as w ithin h is s y s te m a n u m b e r of th e o re m s dealing w ith both co n d itio n al and a b so lu te o b lig atio n and co n d itio n al and a b so lu te p e rm is s io n . On the b a sis of th is s tr u c tu r e , he in tro d u c e s the c o n ce p t of m o ra l c o m m itm e n t ( d e r iv e d o b lig a tio n ) . The e x p r e s sio n he u s e s fo r m o ra l c o m m itm e n t is ( q C p / c ) . It is intended to 47 be in te r p r e te d as " q c o m m its us to p in c irc u m s ta n c e s c ." ^ We have s u b s titu te d o rd in a ry p a re n th e s e s fo r the s p e c ia l b ra c k e ts which R e s c h e r u s e s to e n c lo se the c o m m itm e n t e x p re s s io n . (q C p /c ) is th en defined a s 0 ( p / c & q ) . T h u s, 'q c o m m its u s to p in c ir c u m s ta n c e c 1 is d efin ed a s 'p is o b lig a to ry in c ir c u m s ta n c e c w hen q is b ein g o r h a s b e en d o n e .’ M aking u s e of th is d e fin itio n in c o n ju n ctio n w ith p re v io u s a x io m s and th e o r e m s of h is s y s te m , R e s c h e r d e riv e s s e v e n th e o r e m s involving the co n cep t of m o r a l c o m m itm e n t (p . 28). Of th e s e se v en , T 6 .1 , T 6 .5 , and T 6. 6 a r e of s p e c ia l in te r e s t. T6.1. ( 0 ( p / c ) & ( pCq / c )) —> O ( q / c ) If it is o b lig a to ry to do p in c ir c u m s ta n c e c and if doing p c o m m its us to doing q in c ir c u m s ta n c e c , th en q is a ls o o b lig a to ry in c ir c u m s ta n c e c . N otice how m u ch c lo s e r to o u r in tu itiv e notions of c o m m itm e n t th is th e o r e m is th an is the c o m m itm e n t law of von W rig h t's S y s te m I: ( OA&O ( A —> B )) —>OB . T6.5 O ( p & q /c ) —> ( p C q /c ) If it is o b lig a to ry to do both p and q in c ir c u m s ta n c e c , th en doing p c o m m its us to doing q in c ir c u m s ta n c e c . T6.6. O* (p ) —>{ qCp/c ) If p is a b so lu te ly o b lig a to ry , th en any a c t c o m m its us to p in c ir c u m s ta n c e c . T h is p ro p o s itio n is one of th o se m e n tio n e d by It is not a n tic ip a te d th a t any confusion w ill r e s u lt f r o m th is change s in c e the in n e r s t r u c tu r e of the e x p r e s s io n is c o m p le te ly d iffe re n t f r o m any o th e r e x p r e s s io n u s e d in the s y s te m . 129 P r i o r a s a " p a r a d o x of d e r i v e d o b l i g a t i o n ." P r i o r s p e a k s of th e p r o p - 48 o s i t io n e x p r e s s e d b y T 6 . 6 a s a " h a r m l e s s " p a r a d o x . R e s c h e r a g r e e s w ith P r i o r o n t h is p o in t a n d is t h e r e f o r e n o t t r o u b l e d b e c a u s e T 6 . 6 is p r o v a b l e in h is s y s t e m . T h e m o r e o b je c tio n a b le of th e d e o n tic p a r a d o x e s - - O * ( •'“p )—>( p C q / c ) , i . e . , a n a b s o l u te ly f o r b i d d e n a c t c o m m i t s u s 49 to a n y a c t w h a t s o e v e r - - i s n o t p r o v a b l e i n R e s c h e r 's s y s t e m . A n o b s e r v a t i o n w h ic h R e s c h e r f a i l s to m a k e is t h a t O * ( p ) a l r e a d y e x p r e s s e s a m o r a l c o m m i t m e n t w h ic h , u p o n a n a l y s i s , a p p e a r s to be a n i m p o s s i b l e o n e . O * ( p ) i s d e f in e d a s 0 ( p / c & - '- c ) . But 0 ( p / c & - w c ) is e q u iv a le n t to (< ^ cC p/c ), b y th e c o m m i t m e n t d e f i n i t io n a n d by th e s t i p u l a t i o n th a t c m a y b e a n a c t . B u t ( - ^ c C p / c ) s a y s th a t o m ittin g a n a c t c c o m m i t s u s to p e r f o r m a c t p in c a s e c is p e r f o r m e d . O* ( p ) th u s e x p r e s s e s a n i m p o s s i b l e c o m m i t m e n t , a n d T 6 .6 now r e a d s : ( - ^ c C p / c ) —>( q C p / c ) , i . e . , if we a r e c o m m i tt e d to p b y a n i m p o s s i b l e s e t o f c i r c u m s t a n c e s , th e n w e a r e c o m m i t t e d to p by a n y a c t a t a ll. P e r h a p s t h is is w h at is m e a n t by r e f e r r i n g to t h i s p a r a d o x a s h a r m l e s s . W h at t h e s e c o n s i d e r a t i o n s i n d ic a t e , 48 prior, "Paradoxes," p. 64. ^ R e s c h e r g iv e s a n i n f o r m a l d e m o n s t r a t i o n o f t h is in n o te 12, p . 30 . 130 n e v e r th e le s s , is th at in its e q u iv a le n t f o r m ( —c C p /c ), O* (p) is not a s a tis f a c to r y fo rm u la tio n f o r th e co n cep t of a b so lu te m o ra l c o m m itm e n t. R e s c h e r, not n o ticing th a t h is definition of 0 * ( p ) a lre a d y involves the definition he su g g e sts fo r m o r a l c o m m itm e n t, gives a d iffe re n t fo rm u la tio n fo r ab so lu te m o ra l c o m m itm e n t. He r e p r e s e n ts a b so lu te m o ra l c o m m itm e n t by (q C p /t), w hich s a y s ' q c o m m its us to p in the tr iv ia l c irc u m s ta n c e th a t is alw ay s r e a liz e d 1 (p . 28). T he e x p re s s io n (qCp/t) is equ ivalent to (qC p/cv~ c) which, in tu rn , is equivalent to 0 ( p/q&( cv— c )) w hich m ea n s th e sa m e as 0 ( p / q ) . The final r e s u lt m e a n s sim p ly th at p is o b lig a to ry under condition q . N otice the s im ila r ity betw een th is fo rm u la tio n fo r a b so lu te c o m m itm e n t and von W rig h t's stip u la tio n th at "A n e c e s s a r y condition fo r say in g th at doing q c o m m its us to p is th a t p is o b lig a to ry u n d e r conditions qH ("N o te , " p. 509 ). T h e re is a d a n g e r th a t a tten tio n to th e fo rm a l c o n s tru c tio n of th is notion of a b so lu te m o ra l c o m m itm e n t m ight m ak e us m is s the sig n ific a n c e of the fin a l r e s u lt. 0 ( p / q ) now e x p r e s s e s both a c o n ditional o b lig atio n and an ab so lu te m o ra l c o m m itm e n t. The s ta te m e n t 'p is o b lig a to ry in c irc u m s ta n c e q ( i . e . , when a c t q is d o n e )' is eq uivalent to 'q m o ra lly c o m m its us to p in e v e ry s e t of c ir c u m s ta n c e s . ' T he u n d e rly in g p u rp o se in in tro d u c in g co n d itio n al o b lig a 131 tio n w as to m a k e p o s s ib le a n a d e q u a te f o r m a liz a tio n of th e c o n c e p t of m o r a l c o m m itm e n t. T h e n o tio n th a t p is o b lig a to ry in c a s e q is done, d o e s s e e m to e x p r e s s th e n o tio n th a t q c o m m its us to p . B ut 0 { p / q ) a lr e a d y a s s u m e s th a t th e c i r c u m s t a n c e s in v o lv e d do n o t a l t e r the m o r a l s ta tu s of p and q . T h e lo g ic a l f o r m of a d e o n tic s y s te m c an n o t of its e l f d e te r m in e th e m o r a l r o le of c i r c u m s t a n c e s . A ll h u m a n a c tio n s ta k e p la c e in a c o n te x t w h ich m a y be of e n o rm o u s c o m p le x ity and w hich y e t m u s t be in c o r p o r a te d in to th e c o n te n t o f a m o r a l ju d g m e n t. A d e o n tic lo g ic a l s y s te m can a t m o s t s u p p ly a c r i t e r i o n f o r d is c e r n in g m is ta k e s in f o r m a l r e a s o n in g ; it can n o t su p p ly us w ith m o r a l ju d g m e n ts . R e s c h e r r e f l e c t s th e s e o b s e r v a tio n s in th e co n clu d in g r e m a r k s of h is p a p e r; T he a s s e r t i o n s of th e s y s te m h e r e p r e s e n t e d hav e little , if any, b e a r in g upon th e q u e s tio n of th e r o le of c ir c u m s ta n c e s in d e te r m in in g p e r m i tt e d a c ts . T h is , it s e e m s , r a t h e r th a n b ein g a s h o r tc o m in g is a s it sh o u ld be. T he ( m o r a l ) b e a r in g of c ir c u m s ta n c e s upon a c ts is bound to be a m a t t e r of a p p lie d r a t h e r th a n t h e o r e ti c a l e th ic s , of c o n te n t r a t h e r th a n lo g ic a l f o r m , of m o r a l p h ilo so p h y r a t h e r th a n d e o n tic lo g ic . ( R e s c h e r , p. 29 ) 5. T h e R e d u c tio n of D eo n tic L o g ic to A le th ic M odal L o g ic S lig h tly m o r e c o m p le x s y s te m s of d e o n tic lo g ic have b e e n 132 s u g g e s te d r e c e n tly by A. R . A n d e r s o n ‘ S an d A. N. P r i o r . ** * T h e s e s y s te m s a r i s e f r o m an a p p ro a c h d iffe rin g in one im p o rta n t a s p e c t, f r o m th at of th e s y s te m s w hich have b een d is c u s s e d th u s f a r ; th is d iffe re n t a p p ro a c h in c o r p o r a te s th e d e o n tic c o n c e p ts into s y s te m s f o r th e a le th ic m o d a litie s . The e s s e n t ia l s te p s in v o lv e d in th is re d u c tio n of d e o n tic logic to a le th ic m o d a l logic a r e s u m m a r iz e d in 52 w hat fo llo w s. Step 1. A p ro p o s itio n a l c o n sta n t, # , iS in tro d u c e d into an a le th ic m o d a l lo g ic ( te c h n ic a lly defin ed by A n d e rso n a s a n o r m a l a le th ic m o d a l logic in " R e d u c tio n ," p. 100). Step 2. It is a s s e r t e d a s a n a x io m th a t # is c o n tin g en t, i . e . , M ( # )&M ( -HP ) . ( ’M1 is the m o d al o p e r a t o r f o r p o s s ib ility . T h e F o r m a l A n a ly sis of N o rm a tiv e C o n c e p ts , T e c h n ic a l R e p o rt No. 2, U.S. O ffice of N aval R e s e a r c h C o n tr a c t No. S A R /n o n r- 6 0 9 (1 6 ) , 1956; A. R. A n d e rso n and O m a r K h ay y am M o o re, " T h e F o r m a l A n a ly s is of N o rm a tiv e C o n c e p ts, " A m e r ic a n S o c io lo g ic a l R ev iew , 2 2 :9 -1 7 , 1957; an d A n d e rso n ] ,T A R ed u ctio n of D eo n tic L o g ic to A le th ic M odal L o g ic, " M ind, 67:100-103, 1958. "M o d a l a n d D eo n tic L o g ic, " A ppendix D to T im e an d M o d ality (O x fo rd , 1957), pp. 140-145. 52 T h is s u m m a r y is b a s e d on the s te p s an d d e fin itio n s g iv en in P r i o r , T im e and M o d a lity , p . 140-145; and A n d e rso n , "A R e d u c tio n of D eontic L o g ic to A le th ic M odal L o g ic ." 53 A n d e rs o n an d P r i o r u s e a c a p ita l s c r i p t l e t t e r P f o r th is p ro p o s itio n a l c o n sta n t, w hich we hav e r e p la c e d by '# ’ to avoid c o n fu s io n w ith th e d eo n tic o p e r a to r f o r p e r m i s s io n ( P ) . 133 54 M ( p ) h a s the in te rp re ta tio n , 'it is p o ss ib le th a t p ' ). Step 3. The deontic o p e ra to rs a r e defined in t e r m s of M and # . As in te rp re ta tio n s of the c o n stan t # , P r i o r su g g e sts "T h e w orld w ill be w o rse off, " " P u n ish m e n t ought to follow , " e tc . ( T im e and M odality, p. 140). A n d e rso n s u g g e sts th at # be i n t e r p r e te d in su ch a way as to d e s c rib e so m e "b ad" s ta te - o f - a f f a ir s ( e ith e r , on a te le o lo g ic a l e th ic a l th e o ry , "bad" b e ca u se of its c o n se q u e n c e s, o r on a d eo n to lo g ical th eo ry , "bad" in h e r e n tly ) . (" R e d u c tio n ," p. 103) U sing P ( p ) f o r 'p is p e rm is s ib le , F ( p ) fo r 'p is f o r b id d e n ,1 and O ( p ) fo r'p is o b lig ato ry , ' we o btain th e follow ing definitions ( a s s u m m a r iz e d by P r i o r in T im e and M o dality, p. 140): Df. P : P ( p ) = M(p&~#) The p ro p o sitio n 'p is p e r m itte d 1 is by definition synonym ous with 'it is p o ssib le fo r p to o c c u r without a bad s ta te - o f - a f f a ir s o c c u rrin g . 1 Df. F : F ( p ) = ~ P ( p ) = ~ M ( p & ~ # ) = p - l-># 54 B oth A n d e rso n and P r i o r use the L u k a sie w ic z n o tation which h a s b een tr a n s la te d ( with the ex cep tio n of the m o d al o p e ra to r M ) into sy m b o ls a lre a d y f a m ilia r to the r e a d e r . in th e se s y s te m s , v a ria b le s p , q , r , . . . , ran g e o v e r p ro p o sitio n s about a c ts and not o v e r n a m e s of a c ts , e .g ., p m ig h t r e p r e s e n t the p ro p o sitio n *Act A is done. ' (S ee A n d e rs o n 's c o m m ent in "R eduction, " pp. 1 0 0 -1 0 1 , footnote 4 ) . 134 The p ro p o s itio n 'p is fo rb id d e n 1 is by d e fin itio n sy n o n y m o u s w ith 'p is not p e rm itte d , 1 'i t is not p o s s ib le fo r p to o c c u r w ithout a bad s ta te - o f - a f f a ir s o c c u r rin g , 1 and 'if p o c c u r s th en a bad s ta te - o f - a f f a ir s m u s t o c c u r. ' Df. O: 0 < p ) = F ( - p ) = ~ M ( ~ p & ~ # ) , - p - ^ # T he p ro p o s itio n 'p is o b lig a to ry ' is by d e fin itio n sy n o n y m o u s with 'o m ittin g p is fo rb id d e n , 1 'i t is not p o s s ib le to o m it p w ithout a b a d s t a te - o f - a f f a i r s o c c u rr in g , ' and 'if p is o m itte d th en a bad s t a te - o f - a f f a i r s m u s t o c c u r. ' A la r g e n u m b e r of th e o r e m s a r e p ro v a b le in m o st o r d in a r y m o d al s y s te m s on th e b a s is of the d e fin itio n s g iv en above to g e th e r w ith A n d e r s o n 's ax io m , M ( # )&M ( ) . P r i o r p o in ts out th a t the s im p le a x io m m a y r e p la c e A n d e rs o n ’s a x io m w ith e q u ally r ic h r e s u l ts ( T im e and M odality, p. 140 ) . He a ls o g iv e s a p ro o f fo r the fo llow in g p ro p o sitio n : M ( )—><— ( O ( p )—> P ( p ) ) , i . e . , it is p o s s ib le to avoid th e bad th in g (bad s t a te - o f - a f f a i r s ) if, a n d only if, w h a te v e r is o b lig a to ry is a ls o p e r m is s ib le . T hu s th e l a t t e r p r o p o s i tion, O ( p ) —> P ( p ) , m a y a ls o s e r v e a s th e s o le a x io m of th e s y s te m . A n d e rs o n o b tain s th e follow in g th e o re m s d ir e c tly f r o m th e s ta te d d e fin itio n s of O a n d P ; O ( p )—> < —( — p - 1 ^ ( )) and F ( p )—> < — < p - * — > { #& M ~#)) ( " R e d u c tio n ," pp.102-103). T he f i r s t th e o r e m s a y s th a t p is o b lig a to ry if, and only if, its d e n ia l s t r i c t l y 135 im p lie s both th e b ad th in g and th e p o s s ib ility of av o id in g th e bad th in g , i. e. , the fa ilu re of p le a d s to a bad but a v o id a b le s t a te - o f - a f f a ir s . T he se c o n d t h e o r e m s a y s th a t p is fo rb id d e n if, and only if, p its e lf le a d s to a bad but a v o id a b le s t a t e - o f - a f f a i r s . A n d e rs o n h as s tip u la te d c e r ta in c o n d itio n s w hich a s y s te m m u s t m e e t if it is to be c o n s id e r e d a n o r m a l d e o n tic logic ( " R e d u c tio n ," p . 1 0 0 -1 0 1 ) . If we d e sig n a te th e m o d a l-d e o n tic s y s te m of P r i o r and A n d e rso n by "D " , th e n the f i r s t c o n d itio n D m u s t s a tis f y is th at it be c lo s e d u n d e r d e ta c h m e n t f o r m a t e r i a l im p lic a tio n and u n d e r a r u le allo w ing in te r s u b s titu ta b ility of m a t e r i a l e q u iv a le n ts f r o m the tw o -v a lu e d p r o p o s itio n a l c a lc u lu s . T h is co n d itio n is e a s ily s e e n to be s a tis f ie d by D b e c a u s e D w as f o r m e d by adding a p r o p o s itio n a l c o n sta n t to a m o d al s y s te m w hich a lr e a d y s a tis f ie d the s ta te d co n d itio n . The se c o n d co n d itio n w hich D m u s t s a tis f y in o r d e r to be c o n s id e re d a n o r m a l deontic logic, is th a t the follow ing two th e o r e m s m u s t be p ro v a b le in D : P ( p ) v P ( ^ ) and P ( p v q ) —><—( P ( p ) v P ( q ) ) ; and the follow ing th r e e e x p re s s io n s m u s t not be p ro v a b le a s th e o r e m s of D : p —> P ( p ) , P ( p ) —>p, M ( p )—> P ( p ) . T he p ro o f th a t the s y s te m D does s a tis f y th is se c o n d c o n d i tio n is g iv en in d e ta il by A n d e rso n (" R e d u c tio n , " pp. 101-102). It is p e rtin e n t to note th a t th e t h e o r e m P ( p ) v P ( •'-p ) ( w hich is p a r t of 136 th e se c o n d c o n d itio n ) is id e n tic a l w ith the p rin c ip le of p e r m is s io n w hich is a s tip u la te d r e s t r i c ti o n of von W rig h t's S y s te m I a n d is s ta te d a s fo llow s: "A ny g iv en a c t is e it h e r its e lf p e r m itte d o r its CC n e g a tio n is p e rm itte d . " S im ila rly , the th e o r e m P ( p v q )—> < — ( P ( p ) v P ( q )) o c c u r s in von W rig h t's S y s te m I as h is se c o n d d is s o lu tio n law , w hich s t a te s th a t P ( A v B ) is id e n tic a l w ith ( P A ) v ( P B ) . T h is th e o r e m a ls o o c c u rs in R e s c h e r 's s y s te m a s T5.4; P * ( p v q ) - r ><— ( P * ( p ) v P * ( q ) ) . A ll of th e law s of von W rig h t's S y ste m I c an be e s ta b lis h e d in s y s te m D p lu s the law 0 ( 0 ( p ) —> p ) , 'it is o b lig a to ry th at 57 w hat is o b lig a to ry be d o n e .' To th e s e r e s u l ts P r i o r ad d s th at s y s te m D p e r m its an in te r e s tin g in v e s tig a tio n of the r e la tio n s b e tw e en deon tic logic and the o r d in a r y m o d al lo g ic. F o r e x a m p le , the m o d al p ro p o s itio n M ( ~ # ) ( 'it is p o ss ib le to avoid the bad th in g ' ) h as been e s ta b lis h e d a s e q u iv a le n t to the d eo n tic p ro p o s itio n O ( p ) —> P ( p ) ( 'w h a te v e r is o b lig a to ry is p e r m i s s ib l e ' ) . T he l a t t e r a p p e a re d as a law of von W rig h t's S y ste m I. U sing th is law , P r i o r sh o w s th a t the K an tian p rin c ip le th a t w h a te v e r is o b lig a to ry m u s t be Von W right, "D eo n tic L o g ic, " p. 9 . 57 P r i o r s ta te s th a t A n d e rs o n p o in te d th is out in h is T he F o r - m a l A n a ly sis of N o rm a tiv e C o n cep ts ( 1956), ( P r i o r , T im e and M odality, p. 140) . 137 p o ssib le ^ ® is p ro v a b le in D ( T im e a n d M o d a lity , p. 142). P r i o r 's p ro o f, a b b r e v ia te d a n d r e i n t e r p r e t e d in o u r s y m b o ls , fo llo w s: (1) O ( p ) —> P ( p ) p r e v io u s ly e s ta b lis h e d law . (2) M ( p & ~ # ) —> M ( p ) f r o m M ( p & q ) —> M ( q ) . (3) P ( p ) —> M ( p ) f r o m d ef. P ( p ) = M ( pit"-# ) , a n d s u b s t i t u tio n in (2). (4) O ( p ) —> M ( p ) ( 1 ) , <3), t r a n s i t i v i t y o f im p lic a tio n . In c o m p a r in g s y s t e m D w ith d e o n tic s y s te m s d is c u s s e d e a r l i e r , one m ig h t w ell c o n c lu d e th a t D is th e " r i c h e s t " s y s t e m y e t p r o p o s e d , in the s e n s e th a t it y ie ld s th e l a r g e s t n u m b e r of d e o n tic p r o p o s itio n s . H o w e v e r, th is s y s te m d o e s n ot d e a l w ith c o n d itio n a l o b lig a tio n a n d c o n d itio n a l p e r m i s s i o n a s d e v e lo p e d in the v o n W rig h t S y s te m II a n d in th e R e s c h e r s y s te m . F r o m a n in tu itiv e p o in t of v iew , the th e o r e m s in v o lv in g the c o n d itio n a l d e o n tic c o n c e p ts a p p e a r m o r e v a lid g e n e r a lly th a n do th o se in v o lv in g th e a b s o lu te d e o n tic c o n c e p ts . T he a b s o lu te s y s te m s s e e m to lo s e th e a s p e c ts of th e " p r a c t i c a l " s y llo g is m of m o r a l ju d g m e n ts , in th e s e n s e th a t no c o n s id e r a tio n is a llo w e d f o r the c o n te x t o r c ir c u m s ta n c e s in w h ich th e a c ts sp o k e n of ta k e p la c e . A lthough a c o n d itio n a l s y s te m c an n o t s p e c ify th e m o r a l n a tu r e of the c i r c u m s t a n c e s , it a t l e a s t T h e " p o s s ib ility " in v o lv e d in th e K a n tia n f o r m u la th a t th e o u g h t im p lie s c a n is n ot s im p ly lo g ic a l p o s s ib ility , it a ls o in v o lv e s th e a b ility of th e a g e n t to p h y s ic a lly p e r f o r m th e o b lig a to ry a c tio n . S in ce th e o p e r a t o r M d e n o te s lo g ic a l p o s s ib ility th e f o r m u la O ( p ) —> M ( p ) only s a y s th a t w h a te v e r is o b lig a to ry is lo g ic a lly p o s s ib le . 138 a llo w s f o r th e ro le w hich c ir c u m s ta n c e s p la y in m o r a l ju d g m e n ts . S y s te m D m u s t c o n ta in s e v e r a l p ro v a b le th e o r e m s w hich a r e not in tu itiv e ly a c c e p ta b le . If " a l l of th e law s of von W rig h t's S y s te m I " a r e p ro v a b le in D , th e n th e law s in v o lv in g m o r a l c o m m itm e n t a r e p ro v a b le in D . B u t von W rig h t h im s e lf h a s r e j e c t e d h is c h a r a c t e r i z a t i o n of c o m m itm e n t a s in tu itiv e ly u n s a tis f a c to r y , p r in c ip a lly b e c a u s e of th e p a ra d o x e s d e riv a b le f r o m th e c o m m it m e n t la w s. M o r e o v e r, th e d is s o lu tio n law s f o r a b s o lu te c o n ju n c tiv e d e o n tic p ro p o s itio n s m u s t a ls o be p ro v a b le in s y s te m D , s in c e th ey a r e ta u to lo g ie s in von W rig h t's S y s te m I. 0 ( p & q ) —> 0 { p ) is su c h a ta u to lo g y , b u t th e v a lid ity of th is t h e o r e m is not in tu itiv e ly c le a r . A p o in t w o rth n o tic in g is th a t if a d is s o lu tio n r u le s u c h a s th is is v a lid , it p r o v id e s a n a r g u m e n t a g a in s t th e e q u iv a le n c e of im p e r a tiv e s a n d n o r m a tiv e s . F r o m 'D on p a r a c h u te s and ju m p ! ' one can n o t d e d u c e th a t 'J u m p ! ' is a lw a y s c o m m a n d e d . It m a y be a r g u e d th a t th is e x a m p le is not a p r o p e r one s in c e th e a c ts in v o lv e d a r e not th e ty p e th a t c a n be a b s o lu te ly c o m m a n d e d . T h is is u n d o u b ted ly a v a lid o b je c tio n ; but th e n th e n a tu r a l q u e s tio n is , w hat kind of a c ts a r e a b s o lu te ly c o m m a n d e d ? If we a r e to b e lie v e K ant, t h e r e is only one c a t e g o r i c a l o r a b so lu te im p e r a tiv e . T h is c a te g o r ic a l im p e r a tiv e e x p r e s s e s w hat w ould be, f o r K ant, th e only a b s o lu te m o r a l o b lig a tio n . On K a n t's view , a lo g ic a l s y s te m fo r a b s o lu te i m p e r a tiv e s o r 139 a b s o lu te d e o n tic p r o p o s itio n s w ould c o n ta in only one p r o p o s itio n and h e n c e w ould b e of little v a lu e . O b v io u sly , m u c h r e m a in s to b e done w ith r e s p e c t to c la r if ic a tio n of th e c o n c e p ts of a b s o lu te o b lig a tio n a n d c o n d itio n a l o b lig a tio n b e fo r e a fin a l d e c is io n c a n be m a d e c o n c e rn in g th e lo g ic a l r e la tio n s of s e n te n c e s c o n ta in in g th e s e c o n c e p ts . A f e a tu r e of s y s te m D w hich s e e m s d e s i r a b l e is th e c h o ic e of a r g u m e n ts f o r th e d e o n tic o p e r a t o r s . A n d e rs o n a n d P r i o r u s e the v a r i a b le s p , q , r , . . . , ra n g in g o v e r p r o p o s itio n s o r " s t a t e s - o f - a f f a ir s " r a t h e r th a n ra n g in g o v e r " a c t- ty p e s , " a s th e y do in th e s y s te m s of von W rig h t a n d R e s c h e r . T he a d v a n ta g e of the f o r m e r c h o ic e of a rg u m e n ts is th a t the c u m b e r s o m e m a c h in e r y of p e r f o r m a n c e -f u n c tio n s b e c o m e s u n n e c e s s a r y . T h e p ro p o s itio n p s a y s th a t an a c t of the s o r t A is done. P ( p ) s a y s th a t it is p e r m i tt e d th a t a n a c t of th e s o r t A be done. O ( p ) s a y s th a t it is o b lig a to ry th a t an a c t of s o r t A be done o r th a t an a c t of s o r t A o u g h t to be d o n e. T h is n o ta tio n m a k e s p o s s ib le a n in f o r m a tiv e c o m p a r is o n of n o r m a tiv e s y s te m s w ith s o m e of the e a r l y i m p e r a tiv e s y s te m s . T he H o f s ta d te r a n d M c K in se y lo g ic of s a tis f a c tio n c o n s id e r s an im p e r a tiv e to be s a tis f ie d if the p r o p o s itio n s ta tin g its th e m e of d e m a n d is t r u e . U sin g 'I 1 fo r th e im p e r a tiv e o p e r a t o r , we c o n clu d e th a t I ( p ) is s a t is f ie d if p is t r u e . A lf R o s s h a s p o in te d out th a t H o fs ta d te r a n d M c K in se y a r e led to th e r e s u l t p —> I ( p ) , i . e . , e v e r y p r o p o s itio n 140 e x p r e s s in g a th e m e of d e m a n d im p lie s its c o rr e s p o n d in g im p e r a tiv e ( R o s s , p. 37). L e t p be the p r o p o s itio n th a t an a c t of p r o m is e - k eep in g is p e rfo r m e d . T h en I ( p ) s a y s 'K eep th is p r o m i s e ! ' U sin g R o s s 's in te r p r e ta tio n of th e lin g u is tic a lly in d ic a tiv e f o r m of an im p e r a tiv e , we m a y e x p r e s s I ( p ) a ls o as 'T h is p r o m is e ought to be k e p t.' B ut th e la tte r o c c u rs a s O (p) w ithin a ll of th e n o rm a tiv e s y s te m s d is c u s s e d in th e p r e s e n t c h a p te r. T he p ro p o s itio n p —> 0 ( p ) is a lw ay s in v a lid in both of th e von W right s y s te m s , in P r i o r 's s y s te m s , in R e s c h e r 's s y s te m , and in A n d e rs o n 's s y s te m . F r o m the fa c t th a t a n a c t is p e rf o r m e d , nothing a t a ll can be lo g ic a lly i n f e r r e d c o n c e rn in g the o b lig a to rin e s s of th a t a c t. Indeed, one of the c o n d i tio n s fo r a n o rm a l d eo n tic logic w hich A n d e rso n h a s s tip u la te d is ev en s t r o n g e r th an th is in th a t it p ro h ib its th e v a lid ity of p —> P ( p ) (fro m the fa c t th a t an a c t is done we can in fe r nothing a t a ll c o n c e rn in g its p e r m i s s i b i l i t y ) . H o fs ta d te r and M c K in sey b a se t h e i r logic of s a tis fa c tio n on th e th e o r e m th a t if q is d e riv a b le from p , th en I ( q ) is d e riv a b le f r o m I ( p ) . The in a d e q u a c y of th is th e o r e m to a cc o u n t f o r p r a c tic a l in f e r e n c e s is c le a r ly sh ow n by R o ss ( p . 3 8 ) an d h a s been d is c u s s e d p re v io u s ly . T he in ad e q u ac y of sa tisfa c tiD n -fu n c tio n s w ith r e s p e c t to s p e c if ic a lly deontic p ro p o s itio n s sh o u ld be e q u a lly c le a r . T h e re can s c a r c e l y be any sig n ific a n c e in m a in ta in in g O ( p ) to be " s a tis f ie d " 141 when p is tru e , and "n o n sa tisfie d " w hen p is not tr u e . It m ay v e r y w ell be the c a s e th a t O ( p ) is tru e and p is fa ls e , i . e . , we m ay be oblig ated to do so m e th in g w hich we have o m itte d . It m ay be fa ls e th at a p r o m is e is kept but tr u e that it ought to be kept. To sa y th a t O ( p ) h as not been s a tis fie d is sim p ly to sa y th a t the p r o m is e h a s not b een kept, but nothing at a ll is s a id about w h e th er o r not it ought to have b een kept. T hus the logic of s a tis fa c tio n can no m o re p ro p e r ly c h a r a c te r iz e n o rm a tiv e in fe re n c e s than it could a cc o u n t fo r im p e ra tiv e in fe re n c e s . A n d e rso n and M o o r e ^ c re d it B o h n e rt (" S e m io tic S tatu s of C o m m an d s, " 1945) w ith having been the f i r s t to in tro d u c e the notion of r e w a r d o r p u n ish m en t into a fo rm a liz e d s y s te m fo r im p e ra tiv e s o r n o rm a tiv e s . B o h n e rt had su g g e ste d th a t an im p e ra tiv e be i n t e r p re te d a s a d isju n ctio n betw een the th em e of dem and and the im p lie d penalty, i .e ., I S ^ S j v P . F o r ex am p le, "S to p !" would be i n t e r p r e te d a s " E ith e r you w ill sto p o r you w ill be shot. " The s y s te m b a se d on th is in te r p r e t s t ion is su b je c t to so m e of the sa m e o b je c tions brought a g a in s t the logic of sa tis fa c tio n . It is f r o m B o h n ert, h o w ev er, th a t A n d e rso n obtained the id ea fo r h is d efinition of p e r m i s sion, P ( p ) = M(p&-^#). T he p r o p o s itio n 'p is p e r m itte d 1 is by 59 "T h e F o r m a l A n a ly sis of N o rm a tiv e C o n c e p ts ," A m e ric a n S ociological R eview , 22:9-17, 1957 . 142 d efin itio n sy n o n y m o u s w ith 'i t is p o s s ib le to do p and avoid th e bad s t a t e - o f - a f f a i r s . ' A n d e rso n h a s u se d th e notion of p u n ish m e n t in su c h a way a s to re d u c e th e deo ntic co n ce p ts to a le th ic m o d a litie s , but th is re d u c tio n avoids th e m a jo r c r i t ic i s m s w hich w e re b ro u g h t a g a in st B o h n e rt's re d u c tio n su g g e stio n . F o r B o h n e rt, —>!S^ was a p ro v a b le th e o re m . In s y s te m D , both p —> P ( p ) and M ( p ) —> P ( p ) a r e in v alid th e o r e m s . An o b jectio n , s i m il a r to one r a i s e d a g a in st B o h n e rt's s y s te m , re m a in s a g a in s t s y s te m D . F r o m P ( p ) we can s t i ll v a lid ly d e riv e P ( p v q ) in the follow ing m a n n e r: (1) P ( p ) = M (p& -H O definition. (2) M (p& *^#)—> M ( p&—# )vM( q^t—# ) law of o r d in a r y m odal logic. (3) P ( p ) —> P ( p ) v P ( q ) (2) s u b s titu tio n . (4) P ( p ) —>Pf p v q ) s in c e P ( p )v P ( q ) —> < — P ( p v q ) is a th e o r e m of D . T hus, fr o m 'i t is p e rm itte d to m a il th e le t t e r ' we can in fe r 'i t is p e r m itte d e ith e r to m a il o r to b u rn it. ' It is doubtful th a t th is in fe re n c e could be c o n s id e re d v a lid o r c o r r e c t f r o m an in tu itiv e p o in t of view . In c re d itin g B o h n e rt with the in tro d u c tio n of the notion of p u n ish m e n t into a fo rm a liz e d im p e ra tiv e s y s te m , A n d e rso n and M oore have o v e rlo o k e d K a rl M e n g e r's 1939 p a p e r, "A L ogic of the Doubtful; On O ptativ e and Im p e ra tiv e L o g ic ." In th is p a p e r M en g er s u g g e ste d th a t " I c o m m a n d pM be in te r p r e te d a s " u n le s s p , s o m e thin g u n p lea sa n t w ill happ en ( e . g. , I s h a ll be a n g ry o r you w ill be 143 p u n is h e d ) " ( p . 5 9 ). U sing 'C p ' f o r 'I c o m m a n d p, ' a n d 'A 1 f o r th e u n p le a s a n t c o n s e q u e n c e , M e n g e r m a k e s th e fo llo w in g d e fin itio n : Cp—><—( ~ p —> A ) . C o m p a re th is w ith A n d e r s o n 's ( a n d P r i o r ' s ) d e fin itio n : O ( p ) = (* - p # ) . T h e sig n of n e c e s s a r y im p lic a tio n ( -*->) p r e v e n ts A n d e r s o n 's d e fin itio n f r o m le a d in g to the a b s u r d c o n c lu s io n s w hich M e n g e r sh o w s fo llo w f r o m h is d e fin itio n w hen the a rg u m e n ts ( p , q , . . . ) a r e c o n s id e r e d a s t r u e o r f a ls e p ro p o s itio n s 60 r a t h e r th a n a s "d o u b tfu l" p r o p o s itio n s . 6. S u m m a ry O u r in v e s tig a tio n s in to th e lo g ic of o b lig a tio n h a v e led us th ro u g h a v a r i e ty of s y s te m s w hich h a v e b e e n p ro p o s e d to h a n d le o b lig a tio n s e n te n c e s . In g e n e r a l, we h av e d is tin g u is h e d tw o b a s ic a p p r o a c h e s to th e p ro b le m : th e im p e r a tiv e a p p ro a c h and th e n o r m a tiv e (deontic) a p p ro a c h . None of the s y s te m s d is c u s s e d h a s b e e n fo u n d c o m p le te ly a d e q u a te a s a lo g ic of o b lig a tio n , a lth o u g h s o m e a r e fiO M e n g e r p o in ts out th a t ( ( —>r )&( p —> q )) —>( — q —> r ) is v a lid in th e c a lc u lu s f o r p r o p o s itio n s . S u b stitu tin g A f o r r , he o b ta in s : ( C p & ( p —> q ) ) —>Cq. T h e l a t t e r h a s th e a b s u r d c o n s e q u e n c e s th a t: (1) c o m m a n d in g one t r u e p r o p o s itio n is to c o m m a n d e v e r y tr u e p r o p o s itio n ( p —>q fo r an y q w hen p a n d q a r e both t r u e ), a n d (2) to c o m m a n d a fa ls e p ro p o s itio n is to c o m m a n d e v e r y p r o p o s itio n ( p —>q f o r any q w hen p is f a ls e ) . ( " T h e L o g ic of th e D oubtful, " pp. 5 9 -6 0 ) . 144 o b v io u sly m u c h b e t t e r s u ite d to th e t a s k th a n a r e o t h e r s . Som e of th e e a r l y im p e r a tiv e s y s t e m s ( th o s e of M ally , H o fs ta d te r an d M c K in se y , an d B o h n e r t ) have b e e n sh o w n to le a d to th e c o m p le te ly u n a c c e p ta b le r e s u l t s of m a k in g th e im p e r a tiv e e le m e n t s u p e rflu o u s an d of h a v in g e v e r y in d ic a tiv e im p ly its c o r r e s p o n d in g im p e r a tiv e ( p —> ! p ) . T he n o r m a tiv e a p p ro a c h , in g e n e r a l, a p p e a r s to y ie ld m o r e f r u itf u l r e s u l t s in f o r m a liz in g th e r e la tio n s h ip s of s e n te n c e s in v o lv in g th e d e o n tic c o n c e p ts . Som e s p e c if ic c o n c lu s io n s w hich o u r in v e s tig a tio n s s u g g e s t a re : ( 1) It s h o u ld be s t i p u la t e d th a t o n ly v o lu n ta ry a c ts c a n a p p e a r in a rg u m e n ts fo r d e o n tic o p e r a t o r s . ( 2 ) A p r in c ip le of p e r m i s s i o n is a n e c e s s a r y p r e r e q u i s i t e f o r a d e o n tic lo g ic , i.e. , e v e r y v o lu n ta ry a c t is e it h e r p e r m i tt e d o r n o t p e r m itte d . ( 3 ) S ince th e y t r a n s c e n d a ll c ir c u m s ta n c e s , c o m b in a tio n s of a b s o lu te d e o n tic p ro p o s itio n s can n o t be of th e s a m e n a tu r e a s " p r a c t ic a l " in f e r e n c e s . T he m in o r p r e m i s e of a p r a c t i c a l s y llo g is m m u s t be a p a r t i c u l a r p ro p o s itio n . ( 4 ) P r o v is io n m u s t be m a d e f o r the r o le of c ir c u m s ta n c e s in m o r a l re a s o n in g . ( 5 ) It is d e s i r a b l e to in c lu d e in a d e o n tic s y s te m the r e l a tio n s h ip b e tw e e n the d e o n tic an d a le th ic m o d a litie s a s e x p r e s s e d by 145 0 ( p )-*-> M ( p ), and to convey th e m e a n in g -c o n n e c tio n s of th e deontic e le m e n ts by th e use of the s t r i c t im p lic a tio n sig n ( -L - > ) . ( 6 ) p —> 0 ( p ) , p —> P ( p ) , M( p )—> P ( p ), and p—> !p a re a ll in v alid in f e r e n c e s . ( 7 ) T he s ta tu s of the a b so lu te d eo n tic c o n ce p ts an d of th e co n d itio n al d eontic co n cep ts is in n eed of c o n s id e ra b le c la r if ic a tio n b e fo re a ju s tific a tio n m ay be given fo r in c o rp o ra tin g th e s e co n cep ts in to a fo rm a liz e d s y s te m . ( 8 ) The re la tio n s h ip b etw een n o rm a tiv e s and im p e ra tiv e s is in n eed of f u r th e r c la rific a tio n . <9) The s ta tu s of d is s o lu tio n -ru le s fo r "co m b in ed " deontic p ro p o s itio n s is s till in doubt. CH APTER IV T H E C O N C E P T O F O B LIG A TIO N AND THE P R O P E R FO R M U L A T IO N O F O B LIG A TIO N SE N T E N C E S A s u rv e y of v a rio u s s y s te m s of im p e r a tiv e and n o rm a tiv e lo g ic s h as led to c e r ta in c o n c lu sio n s and s tip u la tio n s r e g a r d in g the logic of o b lig atio n . S pecific po in ts of view r e g a r d in g the n a tu re of o b lig a tio n a r e im p lic itly c o n ta in e d in th e se c o n c lu sio n s and a r e re s p o n s ib le f o r th e s tip u la tio n s . It is now in c u m b e n t upon us to m a k e e x p lic it th e s e po in ts of v iew r e g a r d in g th e c o n c e p t of o b lig a tio n . A m o re d e v elo p ed c h a r a c te r iz a tio n of o b lig a tio n should p e r m it a d e c is io n a s to w h e th e r o b lig a tio n s e n te n c e s a r e m o re p r o p e r ly to be r e n d e r e d a s n o r m a tiv e s o r as im p e r a tiv e s , and, co n seq u e n tly , a s to w h e th e r the logic of o b lig a tio n is b e s t f o rm u la te d w ithin a n o rm a tiv e s y s te m o r an im p e r a tiv e s y s te m . * 1 It w as im p lie d in th e p re c e d in g c h a p te r th a t th e n o rm a tiv e a p p ro a c h h o ld s the m o s t p r o m is e fo r a lo g ic of o b lig a tio n . T he fin d in g s of th e p r e s e n t c h a p te r sh o u ld s e r v e to ju s tify th is p o sitio n and to f u r t h e r d e lin e a te th e n e c e s s a r y a s p e c ts w hich a s y s te m a d e q u ate a s a lo g ic of o b lig a tio n m u s t c o n tain . 146 147 1. The C oncept of O b ligation In C h a p te r I we d ecid ed to c o n s id e r a s an o b lig atio n s e n te n c e any se n te n c e w hich s a y s of a p o ss ib le h u m an a c tio n th a t it ought ( o r ought n o t ) to be done by a h u m an ag en t. T he co n cep t of o b lig atio n is in te n tio n a lly lim ite d to o b lig atio n s p e rta in in g to a c tio n s th a t a re sp e c ific a lly h u m an . T he p ro p r ie ty of applying the t e r m 'o b lig a to ry ' to a ctio n s o th e r th an h u m an is not denied; it is sim p ly not c o n s id e re d h e r e . We m u st now d ecid e ju s t what it m e a n s to s a y of an a c tio n th a t it is o b lig a to ry o r th a t it ought to be done. F u n k and W agnalls give th e follow ing d efin itio n fo r the t e r m 'o b lig a tio n ' : The binding o r c o n s tra in in g p o w er of so m e m an d a te , i n t e r nal o r e x te rn a l, and r e g a r d e d a s enjoining a duty; the binding p o w e r of a p ro m is e , c o n tra c t, oath, o r vow, o r of law , n a tu r a l, civil, p o litic a l, o r m o ra l; th a t w hich c o n s titu te s le g a l o r m o ra l duty, c o n s tra in s a p e rs o n to the p e rfo rm a n c e of its r e q u ire m e n ts , and r e n d e r s h im lia b le to its s a n c tio n s in c a s e of 9 fa ilu re in th a t p e rfo rm a n c e . The binding o r c o n s tra in in g a s p e c t of o b lig atio n is r e f e r r e d to in 3 T he D ic tio n a ry of P h ilo so p h y as a kind of n e c e s s ity : A lw ays , in any c a s e of obligation, th e re is a kind of n e c e s s ity f o r so m eo n e to do s o m e th in g .............. ^ F unk and W agnalls New S ta n d a rd D ic tio n a ry of the E n g lish L anguage (New Y ork, 19387^ s . v~ ^ D ag o b ert D. R u nes, e d . , 1st ed. ( New Y ork, 1942). 148 T he n e c e s s ity involved in an ob ligation m a y be of v a rio u s k i n d s - - s h e e r p h y s ic a l co m p u lsio n , so c ia l p r e s s u r e , p ru d e n tia l n e c e s s ity , e tc .* T h e binding e le m e n t o r " n e c e s s ity " involved in the g e n e ra l c o n cep t of o b lig atio n m a y be d e riv e d f r o m a v a rie ty of s o u r c e s . It is p o s s ib le to d istin g u ish ty p es of o b lig atio n in a c c o rd a n c e with the p a r tic u la r s o u rc e of th e binding e le m e n t involved. T he a rtic le c ited fr o m The D ic tio n a ry of P h ilo so p h y su g g e sts p h y sic a l co m p u lsio n , s o c ia l p r e s s u r e , and p ru d e n tia l c o n s id e ra tio n s as p o ss ib le s o u rc e s of th is binding e le m e n t. P . H. N o w ell-S m ith d istin g u is h e s fo u r types of o b lig atio n : o b lig atio n by c ir c u m s ta n c e s , o b lig atio n by t h r e a t s , 5 le g a l and q u a s i- le g a l o b lig a tio n , and m o r a l oblig atio n . A b rie f c o n s id e r a tio n of the s o u rc e of the binding e le m e n t of e a c h of th ese types of o b lig a tio n w ill c la rify the type of n e c e s s ity involved in any o b lig a tion. It is p r o p e r to s a y th at c irc u m s ta n c e s oblige us, but the w ord lo b lig e' is n ot h e re sy n o n y m o u s w ith 'c a u s a lly n e c e s s ita te . 1 N ow ell- Sm ith points out th a t th e re is a s e n s e in w hich it is p r o p e r to s a y 'th e fa c t th a t the ro a d w as flooded obliged m e to tak e a d e to u r;' but th is * W. K. F . (W illia m K. F r a n k e n a ), a rtic le on "O bligation" in The D ic tio n a ry of P h ilo so p h y , pp. 217-218 . ^ P . H. N ow ell-Sm ith, E thics (London, 1 9 5 4 ), pp. 201-211 . 149 does not m e a n th at I w as p h y sic a lly fo rc e d a ro u n d the ro a d ( E th ic s , p. 201 ). T he obligation to take a d e to u r a r o s e b e c a u se of a flooded ro ad , but the tak in g of the d e to u r is not c a u sa lly n e c e s s ita te d . B ut ev en though we a r e n ot c a u s a lly fo rc e d to tak e the d e to u r ( ta k in g - th e - d e to u r is not an in v o lu n ta ry a c t ) , we a r e s till in so m e s e n se c o n s tra in e d to do so . We would not choose to tak e the d e to u r if the ro a d had not been flooded. N o w ell-S m ith has se e n c le a r ly th at, a l though th e c o n s tra in t of an o b lig atio n of c irc u m s ta n c e r e s t r i c t s th e '’fre e d o m " of o u r ch o ice, it does not rem o v e from the c h o se n a c t its v o lu n ta ry c h a r a c te r . 'F r e e , ' u se d in th is s e n s e , is not opposed to 'in v o lu n ta ry ' but to 'o b lig a to r y .' An o b lig atio n w hich d e riv e s its binding e le m e n t f r o m a th r e a t is s i m il a r to an o b lig atio n involving n a tu ra l c ir c u m s ta n c e s . If a p e r so n p e rfo rin s a c e r ta in a c tio n b e c a u se he is being th re a te n e d with a gun, th en he s till a c ts v o lu n ta rily in the s e n s e th at he c h o o se s to p e r fo rm th at action, but the choice is not " f re e " in s o fa r as the th r e a t c o n s tra in s him ; the th r e a t in te r f e r e s with his f r e e ch o ice. L e g a l o b lig atio n s a r e th o se w hich owe th e ir binding e le m e n t to the S tate, i . e . , th ey a re the o b lig atio n s im p o se d by the law of the land. T he q u a s i- le g a l o b lig atio n s which N o w ell-S m ith m en tio n s a r e o b lig atio n s im p o se d by ru le s o r law s o th e r th a n th o se of the S tate, 150 C e .g ., sc h o o l, club, o r s o c ia l r u le s . T he p e n a ltie s a s s o c ia te d w ith b re a k in g th e s e ( q u a s i - l e g a l ) r u le s o r law s m ak e q u a s i- le g a l o b lig a tio n s an alo g o u s to o b lig a tio n by th r e a ts and o b lig atio n by n a tu r a l c ir c u m s ta n c e s . The a c tio n s involved a re s till v o lu n ta ry a c tio n s, but they a r e not f r e e in the s e n se that, e x cep t fo r th e r u le s , th ey would not have b een done. M o ra l o b lig atio n h as m u c h in co m m o n w ith a ll of the o th e r ty p es of o b lig a tio n m en tio n ed . S o m e tim e s m o r a l o b lig atio n s and leg a l o b ligations a r e id e n tic a l, a s when the law of th e land fo rb id s an a c tio n w hich is m o ra lly w ro ng a s w ell as being c rim in a l. We m ay ev en sa y th a t it is m o ra lly o b lig a to ry to o b s e rv e the law of the land ev en w hen the a c tio n fo rb id d e n by the law is not its e lf c o n s id e re d to be m o ra lly w rong. B oth m o r a l and c iv il law s a re a tten d e d by s a n c tio n s although th e sa n c tio n s d iffer in d iffe re n t c a s e s . M o ra l obligation, like all o th e r ty p es of oblig atio n, c o n s tra in s o u r free c h o ic es but does not a l t e r the v o lu n ta ry n a tu re of th e a ctio n involved. A m o r a l o b lig atio n o b lig es us to a c t in a way in w hich, ex cep t fo r the oblig atio n, we would not have a c te d . F o r e x am p le , I am not f r e e to a c c e p t an in v ita tio n to d in n e r b e c a u se I a m o b lig ated by h av in g m ad e a p re v io u s ® N ow ell-S m ith , E th ic s, p. 209 . 151 7 p r o m is e to dine w ith so m e o n e e ls e . T h u s, m o r a l o b lig a tio n s a r e s e e n to h av e m u ch in c o m m o n w ith o th e r ty p e s o f o b lig a tio n . T he d is tin g u is h in g f e a tu r e of m o r a l o b lig a tio n s w hich N o w e ll-S m ith e m p h a s iz e s is th a t th e y a r e s e lf-im p o s e d , w h e re a s a ll o th e rs a r e not ( E th ic s , p. 210 ) . T h is is in a g r e e m e n t w ith the K an tian c h a r a c t e r iz a tio n of th e m o r a l ag en t a s a " la w g iv e r unto h im s e lf" and w ith a ll o th e r c o n ce p tio n s of m o r a l o b lig a tio n w hich hold th a t a m a n is bound by h is own c o n s c ie n c e . T h e q u e stio n w hich m u s t be a n s w e re d w ith r e s p e c t to the lo g ic a l s t r u c tu r e of o b lig a tio n s e n te n c e s is w h e th e r o r not th e d if f e r e n t ty p e s of o b lig a tio n ju s t r e f e r r e d to r e q u ir e d iffe re n t lo g ic a l s y s te m s . Do the p e c u lia r itie s of m o r a l ob lig atio n , fo r e x a m p le , involv e a lo g ic a l s t r u c t u r e d iffe re n t from th a t of le g a l o b lig a tio n ? It m u s t be r e m e m b e r e d th a t th e ty p e s of o b lig a tio n w e re d istin g u is h e d in a c c o rd a n c e w ith the s o u r c e of the binding e le m e n t involved. T he binding e le m e n t its e lf w as r e f e r r e d to a s a kind of n e c e s s ity but, in none of the c a s e s c o n s id e re d , w as th is n e c e s s ity d e te rm in e d to be e ith e r a lo g ic a l o r a c a u s a l n e c e s s ity . Som e ty p e s of o b lig a tio n a re undou btedly c o n s id e re d m o re b in d in g than o t h e r s - - w e w ould w ish to m a in ta in , fo r in s ta n c e , th a t, in c a s e s of c o n flict, m o r a l o b lig a tio n s 7 T his exam p le is taken from N ow ell-S m ith , p. 210 . 152 ta k e p r e c e d e n c e o v e r le g a l o b lig a tio n s . In a d d itio n , w ith in e a c h ty p e of o b lig a tio n t h e r e is u n d o u b te d ly a d is tin g u is h a b le h i e r a r c h y , e . g . , one c iv il law m a y ta k e p r e c e d e n c e o v e r su io th er, th e m o r a l o b lig a tio n to p r e s e r v e life m a y ta k e p r e c e d e n c e o v e r th e m o r a l o b lig a tio n to o b e y c iv il la w s, e tc . B ut in no c a s e c a n w e s a y th a t a n y ty p e of o b lig a tio n o r an y s p e c if ic o b lig a tio n b in d s w ith th e f o r c e of lo g ic a l o r c a u s a l n e c e s s i t y . T h e lo g ic a l r e l a ti o n s b e tw e e n o b lig a tio n s e n t e n c e s a r e not a ffe c te d by th e s o u r c e o f th e o b lig a tio n . T h e o b lig a tio n s e n te n c e i t s e l f m u s t be c o n s i d e r e d a s th e g iv e n in a n y p r o p o s e d lo g ic a l s c h e m a ti s m , an d the v a ry in g s o u r c e of th e g iv e n s h o u ld not a ff e c t th e p u r e ly lo g ic a l r e l a ti o n s h i p s . E th ic a l t h e o r i s t s h a v e d if f e r e d g r e a t l y w ith r e s p e c t to w hat is to be c o n s id e r e d the s o u r c e of m o r a l o b lig a tio n . T h e s o u r c e s c o n te n d e d f o r in c lu d e G od, a p e c u l ia r " m o r a l s e n s e , " in tu itio n , th e n a tu r a l law , h u m a n n a tu r e , a n d m a n y Q o t h e r s . O b v io u sly , if th e s o u r c e of o b lig a tio n a ff e c ts th e lo g ic a l s t r u c t u r e o f o b lig a tio n s e n t e n c e s , th e n t h e r e w ill be a s m a n y " l o g ic s " of m o r a l o b lig a tio n a s t h e r e a r e e th ic a l t h e o r i e s . B u t s in c e the s o u r c e of th e o b lig a tio n d o e s n o t p la y a s p e c if ic a lly lo g ic a l r o l e in O D is a g r e e m e n ts a m o n g e th ic a l t h e o r i s t s a r e s e l d o m a b o u t w h ic h a c tio n s a r e c o n s i d e r e d to be o b lig a to ry but, r a t h e r , why th e y a r e c o n s i d e r e d to be o b lig a to r y . A p u r e ly lo g ic a l s c h e m a t i s m f o r o b lig a tio n s e n te n c e s c a n n o t s u p p ly th e a n s w e r to th is w hy. 153 e ith e r c a s e , ® a lo g ic a l s y s te m a d e q u a te f o r a g e n e r a l c o n ce p t of m o r a l o b lig a tio n sh o u ld a ls o be a d e q u a te fo r a g e n e r a l c o n c e p t of o b lig a tio n . E v e r y c a s e in w hich th e c o n ce p t of o b lig a tio n a p p lie s c o n c e rn s a v o lu n ta ry h u m an a c tio n . T h is a s p e c t of o b lig a tio n is e s s e n t ia l if any s ig n ific a n c e is to be a tta c h e d to th e notion of p e rs o n a l r e s p o n s ib ility f o r o u r a c tio n s , both good and bad. T h e binding e le m e n t of an o b lig a tio n , h o w e v e r s tr o n g it m a y be, c an n e v e r be s a id to im p o s e a lo g ic a l o r a c a u s a l n e c e s s ity upon a h u m an a g en t. B oth A r is to tle a n d St. T h o m a s had in s is te d th a t th e s e n te n c e s w hich o c c u r in p r a c tic a l s y llo g is m s a r e c o n c e rn e d w ith v o lu n ta ry a c ts . T h e only s ig n ific a n t d e lib e ra tio n s we c an hav e ab o u t a c tio n s c o n c e rn th o se a c tio n s w hich a r e in o u r p o w e r and, h e n ce , a r e v o lu n ta ry . T h u s, A r is to tle s a y s th a t " a c tio n s c o n c e rn in g m e a n s m u s t be a c c o rd in g to choice and v o lu n ta ry " ( N ic o m a c h e a n E th i c s , 1113b 5 ); he ad d s th a t " w h e re it is in o u r p o w e r to a c t it is a ls o in o u r p o w e r not to a c t an d vice □ N o w e ll-S m ith a g r e e s w ith o u r c o n c lu sio n w hen he s ta te s th a t " th e r e do n o t s e e m to be an y s h a r p lo g ic a l d iffe re n c e s b etw een the way in w hich m o r a l r u l e s a r e c o n n e c te d w ith 'o u g h t1 and 'right* and the w ay in w hich n o n m o ra l r u le s a r e " ( E th ic s , p. 216 ) . N ic o m a c h e a n E th ic s , B k .III, Ch. 5 ; S u m m a T h eo lo g ic a , I-U , 6, 1, and I - U , 17, 5. 154 v e r s a 1 1 ( 1113b 8) . The K antian fo rm u la th a t 'th e ought im p lies c a n 1 and K ant’s s ta te m e n t th a t "It is alw ays in e v e ry o n e 's pow er to sa tisfy the c a te g o ric a l com m and of m o ra lity , f u r th e r su p p o rt the co n ten tion th a t we can only be obliged to do th at which is in our p o w er. It is e s s e n tia l th at the p h y sic a l p o ssib ility of p e rfo rm in g an a a c t be not confused with the log ical p o ssib ility of its being p e rfo rm e d . E v e ry actio n which can be p h y sic ally p e rfo rm e d by an agent m ust a ls o be lo g ically p o ssib le , i. e . , it cannot involve a lo g ical co n trad ictio n . But not e v e ry actio n which is logically p o ssib le is a ls o p h y sically p o ssib le to a p a rtic u la r hum an agent in a p a rtic u la r c irc u m s ta n c e . T hus, it m ay be lo g ically p o ssib le fo r e v e ry m an to do a h an d sp rin g , but it is p h y sic ally im p o ssib le fo r so m e m en. H ence, when we sa y that ought im p lie s c a n , we m ean that, if we a re obliged to p e rfo rm an act, it m u st be in o ur pow er to p e rfo rm it. H ow ever, in all sy s te m s which include th e deontic concepts w ithin a s y s te m of ale th ic m odal logic, the e x p re s s io n 'i t is p o ssib le th a t' r e f e r s to logical p o ssib ility . It is, th e re fo re , q u estio n ab le w heth er P r i o r 's th e o re m O ( p ) —> M ( p ) actu ally e x p re s s e s the type of p o ssib ility a p p ro p ria te to the concept of obligation. O ( p ) —> M ( p ) sa y s th a t if p is ob ligatory , th en p is (lo g ic a lly ) p o ssib le ; and th is is c e rta in ly c o r - The C ritiq u e of P r a c tic a l R eason, p. 150 . 155 r e c t. H ow ever, w hen we in s is t th a t we m u s t be able to do w hat we a r e obliged to do, we m e a n th a t the p ro p o s e d a c tio n m u s t be p h y s ic a l ly p o ss ib le a s w ell as lo g ic a lly p o s s ib le . But O ( p ) —> M ( p ) does not convey th e notion of p h y sic a l p o s s ib ility and, h en ce, does not c o m p le te ly e x p r e s s th e fo rm u la th a t the ought im p lie s can. C e r ta in a s p e c ts of c iv il law s m ay r e q u ir e s p e c ia l a tte n tio n with r e s p e c t to the q u e stio n w hen a law m a y be s a id to be o b lig a to ry . T he binding e le m e n t of a le g a l o b lig atio n in v o lv e s the a u th o rity of the la w -m a k in g body as w ell as a c o n s id e ra tio n of the co n ten t of the 12 law . T he law s of S oviet R u s s ia , fo r e x am p le , do not bind a c itiz e n of th e U nited S tates ( u n le s s he h app ens to be in Soviet R u s s ia ) . With r e s p e c t to th e bin ding p o w e r of any c iv il le g a l s y s te m th e r e a p p e a rs to be one b a s ic o b lig atio n (w h ic h m ay be both le g a l and m o r a l ) - - t h e 12 An in fo rm a l d is c u s s io n of the co nd itio ns a ffe ctin g the o b li g a t o r y c h a r a c te r of law s is co n tain ed in E tien n e G ilson, T he C h ris tia n P h ilo so p h y of St. T h o m as A quinas ( New Y ork, 1956), pp. 264-270 . In th is s e c tio n G ilso n a ls o s ta te s th a t "A ctu ally , when we t r y to g et hold of th e e s s e n tia l m ea n in g of th e w ord 'law , 1 we find, beyond the id e a of m e r e ru le , the m u ch m o re p ro fo u n d notion of o b lig atio n " ( p. 264). Since, "It is e v e ry w h e re r e a s o n w hich is th e ru le and m e a s u r e of w hat is done" ( p. 205 ), th en law m u s t be a t le a s t bound by r e a s o n . B ut, "to s a y th a t law is a p r e s c r ip tio n of r e a s o n d e t e r m in in g w hat ought to be done is to link law with p r a c tic a l re a s o n , w hose p r o p e r duty it is to p r e s c r i b e w hat a c ts should be p e rfo rm e d " (p . 265). F r o m G ils o n 's r e m a r k s it is e a s ily s e e n th at w ithin th e T h o m istic fra m e w o rk , law s a r e u ltim a te ly p r e s c r ip tio n s of p r a c tic a l r e a s o n . On th is account, th e lo g ic al s t r u c tu r e of le g a l o b lig atio n s e n te n c e s w ill be the s a m e as th a t of any p r a c tic a l re a s o n in g p r o c e s s . 156 o b lig atio n to c o n fo rm to th e law s of th at s y s te m . The p ro b le m of d e te rm in in g w h e th er o r not a given law is binding in a g iven c ir c u m s ta n c e is th e r e f o r e tw ofold: the law m u st be e x a m in e d a s to its a u th o rita tiv e n e s s , and it m u st be e x am in ed as to the b e h a v io r w hich it m a k e s o b lig a to ry ( the content of the law ). The lo g ic a l r e la tio n sh ip s betw een law s c o n s id e re d f ro m the point of view of th e ir co ntent ( a s o b lig atin g c e r ta in b e h a v io r ) a re the sa m e as th e lo g ic a l r e la tio n sh ip s betw een obligatio n s e n te n c e s in g e n e ra l. A p p licatio n s of a law to a p a r tic u la r s ta te of a ffa irs is often re g a rd e d a s involving a p r a c tic a l sy llo g is m . T hus, a ju d g m en t as to c rim in a l lia b ility fo r a c e r ta in a c t in v o lv es su b su m p tio n of the p a r tic u la r c a s e u n d er a g e n e ra l 13 p rin c ip le (th e leg a l n o r m ) . T he a u th o rita tiv e n e s s of a leg a l n o rm , h o w ever, cannot be d e te rm in e d by lo g ical c o n s id e ra tio n s but is a m a tte r fo r e m p ir ic a l v e rific a tio n . A law lack in g p ro p e r a u th o rity cannot im p o se a le g a l obligatio n upon us; hence, any se n te n c e which is s a id to e x p re s s a le g a l o blig ation is a lre a d y a s s u m e d to be a u th o r - 13 F o r a c r i t ic i s m of the tra d itio n a l c o n cep tio n s of a judge a s so m e s o r t of leg al lo g ic ian s e e Alf R o ss, ’’im p e ra tiv e s and L ogic, " P h ilo so p h y of S cien ce, 11:30-46, 1944, e s p e c ia lly pp. 4 5 -4 6 . R o ss holds th a t th e p rin c ip a l ta s k of a judge is to supply the m in o r p r e m is e of th e su b su m p tio n s y llo g is m . T he judge m u st d e te rm in e w h eth er the p a r tic u la r c a s e in q u e stio n is a c tu a lly w ithin the sco p e of th e g e n e ra l im p e r a tiv e ( m a jo r p r e m i s e ) and th is d e te rm in a tio n is not th e sa m e a s sc ie n tific v e rific a tio n of a f a c t— it is a d e c isio n b a se d on the in ten d e d u sag e of the language of the law . 157 ita tiv e . T h e p r o v is io n s of a g e n e r a l lo g ic of o b lig a tio n , t h e r e f o r e , s h o u ld a p p ly to th e c o n te n t of a le g a l n o r m only. E m p i r i c a l in v e s ti- 14 g a tio n s a lo n e c an d e te r m in e its a u th o r ita tiv e n e s s . B oth le g a l a n d m o r a l o b lig a tio n s a r e a c c o m p a n ie d by s a n c tio n s , but th e r o le w hich s a n c tio n s p la y in th e d e te r m in a tio n of a n o b lig a tio n h a s o ften b e e n m is c o n s tr u e d . S a n c tio n s, a s su c h , do not d e te r m in e th e o b lig a to ry c h a r a c t e r of an a c tio n . S a n c tio n s a r e o ften im p o s e d by l e g i s l a t o r s to e n c o u ra g e c e r t a i n a c tio n s o r to d e te r m e n f r o m c e r t a i n a c tio n s . In th e U n ited S ta te s to d ay , t r a n s p o r tin g a k id n a p p ed p e r s o n a c r o s s a s ta te lin e is a f e d e r a l o ffe n s e , p u n ish a b le by d e a th . It is not th e d e a th p e n a lty , h o w e v e r, w hich m a k e s k id n ap p in g w ro n g (and h e n ce fo rb id d en ). T he s e v e r i t y of the p e n a lty m a y d e te r w o u ld -b e k id n a p p e rs fro m p e r f o r m in g a fo rb id d e n a c t, i . e . , f e a r of c o n s e q u e n c e s m a y s o m e tim e s e x p la in why we a c t. B ut to s a y th a t s a n c tio n s s o m e tim e s su p p ly th e m o tiv e s f o r a c tio n is not the s a m e a s to s a y th a t s a n c tio n s d e te r m in e the o b lig a to ry n a tu r e of a c tio n s . T he *4 F o r a d e ta ile d a c c o u n t of the s y n ta c tic a l p e c u l ia r i ti e s of le g a l n o r m s s e e H an s K e lse n , G e n e r a l T h e o ry of L aw an d S tate ( C a m b r id g e , M a s s ., 1945), a n d F e lix E . O p p e n h eim , " O u tlin e of a L o g ic a l A n a ly s is of L aw ," P h ilo s o p h y of S c ie n c e , 11 :1 4 2 -1 6 0 , 1944. In W hat is V a lu e ? E v e r e tt W. H a ll r e l a t e s th e fin d in g s of K e ls e n and O p p e n h e im to th e g e n e r a l p r o b le m of fin d in g a lo g ic of im p e r a tiv e s ( s e e e s p e c ia lly p . 115-125). 158 tw o s o u r c e s of th e b inding e le m e n t of a le g a l o b lig a tio n a r e the a u th o rity of th e la w g iv e r and the co n ten t of the law . S a n c tio n s a c c o m p an y a n a c tio n but do not c o n stitu te the s o u r c e of th e o b lig a to ry c h a r a c t e r of an a ctio n . K ant h eld th a t th e m o r a l w o rth ( m o ra lly o b lig a to ry c h a r a c t e r ) of a n a c tio n is not d e te rm in e d by the r e w a r d s o r p u n ish m e n ts w hich m a y a c c o m p a n y the a c tio n . In g e n e ra l, a ll d e o n to lo g ic a l th e o r ie s and a ll m o r a l th e o r ie s w hich s t r e s s the im p o rta n c e of p e r s o n a l in te n tio n m a in ta in the p o sitio n th at sa n c tio n s do not d e s tr o y the au to n o m y of m o r a lity . T h e p r e s e r v a tio n of m o r a l autonom y, h o w e v er, d o es not a u to m a tic a lly fo r c e s a n c tio n s in to the r o le of a c c id e n ta l e x p ed ien ts to a c tio n . T he c o n ce p tio n of an o r d e r e d u n iv e r s e m ay c a r r y w ith it an in h e r e n t notion of r e w a r d and p u n ish m e n t. E tie n n e G ilso n s ta te s th a t "W hen b o d ies a re in o r d e r , good follow s n e c e s s a r il y from any a c tiv ity th at is in c o n fo rm ity w ith n a tu r a l law " ( C h r i s t ia n P h ilo so p h y of St. T h o m a s Aquin a s , p. 209 ) . T he T h o m is tic v iew of sa n c tio n ( a s in te r p r e te d by G ilso n ) finds nothing m o re in a sa n c tio n th an s t r i c t o b s e rv a n c e of th e law , a r e a liz a tio n of a p e rf e c t b a la n c e b e tw e e n a c ts and th e ir c o n s e q u e n c e s . T hus it is p o s s ib le to hold th a t s a n c tio n s , alth o u g h they do not d e te r m in e the o b lig a to ry c h a r a c t e r of an a ctio n , a lw ay s a c c o m p a n y an a ctio n . On a s t r i c t l y m o r a l lev el, we m ig h t s a y th a t an a c tio n is not good b e c a u s e it w ill be re w a rd e d , but 159 it w ill be r e w a r d e d b e c a u s e it is good. T he t e r m s 're w a rd * and 'g o o d ' m a y s t i ll be s u b je c t to v a ry in g in te r p r e ta tio n s . One of th e d e fin itio n s of o b lig a tio n given in the m o d al s y s te m s p ro p o s e d by A n d e rso n and P r i o r w as O ( p ) = •xp -•-> # , i . e . , 'p is o b lig a to ry 1 is by d efin itio n sy n o n y m o u s w ith 'if p is o m itte d th en a bad s t a te - o f - a f f a i r s m u s t o c c u r . 1 O u r view of the r o le of s a n c tio n s w ill p e r m i t the follow ing s ta te m e n t; 'i f p is o b lig a to ry , th en , if p is o m itte d , a bad s ta te - o f - a f f a i r s w ill o c c u r. 1 But th e sy n o n y m ity of th e A n d e r s o n - P r i o r d efin itio n cannot be allo w ed if we w ish to m a in tain th a t sa n c tio n s do not d e te rm in e th e o b lig a to ry c h a r a c t e r of an a c t. T he re la tio n s h ip b etw een th e o b lig a to ry c h a r a c t e r of an a c tio n and the s a n c tio n s w hich a c c o m p a n y th a t a c tio n is b e tte r e x p r e s s e d as one of s t r i c t im p lic a tio n , e . g . , O ( p ) -L> ( - — p-1 ^ #) . T he A n d e rs o n - P r i o r d efin itio n of p e r m itte d a c ts m ay a ls o be c o n s id e r e d a s in a d e q u ate fo r r e a s o n s s i m il a r to th o se bro u g h t a g a in s t th e ir d efinition of o b lig a to ry a c ts . W hile we would w ish to m a in ta in th at, if an a c t is p e rm itte d , th en it is p o s s ib le fo r th a t a c t to o c c u r w ithout a bad s t a t e - o f - a f f a i r s o c c u rrin g , we would not hold th a t the p o s s ib ility of avo iding a bad s t a te - o f - a f f a i r s d e te r m in e s the a c t to be p e r m is s ib le . A n d e r s o n 's d efin itio n P ( p ) = M ( p&~# ) d o es not e x p r e s s th is r e l a ti o n sh ip b etw een the s a n c tio n and the c o n ce p t of p e r m is s io n c o r r e c tly . T he r e la tio n s h ip is b e tte r e x p r e s s e d a s one of s t r i c t im p lic a tio n , 160 e .g ., P ( p ) - L> M ( p & - # ) . C o n sid e ra tio n of the ro le of sa n ctio n s in m a tte r s of obligation, com b ined with our c h a ra c te riz a tio n of the binding e le m e n t of an o b ligation, lead s us to a s s e r t that von W rig h t's f ir s t in sig h t with r e s p e c t to the re la tio n sh ip betw een the deontic and the a le th ic m o d a litie s was 15 fund am en tally c o r r e c t. Although the two types of m odality a r e analogous, and we m ay e x p re s s c e rta in re la tio n s h ip s betw een o b lig a tion and p o ssib ility , and p e rm is s io n and p o ssib ility , we can n e v er s tr ic tly define obligation o r p e rm is s io n in te r m s of p o ssib ility . The n e c e s s ity which an obligation im p o se s is n e ith e r a c a u sa l n o r a lo g ical n e c e ssity ; but the p o ssib ility of p e rfo rm in g an o b lig ato ry a c t is m o re than a log ical p o ssib ility . A n d e rso n 's a tte m p t to red u ce deontic logic to aleth ic m odal logic fa ils to account fo r the s p e c ia l n a tu re of the binding e le m e n t of obligation; P r i o r 's proof (based on A n d e rso n 's definitions ) fo r the K antian fo rm u la , ought im p lie s can, co n fu ses lo g ical with p h y sic al p o ssib ility ; and, finally, the b a sic A n d e r s o n - P r io r definitions re fle c t a m isco n cep tio n of the ro le of san ctio n s in m a tte r s of obligation. ^ In "D eontic L o g ic ,1 1 Mind, 60:1-15, 1951, von W right pointed out s im ila r itie s betw een th e deontic and the a le th ic m o d alities but the d ifferen c e s which he a ls o pointed out w ere sig n ific a n t enough to w a rra n t h is co n clu sio n th at deontic logic is independent of a le th ic m odal logic. 161 S a n c tio n s a r e not to be c o n fu sed w ith c ir c u m s t a n c e s . W h erea s s a n c tio n s do not d e s tr o y the au tono m y of an o b lig atio n , th e c i r c u m s ta n c e s in w hich a p a r t i c u l a r a c tio n is to ta k e p la c e m u s t be given c o n s id e ra tio n . H um an a c tio n s a r e not p e r f o r m e d in c o m p le te iso la tio n ; th ey ta k e p la c e in w hat is s o m e tim e s an e x tr e m e ly c o m p lic a te d c o n te x t. In s o fa r a s we a r e s a id to r e a s o n p ra c tic a lly , we c o n c e rn o u r s e lv e s w ith the im m e d ia te c ir c u m s ta n c e s of a p r o p o s e d a c tio n K ant is s o m e tim e s in te r p r e te d as hav in g h e ld th a t c ir c u m s ta n c e s a r e not re le v a n t to th e o b lig a to ry n a tu re of a p a r tic u la r a c tio n . T he c a te g o r i cal im p e r a tiv e s s ta te s : "A ct only on th a t m a x im w h e reb y thou c a n s t a t the s a m e tim e w ill th a t it sh o u ld b e c o m e a u n iv e r s a l law " ( G ru ndlegun g, p. 47 ) . B ut nothin g r e q u ir e s th a t th is fo r m u la be in te r p r e te d a s ig n o rin g the ro le of c ir c u m s ta n c e s . T hat o u r m a x im s of a c tio n should be u n iv e r s a liz a b le m a y be in te r p r e te d to m ea n th a t o u r m a x im sh o u ld hold as a d e te rm in in g p rin c ip le fo r the condu ct of 16 a ll m e n w h e n ev e r th ey fa c e an an alo g o u s s e t of c ir c u m s ta n c e s . W h eth er o r not K ant a ttrib u te d a s ig n ific a n t ro le to th e c ir c u m s ta n c e s s u rro u n d in g h u m an a c tio n s, we m u s t re c o g n iz e th a t c ir c u m s ta n c e s a r e re le v a n t to d e lib e ra tio n s about the o b lig a to rin e s s of a p a r t i c u l a r a c t. ^ T h is in te r p r e ta tio n w as d is c u s s e d in C h a p te r III in c o n n e ctio n w ith R e s c h e r 's a x io m s y s te m fo r d e o n tic lo g ic. 162 St. T h o m a s h e ld th at alth o u g h c ir c u m s ta n c e s of h u m a n a c ts a r e a c c id e n ts of th e s e a c ts , th ey m u st, n e v e r th e le s s , e n te r in to th e c o n s id e ra tio n s of the theo lo g ian , the m o r a lis t, th e p o litic ia n , and th e r h e to r ic ia n . He s ta te s th a t "th e finding o r the n e g le c t of the golden m e a n of v irtu e in h u m an a c ts and p a s s io n s i s a q u e stio n of c ir c u m s ta n c e s , " and th a t "it is by c ir c u m s ta n c e s th a t a c ts a r e r e n d e r e d p r a is e w o r th y o r b la m e w o rth y , e x c u sa b le o r c r im in a l. In th e p r a c tic a l s y llo g is m a c tu a l c ir c u m s ta n c e s a r e ta k e n into a c count by the m in o r p r e m is e . T h is can be d e m o n s tra te d by c o n s id e r ing an e x a m p le . I ought to obey the le g itim a te c o m m a n d s of m y s u p e r io r o ffic e r. T h is c o m m a n d is a le g itim a te c o m m a n d of m y s u p e r io r o ffic e r. I ought to obey th is c o m m a n d . V e rific a tio n of the m in o r p r e m i s e in v o lv e s an e m p ir ic a l in v e s tig a tio n of the c ir c u m s ta n c e s s u rro u n d in g 'th is c o m m a n d ' in o r d e r to d e te r m ine w h e th e r it w as in fa c t is s u e d by m y s u p e r i o r o ffic e r, and w h e th er it s a tis f ie s the a p p ro p r ia te c r i t e r i a fo r le g itim a te c o m m a n d s . Von W rig h t’s S y ste m II and R e s c h e r 's a x io m s y s te m a ls o p ro v id e fo r the r o le of c ir c u m s ta n c e s . 0 ( p / c ) s a y s th a t p is o b lig a to ry in c ir c u m s ta n c e s c . A p p licatio n of th is p rin c ip le to a p a r tic u la r a c t of a p a r t i c u l a r ag en t in v o lv es e m p ir ic a lly v e rify in g 17 S u m m a T h eo lo g ic a , I-II, 7 , 1 and 2 . 163 th a t the c ir c u m s ta n c e s c a c tu a lly do p re v a il. Von W right w as led to develop th is s y s te m of co n d itio n al o b lig atio n b e c a u se of th e a p p a re n t fa ilu re of h is " a b s o lu te " s y s te m to acco u n t fo r the notion of co m m it* m e n t o r d e riv e d o blig atio n . It is ev id en t th at the notions of " a b s o lu te " o b lig atio n and "co n d itio n al" o b lig atio n a re in n eed of c la rific a tio n b e fo re p r o p e r a p p r a is a l can be m ad e of th o se s y s te m s w hich a r e in ten d e d to p ro v id e the lo g ic a l s t r u c tu r e of th e s e n o tions. An a b so lu te o bligation is an oblig atio n th a t holds fo r a ll m en in e v e ry p o ss ib le s e t of c ir c u m s ta n c e s . In a tte m p tin g to give an a p p ro p ria te in te rp r e ta tio n to a s y s te m which e s ta b lis h e s lo g ical r e l a tio n sh ip s betw een ab so lu te o b lig atio n s, we a sk th e n a tu ra l q u estio n , " A re th e r e any su c h o b lig a tio n s ? " O ur a n s w e r is, y e s; but we m u st qualify o u r a n sw e r with what m ay se e m to so m e to be a r a d ic a l a s s u m p tio n - - th e r e is only one ab so lu te obligation, n am ely: One alw ays ought to do good and avoid e v il. Good a c tio n s, ho w ev er, m ay be v a rio u s ly in te r p r e te d as a ctio n s which a re in a c c o rd a n c e w ith re a s o n , a ctio n s w hich a r e in a c c o rd a n c e with the c a te g o ric a l im p e ra tiv e , a ctio n s w hich p ro d u ce the g r e a te s t h a p p in e ss fo r the g r e a t e s t n u m b e r, e tc . A p p licatio n of the one a b so lu te o b lig atio n to a group of a ctio n s o r to any one a ctio n in v o lv e s, th e re fo re , th e a c c e p ta n c e of a d efinition fo r the t e r m 'g o o d .' T he a b so lu te c h a r a c te r of the o b lig atio n to do good is th en b a s e d upon the fa c t th at th is o b lig atio n holds fo r a ll i n t e r p r e 164 ta tio n s of 'g o o d 1 a n d in a ll p o s s ib le c ir c u m s ta n c e s . W ith r e s p e c t to von W rig h t's " a c t- ty p e s " o r " a c t - p r o p e r t i e s " we can not s a y th a t we have an a b so lu te o b lig a tio n in the s e n s e in w hich we have defined 'a b s o lu te . ' O b lig atio n s w ith r e s p e c t to a c t-ty p e s lik e the o b lig a tio n to k eep p r o m is e s , to a v o id k illin g , s te a lin g , e tc . , a r e not a b so lu te o b lig a tio n s in th e s e n s e in w hich the o b lig a tio n to do good is a b s o lu te . C ir c u m s ta n c e s m u s t be ta k e n into c o n s id e ra tio n in d e lib e ra tin g abo ut e v e r y o b lig atio n to a c t; only th e o b lig a tio n to do good applies to a ll a c tio n s in g e n e ra l, i.e. , to a c ts as a c ts no m a t t e r what the c ir c u m s ta n c e s of th e a c ts . T h e r e a r e o b lig a tio n s w hich hold fo r g e n e r a l a c t- ty p e s , i, e. , fo r a c ts w hich a r e c h a r a c t e r i z e d by c e r ta in g e n e r a l c ir c u m s ta n c e s . F o r th is c la s s of o b lig a tio n s we s h a ll u se the t e r m 'u n iv e r s a l o b lig a tio n. 1 A u n iv e r s a l o b lig a tio n m a y th en be s a id to hold fo r a ll m en in an alo g o u s c ir c u m s ta n c e s , but not in e v e ry p o s s ib le c ir c u m s ta n c e . E v e r y s ta te m e n t of a u n iv e r s a l o b lig atio n e ith e r im p lic itly o r e x p lic itly s tip u la te s the g e n e r a l c ir c u m s ta n c e s w hich a r e in v o lv ed in the o b lig a to ry o r fo rb id d e n a c tio n . T he u n iv e r s a l o b lig a tio n to keep p r o m is e s c o n ta in s im p lic itly a re f e r e n c e to c ir c u m s ta n c e s , n a m e ly , th o s e c ir c u m s ta n c e s w hich d e te r m in e an a c t to be an a c t of p r o m is e - k eepin g. S im ila rly , th e s ta te m e n t th at s te a lin g is fo rb id d e n im p lic itly co n ta in s a r e f e r e n c e to th e c ir c u m s ta n c e s w hich d e te rm in e an act to 165 be an a c t of th eft. T he u n iv e r s a l o b lig a tio n to obey th e law s of th e S tate im p lic itly c o n ta in s a r e f e r e n c e to th e c ir c u m s ta n c e s w hich d e te r m in e a law to be binding, the a u th o rity of th e la w -g iv e r, e tc . A p p lic a tio n of a u n iv e r s a l o b lig a tio n to a p a r t i c u l a r a c t in v o lv e s an e x a m in a tio n of the c ir c u m s ta n c e s s u rro u n d in g th a t p a r t i c u l a r a c t in o r d e r to d e te rm in e if th e s e c ir c u m s ta n c e s fit th e p r e s c r ip tio n s of the u n iv e r s a l o b lig atio n . We s h a ll c a ll an o b lig a tio n to p e r f o r m a p a r t i c u l a r a c t a n in d iv id u al o b lig a tio n . A se n te n c e e x p r e s s in g an in d iv id u al o b lig a tio n is of the type: 'I ought to k eep th is ( p a r t i c u l a r ) p r o m i s e . 1 T he re la tio n s h ip s b e tw e en a b s o lu te , u n iv e r s a l, and in d iv id u al o b lig a tio n s a r e d e m o n s t r a t e d by th e follow ing s e t s of in f e re n c e s : (1) One ought to do good and a v o id e v il. (A b s o lu te o b lig a tio n ) K eep in g o n e 's p r o m is e s is a good and not an e v il a c t. One ought to k e ep o n e 's p r o m is e s . ( U n iv e rs a l o b lig a tio n ) (2) One ( All m e n ) ought to keep o n e 's ( th eir) p r o m is e s . ( U n iv e rs a l o b lig a tio n ) I a m a m an . I ought to keep m y p r o m is e s . ( U n iv e rs a l o b lig a tio n ) (3) I ought to k e e p m y p r o m is e s . ( U n iv e r s a l o b lig a tio n ) T h is is one of m y p r o m is e s . I ought to k e ep th is p r o m is e . (In d iv id u a l o b lig a tio n ) V e rific a tio n of the m in o r p r e m is e of (1) in v o lv e s a c c e p ta n c e of a d efin itio n of 'g o o d ' and a s c e r ta in in g th a t a c ts of p r o m is e - k e e p in g fa ll w ithin th e sc o p e of th a t d e fin itio n . T he s p e c ific c h a r a c t e r i s t i c s 166 of o b lig a tio n a r e not in v o lv e d in (2) but th e c o n tr a s t b e tw e e n (2) and (3) sh o u ld c le a r l y d e m o n s tr a te th a t 'in d iv id u a l o b lig a tio n ' r e f e r s to a p a r t i c u l a r a c t of a p a r t i c u l a r a g e n t, w hile a p a r t i c u l a r a g e n t m a y s t i l l be p r o p e r l y s a id to h av e u n iv e r s a l o b lig a tio n s . O u r th r e e f o ld d iv is io n of o b lig a tio n s e n te n c e s r e s t r i c t s the p o s s ib ilitie s f o r lo g ic a l s c h e m a ta to tw o g e n e r a l a p p r o a c h e s ; (a) th e " v e r t i c a l " r e la tio n s h ip s b e tw e e n a b s o lu te and u n iv e r s a l o b lig a tio n , and b e tw e e n u n iv e r s a l and in d iv id u a l o b lig a tio n , m a y be s c h e m a tiz e d ( a s a b o v e ) in a m a n n e r c o m p le te ly a n a lo g o u s to o r d in a r y s u b s u m p tio n u n d e r a g e n e r a l p rin c ip le ; (b) th e only " h o r iz o n ta l" lo g ic a l r e l a tio n s h ip s p e r tin e n t to a lo g ic of o b lig a tio n a r e th o s e r e la tio n s h ip s w hich o b ta in b e tw e e n u n iv e r s a l o b lig a tio n s e n te n c e s . T h e o b s e r v a tio n s we h a v e m ad e c o n c e rn in g th e c o n ce p t of o b lig a tio n m a y be b rie f ly s u m m a r i z e d a s fo llo w s; (1) e v e r y s e n te n c e w hich e x p r e s s e s an o b lig a tio n m u s t s a y of an a c tio n th a t it ought ( o r ought n o t) to be done by a h u m a n a g en t; (2) th e b inding e le m e n t of an o b lig a tio n is a kind of n e c e s s ity but is n e ith e r a lo g ic a l n o r a c a u s a l n e c e s s ity ; (3) it m u s t be in th e p o w e r of the a g e n t to p e r f o r m (and h e n c e to o m it) th e o b lig a to ry a c tio n ; (4) th e lo g ic a l s t r u c t u r e of o b lig a tio n s e n te n c e s is a s s u m e d to be th e s a m e fo r a ll ty p e s of o b lig a tio n ( i . e . , for le g a l, m o r a l, .... o b lig a tio n ) ; (5) s a n c tio n s a r e e s s e n tia lly r e la te d to, but do not d e te r m in e , o b lig a tio n ; (6) the 167 r o le of c ir c u m s ta n c e s p ro v id e s a u se fu l c la s s if ic a tio n of o b lig a tio n s a s a b so lu te , u n iv e rs a l, o r in d iv id u a l; (7) fin ally , th is th re e fo ld c la s s if ic a tio n of o b lig a tio n sh ould av o id m a n y of th e d iffic u ltie s e n c o u n te re d in th o se d eo n tic s y s te m s w hich co n fu se a b so lu te w ith u n i v e r s a l o b lig a tio n and u n iv e r s a l w ith in d iv id u a l o b lig atio n . T h e a s p e c ts of the c o n c e p t of o b lig a tio n w hich we have po in ted out p ro v id e us with a s e t of c r i t e r i a to guide the s e le c tio n of a s e n te n tia l f o r m a p p r o p r i a te fo r e x p r e s s io n s of o b lig a tio n . W ith th e s e c r i t e r i a in m in d we m u s t now d ecid e w h e th e r o b lig a tio n s e n te n c e s a r e m o re p r o p e r ly r e n d e r e d a s n o rm a tiv e s o r a s im p e r a tiv e s , and c o n s id e ra tio n m u st be given to the r e la tio n s h ip of e ach p o ss ib le fo rm u la tio n to the o r d i n a r y in d ic a tiv e m ood. 2. O b lig atio n S en ten ce s a s N o rm a tiv e s W e b ste r d efin es n o rm a tiv e a s " R e la tin g to, o r e s ta b lis h in g a n o rm , " and a n o r m a s "A R ule o r a u th o rita tiv e s ta n d a rd ; m odel; 18 ty p e; p a t t e r n ." A n o rm a tiv e se n te n c e w ould be one w hich e s t a b lis h e s a ru le o r a u th o rita tiv e s ta n d a r d . If we a d m it the p o s s ib ility of e x p r e s s in g any ru le o r s ta n d a r d in a se n te n c e w hich c o n ta in s I Q W e b s te r’s New In te rn a tio n a l D ic tio n a ry of th e E n g lish L an g u ag e { S p rin g field , M ass., 1933), s.v . 168 ’o u g h t1 a s an a u x ilia ry v e rb , we can sa y , in a g re e m e n t w ith E v e r e tt W. H all, th a t n o rm a tiv e s e n te n c e s a r e " s e n te n c e s c o n ta in in g 'o u g h t' a s an a u x ilia ry v e rb . T h is c h a r a c te r iz a tio n of n o rm a tiv e s e n te n c e s p e r m its us to conclud e im m e d ia te ly th a t o b lig a tio n s e n te n c e s a r e p r o p e r ly r e n d e r e d a s n o r m a tiv e s . It is obviou s, h o w e v er, th at not a ll n o rm a tiv e s a r e o b lig atio n s e n te n c e s . S e n te n c e s like 'A c o rn s ought to g ro w into o a k s' and 'T h e t r a i n ought to be h e re any m in u te , ' do not r e f e r to p o s s ib le h u m an a c tio n s and h e n ce cannot be o b lig a tio n s e n te n c e s . T hey do fu lfill H a ll's r e q u ir e m e n t f o r n o r m a tive s e n te n c e s , h o w e v e r. T h ey " s ta te th a t so m e fa c t ought to be ( o r to have been)" ( W hat is V alu e? p. 155) . H all e x c lu d e s m e r e ly c a u s a l s e n te n c e s from the c la s s of n o rm a tiv e s e n te n c e s , i . e . , he s u g g e s ts th a t so m e 'o u g h t- s e n te n c e s ' a r e not n o rm a tiv e . T h is a c c o rd s with o u r o b s e rv a tio n th a t the n e c e s s ity in v o lv ed in an o b lig a tio n s e n te n c e is not a c a u s a l n e c e s s ity . H a ll's r e a s o n fo r e x clu d in g c a u s a l u s e s of 'o u g h t' is th a t th ey give a n e c e s s a r y c o n d itio n fo r th e o c c u r r e n c e of a s t a te - o f - a f f a i r s , but th ey do not r e a lly s a y of a s ta te - o f - a f f a i r s th a t it ought to o c c u r . T hus we m ight r e n d e r the s e n te n c e , 'In o r d e r fo r the engin e to ru n , it is n e c e s s a r y th a t the sw itc h be tu rn e d on, ' a s rIn o r d e r f o r the en g in e to ru n , th e sw itc h ^ E v e r e tt W. H all, W hat is Value ? ( New Y o rk 1952 ), p. 154. 169 ought to be tu rn e d o n . ' T h is c a u s a l u se of 'ought* is m o r e c o r r e c tly view ed a s d e s c rip tiv e r a t h e r th an n o rm a tiv e . T he r e la tio n s h ip b e tw ee n o b lig a tio n s e n te n c e s and n o rm a tiv e s w hich we hav e e s ta b lis h e d m a y be s ta te d in the follow ing way: a ll o b lig atio n s e n te n c e s a r e p r o p e r ly e x p r e s s e d a s n o r m a tiv e s , but not a ll n o rm a tiv e s e n te n c e s e x p r e s s o b lig a tio n s ( i . e . , not a ll n o r m a tiv e s a r e o b lig a tio n s e n te n c e s ) . A f u r th e r r e le v a n t o b s e rv a tio n is th a t not a ll s e n te n c e s co n tain in g 'o u g h t' as an a u x ilia r y v e r b a re n o rm a tiv e s , although a ll n o rm a tiv e s co n ta in ( a t le a s t im p lic itly ) 'o u g h t' a s an a u x ilia r y v e rb . It follo w s a ls o th a t not a ll "oug ht - s e n te n c e s " a r e o b lig a tio n s e n te n c e s , ev en though a ll o b lig a tio n se n te n c e s a r e o u g h t-s e n te n c e s . If th e r e is a lo g ic al s c h e m a tis m a p p r o p r ia te fo r n o rm a tiv e s ( if th e r e is a lo g ic of n o rm a tiv e s ), th en the logic of o b lig atio n s e n te n c e s w ill o c c u r w ithin the sc o p e of th at lo g ic. T h is p la c e s a r e s t r i c ti o n upon a logic of n o rm a tiv e s w hich sh o u ld not p a s s unnoticed: lo g ic a l re la tio n s h ip s w hich hold f o r all n o rm a tiv e s m u st hold fo r o b lig atio n s e n te n c e s , but not a ll lo g ical r e la tio n s h ip s b etw een n o r m a tiv e s w hich a r e o b lig a tio n s e n te n c e s need hold f o r a ll n o rm a tiv e s . T h u s, w ithin a n o rm a tiv e lo g ic, it is p o s sib le to add a x io m s w hich hold fo r o b lig a tio n s e n te n c e s but do not n e c e s s a r il y hold fo r o th e r n o rm a tiv e s . A ll f u r th e r d is c u s s io n of n o rm a tiv e s in th is c h a p te r is in - 170 ten d e d to re la te only to th o se n o rm a tiv e s w hich e x p re s s o b lig atio n s, i . e . , w hich s e r v e a s o bligation s e n te n c e s . It is not an e a s y ta s k to d is c e r n the p r e c is e re la tio n s h ip b e tw een n o rm a tiv e and in d ic ativ e s e n te n c e s . N o rm a tiv e s e n te n c e s a r e s a id to be p r e s c r ip tiv e in th a t they p r e s c r ib e what ought to be done. In d icativ e s e n te n c e s a r e s a id to be d e s c rip tiv e in th at they d e s c rib e a fa c tu a l s ta te of a ffa irs ( w hat is b ein g done ) . Stephen C. P e p p e r s u g g e s ts that the d istin c tio n b etw een ’p r e s c r ip tio n 1 and 'd e s c rip tio n ' is not the s a m e as the d istin c tio n betw een 'o u g h t' and 'i s ' : The o pposition of 'p r e s c r ip tio n ' to 'd e s c r ip tio n ' is not p a ra lle l with th a t of 'o u g h t' to ' i s . ' Both p r e s c r ip tio n s and d e s c rip tio n s a re v e rb a l e x p re s s io n s . What the 'o u g h t1 is we do not y et know, but the 'i s ' r e f e r s to fac t and is n e ith e r tru e n o r fa ls e . Now, u n le ss an 'o u g h t' is s p ir ite d off into so m e n o n factu al re a lm , it is difficult to se e how it can ev en be r e f e r r e d to u n le s s it is a fa c t of som e k in d --s o m e s o r t of being, som e s o r t of ' i s . ' . . . any p a r tic u la r p re s c r ip tio n o r d e s c r i p tion is a fact, and its o c c u rre n c e an 'i s . ' So, in an u ltim a te se n s e , ev ery th in g , includ ing p r e s c r ip tio n s and w h a tev e r an 'o u ght' m ay be, is an 'i s . ' If th e re a re any o c c u rr e n c e s of 'o u g h ts' they would s u r e ly be so m e c la s s o r s e le c tio n of 'i s 's . ' E v e ry 'i s ' is not an 'ought, ' but e v e ry 'o u g h t' is an 'i s ' o r nothing. The d ifferen c e b etw een p r e s c r ip tio n s and d e s c rip tio n s is not the d if fe re n c e b etw een nonfact and fac t but betw een the r e f e r e n c e s of the two ty p es of s e n te n c e s . P e p p e r sa y s of the r e f e r e n c e s of a p r e s c r ip tio n ^ Stephen C. P e p p e r, The S o u rc e s of V alue ( B e rk e le y , 1958^ p. 704 ( note 3 to C h a p te r 1 ) . 171 and a d e s c rip tio n that: The f i r s t h as an obed ien ce re f e r e n c e which m ay be s a tis f ie d o r f r u s tr a te d ; the se co n d h as a r e f e r e n c e to fa c t w hich m ay be tru e o r fa ls e . T h ese a r e d iffe re n t kinds of r e f e r e n c e s . A p r e s c rip tio n is thus c le a r ly so m e th in g th a t cannot be r e g a r d e d as a kind of d e s c rip tio n o r lin g u istic a lly re d u c e d to one. B ut p r e s c r i p tio n s can be d e s c rib e d like any o th e r o c c u r r e n c e s . And the re la tio n s of p r e s c r ip tio n to o th e r fa c ts can be d e s c rib e d . ( The S o u rc e s of V alue, p. 704) T he su g g e stio n th at n o rm a tiv e s , as p r e s c r ip tio n s , have an obedience r e f e r e n c e which m ay be s a tis fie d o r f r u s tr a te d is s i m il a r to the H o fsta d te r an d M cK insey su g g e stio n d is c u s s e d in C h a p te r I I . H o fsta d te r and M cK insey had p ro p o se d s a tis fa c tio n and n o n s a tis fa c tion as s e m a n tic a l v a lu e s fo r p r e s c r ip tio n s ( a s im p e ra tiv e s ) . H o fs ta d te r and M cK insey, h ow ever, had re d u c e d p r e s c r ip tio n s to 21 d e s c rip tio n s , an o p e ra tio n w hich P e p p e r w ill not allow and w hich, as we have a lre a d y se en , le a d s to m any u n accep tab le r e s u lts in the sa tis fa c tio n -fu n c tio n in te rp r e ta tio n of im p e ra tiv e logic. A lf R o ss m en tio n ed n o rm a tiv e s a s o c c u r rin g in the " lin g u is tic a lly in d ic ativ e m ood, " but b e c a u se n o rm a tiv e s co n tain an im m e d i ate d em and fo r a ctio n (a c c o rd in g to th e ir m e a n in g ) and co n tain no 21 P a r t of the b a sic th e o re m of the H o fsta d te r-M c K in se y s y s te m of im p e ra tiv e logic s ta te d that: " if is any im p e ra tiv e of L anguage Ic , th en th e r e e x is ts a se n te n c e Sj , of L anguage I , su ch th a t C j = !S i is p ro v ab le in L anguage I " (" O n the L ogic of I m p e ra tiv e s , " P h ilo so p h y of S cience, 6 :4 5 2 ). 172 ( e p is te m o lo g ic a l) d e s c rip tio n of fa c t, th e ir lo g ic a l r e la tio n s w e re su p p o se d (b y R o s s ) to be the s a m e a s th o se p r e s c r ip tio n s which o c c u r in th e lin g u istic a lly im p e r a tiv e m ood. 22 E v e r e tt W. H all g iv es th e follow ing a s an ex am p le of a n o rm a tiv e se n te n c e : 'T h e rig h t th in g to do is to keep y o u r p r o m is e 1 { W hat is V alue? p. 155 ) . T h is e x a m p le of H a ll's points up th e fa c t th a t n o rm a tiv e s o c c u r in the lin g u is tic a lly in d ic a tiv e m ood, a s R o ss had su g g e ste d , R o s s 's c o n clu sio n , h o w ev er, th at, sin c e n o rm a tiv e s a r e p r e s c r ip tio n s a c c o rd in g to th e ir m ean in g , they m u st re c e iv e the sa m e lo g ic a l t r e a t m e n t a s im p e r a tiv e s , is not th e only p o s s ib le ( n o r the b e s t ) c o n c lu s io n th a t can be d raw n . T he b e h a v io r of 'it is y o u r duty to, ' 'th e r ig h t thing to do, ' 'it is o b lig a to ry th a t, 1 and 'o n e ought to ' s e e m s c lo s e ly an alo g o u s to th a t of 'i t is n e c e s s a r y th at, ' and 'i t is p o ss ib le th at. 1 T h u s, an o b lig a tio n s e n te n c e e x p re s s e d a s a n o rm a tiv e m ay be c o n s id e re d a m o d al se n te n c e , ju s t as a s e n te n c e beg in n in g 'i t is n e c e s s a r y th a t' is c o n s id e re d a m o d al s e n te n c e . B oth ty p es of s e n te n c e s a re lin g u is tic a lly in d ic a tiv e but d em and s p e c ia l m o d al lo g ic s to a cc o u n t f o r th e ir d iffe re n c e s in m e a n in g fro m o th e r ( o r d i n a r y ) in d ic a tiv e s e n te n c e s . The r e f e r e n t of a n o rm a tiv e se n te n c e s t i l l r e m a in s in q u e s - A lf R o ss, " im p e r a tiv e s and L ogic, " P h ilo so p h y of S cien ce, 11:31-32. 173 tion, a s do th e a p p ro p ria te s e m a n tic a l v alu e t e r m s . H all s u g g e s ts th a t a n o rm a tiv e r e f e r s to (o b je c tiv e ) v a lu e in m u ch th e s a m e w ay as a d e s c r ip tiv e s e n te n c e r e f e r s to fa c t. He s u g g e s ts ’le g itim a te ' a s the s e m a n tic a l valu e t e r m f o r n o rm a tiv e s , c o rre s p o n d in g to 't r u e ' as the v alu e t e r m f o r d e s c rip tiv e in d ic a tiv e s e n te n c e s ( W hat is V a lu e? C h. 6 ) . He co n ten d s th a t a ll v a lu e -s e n te n c e s m ay be fo rm u la te d a s n o r m a tiv e s and h en ce c o n clu d es that: v alu e is th e r e f e r e n t of a le g itim a te v a lu e - s e n te n c e , th a t w hich m a k e s it le g itim a te ( being p a r a lle l to fa c t as the r e f e r e n t of a tr u e d e s c r ip tiv e s e n te n c e , th a t w hich m a k e s it tr u e ) . ( W hat is Value ? p. 189 ) On H a ll's view we can sa y th a t n o rm a tiv e s r e f e r to v a lu e s in a m a n n e r a n alo g o u s to the way in w hich o r d in a ry d e s c r ip tiv e in d ic a tiv e s e n te n c e s d e s c rib e fa c ts . H a ll's value a p p a re n tly belongs to the s a m e c la s s of i s 's th a t P e p p e r 's ought b elo n g s to; but ju s t a s P e p p e r does not know w hat an ought is , so, too, H all h a s not told us what a value is . It is d ifficu lt to conceive of valu e as an o b jectiv e so m e th in g w hich is a t th e s a m e tim e n o n factu al; P e p p e r is q u ite c o r r e c t w hen he s u g g e s ts th a t an ought " is a fa c t of so m e kind" if it is an y th in g a t a ll (T h e S o u rc e s of V alue, p. 704 ). P e p p e r 's su g g e stio n th at p r e s c r i p tio n s h ave an o b ed ien ce r e f e r e n c e m ay be c o r r e c t in a c e r t a i n s e n s e of the w o rd 'r e f e r e n c e , ' but o b e d ie n ce w ill not do a s a p r o p e r r e f e r en t in a s y s te m in ten d ed to give th e lo g ic a l r e la tio n s of p r e s c r ip tiv e 174 s e n te n c e s . W h eth er o r not a p r e s c r ip tio n is o b ey ed h a s no e ffe c t w h a tso e v e r upon th e lo g ic a l s ta tu s of th e p r e s c r ip tio n , i. e. , a p r e s c r ip tio n w hich is n o t ob ey ed c a r r i e s the s a m e lo g ic a l "w e ig h t" a s one w hich is obeyed. F a ilu r e to obey the p r e s c r ip tio n 'I ought to keep th is p r o m is e 1 does not m ak e the p r e s c r ip tio n i n c o r r e c t in any s e n s e , n o r does it a ffe ct the v a lid ity of the lo g ic a l in f e re n c e s by w hich one p ro c e e d s f r o m 'A ll p r o m is e s ought to be k ep t' to 'I ought to keep th is p r o m is e . 1 In the c a s e of o rd in a ry d e s c r ip tiv e in d ic a tiv e se n te n c e s , h o w e v er, the fa ls ity of a se n te n c e does m ake the d e s c r i p tion i n c o r r e c t and does a ffe c t the v a lid ity of any lo g ic a l in fe re n c e in w hich the d e s c rip tiv e s e n te n c e o c c u rs . If, follow ing th e su g g e stio n s of K ant, von W righ t, and o th e r s , we c o n s id e r o b lig atio n s e n te n c e s a s m o d al s e n te n c e s , the p r o b le m of d e te rm in in g the r e f e r e n t of an o b lig atio n se n te n c e b e c o m e s analogou s to the p ro b le m of d e te rm in in g the r e f e r e n t of an a le th ic m o d al s e n te n c e . It is g e n e ra lly re c o g n iz e d th a t m o d a litie s a re not tr u th - fu n c tio n s. P r i o r s u g g e s ts th a t 'i t is tru e th a t p 1 is j u s t one type of th e g e n e r a l f o r m 'it is X th a t p' and fo r 'X ' in th is f o r m we m ay 23 s u b s titu te 'tr u e , 1 'n e c e s s a r y , ' 'p o s s ib le , ' o b lig a to ry , ' e tc . A. N. Prior, F orm al Logic (Oxford, 1955), pp. 2 18-219. 175 24 F r e g e 's d istin c tio n betw een s e n s e and r e f e r e n c e , and C a rn a p 's notions of e x te n sio n and in te n s io n 2® p ro v id e p o ssib le m e a n s of r e latin g the r e f e r e n t of a se n te n c e in a m odal co ntext to the r e f e r e n t of a se n te n c e in an o rd in a ry d e c la ra tiv e co n tex t. F r e g e h e ld th a t the re f e re n c e (n o m in a tu m ) of an o rd in a r y d e c la ra tiv e se n te n c e is its tru th -v a lu e , and th e s e n s e (S in n ) of a se n te n c e is the p ro p o sitio n w hich the se n te n c e s ta te s . In oblique co n tex ts ( in d ir e c t d is c o u rs e , b e lief s e n te n c e s , m odal s e n te n c e s ), w h ere a d e c la ra tiv e se n te n c e o c c u rs a s a dependent c la u s e w ithin a m o d al se n te n c e ( f o r e x a m p le ) , the n o m in atu m of that c la u se is the p ro p o sitio n which it s ta te s . T hus, on F r e g e 's view , the n o m in a tu m of a se n te n c e in an oblique co n tex t is what would be its se n se in an o rd in a ry context. C a r n a p 's t e r m 'e x te n sio n , ' roughly speaking, c o rre s p o n d s to F r e g e 's 'n o m in atu m , ' and his 'in te n sio n ' to F r e g e 's 's e n s e . ' On C a r n a p 's view the e x te n sio n of a se n te n c e is its tru th -v a lu e and the in te n sio n of a se n te n c e is the p ro p o sitio n it s ta te s . M odal s e n te n c e s a r e c o n s id e re d by C a rn ap 2^ G ottlob F r e g e , "U e b e r Sinn und B e d e u tu n g ,1 1 Z e its c h rift fu r P h ilo so p h ic und P h ilo so p h isc h e K ritik , 100:25-50, 1892; E n g lish tra n s la tio n s in H e rb e r t F e ig l and W ilfred S e lla rs , R ead in g s in P h ilo so p h ic a l A n a ly sis (N ew Y ork, 1 9 4 9 ), pp. 85-102; and P e te r G each and M ax B lack ( ed. ), T ra n s la tio n s f ro m th e P h ilo so p h ic a l W ritings of G ottlob F r e g e (O x fo rd , 1 9 5 2 ), pp. 56-78 . 25 Rudolf C arn ap , M eaning and N e c e ss ity , 2nd ed. (C h icag o , 1956) . 176 to be n o n e x te n s io n a l w ith r e s p e c t to t h e i r c o m p o n e n ts . ^ T h u s, f o r C a rn a p th e e x te n s io n ( n o m in a tu m ) of d e c la r a tiv e s e n te n c e p d o e s not c h an g e to its o r d i n a r y in te n s io n ( s e n s e ) w hen p o c c u r s a s a d e p e n d e n t c la u s e in a m o d a l s e n te n c e . The s ig n ific a n t d iffe re n c e b e tw e e n th e o c c u r r e n c e of p in a m o d a l s e n te n c e an d p a s an i n d e p e n d e n t d e c la r a tiv e s e n te n c e is th a t, in a m o d al s e n te n c e , p is no lo n g e r in te r c h a n g e a b le w ith e v e r y o th e r e x p r e s s io n e q u iv a le n t to it. ^ T he n o tio n th a t m o d a l c o n te x ts a r e b a s ic a lly in te n s io n a l and th a t th e m o d a litie s a r e not th e m s e lv e s tr u th - f u n c tio n s p ro v id e s a hint f o r a n a ly s is of th e d e o n tic m o d a litie s . 'It is n e c e s s a r y th a t p f m ay be t r u e o r f a ls e , but the s e n te n c e w hich 'p ' r e p r e s e n t s can n o t be r e p la c e d by e v e r y o th e r e x p r e s s io n w hich is e q u iv a le n t to it. S i m i la r - 26 R oughly a s e n te n c e is s a id to be e x te n s io n a l w ith r e s p e c t to an e x p r e s s io n o c c u r r in g in it, if the e x p r e s s io n is in te rc h a n g e a b le a t th is p la c e w ith e v e r y o th e r e x p r e s s io n e q u iv a le n t to it. F o r a te c h n i c a l d is c u s s io n of h is n o tio n s of e x te n s io n a l, n o n e x te n sio n a l, and in te n s io n a l c o n te x ts , s e e R udolf C a rn a p , M ean in g an d N e c e s s ity , e s p e c i a l - ly pp. 4 6 - 5 2 . 27 F o r a d is c u s s io n of th e d iff e re n c e s b e tw e e n C a r n a p 's m e th o d of s e m a n tic a l a n a ly s is and the m e th o d of th e n a m e r e la tio n a s u tiliz e d by F r e g e , C h u rc h , Q u ine, and R u s s e ll, s e e C h a p te r 3 of M ean in g and N e c e s s ity . C a rn a p d i s c u s s e s th e v a r io u s m e th o d s of a n a ly s is a s they r e l a t e to s o lu tio n s of the a n tin o m y of the n a m e - r e l a t i o n . He p o in ts out the a d v a n ta g e s an d d is a d v a n ta g e s of th e v a rio u s f o r m s of th e m e th o d of the n a m e - r e la tio n , c o n c lu d in g th a t th is m e th o d is not s u ita b le f o r s e m a n tic a l a n a ly s is . H is own m eth o d , in v o lv in g th e n o tio n s of e x te n sio n an d in te n s io n , is s u g g e s te d a s a m o re s u ita b le a p p ro a c h to s e m a n tic a l a n a ly s is . 177 ly, we m ay te n ta tiv e ly s a y th a t 'It is o b lig a to ry th a t p' m ay be tr u e o r fa ls e , but the se n te n c e w hich 'p ' r e p r e s e n ts can n o t be r e p la c e d by e v e ry o th e r e x p re s s io n w hich is eq u iv a le n t to it. In a le th ic m o d al s e n te n c e s , h o w e v er, the m o d al o p e ra to r s fo r n e c e s s ity and p o s s ib ility a re o p e r a to r s fo r lo g ic a l n e c e s s ity and lo g ic a l p o s s ib ility . T hus, follow ing C a rn a p , yre can ad o p t the convention th at 'It is n e c e s s a r y th a t p' is tru e , if and only if the se n te n c e w hich 'p ' r e p r e s e n ts is lo g ic a lly tr u e . No a n alo g o u s co nven tion c an be a d o p ted fo r the d eo n tic m o d a litie s . T he co ntent of p a s it o c c u r s in an o b lig atio n se n te n c e is su c h that the tru th - v a lu e of p can have no e ffe c t upon th e tr u th - v a lu e of 'It is o b lig a to ry th a t p.'^® Since we w ish to s a y th a t, in ad d itio n to havin g a m e a n in g 29 ( s e n s e , in te n s io n ) , o b lig a tio n s e n te n c e s m ay a ls o be tru e o r OQ T he d ep en d en t c la u s e 'p ' of an o b lig a tio n se n te n c e is a l w ays of th e f o rm 'a n a ctio n of type A be d o n e .1 The tr u th - v a lu e of the in d ep en d en t se n te n c e 'A n a c tio n of type A is d o n e 1 can not affe ct the o b lig a to rin e s s of A; w h eth er o r not A is done h a s nothing to do with w h e th er o r not A is o b lig a to ry . H ence, we r e j e c t a ll a tte m p ts to is o la te the d eo n tic e le m e n t f r o m an o b lig a tio n s e n te n c e so th a t the " c o r r e c t n e s s , " " le g itim a c y ," " t r u t h ," e tc . of the whole s e n te n c e is so m e h o w d e te rm in e d by the tru th o r f a ls ity of th e " d e c la r a tiv e " e le m e n t o r " th e m e of d e m a n d ." In th is r e s p e c t o b lig atio n s e n te n c e s a re an alo g o u s to 'I b e lie v e th a t p, ' w h e re, again, the tr u th - v a lu e of the s e n te n c e r e p r e s e n te d by 'p* is ir r e le v a n t to the tr u th - v a lu e of the e n tir e se n te n c e . 29 T he s e n s e of an o b lig a tio n s e n te n c e is th e p ro p o s itio n w hich it s ta te s , n a m e ly , th at a c e r ta in a ctio n ought to tak e p la c e . If we fo l- 178 f a l s e , w e m u s t in d ic a te how th a t t r u t h o r f a l s i t y c a n be d e te r m i n e d . T h e s u b s u m p tio n i n f e r e n c e s w h ic h w e r e s u g g e s t e d in c o n n e c tio n w ith th e v e r t i c a l r e l a t i o n s h i p s a m o n g a b s o lu te , u n i v e r s a l , a n d in d iv id u a l o b lig a tio n s p r o v id e a c lu e to a p o s s ib l e v e r i f i c a t i o n p r o c e d u r e f o r o b lig a tio n s e n t e n c e s . W illia m H. W e r k m e i s t e r , in a n a r t i c l e on " N o r m a t i v e Propositions,"^ s u g g e s ts a s i m i l a r s e t of s u b s u m p tio n i n f e r e n c e s , a lth o u g h h e d o e s n o t r e l a t e th e m a c h in e r y of s u b s u m p tio n i n f e r e n c e s s p e c i f i c a ll y to t r u t h - v a l u e s . T h e fo llo w in g is W e r k m e i s t e r 's s a m p le s c h e m a t i c o u tlin e fo r " ju s tif y in g " a n o r m a t iv e p r o p o s itio n w ith in a g iv e n n o r m a t iv e s y s te m : B a s ic N o rm : O ne ought to do e v e r y th in g a n d o n ly th a t w h ic h is g o o d . B a s ic D e fin itio n : 'G o o d 1 is a n y th in g t h a t c o n tr i b u te s to th e g r e a t e s t h a p p in e s s of th e g r e a t e s t n u m b e r of p e o p le . T h e o r e t i c a l P r o p o s itio n : T o k e e p o n e 's p r o m i s e is good ( in th e s e n s e d e fin e d ) . G e n e r a l N o r m a tiv e P r o p o s itio n : O ne o u g h t to k e ep o n e 's p r o m i s e . lo w e d F r e g e 's a n a l y s i s , o u r s e a r c h f o r a m e th o d o f d e te r m i n i n g th e t r u t h o r f a l s i t y of an o b lig a tio n s e n t e n c e w o u ld be s i m p l i f i e d - - h e s t a t e s t h a t 't o f o r b i d ', 't o c o m m a n d 1, e tc . o c c u r in f r o n t of i m p e r a tiv e c l a u s e s a n d " I m p e r a t i v e s h a v e no n o m in a ta ; th e y h a v e o n ly s e n s e " ( " O n S e n s e a n d N o m in a tu m ," F e i g l a n d S e l l a r s ( e d . ) , H e a d in g s in P h ilo s o p h ic a l A n a ly s is , p. 94 ) . H o w e v e r, we c a n n o t r e d u c e o b lig a tio n s e n t e n c e s to s i m p le i m p e r a t i v e s a n d m u s t t h e r e f o r e sh o w how it is p o s s ib le f o r o b lig a tio n s e n t e n c e s ( a s n o r m a t iv e s ) to b e t r u e o r f a l s e . 30 " N o r m a tiv e P r o p o s it i o n s a n d th e I d e a l of an I n t e g r a t e d a n d C lo s e d S y s te m , " P h ilo s o p h y of S c ie n c e , 1 8 :1 2 5 -1 3 1 , 1951 . 179 S p e c ific N o r m a tiv e P r o p o s i t i o n : I o u g h t to k e e p m y p r o m i s e . ( ^ N o r m a tiv e P r o p o s i t i o n s , M pT . 1 2 9 ) W e r k m e i s t e r s u g g e s t s a n a n a lo g y b e tw e e n th e lo g ic a l s t r u c t u r e of h is p r o p o s e d s y s t e m ( o r a n y n o r m a t iv e s y s t e m ) a n d th e lo g i c a l s t r u c t u r e o f a s y s t e m o f g e o m e tr y . J u s t a s e a c h s y s t e m o f g e o m e t r y c o m p le te ly c h a r a c t e r i z e s its p a r t i c u l a r ty p e o f s p a c e , s o e a c h d e fin itio n of fg o o d ' d e t e r m i n e s a s p e c if ic s e t o f v a lu e - s u b s u m p t io n s . J u s t a s d if f e r e n t g e o m e t r i e s c a n b e d e v e lo p e d by c h a n g in g th e k e y d e fin itio n s a n d p o s t u l a t e s , so , to o , c a n d if f e r e n t s y s t e m s of s u b s u m p tio n u n d e r a n e n d - v a lu e be d e v e lo p e d by v a r y in g th e b a s i c d e fin itio n of g o o d . A p u r e o r t h e o r e t i c a l g e o m e tr y b e c o m e s a p p lic a b le to th e p h y s ic a l w o rld w h en s o m e k e y i d e a is c o n n e c te d w ith a p h y s ic a lly r e a l th in g . A s y s t e m of v a lu e - s u b s u m p t io n s is lik e w is e t h e o r e t i c a l u n til th e s t ip u la tio n is m a d e t h a t p e o p le o u g h t to a c t in a c c o r d a n c e w ith th a t s y s t e m . T h u s (o n W e r k m e i s t e r ’s v ie w ) th e t h e o r e t i c a l p r o p o s i t io n ( ab o v e ) b e c o m e s a p p lie d w hen a c c e p ta n c e of a b a s ic d e fin itio n o f 'g o o d 1 m a k e s th a t t h e o r e t i c a l p r o p o s itio n s u b s u m a b le u n d e r th e b a s i c n o r m . In th is w ay a n o r m a t iv e p r o p o s i t io n is s a i d to be " j u s t if i e d " by a t h e o r e t i c a l p r o p o s itio n , w h ic h s e r v e s a s th e m i n o r p r e m i s e o f th e s y l l o g is m in w h ich it o c c u r s ( t h e m a j o r p r e m i s e is th e b a s ic n o r m a n d th e c o n c lu s io n is th e g e n e r a l n o r m a t iv e p r o p o s itio n ) . 180 If th e b a s i c n o r m i s a s s u m e d to " t r u e " ( c o r r e c t in s o m e s e n s e ) , t h e n w h a t e v e r is v a l i d l y d e r i v a b l e f r o m t h a t n o r m i s a l s o p r o p e r l y r e f e r r e d to a s " t r u e . " In g e o m e t r y , w h e n a t h e o r e m is p r o v e n f r o m th e s e t o f a x i o m s a n d d e f i n i ti o n s , t h e n th e s t a t e m e n t of t h a t t h e o r e m is p r o p e r l y s a i d to b e p r o v a b l e . In a c e r t a i n s e n s e we s p e a k o f p r o v a b l e t h e o r e m s a s b e in g 't r u e in s y s t e m X, ' a s w e i m p l i c i t l y do w h e n w e p r e f a c e c e r t a i n p l a n e g e o m e t r y " t r u t h s " b y th e p h r a s e 'i n a p l a n e . ' T h e l o g i c a l s t r u c t u r e of a n y s y s t e m , h o w e v e r , is n o t a f f e c t e d by th e f a c t th a t w h a t is " t r u e " in t h a t s y s t e m m a y n o t be " t r u e " in a n o t h e r s y s t e m . W ith r e s p e c t to o u r t h r e e f o l d c l a s s i f i c a t i o n of o b l ig a t io n s e n t e n c e s w e c a n d i s t i n g u i s h b e tw e e n t h o s e s e n t e n c e s w h ic h e x p r e s s o b l ig a t io n s w h ic h n e c e s s a r i l y h o ld ( a n a lo g o u s to 'n e c e s s a r y t r u t h ' ) , a n d t h o s e w h ic h a r e c o n tin g e n t. T h e a b s o l u te o b lig a tio n s e n t e n c e i s in s o m e s e n s e n e c e s s a r y , s i n c e it e x p r e s s e s a n o b lig a tio n w h ic h h o ld s in e v e r y p o s s i b l e c i r c u m s t a n c e ( s i m i l a r to L e i b n i z 's 't r u e in a l l p o s s i b l e w o r l d s ' ) . A u n i v e r s a l o b l ig a t io n s e n t e n c e e x p r e s s e s a n o b lig a tio n t h a t h o ld s f o r a l l m e n in a n a lo g o u s c i r c u m s t a n c e s b u t n o t in a l l c i r c u m s t a n c e s . T h e m i n o r p r e m i s e w h ic h e s t a b l i s h e s a u n i v e r s a l o b lig a tio n s e n t e n c e d o e s n o t r e f e r to e x t r a - l i n g u i s t i c f a c t s , h o w e v e r , b u t to th e d e f i n i ti o n s o f th e a c t - t y p e o r a c t - p r o p e r t y in q u e s t io n . A u n i v e r s a l o b l ig a t io n s e n t e n c e th e n , i s " t r u e " b y v i r t u e o f t h e d e f i n i ti o n s a n d th e r u l e s of s y l l o g i s m ( s u b 181 s u m p tio n ) , hence a u n iv e rs a l o b lig atio n se n te n c e is a ls o n e c e s s a r y in th e s e n s e analogous to the n e c e s s ity of 'lo g ic a l t r u t h . ' Individual o b lig atio n s e n te n c e s a re e s ta b lis h e d by a m in o r p r e m is e which is fa c tu a lly tr u e , i . e . , the m in o r p r e m is e of a s y llo g is m w hose c o n c lu sio n is an ind ividual o bligation se n te n c e is a s ta te m e n t about the fa c tu a l c ir c u m s ta n c e s su rro u n d in g a p a r tic u la r a ct. Individual o b lig a tio n s e n te n c e s , th e r e f o re , a r e s a id to be p a r tic u la r o r contingent t r u t h s . We have show n how o b lig atio n s e n te n c e s m ay be p ro p e rly r e n d e r e d as n o rm a tiv e s e n te n c e s and f u r th e r s u g g e s te d a way in w hich th o se n o rm a tiv e s which e x p re s s o b lig a tio n s m ay have a lo g i c a l s tr u c tu r e analogous to th at of a le th ic m o d al s e n te n c e s . In C h a p te r V the d etails of a lo g ic al s y s te m fo r the " v e r tic a l" r e la tio n sh ip s b etw een a b so lu te and u n iv e rs a l, u n iv e rs a l and individual, o b lig atio n s w ill be given. In addition, the n u cleu s of a s y s te m fo r the deontic m o d a litie s (th e o b lig ato ry , the fo rb id d en , and the p e r m itte d ) will be given. T h e re re m a in s b efo re u s the ta s k of c l a r i fying the re la tio n s h ip s b etw een n o rm a tiv e s e n te n c e s and im p e ra tiv e s e n te n c e s , and of ju stify in g o u r p o sitio n th a t o b lig atio n s e n te n c e s a re p ro p e rly r e n d e r e d a s n o rm a tiv e s but not as im p e ra tiv e s . 182 3. O b lig atio n S e n ten c es and Im p e r a tiv e s In C h a p te r II a n u m b e r of p ro p o s a ls fo r a logic of im p e r a tiv e s w e re c o n s id e re d . A tte m p ts to acco u n t f o r th e lo g ic a l c h a r a c t e r i s t i c s of o b lig a tio n s e n te n c e s w ithin im p e r a tiv e s y s te m s w e re found to be in a d e q u a te . T he a d v a n ta g e s of the n o rm a tiv e s y s te m s d is c u s s e d in C h a p te r III p ro v id e ju s tific a tio n fo r ch o o sin g the n o rm a tiv e a p p ro a c h r a t h e r th a n th e im p e r a tiv e a p p ro a c h to the logic of o b lig a tio n . It is o u r c o n te n tio n th a t the n o rm a tiv e a p p ro a c h is not only m o re a d v a n ta g eo u s but th a t the im p e ra tiv e a p p ro a c h can n e v e r a d e q u a te ly r e p r e s e n t th e lo g ic a l c h a r a c t e r i s t i c s of o b lig a tio n s e n te n c e s . O b lig atio n s e n te n c e s a r e not p r o p e r ly r e n d e r e d in the im p e ra tiv e m o o d - - a n o b lig a tio n to p e r f o r m an a c tio n is not the sa m e as a c o m m an d to p e r f o r m an a c tio n . O b lig atio n s and c o m m an d s a re s i m i l a r in th e ir p r a c tic a l a s p e c ts ; th ey both r e f e r to a c tio n s to be done. It is e s s e n tia l, h o w e v er, th a t we a v o id co n fu sin g t h e i r p r a c tic a l a s p e c ts w ith t h e i r lo g ic a l a s p e c ts . T he co n cep t of o b lig atio n c a r r i e s w ith it a binding e le m e n t, a kind of n e c e s s ity . T h is b in d in g e le m e n t c a n be a tta c h e d to a c o m m an d only if we o b tain an a ff ir m a tiv e a n s w e r to the q u e stio n , " is th is c o m m a n d o b lig a to ry ? " One m a y have an o b lig a tio n to obey a c o m m an d , but the o b lig a tio n to obey a c o m m a n d and the c o m m a n d its e lf a r e not 183 id e n tic a l. If we r e s t r i c t o u r c o n sid e ra tio n s fo r the m o m e n t to what we have c a lle d in d iv id u al o b lig atio n s e n te n c e s , we m ay r e g a r d the p r a c tic a l re a s o n in g p r o c e s s a s a m ethod by w hich we tak e c o u n se l w ith o u rs e lv e s . T he co n clu sio n of a p r a c tic a l s y llo g is m m ay be re g a r d e d a s a ju d g m en t of p r a c tic a l re a s o n , as when I conclude: M I ought to do th is . " On the o th e r hand, in ad d itio n to th is ju dgm ent, I m ay c o m m an d m y self: "Do th is l" The co u n selin g function of re a s o n with r e s p e c t to an individual o blig ation is c le a r ly not id e n tic a l with the co m m anding function; the obligatio n se n te n c e is c le a r ly not a 31 co m m an d . A lthough the re la tio n s h ip of id en tity b etw een o b lig atio n s e n te n c e s and im p e ra tiv e se n te n c e s is re je c te d , the s i m il a r it i e s b e tw een the two ty p es of se n te n c e w a rr a n t a s e a r c h fo r s o m e o th e r 31 F o r d is c u s s io n s of the d istin c tio n betw een co u n sel and c o m m and, se e St. T h o m as A qu inas, S um m a T h eo lo g ica, I - I I , T7, 1, E tienne G ilson, The C h ris tia n P h ilosophy of St. T h o m a s A quinas, p. 255; and P . H. N ow ell-S m ith, E th ic s , pp. 1 9 1 -1 9 3 . St. T h o m a s holds th a t r e a s o n can d e c la re so m e th in g in two w ays: the f i r s t is e x p r e s s e d in the in d icativ e m ood, e . g . , " T h is is what you should do;" the se c o n d way th a t re a s o n d e c la re s so m e th in g to a m an is by m oving h im th e re to and is e x p re s s e d in the im p e ra tiv e m ood, e. g . , "Do th is I" St. T hom as s ta te s th at the indicative d e c la ra tio n is a ju d g m en t of the re a s o n alone w hile the com m and, though an a ct of re a s o n , p re s u p p o s e s an a c t of the w ill ( Sum m a T h e o lo g ic a , I-II, 17, 1) . N o w ell-S m ith su g g e sts th a t the logic of 'o u g h t-s e n te n c e s , 1 " is a l ways th a t of advising, n e v e r th a t of co m m an d in g " (E th ic s , p. 1 9 2 ). 184 re la tio n s h ip . R. M. H are b e lie v e s th a t the r e la tio n s h ip b etw een o b lig a tio n s e n te n c e s and im p e ra tiv e s is one of lo g ic a l e n ta ilm e n t. He holds th at w hen ever a n o rm a tiv e se n te n c e i s u se d e v a lu a tiv e ly (to 3 2 e x p re s s an o b lig a tio n ), it lo g ic ally e n ta ils an im p e ra tiv e . In d efen se of his a s s e r tio n H a re o ffe rs an a n a ly s is of n o rm a tiv e s e n te n c e s in which he d istin g u is h e s the so c io lo g ic a l and p sy c h o lo g ic a l u sa g e s of n o rm a tiv e s fro m th e ir e v alu ativ e u s a g e s . He t r e a ts 'I ought to do X 1 as a co nfused m ix tu re of th re e ju d g m e n ts: (1) 'X is r e q u ire d in o r d e r to c o n fo rm to th e s ta n d a r d which people g e n e ra lly a c c e p t' ( s ta te m e n t of so c io lo g ic a l fa c t); (2) 'I have a feelin g th a t I ought to do X ’ ( s ta te m e n t of p sy c h o lo g ic a l f a c t) ; (3) 'I ought to do X ' ( v a lu e - ju d g m e n t) . (T h e L anguage of M o ra ls, p. 167) H a re contend s th a t w h en ev er no im p e ra tiv e is ejitailed by a n o rm a tiv e ju d g m en t, it is of type (1) o r (2 ), o r a m ix tu re of both; but when the jud gm ent e n ta ils an im p e ra tiv e , th en it is of type (3) . He o ffers no p ro o f fo r th is contentio n but m ak e s it tr u e by definition: I p ro p o se to s a y th at the te s t, w h e th er so m e o n e is using the ju d g em en t 'I ought to do X* as a v a lu e -ju d g e m e n t o r not is, fD oes he o r does he not re c o g n iz e that if he a s s e n ts to the ju d g em en t, he m u s t a ls o a s s e n t to the co m m an d " L e t m e do X " ? 1 ( The L anguage of M o ra ls, pp. 168 -169) Since ju d g m e n ts of ty p es (1) and (2) a r e s ta te m e n ts of fa c t about the sta te m e n t 'I ought to do X , ' H a re c o n clu d es th at the *^R. M. Hare, The Language of Morals (Oxford, 1952), Ch. 11. 185 p r im a r y s e n s e of 'I ought to do X' is not g iven by e ith e r (1) o r (2 ). T he s e n te n c e s of type (3) can n e v e r be a n a ly se d n a tu r a lis tic a l- ly so long as we a c c e p t the p rin c ip le th at im p e r a tiv e s cannot be d e riv e d fro m in d ic a tiv e s . By H a re ’s definition, a se n te n c e of type (3) m u s t e n ta il at le a s t one im p e ra tiv e , and, if (3) w e re a n a ly se d n a tu ra lis tic a lly , " th is would m e a n it w as eq u iv a le n t to a s e r i e s of in d ic ativ e s e n te n c e s " ( p . 171) . T he p o sitio n in w hich H a r e ’s a n a ly sis lea v es n o rm a tiv e se n te n c e s sho uld be c a re fu lly noted. He a s s e r t s th at 'I ought to do X , 1 when used ev alu ativ ely , e n ta ils an im p e ra tiv e . 'I ought to do X 1 is n o rm a tiv e ( p r e s c r i p t i v e ) , but it is o s te n s ib ly n e ith e r in the in d icativ e nor the im p e ra tiv e m ood. T h e re is no lo g ic a l re la tio n s h ip b etw een d e s c rip tiv e in d ic a tiv e s and n o rm a tiv e s , but a n o rm a tiv e judg m ent, when u se d e v alu ativ ely , lo g ically e n ta ils an im p e ra tiv e . T h ese r e s u lts a r e ob tain ed fro m H a r e ’s b a sic contention th at n o rm a tiv e m o r a l ju d g m e n ts, w henev er they a r e u se d e v alu ativ ely , function a s guides to ch o ic es o r a ctio n s. But anyone who a s s e n ts to a judgm ent which r e a lly do es guide his c h o ic e s o r a ctio n s m u st a ls o a s s e n t to an im p e ra tiv e d e riv a b le fro m th a t judgm ent; We a r e th e re fo re c le a r ly e n title d to s a y th a t the m o r a l ju d g em en t e n ta ils the im p e ra tiv e ; fo r to s a y th a t one ju d g e m ent e n ta ils a n o th e r is sim p ly to s a y th a t you cannot a s s e n t to th e f i r s t and d isse n t f r o m the second u n le s s you have m i s u n d e rsto o d one o r the o th e r; and th is 'c a n n o t' is a lo g ic a l 'c a n - 186 n o t1- - i f so m e o n e a s s e n ts to the f i r s t and not to the se co n d , th is is in its e lf a su ffic ie n t c r ite r io n fo r sa y in g th a t he has m is u n d e rs to o d the m e a n in g of one o r th e o th e r. T hus to sa y th at m o r a l ju d g e m e n ts guide a c tio n s , and to sa y th a t they e n ta il im p e r a tiv e s , c o m e s to m uch the s a m e thing. ( The L an guag e of M o ra ls, p. 172) H a re is undoubtedly c o r r e c t in h is a s s e r tio n th a t m o ra l ju d g m e n ts a r e s o m e tim e s u se d e v a lu a tiv e ly in h is s e n s e , i. e . , to guide a c tio n s . In o u r c h a r a c te r iz a tio n of o b lig atio n s e n te n c e s we s a id th a t th ey r e f e r to p o ss ib le hum an a c tio n s and c a r r y so m e s e n s e of c o n s tra in t, so m e binding e le m e n t. T h is c h a r a c te r iz a tio n is c o m p a tib le w ith H a r e 's u se of ev alu ativ e m o ra l ju d g m e n ts a s guides fo r a ctio n . T h e re is no obvious o b jectio n to p e rm ittin g so m e r e l a tio n sh ip jakinjto e n ta ilm e n t b etw een a n o rm a tiv e and an im p e ra tiv e . We a r e not s a tis fie d , h o w ev er, th at H a r e 's a n a ly s is has e s ta b lis h e d th at e v e ry n o rm a tiv e o b lig atio n se n te n c e lo g ic a lly e n ta ils an i m p e r a tiv e . H a re h im s e lf a d m its th at he has no fo rm a l d e m o n s tra tio n of th is e n ta ilm e n t re la tio n s h ip and m u s t th e r e f o re e s ta b lis h it by his own d efin itio n (p p . 1 68-169) . But even su p p o sin g th at we g ra n t th a t e v e ry ob ligation se n te n c e lo g ically e n ta ils an im p e r a tiv e , it d o es not follow th at, th e re f o re , the logic of o b lig atio n is id e n tic a l with the logic of im p e ra tiv e s . To s a y th at im p e r a tiv e s a r e e n ta ile d by o b lig a tion s e n te n c e s is not to sa y th at im p e ra tiv e s e x p re s s o b lig a tio n s. But H are w ish es to show how a logic of im p e r a tiv e s can be a d eq u ate f o r 187 o b lig atio n se n te n c e s ; so he tak e s an a d d itio n al ste p beyond an e n ta il m en t r e la tio n s h ip - - h e s u b s titu te s im p e ra tiv e s fo r ( e v a lu a tiv e ) m o r a l ju d g m e n ts. H a r e 's b a sic ru le fo r in fe re n c e s in w hich im p e r a tiv e s a r e involved does not s ta te sim p ly th a t im p e r a tiv e s cannot be d e riv e d fro m in d ic a tiv e s . His ru le s ta te s th a t " No im p e ra tiv e c o n clu sio n can be v alid ly d raw n f ro m a s e t of p r e m is s e s w hich does not co n tain a t le a s t one im p e ra tiv e " ( p . 28) . T h e re fo re , if an im p e ra tiv e is e n ta ile d ( l o g ic a l l y ) by any ju d g m en t a t all, th a t ju d g m e n t m u s t "co n ta in " th at im p e ra tiv e . T his is to s a y th a t any m o ra l ju d g m en t w hen u se d e v alu ativ ely (b y H a r e 's d e fin itio n ) is a lre a d y in the im p e ra tiv e m ood. H a re does not re a lly r e g a r d the c la s s of p r e s c r ip tiv e n o rm a tiv e s e n te n c e s a s d istin c t fr o m both th e in d ic ativ e and the im p e ra tiv e m oods, but r e g a r d s it as a lre a d y in th e im p e ra tiv e m ood. H are gives an a n a ly tic a l m o d el in w hich he r e n d e r s what we have c a lle d o b lig atio n s e n te n c e s by an a r tif ic ia l 'o u g h t' se n te n c e w hich is an im p e ra tiv e by definition, and is in ten d ed to fu lfill the functions of the o rd in a ry 33 'ought. 1 T hus, H a re s u b s titu te s im p e ra tiv e s f o r n o rm a tiv e s and The L anguage of M o ra ls, Ch. 12. H a re d iv id es a ll se n te n c e s into two e le m e n ts which he c a lls p h r a s tic and n e u s tic . He u se s 'y e s ’ as the sy m b o l fo r an in d ic ativ e n e u stic , and 'p le a s e ' a s the sy m b o l fo r an im p e ra tiv e n e u stic . The in d icativ e se n te n c e 'A ll P 's a r e Q' w hen s p lit into p h r a s tic and n e u stic b e c o m e s: ’A ll P 's being Q , 188 s u g g e s ts th at the lo g ic of o b lig a tio n is th e logic of a "m o d ifie d " im p e r a tiv e m o od. O b lig atio n s e n te n c e s do not s im p ly e n ta il i m p e r a tiv e s , n o r a r e im p e r a tiv e s in s o m e s e n s e " ju s tifie d " by o b lig a tio n s e n te n c e s -- o b lig a tio n s e n te n c e s a r e im p e r a tiv e s in H a r e 's s y s te m . O u r c o n te n tio n th a t th e c o n ce p t of o b lig a tio n is d is tin c t f r o m the c o n ce p t of c o m m a n d p re v e n ts us f r o m a c c e p tin g H a r e 's c o n c lu s io n s and f r o m r e g a rd in g in te r p r e te d im p e r a tiv e s y s te m s a s a d e q u ate to th e c o n ce p t of o b lig atio n . T he re d u c tio n of n o r m a tiv e s to im p e r a tiv e s c a n only be a c c o m p lis h e d by u ltim a te ly denying th e d i s tin c tio n b e tw e e n an o b lig a tio n and a c o m m a n d . T h is is too high a p r ic e to pay, p a r tic u la r ly s in c e th e a v a ila b le im p e r a tiv e s y s te m s (u p o n in te r p r e ta tio n ) a r e f a r le s s a d eq u a te to the c o n c e p t of o b lig a tio n th an a r e th o se s y s te m s w hich d e al d ir e c tly w ith n o r m a tiv e s . In S ectio n 1 of the p r e s e n t c h a p te r th e e s s e n tia l e le m e n ts of o b lig a tio n w e re d is c u s s e d , an d o b lig a tio n s w e re c la s s if ie d a s a b s o lu te, u n iv e r s a l, o r in d iv id u a l. In S ectio n 2 we show ed how o b lig a - y e s . ' T he in d ic a tiv e n e u s tic is r e p la c e d by an im p e r a tiv e one, y ield in g : ’A ll P ’s being Q , p l e a s e . ’ F o r the l a t t e r im p e r a tiv e s e n te n c e H a re s u b s titu te s the s e n te n c e 'A ll P 's ought to be Q . 1 H a r e 's a r t i f ic i a l 'o u g h t' is its e lf an im p e r a tiv e , a n d H a re o ffe rs th is a r t i f ic i a l ’ough t' as an in te r p r e ta tio n f o r th e 'o u g h t' in a n o rm a tiv e o b lig a tio n s e n te n c e . W hen he s u g g e s ts th a t th e a r tif ic ia l ' ought' m ay be s u b s titu te d fo r th e n o rm a tiv e 'ought, ’ H a re i s a c tu a lly sa y in g th a t im p e r a tiv e s a re at le a s t e q u iv a le n t to ( i f not id e n tic a l w ith ) o b lig a tio n s e n te n c e s . 189 tio n s m ay be p r o p e r ly e x p re s s e d by n o rm a tiv e s e n te n c e s and d is c u s s e d the analogo us re la tio n s h ip s b etw een the deontic and a le th ic m o d a litie s . T h e s e findings, in conjunction with the c o n clu sio n s which w e re draw n f r o m o u r a n a ly sis of p re v io u s ly p ro p o se d s y s te m s , p ro v id e a n u m b e r of co n d itio n s which m u s t be s a tis f ie d by a s y s te m w hose in te r p re ta tio n r e fle c ts the lo g ical a ttrib u te s of o b lig atio n s e n te n c e s . A n u m b e r of th e se conditions w e re m et by so m e of the s y s te m s d is c u s s e d in C h a p te r I I I . We now p ro c e e d to the ta s k of in d icatin g how m o re of th e s e conditions m ay be in c o rp o ra te d into a s y s te m which, a t the sa m e tim e , avoids the m a jo r d isa d v a n ta g e s of the s y s te m s p re v io u s ly p ro p o se d . CHAPTER V SCH EM A TA F O R T H E "V E R T IC A L " AND "H O R IZ O N T A L " R E L A T IO N SH IPS O F O B LIG A TIO N SE N T E N C E S In C h a p te r IV , o b lig a tio n s e n te n c e s w e re c la s s if ie d as a b so lu te , u n iv e rs a l, o r in d iv id u al, a c c o rd in g to w h e th e r th e o b lig a tio n e x p r e s s e d ho ld s in e v e r y p o s s ib le c ir c u m s ta n c e , in an alo g o u s c ir c u m s ta n c e s , o r fo r th is p a r t i c u l a r a c t in th is p a r t i c u l a r c i r c u m s ta n c e . We h av e s tip u la te d th at th e r e is only one a b so lu te oblig atio n , n a m e ly , the o b lig atio n to do good and a v o id e v il. A c c e p ta n c e of a d efin itio n of 'g o o d ' p e r m its th e d e riv a tio n of u n iv e rs a l o b lig a tio n s e n te n c e s f r o m the b a s ic a b so lu te o b lig a tio n s e n te n c e . A c ts ( g e n e r a l " a c t- ty p e s " ) a r e c a lle d u n iv e rs a lly o b lig a to ry if th ey fa ll w ithin th e sco p e of th e a b so lu te o b lig atio n . H ence, th e r e la tio n s h ip of u n iv e rs a l to a b so lu te o b lig a tio n s e n te n c e s is th a t of su b su m p tio n u n d e r a g e n e r a l p rin c ip le . S im ila rly , an a c t ( p a r t i c u l a r a c t ) is c a lle d in d iv id u a lly o b lig a to ry if the p a r t i c u l a r a c t is of the g e n e r a l a c t- type and the p a r t i c u l a r c ir c u m s ta n c e s of th a t a c t fa ll w ithin the sc o p e of th e s e t of g e n e r a l c ir c u m s ta n c e s of a u n iv e r s a lly o b lig a to ry a c t. T h u s, th e re la tio n s h ip of in d iv id u al o b lig a tio n s e n te n c e s to 190 191 u n iv e rs a l o b lig atio n s e n te n c e s is th at of su b su m p tio n u n d e r a g e n e ra l p r in c ip le . T he su b su m p tio n in fe re n c e s fo r a b so lu te , u n iv e rs a l, and in d iv id u al o b lig atio n s e n te n c e s d e s c rib e the v e r tic a l re la tio n s h ip s of th e s e s e n te n c e s . Since th e re is only one a b so lu te o b lig atio n s e n ten c e, th e re can be no use fo r a h o riz o n ta l s c h e m a fo r a b so lu te o b lig a tio n s e n te n c e s . ^ A h o riz o n ta l s y s te m f o r u n iv e r s a l o b lig atio n se n te n c e s s h o u ld p ro v id e the lo g ic al s c h e m a tis m f o r conju nctive, d isju n c tiv e , conditional, and b i-c o n d itio n a l u n iv e rs a l o b lig atio n s e n te n c e s . It a ls o s e e m s m o st fe a sib le to r e la te the c o n c e p ts of p e r m is s io n and p ro h ib itio n to the co n cep t of o b lig atio n on th e le v e l of u n iv e rs a l ob ligation. T he d e v elo p m en t of a h o riz o n ta l s y s te m fo r in d iv id u al o bligation s e n te n c e s s e e m s n e ith e r n e c e s s a r y nor d e s i r able. F o r , in the f i r s t p lac e, e v e ry ind ividual o b lig atio n se n te n c e is d e riv a b le in v e rtic a l m a n n e r f r o m so m e s e t of u n iv e rs a l o b lig a tion s e n te n c e s . And, se co n d ly , ev en sh o u ld a lo g ic a l re la tio n s h ip obtain b etw een two individual o b lig atio n s e n te n c e s , th is re la tio n s h ip w ill hold only fo r th e s e two s e n te n c e s ; g e n e ra liz a tio n of th is r e la tio n sh ip w ill tak e the fo r m of an e x te n sio n to s e n te n c e s e x p re s s in g an * A v e r tic a l s c h e m a tis m in clu d es o b lig atio n s e n te n c e s of m o re th an one of the th r e e ty p es. A h o riz o n ta l s c h e m a tis m in v o lv es r e l a tio n sh ip s betw een o b lig atio n s e n te n c e s of the sa m e type. 192 a n a lo g o u s s e t of c i r c u m s t a n c e s - - h e n c e , w ill r e t u r n u s to th e le v e l of u n i v e r s a l o b lig a tio n s e n t e n c e s . We s h a l l now s e t f o r th tw o s y s t e m s e a c h of w h ic h w ill d e a l w ith th e lo g ic a l r e l a ti o n s h i p s of o b lig a tio n s e n t e n c e s . T h e f i r s t s y s t e m p r e s e n t s a s c h e m a t i s m f o r d is p la y in g th e v e r t i c a l r e l a ti o n s h i p s of o b lig a tio n s e n t e n c e s . T he s e c o n d s y s t e m p ro v id e s a s e t of a x io m s f o r th e h o r iz o n ta l r e l a ti o n s h i p of u n i v e r s a l o b lig a tio n s e n t e n c e s . T h e s e a x io m s r e l a t e the c o n c e p ts of p e r m i s s i o n a n d p r o h ib itio n to t h a t of o b lig a tio n . 1. A V e r ti c a l S y s te m f o r O b lig a tio n S e n te n c e s T h e s y s t e m a t i c r e p r e s e n t a t i o n of s u b s u m p tio n in f e r e n c e s f o r o b lig a tio n s e n te n c e s w ill be d e v e lo p e d in s t r i c t a n a lo g y w ith th e c a t e g o r i c a l s y llo g is m of t r a d i ti o n a l lo g ic . A ny s y llo g is m w hich c o n t a i n s a n o b lig a tio n s e n te n c e a s one of its e le m e n ts w ill b e c a lle d a p r a c t i c a l s y llo g is m . T r a d i ti o n a l s y s t e m s r e c o g n iz e f o u r f o r m s of c a t e g o r i c a l p r o p o s itio n s , w hich a r e r e f e r r e d to, r e s p e c t iv e ly , a s th e A , E , I , a n d O f o r m s , a n d w h ic h m a y be w r itte n a s fo llo w s: A A ll x is y . ( A f f ir m a tiv e u n i v e r s a l j u d g m e n t ) E No x is ( N e g a tiv e u n i v e r s a l ju d g m e n t) I S o m e x is y. ( A f f ir m a tiv e p a r t i c u l a r j u d g m e n t ) O S o m e x is n ot y . ( N e g a tiv e p a r t i c u l a r j u d g m e n t ) B y m a k in g th e o b v io u s s u b s titu tio n s fo r x a n d y , we o b ta in th e 193 fo llo w in g fo u r f o r m s of o b lig a tio n s e n te n c e s : A A ll a c ts of ty p e X a r e o b lig a to ry . E No a c ts of type X a r e o b lig a to ry . I Som e a c ts of ty pe X a r e o b lig a to ry . O Som e a c ts of type X a r e n ot o b lig a to ry . T he law s of im m e d ia te in fe r e n c e ( c o n v e rs io n , o b v e rs io n , and c o n tr a p o s i ti o n ) a n d the la w s of th e s q u a r e of o p p o sitio n hold fo r th e A , E , I , and O f o r m s of o b lig a tio n s e n te n c e s j u s t a s th ey do f o r a ll o th e r c a te g o r ic a l f o r m u la s . H o w ev e r, th e n u m b e r of v a lid m o o d s of the ( p r a c t i c a l ) s y llo g is m in w hich the A , E , I , an d O f o r m s of o b lig a tio n s e n te n c e s m a y o c c u r is c o n s id e r a b ly l e s s th a n the o n in e te e n v a lid m o o d s of th e ( t h e o r e t i c a l ) c a te g o r ic a l s y llo g is m . In c o n s tr u c tin g a s e t of r u l e s fo r d e te rm in in g w h e th e r a g iv en s y llo g is tic i n f e r e n c e - p a t te r n is v a lid f o r o b lig a tio n s e n t e n c e s , we a s s u m e th a t e v e r y o b lig a tio n s e n te n c e w hich o c c u r s in a s y llo g is m s a t is f ie s th e g e n e r a l c o n d itio n s f o r o b lig a tio n s e n te n c e s la id down in S ectio n 1 of C h a p te r IV ( i . e . , the a c tio n s r e f e r r e d to a r e v o lu n ta ry , p h y s ic a lly p o s s ib le , h u m a n a c tio n s , e tc . ) . We s h a ll a ls o a s s u m e th a t the ^ Som e a u th o rs of e le m e n ta r y lo g ic te x ts lis t tw e n ty -fo u r v a lid m o o d s of the c a te g o r ic a l s y llo g is m , fiv e of w h ich h av e "w e a k e n e d " c o n c lu s io n s , i. e. , th ey a s s e r t l e s s th a n c a n be lo g ic a l ly i n f e r r e d f r o m th e p r e m i s e s . T he AAI m o o d of th e f i r s t f ig u re , fo r e x a m p le , is v a lid b u t the I - c o n c lu s io n is l e s s th a n c a n be i n f e r r e d f r o m th e A - p r e m i s e s . 194 Q r u le s of th e s y llo g is m hold f o r p r a c t ic a l a s w ell a s th e o r e tic a l s y llo g is m s - - h e n c e , th a t th e v a lid m o o d s of th e p r a c t ic a l s y llo g is m m a y b e s e le c te d f r o m th e lis t of v a lid m ood s of th e th e o r e tic a l s y l lo g is m . T he n in e te e n v a lid m o o d s of the th e o r e tic a l s y llo g is m a r e the follow ing: 1st F ig u re : AAA, EAE, A n, EIO 2nd F ig u r e : EAE, AEE, EIO, AOO 3 rd F i g u r e : AAI, EAO, IAI, AU, OAO, EIO 4th F ig u re : AAI, AEE, IAI, EAO, EIO We now s tip u la te th e co n v en tio n s and r u le s w hich a r e in te n d ed to c o m p r is e a te s tin g m e th o d fo r d e te rm in in g the v a lid m o o d s of the p r a c t ic a l s y llo g is m . C o n v e n tio n s: ( a ) A s y llo g is m , th e c o n c lu sio n of w hich is a u n iv e r s a l o b lig a tio n s e n te n c e , w ill be c a lle d a g e n e r a l p r a c tic a l s y llo g is m . ( b ) A s y llo g is m , th e c o n c lu sio n of w hich is an in d iv id u a l o b lig a tio n s e n te n c e , w ill be c a lle d a s t r i c t l y p r a c tic a l s y llo g is m . 3 F o r a l is t of th e ru le s of the s y llo g is m se e J a c q u e s M a rita in , F o r m a l L o g ic, 2nd e d . , t r a n s . Im e Id a C hoqu ette ( N ew Y ork, 1 9 4 6 ), pp. 181-182; H e r b e r t L . S e a rle s , L og ic and S c ie n tific M ethod, 2nd e d . {N ew Y o rk , 1 9 5 6 ), pp. 127-128; W illia m H. W e r k m e is te r , An In tro d u c tio n to C r itic a l T h in k in g , r e v . ed. (L in c o ln , N e b ., 1 9 5 7 ), p. 296; and o th e r te x ts w hich d e a l w ith the c a te g o r ic a l s y llo g is m . A l though th e n u m b e r of r u le s v a r ie s ( M a rita in l is ts eig h t, S e a rle s nin e, and W e r k m e is te r s i x ) , e a c h of the th r e e s e t s of r u le s c an be show n to be e q u iv a le n t to e a c h of the o th e r two and the r e s u l ts of ap p ly in g th e s e r u le s a re id e n tic a l (th e lis ts of v a lid m o o d s of the c a te g o r ic a l s y llo g is m a re i d e n t i c a l ) . 195 G e n e ra l R u les f o r a ll p r a c tic a l sy llo g is m s: (1) The m a jo r p r e m is e m u s t be e ith e r an a b so lu te o bligation se n te n c e o r a u n iv e rs a l o bligation se n te n c e . (2) T he m in o r p r e m is e cannot be an o bligation se n te n c e . (3) The co n clu sio n m u st be e ith e r a u n iv e rs a l o r an individual o b lig atio n se n te n c e . S p ecial R u le s : (1) The m a jo r p r e m is e of a g e n e ra l p r a c tic a l s y llo g is m m u s t be an ab so lu te o blig ation se n te n c e . (2) The m a jo r p r e m is e of a s tr ic tly p r a c tic a l s y llo g is m m u s t be a u n iv e rs a l o b lig atio n se n te n c e . An im m e d ia te g e n e ra l r e s u lt of the ru le s of the p r a c tic a l s y llo g is m is th a t p r a c tic a l s y llo g is m s a r e r e s t r i c te d to th e v e rtic a l re la tio n s h ip s of o bligation s e n te n c e s . It should be noted th a t individual o bligation s e n te n c e s e x p re s s s in g u la r ju d g m e n ts and not p a r tic u la r ju d g m e n ts, i . e . , individual o b lig atio n se n te n c e s a re not of the fo rm 'S om e a c ts of type X a r e o b lig a to ry . ' Individual o bligation s e n te n c e s , being s in g u la r, a re tr e a te d ( in th e th e o ry of the s y llo g is m ) in th e sa m e m a n n e r as A 4 and E s e n te n c e s . It follow s, th e re fo re , in v irtu e of G e n e ra l Rule ^ I t is not e x actly c o r r e c t to sa y th a t sin g u la r p ro p o sitio n s b e have lo g ic a lly in the s a m e m a n n e r as u n iv e rs a l p ro p o s itio n s . With 196 (3 ), th a t no I o r O s e n te n c e s can o c c u r a s c o n c lu sio n s of a p r a c t i c a l s y llo g is m . But if the c o n c lu sio n of a s y llo g is m is not an I o r a n 5 O s e n te n c e , n e ith e r of the p r e m i s e s c an be an I o r an O s e n te n c e . Of th e n in e te e n v a lid m oods of the s y llo g is m , th e r e f o r e , only five can p o s s ib ly be v a lid m o o d s of th e p r a c t ic a l s y llo g is m , n a m e ly : 1st F ig u re : AAA, E A E 2nd F ig u re : E A E , A E E 4th F ig u r e : A E E T he follow ing m o d e ls of the A and E f o r m s of th e d iffe re n t ty p es of o b lig a tio n se n te n c e w ill aid us in d e te rm in in g th e v a lid m oods of the g e n e r a l and s t r i c t l y p r a c t ic a l s y llo g is m s : A b so lu te O b lig atio n S e n te n c e s A A ll a c ts w hich a r e good (a n d not e v il ) a r e o b lig a to ry . E No a c ts w hich a r e e v il ( an d not g o o d ) a r e o b lig a to ry . U n iv e rs a l O b lig atio n S e n te n c e s A A ll a c ts of type Y a r e o b lig a to ry . E No a c ts of type Y a r e o b lig a to ry . r e s p e c t to the s y llo g is m an d th e th e o ry of c o n v e rs io n of p ro p o s itio n s , s in g u la r p ro p o s itio n s a r e a s s im ila te d to u n i v e r s a l s . H o w ev e r, w ith r e s p e c t to o p p o sitio n , s in g u la r s do not b e h a v e lik e u n i v e r s a l s - - a f f ir m a tiv e an d n e g a tiv e s in g u la r p ro p o s itio n s a r e c o n tr a d ic to r ie s ( e .g ., 'S o c r a te s is a m a n 1 and ’S o c ra te s is not a m an* a r e c o n tr a d ic to rie s ) ; a ffirm a tiv e and n e g a tiv e u n iv e r s a ls a r e c o n t r a r i e s ( e . g . , 'A ll m e n a r e m o r t a l 1 and 'N o m e n a r e m o r ta l' a r e c o n t r a r i e s ) . 5 One of th e b a s ic r u le s of the s y llo g is m is th a t th e t e r m s m u s t n e v e r be b r o a d e r in th e c o n c lu sio n th a n in the p r e m i s e s . T h e r e fo re , if th e c o n c lu sio n is u n iv e r s a l ( o r s i n g u l a r ) , the p r e m i s e s m u s t be u n iv e r s a l ( o r s in g u la r ) . 197 In d iv id u al O b lig atio n S en ten ces A T h is a c t is o b lig a to ry . E T h is a c t is not o b lig a to ry . T he follow ing a r e e x a m p le s of the five p o s s ib ly v a lid m oods of th e p r a c tic a l sy llo g is m : 1st F ig u re A A ll a c ts of type X a r e o b lig a to ry . A T his a c t is an a c t of type X . A T h is a c t is o b lig a to ry . E No a c ts of type X a re o b lig a to ry . A T h is a c t is an a c t of type X . E T h is a c t is not o b lig a to ry . 2nd F ig u re E No o b lig a to ry a c ts a r e a c ts of type X . A T h is a c t is an a c t of type X . E T h is a c t is not o b lig a to ry . A A ll o b lig a to ry a c ts a re a c ts of type X . E T h is a c t is not an a c t of type X . E T h is act is not o b lig a to ry . 4th F ig u re A A ll o b lig a to ry a c ts a re a c ts of type X , E No a c t of type X is th is a ct. E T h is a c t is not o b lig a to ry . In e a c h of th e s e five e x a m p le s th e c o n clu sio n is an individual o b lig atio n s e n te n c e . T h e re fo re , by C onvention (b), a ll five s y llo g is m s m u s t be s t r i c t l y p r a c tic a l s y llo g is m s . But by S p ecial Rule ( 2 ) th e m a jo r p r e m is e of e v e ry s tr ic tly p r a c tic a l s y llo g is m m u st be a u n iv e r s a l o b lig atio n s e n te n c e . The A E E m oods of the 2nd and 198 4th fig u re s cannot m e e t th is re q u ire m e n t of S p ecial Rule ( 2 ) - - th e m a jo r p r e m is e ’A ll o b lig a to ry a c ts a r e a c ts of type X 1 is not a u n iv e rs a l o b lig atio n se n te n c e (n o s ta te m e n t about " a ll o b lig a to ry a c ts " can s a tis fy o u r defin itio n of a u n iv e rs a l o b lig atio n s e n te n c e ) . S u b stitution of th e nam e of a u n iv e rs a l a c t-ty p e fo r ’a c ts of type X ’ w ould y ield obviously u n d e sira b le s ta te m e n ts , su c h a s: ’A ll o b lig a to ry a c ts a r e a c ts of p ro m is e -k e e p in g , ’ and ’A ll o b lig a to ry a c ts a re a c ts of obedience to p a r e n t s . ’ T he only a c c e p ta b le in te rp re ta tio n of 'A ll o b lig a to ry a c ts a re a c ts of type X' is as an a b so lu te obligation s e n te n c e - - 'A ll o b lig a to ry a c ts a r e a c ts which a r e good (a n d not e v i l ) . 1 T hus, the A E E m oods of the 2nd and 4th fig u re s a r e p r e vented f ro m being valid f o r the s tr ic tly p r a c tic a l sy llo g is m but can be show n to be v a lid fo r the g e n e ra l p r a c tic a l s y llo g is m - - a s in the f o l low ing e x a m p le s: 2nd F ig u re A A ll o b lig a to ry a c ts a re a c ts which a re good ( and not e v i l ) . E No a c ts of type Y a re good ( and not e v i l ). E No a c ts of type Y a re o b lig a to ry . 4th F ig u re A A ll o b lig a to ry a c ts a r e a c ts which a r e good ( and not e v i l ) . E No a c ts which a r e good ( and not e v i l ) a r e a c ts of type Y . E No a c ts of type Y a r e o b lig a to ry . The o th e r th re e of the five p o ss ib ly v alid m oods can a ls o be show n to be valid f o r the g e n e ra l p r a c tic a l sy llo g ism . F o r e x am p le, the AAA 199 m o o d of th e 1 st f ig u re is v a lid fo r the fo llow ing g e n e r a l p r a c tic a l sy llo g is m : A A ll a c ts w hich a r e good ( a n d not e v il) a r e o b lig a to ry . A A ll a c ts of ty pe Y a r e good ( an d not e v i l ) . A A ll a c ts of type Y a r e o b lig a to ry . We co n clu d e th a t th e r e a r e five v a lid m o o d s of th e g e n e r a l p r a c t ic a l s y llo g is m , but th a t o f th e s e only th r e e a r e v a lid fo r th e s t r i c t l y p r a c t ic a l s y llo g is m ( AAA and E A E of th e 1st fig u re , and E A E of the 2nd fig u re ) . T he te s tin g p r o c e d u re fo r the v a lid ity of p r a c t ic a l s y llo g is m s w as d e v elo p ed by the ad d itio n of five r u le s and tw o c o n v en tio n s to th e r u le s of the ( t h e o r e t i c a l ) s y llo g is m of tr a d itio n a l lo g ic . If we c o n s id e r e a c h v a lid m o o d of th e th e o r e tic a l s y llo g is m a s a c la s s w hose m e m b e r s a r e t r ip l e s of v a ry in g k inds of s e n te n c e s , the v a lid m ood s of the p r a c t ic a l s y llo g is m a r e r e s t r i c t e d s u b c la s s e s of five of the v a lid m oods of the th e o r e tic a l s y llo g is m . If we w ish e d to r e p la c e the p r e d ic a te t e r m O b lig a to r y 1 by th e p r e d ic a te s *fo rb id d en ! and 'p e r m itte d , 1 we could (w ith th e a p p ro p r ia te m o d ific a t io n s ) d isp la y the v e r tic a l re la tio n s h ip s b etw een s e n te n c e s which e x p r e s s the fo rb id d e n o r p e r m itte d m o d es of a c t s . F r o m a lo g ic a l p o in t of view , h o w e v e r, the m o re in te r e s tin g a s p e c ts of the c o n c e p ts of fo rb id d e n and p e r m itte d a c ts a r e r e v e a le d w hen th e se c o n ce p ts a r e r e l a te d to the co n cep t of o b lig a tio n . T he in te r r e la tio n s h ip s of the m o d a l c a te g o r ie s of th e o b lig a to ry , the fo rb id d e n , an d th e p e r m itte d 2 0 0 w ill be e s ta b lis h e d in o u r se c o n d s y s te m w hich p r e s e n ts th e lo g ic a l s t r u c t u r e of th e h o riz o n ta l re la tio n s h ip s of u n iv e r s a l o b lig atio n s e n te n c e s .^ 2. An A x io m S y s te m fo r th e H o riz o n ta l R e la tio n s h ip s of O b lig atio n S e n te n c e s T h e a x io m s y s te m w hich we s h a ll now o u tlin e w ill be den o ted by fH r ( f o r h o r iz o n ta l* ) . T he s y m b o ls , r u le s of fo rm a tio n , d e fin i tio n s, and a x io m s of H w ill be g iv en and so m e of the p ro v a b le th e o r e m s of H w ill be lis te d . We s h a ll adopt the co n v en tio n th a t a ll sy m b o ls w ill be u se d both n o rm a lly and a u to n y m o u sly . L is t of S y m bols of H and T h e ir In ten d e d I n te r p r e ta tio n s a. T h e lo w e r c a s e l e t t e r s p , q , r , . . . , w ill be u se d as p ro p o s itio n a l v a ria b le s , ra n g in g o v e r p ro p o s itio n s abo ut u n iv e rs a l a c t- ty p e s . T he p ro p o s itio n p is : An a c t of type X is done. X , Y , . . . , ra n g e o v e r the v a rio u s a c t- ty p e s . b. T he lo w e r c a s e l e t t e r s c , d , e , . . . , w ill ra n g e o v e r 6 S tric tly sp e a k in g , the s c h e m a ta of the p r a c t ic a l s y llo g is m can, a t m o s t, be c o n s id e re d a p a r t i a l s y s te m a tiz a tio n of the v e r tic a l r e la tio n s h ip s of o b lig a tio n s e n te n c e s . T he r u le s of th e p r a c tic a l s y l lo g is m do not c o m p r is e a c o m p le te s y s te m in the m o d e rn te c h n ic a l s e n s e of the w ord. 201 s e ts of c ir c u m s ta n c e s . T he n o tatio n p / c is in te r p r e te d a s 'A n a c t of type X is done in c ir c u m s ta n c e s c . 1 -'-p/c s a y s th a t an a c t of type X is not done in c ir c u m s ta n c e s c . c. T he c a p ita l le tte r s O , F , and P , re s p e c tiv e ly , w ill be u se d a s o p e ra to rs fo r the deontic m o d a litie s of the o b lig a to ry , the fo rb id d en , and the p e rm itte d . T he in ten d ed in te r p r e ta tio n of O is: •it is o b lig a to ry th a t . . . , 1 of F : 'it is fo rb id d e n th a t . . . , 1 and of P : 'it is p e rm itte d th a t . . . . ' The n o tation 0 ( p / c ) is i n t e r p re te d as 'It is o b lig a to ry th a t an a c t of type X be done in c ir c u m s ta n c e s c '- -w h ic h , f o r con v en ien ce, is sh o rte n e d to 'p is o b lig a to ry in c irc u m s ta n c e s c . 1 0 ( - '- p / c ) s a y s th at it is o b lig a to ry th a t an a c t of type X be not done ( o m itte d ) in c ir c u m s ta n c e s c ( -^p is o b lig a to ry in c ) . d. The c u rl ( ~ ) , wedge ( v ) , a m p e rs a n d (& ), 7 0 ( p / c ) is in ten d ed to be a ty p ic a l u n iv e rs a l o b lig atio n s e n te n c e . F ( p / c ) and P ( p / c ) a re intend ed to be the analo g o u s u n iv e r s a l p ro h ib itio n and u n iv e rs a l p e r m is s io n s e n te n c e s . T h e re f e r e n c e to c ir c u m s ta n c e s in a u n iv e rs a l deontic se n te n c e m a y be e ith e r e x p lic it o r im p lic it. The " e x p lic it" se n te n c e 'T a k in g the p r o p e r ty of a n o th e r in c irc u m s ta n c e s c is forbidden* h a s the s a m e m ea n in g as the " im p lic it" se n te n c e 'S tealin g is f o r b id d e n .' F ( p / c ) s y m b o liz e s th e se n te n c e w hich co n ta in s the e x p lic it re f e r e n c e to c ir c u m s ta n c e s . To sy m b o liz e the se n te n c e w hich co n tain s the im p lic it r e f e r e n c e to c ir c u m s ta n c e s we m u s t m ove to a n o th e r language le v e l in w hich the " im p lic it" s e n te n c e s have the fo rm : F ( s t e a l i n g ) . The s y s te m H w ill co n tain only the e x p lic it fo rm u la tio n s of u n iv e rs a l deon tic s e n te n c e s . 2 0 2 a r r o w ( —>), and the double a r r o w ( —><— ), re s p e c tiv e ly , w ill be u s e d a s the n eg atio n sig n , the d isju n c tio n sign, the con ju n ctio n sign, the ( s t r i c t ) co n d itio n al sign, and th e ( s t r i c t ) b i-c o n d itio n a l sig n . Q T he in te n d ed in te rp r e ta tio n s a re a s fo llo w s:0 -'-p : It is not the c a s e th a t p (a n a c t of type X is done ) p v q : E ith e r p ( an a c t of type X is d o n e) o r q ( an a ct of type Y is done ) but n ot both. p & q : Both p an d q . p —>q: If p th en q b e c a u se of a c o n n ectio n in m ean in g b etw een p and q , i . e . , if an a c t of type X is done, th en an a c t of type Y is done b e c a u se of a c o n n ectio n b etw een the two a c ts . A lso: p involves q - p —><— q: p if, and only if, q b e c a u se of a c o n n ectio n in m ean in g b etw een p and q . R ules of F o r m a tio n 1. p , q , r , . . . , a r e p ro p o sitio n a l fo rm u la s of H . 2. T he r e s u lt of co m b in in g any two p ro p o sitio n a l fo rm u la s of H with the c o n n ec tiv es v , & , —> , o r —><— , is a ls o a p ro p - o sitio n a l fo rm u la of H , F o r e x am p le : p v q , p& q, q —> r , r —> < —p , . . . , a re p ro p o s itio n a l fo rm u la s of H . 3. T he r e s u lt of ju x ta p o sin g a p ro p o sitio n a l fo rm u la , a s tr o k e ( / ) , and a c irc u m s ta n c e v a ria b le ( c , d , . . . ) , is a c ir c u m sta n c e fo r m u la of H . F o r e x a m p le : p/c, p & q /c, r v q /d , . . . , are Q ( p / c ) , 0 ( p / c ) , F ( p / c ) , and P ( p / c ) m ay e ac h be s u b s titu te d f o r p in e v e ry c a s e . 203 c ir c u m s ta n c e fo r m u la s of H . 4. The r e s u l t of p re fix in g a s in g u la r, d isju n c tiv e , o r c o n ju n ctiv e c ir c u m s ta n c e fo rm u la by one of th e th r e e d e o n tic o p e r a to r s is a d e o n tic fo r m u la of H . F o r e x a m p le : 0 ( p / c ) , 0 ( p v q / c ) , F ( p & q / c ) , P ( r v q / d ) , a r e d eo n tic f o rm u la s of H . 5. Any p ro p o s itio n a l fo rm u la o r c ir c u m s ta n c e f o rm u la o r d eo n tic fo r m u la is a w e ll- f o r m e d - f o r m u la (wff) of H. 6. The n e g atio n of any wff of H is a ls o a wff of H . F o r e x a m p le : ->-p, ~ p / c , -'-(pvq)/c, ~ - 0 ( p /c ) , ~ P { p & q / c ) , a r e wffs of H . 7. T he r e s u l t of co m b in in g any tw o wffs of H w ith the c o n n e c tiv e s v , & , —> , o r —X — , is a wff of H . F o r e x am p le : p&O {p /c ), p / c —> F ( p / c ) , p / c —> F ( p / c ) , 0 ( p/c )—><— ( ~ q / c ), 0 ( p v q / c ) v ~ F ( r & q / d ) , a r e wffs of H . D efin itio n s 0 ( p / c ) is a u n iv e r s a l o b lig a tio n s e n te n c e . T he co n cep t of u n iv e r s a l o b lig atio n , as c h a r a c te r iz e d in C h a p te r IV , p la c e s c e r ta in r e s t r i c ti o n s upon o u r ch o ice of p ro p o s itio n s fo r th e s y s te m H . A p ro p o s itio n p of H is a p ro p o s itio n about a c ts , b ut th e s e a c ts m u s t be v o lu n ta ry h u m an a c ts , and th ey m u s t be p h y s ic a lly p o s s ib le to th e a g e n t who is bound by the o b lig a tio n . The o p e r a to r O will 204 be p rim itiv e in s y s te m H , i. e . , no e x p lic it d efin itio n of O w ill be g iven in H . F and P a r e defined in t e r m s of O . D l. L e t F ( p / c ) be sy n o n y m o u s w ith 0(~*pfc), i .e ., ’It is fo rb id d en th at an a c t of type X be done in c ir c u m s ta n c e s c 1 is sy n o n y m o u s with 'It is o b lig a to ry th at an a c t of type X be o m itte d in c ir c u m s ta n c e s c . 1 F o r co n v en ien ce we a b b re v ia te the E n g lish tr a n s la tio n of D l to: 'p is fo rb id d e n in c 1 is synonym ous with p is o b lig a to ry in c . 1 D2. L et P ( p / c ) be sy n onym ou s w ith ~ F ( p / c ) , i .e ., 'p is p e rm itte d in c 1 is sy n o n y m o u s with 'p is not fo rb id d e n in c . ' A xiom s of H It is intend ed th at H s h a ll be b a s e d upon a c a lc u lu s for m odal p ro p o sitio n a l logic. A c co rd in g ly , we a s s u m e th a t th e re has been laid down a s e t of ax io m s and ru le s of in fe re n c e s u ita b le for su c h a c a lc u lu s. In ad d itio n to th e s e , H co n ta in s no f u r th e r r u le s of in fe re n c e , but does c o n ta in the follow ing s p e c ia l a x io m s: R l. O ( p v q / c ) —> O ( p / c ) vO ( q / c ) R2. O ( p&q / c ) —> <— O ( p / c ) &O ( q / c ) Rl and R2 a r e the d isso lu tio n r u le s of H . R l s a y s th a t if it is o b lig a to ry to do p o r q in c irc u m s ta n c e s c , th en e ith e r p is o b lig a to ry in c o r q is o b lig a to ry in c . T he r e v e r s e of R l is 205 ex clu d ed f ro m s y s te m H to avoid the u n d e s ira b le co n seq u en ce: 0 ( p / c ) —> 0 ( p v q / c ) . R2 s a y s th a t both p and q a r e o b lig a to ry in c if, and only if, p is o b lig a to ry in c and q is o b lig a to ry in c , The c ir c u m s ta n c e s c p ro v id e th e c o n n ectio n w hich ju s tifie s allow ing the c o n seq u e n ce 0 ( p & q / c ) —> 0 ( p / c ) of R2 to be p ro v a b le in H . In addition to R l and R2 , H co n tain s a ls o the follow ing a x io m s : A l. 0 ( p /c ) v - ^ 0 ( p / c ) - - L aw of ex clu d ed m id d le fo r ob- 9 lig a tio n s e n te n c e s . A2. 0 ( p / c ) —> M I) ( ~ p / c ) If p is o b lig a to ry in c ir c u m s ta n c e s c , th en it is not o b lig a to ry to o m it p in c . A3. 0 ( p /c } & ( p / c —>q/c ) —> 0 ( p & q /c ) fo r q ^ ~ p - - If p is o b lig a to ry in c and the doing of p in c n e c e s s a r ily involves the doing of q in c , th en it is o b lig a to ry to do both p and q in c . ^ ^ The c a lc u lu s f o r the m o d al p ro p o sitio n a l logic upon which H is b a se d , a lre a d y c o n ta in s a law of th e e x clu d ed m id d le . H ow ever, sin c e o b lig a tio n s e n te n c e s have h ith e rto b een ex clu d ed fro m m o d al p ro p o sitio n a l lo g ic s we m ak e e x p lic it the law of ex clu d ed m iddle fo r o b lig atio n s e n te n c e s ( A l ) . It sh o u ld be u n d e rsto o d th at A l is sim p ly a s p e c ia l c a s e of the g e n e ra l law of the e x clu d ed m iddle and s t r i c t l y sp e ak in g , n eed not have b een m ad e a s p e c ia l ax io m of H . C o n sid e r the s im ila r ity betw een A3 and the a n cien t m ax im : W hoever w ills the end a ls o w ills the m e a n s n e c e s s a r y fo r the a tta in m e n t of th at end. 206 T h e o re m s of H T l . F ( p / c ) v P ( p / c ) — E ith e r p is fo rb id d e n in c i r c u m s ta n c e s c o r p is p e r m itte d in c ir c u m s ta n c e s c . T l e x p r e s s e s the in tu itiv e ly obvious p ro p o s itio n th a t in a c e r ta in s e t of c i r c u m s ta n c e s a given a c t is e ith e r fo rb id d e n o r p e rm itte d . T l s e r v e s as a P r in c ip le of P e r m is s i o n fo r H . P ro o f of T l: (1) O ( p / c ) V "-0 ( p / c ) - - A l. (2) O ( — p /c ) v ~ 0 ( ~ p /c ) -- (1), su b s titu tio n . (3) F ( p / c ) v - ~ F ( p / c ) -- (2), D l , su b s titu tio n . (4) F {p/c ) vP ( p/c ) -- (3), D2 , su b s titu tio n . T 2. ~ ( F ( p / c ) & P ( p / c ) ) -- It is not the c a s e th at it is both fo rb id d e n to do p in c ir c u m s ta n c e s c and p e r m itte d to do p in c ir c u m s ta n c e s c . P ro o f of T2; {1) F ( p/c ) vP {p/c ) -- Tl. (2) F ( p/c ) &P ( p / c )) -- (1), d efin itio n of v . T 3. 0 ( p / c ) —> P ( p / c ) -- If p is o b lig a to ry in c i r c u m s ta n c e s c , th en p m u s t be p e r m itte d in c ir c u m s ta n c e s c . P ro o f of T 3 ; (1) O ( p / c ) —> — O ( ~ p / c ) -- A2. (2) 0 ( p / c ) —> ~ F ( p / c ) -- (1), D l , s u b s titu tio n . (3) 0 ( p / c )—> P ( p / c ) — (2), D 2 , s u b s titu tio n . T 4. O ( p /c ) &F ( p/c )) - - It is not the c a s e th a t p is 207 o b lig a to ry in c irc u m s ta n c e s c and p is fo rb id d e n in c ir c u m s ta n c e s c . P ro o f of T 4 ; (1) O ( p/c ) &F ( p / c ) (2) O ( p / c ) (3) 0 ( p / c ) —> P ( p / c ) (4) P ( p / c ) (5) F ( p/c ) (6) F ( p / c ) &P (p /c ) (7) - ( F ( p / c ) & P ( p / c ) ) (8) M O ( p / c ) & F ( p / c ) ) A ssu m p tio n . (1 ), conjunction e lim in a tio n . T3. (2), (3), m odus p o n en s. (1), c o n ju n ctio n e lim in a tio n . (4), (5), conjunction in tro d u c tio n . T2 . (1), (6), (7). re d u c tio ad a b s u rd a m . T5. ~ ( O ( pvq/c ) &F ( p/c ) &F ( q/c )) -- It is not the c a se th at e ith e r p o r q is o b lig a to ry in c ir c u m s ta n c e s c and p is fo rb id d en in c and q is fo rb id d en in c . T5 e x p r e s s e s the p e rp le x u s s im p lic ite r p ro p o sitio n of St. T h o m a s --o n e can n o t be o b lig ed to choose b etw een fo rb id d e n a lte rn a tiv e s . P ro o f of T5: (1) O ( p v q /c ) &F ( p /c ) &F ( q/c ) -- A ssu m p tio n . <2) O ( pvq/ c ) (3) 0 ( p/c ) vO ( q/c ) (4) F ( p/c ) (5) -w( F < p/c ) & 0 ( p / c ) ) (6) ~ 0 ( p / c ) (7) O ( q/c ) (8) F ( q/c ) (9) O ( q /c ) &F ( q / c ) (10) ~ ( 0 ( q / c ) &F ( q / c ) ) (1), co n ju n ctio n e lim in a tio n . (2), Rl. (1), con ju n ctio n e lim in a tio n . T4 . (4), (5), d efin itio n of A . (3), (6), d efin itio n of v . (1), c o n ju n ctio n e lim in a tio n . (7), (8), c o n ju n ctio n in tro d u c tio n . - - T 4 . (11) ^ ( 0 ( p v q / c ) & F ( p / c ) & F ( q / c ) ) -- (1), (9). (10), re d u c tio ad a b s u rd a m . Som e o th e r th e o re m s which a r e p ro v a b le in H a re : 208 T 6. O ( p & q /c )—> 0 ( p /c ) -- R2. T7. 0 ( p & q / c ) —> 0 ( q / c ) -- R 2 . T8. ( 0 ( p / c ) & ( p / c —> q /c ))—> 0 ( q / c ) — A3, T7 . T9. ( 0 ( p v q / c ) & ( p / c —> r / c ) & ( q / c —> r / c ) ) —> 0 ( r / c ) - - R 1 , T 8. T 10. 0 ( p v q / c ) —> P ( p / c ) v P ( q / c ) -- R l , T 3 . The p ro o fs of T6 - T10 a r e not g iv en h e re but c a n e a s ily be e s ta b lis h e d by applying th e r u le s , a x io m s, and th e o re m s in d ic a te d a f te r the s ta te m e n t of e a c h th e o r e m . We have not lis te d a ll of the th e o re m s p ro v a b le in H b u t th o s e lis te d a r e am o n g the m o s t im p o r ta n t th e o r e m s involving u n iv e r s a l o b lig a tio n s e n te n c e s . T he P r in c ip le of P e r m is s i o n ( T l ) , the p ro p o s itio n th a t one m a y n e v e r be p e rp le x u s s im p lic ite r ( T5 ) , and th e p ro p o s itio n th a t w h a te v e r is o b lig a to ry is p e r m itte d ( T3 ), a r e p a r tic u la r ly im p o rta n t th e o r e m s w hich one w ould e x p ec t to o c c u r in an y h o riz o n ta l s y s te m fo r o b lig a tio n s e n te n c e s . T he only a x io m s of H r e q u ir e d f o r the p ro o f of T l , T 3 , an d T5 a r e a x io m s A l an d A 2 . The s i m p li c ity and in tu itiv e o b v io u sn e ss of A l and A 2 , and th e im p o rta n c e of the th e o r e m s p ro v a b le f r o m th e m , ju stify th e ir in c lu sio n in H . R l and R 2 , w hich p ro v id e fo r th e d is s o lu tio n of com pound o b lig atio n s e n te n c e s , a r e p e rh a p s m o re c o n tr o v e r s ia l th a n A l and A 2 . N e v e r th e le s s , R l and R2 a r e c le a r ly in a c c o rd w ith o u r c h a r a c te r iz a tio n of the c o n ce p t of u n iv e rs a l o b lig a tio n and h en ce a r e ju s tifia b ly in clu d ed 209 in H. A3 p ro v id e s a fo r m a l s ta te m e n t of the c o m m itm e n t r e la tio n sh ip w hich h a s p ro v e d s o tr o u b le s o m e in p re v io u s ly p ro p o s e d s y s te m s . A3 f o r m a lly s t a te s th e in tu itiv e ly obvious p ro p o s itio n th a t if one is o b lig a ted to p e r f o r m an a ctio n in c e r ta in c ir c u m s ta n c e s , th en th is o b lig a tio n e x te n d s to any a c tio n w hich the f i r s t a c tio n n e c e s s a r ily in v o lv e s. B e s id e s th e o re m s T8 and T 9 , w hich u tiliz e A 3 , we c an p ro v e th e im p o rta n t th e o r e m T i l : ( ( p / c —> q / c ) t F ( q / c ) )—>MD(p/c). T i l s a y s th a t if p e rf o r m in g an a c t in a c e r ta in s e t of c ir c u m s ta n c e s n e c e s s a r il y in v o lv e s p e rf o r m in g an a c t w hich is fo rb id d e n in th o se c ir c u m s ta n c e s , th en th e f i r s t a c t can n o t its e l f be o b lig a to ry in th o se c ir c u m s ta n c e s . P ro o f of T il : (1) ( p / c —> q / c ) & F ( q / c ) -- A s su m p tio n . (2) O ( p/c ) A s su m p tio n . (3) ( p / c —> q / c ) (1), c o n ju n c tio n e lim in a tio n . (4) O ( q / c ) (2), (3), T 8 . (5) F ( q / c ) (1), c o n ju n c tio n e lim in a tio n . (6) O ( q/c ) &F ( q/c ) (4), (5), c o n ju n ctio n in tro d u c tio n (7) ~ < 0 < q / c ) & F ( q / c ) ) — T4 . (8) ~ 0 ( p / c ) (2), (6), (7), re d u c tio ad a b s u rd a m . O ) ( ( p / c —> q / c ) & F ( q / c ) ) —> ~ 0 ( p / c ) -- (1) - (8), deductio n th e o r e m . T he im p o rta n c e of T 8 , T 9 , and T i l , an d the in tu itiv e o b v io u sn e ss of A3 , p ro v id e ju s tific a tio n f o r th e in c lu sio n of A3 in H . B y in tro d u c in g a m o d a l o p e r a t o r f o r p o s s ib ility ( e . g . , M ) 2 1 0 into th e s y s te m H , we could, w ith th e a p p ro p r ia te r u le s of f o r m a tion , s e le c t a x io m s w hich could m a k e e x p lic it th e r e la tio n s h ip s b e tw e e n th e d e o n tic and a le th ic m o d a litie s w hich a r e im p lic itly c o n ta in e d in H . We have a lr e a d y r e s t r i c t e d th e p r o p o s itio n s of H to a c ts w hich a r e " p o s s ib le " h u m a n a c ts . It w ould be d e s ir a b le to have, as th e o r e m s ( o r a x io m s ) of th e ex p an d ed s y s te m , the follo w in g f o r m u la s: 0 ( p / c )—> M ( p / c ), P ( p/c )—>M ( p/c ), F (p /c )—> M (p /c ), -“ ( 0 ( p / c ) &-*-M (p/c ) ) . On th e o th e r hand, the follow ing th e o re m s m u s t not be p ro v a b le in the ex p an d ed s y s te m : M ( p / c ) —> 0 ( p / c ) , M ( p / c ) —> P ( p / c ) , M( p /c ) —> F ( p / c ) . T he a le th ic m o d al o p e r a to r M , h o w e v e r, c an only be u se d in H to s a y of an a c t th a t it is lo g ic ally p o s s ib le in c e r ta in c ir c u m s ta n c e s . A m o r e d e s ir a b le o p e r a to r in a n ex p an d ed s y s te m w ould be an o p e r a to r f o r p h y s ic a l ( p e r h a p s " c a u s a l" ) p o s s ib ility . We sh o u ld then be ab le to e x p r e s s (in the ex p an d ed s y s t e m ) the p ro p o sitio n th a t w h a te v e r is o b lig a to ry in c e r ta in c ir c u m s ta n c e s is p h y sic a lly p o s s ib le in th o se c ir c u m s ta n c e s . T he p h y s ic a l c a p a b ilitie s of the a g e n t and the c a u s a l re la tio n s h ip s of the c ir c u m s ta n c e s in v o lv ed a ll p lay a ro le in d e te rm in in g the p h y s ic a l p o s s ib ility of p e rf o r m in g an a c t. We s h a ll not a tte m p t h e r e a re s o lu tio n of th e d iffic u ltie s w hich m u s t be m e t in o r d e r to a r r i v e a t a s a tis f a c to r y f o r m a l c h a r a c t e r i z a 211 tio n of p h y sic a l p o ss ib ility . A r th u r W. B u rk s, h a s developed a f o rm a l s y s te m fo r the language w hich he c a lls the logic of c a u s a l p r o p o s itio n s . ^ B u r k s ’s s y s te m co n tain s sy m b o ls fo r c a u s a l n e c e s s ity , c a u s a l p o ssib ility , and c a u s a l im p lic a tio n . T he fo r m a l in tro d u c tio n of th e s e sy m b o ls into an expanded h o riz o n ta l s y s te m fo r obligation s e n te n c e s would r e q u ir e ev alu atio n of the com plex r e l a tio n sh ip s of the c a u s a l co n cep ts with e a c h o th e r and w ith the c o n c e p ts of lo g ical n e c e s s ity , lo g ic al p o ssib ility , m a te r ia l im p lica tio n , 13 and s t r i c t im p lica tio n . T he s y s te m H is s i m il a r to the s y s te m s of von W right, R e s c h e r, P r io r , and A n d e rso n in th at it t r e a ts o b ligation s e n te n c e s "T h e L ogic of C a u sa l P ro p o s itio n s , " Mind, 60:363-382, 1951; and "D isp o s itio n a l S ta te m e n ts, " P h ilo so p h y of S cience, 22:175-193, 1955. * ^ "T h e L ogic of C a u sa l P ro p o s itio n s , " p. 363 . The c o r r e c t n e s s of callin g a language a "lo g ic" of anything m ay be d isp u ted but the p r o p e r use of the te r m s ’lan g u ag e' and 'lo g ic ' is not u n d e r d i s c u ssio n h e r e . ^ B u rk s ("D isp o sitio n a l S ta te m e n ts, " p. 176 ) d istin g u ish e s betw een d e g e n e ra te and n o n d e g en e ra te c a u s a l n e c e s s ity a c c o rd in g to the re la tio n sh ip of c a u s a l n e c e s s ity to lo g ical n e c e s s ity ( a n o ndegen e r a te c a u sa lly n e c e s s a r y p ro p o sitio n is c a u sa lly n e c e s s a r y but not lo g ic ally n e c e s s a r y ) . In addition, he defines n o n p ar ado x ic a l c a u s a l im p lic a tio n as a c o m p lex re la tio n s h ip involving m a te r ia l im p lic a tio n and n o n d e g en e ra te c a u s a l n e c e s s ity . V a rio u s ty p es of c a u s a l p o s s i bility can be d istin g u ish ed c o rre sp o n d in g to the ty p es of c a u sa l n e c e s s ity . 2 1 2 as m o d al s e n te n c e s . H d iffe rs f r o m the s y s te m s of von W right and R e s c h e r and is s im ila r to the s y s te m s of P r i o r and A n d e rso n in having p ro p o sitio n a l v a r ia b le s r a t h e r th an v a ria b le n a m e s of a c t- ty p es fo r a rg u m e n ts of th e deontic o p e r a to r s . T he o b lig atio n s e n te n c e s of H a re in te r p r e te d a s u n iv e rs a l o b lig atio n s e n te n c e s - - th ey e x p re s s o b lig atio n s w hich hold fo r a ll m e n in analo gous c ir c u m s ta n c e s . In th is r e s p e c t the s y s te m H d iffe rs f ro m the a b so lu te s y s te m s of von W right ( h is S y ste m I ) , P r i o r , and A n d e rso n . T he o b lig atio n s e n te n c e s of von W rig h t's S y stem II and R e s c h e r 's s y s te m of co n d itio n al obligation, h o w ev er, m ay be in te r p r e te d a s e x p re s s in g u n iv e rs a l o b lig a tio n s. The o p e ra to r O is p r im itiv e in H , and in th is r e s p e c t H d iffe rs fro m a ll of the o th e r p re v io u s ly m en tio n ed deontic s y s te m s . 3. C om b ined O p e ra tio n s of the V e rtic a l and H o riz o n ta l S y ste m s T he v e r tic a l s y s te m (h e n c e fo rth c a lle d 'V ' ) , o u tlined in P a r t 1 of th is c h a p te r, su p p lie s the u n iv e rs a l o b lig a tio n se n te n c e s ( e .g . , 0 ( p / c ) ) a s c o n clu sio n s of th e g e n e r a l p r a c tic a l sy llo g is m . T h u s, the s y s te m V a s s i s t s us in d e te rm in in g w h e th er a u n iv e rs a l o b lig atio n can be s a id to e x is t ( in so m e s e n s e ) . G iven a u n iv e r s a l ob lig a tio n se n te n c e , the s y s te m H th en d isp la y s so m e of the lo g ic al 213 c h a r a c t e r i s t i c s of th a t se n te n c e and the in te r r e la tio n s h ip s of o b lig a tion, p e rm is s io n , and p ro h ib itio n s e n te n c e s . T he s t r i c t l y p r a c tic a l s y llo g is m of the s y s te m V d e s c r ib e s the d e lib e ra tio n p r o c e s s in volved in a n sw e rin g th e q u e stio n , "W hat ought I to do in th is p a r tic u l a r c ir c u m s ta n c e ? " T he m a jo r p r e m is e of th e s t r i c t l y p r a c tic a l s y llo g is m is a u n iv e r s a l o b lig atio n s e n te n c e . If we s e e k a n s w e rs to the q u e stio n s " is th is p a r t i c u l a r a c t p e r m itte d ? " o r " Is th is p a r tic u la r a c t fo rb id d e n ? , " we once m o re u tiliz e the s t r i c t l y p r a c tic a l s y llo g is m - - b u t with a r e f e r e n c e to th e r e s u lts o b tain ed in H . T he follow ing is an in fo rm a l e x a m p le of the co m b in ed o p e ra tio n of V and H . (1) 0 ( p / c ) - - G iv en a s the c o n clu sio n of a g e n e r a l p r a c tic a l s y llo g is m of V . (2) O ( p /c )—> P ( p/c ) -- T3 of H. (3) P ( p / c ) — (1), (2), m odus ponens fo r s t r i c t im p lic a tio n (a x io m of H ) . P ( p / c ) m ay be c o n s id e re d the m a jo r p r e m is e of a s t r i c t l y p r a c tic a l s y llo g is m f o r p e r m is s io n s e n te n c e s . (4) T h is a c t is an a c t of type X and th e s e c ir c u m s ta n c e s a r e of th e ty pe c - - m in o r p r e m is e of a s t r i c t l y p r a c tic a l s y llo g is m of V, fa c tu a lly v e rifie d . (5) T h e re fo re , th is a c t is p e rm itte d - - c o n clu sio n of a s tr ic tly p r a c tic a l s y llo g is m of V , with p r e m is e s (3) and (4). C H A P T E R VI C O N C L U D IN G SU M M A RY A r i s t o t le , St. T h o m a s A q u in a s, a n d K ant a r e a m o n g the m a j o r p h ilo s o p h e r s who h a v e h e ld th a t we m a y h a v e r e c o u r s e to s o m e lo g ic a l p r o c e s s of r e a s o n in g in d e te r m in in g w h e th e r a n a c t s h o u ld o r s h o u ld n o t b e do n e. C e r ta in m o d e r n p h ilo s o p h e r s , h o w e v e r, a d o p tin g th e K a n tia n e m p h a s is on th e i m p e r a tiv e fu n c tio n of o b lig a tio n s e n te n c e s , h a v e r e j e c t e d th e p o s s ib ility th a t o b lig a tio n s e n te n c e s m a y o c c u r a s e le m e n ts in a lo g ic a l in f e r e n c e . * If o b lig a tio n s e n te n c e s a r e i m p e r a t i v e s , th e n th e y c a n n o t be t r u e o r f a ls e , and, o s te n s ib ly , B e r n a r d M ayo, w h o se book, E th ic s an d th e M or a l L ife (L o n d o n , 1958), a p p e a r e d to o la te f o r c o n s id e r a tio n in th e m a j o r s e c tio n s of th is d i s s e r t a t io n , e m p h a s iz e s o u r c o n te n tio n ( see C h a p t e r I ) th a t K a n t in s tig a te d a fu n d a m e n ta l s h if t in e th i c a l t h e o r y . M ayo a s s e r t s th a t m o d e r n e th ic s is a s e t o f fo o tn o te s to K a n t- - th e p o s t - K a n tia n e th ic a l t h e o r i s t s e m p h a s iz e m o r a l p r i n c i p le s , s t r e s s i n g s u c h w o rd s a s ’r i g h t 1 an d 'w r o n g 1 r a t h e r th a n ’good, ' a n d ’d u ty ’ r a t h e r th a n ’v i r t u e . 1 T h e m o d e r n e m p h a s is o n a c tio n s done in a c c o r d a n c e w ith m o r a l p r in c ip le s i s c h a r a c t e r i z e d by M ayo a s a p h ilo s o p h y of d o in g a s o p p o se d to th e t r a d i ti o n a l G r e e k e th ic s of b e in g . T h e i m p o r t a n t m o d e r n e th ic a l q u e s tio n is "W h a t ou g h t I to d o ? W hile th e c o r r e s p o n d in g q u e s tio n f o r P la to a n d A r i s t o t le w as " W h a t ou g h t I to b e ? " T h e d r a w b a c k to th e m o d e r n a p p r o a c h is th a t " a n e th ic s of B e in g m u s t in c lu d e th is o b v io u s fa c t, th a t B e in g in v o lv e s D o in g ;w h e re a s a n E th ic s of D oing . . . m a y e a s ily o v e rlo o k it" ( M ayo, p . 210) . 214 215 s e n t e n c e s w h ic h c a n n o t be t r u e o r f a l s e c a n n o t o c c u r a s e le m e n t s in lo g ic a l i n f e r e n c e s . T h e a l t e r n a t i v e w h ic h we c h o s e to p u r s u e in i n v e s t ig a ti n g th e lo g ic of o b lig a tio n is t h a t o b lig a tio n s e n t e n c e s ( w h e t h e r c o n s i d e r e d t r u e o r f a l s e o r n o t ) m a y o c c u r in i n f e r e n c e s of a d i f f e r e n t ty p e f r o m t h e o r e t i c a l i n f e r e n c e s . We w e r e a b le to d is tin g u is h tw o m a j o r a p p r o a c h e s in th e c o m p a r a t i v e l y r e c e n t a tt e m p t s to c o n s t r u c t f o r m a l i z e d s y s t e m s f o r o b lig a tio n s e n t e n c e s . T h e i m p e r a t i v e a p p r o a c h a t t e m p t s to in c lu d e th e lo g ic o f o b lig a tio n a s a p a r t o f a g e n e r a l lo g ic o f i m p e r a t i v e s . T h is a p p r o a c h w a s sh o w n to be r e l a t i v e l y u n f r u itf u l. S o m e of th e i m p e r a t i v e s y s t e m s m a d e th e i m p e r a t i v e e l e m e n t i t s e l f s u p e r f lu o u s , c o n c lu d in g th a t an i m p e r a t i v e c a n b e d e r i v e d f r o m a n in d ic a tiv e a lo n e . T h e i m p e r a t i v e a p p r o a c h in g e n e r a l c a n n o t h o p e to d is p la y th e lo g ic a l c h a r a c t e r i s t i c s of o b lig a tio n s e n t e n c e s s o lon g a s it f a ils to r e c o g n i z e th e d is tin c tio n b e tw e e n a n o b lig a tio n to p e r f o r m a n a c tio n a n d a c o m m a n d to p e r f o r m a n a c tio n . T h e n o r m a t iv e a p p r o a c h , b e g in n in g w ith v o n W rig h t’s o " D e o n tic L o g ic , 1 1 s h o w s f a r m o r e p r o m i s e of p r o v id in g a n a d e q u a te f o r m a l i z e d s y s t e m f o r o b lig a tio n s e n t e n c e s . T h e o u ts ta n d in g f e a t u r e o f th e n o r m a t iv e a p p r o a c h is th e f a c t th a t i t r e c o g n i z e s a n 2 M ind, 6 0 : 1 - 1 5 , 1951 . 216 indepen dent deontic m o d a lity --o b lig a tio n s e n te n c e s a r e not re d u c e d to s im p le d e s c rip tiv e s e n te n c e s , n o r a r e th ey tr e a te d a s c o m m a n d s. The d eontic m o d a litie s ( obligation, p e rm is s io n , and p r o h ib itio n ) a re analogous to the a le th ic m o d a litie s in m any w ays. By in tro d u c in g o p e ra to rs fo r the deontic m o d a litie s into a s y s te m c o n tain in g p r o p o sitio n s about a c ts ( o r n am es of a c ts ), a s y s te m of m o d al logic m ay be d eveloped fo r o bligation s e n te n c e s s i m il a r to the s y s te m s developed fo r the a le th ic m o d a litie s . A. R. A n d e rs o n 's a tte m p t to 3 re d u c e deontic logic to a le th ic m o d al logic is b a s e d on a m is c o n cep tio n of the ro le which sa n c tio n s play in th e d e te rm in a tio n of o b lig a tio n s. T he re d u c tio n of obligation s e n te n c e s to a le th ic m o dal s e n te n c e s is ju s t a s u n a cc ep tab le as th e ir re d u c tio n to sim p le in d ic a tiv e s o r s im p le im p e r a tiv e s . S e v e ra l of the s h o rtc o m in g s of the s y s te m s b a se d upon the n o rm a tiv e a p p ro a c h can be tr a c e d to a fa ilu r e p ro p e rly to acco u n t fo r the ro le of the c irc u m s ta n c e s affecting any given actio n . C o n s id e ra tion of the b a sic re la tio n s h ip s betw een the o b lig a to rin e s s of an actio n and the c irc u m s ta n c e s involved in p e rfo rm in g th at actio n led us to d istin g u ish th r e e ty p es of ob lig atio n . An a b so lu te obligation is one ^ " R eduction of D eontic L ogic to A lethic M odal L o g ic ," Mind, 6 7 :1 0 0 -1 0 3 , 1958. 217 w hich holda in e v e ry p o ss ib le s e t of c ir c u m s ta n c e s ; a u n iv e rs a l ob - lig a tio n holds f o r a ll m en in analogous s e ts of c ir c u m s ta n c e s ; an in d iv id u al obligation is th e o b lig atio n of th is p a r tic u la r a g e n t to p e r fo rm th is p a r tic u la r a c t. The v e r tic a l re la tio n s h ip s of th e th re e ty p es of oblig atio n se n te n c e a re d e s c rib e d in a s y s te m of s u b s u m p tio n in fe re n c e s ( p r a c tic a l s y llo g is m s ) , the d e ta ils of w hich a r e g iven in S ection 1 of C h a p te r IV . A s m a ll n u m b e r of r u le s p ro v id e d us with a te s tin g p ro c e d u re fo r d e te rm in in g the v a lid m o o d s of the p r a c tic a l s y llo g is m . The g e n e ra l p r a c tic a l s y llo g is m ( a s y llo g is m , the c o n clu sio n of which is a u n iv e rs a l o b lig atio n s e n t e n c e ) was show n to have five v a lid m o o d s. Of th e s e five, only th r e e a r e valid fo r the s tr ic tly p r a c tic a l s y llo g is m ( a sy llo g is m , the c o n clu sio n of w hich is an indiv idu al o b lig atio n se n te n c e ) . The h o riz o n ta l lo g ical re la tio n s h ip s of o b lig atio n s e n te n c e s a r e re le v a n t only on the le v e l of u n iv e rs a l o b lig atio n s e n te n c e s sin c e individ ual o b lig atio n s a r e contingent upon p a r tic u la r c ir c u m s ta n c e s , and we have a s s u m e d th at th e re c an be only one a b so lu te oblig atio n . The s y s te m H , d e ta ils of w hich a r e given in S ection 2 of C h a p te r IV, is an a x io m s y s te m which fo rm a lly d isp la y s s e v e r a l of the h o riz o n ta l lo g ic a l re la tio n s h ip s of o b lig atio n s e n te n c e s . The c o n c ep ts of p ro h ib itio n and p e r m is s io n a re in tro d u c e d d e fin itio n a lly in H in te r m s of obligation. 218 The d ev elo p m en t of s y s te m s fo r o b lig a tio n s e n te n c e s w hose r e s u lts a r e in tu itiv e ly a c c e p ta b le p ro v id e s an a ffirm a tiv e a n s w e r to th e q u e stio n , "Is th e r e a logic of o b lig a tio n ? " F o r m a liz e d s y s te m s , h o w ev er, sh o u ld not be view ed as co n tain in g the a n s w e rs to any m o ra l, le g a l, o r o th e r q u e stio n s involving oblig atio n . T he s y s te m s V and H , f o r e x am p le , m ay r e v e a l the lo g ic a l re la tio n s h ip of one o b lig atio n se n te n c e to a n o th e r, but n e ith e r V n o r H contains any in fo rm a tio n about the o b lig a to rin e s s of any g e n e ra l a c t-ty p e s o r of any p a r tic u la r a c ts . We m ay em p loy the s c h e m a ta of s y s te m s like V and H (and it is o u r c o n ten tio n th a t we do indeed em ploy su c h s c h e m a ta w h e th er c o n sc io u sly o r u n c o n sc io u s ly ) in d e lib e ra tin g about a c tio n s, but the a c tu a l ju d g m e n ts and the re s p o n s ib ility fo r th e m a r e s till o u rs . A L IST O F WORKS C IT E D A n d e rso n , A la n R o s s . T he F o r m a l A n a ly sis of N o rm a tiv e C o n c e p ts. T e c h n ic a l R e p o rt No. 2 , U. S. O ffice of N aval R e s e a r c h C o n tra c t No. S A R /N o n r-6 0 9 ( 16 ) , 1956 . "A R ed u ctio n o f D eon tic L og ic to A leth ic M odal L o g i c ," M ind, 6 7 :1 0 0 -1 0 3 , 1958. A n d e rso n , A lan R o s s , and O m a r K hayyam M o o re . " T h e F o r m a l A n a ly sis of N o rm a tiv e C o n c e p ts ," A m e ric a n S o cio lo g ical R eview , 22:9-17, 1957. A n sc o m b e , G. E . M. In ten tio n . Ith a c a , N. Y . , 1957. A q u in as, St. T h o m a s . S u m m a T h eo lo g ic a , t r a n s . F a th e r s of th e E n g lis h D o m in ic a n P ro v in c e , 2nd ed. 22 vols . L ondon, 1921-25. _____________________ . De V e rita te ( T r u t h ) , t r a n s . R o b e rt W. M ulligan . 3 vols" C hicago, 1952-54 . A r is to tle . N ic o m a c h e a n E th i c s , t r a n s . W. D. R o s s . In R ic h a rd M cK eon, e d . , T he B a sic W orks of A ris to tle . New Y ork, 1941. A y e r, A lfre d J u le s . L an g u ag e, T ru th an d L o g ic , 1st ed. L ondon, 1936. B o h n e rt, H e r b e r t G ay lo rd , " T h e S e m io tic S tatu s of C o m m a n d s, " P h ilo so p h y of S c ie n c e , 12:302-315, 1945. B u rk s , A rth u r W. " T h e L o g ic of C a u sa l P r o p o s itio n s , " M ind, 60:363-38 2, 1951. ____________________. " D is p o s itio n a l S ta te m e n ts, " P h ilo so p h y of S cien ce, 22:175-193, 1955. 219 220 C a rn a p , R udolf. P h ilo so p h y and L o g ic a l Syntax. London, 1935. _________________. T he L o g ic a l Syntax of L a n g u a g e . New Y ork, 1937. _________________ . M eaning and N e c e s s ity , 2nd ed. C hicago, 1956. C a r r i t t, E d g a r F r e d e r i c k . The T h e o ry of M o r a ls . London, 1928. C a ste n a d a , H e cto r N e ri. "T h e L ogic of O bligation, " P h ilo so p h ic a l S tu d ie s, 10:17-23, 1959. C opleston, F r e d e r i c k . A H isto ry of P h ilo so p h y . 4 v o ls. W e s tm in s te r, M d ., 1946-58. D ubislav, W alter, " Z u r U n b e g ru n d b ark e it d e r F o rd e ru n g s s a tz e , " T h e o r ia , 3:330-342, 1937. F itc h , F r e d e r ic k B. (Rev. of G re llin g ’s " Z u r L ogik d e r S o ilsa e tz e " ), J o u rn a l of Sym bolic L ogic, 5:39, 1940. F re g e , G ottlob. "O n Sense and N om inatum , " in H e r b e r t F e ig l a n d W ilfred S e lla r s , e d s ., R ead in g s in P h ilo so p h ic a l A n a ly sis. New Y ork, 1949. F unk and W agnalls N ew S ta n d ard D ic tio n a ry of the E n g lish L an guag e. New Y ork, 1938. G ilson, E tie n n e . The C h ris tia n P h ilo so p h y of St. T h o m a s A quinas. New Y ork, 1956. G re llin g , K u rt. " Z u r L ogik d e r S o llsa e tz e , " U nity of S cience F o r u m , Ja n u a ry , 1939, p p . 44-47. H all, E v e r e tt W, "A C a te g o ria l A n a ly sis of V alue, " P h ilo so p h y of S c ie n c e , 14:333-344, 1947. W hat is V alu e? New Y ork, 1952. H a re , R ic h a rd M erv y n . T he L anguage of M o ra ls . O xford, 1952. H o fsta d te r, A lb e rt, and J . C. C. M cK insey. "O n the L o g ic of I m p e r a tiv e s ," P h ilo so p h y of S cience, 6:446-457, 1939. 221 H um e, D avid. S e lec tio n s, ed. C h a rle s H. H endel, J r . New Y ork, 1927. Jo rg e n s e n , Ju rg e n . " Im p e ra tiv e s and L o g ic ," E rk e n n tn is , 7:288-296, 1938. K ant, Im m a n u e l. C ritiq u e of P u re R easo n , t r a n s . N o rm a n K em p S m ith. London, 1929. C ritiq u e of P r a c tic a l R e a so n and O th e r W orks on th e T h eo ry of E th ic s , tr a n s . T h o m a s K ings m ill Abbott, 6th ed. London, 1909. __________________. M etap h y sics of E th ic s , tr a n s . J . W. S em p le. E dinburg h, 1836. K elsen , H ans. G e n e ra l T h e o ry of L aw and State, t r a n s . A n d re s W edberg. C a m b rid g e, M a s s ., 1949. M cL aughlin, R. N. " F u r t h e r P ro b le m s of D e riv e d O bligation, " Mind, 64:400-402, 1955. M ally, E r n s t. G ru n d g e se tz e des S ollens, E le m ente d e r L ogik d es W illen s. G ra s , 1926. M a rita in , J a c q u e s . F o r m a l L ogic, t r a n s , Im eld a C hoquette, 2nd ed. New Y ork, 1946. Mayo, B e r n a rd . E th ic s and the M o ra l L ife . London, 1958. M eng er, K a rl. "A L ogic of the Doubtful. On O ptative and Im p e ra tiv e L ogic, " R e p o rts of a M a th e m a tic a l C olloquium , 1939. (P u b lic a tio n s of the U n iv e rs ity of N o tre D am e, 2nd s e r i e s , is s u e 1 , pp. 53-64. ) N ow ell-S m ith, P . H. E th i c s . London, 1954. O ppenheim , F e lix E. "O utline of a L o g ic a l A n a ly sis of L a w ," P hiloso phy of S cience, 11:142-160, 1944. P e p p e r, Stephen C. The S o u rc e s of V alue. B e rk e le y , 1958. 222 Poincar£, Henri. Derniferes Pensles, ed. E. Flammarion. Paris, 1913. Prichard, Harold Arthur. Moral Obligation. Oxford, 1949. Prior, Arthur N. "The Paradoxes of Derived Obligation," Mind, 63:64-45, 1954. • Formal Logic. Oxford, 1955. . Time and Modality. Oxford, 1957. Reach, K. "Some Comments on Grelling’s Paper 'Zur Logik der Solliftetze’, " Philosophy of Science Forum, April, 1939, p. 72. Rescher, Nicholas. "An Axiom System for Deontic Logic, ” Philosophical Studies, 9:24-30, 1958. Ross, Alf. "Imperatives and Logic," Philosophy of Science, 11:30-46, 1944. Ross, Sir David. The Right and the Good. Oxford, 1930. . Foundations of Ethics. Oxford, 1939, Runes, Dagobert D., ed. The Dictionary of Philosophy, 1st ed. New York, 1942. Searles, Herbert L. Logic and Scientific Method, 2nd ed. New York, 1956. Stevenson, Charles L. Ethics and Language. New Haven, 1944. Storer, Thomas. "The Logic of Value Imperatives," Philosophy of Science, 13:25-40, 1946, Warner, Rex. The Greek Philosophers. New York, 1958. Webster’s New International Dictionary of the English Language. Springfield, Mass., 1933. 223 W e r k m e is te r , W illiam H. " N o rm a tiv e P ro p o s itio n s and the Id eal of an In te g ra te d and C lo se d S y s te m ," P h ilo so p h y of S c ie n c e , 18:124-131, 1951. . An In tro d u c tio n to C r itic a l T hinking, re v . ed. L incoln, N e b ., 1958. W right, G e o rg H e n ric k von. An E s s a y in M odal L ogic. A m s te rd a m , 1951. "D eontic L ogic, n M ind, 60:1-15, 195L _. "A Note on D eontic L ogic and D e riv e d O bligation, " Mind, 65:507-509, 1956. _. 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Creator Wakin, Malham M. (author)

Core Title The Logic Of Obligation

Contributor Digitized by ProQuest (provenance)

Degree Doctor of Philosophy

Degree Program Philosophy

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag OAI-PMH Harvest,Philosophy

Language English

Advisor Werkmeister, William H. (committee chair), Brackenbury, Robert L. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-48234

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Document Type Dissertation

Rights Wakin, Malham M.

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA