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O N PO P P E R 'S U S E O F T A R S K I ' S T H E O R Y O F T R U T H

I. GRATTAN -GUINNESSIIn a r e c e n t p a p e r , S . Ha a c k h a s c l a ime d th a t Ta r s k i d o e s n o t

p r es e n t his t h e o r y o f t r u t h as a c o r re s p o n d e n ce t h e o r y ) K . R . P o p p e rh a s p o in t e d o u t i n a r e p ly t h a t Ta r s k i does r e g a rd h i s t h e o ry a s ac o r r e s p o n d e n c e t h e o ry . " S in ce e a c h a u th o r g iv es r e f e r e n c e s t oTarsk i ' s wr i t ings to back up h i s pos i t ion , the re seems to be a con t ra -d i c t i o n i n t h e a ir - a n ir o n i c s i t u a ti o n fo r a t h e o ry o f t r u th . P e rh a p sthe co n te x ts o f the passages wi ll r e so lve the d i f f ic u l ty .Popper f i r s t c i t e s th i s passage f rom the beg inn ing o f Tarsk i ' s1 9 35 p a p e r o n t r u t h : ' I w o u l d o n l y m e n t i o n t h a t t h r o u g h o u t t h iswork I sha l l be concerned exc lus ive ly wi th g rasp ing the in ten t ionswhich a re con ta ined in the so -ca l led classical c o n c e p t i o n o f t r u t h( " t r u e - c o r r es p o n d i n g w i th r e a l i t y " ) i n c o n t r a s t , f o r e x a m p l e ,w i th t h e utilitarian c o n c e p t io n ( " t r u e - i n a c e r t a in r e s p e c t u s e-f u l " ) ' : Tw o p a rag ra p h s la t e r , Ta r s k i su mm a r is e s t h e f ir s t s e c t i o n o fh is paper : ' In w co l loqu ia l language i s the ob jec t o f ou r invest iga -t ions . Th e resu l t s a re e n t i re ly nega t ive . W i th respec t to th i s languagen o t o n l y d o e s t h e d e f i n i t io n o f t r u t h s ee m t o b e i m p o s s ib l e, b u t e v e nt h e c o n s is t en t u s e o f t h i s c o n c e p t i n c o n f o r m i t y w i t h t h e l aw s o flogic ' .

Popper ' . s second passage comes f rom a paper o f Tarsk i o f1 9 3 6 : 'W e r e g ard t h e t r u t h o f a s e n t e n c e a s i t s " c o r r e s p o n d e n c ew i th rea l i ty" ,.4 Tw o paragraphs ea r lie r Tarsk i wr i te s : 'T he languagefor w hich such a [ s t ruc tu ra l ] desc r ip t ion can be g iven a re ca l ledformalized languages. No w s in c e t h e d e g re e o f e x a c t i t u d e o f a l lfu r the r inves t iga t ions depends essen t ia l ly on the c la r i ty and p re -c i s ion o f th i s desc r ip t ion , i t is only the semant ics o f forma lisedlanguages wh ich can be construc ted by exact m etho ds ' .Th e imp re s s io n p ro v id e d b y t h e s e c o n t e x t s i s t h a tTa r s k i isr e s t ri c t in g h i s t h e o ry o f t r u th t o f o rma l i s ed l an g u a ge s . Th e im-press ion is co nf i rm ed in the passage f rom Tarsk i ' s 1 944 pa perc i t e d b y Ha a c k . Af t e r d e s c rib in g v a r io u s d e f in i t i o n s o f t r u t h , i n c lu d -

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I. GRATTAN.GUINNESSing th e c o r r e s p o n d e n c e t h e o ry , h e wr i te s : ' n o n e o f th e m i s s u f fi -c i e n t ly p r ec is e a n d c le a r [ . . . ] a t a n y ra t e , n o n e o f t h e m c an b ec o n s id e r e d a s a t i s f a c to ry d e f in i t i o n o f t r u th ' . 5Th u s Ta r s k i a f f irms hi s o w n th e o ry o f t r u th a s a c o r r e s p o n d e n c eth e o ry fo r f o rma l i z e d l a n g u a g e s , b u t i s c h a ry o f d e f in in g t r u th(b y a n y me a n s , a p p a re n t ly ) f o r n a tu r a l l a n g u a g e s . I t h in k t h a tHaack shou ld have made th i s po in t c lea re r by c i t ing the passageswh ic h P o p p e r h a s q u o te d . H o we v e r , h e ~ p a p e r a l r e a d y c o n ta in s ac o m m e n t o n P e p p e r ' s re p l y : ' P o p p e r ta k e s i t - d e s p it e w h a t T a r sk is a y s t o t h e c o n t r a ry - t h a t Ta r s k i 's t h e o ry c a n b e a p p li e d t o n a tu r a la s we ll a s f o rma l l a n g u ag e s '. 6 I n t h a t r e p ly P o p p e r h ims e l f d o e s n o tp o in t o u t t h e d i s t in c t i o n b e twe e n n a tu r a l a n d fo rma l l a ng u a g es ,and seems to co nve y the imp ress ion tha t Tarsk i a sse rt s co r re -s p o n d e n c e a s a t h e o ry o f t r u th fo r n a tu r a l la n g u ag e s a l s o , 'd e s p i t ewh a t Ta r s k i s a y s t o t h e c o n t r a ry ' .I n h is m o re e x t e n d e d wr i ti n g s o n T a r s k i' s t h e o ry , P o p p e r p o in t sou t tha t i t is no t poss ib le to g ive a genera l c r i t e r io n o f t ru th fo rna tu ra l l anguages f l Never the less , he th inks t ha t the v iew tha t Tarsk i 'sde f in i t ion ' is app l icab le on ly fo r fo rm al ized languages is , I th in k ,m i s t a k e n . I t is a p p li c ab l e t o a n y c o n s i s t e n t , a n d e v e n to a " n a tu r a l "language , i f on ly we lea rn f rom Tarsk i ' s ana lys i s how to dodge i t sincons is tenc ies ' . Th us i t app l ie s to ' a w ho le range o f merle o r l essa r t if i c ia l tho ug h no t fo rm al ized languages ' , a Th e a r t i f ic ia l i ti e s in -e lu d e t h e a v o id a n c e o f s e ma n t i c c lo s u re , a n d p r e s u m a b ly t h e i n t ro -d u c t io n o f s o me lo g ic a l m a c h in e ry t o d e f in e s a t i sf a c t io n .P o p p e r d o e s n o t d is cu ss o n e a s p e c t o f Ha a c k ' s p o s i t i o n . S h epo in ts ou t tha t , s ince in Tarsk i ' s theory t rue p ropos i t ions a re sa t i s -f i e d b y a l l s e q u e n c e s , i t d o e s n o t r e ly o n a n y p a r t ic u l a r s e q u e n c e o fo b j e c t s a n d s o a d mi t s a n a ly t ic ca s es - wh e re c o r r e s p o n d e n c e t o t h ef a c ts is n o t e n t a i l e d - as w e l l a s t h e s y n t h e t i c ca se s w h i c h a r eP e p p e r ' s c o n c e rn . 9 P o p p e r m ig h t r e p ly t h a t i t i s t r u th w i t h c o n t e n ttha t i s o f in te res t , wh ich an a ly t ic cases the re fo re necessa r i ly lack .

IITh e o r i e s o f t r u th r e ma in a c o n t ro v e r s i a l i s s u e b e twe e n p h i lo s -o p h e r s . Co r r e s p o n d e n c e t h e o r i s t s s u c h a s P o p p e r , a n d s e ma n t i c sth e o r i s t s s u c h a s Ta r s k i , a r e b o th c h a l l e n g e d b y a d v o c a t e s o f o th e rth e o r i e s , s u c h a s c o h e re n c e , p r a g ma t i sm a n d r e d u n d a n c y , t~ M yp u rp o s e h e r e i s t o c o n s id e r v a r io u s a s p e c t s o f t h e c o r r e s p o n d e n c et h e o r y a s i t i s s i t e d i n P e p p e r ' s p h i l o s o p h y . Seven issues seem tos t an d o u t .

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POPPER'S USE OF TAR SKI'S THE ORY OF TRU TH(1 ) P o p p e r w r it e s t h a t Ta r s k i s o lv e d t h e ' a p p a re n t ly h o p e l e s sp r o b l e m ' o f e l u c id a ti n g t h e n o t i o n o f c o r r e s p o n d e n c e b y r e d u ci n gi t to the ' s impler id ea ' o f sa t is fac t ion . 11 He emphasises that Ta rski ' sd e f in i t i o n o f s a t i s f a c t i o n i s e x e c u t e d w i th r e s p e c t t o f o rma l i z e dlanguages , bu t p resses ahead wi th i t s use in more genera l con tex ts ,wh ere na tu ra l l anguages p resu m ably ob ta in . B u t the re even the' s im ple r ' no t i on o f sa t i s fac t ion p resen ts d i f f icu l t i e s fo r the es tab l i sh .m e n t o f a n a b s o lu t e o b j e c ti v e t h e o r y o f t r u t h . F o r th et c h o i c e o fo b j e c t s o f t h e (p h y s i c a l ) wo r ld as, t h e r e f e r e n t s o f t h e a rg u me n t so f t h e s e n t e n t i a l f u n c t io n s c o u ld i t s e l f b e t h e o re t i c a l , e v e n s u b -j e c t i v e . I f s o m e o n e p o in t s t o t h e s le e pin g c a t a n d s a y s: ' Lo o k , o fcourse snow i s wh i te , ca n ' t y ou see it fo r yourse l f? . ', w ho i s to sayth a t h e i s n o t a c o r r e s p o n d e n c e t h e o r i s t ? I n a p as sa ge c i t e d b y Ha a c k ,Ta r s k i p o in t s o u t t h a t h is t h e o ry is ' c o m p le t e ly n e u t r a l ' t o w a rd sep is temolog ica l pos i t ions - even one , the re fo re , based on mis-id e n t i f i c a ti o n s , o r p o o r k n o wle d g e o f t h e l an g u a ge i n v o lv e d . 12(2 ) ' S n o w is w h i t e ' is a f a v o u r i t e e x a m p le , w i th b o th Ta r s k i a n dP o p p e r , o f t r u th d e f in e d a s c o r r e s p o n d e n c e w i th f a c t s . As su min gth a t s n o w is a c tu a l ly t h e r e f e r e n t o f t h e s t a t e m e n t , th i s e x a m p les tr ik e s o n e a s e x c e l l e n t e x a mp le o f t h e d i f f i c u l t y of assoc ia t ing ano b je c t i v e t h e o ry o f t r u th w i th f a c t s . I s t h e s n o w wh i t e , o r r a th e ro f f -wh i t e b y n o w? Ho w i s i t b e in g l i t , a n y wa y ? F a c t s a r e o f c o u r s eh ig h ly t h e o r y q m p r e g n a t e d , a s P o p p e r h a s e m p h a s is e d o f t e n ; b u tth e n t h e y mu s t b e u n s ui ra b l e c a n d id a t e s f o r t h e s i te o f t h e o b j e c t -iv i ty and a bso lu teness wh ich he seeks .

3 ) As an e x a m p le o f th e la s t p o in t , c o n s id e r t h i s j u d g e m e n t b yP o p p e r : ' T a rs k i's t h e o r y a ll ow s u s [ . . . ] t o d e f i n e r e a l i t y as tha t towh ic h t r u e s t a t e me n t s c o r r e s p o n d ' . ~3 Th i s d e f in i t i o n i s in f a c tcons i s ten t wi th some pos i t iv i s t and even so l ips i s t ep is temolog ies ;i n d e e d , i t ma y b e m o r e i n t u n e w i th t h e m fo r t h e fo l l o win g r e a s o n ,u n r e m a r k e d a n d p r e s u m a b l y u n n o t i c e d b y P o p p e r . T h e s et o f t r u es t a t e me n t s i s d e n u m e r a b l e , s ince i t i s l ex icograp h ica l ly o rde rab le .He n c e r e a l it y is c o m p o s e d o f a d e n u m e ra b l e s e t o f (c la ss es o f )r e f e r e n t s o f t r u e p r o p o s i t i o n s . I d o u b t w h e t h e r o n e c o u l d a c t u a l l yp ro v e o r r e fu t e t h is c l aim in a f o rma l wa y , b u t i t s e e ms to f i t ill w i tht h e c o n c e p t i o n o f r e a l it y t h a t P o p p e r e x p o u n d s at l e n g th el se w h e r e( i ts i n d e p e n d e n c e o f e x p e r i e n c e r s , a n d s o o n ) .( 4 ) I w o u l d m u c h p r e f e r t o s ee P e p p e r ' s e p i s te m o l o g y o r ie n t e dn o t t o wa rd s f a c tu a l t r u th b u t t o wa rd s wh a t e l s e wh e re I h a v e c a l l e d

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I . GRATTAN.GUINNESS'o n t o l o g i c a l c o r r e c t n e s s ' 3 4 Th e o r i e s a r e o n t o l o g i c a l ly c o r r e c t i ft h e y d e sc ri b e h o w t h e p a r t i c u la r p h e n o m e n a a c t u a l l y - t h a t is ,o n t o l o g i c a l ly - o c c u r . ( I a s su m e t h a t w e c o u l d i n v e n t l a n g u ag e ssu f f i c i en t ly r i ch to express such theor i es . ) In a phys ica l w or ldl i k e o u r s , w h e re i t s su b s t a n c e s s e e m t o b e c o m p o se d o f 'm i c ro -s i z e d ' e s s e n c e s a n d i t s c a u sa l c o r r e c t i o n s a r e a t l e a s t n o t e x p e r i -e n t i a ll y o b v i o u s , t h e d i s t in c t i o n b e t w e e n o n t o l o g i c a l c o r r e c t n e s sa n d f a c tu a l t r u t h is im p o r t a n t . F o r e x a m p l e , a t h e o r y c a n b e b o t ho n t o l o g i c a l l y in c o r r e c t b u t f a c t u a l l y t r u e , i f i t d e sc r ib e s p h e n o m e n ai n a w a y t h a t a c t u a l l y d o e s n o t a p p l y b u t w h i c h c o r r e sp o n d s t o t h efa c t s a s w e l l a s e x p e r i m e n t a n d e x p e r i e n c e c u r r e n t l y a l lo w , t sS c i e n ti f ic " th e o ri es a r e o f t e n c o n c e rn e d w i t h 'm i c ro ' r a t h e r t h a ns u r fa c e e f f e c t s; q u a n t u m m e c h a n i c s , o n e o f P e p p e r ' s f a v o u r i tesc i en t if i c a reas , i s fu ll o f exa m ples .(5 ) ' S n o w is w h i t e ' a lso c l e a rl y e x e m p l i f ie s a n o t h e r d i f f i c u l t yi n a p p l y in g Ta r sk i ' s t h e o r y t o g e n e ral c o n t e x t s - n a m e l y , i ts u se o fthe c lassica l logic as the un der ly ing logic . Sn ow is w hi te or i t i sn o t w h i t e , t e r t i u m n o n d a tu r ; b u t o f c o u r se a s I i n d i c a te d i n (2 )a b o v e , sn o w c a n g o t h ro u g h v a r io u s sh a d e s . M a n y s c ie n t if ic t h e o r i e sa lso u se i n e x a c t c o n c e p t s , a n d t o b a se a t h e o ry o f t r u t h a s c o r r e -spondence wi th the fac t s on c l ass i ca l l og ic i s t o re s t r i c t t ha t t heoryo f t r u t h t o a sm a ll c la s s o f p h e n o m e n a . O n t h e o t h e r h a n d , I su sp e c ttha t a cla ss ical und er ly ing log ic cou ld be used w hen t ru th i s de f inedre l a t ive to on to log ica l co r re c tness ; fo r a sc i en t i f i c t he or y is on to log-i c a ll y c o r r e c t o r n o t . (U n fo r t u n a t e l y , w e sh a ll n e v e r b e a b l e t o p ro v et h a t a c o r r e c t t h e o ry is c o r r e c t , f o r t h e n e x t t e s t m i g h t r e fu t e i t; b u tt h a t is a n o t h e r m a t t e r . ) I f t r u t h is to b e d e f i n e d r e l a t iv e t o f a c t s ,w h e t h e r b y c o r r e s p o n d e n c e o r s o m e o t h e r w a y , t h e n I t h i n k t h a tso m e n o n -c l a s s i c a l l o g i c i s n e e d e d , t o t r y t o c a p t u re t h e c o m p o n e n to f vagueness i n o u r t h e o r i e s o f w h i c h ' s n o w is w h i t e ' is su c h a g o o dexa m ple .16(6 ) Th e c o n c e p t o f v a g u e n es s is so m e t i m e s a s so c i a t e d , a n d e v e nc o n fu se d , w i t h t h a t o f b e l i e f. P o p p e r p l a c e s b e l i e f s i n h i s W o r l d 2 o fs u b je c ti v e k n o w l e d g e , b u t o f c o u r s e t h e y c a n b e t h e r e f e r e n t s o fobject ive World-3 theor ies o f be l ie f: a m o n g p s y c h ol o gi st s s t u d y i n gp e r so n a l i t y , f o r e x a m p l e , o r n e u ro p h y s i o l o g i s t s w o n d e r i n g i f b e l i e f sa re exp l i cab le in t e rms o f neura l s t a t e s . Such sc i en t i s t s wi l l need at h e o ry o f t h e r e l a ti o n sh i p b e t w e e n a b e l i e f a n d i t s r e f e r e n t ; a n d t h u sa r i s e s t h e w e l l -k n o w n c r i t i c i sm o f t h e a p p l i c a b i l i t y o f t h e c o r r e -

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POPPER'S USE OF TA RSKI'S THEO RY OF TRU THsp o n d e n c e t h e o ry t o b e l i e f p r e d i c a t e s , n o t o u t o f t h e w a y i n W o r l d 2 ,b u t p r e se n t i n P o p p e r ' s W o r l d 3 o f o b j e c t i v e k n o w l e d g e .P o p p e r m i g h t a s s er t t h a t , s i n ce 'W o r ld 3 is th e w o r l d o f t h ep r o d u c t s o f t h e h u m a n m i n d ' , I T t h e r e e x i s t s a n o b j e c t t o w h i c h t h eb e l i e f c o r r e sP o n d s . B u t , a p a r t f ro m t h e q u e s t io n -b e g g i n g c h a ra c t e ro f t h e a s s e r ti o n (h o w w o u l d o n e k n o w t h a t t h e o b j e c t is therei f t h e b e l i e f h a d n o t b e e n u t t e r e d ? ) , i t su r e l y c a n n o t h a v e th e s a m es t a t u s a s th e f a c t s to w h i c h h is t h e o ry o f t r u t h h a s s t a t e m e n t sc o r r e s p o n d .( 7 ) P o p p e r a f f i r m s t h e e p i st e m o lo g i ca l p r i m a c y o f s t a t e m e n t s ,a n d s e e m s t o r e g a rd a n a l y se s o f c o n c e p t s a s e s s e n ti a li sm o r o rd i n a ry -l anguage ana lys i s , t s Sad ly , he i s ve ry o f t en r igh t ; bu t i n add i t ionthe re a re many cases in sc i en t i f i c t heor i s ing where non-essen t i a l i s tcon cep tua l ana lys i s is requ i red . Fo un da t io na l t heor i es in a sc i encec o n t a i n m a n y e x a m p l e s , e sp e c ia ll y i f th e t h e o r y h a s a m a t h e m a t i c a lc o m p o n e n t . I n d e e d , Tar sk i~s t h e o r y o f t r u t h i t s e lf i s, t o o n e a d m i re r ,a 'success ful descr ipt ion o f a me tho d for def in in g " true "; 19 t h u si t i s a t heo ry o f t he c o n c e p t o f t r u t h . H e n c e a n e x p o s i t i o n o f T a r s k i ' st h e o ry a s a c o r r e sp o n d e n c e t h e o ry fo r n a t u ra l l an g u a g es (w h i c hP o p p e r a s s er ts ) su re l y r e q u i re s so m e c o n c e p t u a l a n a l y si s o f s t a t e -m e n t s (w h i c h P o p p e r d i sp a ra g e s ) .A s I h a v e m e n t i o n e d p o i n ts o f d i s cr e p a n c y b e t w e e n P o p p e r a n dTa r sk i , h ere is a n o t h e r q u o t a t i o n f ro m T a r sk i ' s 1 9 4 4 p a p e r o n t ru t h :' I n f a c t , I a m r a t h e r i n c l i n e d t o a g re e w i t h t h o se w h o m a i n t a i n t h a tt h e m o m e n t s o f g r e a t e s t c r e a t i v e a d v a n c e m e n t i n s c i e n c e f r e q u e n t l yc o i nc i de w i t h t h e i n t r o d u c t io n o f n e w n o t i o n s b y m e a n s o f d e fi n i-t io n ' .20

I I II d r a w t w o c o n c l u s i o n s f ro m t h is d is c u s s io n . F i r s tl y , P o p p e r ' sa d v o c a c y o f t r u t h a s c o r r e s p o n d e n c e t o t h e f a c ts s e e m s t o m e t o b ea p r o b l e m a t i c p a r t o f his e p i s t e m o l o g y , w h e t h e r o r n o t T a r s k i ' ss e m a n t i c t h e o ry is h e l d to e x p l i c a t e t h e m a c h i n e ry o f c o r r e sp o n d e n c e ;t h e e m p h a s i s o n f a c t s r ai se s d o u b t s , a n d e v e n s e e m s o u t o f t u n ew i t h o t h e r a s p e c ts o f h is p h il o s o p h y . S e c o n d l y , a n d m o r e b r o a d l y ,t h e c o m p e t i t i o n b e t w e e n d i f f er e n t th e o bi es o f t r u t h m a y n o t b eo n e f o r t h e possession o f t h e c o n c e p t o f t r u t h b u t a d e m a r c a t i o nd i sp u t e b e t w e e n c o n t e x t s i n w h i c h t h e se t h e o r i e s a p p l y . F o r e x -a m p l e , i n (6 ) o f t h e p re v i o u s s e c t i o n a s c e n a r i o w a s sk e t c h e d i nw h i c h i t w o u l d b e p o s s ib le t o a d v o c a t e o n e t h e o r y o f t r u t h f o r

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I. GRATTAN-GUINNESSbeliefs and another for the scientific investigation of beliefs. I do no tsee why a n y theory of truth should be expected to cover (say)social justice, analytic num ber theory, personality testing, qua ntu mmechanics, paths of projectil es, musical temperamen t, religiousconviction a n d viral inf ecti on; yet these are all topics in which tru thcan have a bearing. It may well be that the problem of definingtruth is u n d e c i d a b l e , and that we need different theories of truthfor different contexts. In other words, we must seek a philosophyof t ru ths .

MIDDLESEX POLYTECHNICQUEENSWAY, ENFIELD

MIDDLESEX EN3 4SFENGLAND

N O T E S

t S. Haack, ' "Is it true what they say about Tarski? " ', Philosophy,51 (1976), 323-336.= K.R. Popper, 'Is it true what she says about T~rski? ', Philosophy, 54(1979), 98.3 A. Tarski, 'The concept of truth in formalised languages' (1931), inLogic, semantics, metamathematics (trans. J.H. Woodger: 1956, Oxford),152-178 (p. 153).4 A. Tarski, 'The establishment of scientific semantics' (1936), in ibM.,404.s A. Tarski, "The semantic conception of truth and the foundations ofsemanties' ,Phllos, phenom, res., 4 (1943-44), 341-375 (p. 343).s Haaek Footnote 1), 323.' See, for example, Pepper's The open society and i ts enemies, vol. 2(1962 ed., London), 369-374; or Ob/ect ive knowledge (1972 ed., Ox-ford), 46, 317-318. On p. 331 of the 1979 edition of the latter workhe repeats his criticism of Haaek.' K.R. Popper, Con/ectures and refutations (1969 ed., London), 223,398-399.Haack (footnote 1), 325.

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P O P P E R 'S U S E O F T A R S K I ' S T H E O R Y O F T R U T H10 Ha a c k p ro v id e s a n e x c e l l e n t s u rv e y in Phi losophy o f logics ( 1 9 7 8 , C a m -

b r i d g e ) , c h . 7 .i t K . R . P o p p e r , The logic o f scient i f ic d iscovery ( 1 9 6 8 e d . , L o n d o n ) ,2 7 4 . I d o n o t u n d e r s t a n d t h e u s e o f ' s i m p l e r ' h e r e . T a r s k i 's t e n - li n e d e f i n -i t i o n o f s a t i s f a ct i o n ( ( f o o t n o t e 3 ) , 1 9 3 ) i s n o t s i m p l e r t h a n t h e t w o - li n ed e f i n i t i o n o f t r u t h (ibid., 1 9 4 ) f r o m a f o r m a l p o i n t o f vi ew . A n d a sP o p p e r i s n o t a n i n s t r u m e n t a l i s t o r c o n v e n t i o n a l i s t , I c a n n o t se e w h ys i m p l i c i t y i s w o r t h c l a i m i n g a n y w a y .

t2 T a r s k i ( f o o t n o t e 5 ) , 3 6 2 ; q u o t e d i n H a a c k ( f o o t n o t e 1 ) , 3 3 0 .~ 3 P o p p e r , Objec t ive knowledge ( f o o t n o t e 7 ) , 3 2 9 .~( S e e m y 'O n P e p p e r ' s p h i l o s o p h y a n d i t s p r o s p e c t s ' , Bri t . / . h i s t . sc i . , 1 2

( 1 9 7 9 ) , 3 1 7 - 3 3 7 ( p p . 3 2 4 - 3 2 6 ) .ts Ib id . , 3 2 6 - 3 3 0 .t~ M y o w n f a v o u r i t e c a n d i d a t e f o r t h i s a p p r o a c h is f u z z y s e t t h e o r y , t h o u g h

I c a n n o t r e c o g n i se t h e v a l i d i t y o f fu z z f f y i n g t r u t h c o n c e p t s th e m s e l v e s ,.a s c a r r i e d o u t i n R . E . B e l l m a n a n d L . A . Z a d e h , ' L o c a l a n d f u z z y l o g i c s' ,i n J . M . D u n n a n d G . E p s t e i n ( e d s. ) Modern uses of multiple-valuedlogic ( 1 9 7 7 , D o r d r e e h t ) , 1 0 5 - 1 6 5 .t~ P o p p e r in h i s a n d J .C . E e c le s ' s T h e sel f and i ts brain ( 1 9 7 7 , B e r l i n ) ,4 4 9 .

** I h a v e i n m i n d t h e t a b l e o f o p p o s i t e s , w h e r e i m p o r t a n t u s e o f p r o p o s i -t i o n s i s c o n t r a s t e d w i t h ( a l le g e d l y ) e s s e n t i a l is t a n a l y s i s o f c o n c e p t s( s e e , f o r e x a m p l e , Conjectures ( F o o t n o t e 8 ) , 1 9 ; Objec t ive knowledge( f o o t n o t e 7 ) , 1 2 4 ) . T h e p o i n t m a d e i n t h i s s e c t i o n a m o u n t s t o a r e q u e s tf o r a m i d d l e c o l u m n t o b e a d d e d t o t h e t a b l e .

~ ) P o p p e r , Objec t ive knowledge ( f o o t n o t e 7 ) , 3 2 8 .2 0 T a r s k i ( f o o t n o t e 5 ) , 3 5 9 .

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