A C T A U N I V E R S I T A T I S L O D Z I E N S I S
__ _ .POLIA PHILOSOPHICA 3 , 1985
Bogdan DJankov
CERTAIN CONSIDERATIONS ABOUT THE EPISTEMOLOGICAL " AND SEMANTIC FOUNDATIONS OF LOGICAL INVESTIGATIONS
AND THEIR APPLICATION
1. I would l i k e to ex p ress most b r i e f l y c e r t a i n th o u g h ts and c o n s id e ra tio n s o f a g e n e ra l c h a r a c te r about th e e p iatem o lo g ic al and sem antic fo u n d a tio n s o f l o g i c a l in v e s tig a tio n s and t h e i r app-l i c a t i o n . Speaking more c o n c re te ly v,hat I mean i s th e n e c e s s i-ty o f a d is c u s s io n o f th e p h ilo s o p h ic a l a s p e c ts o f two b a s ic qu-e s tio n a l 1) th e essen ce anti so u rces o f th e development o f re-se a rc h in th e f i e l d o f th e s o - c a lle d pure l o g i c , and 2 ) th e in -t e r r e l a -t i o n and i n -t e r a c -t i o n be-tween pu re and a p p lie d lo g i c .
I t seems to me a p p ro p ria te to in d ic a te th e m otives which a re prom pting me to b rin g to th e fo re t h a t kind o f q u e s tio n s and which make me b e lie v e t h a t t h e i r d is c u s s io n would be o f « p r in c i p le d t h e o r e t i c a l end m ethodological v a lu e . With a c e r t a i n approxima-t i o n , s e v e ra l b a s ic approxima-ty p es o f c o n s id e ra approxima-tio n s could be adduced, as fo llo w s:
F i r s t o f a l l , i t should be most d e f i n i t e l y n oted th a t owing to th e f a c t o f th e q u it e r a p id ly in c re a s in g d iv erg en ce between contem porary l o g i c a l I n v e s ti g a tio n s , th e view i s o f l a t e more and more c l e a r l y ta k in g shape among some p h ilo so p h e rs t h a t we a rę _ fa -ced w ith a dangerous tendency tow ards a p l u r a l i z a t i o n o f lo g i c . As a m a tte r o f f a c t , th e q u e s tio n comes up o f w hether th e re i s , o r i s n o t, u n ity i n contem porary l o g i c a l i n v e s t ig a t io n s . Of c o u i w
s e , p lu r a lis m d e n ie s th e e x is te n c e o f such u n ity ,
gefcond, i t could be s a id t h a t th e r e i s an im p lic it and g e -n e r a l ly acc ep ted view o f th e u -n iv e rs a l v a l i d i t y o f lo g i c . B ut, i f lo g ic r e a l l y i s a u n iv e rs a l s c ie n c e , what makes i t im p erativ * t h a t th e u n i v e r s a l i t y o f lo g i c a l r e l a t i o n s and laws haa to be rea-l i z e d th ro u g h s u c h ę g r e a t v a r i e t y o f modi o f lo g i c a l u n iv e r s a l !
-ty? Because we, a s a s a t t e r o f f a c t , do speak b oth o f a c l a s s i -c a l and a n o n -c la a s t-c a l l o g i -c , o f en ep iatem i-c end a d e o n ti-c so-cial lo g i c , and so on. But do We n o t in th a t way t o l e r a t e a l o - . g ic a l c o n tr a d ic tio n in th e tre a tm e n t o f th ę very q u e s tio n o f th e u n iV e ra a lity o f lo g i c a l c a te g o rie s » r e l a t i o n s , end laws? A t t h a t l o g i c 's h is to r y i t s e l f i a always th e re to remid us t h a t l i k e any o th e r d eveloping s c i e n t i f i c d i s c i p l i n e lo g io i s an open, i . e . an incom plete th e o ry , which i a s te a d i ly e n ric h in g I t s e l f w ith new system s, •
T h ird , to my mind th e q u e s tio n co n tin u e s to be open o f th e s p e c if i c d i s t i n c t i v e sig n s o f lo g i c a l th e o ry in th e p ro p e r sense o f th e term , w hich, i t ie claim ed , d i f f e r e n t i a t e i t from i t s v a rio u s c o n c re tiz a tia n s * T h is q u e s tio n em erges, sa y , w ith re g a rd , to t^ e d e te rm in a tio n o f th e s p e c if i c lo g i c a l s t a t u s o f quantum lo g i c . As a m a tte r o f f g c t , w ith what r i g h t .and on what grounds do we spea* o f a quantum lo g ic as a lo g ic i n th e p ro p e r w a n in g o f th e term? I s n ot quantuw lo g i c sim ply an in s ta n c e o f a ( l e t US c a l l i t s o ) i^axlmum c o n c r e a tlz a tlo n , o f n o n c le s s ic a l (p o ly v a le n t) l o g i c a l system s w ith .re g a rd to a c o n c re te o b je c t f i e l d ? O r, i s a th r e e - v alu ed lo g ic a l system o f equ al v alency w ith a g iv e n
sys-tem o f quantum lo g ic ? ’ ‘.C
F o u rth , how sh o u ld , from an e x te n s io n a l and an in te n s io n s ! s ta n d p o in t, th e i n t e r r e l a t i o n s h i p o r th e i n t e r a c t i o n be undeiv sto od between purs lo g ic and a p p lie d lo g lc 7 In o th e r w ords, qught n o t a p p lie d lo g ic to be' c o n sid e re d »ą such an e x te n sio n o f a g i
-ven system o f pure l o g i c , i n which o n ly , ' and sim ply determ ined
p a r t i c u l a r e x t r a lc g i c a l o p e r a tio n s ( r e l a t i o n s ) and c o n s ta n ts a re inclu d ed ? Or, i s n o t, on th e o th e r hand, a p p lie d lo g i c a su p er- c o n c re tiz e d i n t e r p r e t a t i o n o f th e l o g i c a l c o n s ta n t o p e r a tio n s ( th e l o g i c a l co n n ec to rs and f u n c to r s ) th ro u g h d e f i n i t e p a r t i c u l a r r e
-l a t i o n s and dependences? i / ;4 ><.-• V. Í-.
I took th e l i b e r t y o f S e ttin g f o r t h th e s e m otives and c o n s i- d e r a tio n s in th e hope 1b a t I w i l l be a b le to proyoke t h i s way an a c tiv e p a r t i c i p a t i o n in th e d is c u s s io n o f th e two q u e s tio n s o f e p r in c ip le d t h e o r e t i c a l end m ethodological ia p o rta n c e f w ith yhioh
I began. I t i s n ot p o s s ib le f o r me h e re to U ndertake * d e t a ile d ; a n a ly s is o f th e s e two q u e s tio n s , and I w ill th e r e f o r e l i m i t «y-
a e \ t to c e r t a i n c o n s id e ra tio n s o f
а
«мre g e n e ra l and programme. ’■ ' ". 1 -f J. ■' ‘Ý-. »■ .
_ The op i c t emo lo g ic a l and «town*lc fu^datlon* ' 129
2 . I f we c a s t a r e tr o s p e c tiv e g lance a t th e h i e to ry o f lo g i c , i t w ill n o t be d i f f i c u l t to f in d t h a t th e r e i e a c e r t a i n p a r a l l e -lism in th e development o f p h ilo so p h ic a l r e s e a r c h , on th e one hand, and formal lo g ic a l in v e s t ig a t io n a , on th e o th e r . There iü a c e r t a i n correspondence b oth between th e c a te g o r ie s o f lo g ic and gnoseology, and th e c a te g o r ie s o f lo g ic and o f o n to lo g y . Of co u r-s e , th e in t e r r e l a t i o n s h i p between th e l o g i c a l and th e o n to lo g ic a l c a te g o r ie s i s o f paramount and d eterm ining im p ortan ce. T his c o rre -l a t i o n m a n ife sts i t s e -l f a -ls o on a g e n e tic p -la n e t the e x te n sio n and p e r f e c tio n o f th e w o rld ’ s o n to lo g ic a l image im p lie s a correaporv- ding development and i n t e n s i f i c a t i o n o f th e div erg en ce tre n d s in th e f i e l d o f th e p ro p e rly lo g ic a l i n v e s t ig a t io n s , o r th e in v e s t i-g a tio n s on th e le v e l o f th e s o - c a lle d p ure lo i-g i c . But each epoch o f l o g i c 's h is to r y n e c e s s a r ily has i t s own q u e s tio n s on th e le v e l o f a p p lie d l o g i c , whose s c a le and im portance a rę determ ined by th e s b c io p r a c tic a l needs o f th e epoch in th e b ro a d e s t sense o f th e te rm , i . e . b o th u nder th e a s p e c t o f th e c o d i f i c a t io n o f th e means and methods o f t h e o r e t i c a l th in k in g and th e t h e o r e t i c a l s u b s ta r - t i a t i o n o f s c ie n c e , and un d er th e a s p e c t o f th e c o d i f i c a t io n o f th e most g e n e ra l means and methods o f th e exp erim en tal and e m p iri-c a l so u riri-ces o f s iri-c i e n t i f i iri-c knowledge. In o u r tim es a l l t h i s assu -mes a q u it e immediate and e v id e n t form o f m a n ife s ta tio n . T his u n do ubtedly b e a rs w itn e ss both o f th e achievem ent o f the n e c e ss
-ary p ro g re ss and o f th e coWing to m a tu rity n o t only along th e l i n e s o f th e g e n e r a l'tr e n d s in th e developm ent o f l o g i c , b u t a ls o o f th e u n q u e stio n a b ly very broad s c a le o f tn e epplied-and-opetbodo- l o g i c a l , and even o f th e a p p lie c M n d - p r a c tic a l, im portance o f th e v a rio u s contem porary l o g i c a l in v e s t ig a t io n s , i f i t i s proceeded in /th a t way, one w ill in th e end e s t a b l i s h an o b je c tiv e o n to lo g i-c a l d e te rm in a tio n b o th o f th e development and th e d i f f e r e n t i a t i o n o f th e lo g i c a l in v e s tig a tio n s on th e le v e l o f th e s o - c a lle d pure lo g i c , and o f th e h e u r i s t i c r o le o f th e l o g i c a l means and methods un d er a m e th o d o lo g ical, and even an a p p lie d - a n d - te c h n o lo g ic a l, as-p e c t.
In t h i s in s ta n c e , however, I would l i k e r a th e r to draw a t -t e n -tio n -t o -th e -two fo llo w in g q u e s -tio n s ; 1 ) . Where Jshould we look f o r th e o b je c tiv e o n to lo g ic a l grounds f o r th e t r a n s i t i o n from c l a s s i c a l to n o n c la s s ic a l lo g ic 7 2) Where should we lo ok f o r th e s p e c i f i c o n to lo g ic a l s t a t u s o f d eo n tio l o g i c p r e c i s e ly as lo g ic ?
C la s s ic a l lo g ic not only assum es, b u t a ls o h y p o s ta tiz e s th e r e s t in th e th in g s t h a t make r e a l i t y . I t i s only on th e s e grounds t h a t о th in g can he p re d ic a te d as a t h i n g - l n - i t s e l f , o r as a th in g • e s s e n t i a l l y d i f f e r e n t o f it* We b e lie v e t h a t c l a s s i c a l l o g i c 's o n to lo g ic a l b a s is i s not sim ply r e s t , b u t r a th e r th é s ta tio n a r y » ^ i . e . n o t only th e r e s t o f tH e o b je c tc , but e q u a lly th e s te a d i-n ess ai-nd r e s i s t i v i t y o f th e form o f th e chai-nge, ii-n o th e r words re-g u l a r i t y re-g e n e ra lly .. But modern s c ie n c e has c l e a r l y shown t h a t i t i s n o t r e ti t, b ut motion which i s th e e s s e n t i a l and b a s ic charac-t e r i s charac-t i c o f b ein g . I f t h i s i s ao , however, i t means t h a t n o t only s c ie n c e g e n e r a lly , b u t lo g ic i t s e l f has to f i x and c o d ify , w ith th e a id o f co n cep ts and in a system o f c o n c e p ts , a ls o th e t r a n s i t i o n s between th in g s . And i t i s b u t n a t u r a l t h a t in th a t- case th e c ateg o ry o f t r a n s i t i o n snould a ls o be acknowledged « s t a t u s o f a l o g i c a l c a te g o ry , because th e tra n s fo rm a tio n o f non- tr u t h in to t r u t h and v lc e - v e r a a , i s a ls o a p ro c e s s . A ty p i c a l low g lc a l model o f t h i s s t a t e o f th in g s cou ld be found in th r e e v alued lo g i c . F u r th e r, motion as change c o n ta in s p o s s i b i l i t y as i t s im-manent dim ension. Hence th e system o f modal c a te g o r ie s p r e s e n ts to u s , in a b s tr a c tio n , th e l o g i c a l model o f th e p o s s i b i l i t i e s in th e r e a l i z a t i o n o f th e modi o f th e e x is te n c e o f being in a most g e n e ra l s h a p e ... In a d e f i n i t e way th e q u e s tio n s o f th e o n to lo g i-c a l fo u n d a tio n s o f th e i-c o n s t r u i-c t i v i s t i i-c i-co n i-cep tio n o f i n f i n i t y and hence o f th e c o n s t r u c t i v i s t i c e x p la n a tio n o f th e q u e s tio n o f infi*. n i t y w ith in th e system o f a c o n s tr u c tiv e lo g i c , can a ls o be con-nected w ith t h i s .
Sure enough, th e e x te n sio n o f o u r o n to lo g ic a l image **f th e world i n th e f i n a l count f in d s a more g e n e ra l e x p la n a tio n in th e l o g i c a l p ic tu r e o f th e on to lo g y o f b ein g .
But I would l i k e to a t once add t h a t h e re a d i f f e r e n t e sse n -t i a l dim ension o f -th e w o rld ’ s o n -to lo g ic a l p ic -tu r e from a lo g i c a l view po in t could a le o be n o te d . W hat.I more c o n c re te ly mean, i s t h a t th e o n to lo g ic a l p i c t u r e o f th e w o r l d - i n - i t s e l f i s e s s e n t i a l l y d i f f e r e n t from th e w o rld 's o n to lo g ic a l p i c t u r e w ith a view to th e p a r t i c u l a r o n to lo g ic a l s t a t u s o f m an's a c tiv e and c r e a tiv e e sse n - c e . And, as a m a tte r o f f a o t , > i t i s w ith rnaft o n ly t h a t we have such a tra n s fo rm a tio n o r r e - c r e á tio n o f th e w orld, which i s con-formed t9 h is w ill and d e s i r e , i t i s w ith him only t h a t we have a p ro g n o s tic a tio n ( i r r e s p e c t i v e o f th e l e t t e r ’s d eg ree o f ap p ro x i-.« ' • • ’ • •" r * '..V ' V ť I А • ". *• ’
m ation) o f th e r e s u l t s and advantages o f such a tra n s fo rm a tio n and re -sh a p in g o f r e a l i t y f o r th e b e n e f it o f man. But reaso n in g from t h i s f a c t , th e o n to lo g ic a l fo u n d atio n o f d e o n tfc lo g ic a lre a d y becomes a p p a re n t. In t h i s c a s e , however, i t a t once becomes d e a r t h a t d e o n tic lo g ic re q u ire s us to q u ite s u b s t a n t i a l l y extend o u r n o tio n o f l o g i c '3 o n to lo g ic a l fo u n d a tio n s g e n e r a lly . I t i s only th e n t h a t I t s fundam ental c h a r a c te r o f lo g i c , i . e . th e f a c t t h a t i t lias not to be numbered as one o f th e v a rio u s a p p lie d lo -g ic s (as some p h ilo so p h e rs b e lie v e i t ou-ght t o ) , can be su b stan -t i a -t e d .
The above c o n s id e r a tio n s , however, g e n e ra l and schem atic th ey may b e, show t h a t th e p re s e n tly e x is tin g v a r ie ty in th e f i e l d o f contem porary l o g i c a l in v e s tig a tio n s i s in r e a liz y d eeply pervaded w ith d e f i n i t e u n ity , a u n ity which h a s , f i r s t and fo rem o st, i t s o n to lo g ic a l fo u n d a tio n s , and hence, d e f i n i t e s p e c i f i c a l l y gnoseo-l o g i c a gnoseo-l , but a ls o h is to r i c a l- a n d - g e n e tic foundations» I T h erefo re any i n t e r p r e t a t i o n o f th e v a r ie ty in th e f i e l d o f lo g ic as lo g ic a l p lu ra lis m , i s unfounded.
Such an approach, however, prompts us to b e lie v e t h a t th e most g e n e r a l, o r u n iv e r s a l, c h a r a c t e r i s t i c s o f b e in g , which a re l o g i c 's o b je c tiv e fo u n d a tio n , have n o t, and p robably can n o t ha-ve only one r e a l i z a t i o n modus. We have grounds to b e lie v e t h a t under an in te n s io n a l a s p e c t and in b e in g 's d eep e r s tr u c tu r e th e re a re v a rio u s ranks o f u n iv e rs a l c h a r a c t e r i s t i c s and r e l a t i o n s , which in r e a l i t y determ ine th e v a rio u s ty p o s o f l o g i c a l t h e o r i e s . That rank i s more e s s e n t i a l , which to a g r e a t e r e x te n t doterminc-s th e dynamism o f b ein g . In th i 3 sense th e sem an tics on n o n c la s s i- c a l lo g ic i s r i c h e r th a n th e sem antics o f c l a s s i c a l lo g i c , ahd so i s th e sem an tics o f d e o n tic lo g ic w ith re s p e c t to th e sem antics o f sta n d a rd modal lo g io . S t r i c t l y sp e a k in g , however, every lo g ic a l system i s incom plete a s from a g e n e ra l sem antic a n g le , because none i s s u f f i c i e n t to r e a l i z e an adequate d e s c r ip tio n o f being i n th e p ro p e r sen se o f th e term . Hence lo g ic w ill always be in a s t a t e o f permanent developm ent, i . e . i t w ill always rem ain an open system .
A pplied lo g ic d i f f e r s from p u re lo g i c m ainly by th e f a c t t h a t by t h e i r ty p e th e g e n e ra l c h a r a c t e r i s t i c s and r e la tio n e i t in v e s t ig a t e s , a re n o t o f the. rank o f u n iv e r s i ty o f th e
charac-t e r i s charac-t i c s and r e la charac-t io n s in v e s charac-tig a charac-te d by pure lo g ic . That i s why a p p lie d lo g ic ia always a c o n e r e tiz a tio n o f a given system o f pure logic*
B u lg a rian Academy o f S cien ces
Bogdan DJankov KILKA UWAG
0 EPISTEMOLOGIOZNYCH I SEMANTYCZNYCH PODSTAWACH BADAN LOGICZNYCH I ICH ZASTOSOWANIE
Celem a rty k u łu J e s t dyskusja pewnych o g ó ln y c h ,e p iste m o lo g ic z - nych i semantycznych podstaw badaA lo g iczn y ch . O sią rozważań sa p y ta n ia o 1) i s t o t ę i ź ró d ła rozwoju tzw . lo g i k i c z y s te j i 2 ; związek lo g i k i c z y s te j z lo g ik ą stosow aną. A utor s t a r a s i$ przy tym u zasad n ić dlaczego t a k i w ła śn ie dobór k w e s tii p o siad a zasad n i-czą te o re ty c z n ą i m etodologiczną w a rto ść , by po ty » u d z i e lić odpo-w ied zi na postaodpo-w ione p y ta n ia .
