Janusz Kaczmarek
On thought and proposition
Acta Universitatis Lodziensis. Folia Philosophica nr 9, 43-49
1993
ACTA
UNIVERSITATIS
LODZIENSIS
F O L IA P H I L O S O P H IC A 9 . 1993
J a nusz K aczm arek
O N T H O U G H T A N D P R O P O S I T IO N
W e c an easily u n d e rs ta n d th e co n cep t o f p ro p o s itio n in the n a tu ra l way: we
s ta rt fro m an y class o f ju d g m e n ts as
T h e sn o w is w hite,
w hich c an be th o u g h t o r u tte rd by som e people. W h a t is c o m m o n in such
in d iv id u al ju d g m e n ts is u su ally defin ed by the term proposition. H ow ever, we
can ask: w h a t is th e co m m o n o f d ifferen t indiv id u al ju d g m e n ts? O ne usually
answ ers: a c o n te n t o f ju d g m e n t, sense, w hich is in d e p e n d en t o f its u tte ra n c e o r
c o n sciou sn ess o f it. So, in d e p e n d en tly o f th e a u th o r, place a n d tim e o f an
u tte ra n c e o f e.g. P y th a g o re 's th e o re m the c o n te n t o f th is th e o re m is in variable,
is c o n sta n t.
N eth erv eles, as G . F reg e h as re m a rk e d , the sam e c o n te n t (w hich w as called
‘G e d a n k e ’ - th o u g h t, by F rege) c an be includ ed in a d e clarativ e , in te rro g ativ e
o r im p e ra tiv e sentence. It seem s, how ever, th a t w h en w e w a n t to deliv er an
in fo rm a tio n , fo r exam ple: to re n d e r the sense o f P y th a g o re ’s th e o re m w e use
d eclarativ e sentences, w e u tte r ju d g m e n ts. T h u s w e a re inclin ed to c o n clu d th a t
w h a t is co m m o n in d ifferen t ju d g m e n ts is n o t only th e c o n te n t o f the
d eclarativ e sentence b u t also the fo rm o f a de clarativ e sentence. L et us notice
th a t a p p a r t fro m a c o m m o n c o n te n t expressed in u tte re n c es th e re is still one
m o re fa c to r in co m m o n i.e. the form . C o n se q u e n tly in m y view , proposition
co m p re h e n d ed as w h a t is c o m m o n an y class o f ju d g m e n ts is n o t o nly ‘the
c o n te n t', b u t „ th e c o n te n t w ith the fo rm o f d e clarativ e sen ten ce".
In logic tra d itio n , th e p ro p o s itio n is usu ally d efined by m ean s o f the
c o ncepts o f m e a n in g a n d sense i.e. as m ean in g o r sense o f d e clarativ e sentence.
H ow ever h ere a p ro b le m arises, the o n e o f u n ivocal u n d e rs ta n d in g o f th o se
term s. T h e c o n ce p t o f m e a n in g is defined in m a n ifo ld w ays in, for exam ple,
th eo ry o f m ean in g (a m o n g o th e rs J. S. M ill, B. R ussell) a n d th e o ry o f m e a n in g
[43]
44
J a n u s z K a c z m a re k
tre a te d as ideal o b ject (E. H usserl. G . F reg e, A . C h u rch ). N e x t, th e term sense
is the m o st оГеп used intu itively a lth o u g h o n e can find in F reg e o r H usserl the
follow ing d e fin itio n: the sense is so m eth in g „w hich c o n ta in s th e w ay o f being
g iven". T h e re is also th e p ro p o sa l o f A jdukiew icz, w h o defines p ro p o s itio n by
m ean s o f th e c o n ce p t o f c o n n o ta tio n .
Let us sketch o u t som e c h arac te ristic s o f th e n o tio n s o f p ro p o sitio n .
1. F R E G E . I th in k th a t th e analy zis o f F rege text sh aw s th a t u n d e rs ta n ­
d in g G edanke as a proposition is n o t q u ite p ro p e r. F rege w rites: „ In d eclarativ e
sen ten ce tw o th ing s sh o u ld be distinguished: the c o n te n t c o m m o n to th eir
q u e stio n an d assertio n . T h e fo rm e r is a th o u g h t (G e d a n k e) o r includes the
th o u g h t. T h u s, th e th o u g h ts c an be expressed w ith o u t being p u t as true. In
de clarativ e sentences these th in g s a re so united th a t th eir a re h a rd ly distin g u is­
hed (se p arate d ). So we distin g uish
1° g ra sp in g th o u g h t, th a t is th ink in g;
2° a ck n o w led g in g the tru th fu ln e ss o f th o u g h t, th a t is U rteil;
3° a sse rtin g o f U rte il, th a t is a ss e rtio n ” 1.
T h e m o st o fte n U rteil is u n d e rs to o d as the sense o f a de clarativ e sentences
w ith the ex cep tio n o f the case w hen it is id en tified w ith th e very sentence.
H o w ev e r F reg e d istin guishes such senses o f sen tences in view o f w hich the
q u e stio n o f tru th fu ln e ss c an arise from tho se senses in view o f w hich this
q u e stio n d o es n o t a p p ie ars (e.g. in view o f the sense o f im p erativ e sentence). In
Über S in n u nd Bedeutung F rege claim s th a t U rte il is a p assag e fro m th o u g h t to
its v alu e2.
2. C H U R C H . In C h u rc h ’s p a p e r3 w e m eet su ch c h arac te ristic o f p ro p o s i­
tio n . P ro p o sitio n is a n a b s tra c t object (as a fu n c tio n o r class) w ith o u t
psych olo g ical asp ects c h a rac te ristic fo r O c k h am p ro p o s itio m e n ta lis a n d fo r
tra d itio n a l ju d g m e n t. C h u rc h defines proposition by m ean s o f sense o f
a sentence; th e sense o f a sentence bein g eith e r w h a t a m a n a p p re h e n d s w hile
u n d e rs ta n d in g a sentence o r w h a t have tw o sen ten ces being c o rre c t tra n s la tio n
in tw o d ifferen t lan guag es. C h u rc h follow s F ra g e ex p lain in g the term
‘G e d a n k e ’ w hich is to m ean (a n d so te rm ‘G e d a n k e ’ d e note): „ n ic h t das
subjective T u n des D en k en s, so n d ern dessen o b jek tiv en In h a lt, d e r fähig ist,
gem einsam es E ig en th u m v o n V ielen zu sein".
3. C A R N A P . U sing the co n ce p t o f e x tension a n d in te n sio n C a rn a p shaw s
th a t propositions a re in ten sion o f sentences. T r u th v alues a re tre a te d as
ex ten sio n s o f sentences. T h u s, p ro p o s itio n becom es th e p ro p e rty o f tru th
1 СГ. G . F r e g e . D er G e d a n ke. E ine logische U ntersuchung, „ B e iträ g e z u r P h ilo s o p h ie d es
d e u ts c h e n Id e a lis m u s ” . 1918.
2 G . F r e g e . Ü ber S in n u n d B ed e u tu n g , „ Z e its c h rift fü r P h ilo s o p h ie u n d p h ilo so p h is c h e
K r itik ” 1892. C.
3 A . C h u r c h , In tro d u ctio n to M a th e m a tic a l L o g ic , P rin c to n U n iv . P ress, P rin c e to n N . J.
1956.
O n T h o u g h t a n d P ro p o s itio n
45
v alu es4. V an d erv ek en re m a rk s 5 th a t in C a rn a p p ro p o s itio n s a re lim ited to the
tru th c o n d itio n s a n d , co n se q u e n tly , every p ro p o s itio n c an be u n d e rs to o d as
a 0-1 sequence. In Introduction to Sem a n tics C a rn a p tre a ts p ro p o s itio n s as
a d e sig n a tu m o f sentences sim ilarity as a in d iv id uals a re ta k e n fo r d e sig n a tu m
o f in d iv id u al c o n sta n ts 6. In Introduction to S y m bolic Logic p ro p o s itio n s rem ain
d e sig n a ta b u t n o t o f th e in d iv id ual level (i.e. extension o f ind iv id u al c o n sta n ts)
b u t th a t o f th e sense o f in d iv idu als (i.e. in ten sio n o f ind iv id u al c o n s ta n ts )7.
4.
A J D U K IE W IC Z . T h e c o n ce p t o f p ro p o s itio n is in tro d u c e d by m ean o f
the c o n ce p t o f c o n n o ta tio n . H o w ev er A jdukiew icz re m a rk s th a t „ th e fo r­
m u la tio n th a t th e c o n n o ta tio n o f a n am e is th e set o f p ro p e rtie s w hich
un iv o cally d eterm in es its e x tension , c a n n o t be c o n sid e re d as a d e fin itio n o f the
c o n n o ta tio n o f a n am e, since a given class o f objects, fo rm in g th e ex ten sio n o f
a nam e, can be un iv o cally d eterm in ed by d ifferen t sets o f p ro p e rties. A nd
a c o n n o ta tio n o f a n am e is n o t ju s t an y set o f p ro p e rtie s w hich univocally
d eterm in es its ex ten sio n , b u t a set d isting u ish ed a m o n t tho se w hich satisfy th a t
c o n d itio n ” 8. A n aly sin g th e exam ples as
„ th e b ro th e r o f J o h n 's m o th e r”
an d
„ th e m o th e r o f J o h n ’s b ro th e r”
A jdukiew icz co n clu d es th a t „ it is necessary:
1° to d e te rm in e th e c o n n o ta tio n o f th e exp ressio n E in such a w ay th a t its
c o m p o n e n t p a rts sh o u ld be som e o b jectiv e re fe re n ts o f all c o m p o n e n t
e x p ression s o f th e ex p ression E, a n d n o t o nly its c o m p o n e n t nam es.
2° to d e te rm in e th e c o n n o ta tio n o f the exp ressio n E in such a w ay th a t it
s h o u ld reflect n o t only th e w o rd s c o n ta in ed in th a t e x pressio n , b u t also the
s y n tac tic p laces w hich th o se w o rds o ccu py in th e ex p ressio n E " 9.
So, th e c o n n o ta tio n o f the expression E is u n d e rs to o d as the fu n ctio n
d e te rm in e d fo r th e u ltim a te sy ntactic places o f the ex p ressio n o b ta in e d from
the ex pressio n E by th e e x p an sio n o f all th e a b b re v ia tio n s it c o n ta in s, w hich
e stab lish es a o n e-o n e c o rre sp o n d en c e betw een th o se places an d the d e n o ta tio n s
o f th e w o rd s o ccu p y in g such places in th e e x p an d e d exp ressio n E.
T h e d e fin itio n o f c o n n o ta tio n is g eneral a n d it m ay also be used w ith
respect to sentences. So, th e c o n ce p t o f proposition we c a n d efin e as
4 R . C a r n a p . In tro d u ctio n to S y m b o lic L o g ic , D o v e r P u b lic a tio n s . N e w Y o r k 1958.
* D . V a n d e r v e k e n . W hat Is a P roposition?, ..C a h ie r s ď é p is té m ó lo g ie " 1991. № 9103
U n iv e rs ité d u Q u é b e c à M o n tré a l.
6 R . C a r n a p. In tro d u ctio n to S e m a n tic s, H a rv a r d U n iv e rs ity P ress. C a m b rid g e . M ass. 1942.
7 C a r p . In tro d u ctio n to S y m b o lic ...
8 К . A j d u k i e w i c z , P ro p o sitio n u s the C o n n o ta tio n o f S en le n n c c , „ S tu d ia L o g ic a ” 1967,
N o . 21.
4 Ibid.
46
J a n u s z K a c z m a re k
a c o n n o ta tio n o f a sentence. F o r ex am p le th e c o n n o ta tio n (p ro p o sitio n ) o f the
sentence
S o k rate s likes A lcibiades
(1Л )
(1,0)
(1,2)
is th e fu n c tio n estab lish in g a o n e-o n e c o rre sp o n d en c e betw een the syntactic
places o f its w o rd s an d th eir d e n o ta tio n , i.e.:
< (1 ,1 ) - S o crates, (1.0) - likes, (1,2) - A lcibiad es > .
5. A U S T IN , S E A R L E . T h ese a u th o rs p o in t o u t som e specific elem ents o f
(u ttered ) sentences o f d ifferen t type as
С
(*) <
L
Sam sm okes h ab itu ally .
D o es Sam sm o k e h ab itu aly ?
W o u ld th a t Sam sm oked h ab itu aly .
N am ely, w h a t is in co m m o n here is the reference to som e objects and
p re d ic a tin g a b o u t it: the differen ce co n sists in illo c u tio n a ry act: o f a sserting,
a sk in g a b o u t, an d w ishing, respectively. T h u s the co n cep t o f reference and
p re d ic a tio n a re d e ta ch e d from c o m p lete sp each act. T h is reference to objects
an d p re d ic a tio n a b o u t them , a p p e a rin g in d ifferen t illo c u tio n a ry act, a rc called
p ro p o sitio n '0. S entences (*) can be tra n s la te d in to schem es:
('P '), ?’P \ W 'P '
w here P is th e n am e o f p ro p o sitio n .
6. V A N D E R V E K E N . V an d erv ek en , w ho tries to co m bine A u stin ’s and
S earle's a p p ro a c h w ith the results o f F rege an d C h u rc h , u n d e rsta n d s proposi­
tions as a З-elem ents sequence
ll(Rn(a i - ..., a„))|| = < { ||R „ ||, ||a ,||........ ||a„||},
{j £ I: < lla iII(j)........ Ila„||(j)> є IIR-nlIÜ)},
{ f e 2Ua: f( I Aa H) =
1}>,
w here a j, ..., a n are in divid ual c o n sta n ts. R n is p re d ic a te o f degree η, I is non
e m p ty set (th e elem en ts o f w hich rep resen t possible w orld s), Ц*|| designate
d e n o ta tio n o f ex p ressio n *, A a is a a to m ic p ro p o sitio n a l term , w hich have
a p a ir a s a d e n o ta tio n , th a t is
||R n(a ,, ..., a n)|| =
< { | | R J , l|a ,||, ..., ||a n||},
{j є I: < ||a , ||( j ) , ..., ||a „ ||© >
є ||R „ ||(j)} >
a n d U a is th e set o f a to m ic p ro p o s itio n s " .
10 J . L. A u s t i n ,
H o w to D o T h in g s w ith W ords, C la re n d o n P ress. O x fo rd 1962; J . R.
S e a r I e. S peech A c ts . A n E ssa y in th e P h ilo so p h y o f L a n g u a g e, C a m b rid g e U n iv e rsity P ress. 1969.
11 D . V a n d e r v e k e n . M e a n in g a n d S p e e c h A c ts , V ol. 1 2, C a m b rid g e U n iv e rsity P ress.
1990/1991; i d e m . W h a t Is a P roposition...
O n T h o u g h t a n d P ro p o s itio n
47
T h e first elem en t o f th e triplex we call th e set o f p ro p o s itio n a l c o n stitu en ts,
the seco n d elem ent rep resen ts the set o f possible w o rld in w hich th e relatio n
satisfied a n d th e th ird elem ent re p re sen ts tru th co n d itio n s. L et us re m a rk th a t
in set o f p ro p o sitio n a l c o n stitu en ts we sp eak a b o u t senses an d n o t a b o u t
objects. V an d erv ek en speaks: „A ll p ro p o sitio n s a re gen eral p ro p o s itio n s w hose
c o n stitu en ts are senses a n d n o t o b je c ts” 12.
It is the c o n c e p tio n o f V an derv ek en an d th e a p p ro a c h o f A jdukiew icz
m e n tio n d a b ov e th a t seem to th e m o st in teresting . W hy? B ecause th e ir analyzis
o f p ro p o s itio n s in dicates th e necessity o f tra n sfe r to the s tru c tu re o f the
p ro p o sitio n a lo n e , a n d p ro v id es the m a n n e r o f d iscern in g the c o n te n t o f
sentence.
N o w , ľ a m g o ing to d iscuss th e c o n ce p tio n o f V a n d erv ek e n in tw ofold
perspective: p h ilo so p h ic al an d logical.
1.
A cco rd in g to A u stin , Searle a n d V a n d erv ek e n p ro p o s itio n is a c o m ­
p o n e n t o f an illo c u tio n a ry a c t a n d , th u s it a p p e a rs in d ifferen t u tte ra n c e s o f
type (*). In spite o f o u r in tro d u c to ry rem ark s, the fo rm o f d e clarativ e sentence,
w hich d eterm in es th e ty p e o f illo c u tio n a ry a c t is n o t c o n sid e re d a p a rt o f
p ro p o sitio n (a n d o th e r illo c u tio n a ry force m a rk e rs likew ise). O n th e o th e r
h a n d V an d erv ek en te n d s to co m b in e the resu lts o f A u stin a n d Searle w orks
w ith th e ‘p u re ’ logical th eo ries o rig in a tin g fro m F reg e a n d C h u rc h . O n this
g ro u n d it is em p h asized th a t p ro p o sitio n s a re 'k n o w le d g e c a rrie r’ an d th e basic
c o m p o n e n t o f scientific theories. M o reo v er, let us n o tice th a t w e are ra th e r
con cern ed w h e th er P y th a g o re claim s th a t in a rig h t-a n g led trian g le
a 2 + b 2 = c 2 a n d n o t ju s t su p p o ses o r expresses his w ish. F u rth e r, observe
th a t if a th e o re m is tra n s la te d fro m o n e lan g uage to a n o th e r, th e n , to preserve
the sense o f p ro p o s itio n , its form m u st be p ro p e rly ren d ered . O b v io u sly , w e d o
n o t tra n s la te P h y ta g o re ’s th e o re m in to q u estio n . I t seem s th a t th e c o n ce p tio n
o f V an d erv ek en p e rm its su ch s itu a tio n ; the p ro p o s itio n being identical.
T h e re fo re, in m y o p in io n , w h a t V an d erv ek en calls p ro p o s itio n sh o u ld be
refered to as thought (in ideal sense), w hich c o rre sp o n d s to F re g e ’s ‘G e d a n k e ’.
A nd proposition sh o u ld be ack n ow led g e as a th o u g h t in the fo rm o f d eclarativ e
sentences. I h o p e th a t th e a b o v e de fin itio n o f p ro p o s itio n re m a in s in a g re em en t
w ith F reg e claim s:
1° „ P ro p o s itio n (U rteil) fo r m e is n o t g ra sp in g o f th o u g h t (G e d a n k e) also,
b u t recognizing its tru th valu e” ,
2° „ In each p ro p o s itio n - even m o st trivial - th ere is a step m a d e fro m the
level o f th o u g h t to the level o f reference” (i.e. logical v alues in this case) an d
3° „ In te rro g a tiv e a n d d eclarativ e sentences c o n ta in th e sam e th o u g h t; b u t
the d e clarativ e sen ten ce includes a n e x tra, n am ely th e assertio n . A n d the
in te rro g ativ e c o n ta in s an e x tra , nam ely th e re q u e st” 13.
12 V a n d e r v e k e n , W h a t Is a P ro p o sitio n ...
13 F r e g e , D e r G edanke...
J a n u s z K a c z m a re k
48
T h e logical rem ark. T h e co n ce p t o f p ro p o s itio n in V andervekens
2.
fo rm u la tio n is - as w e have re m a rk e d - very g en eral. It is so gen eral th a t in
case o f such sentences as
(**) T h e p re sid en t o f the U S A k n ow s th e m iss o f th e w orld;
th e follow ing p a ra d o x occur: the possible w orld (co n tex t) in w hich the
sentences are tru e are k n o w n , w hile we c a n n o t sp ea k a b o u t th e sense o f such
sentences (p ro p o sitio n s) in a possible w o rld. So it is necessary to build
a d e fin itio n o f p ro p o sitio n w hich w ou ld e n ab le sp ea k in g a b o u t p ro p o sitio n in
po ssib le w orld . E ach p ro p o s itio n co m prises a re la tio n b etw een o bjects w hich
a re u n d e rs to o d in som e aspects (th a t is as co n cep t). L et us re m a rk , how ever,
th a t c o n sid c ra tin g the sense o f a n a m e we m ean the w ay o f ‘bein g given’ o f this
objects. C o n se q u e n tly , a d m itin g the results o f F rag e , in u n d e rs ta n d in g o f
p ro p o sitio n , w e m u st ta k e possible w orld in to a c c o u n t, th a t is the reference to
th e co n ce p t o f objects. T h e sentence (**) expresses d ifferen t p ro p o sitio n s
d e p en d in g o n w e th er u tte re d in 1980 o r in 1990 fo r ex am p le. W hile u tte rin g
this sentence w e express th e p ro p o s itio n in w hich
1) w e m ean som e o bjects (fo r exam p le G . B ush a n d th e m iss X);
2) th ese objects are u n d e rs to o d by m ean s o f c o n c e p t „ b ein g a p re sid e n t”
an d ..b ein g a m iss o f th e w o rld ” ,
3) the o bjects are in a d e q u a te relatio n.
T h en , it seem s, th a t th e d e fin itio n o f p ro p o s itio n given by V anderveken
sh o u ld be a little m odified. D e n o ta tio n o f p ro p o s itio n a l term in po ssible w orld
і is (in case - n = 2):
l|R 2(a |. a2)||i = < {||R 2||, l|a,||, ||a2||}, {||R 2lli, llailh, ||а2||;},
{і o r * } > ,
w here * is g a p an d
||(R 2(a ,, a 2))||i =
< { ||A a ||j}, {f e 2<u »> :f(||A a ||i) =
1}>,
w here A a is a b b re v ia tio n fo r R 2(a i,a 2) a n d U j is set o f all a to m ic p ro p o sitio n
(a to m ic th o u g h t) in possible w o rld i.
T h e m o d ified d efin itio n o f p ro p o s itio n gives us th e possibility to shaw th a t
sentence (**) expresses d ifferen t p ro p o sitio n o nes in d ifferen t c o n te x t o f
u tte ra n c e. M o re o v er, I th in k , the d e fin itio n satisfies th e c o n d itio n s assum ed by
V an d erv ek en. It also seem s th a t the m o d ifica tio n o f sem antics sh o u ld n o t com e
accross g re a te r difficults. F o r exam ple, we define
ІІАр л Bplli =
l|-Ap||i =
< { l|A a ||i} и
{||B a ||;}, id 2( ||A p||i) n
id 2(||B p ||i) > ,
< i d |( ||A p ||i), {f: f є 2и » a n d f ф id 2(||A p ||;)} >
O n T h o u g h t a n d P ro p o s itio n
49
an d
l|t(A p)||j =
T iff exist a t least o ne f є id2(|[A.p||j) such th a t fo r all
u j £ id |( ||A p ||j) [f(uj) =
1 iff id.-ifu,!) = і],
w here Αρ,Βρ a re a b b re v ia tio n fo r term s fo r p ro p o s itio n s , t is sy n categ o rem atic
exp ressio n . t(A p) is an ele m en ta ry sentence o f lan g u ag e L w hich is tru e in
a w orld if an d only if the p ro p o s itio n expressed by A p is tru e in th a t w orld.
D e p a rtm e n t o f Logic
L o d ź U n iv ersity
P o la n d
Ja n u s z K a czm a re k
O M Y Ś L I I S Ą D Z IE W S E N S IE L O G IC Z N Y M
P ojęcie s ą d u w sensie logicznym nic je s t je d n o z n a c z n ie s c h a ra k te ry z o w a n e w lite ra tu rz e
logicznej. J e d n a k ż e w e w sz y stk ich w a żn y ch d e fin ic ja c h w s k a z u je się n a zn a cz en ie, sens lub
k o n o ta c ję z d a ń o z n a jm u ją c y c h .
W a r ty k u le a u t o r p o d a je ró ż n e d efin ic je i c h a ra k te ry s ty k i
w y p ra c o w a n e m . in. p rz ez F reg e g o . C h u rc h a . Ą jd u k ic w ic z a i V a n d c rv o k e n a o ra z w sk a z u je na
g łó w n e c z y n n ik i, k tó re n ale ży p o d d a ć a n a liz ie p rz y o p ra c o w y w a n iu defin ic ji s ą d u .
W y c h o d z ą c od p o jęc ia s ą d u j a k o teg o , co w s p ó ln e w ró ż n y c h s ą d a c h w sen sie p s y c h o lo g ic z ­
n ym a u t o r fo rm u łu je w ła s n ą d efin ic ję s ą d u w sensie lo g iczn y m ta k . a b y u w z g lę d n io n e były:
1) s t r u k t u r a są d u :
2) sen s z d a ń o z n a jm u ją c y c h :
3) m o żliw y św ia t, w k tó ry m d a n e z d a n ie je s t w y p o w ie d z ia n e .