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
FOLIA PHILOSOPH ICA 9, 1993
Janusz Kaczm arek
ON T H O U G H T A N I) PR O PO SIT IO N
Wc can easily understan d the concept o f pro p o sitio n in the n a tu ra l way: we start from any class o f judgm ents as
T h e snow is white,
which can be th o u g h t or utterd by som e people. W hat is com m on in such individual ju d g m en ts is usually defined by the term proposition. H ow ever, we can ask: w hat is the com m on o f different individual judgm ents? O ne usually answers: a co n ten t o f ju d g m en t, sense, which is independent o f its utterance or consciousness o f it. So, independently o f the a u th o r, place an d tim e o f an utteran ce o f e.g. P ythagore’s theorem the co n ten t o f this theorem is invariable,
is co n stan t. ,
N etherveles, as G . Frege has rem arked, the sam e co n ten t (which was called ‘G e d a n k e ’ - th o u g h t, by Frege) can be included in a declarative, interrogative o r im perative sentence. It seems, however, th a t w hen we w ant to deliver an inform ation, for exam ple: to render the sense o f P y th a g o re’s theorem we use declarative sentences, we u tter judgm ents. T hus we are inclined to conclud th at w hat is com m on in different judgm ents is no t only the co n ten t o f the declarative sentence bu t also the form o f a declarative sentence. Let us notice th a t a p p a rt from a com m on co n ten t expressed in utterences there is still one m ore facto r in com m on i.e. the form . C onsequently in m y view, proposition com prehended as w hat is com m on any class o f ju d g m en ts is n o t only ‘the c o n te n t’, bu t „th e co n ten t w ith the form o f declarative sentence” .
In logic trad itio n , the prop o sitio n is usually defined by m eans o f the concepts o f m eaning an d sense i.e. as m eaning or sense o f declarative sentence. H ow ever here a problem arises, the one o f univocal u n d erstan d in g o f those term s. T he concept o f m eaning is defined in m anifold w ays in, for exam ple, theory o f m eaning (am ong o thers J. S. M ill, B. Russell) an d theory o f m eaning
treated as ideal object (E. H usserl, G . Frege, A. C hurch). N ext, the term sense is the m ost ofen used intuitively although one can find in Frege o r H usserl the follow ing definition: the sense is som ething „w hich contains the way o f being given . T here is also the proposal o f A jdukiewicz, w ho defines p ro p o sitio n by m eans o f the concept o f co n n o tatio n .
Let us sketch ou t som e characteristics o f the n otions o f proposition. 1. F R E G E . I think th at the analyzis o f Frege text shaws th a t u n d e rsta n -ding Gedanke as a proposition is not quite proper. Frege writes: „ In declarative sentence tw o things should be distinguished: the co n ten t com m on to their question and assertion. T he form er is a th o u g h t (G edanke) o r includes the thought. T hus, the th o u g h ts can be expressed w ithout being put as true. In declarative sentences these things are so united th a t their arc hardly distinguis-hed (separated). So we distinguish
1° grasping th o u g h t, th a t is thinking;
2° acknow ledging the truthfulness o f th o u g h t, th a t is U rteil; 3° asserting o f U rteil, th a t is assertio n ” 1.
T he m ost often U rteil is u n derstood as the sense o f a declarative sentences with the exception o f the case when it is identified with the very sentence. H ow ever Frege distinguishes such senses o f sentences in view o f which the question o f truthfulness can arise from those senses in view o f which this question does not appiears (e.g. in view o f the sense o f im perative sentence). In Über Sinn und Bedeutung Frege claim s th a t U rteil is a passage from th o u g h t to its value2.
2. C H U R C H . In C h u rc h ’s p a p e r3 we m eet such characteristic o f p ro p o si-tion. P ro p o sitio n is an ab stra ct object (as a function or class) w ithout psychological aspects characteristic for O ckham p ro p o sitio m entalis an d for trad itio n al ju dgm ent. C hurch defines proposition by m eans o f sense o f a sentence; the sense o f a sentence being either w hat a m an ap p reh en d s while u n d erstanding a sentence o r w hat have two sentences being correct tran slatio n in tw o different languages. C hurch follows F rage explaining the term ‘G e d a n k e ’ which is to m ean (and so term ‘G e d a n k e ’ denote): „nicht das subjective T un des D enkens, sondern dessen objektiven Inhalt, d er fähig ist, gem einsam es E igenthum von Vielen zu sein” .
3. C A RN AP. Using the concept o f extension and intension C a rn a p shaw s th a t propositions are intension o f sentences. T ru th values are treated as extensions o f sentences. T hus, prop o sitio n becomes the p ro p erty o f tru th
1 Ct. G . F r e g e , D er Gedanke. Eine logische Untersuchung. „Beiträge zur Philosophie des deutschen Idealismus” , 1918.
2 G. F r e g e , Über Sinn und Bedeutung. „Zeitschrift für Philosophie und philosophische Kritik" 1892. C.
3 A. C h u r c h , Introduction to M athem atical Logic, Princton U niv. Press, Princeton N J 1956.
values4. V anderveken re m a rk s5 th at in C arn a p p ropositions are limited to the tru th conditions and, consequently, every proposition can be u n derstood as a 0 I sequence. In Introduction to Sem antics C a rn a p treats p ropositions as a designatum o f sentences sim ilarity as a individuals are taken for designatum o f individual c o n stan ts'1. In Introduction to Sym bolic Logic p ro p o sitio n s rem ain designata but not o f the individual level (i.e. extension o f individual co n stan ts) but th at o f the sense o f individuals (i.e. intension o f individual c o n sta n ts)7.
4. A JD U K IE W IC Z . The concept o f p roposition is intro d u ced by m ean o f the concept o f c o n n o tatio n . H ow ever A jdukiew icz rem arks th a t „th e fo r-m ulation th at the co n n o ta tio n o f a nar-m e is the set o f p ro perties which univocally determ ines its extension, ca n n o t be considered as a definition o f the c o n n o tatio n o f a nam e, since a given class o f objects, form ing the extension o f a nam e, can be univocally determ ined by different sets o f properties. A nd a c o n n o ta tio n o f a nam e is not ju st any set o f p ro perties which univocally determ ines its extension, but a set distinguished am o n t those which satisfy that c o n d itio n ” 8. A nalysing the exam ples as
„th e b ro th e r o f J o h n ’s m o th e r” and
„th e m oth er o f J o h n ’s b ro th e r"
A jdukiew icz concludes th at „it is necessary:
1° to determ ine the c o n n o tatio n o f the expression E in such a way th a t its co m ponent p a rts should be som e objective referents o f all co m ponent expressions o f the expression E, and not only its co m p o n en t nam es.
2° to determ ine the c o n n o tatio n o f the expression E in such a way th at it should reflect no t only the w ords contained in th a t expression, but also the syntactic places which those w ords occupy in the expression E” 9.
So, the c o n n o ta tio n o f the expression E is un d ersto o d as the function determ ined fo r the ultim ate syntactic places o f the expression o b tain ed from the expression E by the expansion o f all the abbrev iatio n s it contains, which establishes a one-one correspondence between those places and the d en o tatio n s o f the w ords occupying such places in the expanded expression E.
T he definition o f co n n o tatio n is general and it m ay also be used with respect to sentences. So, the concept o f proposition we can define as
4 R. C a r n a p , Introduction to Sym bolic Logic, Dover Publications, N ew York 1958. 5 D. V a n d e r v e k e n , H’licil Is a Proposition?, „Cahiers d'épistém ólogie” 1991, № 9103 Université du Québec ä Montreal.
6 R. C a r n a p, Introduction to Semantics, Harvard University Press, Cambridge. M ass. 1942. 1 C a r p , Introduction to Sym bolic...
* K. A j d u k i e w i c z , Proposition as the Connotation o f Sentennce, „Studia Logica" 1967, N o. 21.
a c o n n o tatio n o f a sentence. F o r exam ple the c o n n o tatio n (proposition) o f the sentence
S okrates likes A lcibiades ( U ) (1,0) (1 ,2 )
is the function establishing a one-one correspondence between the syntactic places o f its w ords and their d en o tatio n , i.e.:
< ( U ) Socrates, (1,0) likes, (1,2) A lcibiades> .
5. A U S T IN , S E A R L E . T hese au th o rs p o in t o u t som e specific elem ents o f (uttered) sentences o f different type as
{
Sam sm okes habitually.D oes Sam sm oke habitualy?W ould th a t Sam sm oked habitualy.
Namely, w hat is in com m on here is the reference to som e objects and predicating ab o u t it; the difference consists in illocutionary act: o f asserting, asking ab o u t, and wishing, respectively. T hus the concept o f reference and predication are detached from com plete speach act. T his reference to objects and predication about them , appearin g in different illocutionary act, are called propositionl0. Sentences (*) can be translated into schemes:
(’F ) , ?’P \ W 'P ’
where P is the nam e o f proposition.
6. V A N D E R V E K E N . V anderveken, w ho tries to com bine A ustin’s and Searle s ap p ro ach with the results o f Frege and C hurch, u nderstands proposi-tions as a 3-elements sequence
ll(R n(ai... a n))|| = < {II R n II, II a i II... ||an||},
{j 6 I: < IIa,II(j), ..., ||an||(j)> e ||R J ( j) } , {f 6 2Ua; f(IIA a II) = 1 } > ,
where a b ..., a n are individual constants, R n is predicate o f degree n, I is non em pty set (the elem ents o f which represent possible w orlds), ||*|| designate d en o tatio n o f expression *, A ;1 is a atom ic p re p o sitio n al term , which have a p air as a d en o tatio n , th a t is
II R n(a i, .... a n)|| = < { | | R n||, II a i II... ||an||},
{j 6 I: < l|aj II(j), ..., ||an||(j)> 6 ||R n||(j)}> and U a is the set o f atom ic p ro p o sitio n s11.
10 J. L. A u s t i n , How to D o Things with Words, Clarendon Press, Oxford 1962; J. R. S e a r l e , Speech Acts. An Essay in the Philosophy o f Language. Cambridge University Press, 1969.
D. V a n d e r v e k e n , Meaning and Speech Acts, Vol. 1-2, Cambridge University Press, 1990/1991; i d e m , What Is a Proposition...
The first elem ent o f the triplex we call the set o f p ropositional constituents, the second elem ent represents the set o f possible w orld in which the relation satisfied an d the third elem ent represents tru th conditions. Let us rem ark th at in set o f p ropositional constituents we speak ab o u t senses and not ab o u t objects. V anderveken speaks: „A ll propositions are general propo sitio n s whose constituents are senses an d not objects” 12.
It is the conception o f V anderveken and the ap p ro ach o f Ajdukiew icz m entiond above th a t seem to the m ost interesting. W hy? Because their analyzis o f p ropositions indicates the necessity o f tran sfer to the stru ctu re o f the pro p o sitio n alone, and provides the m anner o f discerning the co n ten t o f sentence.
N ow , I am going to discuss the conception o f V anderveken in tw ofold perspective: philosophical and logical.
1. A ccording to A ustin, Searle and V anderveken prop o sitio n is a co m -p onent ol an illocutionary act and, thus it a-p -p ears in different utterances o f type (*). In spite o f o u r in tro d u cto ry rem arks, the form o f declarative sentence, which determ ines the type o f illocutionary act is not considered a p a rt o f proposition (and o th er illocutionary force m arkers likewise). O n the o ther h and V anderveken tends to com bine the results o f A ustin and Searle w orks with the ‘p u re ’ logical theories originating from Frege and C hurch. O n this gro u n d it is em phasized th a t propositions are ‘know ledge ca rrier' and the basic co m ponent o f scientific theories. M oreover, let us notice th a t we are rath er concerned w hether P ythagore claim s th at in a right-angled triangle a 2 + b 2 = c2 an d not ju s t supposes o r expresses his wish. F u rth er, observe th a t if a theorem is translated from one language to a n o th er, then, to preserve the sense o f p roposition, its form m ust be properly rendered. O bviously, we do not tran slate P hytag o re’s theorem into question. It seems th a t the conception o f V anderveken perm its such situation; the p ro p o sitio n being identical.
T herefore, in my opinion, w hat V anderveken calls prop o sitio n should be refered to as thought (in ideal sense), which co rresponds to F rege’s ‘G e d a n k e ’. A nd proposition should be acknow ledge as a th o u g h t in the form o f declarative sentences. I hope th a t the above definition o f p ro p o sitio n rem ains in agreem ent with Frege claims:
1° „P ro p o sitio n (U rteil) fo r me is no t grasping o f th o u g h t (G edanke) also, bu t recognizing its tru th value” ,
2° „In each p ro p o sitio n - even m ost trivial - there is a step m ade from the level o f th o u g h t to the level o f reference” (i.e. logical values in this case) an d 3° „In terro g ativ e and declarative sentences con tain the sam e thought; bu t the declarative sentence includes an extra, nam ely the assertion. A nd the interrogative contains an extra, nam ely the request” 13.
12 V a n d e r v e k e n , What Is a Proposition... 13 F r e g e , Der Gedanke...
2. T he logical rem ark. T he concept o f p ro p o sitio n in V andervekens form ulation is - as we have rem arked very general. It is so general th at in case o f such sentences as
(**) T he president o f the U SA know s the miss o f the w orld;
the lollow ing paradox occur: the possible w orld (context) in which the sentences are true are know n, while we ca n n o t speak ab o u t the sense o f such sentences (propositions) in a possible world. So it is necessary to build a definition o f proposition which w ould enable speaking a b o u t prop o sitio n in possible w orld. Each proposition com prises a relation between objects which are understood in som e aspects (th a t is as concept). Let us rem ark, however, th at considerating the sense o f a nam e we m ean the way o f ‘being given’ o f this objucts. C onsequently, adm iting the results o f F rage, in understan d in g o f proposition, we m ust take possible w orld into account, th at is the reference to the concept o f objects. T he sentence (**) expresses different propositions depending on w ether uttered in 1980 o r in 1990 for exam ple. W hile uttering this sentence we express the p roposition in which
1) we m ean som e objects (for exam ple G . Bush and the miss X); 2) these objects are understood by m eans o f concept „being a presid en t” and „being a miss o f the w orld",
3) the objects are in ad eq u ate relation.
T hen, it seems, that the definition o f p ro p o sitio n given by V anderveken should be a little m odified. D e n o ta tio n o f p ropositional term in possible world i is (in case - n = 2):
l|R2( a i , a2)||i = < { | | R 2 ||, lla ,||, ||a2 ||}, { | | R2|li, ||а ,||ь ||a2|li},
{i o r * } > , where * is gap and
IKR2(ai, a2))||j = < { IIAa||i}, {f 6 2*u“> :f(||Aa||j) = 1 } >,
w here A a is abbreviation for R 2( a |,a 2) and UJ is set o f all atom ic proposition (atom ic th o u g h t) in possible w orld i.
T he m odified definition o f proposition gives us the possibility to shaw that sentence (**) expresses different pro p o sitio n ones in different context o f utterance. M oreover, I think, the definition satisfies the conditions assum ed by V anderveken. It also seems th at the m odification o f sem antics should not com e accross greater difficults. F o r exam ple, we define
HAp A Bplh = < { IIAa ||i} u {||Ba ||i}, id2(||ApHi) n id2(||B p ||i) > , 11-ApHi = < id , ( IIApHi), {f: f e 2U* and f ф id2(IIAp ||j)}>
and
l|t(A p)||i = T iff exist at least one f e id2(||A p ||i) such th at for all ui e id|(IIApHj) [l'(uj) = 1 iff id3(u,}) = i],
w here A p,Bp are abb rev iatio n for term s for propositions, t is syncategorem atic expression, t(A p) is an elem entary sentence o f language L which is tru e in a world if and only if the p ro p o sitio n expressed by A p is tru e in th a t w orld.
Departm ent o f Logic Ł ódź University Poland
Janus: Kaczmarek
O MYŚLI I SĄ D Z IE W SEN SIE LO G IC ZN Y M
Pojęcie sądu w sensie logicznym nie jest jednoznacznie scharakteryzowane w literaturze logicznej. Jednakże we wszystkich ważnych definicjach wskazuje się na znaczenie, sens lub konotację zdań oznajmujących. W artykule autor podaje różne definicje i charakterystyki wypracowane m. in. przez Fregego, Churcha, Ajdukicwicza i Vandervckcna oraz wskazuje na głów ne czynniki, które należy poddać analizie przy opracowywaniu definicji sądu.
W ychodząc od pojęcia sądu jako tego. co wspólne w różnych sądach w sensie psychologicz-nym autor formułuje własną definicję sądu w sensie logiczpsychologicz-nym tak. aby uwzględnione były:
1) struktura sądu:
2) sens zdań oznajmujących;
