O myśli i sądzie w sensie logicznym

ACTA UNIVERSITATIS LODZIENSIS FOLIA PHILOSOPHICA 9, 1993 https://doi.org/10.18778/0208-6107.09.04 Janusz Kaczmarek ON TH O U G H T ANI) PR O PO SITIO N Wc can easily understand the concept o f proposition in the n atu ral way: we start from any class o f judgm ents as T he snow is white, which can be thought or utterd by some people. W hat is com m on in such individual judgm ents is usually defined by the term proposition. How ever, we can ask: w hat is the com m on o f different individual judgm ents? One usually answers: a content o f judgm ent, sense, which is independent o f its utterance or consciousness o f it. So, independently o f the au th o r, place and tim e o f an utterance o f e.g. P ythagore’s theorem the content o f this theorem is invariable, is constant. , N etherveles, as G . Frege has rem arked, the sam e content (which was called ‘G ed an k e’ - thought, by Frege) can be included in a declarative, interrogative or im perative sentence. It seems, however, th at when we w ant to deliver an inform ation, for example: to render the sense o f P ythagore’s theorem we use declarative sentences, we utter judgm ents. Thus we are inclined to conclud that w hat is com m on in different judgm ents is not only the content o f the declarative sentence but also the form o f a declarative sentence. Let us notice th at a p p a rt from a com m on content expressed in utterences there is still one m ore factor in com m on i.e. the form. C onsequently in my view, proposition com prehended as w hat is com m on any class o f judgm ents is not only ‘the co n ten t’, but „the content with the form o f declarative sentence” . In logic tradition, the proposition 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 understanding o f those term s. T he concept o f m eaning is defined in m anifold ways in, for example, theory o f m eaning (am ong others J. S. Mill, B. Russell) an d theory o f m eaning treated as ideal object (E. Husserl, G. Frege, A. C hurch). Next, the term sense is the m ost ofen used intuitively although one can find in Frege o r Husserl the following definition: the sense is som ething „w hich contains the way o f being given . T here is also the proposal o f Ajdukiewicz, who defines p roposition by m eans o f the concept o f connotation. Let us sketch out som e characteristics o f the notions o f proposition. 1. F R E G E . I think that the analyzis o f Frege text shaws th at un d erstan ding Gedanke as a proposition is not quite proper. Frege writes: „ In declarative sentence two things should be distinguished: the content com m on to their question and assertion. T he form er is a thought (G edanke) o r includes the thought. Thus, the thoughts can be expressed w ithout being put as true. In declarative sentences these things are so united th at their arc hardly distinguished (separated). So we distinguish 1° grasping thought, th at is thinking; 2° acknow ledging the truthfulness o f thought, th at is U rteil; 3° asserting o f Urteil, th at is assertion” 1. T he m ost often U rteil is understood 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 at Urteil is a passage from thought to its value2. 2. C H U R C H . In C h u rch ’s p ap e r3 we meet such characteristic o f p rop osition. P roposition is an ab stract object (as a function or class) w ithout psychological aspects characteristic for O ckham propositio m entalis and for traditional judgm 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 app rehends while u nderstanding a sentence o r w hat have two sentences being correct translation in two different languages. C hurch follows Frage explaining the term ‘G ed an k e’ which is to m ean (and so term ‘G ed an k e’ denote): „nicht das subjective T un des Denkens, sondern dessen objektiven Inhalt, der fähig ist, gem einsam es Eigenthum von Vielen zu sein” . 3. C A RN AP. Using the concept o f extension and intension C arn ap shaws th at propositions are intension o f sentences. T ruth values are treated as extensions o f sentences. Thus, proposition becomes the p roperty o f truth 1 Ct. G. F r e g e , Der 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 Univ. Press, Princeton N J 1956. values4. V anderveken rem ark s5 that in C arn ap propositions are limited to the truth conditions and, consequently, every proposition can be understood as a 0 I sequence. In Introduction to Sem antics C arn a p treats propositions as a designatum o f sentences sim ilarity as a individuals are taken for designatum o f individual constants'1. In Introduction to Sym bolic Logic p rop ositions rem ain designata but not o f the individual level (i.e. extension o f individual constants) but that o f the sense o f individuals (i.e. intension o f individual co n stan ts)7. 4. A JD U K IE W IC Z . The concept o f proposition is introduced by m ean o f the concept o f co nnotation. However Ajdukiewicz rem arks th at „the form ulation that the co n n o tatio n o f a nam e is the set o f properties which univocally determ ines its extension, cannot be considered as a definition o f the co nnotation 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. And a co n n o tatio n o f a nam e is not just any set o f properties which univocally determ ines its extension, but a set distinguished am ont those which satisfy that condition” 8. Analysing the exam ples as „the b ro th er o f Jo h n ’s m o th er” and „the m other o f Jo h n ’s b ro th er" Ajdukiewicz concludes that „it is necessary: 1° to determ ine the co nnotation o f the expression E in such a way th at its com ponent p arts should be some objective referents o f all com ponent expressions o f the expression E, and not only its com ponent nam es. 2° to determ ine the co nnotation o f the expression E in such a way that it should reflect not only the w ords contained in th at expression, but also the syntactic places which those w ords occupy in the expression E” 9. So, the co n n o tatio n o f the expression E is understood as the function determ ined for the ultim ate syntactic places o f the expression obtained from the expression E by the expansion o f all the abbreviations it contains, which establishes a one-one correspondence between those places and the denotations o f the w ords occupying such places in the expanded expression E. The definition o f connotation 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, New 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. Mass. 1942. 1 C a r p , Introduction to Symbolic... * 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. 9 Ibid. a co nnotation o f a sentence. F o r exam ple the co nnotation (proposition) o f the sentence Sokrates likes Alcibiades (U ) (1,0) (1,2) is the function establishing a one-one correspondence between the syntactic places o f its words and their denotation, i.e.: <(U) Socrates, (1,0) likes, (1,2) A lcibiades> . 5. A U ST IN , SEA R LE. These au th o rs p oint ou t some specific elem ents o f (uttered) sentences o f different type as Sam sm okes habitually. Does Sam sm oke habitualy? { W ould th at Sam sm oked habitualy. Namely, w hat is in com m on here is the reference to som e objects and predicating ab out it; the difference consists in illocutionary act: o f asserting, asking ab out, and wishing, respectively. Thus the concept o f reference and predication are detached from com plete speach act. This reference to objects and predication about them , appearing 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 approach with the results o f Frege and C hurch, understands propositions as a 3-elements sequence ll(Rn(ai....... a n))|| = < {IIR n II, IIa i II....... ||an||}, {j 6 I: < IIa,II(j), ..., ||an||(j)> e ||R J (j)} , {f 6 2Ua; f(IIA aII) = 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 worlds), ||*|| designate denotation o f expression *, A ;1 is a atom ic p rep ositional term , which have a p air as a denotation, th at is II R n(a i, .... a n)|| = < { | | R n||, IIa 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 rop o sitio n s11. 10 J. L. A u s t i n , How to Do 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 propositional constituents, the second elem ent represents the set o f possible w orld in which the relation satisfied and the third elem ent represents truth conditions. Let us rem ark that in set o f propositional constituents we speak ab o u t senses and not ab out objects. Vanderveken speaks: „All propositions are general propositions whose constituents are senses and not objects” 12. It is the conception o f Vanderveken and the app roach o f Ajdukiewicz m entiond above th at seem to the m ost interesting. W hy? Because their analyzis o f propositions indicates the necessity o f transfer to the structure o f the proposition alone, and provides the m anner o f discerning the content o f sentence. Now, I am going to discuss the conception o f V anderveken in twofold perspective: philosophical and logical. 1. A ccording to A ustin, Searle and V anderveken proposition is a com ponent ol an illocutionary act and, thus it appears in different utterances o f type (*). In spite o f o ur introductory rem arks, the form o f declarative sentence, which determ ines the type o f illocutionary act is not considered a p art o f proposition (and o ther illocutionary force m arkers likewise). On the other hand V anderveken tends to com bine the results o f A ustin and Searle works with the ‘p u re’ logical theories originating from Frege and C hurch. On this ground it is em phasized th at propositions are ‘knowledge carrier' and the basic com ponent o f scientific theories. M oreover, let us notice th at we are rather concerned w hether P ythagore claim s that in a right-angled triangle a 2 + b 2 = c2 and not ju st supposes o r expresses his wish. F urther, observe th at if a theorem is translated from one language to another, then, to preserve the sense o f proposition, its form m ust be properly rendered. Obviously, we do not translate P hytagore’s theorem into question. It seems th at the conception o f V anderveken perm its such situation; the p roposition being identical. T herefore, in my opinion, w hat V anderveken calls proposition should be refered to as thought (in ideal sense), which corresponds to F rege’s ‘G ed an k e’. A nd proposition should be acknow ledge as a thought in the form o f declarative sentences. I hope th at the above definition o f p roposition rem ains in agreem ent with Frege claims: 1° „P rop osition (U rteil) for me is not grasping o f thought (G edanke) also, but recognizing its tru th value” , 2° „In each p roposition - even m ost trivial - there is a step m ade from the level o f thought to the level o f reference” (i.e. logical values in this case) and 3° „Interrogative and declarative sentences contain the sam e thought; but the declarative sentence includes an extra, nam ely the assertion. And 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. The logical rem ark. The concept o f p roposition in Vandervekens form ulation is - as we have rem arked very general. It is so general that in case o f such sentences as (**) The president o f the USA knows the miss o f the world; the lollow ing paradox occur: the possible world (context) in which the sentences are true are know n, while we cannot 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 would enable speaking ab o u t proposition in possible world. Each proposition com prises a relation between objects which are understood in some aspects (th at is as concept). Let us rem ark, however, that 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 understanding of proposition, we m ust take possible world into account, that is the reference to the concept o f objects. The sentence (**) expresses different propositions depending on w ether uttered in 1980 o r in 1990 for example. While uttering this sentence we express the proposition in which 1) we m ean some objects (for exam ple G . Bush and the miss X); 2) these objects are understood by m eans o f concept „being a president” and „being a miss o f the w orld", 3) the objects are in adequate relation. Then, it seems, that the definition o f p roposition given by Vanderveken should be a little m odified. D eno tatio n o f propositional term in possible world i is (in case - n = 2): l|R 2( a i, a2)||i = < { | | R 2 ||, lla ,||, ||a2 ||}, { ||R 2 |li, ||а ,||ь ||a 2 |li}, {i o r * } > , where * is gap and IKR2(ai, a2))||j = < { IIAa||i}, {f 6 2*u“> :f(||Aa||j) = 1 } >, where A a is abbreviation for R 2( a |,a 2) and UJ is set o f all atom ic proposition (atom ic thought) in possible w orld i. T he m odified definition o f proposition gives us the possibility to shaw that sentence (**) expresses different proposition ones in different context o f utterance. M oreover, I think, the definition satisfies the conditions assum ed by Vanderveken. It also seems that the m odification o f sem antics should not come accross greater difficults. F o r exam ple, we define HAp A Bplh = 11-ApHi = < { IIAa ||i} u {||Ba ||i}, id2(||ApHi) n id2(||B p ||i) > , < 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 that for all ui e id|(IIApHj) [l'(uj) = 1 iff id3(u,}) = i], where A p,Bp are abbreviation for term s for propositions, t is syncategorem atic expression, t(A p) is an elem entary sentence o f language L which is true in a world if and only if the p roposition expressed by A p is true in th at world. Department o f Logic Łódź University Poland Janus: Kaczmarek O MYŚLI I SĄ D ZIE W SENSIE LO GICZNYM 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 główne czynniki, które należy poddać analizie przy opracowywaniu definicji sądu. W ychodząc od pojęcia sądu jako tego. co wspólne w różnych sądach w sensie psychologicznym autor formułuje własną definicję sądu w sensie logicznym tak. aby uwzględnione były: 1) struktura sądu: 2) sens zdań oznajmujących; 3) możliwy świat, w którym dane zdanie jest wypowiedziane.