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miércoles, 27 de abril de 2011

Kazimierz Ajdukiewicz’s early philosophy of language, Janusz Maciaszek

Janusz Maciaszek                                                                              28.04.2011, 16.30

University of Łódź

Kazimierz Ajdukiewicz’s early philosophy of language

(Draft of the paper)

1. The general overview of the theory

Kazimierz Ajdukiewicz (1890 - 1963) was one of the representatives of the Lvov-Warsaw school of analytic philosophy. In early thirties Ajdukiewicz developed very original theory of meaning called directival theory of meaning. This theory was purely pragmatic and holistic. It was based on the notion of belief understood as a disposition to approve sentences in certain circumstances, what anticipated Quine’s theory of translation manual from Word and Object.

The inspirations of Ajdukiewicz were many fold:

-          Frege – the basic unit of analysis is a sentence and not a word. Linguistic meaning is a vehicle of knowledge, but Ajdukiewicz did not accept senses as abstract objects. In consequence he did not even try to analyse intensional contexts.

-          Husserl – the mental act of believing what a sentence says (or thinking that it is as the sentence says) is in the same time an act of perceiving its physical shape. But the moment (in Husserl’s nomenclature) of believing what a sentence says was explained by the relations of words of the sentence in question (its physical shape) to other beliefs they appear in, e.g. I believe in a sentence “Santiago is in Spain” or I think that it is as this sentence says because I have many other beliefs about Santiago and may other beliefs about Spain. This approach implies the belief holism. Another notion that Ajdukiewicz is due to Husserl is the notion of motivation.

-          French conventionalism – the description of empirical data in the form of scientific theory depends on conventions. In consequence there are various independent and not translatable descriptions of the same reality. Ajdukiewicz called himself a radical conventionalist (1934b). His radicalism consisted in his approach to the natural language. Contrary to modest conventionalists he considered natural language as depending on conventions like the languages of scientific theories. In consequence Ajdukiewicz formulated his own version of Duhem-Quine theses.

-          Verifacationism. Unfortunately Ajdukiewicz did not manage to get rid of some influence of vericationism, which was very popular in this époque. It provoked a minor drawback of his theory that can be easily corrected.

The theory of Ajdukiewicz was presented in two papers. The 1931 paper (On the meaning of expressions) was a preliminary one (the theory was not presented in a formal way), but it is interesting mainly because of the arguments in favour of belief and meaning holism. In the 1934a paper (Language and meaning) Ajdukiewicz proposed a formal expositions of the theory. Unfortunately this exposition has some deficiencies, and it is very difficult to be accept it in this form. In the 1934b paper (The picture of a world and conceptual apparatus) Ajdukiewicz presented very interesting exposition of conventionalism which was the philosophical background of the theory. In this paper he indicated that nets of beliefs are just the picture of a world, and conceptual apparatus is just the net of meaning.

After rejecting conventionalism Ajdukiewicz rejected the directival theory when Alfred Tarski formulated his famous objection. After the war he formulated another theory of meaning which was not so original as the previous one. In my opinion the theory, especially in 1931 form is interesting in itself, and it anticipates some later theories or can be applied within them. Some of the obvious drawbacks of the 1934a theory can be rectified. After this correction the theory is not necessarly connected with its original philosophical background. The theory is very promising as an example of a non-referential semantics (theory of meaning) and can be extended to the theory comprising much wider scope of linguistic phenomena than the original one.

2. Ajdukiewicz’s 1931 theory

Ajdukiewicz’s theory of meaning is based on the primitive notion of belief. In his 1931 paper (On the Meaning of Expressions) Ajdukiewcz gives some elaborated arguments for his contention that a necessary and sufficient condition of believing in a sentence is to believieng in many other sentences. The arguments of Ajdukiewicz are complicated, and the structure of his reasoning is not clear. To make it more comprehensible it is necessary to add some commentaries and indicate implicit goals Ajdukiewicz wanted to achieve in every step of his reasoning. As far as I know nobody have tried to reconstruct Ajdukiewicz reasoning in details yet.

1. Ajdukiewicz starts with the Husserlian notion of motivation. Some circumstances, or better experiencing some circumstances, motivate us to believe in a sentence. But the sentence is an expression that has meaning, and we can believe in a sentence because it has meaning. The sentence is not just a physical shape, though we experience its physical shape. Moreover its parts also have meanings and physical shapes. So the next question is: “What is the meaning of a particular expression?”

2. As a pre-theoretical notion, the meaning of an expression is compared to Fregean sense conceived as an aspect in which an object is given to us. In his theory Ajdukiewicz conceives this aspect as something internal to the language, and not belonging to the reality (physical or abstract). Then Ajdukiewicz analyses the question “What is the meaning of….?”

3. When we ask the question or answer the question “What is the meaning of …?” we use quotations. Ajdukiewicz considers three possible ways of using a quotation. In the first one the quotation is just the name of the inscription inside. Sometimes we use quotations in this way, e.g. The parrot cried “rree”. The second possibility is that the quotation is the name of all inscriptions of the same physical shape as the inscription inside: My parrot can cry “rree” or My parrot can cry “rana”. But sometimes we use quotations in another sense, e.g. This man uses often the word “rana”. In this context we assume that the man in question uses the word “rana” as a word of a definite language. Unfortunately the quotation marks do no indicate the language, so if “rana” is a Spanish word it means “frog”, but if it is Polish it means “wound”. In consequence if we use quotations we unconsciously make hiiden reference to a language. Let us imagine that we can train a parrot to cry “rana” when it sees a frog (it experience the sight of a frog). Does it men that the parrot speaks Spanish or partially speaks Spanish? To answer this question we have to answer the question “What does it mean to speak Spanish?”

4. To answer the last question Ajdukiewicz proposes three possibilities. In the first one to speak Spanish means to pronounce sounds that are in conformity with Spanish vocabulary and grammar. In this sense a parrot that just repeats Spanish words and phrases can speak Spanish. But let us consider the well trained parrot that cries “rana” when it sees a frog, etc. We can say that it can speak Spanish in another sense. To speak Spanish means to pronounce sounds that are in conformity with Spanish vocabulary and grammar and behave in the same time in a way that is provided for these sounds by this language. May be the parrot can speak Spanish in this sense and I can also speak Spanish in this sense (I hope that little better than even a well trained parrot). But Ajdukiewicz maintains that the indicated sense of a phrase “To speak Spanish” is not the intended sense of this phrase. Let us consider some borrowings from one language to another. If I indicate a group of generals that govern a country and pronounce a word “junta” it is impossible to decide if I speak Spanish of Polish because this behaviour is provided for this sound by both languages. To decide if pronouncing “junta” in the described circumstances one speaks Polish or Spanish we have to refer to the linguistic dispositions of a speaker. To be more precise, to speak Spanish means to pronounce sounds that are in conformity with Spanish vocabulary and grammar, behave in a way that is provided for these sounds by this language, and be ready to actualize dispositions to react to expressions of this language. E.g. if you ready to accept en elliptical sentence “Junta” when indicating a civil government you probably speak rather Spanish then Polish. But here another problem arises: what does it mean to have dispositions to react to expressions of a particular language. But what does it mean “to react to expressions of a particular language”. One possible answer is to have a mental image (idea) of the reference, e.g. the mental image of a group of generals, or a mental image of whatever group in power. Another possibility is to have properties of the reference or believe that the reference has certain properties. In the first approach you speak Spanish if you actualize dispositions to have mental images (ides) specific to this language; in the second approach you speak Spanish if you believe that the objects your words refer to have certain properties nad you use this words because the objects have these properties. In the next step Ajdukiewicz analysis two classical theories of meaning: the associationist one and connotative one (millianism).

5. Critique of associacionism

One can say that associationism is false because after Frege everybody knows that a reasonable theory of meaning should ascribe meanings to all expressions and not only to names. Nevertheless it is worth to analyse this critique as an important step towards Ajdukiewicz’s original solution. At the very beginning Ajdukiewicz reconstructs associationist theory of meaning:

(A1) The meaning of an expression A of a type W in the language L is a thought of a type M iff:

a. the expressions of the type W belong to L

b. for every user X, X uses an expression A of the type W as the expression of L iff the use of A is associated a thought B of the type M.

(more precisely: an experience of a physical shape of A of type W is associated with an experience of a thought B of the type M)

According to Ajdukiewicz the use of A is in fact the use of the elliptical sentence.

Then Ajdukiewicz shows that the second condition (b) is false, because the thought B associated with the use of A is neither sufficient, nor necessary condition of the use of A as the expression of L. It is not a necessary condition because we can use an expression (e.g. “taller that Tom”) without any associated thoughts (the mental image of Tom is not the associated thought we are looking for) and we can experience the same associated thoughts when using an expression of a certain type, and not use it as expressions of the same language (e.g. all of you have probably the same mental image /idea/ associated with the sound “foca” as the users of Polish, nevertheless if you pronounce “foca” you use it as a Spanish word and not as a Polish word).

The next step proposed by Ajdukiewicz is the extended associative theses. Maybe – he writes – in the past there was an accidental and habitual association of the type of a physical shape of an expression with a thought of a certain type. In consequence experiencing the mental image of the physical shape of an expression is in the same time having the thought of that type, e.g. the experience of the mental image of the physical shape of an expression “dean” is in the same time the experience of the image of an elderly man with a beard, or a middle-aged elegant woman.

(A2) The meaning of an expression of a type W in the language L is a thought of a type M iff:

a. the expressions of the type W belongs to L

b. for every user X, X uses an expression A of the type W as the expression of L iff

- the type of experience of the physical shape of the expressions of type W is associated (in the indicated sense) with the type of thought M,

- the experience of the physical shape of an expression A of the type W is in the same time the experience of a certain thought of the type M.

The extended association is accidental and private, and the meanings are inter subjective. In consequence even the extended associative theses is false – a thought of a certain type cannot be the meaning of an expression.

6. Critique of millianism

Associationism is false because it cannot explain the intersubjectivity of meanings. But may by the millianism as a externalist theory can explain it. Ajdukiewicz formulates the theses of millianism in the following form:

(M) A name N connotes (in L) properties C1, C2, …, Cn iff every user of L:

a. if he believes that an object A have the properties C1, C2, …, Cn, he is ready to believe in a sentence “X is N” (where X is the name or description of an object A)

b. if he believes in a sentence “X is N”, he is ready to believe that A have the properties C1, C2, …, Cn.

Ajdukiewicz argues that (M) is false because some names have no connotations (b), and even believing that an object A have the properties C1, C2, …, Cn does not suffice to believe in a sentence “X is N”:

Let us imagine two people O1 and O2 who believe that a geometrical figure A have some properties, and in consequence believe in a sentence S: “X is a rectangle” (X being the name of A). But the beliefs in question can be expressed by two different sentences:

S1:  X is a parallelogram and a quadrangle inscribed in a circle”

S2: “X is a parallelogram and a quadrangle with equal sums of opposite angles.

(the expressions “a quadrangle inscribed in a circle” and “a quadrangle with equal sums of opposite angles” are the names of the same property).

Let us imagine that O1 believes in S because he believes in S1 and not because he believes in S2. Let us also imagine that that O2 believes in S because he believes in S2, and not because he believes in S1. In consequence the belief that A have the properties of a rectangle does not suffice to believe in a sentence “X is a rectangle”.


The experience of a sentence of a certain language can be characterised in three ways:

a) the use of a sentence as a sentence of this language

b) the actualization of a belief expressed by the sentence

c) the experience of a physical shape of the sentence

In consequence Ajdukiewicz proposed to define meanings for the coherent nets of beliefs. A user believes in these sentences because he is motivated by three kinds of meaning directives: axiomatic, inferential and empirical, where a meaning directive is a relation between types of sentences and types of (mental) experience that motivate a user of a language to accept sentences of this type.

The axiomatic directives motivate the user to accept some sentences in all circumstances, the inferential directives motivate the user to accept some sentences if other sentences were previously accepted, and the empirical directives motivate the user to accept some sentences if empirical data of a relevant sort are experienced. (Unfortunately it is a drawback of Ajdukiewicz’s theory. Ajdukiewicz was obliged to name empirical data introducing unwillingly another language. In my opinion this can be eliminated by treating them not as sentences with hidden time, space, and subject variables).

            Then Ajdukiewicz defines the notion of  : expressions a and b are synonyms iff for any motive M, a and b are mutually interchangeable in all sentences accepted in face of M. This relation is the relation of equivalence, so the synonyms constitute class of abstraction of all expressions of a language. In consequence Ajdukiewicz defines meaning of an expression W in L as a common property of all synonyms of W in L, and only of these synonyms.

The deficiences of the theory:

1. The meaning is considered as a property but Ajdukiewicz does not indicate which property (he tried to eliminate this drawback in the 1934a article in favour of the representation of meaning)

2. Ajdukiewicz does not take into account any kind of compositionality of meanings. Of course he accepts compositionality on the syntactical level, but his pragmatic theory does not explain how it is possible to understand a sentence if we understand its parts. This difficulty is difficult to overcome on the ground of Ajdukiewicz’s original theory.

3. It is not clear how it is possible (within Ajdukiewicz’s theory) to understand the sentences that do not express our believes.

Unfortunately the lat two problems were not solved by Ajdukiewicz in his 1934a paper. But this paper at least show us why these problems were neglected by Ajdukiewicz.

3. The strict theory form 1934a paper Language and Meaning

In 1934a paper Ajdukiewicz introduced rather complicated set of definitions that enabled him to formulate strict theory of meaning. The main idea remained unchanged. The meanings are anchored in the net of beliefs divided in three parts be the kinds meaning directives. Ajdukiewicz abandons the area of natural language (except some remarks) in favour of the languages of scientific theories. His reasoning is roughly as follows:

1. He defines the notion of a denotation of a meaning directive in a following way. For an axiomatic directive it is a class sentences (e.g. {(p Ú ~p), (q Ú ~q), …}). For a deductive directive a class whose elements are pairs of set of sentences and a sentence. For a empirical directive, a class consisting of pair of a particular empirical experience and a sentence.

2. He introduces a notion of the essential role of an expression in a meaning directive. An expression has an essential role in a directive if its substitution in at least one pair of the denotation of this directive for at least one expression of the same category does not belong to this denotation. E.g. p and q does not have essential role in the denotation of the previous example, but Ú and ~ have essential role.

3. He defines the interdependence of meanings of expressions in a language (or better in a net of beliefs). Two expressions are interdependent if both of them have essential role in at least one meaning directive.

These notions permit Ajdukiewicz to distinguish two kinds of languages: open languages and closed languages. Close languages, fictional as Ajdukiewicz admitted later, can be conceived as the languages of “finished” physical theories that describe the reality in all details, so nothing essential can be added to them. These languages can be roughly conceived as languages that cannot be conservatively extended. According to Ajdukiewicz the reality can be described by infinitely many closed languages. The nets of meanings in these languages were intended to pay role of conceptual apparatus or conventions in the conventionalist sense.

In order to define the representation of an expression in a closed language Ajdukiewicz imposed very strict rules on translation between languages, and he introduced the notion of a matrix that corresponds to a class of mutually translatable languages (or better nets of beliefs expressed in these languages). Every matrix consists of three parts that correspond to three types of meaning directives. Every part consists of sequences that consist of a sentence that expresses a belief of a relevant sort, and its parts given in the defined order. The meaning of an expression (simple or compound) in a language is represented by a class of abstraction of all expressions that can substitute the expression in question in the matrix of the language, and was represented by its position in a corresponding matrix. The position is defined in a rather complicated way as a family of sequences of numerals, but it suffices to say that the meaning of an expression is represented by or simply is the position of that expression in a matrix that in fact corresponds to a class of isomorphic structures of believes.

EXAMPLE (for an open language)

Let us consider the system of logic of Łukasiewicz. The matrix for this system would be as follows:

Axiomatic part:

1.       A Þ (B Þ A), Þ, A, B Þ A, Þ, B, A

2.       (A Þ (B Þ C)) Þ ((A ÞB) Þ (A Þ C)), Þ, A Þ (B Þ C), Þ, A, B Þ C, Þ, B, C, (A ÞB) Þ (A Þ C), Þ, A ÞB, Þ, A, B, A Þ C, Þ, A, C

3.       (~A Þ ~B) Þ (B Þ A), Þ, (~A Þ ~B), Þ, ~A, ~, A, ~B, ~, B, B Þ A, Þ, B, A

Deductive part:

1.       A; A Þ B, Þ, A, B ½ B

2.       A Ù B, Ù, A, B ½ ~(A Þ ~B), ~, A Þ ~B, Þ, A, ~B, ~, B

3.       ~(A Þ ~B), ~, A Þ ~B, Þ, A, ~B, ~, B ½ A Ù B, Ù, A, B

4.       A Ú B, Ú, A, B ½ ~A Þ B, Þ, ~A, ~, A, B

5.       ~A Þ  B, Þ, ~A, ~, A, B ½ A Ú B, Ú, A, B

6.       A Û B, Û, A, B ½ (A Þ B) Ù (B Þ A), Ù, A Þ B, Þ, A, B, B Þ A, Þ, B, A

7.       (A Þ B) Ù (B Þ A), Ù, A Þ B, Þ, A, B, B Þ A, Þ, B, A ½ A Û B, Û, A, B

(No empirical part).

It is easy to see that negation and implication are interdependent.

The position that represents the meaning of the implication is as follows:

(1, 2, 5), (2, 2, 4, 7, 11, 13, 15, 17), (3, 2, 4, 12) (for axiomatic part)

(1’, 3), (2’’, 4), (3’, 4), (4’’, 2), (5’, 2), (6’’, 4, 8), (7’, 4, 8) (for deductive part)

It is even difficult to imagine how one would give representations of meaning in a more complicated language.

4. Tarski’s objection

In a private conversation with Ajdukiewicz that took part in the late thirties Alfred Tarski noticed that if we have a axiomatic directive A ¹ B, and A and B do not play an essential role in any other directive, then A and B would denote different objects, but would have the same position in a matrix of a language, and, in a consequence, the same meaning. Ajdukiewicz treated this objection as a very important and announced that he would not accept the theory any more.

The first and obvious remark is that the language indicated by Tarski is not a closed one, but an open one. But Ajdukiewicz always declared that his theory was designed for closed languages. In my 2007 book Ajdukiewicz’s Meaning Holism I analysed the objection and indicated some special features of representation of meanings for languages like the one proposed by Tarski. In fact Tarski’s objection is an example of the lack of knowledge. It resemble to some extend Putnam’s Twin Earth Argument. But contrary to Putnam and Ajdukiewicz I interpret such arguments not in favour of externalism, but as the arguments for non-referential semantics.

The second remark concerns the notion of reference that appears in the objection. Ajdukiewicz’s theory of meaning is not referential, so the objection is not dangerous for the theory. The possible explanation is as follows. Abandoning conventionalism Ajdukiewicz doubted in non-referential theory of meaning, and the objection was jus a pretext to give up the theory.

5. Closing remarks

In spite of the evident drawbacks of the theory I maintain that after some modifications it can be applied to natural languages conceived as open languages in Ajdukiewicz’s sense.

  1. The obvious drawback of this approach is that the sentences that do not express speaker’s believes have neither meaning not its representation. In fact Ajdukiewicz developed his theory for closed languages of scientific theories, where all interested sentences are contained in the set of believes. This problem is the result of lack of any rules of compositionality of meaning in Ajdukiewicz’s theory. In consequence here is no rule that connects meanings of primitive expressions with the meaning of a sentence that contains these expressions. In consequence we cannot represent a meaning of a sentence that expresses no belief even if we can represent meanings of its parts. One remedy is to incorporate into the theory of language a Tarski’s style theory of truth as a mean of recursive meaning ascription.
  2. Ajdukiewicz treated natural language as a class of mutually non-translatable languages conceived as proto-scientific theories in conventionalist approach. The fact of communication between two people who speak two different natural languages (and the possibility of learning a foreign language as well) is the following: different languages consist of mutually translatable languages, i.e. languages that have the same matrices but differ in the physical shape of sentences that actualize believes. But the non-translatability concerns closed languages. For open languages Ajdukiewicz’s strong notion of translatability cannot be maintained.
  3. Another disadvantage of the theory is that the change of one belief results in the change of meaning of all expressions if one belief has been changed. The consequence of this contention is highly improbable: the condition of mutual understanding or translation is the identity of beliefs of a speaker and the interpreter. But in the case of open languages non-translatability cannot be maintained and after some modification the problems of meaning ascription and belief ascription can separated. It can be done in Davidsonian style.
  4. Ajdukiewicz was not interested in intensional contexts, speech acts, and propositional attitudes. It is difficult to see how Ajdukiewicz’s theory could be extended to performative sentences. In case of intensional contexts the extended Ajdukiewicz’s theory would be non satisfactory. But there is one point worth noticing. The notion of coextensional substitution makes of course no sense in Ajdukiewicz’s approach as instead of it we have another kind of substitution – the substitution synonimes that do not change the matrix of a language. (It is worth noticing that it is possible to find the difference between the counterparts of synonymy and co-extensionality of expressions – see my 2007 book).


Let assume that the user of the language believes in some sentences where the names “Tully” and “Cicero” appear. Each of the names can be substituted by another in all user’s believes – so they are synonyms (it is easy to see that there is a difference between counterparts of synonyms and co-extensional expressions in Ajdukiewicz approach). Let us add to his believes two additional: “John believe that Tully was roman orator” and “John does not believe that Cicero was roman orator” (our speaker is not John of course). In the new extended language “Cicero” and “Tully” are no more synonyms. In consequence if we extend Ajdukiewicz’a theory to the sentences that ascribe propositional attitudes there would be no synonyms. If we are restrict to speakers beliefs expressed in an extensional language as in original Ajdukiewicz’s approach there are synonyms for the speaker. But if we extend the language to the sentences that ascribe propositional attitudes to other people – the synonymy disappears. This difficulty can easy be overcome if we adopt Davidson’s theory of interpretation and his paratactic analysis. The theory of language that comprises both theories is (in my opinion) a very promising one.

1 comentario:

  1. Será expuesta en el IX Coloquio Compostelano de Lógica y Filosofía Analítica mañana 28 de abril. Nos la envía:
    Estimad@s Tod@s:
    Es un placer invitaros a la sesión del XI Coloquio Compostelano de Lógica y Filosofía Analítica que tendrá lugar el próximo jueves 28 de abril de 2011 a las 16.30h. en el seminario 330 de la Facultad de Filosofía.
    Nuestro invitado es el profesor Janusz Maciaszek de la Universidad de Lodz, Polonia.
    El profesor Maciaszek disertará sobre "La temprana filosofía del lenguaje de Kazimierz Ajdukiewicz".

    Adjunto texto en inglés aunque el profesor Maciaszek habla español.
    Un saludo,

    Concha Martínez Vidal
    Departamento de Lóxica e Filosofía Moral
    Facultade de Filosofía
    Praza de Mazarelos s/n
    15782 Santiago de Compostela
    Tele. 881812530 Fax: 881812542

    Gracias !!!!


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