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Ajdukiewicz, like other typical members of the Lwów-Warsaw School, the main Polish analytic movement, was basically interested in logic, philosophy of language, epistemology, and philosophy of science. In the 1930s, he proposed a form of radical conventionalism, an extension of the conventionalism of Duhem and Poincaré. Later, he rejected this radical conventionalism in favour of a semantic epistemology. In the philosophy of science he tried to build a general theory of fallible inferences based on decision theory. Ajdukiewicz’s most important

contribution to logic is his formal notation for syntactic categories. 1 Life

Ajdukiewicz was born on 12 December 1890 in Tarnopol, a town in the Austro-Hungarian Empire (now in Ukraine). In 1908-12 he studied philosophy at the University of Lwów, mainly under Kazimierz Twardowski. He was also trained by Jan Łukasiewicz in logic and Wacław Sierpiński in mathematics. In 1912 he obtained his Ph.D.; his dissertation concerned Kant’s theory of space. In 1913 Ajdukiewicz studied in Göttingen where he attended courses given by David Hilbert and Edmund Husserl. He obtained his Habilitation degree from the University of Warsaw with a dissertation on the foundations of mathematics. In 1921-6 he was an associate professor (docent) at the University of Lwów. In 1926 he was appointed as professor of philosophy at the University of Warsaw. In 1928 he returned to Lwów, where he was given a professorship. During the Second World War he lived in Lwów and taught in clandestine Polish schools. In 1945 Ajdukiewicz accepted a professorship at the University of Poznan. In 1955 he moved to the University of Warsaw. He died on 12 April 1963 in Warsaw.

2 Radical conventionalism

Radical conventionalism is closely related to Ajdukiewicz’s theory of language and meaning. The meanings of expressions in a language generate rules for accepting sentences of L. Ajdukiewicz singles out three kinds of meaning-rules: axiomatic (they require the unconditional acceptance of certain sentences, for example ‘A is A’), deductive (for example, B follows from ‘if A then B’ and A), and empirical (the sentence ‘snow is white’ is asserted in a situation in which a person asserting this sentence perceives that snow is white).

It follows from the foregoing explanations that meanings determine meaning-rules. But in general, meaning-rules do not determine the meanings of expressions; this holds, for example, for ordinary language. However, the situation radically changes when we pass to closed and connected languages. Roughly speaking, a language L is open if it can be extended to a new language L′ without changes in the meanings of the expressions of L;

otherwise, L is closed. A language L is disconnected if there is a non-empty subset X of expressions of L such that no element of X is related by meaning-rules of L to its remaining expressions; otherwise, L is connected. An important consequence of the theory of closed and connected languages is this: if L is a closed and connected language, it is impossible to enrich L by new expressions in such a way that old meanings are preserved.

For Ajdukiewicz, mature, particularly scientific, knowledge is expressed in closed and connected languages. The set of meanings of a closed and connected language L is its conceptual apparatus. From general theorems on closed and connected languages, one can infer that two conceptual apparatuses are either identical or mutually

non-translatable. The acceptance or rejection of sentences is always related to a definite language L. If L is closed and connected, empirical situations do not force us either to accept or reject any sentence, because we can always change our conceptual apparatus. This is an essential strengthening of usual conventionalism. For Poincaré and Duhem, we are free to change our theoretical principles, because they are hidden conventions. For Ajdukiewicz, experiential reports are also closely related to conceptual apparatus, and since every conceptual apparatus produces a world-perspective, we can say that theories and observational reports are accepted not absolutely but relative to world-perspectives. This is why Ajdukiewicz called his conventionalism ‘radical’, contrary to the moderate view of the Frenchmen (see Conventionalism).

3 Semantic epistemology

In the middle 1930s Ajdukiewicz rejected radical conventionalism, because he came to the view that his idea of Ajdukiewicz, Kazimierz (1890-1963)

connected and closed languages was a ‘paper fiction’. The change was also strongly motivated by the work of Tarski which convinced many philosophers that semantics has important applications in philosophy. When he was a radical conventionalist, Ajdukiewicz did not draw any ontological theses from his epistemological

considerations; but his semantic epistemology is an attempt to bring together epistemology and ontology. If we speak about the world, we use an object-language. Since epistemology intends to say something about the world and our knowledge of it, an epistemologist must use a meta-language in order to capture knowledge and its object. Ajdukiewicz, employing metalogic and semantics, gave a rigorous analysis of Rickert’s transcendental idealism and Berkeley’s subjective idealism (see Berkeley, G.). For Ajdukiewicz, both kinds of idealism are incorrect, because they neglect basic results of metalogic and semantics. Ajdukiewicz rejects Rickert’s idealism, because truth, contrary to Rickert, cannot be established exclusively by purely deductive procedures; the incompleteness of arithmetic is an essential premise of Ajdukiewicz’s argument. Berkeley’s thesis that ordinary objects are

complexes of our ideas is rejected, because it conflates syntax and semantics. According to Ajdukiewicz, Berkeley uses a language which is very similar to the language of syntax and offers a syntactic-like definition of existence. However, since existence is basically a semantic concept and semantics is not fully definable in syntax, Berkeley’s argument fails. Thus, semantic epistemology leads to a realist account of existence.

4 Philosophy of science

In addition to his discussions of radical conventionalism, which implies that there is no absolute gap between theories and experiential reports, Ajdukiewicz also worked on concrete problems in the philosophy of science. In particular, he was interested in the logic of fallible inferences. His approach was based on concepts borrowed from decision theory. In general, acceptances (rejections) of sentences are actions which are associated with profits and losses. Assume that A is a sentence to be accepted and that Z is the minimal acceptable profit for the agent, when A is true, and S is the minimal acceptable loss, when A is false. According to Ajdukiewicz the ratio S=(S + Z) expresses the degree of certainty which an agent accepting A can ascribe to this sentence. This relates degrees of certainty to mathematical probabilities. Having this framework, Ajdukiewicz tried to establish the degree of conclusiveness of a fallible scheme of inference. Assume that K is background knowledge. We are interested in the degree of conclusiveness of a fallible (for example, inductive) inference from premises P to a hypothesis H. This inference is conclusive if the degree of certainty of H does not exceed the ratio of its initial probability to the initial probability of premises, relative to K. Ajdukiewicz’s analysis of fallible inferences is a typical example of his pragmatic approach to methodological problems, which consists in relating analysed concepts to attitudes of epistemic agents.

5 Contributions to logic

Ajdukiewicz’s notation for syntactic categories is his main contribution to logic. The following example shows how this notation works. We have two basic categories: sentences (s) and terms (n). Now, consider an expression ‘is tall’. It forms a sentence together with a term, for example ‘Tom’. We ascribe to ‘is tall’ the symbol s/n which informs us that ‘is tall’ is a function forming a sentence with a term as an argument. Now we build a sequence of symbols for the sentence ‘Tom is tall’. The sequence is this: n, sn. It is obtained by writing the symbols for the categories of all the expressions occurring in the considered sentence. We can simplify the sequence by performing ‘arithmetical’ operations on symbols by analogy with operations on ratios. Thus, we can ‘shorten’ fn; s=ng by dividing both members by n; we assume that n/n can be cancelled. Thus, we obtain s as the sole member. A general rule is this: if the simplification ends with n or s, the original expression is syntactically correct; otherwise not. This idea gave rise to constructions known as Leśniewski-Ajdukiewicz-Lambek grammar, originated with Leśniewski, continued by Ajdukiewicz, and fully developed by Lambek (see Syntax).

See also: Poland, philosophy in

JAN WOLEŃSKI List of works

Ajdukiewicz, K. (1921) Contributions to the Methodology of Deductive Sciences (in Polish), Lwów: Polskie Towarzystwo Filozoficzne; partially trans. J. Giedymin (1966), Studia Logica 19: 9-46.(Ajdukiewicz’s

Habilitation.)

Ajdukiewicz, K. (1934a) ‘Sprache und Sinn’, Erkenntnis 4: 130-8; trans. J. Wilkinson, ‘Language and Meaning’ Ajdukiewicz, Kazimierz (1890-1963)

in The Scientific World-Perspective and Other Essays 1931-1963, Dordrecht: Reidel, 1978: 35-66.(A presentation of the theory of closed and connected languages.)

Ajdukiewicz, K. (1934b) ‘Das Weltbild und die Begriffsapparatur’, Erkenntnis 4: 259-87; trans. J. Wilkinson, ‘The World-Picture and the Conceptual Apparatus’ in The Scientific World-Perspective and Other Essays

1931-1963, Dordrecht: Reidel, 1978: 67-89. (A basic paper on radical conventionalism.)

Ajdukiewicz, K. (1936) ‘Die syntaktische Konnexität’, Studia Philosophica I: 1-276; trans. H. Weber,

‘Syntactic Connexion’ in The Scientific World-Perspective and Other Essays 1931-1963, Dordrecht: Reidel, 1978: 118-39.(Notation for syntactic categories.)

Ajdukiewicz, K. (1948) ‘Epistemologia i semiotyka’, Przeglad Filozoficzny 44: 336-47; trans. J. Giedymin, ‘Epistemology and Semiotics’ in The Scientific World-Perspective and Other Essays 1931-1963, Dordrecht: Reidel, 1978: 182-91.(Semantic epistemology.)

Ajdukiewicz, K. (1958) ‘Zagadnienie racjonalnosci zawodnych sposobow wnioskowanis’, Studia Filozoficzne 4 (7): 14-19; trans. D. Pearce, ‘The Problem of Rationality of Non-Deductive Types of Inference’ in The

Scientific World-Perspective and Other Essays 1931-1963, Dordrecht: Reidel, 1978: 239-53.(Ajdukiewicz’s

analysis of fallible modes of inference.)

Ajdukiewicz, K. (1973) Problems and Theories of Philosophy, trans. H. Skolimowski and A. Quinton,

Cambridge: Cambridge University Press.(An elementary introduction to philosophy; this book was originally published in Polish in 1949.)

Ajdukiewicz, K. (1974) Pragmatic Logic, trans. O. Wojtasiewicz, Dordrecht: Reidel.(An extensive treatise on methodology; this book was originally published in Polish in 1965.)

Ajdukiewicz, K. (1978) The Scientific World-Perspective and Other Essays 1931-1963, Dordrecht: Reidel.(A collection of basic papers by Ajdukiewicz.)

References and further reading

Sinisi, V. and Woleński, J. (eds) (1995) The Heritage of Kazimierz Ajdukiewicz, Amsterdam: Rodopi. (A collection of essays on Ajdukiewicz’s philosophy; includes the complete bibliography of Ajdukiewicz’s writings and a selected bibliography on Ajdukiewicz.)

Woleński, J. (1989) Logic and Philosophy in the Lvov-Warsaw School, Dordrecht: Kluwer.(Chapter X gives a presentation of Ajdukiewicz’s epistemology.)