|Edited by Vito Sinisi & Jan Wolenski
Amsterdam-Atlanta, GA: Rodopi, 1995
The thesis expressed by Ajdukiewicz’s semantic version of transcendental idealism is basically this: the Kantian a priora are translated into linguistic a priora and Rickert’s transcendental norm becomes an analogue of the meaning rules of a language. But then, conventionalism which is valid for those rules could be valid also in other ambits. The linguistic a priora testify to the presence of certain a priori conceptual nodes in the construction of our vision of the world. Given that the conceptual structure and reality correspond at these nodes, between one node and another there is a network of relations, which can be organized in different ways, depending on various visions of the world or on different scientific theories. Ajdukiewicz’s conventionalism, in fact, unlike Poincaré’s, and influenced in this by Kant, treated axioms and principles to be true, as much as they occur in a language. Which is a way of rendering the requirements of conventionalism compatible with those of the realistic theory of truth.
The paper presents the historical role of some early works of Kazimierz Ajdukiewicz in the discovery of the deduction theorem and in the formulation of the semantic definition of logical consequence as well as of the rule of infinite induction and of the calculus of syntactic types. It emphasizes also that Ajdukiewicz was a pioneer of metamathematical investigations in Poland.
Each name denotes that, if anything, of which it is a name (its denotation or designation). Each name connotes that, if anything, of which it is an expression (its connotation, meaning, or sense). A name having a denotation but no connotation is said to denote directly (or immediately). A name having a denotation and a connotation is said to denote indirectly (or mediately). Some logicians, e.g. Mill and Ajdukiewicz, favor immediate denoting; others, including Frege, favor mediate denoting. In the context of a formalized type-theoretic language having the standard denotational semantics, this article presents a method whereby “concept surrogates” can be constructed exclusively from denotational elements, thus providing a kind of middle ground between theories of immediate naming and theories of mediate naming.
This paper was presented by the author on the occasion of his acceptance of an honorary doctoral degree from the University of Buffalo (SUNY) in the May of 1990.
The paper is based on two assumptions: (1) Human knowledge is realized in thinking, (2) thinking is realized in concepts. The point of departure, and at the same time the point of destination, of philosophy is thought understood as a net of concepts inter-determining one another’s meaning. The real meaning of a concept is nothing but its place in such a net. The paper analyzes Ajdukiewicz’s semantic theory using the extra-contextual conceptual analysis (M. Czarnawska, Mysl i Pojecie, Bialystok 1991). It tries to find out whether there is a transition from concept to thought in Ajdukiewicz’s theory.
The paper presents Ajdukiewicz’s approach to the analysis of existence in which Ajdukiewicz modifies the ontology of Lesniewski so as to take into account the distinction between real and intentional existence, as well as between real and intentional objects. Modifying the considerations of Ajdukiewicz and proceeding from the thesis of intentionality it will be given an outline for a further-going categorization of objects, as well as on the definition of the predicate of existence with regard to certain types of empirical objects.
The paper examines Ajdukiewicz’s radical conventionalism and compares it with ideas of Leroy and Poincaré. At first, the author outlines the evolution of Ajdukiewicz’s conventionalism and outlines the conventionalism of French philosophers. The next part of the paper considers relations between Ajdukiewicz’s languages and his radical conventionalism. In particular, the influence of logical semantics on Ajdukiewicz’s conventionalistic epistemology is discussed. The author argues that Ajdukiewicz treated objections against his definition of synonimity too seriously, because weakening the notion of language with respect to the conditions of closeness and connectedness allows to defend the thesis of radical conventionalism.
Five fundamental operations can be carried out on objects obtained by means of intersecting two classifications of semiotic entities (existing and non-existing, on the one hand, and known and unknown, on the other hand); these are: constructing, reconstructing, demonstrating, modifying, and eliminating. The author considers in detail the operations of constructing (especially correlating) and modifying. Then he tries to define, in terms of his conceptual apparatus, the traditional operations of translating, explicating, reducing (in Tadeusz Kotarbinski’s sense), and paraphrasing (in Kazimierz Ajdukiewicz’s sense).
In this paper I will present Ajdukiewicz’s analysis of the idealist claims that can be found in three articles and one book: “A Semantical Version of the Problem of Transcendental Idealism” (Polish original 1937), “Epistemology and Semiotics” (Polish original 1948), Problems and Theories of Philosophy (Polish original 1949), “On the Notion of Existence: Some Remarks Connected with the Problem of Idealism” (1949-1950). In my exposition I want to be faithful to what Ajdukiewicz says, but in order to give as concise and clear a summary as possible, I have somewhat standardized the formulations of the idealist claims which Ajdukiewicz analyzes in his different papers. In the paper, I first explain how Ajdukiewicz distinguishes between subjective and objective idealism. Then I recall Carnap’s contribution to the realism/idealism debate, and after that I examine Ajdukiewicz’s three papers in turn. Finally, I propose a solution to one of the basic difficulties which Ajdukiewicz has found in the idealist claims.
In this paper I argue that Ajdukiewicz as a pioneer of categorial grammar raised the question of the syntactic category of proper names in natural languages and enabled further investigations into the topic. I hint also at some connections between the modern model-theoretic approach to proper names and Ajdukiewicz’s ideas.
The paper develops Ajdukiewicz’s point that science needs real definitions as univocal descriptions of things. Real definitions, unlike those (called nominal) which are mere expressions-replacement rules, should result from the following procedure: (i) we distinguish the object in question which is general in the sense that can be formally rendered by the epsilon operator through listing a selected set of its properties which is not shared by any other object; (ii) we give it a name to mean these properties. This should allow us to deduce other properties being of consequence for the theory in question. Thus, the introduction of a real definition is a creative act like that of discovering a new object, or inventing new axioms.
This essay concentrates on relations between syntax and ontology. A kind of categorial semantics connected with the standard categorial grammar is examined, and ontological presuppositions of this semantics are critically discussed. The naming relation for functorial expressions postulated by categorial semantics is regarded as the most debatable. The Frege’s Principle and other semantical rules adopted by categorial semantics are discussed. The proposal of a more intuitive semantical rule for predicates, and then the question of adequacy of categorial grammar for a natural language are considered.
In some papers Ajdukiewicz puts forward a hypothesis that the logical theory of language is based on idealization of the natural languages whereas linguistics is interested in the natural languages from the empirical point of view. The paper refers to a definite approach to the method of idealization in order to test whether the hypothesis works. It turns out that it does not. Still, the intuitions underlying Ajdukiewicz’s distinction prove to be fruitful enough to decipher them in order to enrich the idealizational approach to science with some new concepts.
Ajdukiewicz’s attitude toward language was inspired by investigations of Husserl and Hilbert. Concepts and propositions are, in Ajdukiewicz’s philosophy of language, the essences of meaning-intentions’ acts (‘ausdrückliche Bedeutungen’ in Husserl’s understanding). As in the case of other philosophical problems, Ajdukiewicz made an explication by means of syntactical and pragmatic terms. The meaning proves to be an inner-language property of an expression.
Ajdukiewicz noted that singular existentials were regarded as meaningful in the Lesniewskian existentials as copula claims tradition but as meaningless within the Frege- Russell existentials as quantifier claims tradition. By utilizing identity (‘=‘) in the Frege- Russell tradition and noting that it shares features with the Lesniewskian copula (both are sentence forming functors that take nouns as arguments), one can criticize the arguments for meaninglessness that were originally given. Nowadays it is quite common to use identity to express singular existentials. The paper’s conclusion is that neither identity nor the copula provide the right basis for understanding existentials, but some feature they share in common.
Ajdukiewicz defended the claim that truth-conditions for indicative conditional are the same as those for material implication. His pragmatics allows to cope with simple counterexamples to this claim, but it fails, as we show, for more complicated ones. We then compare Ajdukiewicz’s theory with that of Stalnaker. It seems that the intuitive plausibility of Stalnaker’s theory is even weaker. We conclude this paper sketching our own hypotheses concerning indicative conditionals.
Ajdukiewicz introduced the concept of syntactic position to resolve the problem of intensional expressions. I wish to set Ajdukiewicz’s proposal against a passage in which Leibniz talks of the way we may refer to individuals. If my interpretation is correct, it will be possible to develop Ajdukiewicz’s proposal by using some of the assumptions used by Leibniz. I shall proceed as follows. First I shall set out those points in “Ars combinatoria” that are of interest to me and clarify my interpretation. Then I shall review those aspects of Ajdukiewicz’s analysis that will be necessary for my subsequent development of it. Thirdly, I shall try to apply Leibniz’ side as to Ajdukiewicz’s proposal.
The law of excluded middle is usually considered to be intrinsically connected with the realistic standpoint and incompatible with the idealistic position. This is just what Ajdukiewicz claims in his critique of transcendental idealism. The analysis of Ajdukiewicz’s argumentation raises the problem of validity of the law of excluded middle for vague (or incomplete) languages. The problem is being solved by differentiating between the logical (or ontological) and the metalogical (or semantical) law of excluded middle: in contrast to the former, the latter is claimed to be invalid for the languages in question, without thereby embracing the idealist position.
The aim of the paper is an analysis of K. Ajdukiewicz’s linguistic ideas in relation to the conception of paradigms of “philosophy of language” developed in semiological linguistics (Stepanow 1985, Rudenko 1990a, Rudenko 1990b). According to the point of view which is well elaborated, there exists a correspondence between the three categories of the natural language and the three paradigms of “philosophy of language” (the latter is defined as a set of various viewpoints on language as well as on its semantic categories, connected with various trends in philosophy): semantic (“philosophy of language” is identified with “philosophy of names”), syntactic (“philosophy of language” is identified with “philosophy of predicates”), pragmatic, or deictic (“philosophy of language” is identified with “philosophy of egocentric words”).
As we approach the end of the century, we see the exhaustion of an important philosophical school namely of analytical philosophy. Its hope concerning the importance of language turned out to be exaggerated; its standard of rationality too brittle and too limited. Above all, this philosophy turned out to be quite inadequate for understanding our present problems. One of the paradoxes is that analytical philosophy wanted to be par excellance respectable philosophy through its stringent analytical rigor. Pursuing this rigor, it has become tedious, irrelevant; a merely technical exercise. As a result, it lost the respect of society. Ajdukiewicz was one of the great champions of analytical philosophy in Poland. He survives better than most because he did not allow himself to be locked entirely in technical boxes. Yet his overall legacy is a dream unfulfilled.
This paper describes Ajdukiewicz’s approach to non-deductive patterns of inference. At first, Ajdukiewicz’s treatment of inductive probability offered by him in the twenties is reconstructed. Generally speaking, for Ajdukiewicz at that time, an inductive rule is sound if it leads more often to true conclusions than to false ones. In the fifties, Ajdukiewicz developed a new theory of inductive inferences based on the decision theory, particularly on the concepts of profit and loss: a scheme of inductive inference is rational with respect to a given task determined by the balance of profits and losses if and only if the degree of confidence in the conclusion does not exceed the degree of the infallibility of the scheme in question.
In the second part of his classic paper on “Syntactic Connexion,” Ajdukiewicz argues that variable-binding operators such as quantifiers, integrals, etc. run afoul of the basic functor/argument scheme and require some form of functional abstraction. This suggestion has ever since become rather popular, particularly under the impact of Church’s Lambda Calculus. In this paper I dispute this view by showing how variable- binders can be accounted for within the framework of a pure categorial grammar, where the only structural operation for generating expressions is functional application. Some remarks are then offered to illustrate the philosophical import of the resulting picture. Particularly, a certain conception of logic is discussed that emerges from the account: the view that logic is essentially a theory in the model-theoretic sense, i.e. the result of selecting a certain class of models as the only “admissible” interpretation structures.
In (1958) Lambek introduced a formal system LSC of deriving reduction for syntactic types, which is essentially stronger than the classical cancellation system of Ajdukiewicz (1935). It was proved that LSC is complete with respect to the S- and GS-semantics based on the notion of residuated semigroups (Buszkowski 1986). In this paper categorial semantics of LSC is described (in preorder categories and toposes) and the soundness and the completeness of LSC with respect to those ones is proved.
One of the major contributions of Kazimierz Ajdukiewicz to the philosophy of language is his fundamental work on logical syntax, i.e. Categorial Grammar, in “Die syntaktische Konnexität” (Ajdukiewicz 1935). The present paper addresses a central development in recent investigations of Categorial Grammar, viz. the introduction of new type forming operations (see e.g. Moortgat 1988, Morrill 1990). If the parsing mechanism of Categorial Grammar is conceived of as a propositional logic, the problem is to motivate and to characterize additional propositional connectives. In what follows, a number of additional operations for the Ajdukiewicz-Lambek Calculus of syntactic types is motivated and positive sequential propositional logic (PSPL), i.e. positive propositional logic without structural rules of inference, is suggested as an extended syntactic calculus. Moreover, a higher-level sequent system together with rule-schemata for introducing connectives into premises and conclusions is presented as a definitional framework for characterizing propositional connectives. The connectives of the extended syntactic calculus PSPL are shown to be functionally complete with respect to this proof-theoretic semantics.
The paper reconstructs Ajdukiewicz’s method of refuting scepticism. Ajdukiewicz does not agree with a common view that scepticism is self-refutable. He points out that this argument against scepticism assumes the validity of the principle of the excluded middle, whereas the sceptic can simply reject this principle. For Ajdukiewicz the main thesis of scepticism is this: no truth-criterion is possible. And he argues that the sceptics confuse the justification of a statement with the justification that the statement is true. Moreover, Ajdukiewicz points out that the applicability of a truth-criterion does not assume that this criterion is valid.