This paper presents four key results. Firstly, it distinguishes between _partial_ and _consistent_ assertion of a sentence, and introduces the concept of an _equivocal_ sentence, which is both partially asserted and partially denied. Secondly, it proposes a novel definition of truth, stating that _a true sentence is one that is consistently asserted_. This definition is immune from the Liar paradox, does not restrict classical logic, and can be applied to declarative sentences in the language used by any particular person. Thirdly, (...) the paper introduces an epistemic model of language, known as _assertional language_, which is used to formalize the definition of truth. Finally, it provides an argument for the falsity of so-called Liar sentences. The paper also discusses Tarski's solution to the Liar paradox and argues for the abandonment of the Tarski Scheme: _'p' is true if and only if p_, in the context of everyday language. The proposed definition of truth can be viewed as a formal account of the correspondence theory. The epistemic model is a powerful concept on its own that allows for combining different languages in a meaningful way. This model is uniquely capable of reflecting on epistemic inconsistencies, such as logical paradoxes, in a consistent manner. (shrink)

The paper aims to add contextual dependence to the new directival theory of meaning, a functional role semantics based on Kazimierz Ajdukiewicz’s directival theory of meaning. We show that the original formulation of the theory does not have a straight answer on how the meaning of indexicals and demonstratives is established. We illustrate it in the example of some problematic axiomatic and inferential directives containing indexicals. We show that the main reason why developing the new directival theory of meaning in (...) this direction is difficult is that the theory focuses on the notion of a sentence (and not the notion of an utterance). To add the latter notion to the theory, we introduce the idea of admissible contextual distribution being an interpretation of the hybrid expression view on indexicals and demonstratives. We argue that this idea introduces a small but important modification to the concept of language matrix and gives way to define two distinct concepts of meaning: for an expression type and for a use of an expression type. (shrink)

This article is polemical. It argues with those philosophers who see, in the semantic theory of knowledge of Kazimierz Ajdukiewicz, the significant and exclusive influence of Alfred Tarski’s semantic output. Listening to these philosophers, one gets the impression that they have overlooked the fact that the term “semantics” meant one thing in the case of Ajdukiewicz, presenting the semantic theory of knowledge, and something different in the case of Tarski, presenting the semantic theory of truth. There is another difference, related (...) to the abovementioned, and fundamental in the case of both these logicians, namely their different approach to language, which seems to escape the attention of those who write about the semantic theory of knowledge. Ajdukiewicz’s approach was intensional, while Tarski’s approach was extensional: for the first of them, the intensional interpretation of language was basic, as for the second, was the extensional interpretation. The philosophers with whom I argue overlook one more fact, namely the impact, difficult to overestimate, that the intentional theory of language of Edmund Husserl had on the emergence of the semantic theory of knowledge. This article tries to restore Tarski’s real role in the matter referred to in the title, and do justice to Husserl: after all, without his philosophy of the semantic theory of knowledge, as a metaepistemological project, it would not have come to be. It was only in the implementation of this project that some of the achievements of Tarski’s semantics were used. (shrink)

Niniejszy artykuł ma polemiczny charakter. Polemizuje on z głosami tych filozofów, którzy w semantycznej teorii poznania Kazimierza Ajdukiewicza widzą znaczący i nadto wyłączny wpływ semantycznego dorobku Alfreda Tarskiego. Słuchając głosów tych filozofów można odnieść wrażenie, że przeoczyli oni fakt, iż termin „semantyka” znaczył co innego w wypadku Ajdukiewicza, prezentującego semantyczną teorię poznania, a co innego w wypadku Tarskiego, prezentującego semantyczną teorię prawdy. Z tą różnicą, dotyczącą znaczeń terminu „semantyka”, wiąże się inna, fundamentalna w wypadku obu tych logików różnica, a mianowicie (...) ich odmienne podejście do języka, co zdaje się umykać uwadze tym piszącym o semantycznej teorii poznania, z którymi zamierzam polemizować. Podejście Ajdukiewicza było intensjonalne, natomiast podejście Tarskiego – ekstensjonalne, co mówiąc mam na myśli to, że dla pierwszego z nich podstawową była intensjonalna interpretacja języka, a dla drugiego – interpretacja ekstensjonalna. Filozofowie, z którymi polemizuję, przeoczają jeszcze jeden fakt, a mianowicie trudny do przecenienia wpływ, jaki na powstanie semantycznej teorii poznania miała intencjonalna teoria języka Edmunda Husserla. Niniejszy artykuł stara się przywrócić właściwą miarę Tarskiemu w tytułowej sprawie oraz oddać sprawiedliwość Husserlowi, bez filozofii którego semantycznej teorii poznania, jako metaepistemologicznego projektu, by nie było. A przecież to ów projekt legitymizował jego realizacje i dopiero w nich były wykorzystywane niektóre osiągnięcia semantyki Tarskiego. (shrink)

> Context • The alleged dichotomy between mind and matter is pervasive. Therefore, the attempt to explain mat- ter in terms of mind (idealism) is often considered a mirror image of that of explaining mind in terms of mat- ter (mainstream physicalism), in the sense of being structurally equivalent despite being reversely arranged. > Problem • I argue that this is an error arising from language artifacts, for dichotomies must reside in the same level of abstraction. > Method • I (...) show that, because matter outside mind is not an empirical observation but rather an explanatory model, the epistemic symmetry between the two is broken. Consequently, matter and mind cannot reside in the same level of abstraction. > Results • It then becomes clear that attempting to explain mind in terms of matter is epistemically more costly than attempting to explain matter in terms of mind. > Implications • The qualities of experience are suggested to be not only epistemically, but also ontologically primary. > Constructivist content • I high- light the primacy of perceptual constructs over explanatory abstraction on both epistemic and ontic levels. > Key words • Idealism, physicalism, pancomputationalism, anti-realism, hard problem of consciousness, epistemic symmetry, explanatory abstraction, levels of abstraction. (shrink)

In the paper, original formal-logical conception of syntactic and semantic: intensional and extensional senses of expressions of any language L is outlined. Syntax and bi-level intensional and extensional semantics of language L are characterized categorically: in the spirit of some Husserl’s ideas of pure grammar, Leśniewski-Ajukiewicz’s theory syntactic/semantic categories and in accordance with Frege’s ontological canons, Bocheński’s famous motto—syntax mirrors ontology and some ideas of Suszko: language should be a linguistic scheme of ontological reality and simultaneously a tool of its (...) cognition. In the logical conception of language L, its expressions should satisfy some general conditions of language adequacy. The adequacy ensures their unambiguous syntactic and semantic senses and mutual, syntactic, and semantic compatibility, correspondence guaranteed by the acceptance of a postulate of categorial compatibility syntactic and semantic categories of expressions of L. From this postulate, three principles of compositionality follow: one syntactic and two semantic already known to Frege. They are treated as conditions of homomorphism partial algebra of L into algebraic models of L: syntactic, intensional, and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, of course, an idealization, but only expressions with high degrees of precision of their senses, after due justification, may become theorems of science. (shrink)

The current discussion of the intentionality nature has become more sophisticated and complex. In this paper I will delineate a number of approaches to intentionality in contemporary philosophy: 1 mentalistic; 2 semantic / linguistic; 3 pragmatic; 4 somatic; 5 and naturalistic. Although philosophers identify and analyse many concepts of intentionality, from the author point of view, there is only one intentionality: mentalistic intentionality. Furthermore, there are the pre-intentionality in the physical world and the meta-intentionality in the world of culture.

The paper is an attempt at a logical explication of some crucial notions of current general semantics and pragmatics. A general, axiomatic, formal-logical theory of meaning and interpretation is outlined in this paper.In the theory, accordingto the token-type distinction of Peirce, language is formalised on two levels: first as a language of token-objects (understood as material, empirical, enduring through time-and space objects) and then – as a language of type-objects (understood as abstract objects, as classes of tokens). The basic concepts (...) of the theory, i.e. the notions: meaning, denotation and interpretation of well-formed expressions (wfes) of the language are formalised on the type-level, by utilising some semantic-pragmatic primitive notions introduced on the token-level. The paper is divided into two parts.In Part Ia theoryof meaningand denotation is proposed, and in Part II - its expansion to the theory of meaning and interpretation is presented.The meaninga wfe is defined as an equivalence class of the relation possessing the same manner of using types (cf. Ajdukiewicz [1934], Wittgenstein [1953]). The concept of denotation is defined by means of the relation of referring which holds between wfe-types and objects of reality described by the given language. (shrink)

The paper concentrates on the problem of adequate reflection of fragments of reality via expressions of language and inter-subjective knowledge about these fragments, called here, in brief, language adequacy. This problem is formulated in several aspects, the most being: the compatibility of language syntax with its bi-level semantics: intensional and extensional. In this paper, various aspects of language adequacy find their logical explication on the ground of the formal-logical theory T of any categorial language L generated by the so-called classical (...) categorial grammar, and also on the ground of its extension to the bi-level, intensional and extensional semantic-pragmatic theory ST for L. In T, according to the token-type distinction of Ch.S. Peirce, L is characterized first as a language of well-formed expression-tokens (wfe-tokens) - material, concrete objects - and then as a language of wfe-types - abstract objects, classes of wfe-tokens. In ST the semantic-pragmatic notions of meaning and interpretation for wfe-types of L of intensional semantics and the notion of denotation of extensional semanics for wfe-types and constituents of knowledge are formalized. These notions allow formulating a postulate (an axiom of categorial adequacy) from which follow all the most important conditions of the language adequacy, including the above, and a structural one connected with three principles of compositionality. (shrink)

The aim of this paper is to show that the account of objective truth taken for granted by logicians at least since the publication in 1933 of Tarski’s “The Concept of Truth in Formalized Languages” arose out of a tradition of philosophical thinking initiated by Bolzano and Brentano. The paper shows more specifically that certain investigations of states of affairs and other objectual correlates of judging acts, investigations carried out by Austrian and Polish philosophers around the turn of the century, (...) formed part of the background of views that led to standard current accounts of the objectivity of truth. It thus lends support to speculations on the role of Brentano and his heirs in contemporary logical philosophy advanced by Jan Wolenski in his masterpiece of 1989 on the Logic and philosophy in the Lvov-Warsaw School. (shrink)

Izydora Da˛mbska was one of the most outstanding representatives of the Lvov-Warsaw School and a disciple of both the School’s founder Kazimierz Twardowski and Kazimierz Ajdukiewicz. Interest in the School was the result of Twardowski’s program of scientific philosophy, which was adopted by the vast majority of his students. This program assumed that the basic condition for practicing philosophy in a scientific manner is the precise use of language by a philosopher. One of the scholars who devoted most attention to (...) language was Kazimierz Ajdukiewicz. Da˛mbska accepted that the philosophical program of the School was opposed to the trend shared by many contemporary schools at the time which belonged to the so called current of linguistic philosophy. According to this trend, language is the only object of philosophical investigation. The analysis of Ajdukiewicz’s concept of language is one of her most interesting achievements in the domain of philosophy of language. This concept, called by Da˛mbska ‘the immanent concept of language’, is the basis of Ajdukiewicz’s well-known radical conventionalism. (shrink)

The paper deals with the problem of logical adequacy of language knowledge with cognition of reality. A logical explication of the concept of language knowledge conceived of as a kind of codified knowledge is taken into account in the paper. Formal considerations regarding the notions of meta-knowledge (logical knowledge about language knowledge) and truth are developed in the spirit of some ideas presented in the author’s earlier papers (1991, 1998, 2001a,b, 2007a,b,c) treating about the notions of meaning, denotation and truthfulness (...) of well-formed expressions (wfes) of any given categorial language. Three aspects connected with knowledge codified in language are considered, including: 1) syntax and two kinds of semantics: intensional and extensional, 2) three kinds of non-standard language models and 3) three notions of truthfulness of wfes. Adequacy of language knowledge to cognitive objects is understood as an agreement of truthfulness of sentences in these three models. (shrink)

In this article, the author attempts to identify the sources of good and evil as undertaken by the Lvov-Warsaw School of Philosophy (LWSP) founded by Kazimierz Twardowski. Such attempts were undertaken by both Twardowski himself and his closest students and associates; Władysław Witwicki, Tadeusz Kotarbiński. Tadeusz Czeżowski, and Kazimierz Ajdukiewicz. The best-known approach is Kotarbiński’s independent ethics in which the author refers to Aristotle perceiving such potential in the characteristics of each individual as to distinguish elementary qualities in the form (...) of opposites including opposition to good and evil. According to this approach, man acts in an evil manner because he stops following the natural voice of his own heart and instead implements set proposals provided by external factors. In the opinion of the author, the proposals formulated within the LWSP can form the basis for a rational explanation of the atrocities committed during World War II which modern ethics, being focused on neutral metaethical issues, fails to do. (shrink)

I shall elaborate more on the idea of anti-irrationalism proposed by the Polish analytic philosopher Kazimierz Ajdukiewicz, a prominent member of the Lvov-Warsaw School of philosophy and logic. In my reading, anti-irrationalism stands in opposition not only to overt irrationalism, which is made clear by the term itself, but also to all forms of rationalism that tip toward something like worship of reason. Having characterized anti-irrationalism as it originally appeared in Ajdukiewicz’s works, I shall propose a certain reformulation of it, (...) so as to capture a broader philosophical legacy in Poland, primarily, yet not exclusively the Lvov-Warsaw School. (shrink)

Prioritized bases, i.e., weakly ordered sets of sentences, have been used for specifying an agent’s ‘basic’ or ‘explicit’ beliefs, or alternatively for compactly encoding an agent’s belief state without the claim that the elements of a base are in any sense basic. This paper focuses on the second interpretation and shows how a shifting of priorities in prioritized bases can be used for a simple, constructive and intuitive way of representing a large variety of methods for the change of belief (...) states—methods that have usually been characterized semantically by a system-of-spheres modeling. Among the methods represented are ‘radical’, ‘conservative’ and ‘moderate’ revision, ‘revision by comparison’ in its raising and lowering variants, as well as various constructions for belief expansion and contraction. Importantly, none of these methods makes any use of numbers. (shrink)

The paper is a brief survey of some sequent calculi which do not follow strictly the shape of sequent calculus introduced by Gentzen. We propose the following rough classification of all SC: Systems which are based on some deviations from the ordinary notion of a sequent are called generalised; remaining ones are called ordinary. Among the latter we distinguish three types according to the proportion between the number of primitive sequents and rules. In particular, in one of these types, called (...) Gentzen’s type, we have a subtype of standard SC due to Gentzen. Hence by nonstandard ones we mean all these ordinary SC where other kinds of rules are applied than those admitted in standard Gentzen’s sequent calculi. We describe briefly some of the most interesting or important nonstandard SC belonging to the three abovementioned types. (shrink)

The aim of this paper is to show that it is the explicativecharacter of Tarski's semantic definition of truth given in his study of 1933 that allows forconsideration of a philosophical background of this definition in the proper sense. Given the explicativecharacter of this definition it is argued that the philosophical tradition that should be taken intoaccount with regard to this philosophical background is the tradition of the Lvov-Warsaw Schoolin its connections with the School of Brentano. As an example of (...) the explanatory power ofconsidering this tradition as far as Tarski's philosophical choices are concerned I use here thenotion of sentence-inscription, i.e., the notion of that entity of which truth is predicated inthe definition in question. One of the consequences of these statements is that philosophicaldiscussions concerning the semantic definition of truth can be regarded from two points ofview. On the one hand, they may take the perspective of its explicational function, i.e., theperspective of its philosophical background. On the other hand, they might consider the philosophicalconsequences of the definition with respect to the goal of the explication, i.e., they may considerits philosophical content independently of its historical background. (shrink)

This essay is an attempt to consider dynamic aspects of scientific theorising from a formal perspective. Our emphasis will be on the aims and methods for constructing formal models of theory dynamics which will be conceived from a general or 'theoretical' rather than 'applied' standpoint.

The affirmative answer to the title question is justified in two ways: logical and empirical. The logical justification is due to Gödel’s discovery that in any axiomatic formalized theory, having at least the expressive power of PA, at any stage of development there must appear unsolvable problems. However, some of them become solvable in a further development of the theory in question, owing to subsequent investigations. These lead to new concepts, expressed with additional axioms or rules. Owing to the so-amplified (...) axiomatic basis, new routine procedures like algorithms, can be reached. Those, in turn, help to gain new insights which lead to still more powerful axioms, and consequently again to ampler algorithmic resources. Thus scientific progress proceeds to an ever higher scope of solvability. The existence of such feedback cycles –in a formal way rendered with Turing’s systems of logic based on ordinal – gets empirically supported by the history of mathematics and other exact sciences. An instructive instance of such a process is found in the history of the number zero. Without that insight due to some ancient Hindu mathematicians there could not arise such an axiomatic theory as PA. It defines the algorithms of arithmetical operations, which in turn help intuitions; those, inturn, give rise to algorithmic routines, not available in any of the previous phases of the process in question. While the logical substantiation of the point of this essay is a well-established result of logico-semantic inquiries, its empiricalclaim, based on historical evidences, remains open for discussion. Hence the author’s intention to address philosophers and historians of science, and to encourage their critical responses. (shrink)

The first aim of this paper is to remind the reader of a very original theory of meaning which in many aspects has not been surpassed by subsequent theories. The theory in question is Kazimierz Ajdukiewicz’s Directival Theory of Meaning. In the first section I present a version of this theory which, I trust, retains the gist of the original but loses its outdated language. In the second section I analyze some problematic consequences of the directival theory and show how (...) they can be addressed. The second aim of this paper is exploiting some of the similarities between the directival theory and later theories of meaning. In the third section I argue that using the directival theory as an interpretative tool enables us to create explications of some of the notoriously vague notions which contemporary theories of meaning employ. (shrink)

Mathematicians and physical scientists depend heavily on the formal symbolism of mathematics in order to express and develop their theories. For this and other reasons the last hundred years has seen a growing interest in the nature of formal language and the way it expresses meaning; particularly the objective, shared aspect of meaning as opposed to subjective, personal aspects. This dichotomy suggests the question: do the objective philosophical theories of meaning offer concepts which can be applied in psychological theories of (...) meaning? In recent years cognitive scientists such as Chomsky [1980], Fodor [1981] and MacNamara [1982] have used philosophical approaches to the meaning of formal language expressions as the basis for their psychological theories. Following this lead it seems appropriate to review some of the main treatments of meaning with a view to their transferability. (shrink)

The philosophical-psychological Lvov-Warsaw School, derived from the philosophical tradition of Franz Brentano, developed his concept of intentionality for many years in an original way. This is particularly evident in Kazimierz Twardowski’s theory of actions and products and Tadeusz Tomaszewski’s theory of action. Kazimierz Ajdukiewicz’s semantic epistemology is also an important yet unfinished achievement (though less related to the issue of intentionality), in the light of which cognitive processes are organically embedded in cultural artefacts and, more specifically, in language. Despite the (...) extraordinary wealth of the Lvov-Warsaw School’s achievements, the theoretical findings of Twardowski and his disciples allow for the extraction of relatively consistent conclusions regarding the specifics of human cognition. Achievements of the Polish school of psychology seem to be important in the long ongoing discussion on the topic of the nature of cognitive processes and the mind. (shrink)

The paper enriches the conceptual apparatus of the theory of meaning and denotation that was presented in Part I (Section 3). This part concentrates on the notion of interpretation, which is defined as an equivalence class of the relation possessing the same manner of interpreting types. In this part, some relations between meaning and interpretation, as well as one between denotation an interpretational denotation are established. In the theory of meaning and interpretation, the notion of language communication has been formally (...) introduced and some conditions of correctness of communication have been formulated. (shrink)

In this paper I present how the normative inferentialist can make the distinction between sentence meaning and content of the utterance. The inferentialist can understand sentence meaning as a role conferred to that sentence by the rules governing inferential transitions and content of the utterance as just a part of sentence meaning. I attempt to show how such a framework can account for prominent scenarios presented by contextualists as a challenge to semantic minimalism/literalism. I argue that inferentialism can address contextualist (...) challenges in a simple and effective manner by understanding sentence meaning as broad, but invariant. (shrink)

In 1931–1934 Kazimierz Ajdukiewicz formulated two versions of the theory of meaning (A1 and A2). Tarski showed that A2 allows synonymous names to exist with different denotations. Tarski and Ajdukiewicz found that this feature disparages the theory. The force of Tarski’s argument rests on the assumption that none of adequate theories of meaning allow synonymous names to exist with different denotations. In the first part of this paper we present an appropriate fragment of A2 and Tarski’s argument. In the second (...) part we consider an elementary interpreted language in which individual constants occur, but not functional symbols. For such a language we define semantically a relation of synonymity for simple names and show that it fulfills syntactical conditions formulated by Ajdukiewicz in A2 and allows synonymous names to exist with different denotations. (shrink)

This paper presents the development of Ajdukiewicz’s conception of analytic sentences. Starting from his pre-war radical conventionalism, the presentation proceeds to Ajdukiewicz’s moderate aposteriorism and, finally, to radical aposteriorism. Various accounts of analyticity by Ajdukiewicz are mentioned and briefly commented on. At the end of the paper, Ajdukiewicz’s influence on Polish philosophy in regard to the issue of analyticity is pointed out.

The following study aims to articulate the key problems, doctrines, concepts and contributions of the conventionalist philosophers. Following the preliminary clarifications, the main body of this dissertation will proceed to a critical and analytical survey of key conventionalist philosophers and their contribution to the development of the convention­ alist outlook. This study will conclude with a brief statement about some of the important contributions to epistemology that can be traced to the work of conventionalists.