
395Introduction. The School: Its Genesis, Development and SignificanceIn Urszula WybraniecSkardowska & Ángel Garrido (eds.), in: The LvovWarsaw School. Past and Present, Springer. pp. 314. 2018.The Introduction outlines, in a concise way, the history of the LvovWarsaw School – a most unique Polish school of worldwide renown, which pioneered trends combining philosophy, logic, mathematics and language. The author accepts that the beginnings of the School fall on the year 1895, when its founder Kazimierz Twardowski, a disciple of Franz Brentano, came to Lvov on his mission to organize a scientific circle. Soon, among the characteristic features of the School was its serious approach to…Read more

219Logical Conceptualization of Knowledge on the Notion of Language CommunicationStudies in Logic, Grammar and Rhetoric 52 (1): 247269. 2017.The main objective of the paper is to provide a conceptual apparatus of a general logical theory of language communication. The aim of the paper is to outline a formallogical theory of language in which the concepts of the phenomenon of language communication and language communication in general are defined and some conditions for their adequacy are formulated. The theory explicates the key notions of contemporary syntax, semantics, and pragmatics. The theory is formalized on two levels: token…Read more

188Categories of First Order QuantifiersLvovWarsaw School. Past and Present. 2018.One well known problem regarding quantifiers, in particular the 1st order quantifiers, is connected with their syntactic categories and denotations.The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized firstorder languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of languag…Read more

179Categories of FirstOrder QuantifiersIn Urszula WybraniecSkardowska & Ángel Garrido (eds.), The LvovWarsaw School. Past and Present, . pp. 575597. 2018.One well known problem regarding quantifiers, in particular the 1storder quantifiers, is connected with their syntactic categories and denotations. The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized firstorder languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of languag…Read more

177Rejection in Łukasiewicz's and Słupecki's SenseIn Urszula WybraniecSkardowska & Ángel Garrido (eds.), The LvovWarsaw School. Past and Present, . pp. 575597. 2018.The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz [20]. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions [22, 23]. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance …Read more

157Meaning and Interpretation. IStudia Logica 85 (1): 105132. 2007.The paper is an attempt at a logical explication of some crucial notions of current general semantics and pragmatics. A general, axiomatic, formallogical theory of meaning and interpretation is outlined in this paper.In the theory, accordingto the tokentype distinction of Peirce, language is formalised on two levels: first as a language of tokenobjects (understood as material, empirical, enduring through timeand space objects) and then – as a language of typeobjects (understood as abstract …Read more

138Logic and Ontology of LanguageIn Bartłomiej Skowron (ed.), Contemporary Polish Ontology, De Gruyter, Mouton. pp. 109132. 2019.The main purpose of the paper is to outline the formallogical, general theory of language treated as a particular ontological being. The theory itself is called the ontology of language, because it is motivated by the fact that the language plays a special role: it reflects ontology and ontology reflects the world. Language expressions are considered to have a dual ontological status. They are understood as either concretes, that is tokens – material, physical objects, or types – classes of to…Read more

115In this paper, two axiomatic theories T− and T′ are constructed, which are dual to Tarski’s theory T+ (1930) of deductive systems based on classical propositional calculus. While in Tarski’s theory T+ the primitive notion is the classical consequence function (entailment) Cn+, in the dual theory T− it is replaced by the notion of Słupecki’s rejection consequence Cn− and in the dual theory T′ it is replaced by the notion of the family Incons of inconsistent sets. The author has proved that the th…Read more

113On Certain Axiomatizations of Arithmetic of Natural and Integer NumbersAxioms 2019 (Deductive Systems). 2019.The systems of arithmetic discussed in this work are nonelementary theories. In this paper, natural numbers are characterized axiomatically in two dierent ways. We begin by recalling the classical set P of axioms of Peano’s arithmetic of natural numbers proposed in 1889 (including such primitive notions as: set of natural numbers, zero, successor of natural number) and compare it with the set W of axioms of this arithmetic (including the primitive notions like: set of natural numbers and relat…Read more

110The LvovWarsaw School. Past and Present (edited book)Springer Birkhauser,. 2018.This is a collection of new investigations and discoveries on the history of a great tradition, the LvovWarsaw School of logic , philosophy and mathematics, by the best specialists from all over the world. The papers range from historical considerations to new philosophical, logical and mathematical developments of this impressive School, including applications to Computer Science, Mathematics, Metalogic, Scientific and Analytic Philosophy, Theory of Models and Linguistics.

92On the typetoken relationshipsBulletin of the Section of Logic 15 (4): 164168. 1986.The twofold ontological character of linguistic objects revealed due to the distinction between “type” and “token” introduced by Ch. S. Peirce can be a base of the twofold, both theoretical and axiomatic, approach to the language. Referring to some ideas included in A. A. Markov’s work [1954] (in Russian) on Theory of Algorithms and in some earlier papers of the author, the problem of formalization of the concrete and abstract words theories raised by J. Słupecki was solved. The construction o…Read more

86Does the Lie Contradict the Truth?Studies in Logic, Grammar and Rhetoric 20 (33). 2010.The main task of this work is not to determine the bases for a moral evaluation of the lie; neither is it to describe its negative qualification. We are interested rather in the very problemate of the truth and the lie itself, considered as a juxtaposition of two of its notions: the truth and the lie, one that aims to provide a positive – as it would seem obvious – answer to the question contained in the title of the present work: Does the lie contradict the truth?

85On Language AdequacyStudies in Logic, Grammar and Rhetoric 40 (1): 257292. 2015.The paper concentrates on the problem of adequate reflection of fragments of reality via expressions of language and intersubjective 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 bilevel semantics: intensional and extensional. In this paper, various aspects of language adequacy find their logical explication on the ground of the formallogical theory T o…Read more

84Alfred Tarski  the man who defined truthFilozofia, Scientific Works of Jan Długosz Academy, Częstochowa 6771. 2008.This article is a translation of the paper in Polish (Alfred Tarski  człowiek, który zdefiniował prawdę) published in Ruch Filozoficzny 4 (4) (2007). It is a personal Alfred Tarski memories based on my stay in Berkeley and visit the Alfred Tarski house for the invitation of Janusz Tarski.

81Rejection in Łukasiewicz's and Słupecki's SenseIn The LvovWarsaw School, Past and Present, . pp. 575597. 2018.The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) sys…Read more

77Rejection in Łukasiewicz's and Słupecki' SenseLvovWarsaw School. Past and Present. 2018.The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz [20]. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions [22, 23]. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance …Read more

74Logic and SensePhilosophy Study 6 (9). 2016.In the paper, original formallogical conception of syntactic and semantic: intensional and extensional senses of expressions of any language L is outlined. Syntax and bilevel intensional and extensional semantics of language L are characterized categorically: in the spirit of some Husserl’s ideas of pure grammar, LeśniewskiAjukiewicz’s theory syntactic/semantic categories and in accordance with Frege’s ontological canons, Bocheński’s famous motto—syntax mirrors ontology and some ideas of Susz…Read more

74On the axiomatic systems of syntacticallycategorial languagesBulletin of the Section of Logic 13 (4): 241249. 1984.The paper contains an overview of the most important results presented in the monograph of the author "Teorie Językow SyntaktycznieKategorialnych" ("Theories of SyntacticallyCategorial Languages" (in Polish), PWN, WarszawaWrocław 1985. In the monograph four axiomatic systems of syntacticallycategorial languages are presented. The ﬁrst two refer to languages of expressiontokens. The others also takes into consideration languages of expressiontypes. Generally, syntacticallycategorial langua…Read more

68On Life According to the Logic of Gift, Toil, and ChallengesStudies in Logic, Grammar and Rhetoric 27 (40). 2012.The present essay deals with certain questions in the feld of humanistic philosophy, ethics and axiology, discussed in the light of still newer and newer challenges of our changing times. It highlights the signicant role of Professor Andrzej Grzegorczyk in solving and overcoming problems encountered in the life of man, which is based on his natural logic and incessant eorts aimed at preservation of fundamental moral values, as well as at shaping the principles of the individual and social life. …Read more

62Meaning and Interpretation. IIStudia Logica 85 (2): 261274. 2007.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 langu…Read more

58On the theory of labelstokensBulletin of the Section of Logic 10 (1): 3033. 1981.This note is based on a lecture delivered at the Conference on the Scien tic Research of the Mathematical Center of Opole, Turawa, May 1011th, 1980. A somewhat extended version will be published in the Proceedings of the Conference. At the same time it is an abstract of a part of a planned larger paper, which will involve the theory of labeltokens. The theory is included into the author's monograph in Polish "Teorie Językow Syntaktycznie Kategorialnych", PWN, WarszawaWrocław 1985 and into it…Read more

49Teoria zdań odrzuconychDissertation, Opole University. 1969.This is the PhD dissertation, written under supervision of Professor Jerzy Słupecki, published in the book: U.WybraniecSkardowska i Grzegorz Bryll "Z badań nad teorią zdań odrzuconych" ( "Studies of theory of rejected sentences"), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Seria B: Studia i Monografie nr 22, pp. 5131. It is the first, original publication on the theory of rejected sentences on which are based, among other, papers: "Theory of rejected propositions. I"and "Theory of …Read more

46What Is the Sense in Logic and Philosophy of LanguageBulletin of the Section of Logic 49 (2): 185211. 2020.In the paper, various notions of the logical semiotic sense of linguistic expressions – namely, syntactic and semantic, intensional and extensional – are considered and formalised on the basis of a formallogical conception of any language L characterised categorially in the spirit of certain Husserl's ideas of pure grammar, LeśniewskiAjdukiewicz's theory of syntactic/semantic categories and, in accordance with Frege's ontological canons, Bocheński's and some of Suszko's ideas of language adequ…Read more

46Logical and philosophical ideas in certain formal approaches to languageSynthese 116 (2): 231277. 1998.This paper reminds, puts in order, sketches and also initiates some researches from the field of logic and philosophy of language. It lays emphasis on the logicallinguistic and ontological developmental lines originated with Polish researchers. The author discusses two opposite orientations of the former line in the process of formalization of language, called here nominalistic and Platonistic. The paper mentions the author's result (1989; 1991) concerning theoretical equivalence of two axiomat…Read more

45Theory of rejected propositions. IStudia Logica 29 (1). 1971.The idea of rejection of some sentences on the basis of others comes from Aristotle, as Jan Łukasiewicz states in his studies on Aristotle's syllogistic [1939, 1951], concerning rejection of the false syllogistic form and those on certain calculus of propositions. Short historical remarks on the origin and development of the notion of a rejected sentence, introduced into logic by Jan Łukasiewicz, are contained in the Introduction of this paper. This paper is to a considerable extent a summary of…Read more

33The theory of rejected propositions. IIStudia Logica 30 (1). 1972.This paper is a continuation of Part I under the same title. Its Chapter III contains results given in the following publications: U. WybraniecSkardowska, Teoria zdań odrzuconych (Theory of Rejected Sentences), (doctoral dissertation under the supervision of Jerzy Słupecki, published as a monograph), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Monografie, Nr 22 (1969), 5131. G. Bryll, Związki logiczne pomiędzy zdaniami nauk empirycznych (Logical relations between sentences o…Read more

33On the eliminatibility of ideal linguistic entitiesStudia Logica 48 (4). 1989.With reference to Polish logicophilosophical tradition two formal theories of language syntax have been sketched and then compared with each other. The first theory is based on the assumption that the basic linguistic stratum is constituted by objecttokens (concrete objects perceived through the senses) and that the types of such objects (ideal objects) are derivative constructs. The other is founded on an opposite philosophical orientation. The two theories are equivalent. The main conclusion…Read more

29Does the Lie Contradict the Truth?Studies in Logic, Grammar and Rhetoric 20 (33): 127153. 2010.The considerations presented in this work are an attempt at giving an answer to the arising doubts: it is obvious to philosophers and logicians that such considerations must be grounded on a relevant conception of the truth and the lie, on bringing up one of the most diﬃcult and disturbing philosophical problems, that is the problemate of the truth, on investigating what the lie is. The confusion about the notions related to the ambiguous terms of “the truth” and “the lie” introduces, in turn, a…Read more

27Logic of Faith and Dead. The Idea and Outline of the Theoretical ConceptionPhilosophia Christine 55 (2): 125149. 2019.This paper discusses the theoretical assumptions behind the conception of the logic of faith and deed (LF&D) and outlines its formalaxiomatic frame and its method of construction, which enable us to understand it as a kind of deductive science. The paper is divided into several sections, starting with the logical analysis of the ambiguous terms of 'faith’ and 'action', and focusing in particular on the concepts of religious faith and deed as a type of conscious activity relating to a matter or…Read more

26Theory of Language Syntax. Categorial ApproachKluwer Academic Publishers. 1991.This book presents a formal and philosophical analysis of language syntax. It refers to some ideas of E.Husserl and G. Frege, to S. Leśniewski's theory of syntactic categories and K. Ajdukiewicz's conception of formal grammar, also to Ch.S. Pierces's distinction between tokens (concrete linguistic entities) and types (ideal linguistic entities) and to A.A. Markov's theory of algorithms. The central aim of the book is  in the spirit of these ideas  to provide both strict yet comprehensive lect…Read more

Cardinal Stefan Wyszynski University In WarsawOther (Parttime)
Areas of Specialization
Science, Logic, and Mathematics 
Areas of Interest
Science, Logic, and Mathematics 
Philosophy, Misc 
Metaphysics and Epistemology 