The main aim of the present paper is to explain a nature of relationships exist between Nelson and Heyting algebras. In the realization, a topological duality theory of Heyting and Nelson algebras based on the topological duality theory of Priestley for bounded distributive lattices are applied. The general method of construction of spaces dual to Nelson algebras from a given dual space to Heyting algebra is described. The algebraic counterpart of this construction being a generalization of the Fidel-Vakarelov construction is (...) also given. These results are applied to compare the equational category N of Nelson algebras and some its subcategories with the equational category H of Heyting algebras. It is proved that the category N is topological over the category H. (shrink)

A. Klimczuk, Creativity, an Essential Condition for the Development of Smart and Age-friendly Cities and Communities, “Journal of Brief Ideas”, 04.02.2019,.

The authors of mediaeval treatises on the modi significandi (often entitled De modis signi­ficandi, or Summa grammatica, or Summa modorum significandi, or Grammatica speculativa) have come to be known as the Modistae who taught in the late Sixties of the 13th till the Thirties of the 14th centuries. The present study is an account of the grammatical theories of this group of mediaeval scholars (mostly the work of Thomas of Erfurt), set in the appropriate context of situation and seen in (...) terms of the part they played in mediaeval semiotic theory, since their theory rests on the study of words and the properties of these words as signs of things. At the end of the present study the influence of the speculative grammar on present linguistic theories is announ­ced. Some influence of the speculative grammar one could discover in many contemporary lin­gui­stic theories like those of Noam Chomsky, Ronald Langacker, Robin Lakoff and even Ray Jackendoff. (shrink)

The concept of erotetic argument is introduced. Two relations between sets of declarative sentences and questions are analysed; and two classes of erotetic arguments are characterized.

This summary was delivered at the closing session of the “Korczak: A New Anthropology of Education” conference on September 21, 2002 in the Polish Culture Institute of Warsaw University’s Polish Studies Faculty. Author points that the primary goal of the conference was to set Korczak’s work against modern-day thought trends and cultural dilemmas. Summing up the result of the conference author notices that the deepest roots of the Korczak’s work lies in the Judaic and Christian traditions but it also draws (...) on European enlightenment, Polish romanticism, and positivism. (shrink)

The linguistic studies written by Anna Wierzbicka have been an occasion for the remarks on the relationship between linguistics and philosophy and for the question whether linguistic enquiries entitle us to put forward philosophical theses. In particular, whether and to what extent we indeed learn something philosophically significant about the world (of culture) and the nature man and his mind by examining language. Defining here position as interdisciplinary, Wierzbicka draws on the studies of the relationship between language and culture, language (...) and mind (language is a mirror of the mind - Leibniz). She claims that philosophy can be made a reliable science, provided it is based on linguistics, and the results of linguistic analyses can be found at the grounds of philosophical theses. Such philosophical references are A. Wierzbicka\'s attempts to combine semantics with generativism (Chomsky). Her intention to bring about a holistic description of language through defining elementary expressions (concepts, meanings), the so-called indefinibilia (\"primitives\") can also be called philosophical in character. They suffice to define all the remaining expressions, and basic universal syntactic constructs in the form of a grammar of elementary units, i.e. the ways of combining elementary units into greater wholes. We think that Wierzbicka\'s procedure, her quest after primary elements (of language) are reducing. A. Wierzbicka\'s main idea, with regard to the relationship between language and mind, may be understood as follows: this is a Janus-faced relationship - one face (empirically accessible) is language, the other one is the mind accessible through investigations on language. Both \"faces\" (spheres) are somehow functionally \"glued together\". In fact, however, Wierzbicka speaks little about the philosophically comprehended nature of man, whereas she speaks much about linguistic varieties and similarities among people. Generally speaking, while she declares herself to be a linguist, she has a philosophical temper and ambitions to generalise, i.e. she conducts linguistic studies with an intention to arrive at philosophical theses (by examining language she wants to obtain knowledge about the world and man). She issues statements which go beyond a purely linguistic knowledge and strictly linguistic data, hence they are not made legitimate by the linguistic material itself. A. Wierzbicka does not explain in more detail her way of understanding philosophy, assuming its intuitive comprehension. From some contexts it can be deduced that she takes it to mean a worldview. Should we call some parts of her reasoning a philosophy, it is then not a realistic philosophy but subject-oriented (first-person philosophising), such that touches upon the problems of the borderline between linguistics and philosophy, more concerned with the axis language-user than language-the world. Simultaneously, it is a non-demarcated and non-autonomic philosophising, exactly within the context of science, for it takes advantage of the results of empirical sciences to pose philosophical theses. The belief that philosophy can be pursued within a linguistic context coincides with the approach of analytical philosophy with its linguistic turn. Despite her declarations to make philosophy more scientific, Wierzbicka\'s arguments on behalf of the generalised (philosophical) theses are more their illustration and explication than a decisive legitimacy. Her belief that one can find some common, primitive linguistic units (simplicia) in the form of a complete set of independent concepts for all languages of the world seems Utopian. It is difficult to do it even in deductive systems, constructed by way of the axiomatic method and with a finite set of initial expressions. (shrink)

This is a spin-off paper to [3, 4] in which we carried out an extensive analysis of Andrzej Grzegorczyk’s point-free topology from [5]. In [1] Loredana Biacino and Giangiacomo Gerla presented an axiomatization which was inspired by the Grzegorczyk’s system, and which is its variation. Our aim is to compare the two approaches and show that they are slightly different. Except for pointing to dissimilarities, we also demonstrate that the theories coincide in presence of axiom stipulating non-existence of atoms.

Relations between theory and empirical knowledge belong to basic problems in philosophy of science and have been undergone detailed philosophical reflection, including epistemological aspects. During last several dozen years, due to development of computer technology, numerical simulations became a common tool in natural sciences. Their epistemological aspects, however, have not worked out yet. A specific role of computer simulations manifests in subcellular biology, where possibilities of performing experiments and observations are limited. Computer simulation is complementary to observation and experiment and (...) comes into complex relations with them. It allows us to come to a conclusion if experiment or observations are impossible to perform. In particular, simulations allow researchers to estimate the parameters that cannot be measured. (shrink)

This note presents a point of view upon the notions of programsubstitution which are the tools for proving properties of programs of algorithmic logics [5], [3] being sufficiently strong and universal to comprise almost all previously introduced theories of programming, and the so-called extended algorithmic logic [1], [2] and algorithmic logic with nondeterministic programs [4]. It appears that the mentioned substitution rule allows us to examine more deeply algorithmic properties of terms, formulas and programs. Besides the problem of Post-completeness and (...) structural completeness of algorithmic logics strengthened additionally by the rule of substitution is raised. (shrink)

In this paper the truth is studied in the frame of autonomous systems theory. The method of the truth verification is worked out in its functional aspect. The verification is based on comparison of the predicted inner state of the autonomous agent, that is the cognitive subject, to the achieved inner state of the agent. The state is achieved as the result of performing the action in the real world—the agent’s environment. The action design is created on the basis of (...) the agent’s model of the world. The truth is defined as the adequacy of the model of the real world in the context of the goal that is assumed to be reached as the effect of the performed action. The concepts of the cognitive subject, the truth bearings and the knowledge are redefined. The classical problems of aletheiology and epistemology are discussed in the light of the proposed approach. The cybernetic construct of an autonomous agent allows the researcher to consider a wide class of cognitive entities, which, in the previous approaches, have been limited only to human beings as cognitive subjects. (shrink)