Squares of Oppositions, Commutative Diagrams, and Galois Connections for Topological Spaces and Similarity Structures

The aim of this paper is to elucidate the relationship between Aristotelian conceptual oppositions, commutative diagrams of relational structures, and Galois connections.This is done by investigating in detail some examples of Aristotelian conceptual oppositions arising from topological spaces and similarity structures. The main technical device for this endeavor is the notion of Galois connections of order structures

Towards a linguistic worldview for artificial languages

Wydział NeofilologiiCelem rozprawy była ocena możliwości zastosowania teorii oraz badań empirycznych formułowanych w ramach metodologii tzw. Lubelskiej Szkoły Etnolingwistycznej do lingwistycznej analizy języków sztucznych oraz zaprezentowanie ograniczeń wynikających z takiego podejścia. W części końcowej rozprawy zostały sformułowane następujące wnioski z badań: 1. Języki sztuczne nie stanowią jednolitej grupy, a ich różnorodne cechy wymuszają różne perspektywy przy próbie zastosowania paradygmatu lubelskiego. 2. Obalony został binarny podział na języki sztuczne i naturalne; zaproponowana została skala naturalności/sztuczności. 3. Językiem, który może w ramach Lubelskiej Szkoły Etnolingwistycznej być traktowany jako naturalny jest bez wątpienia esperanto. 4. Wszelkie badania języków sztucznych w ramach paradygmatu lubelskiego wymagają uwzględnienia transferu z innych języków znanych respondentom a także wpływów kulturowych. Wykazano również istnienie JOS typowego dla esperanta i konsekwentnie prezentowanego w następujących obszarach: • koncepty kulturowe związane z Ruchem; • stereotyp esperantysty.The main objective of the present dissertation was to evaluate the applicability of the theory and practice developed within the methodological framework of the so-called Ethnolinguistic School of Lublin to the linguistic analysis of artificial languages and to present the limitations of such an approach. The following research conclusions were formulated: 1. Artificial languages are not a homogeneous group, and their various characteristics necessitate different perspectives in the application of the Lublin paradigm. 2. The binary division between artificial and natural languages is disproved; a scale of naturalness/artificiality is proposed. 3. The language which may be treated as natural within the Ethnolinguistic School of Lublin is undoubtedly Esperanto. 4. Any study of artificial languages within this paradigm needs to take into account a transfer from other languages known to the respondents as well as cultural influences. The existence of a linguistic worldview typical of Esperanto and presented consistently in the following areas was proved: • cultural concepts related to the Movement • stereotype of an Esperantis

Multispace & Multistructure. Neutrosophic Transdisciplinarity (100 Collected Papers of Sciences), Vol. IV

The fourth volume, in my book series of “Collected Papers”, includes 100 published and unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated, scientific souvenirs, scientific blogs, project proposals, small experiments, solved and unsolved problems and conjectures, updated or alternative versions of previous papers, short or long humanistic essays, letters to the editors - all collected in the previous three decades (1980-2010) – but most of them are from the last decade (2000-2010), some of them being lost and found, yet others are extended, diversified, improved versions. This is an eclectic tome of 800 pages with papers in various fields of sciences, alphabetically listed, such as: astronomy, biology, calculus, chemistry, computer programming codification, economics and business and politics, education and administration, game theory, geometry, graph theory, information fusion, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, psychology, quantum physics, scientific research methods, and statistics. It was my preoccupation and collaboration as author, co-author, translator, or cotranslator, and editor with many scientists from around the world for long time. Many topics from this book are incipient and need to be expanded in future explorations

World and Logic

What is the relationship between the world and logic, between intuition and language, between objects and their quantitative determinations? Rationalists, on the one hand, hold that the world is structured in a rational way. Representationalists, on the other hand, assume that language, logic, and mathematics are only the means to order and describe the intuitively given world. In World and Logic, Jens Lemanski takes up three surprising arguments from Arthur Schopenhauer’s hitherto undiscovered Berlin Lectures, which concern the philosophy of language, logic, and mathematics. Based on these arguments, Lemanski develops a new position entitled ‘rational representationalism’: the world is always structured by human beings according to linguistic, logical, and mathematical principles, but the basic vocabulary of these structural descriptions already contains metaphors taken from the world around us