The origins of mathematics, a close connection and interpenetration of its parts, and uniform procedures of dealing with the mathematical matter - all of them speak in favour of the integrality of mathematics. It seems that a strong argument for such a view is a fundamental object of contemporary mathematics; namely a real line, which contains real numbers (so arithmetics as well) and constitutes a basis of geometry, mathematical analysis and all derivative branches. From the basic-structures perspective it is clear (...) that the real line is an exceptionally complex structure, for it contains the ordered structure (generated by the less-than relation), the algebraic structure (generated by addition and multiplication), the gemetrical structure (generated by translations and reflections) and the topological structure (generated by open intervals). This example explains, at least to some extent, the integrality and also the vivacity of mathematics. On the other hand, the integrality has not been confirmed by comprising the whole mathematics in one axiomatised, deductive theory. Moreover, the increasing „volume” of mathematics, unwillingness of mathematicians to cross the specialisation-barriers, emphasis on utility (models) and difficulties with axiomatisations of some parts of mathematics cast some doubts on the integrality in question. (shrink)

The article recalls shortly the early story of cooperation between the already existing Lvov philosophical school, headed by Twardowski, and the just then establishing Warsaw mathematical school, headed by Sierpiski. After that recollection the article proceeds to contributions made by men influenced by the two schools. Most prominent of them was Alfred Tarski whose work in those times, concentrated mainly upon the theory of deduction, axiom of choice, cardinal arithmetic, and measure problem, has been described in some detail.

Primary object of interest of mathematicians can be identified as a „mathematical matter”, the concept analogous to „physical matter” or „biological matter”. The „mathematical matter” is the soil upon which mathematics grows. One can distinguish three levels of it: some abstract but not necessarily clear conceptions, operational notions (like number) but not necessarily openly defined, theories not necessarily axiomatic. The „mathematical matter” originates in the abstract reflection upon events and forms in time and space. Its important elements are notions formed (...) mostly in the process of idealization and/or abstraction. Once formed, notions usually evolve being, e.g., simplified or complexified. Mathematics is a mirror of the world, most abstract and therefore fundamental. Although it is a free activity of human mind, mathematics reflects some deep ideas (beauty, simplicity etc.) while most interesting notions come up in tension fields between pairs of poles: the notion of a function can be seen as a bridge connecting variability and immutability, while that of a limit – connecting finiteness and infinity. A fusion of freedom and internal restrictions leads to mathematics which is simple, beautiful and effective. (shrink)

The vivacity of mathematics results (partly) from the fact that mathematics is stretched between several poles, not being committed to any one. The paper presents the following polarities: realism - idealism, the finite - the infinite, the discrete - the continuous, the approximate - the exact, certitute - probability, simplicity - complexity, unity - multiplicity.

la historia del escepticismo es oscura. Si bien se reconoce la existencia, misteriosa y discutida, de un escepticismo académico platónico, hay algunas dudas de la realidad inequívoca de una escuela pirrónica radical. En este artículo vamos a discutir, primero, hasta qué punto puede hablarse de escuela, secta o grupo filosófico pirrónico, y, segundo, si, como veremos, hay dudas del reconocimiento de este homogéneo grupo ¿por qué se habla de ella de ‘escuela’, ‘secta’ o ‘sistema’ pirrónico?

Die Buchreihe Konzepte der Sprach- und Literaturwissenschaft gibt Aufschluss über Prinzipien, Probleme und Verfahrensweisen philologischer Forschung im weitesten Sinne und dient einer Bestimmung des Standorts der Linguistik und Literaturwissenschaft. Die Reihe übergreift Einzelsprachen und Einzelliteraturen. Sie stellt sich in den Dienst der Reflexion und Grundlegung einer allgemeinen Sprach- und Literaturwissenschaft. Die Bände sind zum Teil informierende Einführungen, zum Teil wissenschaftliche Diskussionsbeiträge.

Databases play a fundamental role in today’s world, being used by most companies, especially those that offer services through the Internet. Today there is a wide variety of database models, each adapted for use according to the specific requirements of each application. Traditionally, the relational models with centralized architectures have been used mostly due to their simplicity and general-purpose query language, which made relational systems suitable for almost any application. However, with the growth of the Internet in recent decades, both (...) in the number of users and in the amount of information, those centralized models began to suffer availability and scalability issues. To address those issues, the use of decentralized architectures and alternative database models began to arise, eventually replacing relational databases and centralized architectures when the requirements on availability and scalability are high. Those database models alternative to the traditional relational model are grouped under the name of NoSQL. In this article, we present a NoSQL database developed as an end of degree work, with a flexible data model based on documents and a fully decentralized architecture based on the Gossip protocol for node discovery and a distributed hash table, in particular the rendezvous hashing algorithm, used to distribute and replicate the data across all the nodes. The main goals of the system are to achieve high availability and high scalability. High availability is achieved thanks to the replication of the data, while high scalability is achieved by its decentralized architecture, which allows multiple entry points from the requests, and the data distribution, effectively increasing the database capacity by increasing the number of nodes. (shrink)

У статті аналізуються причини, особливості та наслідки трансформації традиційного гендерного ладу. Стверджується, що в наш час відбувається надзвичайно потужна трансформація культурної парадигми. Одним із наслідків цієї трансформації є зміна звичного гендерного ладу та гендерної ідентичності. Автор доводить, що трансформація традиційного (патріархального) гендерного ладу здійснює вагомий вплив на соціальне буття людини, зокрема, на самоідентифікацію сучасної людини. Філософським підґрунтям трансформації традиційного гендерного ладу є відмова від універсалізму, «визнання іншого» та відхід від концепції «маскулінного характеру культури». Найбільш соціально значущий наслідок трансформації гендерного ладу (...) – поступове вирівнювання гендерних ролей чоловіка та жінки. Аналізуючи український контекст проблеми гендерних відносин, автор робить висновок, що українське суспільство значною мірою є ще патріархальним, про що свідчить домінування патріархальної культури та патріархальних стереотипів і цінностей. (shrink)

Translated excerpts from works by various authors; original titles and names of the translators given in captions.

A stereoscopic view on a particular historical event, in which contemporary assessments are combined with mental stereotypes of a medieval man, allows a slightly different assessment of the chronicle plot about the posthumous “baptism of bones” of Oleg and Yaropolk, Princes of Kyivan Rus, in 1044. While from theological positions it is perceived as an absurdity and a direct violation of the rules of the church, in the Middle Ages this act did not contradict the mass religious beliefs. From an (...) ethical point of view, the action of Yaroslav the Wise was regarded as concern for the souls of the ancestors who died pagans and therefore did not claim for the salvation. The soteriological optimism that prevailed in the eleventh century in countries of the late Christianization, including Kyivan Rus, gave hope that living people were able to influence the fate of the souls of the dead. From a political point of view, the baptism of the ashes of the ancestors and their reburial in the family tomb of the Princes of Kyiv in the Church of the Tithes was aimed at expanding the circle of heavenly patrons and protectors of the princely dynasty, expanding the period of the Christian history of Kyivan Rus, and, as a result, legitimizing the power of Yaroslav the Wise. (shrink)