Foundations of Mathematics and Mathematical Practice. The Case of Polish Mathematical School

The foundations of mathematics cover mathematical as well as philosophical problems. At the turn of the 20th century logicism, formalism and intuitionism, main foundational schools were developed. A natural problem arose, namely of how much the foundations of mathematics influence the real practice of mathematicians. Although mathematics was and still is declared to be independent of philosophy, various foundational controversies concerned some mathematical axioms, e.g. the axiom of choice, or methods of proof (particularly, non-constructive ones) and sometimes qualified them as admissible (or not) in mathematical practice, relatively to their philosophical (and foundational) content. Polish Mathematical School was established in the years 1915–1920. Its research program was outlined by Zygmunt Janiszewski (the Janiszewski program) and suggested that Polish mathematicians should concentrate on special branches of studies, including set theory, topology and mathematical logic. In this way, the foundations of mathematics became a legitimate part of mathematics. In particular, the foundational investigations should be conducted independently of philosophical assumptions and apply all mathematically accepted methods, finitary or not, and the same concerns other branches of mathematics. This scientific ideology contributed essentially to the remarkable development of logic, set theory and topology in Poland

Art-biografie Andrzeja Wróblewskiego

The essay concerns the ways of reading and understanding the biographies of Andrzej Wróblewski, one of the prominent representatives of modernist and post-war painters. One special case is the art-biography projectshowing the need to reinterpret the author’s current biographical facts. The reading of texts by Jan Michalski, Magdalena Ziółkowska, Wojciech Grzybała and Andy Rottenberg shows this mechanism – expanding theconstellations of Andrzej Wróblewski.The essay concerns the ways of reading and understanding the biographies of Andrzej Wróblewski, one of the prominent representatives of modernist and post-war painters. One special case is the art-biography projectshowing the need to reinterpret the author’s current biographical facts. The reading of texts by Jan Michalski, Magdalena Ziółkowska, Wojciech Grzybała and Andy Rottenberg shows this mechanism – expanding theconstellations of Andrzej Wróblewski

Investigations into Proof Structures

We introduce and elaborate a novel formalism for the manipulation and analysis of proofs as objects in a global manner. In this first approach the formalism is restricted to first-order problems characterized by condensed detachment. It is applied in an exemplary manner to a coherent and comprehensive formal reconstruction and analysis of historical proofs of a widely-studied problem due to {\L}ukasiewicz. The underlying approach opens the door towards new systematic ways of generating lemmas in the course of proof search to the effects of reducing the search effort and finding shorter proofs. Among the numerous reported experiments along this line, a proof of {\L}ukasiewicz's problem was automatically discovered that is much shorter than any proof found before by man or machine.Comment: This article is a continuation of arXiv:2104.1364

A system of the logic of change

In this paper the problem of an adequate system of the logic of change for the contemporary natural sciences is explored. Some general considerations concerning the construction and assessment of non-classical logics are made. Finally two systems of the logic of change for modern physics are constructed and examined

Ksiądz profesor dr Aleksander Usowicz CM. Wspomnienia

The paper presents the personality and the scientific record of Rev. prof. Aleksander Usowicz CM. He was an acknowledged representative of the neo-Scholasticism, the main philosophical movement in the mid 50 of 20th c. at the Theological Faculty of the Jagiellonian University in Krakow.In fact, scientific interest of Usowicz went beyond the field of philosophy. He was also interested in theology. Among many lecturers he delivered, the most important was one about the introduction to theology. Its aim was to provide students with the basics of the history of theological thought.It must be remembered that Usowicz was a reviewer of the habilitation work of Fr. Karol Wojtyła. He was also a tutor and scientific supervisor of many later professors of philosophy and theology.The paper presents the personality and the scientific record of Rev. prof. Aleksander Usowicz CM. He was an acknowledged representative of the neo-Scholasticism, the main philosophical movement in the mid 50 of 20th c. at the Theological Faculty of the Jagiellonian University in Krakow.In fact, scientific interest of Usowicz went beyond the field of philosophy. He was also interested in theology. Among many lecturers he delivered, the most important was one about the introduction to theology. Its aim was to provide students with the basics of the history of theological thought.It must be remembered that Usowicz was a reviewer of the habilitation work of Fr. Karol Wojtyła. He was also a tutor and scientific supervisor of many later professors of philosophy and theology