Robert Janusz

Church's Thesis (CT) was first published by Alonzo Church in 1935. CT is a proposition that identifies two notions: an intuitive notion of an effectively computable function defined in natural numbers with the notion of a recursive function. Despite the many efforts of prominent scientists, Church's Thesis has never been disproven. There exists a vast literature concerning the thesis. The aim of this book is to provide a one volume summary of the state of research on Church's Thesis. These include the following: different formulations of CT, CT and intuitionism, CT and intensional mathematics, CT and physics, the epistemic status of CT, CT and philosophy of mind, provability of CT and CT and functional programming. Adam Olszewski, is assistant professor of the philosophy of mathematics and mathematical logic at the Department of Philosophy of Pontifical Academy of Theology, Cracow (Poland). Jan Wolenski is professor of philosophy, Institute of Philosphy, Jagiellonian University, Cracow (Poland). He is one of the most distinguished logicians in Poland. Robert Janusz is assistant professor in the Department of Philosophy of Ignatius College, Cracow (Poland).

In the article some philosophical issues regarding the emergence of the modern cosmology are discussed. The mathematical field equations enabled for the first time in the history to set a cosmological problem as a physical one. The “power” of mathematics was not easy to be read by the pioneers of cosmology. Also the philosophical perspective on the Universe changed in front of this “power” expressed by Einstein and de Sitter in their models. In the paper we propose also some new ideas related to the mathematics of cosmology as a physical science.

The Center of Interdisciplinary Studies in Cracow has a very rich tradition that has been studied by many and recently by Kamil Trombik. The very difficult period for the Church and for philosophy during the materialistic Marxist ideology was an opportunity for card. K. Wojtyła to outline a new mode of dialog between science and religion. The future Center, organized by Michał Heller and Józef Życiński not only captured this idea but transformed it into an academic institution centered on the idea of philosophy in science, which was also developed at the Vatican Observatory by W.G. Stoeger et al. Trombik’s book is an excellent study of the historical context and initial years of activity of the Center and its development.

The article is about an interaction between philosophy and informatics. The discussion is based on a complex example - a country, which has an evolving domain. In contemporary computer science very complex systems are modeled. However it would be impossible to model such systems with every detail, because it would be too difficult, it would be as complex as the reality itself. Frequently complex domains don't have an exact description of their behavior: some have an inadequate description, some have a contradictory one. To model such complex domains a computer science specialist acts like a philosopher: makes classifications, explanations, etc. On the other hand there have to be some philosophical presuppositions - a conviction that a logical analysis and design will work in the domain being modeled: a postulate is introduced that logos is able to capture-in the reality. The descriptions are continuously purified from irrational influences.

Filozofię można nazwać „matką” naukowych teorii: czysto empirycznych i czysto matematycznych. Historia elektryczności i magnetyzmu ukazuje ważne jednoczenie się obu podejść. Unifikacja dokonująca się w nauce pozwala oczyszczać filozofię z mitycznych naleciałości, zaś nauce daje realistyczne odniesienie do świata, bez którego groziłby jej pusty formalizm. Omawiane tu problemy ukazują, że formy matematyczne są właściwą bazą dla nauki i przez to wskazują na filozoficzną, racjonalnie precyzyjną podstawę naszej rzeczywistości.

The Center of Interdisciplinary Studies in Cracow has a very rich tradition that has been studied by many and recently by Kamil Trombik. The very difficult period for the Church and for philosophy during the materialistic Marxist ideology was an opportunity for card. K. Wojtyła to outline a new mode of dialog between science and religion. The future Center, organized by Michał Heller and Józef Życiński not only captured this idea but transformed it into an academic institution centered on the idea of philosophy in science, which was also developed at the Vatican Observatory by W.G. Stoeger et al. Trombik’s book is an excellent study of the historical context and initial years of activity of the Center and its development.

Filozofia elektryczności i magnetyzmu ma bardzo bogatą historię. Trudne do wytłumaczenia zjawiska elektryczne i magnetyczne nie poddawały się łatwo ujęciom racjonalny, tym naiwniej mówiono o nich na sposób fantastyczny, mityczny. W artykule omawiana jest pobieżnie historia opisu tych zjawisk, która doprowadziła do sformułowania pierwszych problemów filozoficznych. Dzisiejsza fizyka matematyczna dokonała unifikacji tych oddziaływań nie na podstawie zmysłowych intuicji „pierwotnych”, ale na podstawie matematycznego modelu. Zatem formy matematyczne i matematyczne struktury nie tylko stanowią właściwą bazę opisu naukowego, ale także wskazują na filozoficzną podstawę naszej rzeczywistości.

Co łączy Arystotelesa z logicznymi bramkami współczesnych komputerów? Tego można się dowiedzieć z podręcznika Bremera - obszernego i filozoficznie ugruntowanego wprowadzenia do logiki. Dzisiaj, po wielu sukcesach wyemancypowanej z filozofii logiki formalnej, jeszcze tylko nieliczni nie uważają jej za dyscypliny naukową. Wielu jednak szuka na różne sposoby filozoficznych interpretacji tej ścisłej dziedziny wiedzy. Dlatego logikę można uprawiać albo banalnie, albo z filozoficzną zadumą, np. na tle historycznych ścieżek jej rozwoju. Nie jest to jednak proste. Opatrzona Przedmową Jana Woleńskiego książka Bremera ma programowo to zadanie spełniać. Goethemu długie sznurowadła butów hiszpańskich kojarzyły się ze sznurowaniem umysłu w logikę. Z pewnością wielkiemu poecie trudno było uchwycić arystotelesowskie podejście do logiki, tak różne od współczesnego, w pełni sformalizowanego, ale jakże prostego jej ujęcia. Bremer obiera dla swych uczniów drogę historii, narażając ich może na podobne stresy, jakie towarzyszyły Goethemu. Po krótkim przeglądzie różnych etapów rozwoju logiki następuje krótkie omówienie relacji łączących logikę tradycyjną z logiką współczesną. Dla filozofa jest to bardzo ciekawe zagadnienie, stad może pewien niedosyt przy czytaniu tego podrozdziału.

To create an astronomical software, one should use the most effective method to produce the quickest hardware calculation. However, the not so effective object oriented paradigm seems to have bigger influence on the astronomical domain. We discuss the status quo of its methodology. The traditional, Turing computation model does not have so distinct influence on knowledge creation because it is hardware-oriented. An object oriented programming language is more influential on discovery, because it works directly in the scientific domain.

In the article some philosophical issues regarding the emergence of the modern cosmology are discussed. The mathematical field equations enabled for the first time in the history to set a cosmological problem as a physical one. The “power” of mathematics was not easy to be read by the pioneers of cosmology. Also the philosophical perspective on the Universe changed in front of this “power” expressed by Einstein and de Sitter in their models. In the paper we propose also some new ideas related to the mathematics of cosmology as a physical science.

One can speak about mathematics too simplistically. On the one hand, school programs are such examples. On the other hand, the function of mathematics in elementary physics very much indicates the profound philosophical significance of mathematics: the author claims that mathematical language is a kind of command language, i.e. it is not just a description, but a control which has a specific power to manage the reality. This language has its proper hierarchy and structures which humans only are just starting to understand and to use in basic ways, not without errors. Therefore some ethics regarding human mathematical thinking are needed: the affirmation of life.

We introduce stellar photometry, its purpose and relationship to other astronomical quantities, presenting it within the context of astronomical research at the Vatican Observatory. We demonstrate the usefulness of the Vilnius Photometric System previously shown at Vilnius Astronomical Obs., Edinburgh Royal Obs., and Università di Roma “La Sapienza”, and then adopted by the Vatican Observatory for use with its Vatican Advanced Technology Telescope on Mount Graham, AZ, USA. The development of astronomical observations has led from photographic plates, through photoelectric detectors to the use of sensitive CCD cameras. Expanding the photoelectric databank of “Vilnius Stars”, we describe the development of new techniques of data-acquisition, calibration to photometric standards, stellar classification and interstellar-matter characterization. Looking ahead, we briefly describe the extensive data set, and our plans for further detailed analyses.

Książka ta jest obszerną pracą o ścisłe historyczno-naukowym charakterze, przedstawiającą życie Stanisława Wydry, jezuity, profesora matematyki na Uniwersytecie w Pradze. Składa się ona z Wprowadzenia i rozdziałów poświęconych: oświeceniu i odrodzeniu narodowemu w Czechach; sytuacji uniwersytetu w Pradze, a w szczególności - Wydziału Filozoficznego; następnie – podręcznikom do matematyki na osiemnastowiecznym uniwersytecie w Pradze; życiu Stanisława Wydry oraz jego pracom naukowym - w tym kilku w szczególności, i wreszcie - jego oddziaływaniu na matematykę i kulturę Czech. Po Dodatku umieszczono wykaz literatury oraz szereg skorowidzów.

Fr. Roberto Busa was an Italian Jesuit. In this article his biography will briefly be presented, and some issues raised by his philosophy analyzed. Busa was known as a pioneer of computerized research in the humanities. With the support of IBM he constructed the Index Thomisticus, containing all the works of St. Thomas Aquinas. He believed that expressions of the human can be mathematically modeled. He was the originator of a specific conception of hypertext, in which logically structured programs are able to challenge the general linguistic mode of thinking, in order to make better communication and understanding possible. However, Busa was also con- scious of the general ethical problems involved (Babel), and he hoped that the basic logic of objects could progress towards the truth of being.