The author presents Einstein's viewpoint on the issue of the relation between mathematics and the world. Mathematics, as Einstein seems to suggest, cannot model the structure of the world in an absolutely adequate way since, if mathematical theorems are certain, they don't apply to the reality. However from the fact that something cannot be done in an adequate way, it doesn't follow that it can't be done at all. Mathematics can and should be applied to desrcibe the reality, but in (...) such a case its theorems are not certain. Mathematics is a formal science. To be able to state something about the world it must be filled with real meaning - which for Einstein means that mathematical asertions, after a suitable interpretation, must be linked through a network of experimental procedures with the world of nature. Einstein, as it appears, applied these general suggestions to approach the problem of geometry of real space. (shrink)

The authors present the main ideas of the computer-assisted proof of Mischaikow and Mrozek that chaos is really present in the Lorenz equations. Methodological consequences of this proof are examined. It is shown that numerical calculations can constitute an essential part of mathematical proof not only in the discrete mathematics but also in the mathematics of continua.

Jak i dlaczego powstał Wszechświat? Problem z naukowym wyjaśnieniem istnienia Wszechświata polega na tym, że zakłada ono pewną fizyczną przyczynę jego istnienia. Ale jakakolwiek fizyczna przyczyna Wszechświata musi być częścią Wszechświata, którego zaistnienie ma wyjaśnić. Z tego powodu każde czysto naukowe wyjaśnienie istnienia Wszechświata jest skazane na zapętlenie. Być może żadna teoria naukowa nie może przerzucić mostu pomiędzy absolutną nicością a istniejącym już Wszechświatem.Okazuje się jednak, że gdy metafizyczne pytanie typu: dlaczego istnieje Wszechświat? zamienimy na „bardziej naukowe”: w jaki sposób (...) powstał Wszechświat?, to mamy szansę na gruncie fizyki przedstawić współczesną wersję „historii” powstania Wszechświata. Kosmolog Lawrence M. Krauss twierdzi, że w tym celu wystarczy porzucić mętne – z punktu widzenia fizyki – pojęcie absolutnej nicości i za punkt wyjścia uznać fizyczną próżnię. Ponieważ – jak wynika z mechaniki kwantowej – kwantowa próżnia to dalece nie to samo co nicość metafizyczna, możliwe jest – w świetle naszej współczesnej wiedzy – powstanie Wszechświata z „niczego”. (shrink)

In the paper there are presented two proposals of the interpretations of the applications of mathematics in the natural sciences - realistic and instrumentalistic. The realistic conception, in accordance with the successes of science, maintains that there exists some kind of correspondence between the mathematical structures and the internal structure of the world. It is expressed in the thesis of the mathematicality of nature. The instrumentalistic approach separates the cognitive content of the scientific theory from the mathematical means of expression (...) of the content. In this approach the mathematical categories do not represent any aspect of the modelled reality. In the final part of the paper the author undertakes such an attempt of approaching the applications of mathematics which, while combining the advantages of the above discussed conceptions, would be devoid of their disadvantages. (shrink)

The paper is an attempt to present the cognitive functions of mathematics in relation to empirical sciences. Firstly - mathematics is a 'generator' of mathematical categories used in natural sciences. In this sense mathematics is a science about the tools of cognition which it creates or perfects. Secondly - mathematics plays the role of 'prism' through which we view the world because some phenomena e.g. from the micro- and macro-world can only be seen through the prism of mathematical structures and (...) notions. And thirdly - mathematics is also a 'selector' of cognitive content. It eliminates from the cognitive field these phenomena which presently can't be grasped by the existing mathematical structures. It is worth noticing that the functions of mathematics: 'selector' and 'prism' are complementary in some sense; although they are opposites ('prism' lets you 'see' something, and 'selector' restricts this 'seeing'), they don't exclude each other. (shrink)

This paper is an attempt to review the historically existing types of demonstration of mathematical theorems. The author shows how the notion of mathematical proof has changed through the time from the moment when mathematicians realised (thanks to the philosophical method) the necessity to justify their theses until a precise notion of proof has appeared in the framework of the formal method. Next, the author considers the possibility of modifying the notion of mathematical proof under the influence of the development (...) of computer sciences. (shrink)

The aim of this paper is a presentation, specification and criticism of the thesis proclaiming the mathematicality of nature. The author distinguishes between the structural and the functional aspects of this thesis. With such an interpretation this thesis has a strong methaphysical interpretation. However such thesis is linked with some problems, concerning the issue of its verification. Therefore the author proposes to consider a neutral thesis proclaiming that nature is amathematical. Then we avoid strong assumptions concerning the structure of the (...) world and better understand not only the successes but also failures of mathematical methods. Besides we gain a new view of the issue of efficacy of mathematical methods in natural sciences. (shrink)

Ostatnie osiągnięcia w kosmologii i fizyce cząstek prowadzą do zaskakujących wniosków. Sugerują istnienie wielu odmiennych – od naszego – wszechświatów. Hipoteza multiwszechświata pojawia się jako wynik rozważań przeprowadzanych zarówno w największej skali na gruncie tzw. teorii wiecznej, chaotycznej inflacji jak i w skali najmniejszej z możliwych – jako wniosek płynący z teorii superstrun, wyartykułowany jako propozycja tzw. kosmicznego „krajobrazu”. Koncepcja multiwszechświata mogłaby w racjonalny sposób wyjaśnić pochodzenie naszego Wszechświata, sposób jego zaistnienia a także szczegóły jego funkcjonowania, w szczególności kwestię jego (...) „dostrojenia” dla rozwoju życia. Ale czy spekulacje na temat wszechświatów, których nigdy nie będziemy mogli zobaczyć oparte na teoriach, które być może nigdy nie będą testowalne empirycznie są jeszcze nauką czy już filozofią? (shrink)

Celem artykułu jest przedstawienie nauczania Kościoła jako wykraczającego poza błędny i rozłączny podział etyki na deontologię i teleologię. Autor przypomina szerokie tło przemian kulturowych, które towarzyszyły kontrowersjom wokół encykliki bł. Pawła VI "Humanae vitae". Teologiczna kontestacja nauczania Magisterium była powodem napisania przez św. Jana Pawła II encykliki "Veritatis splendor". Papież rozwiewa doktrynalne wątpliwości zasiane przez proporcjonalistów, przedstawiając im niezwykle przemyślaną i tradycyjną koncepcję źródeł moralności. Wychodząc od priorytetu celowości ludzkiego działania Papież podkreślił wagę przedmiotu czynu. Dla moralnego dobra ludzkiego czynu (...) konieczne jest jego podwójne właściwe odniesienie: wertykalnie do celu ostatecznego, czyli Boga, oraz horyzontalnie wobec człowieka poprzez przedmiotową zgodność działania z ludzkim dobrem. Papieskie rozważania zostają uzupełnione komentarzem do "Summy Teologii" św. Tomasza, który w analogiczny sposób przedstawia źródła moralności ludzkiego czynu. Rozróżniając wewnętrzny i zewnętrzny akt woli, św. Tomasz pokazuje właściwe źródła moralności każdego z tych aktów. W pierwszym przypadku jest to właściwy przedmiot woli, który jest tożsamy z dobrem; natomiast w drugim – konieczny jest ponadto właściwy przedmiot innych władz. Właściwa antropologia przywraca fundament pod adekwatne rozumienie zarówno prawa naturalnego, jak i potrzebę etyki cnót, która okazuje się wielką praktyczną pomocą dla człowieka w drodze do właściwej mu doskonałości. Przedstawione podstawowe prawdy nauczane od lat przez Magisterium o tyle domagają się przypomnienia, że współczesna dominująca kultura wytrwale dekonstruuje racjonalny porządek tego nauczania czyniąc zeń karykaturę. Papieskie analizy pozwalają oczyścić etyczne kryteria rozeznawania dobra i zła, przypominając o zaproszeniu do piękna teologalnego życia w Chrystusie. Umożliwia ono zdrowy krytyczny osąd konkretnych sytuacji, jak również możliwość uniknięcia rozpowszechnionych współcześnie błędów i wynikającego z nich kryzysu tożsamości. (shrink)

We generalize the Bolzano-Weierstrass theorem on ideal convergence. We show examples of ideals with and without the Bolzano-Weierstrass property, and give characterizations of BW property in terms of submeasures and extendability to a maximal P-ideal. We show applications to Rudin-Keisler and Rudin-Blass orderings of ideals and quotient Boolean algebras. In particular we show that an ideal does not have BW property if and only if its quotient Boolean algebra has a countably splitting family.

In the academic year 1920-1921 at the University of Freiburg, Martin Heidegger gave a series of extraordinary lectures on the phenomenological significance of the religious thought of St. Paul and St. Augustine. The publication of these lectures in 1995 settled a long disputed question, the decisive role played by Christian theology in the development of Heidegger’s philosophy. The lectures present a special challenge to readers of Heidegger and theology alike. Experimenting with language and drawing upon a wide range of now (...) obscure authors, Heidegger is finding his way to Being and Time through the labyrinth of his Catholic past and his increasing fascination with Protestant theology. A Companion to Heidegger's Phenomenology of Religious Life is written by an international team of Heidegger specialists. (shrink)

Tri filosofskikh "opravdanii︠a︡" (teodit︠s︡ei︠a︡, antropodit︠s︡ei︠a︡, kosmodit︠s︡ei︠a︡ Serebri︠a︡nogo veka) -- Russkai︠a︡ sofiologii︠a︡ i kabbala -- S. Bulgakov : nauka sofiologii︠a︡ (ili konet︠s︡ religii) -- Tretiĭ Zavet o. Sergii︠a︡ Bulgakova -- Tretʹezavetnai︠a︡ misterii︠a︡ ("malai︠a︡" trilogii︠a︡ Bulgakova).

In print for the first time in over ten years, Act and Crime provides a unified account of the theory of action presupposed by both Anglo-American criminal law and the morality that underlies it. The book defends the view that human actions are always volitionally caused bodily movements and nothing else. The theory is used to illuminate three major problems in the drafting and the interpretation of criminal codes: 1) what the voluntary act requirement both does and should require; 2) (...) what complex descriptions of actions prohibited by criminal codes both do and should require ; and 3) when two actions are 'the same' for purposes of assessing whether multiple prosecutions and multiple punishments are warranted. The book both contributes to the development of a coherent theory of action in philosophy, and it provides both legislators and judges a grounding in three of the most basic elements of criminal liability. (shrink)

In this short, dense essay, Jean Cavaillès evaluates philosophical efforts to determine the origin - logical or ontological - of scientific thought, arguing that, rather than seeking to found science in original intentional acts, a priori meanings, or foundational logical relations, any adequate theory must involve a history of the concept. Cavaillès insists on a historical epistemology that is conceptual rather than phenomenological, and a logic that is dialectical rather than transcendental. His famous call (cited by Foucault) to abandon "a (...) philosophy of consciousness" for "a philosophy of the concept" was crucial in displacing the focus of philosophical enquiry from aprioristic foundations toward structural historical shifts in the conceptual fabric. This new translation of Cavaillès's final work, written in 1942 during his imprisonment for Resistance activities, presents an opportunity to reencounter an original and lucid thinker. Cavaillès's subtle adjudication between positivistic claims that science has no need of philosophy, and philosophers' obstinate disregard for actual scientific events, speaks to a dilemma that remains pertinent for us today. His affirmation of the authority of scientific thinking combined with his commitment to conceptual creation yields a radical defense of the freedom of thought and the possibility of the new. (shrink)

v. 1. pt. 1. Babaji's glimpses of the Tamil 18 Siddhas. pt. 2. [non-Roman data].

Kierkegaard's Concluding Unscientific Postscript is a classic of existential literature. It concludes the first and richest phase of Kierkegaard's pseudonymous authorship and is the text that philosophers look to first when attempting to define Kierkegaard's own philosophy. Familiar Kierkegaardian themes are introduced in the work, including truth as subjectivity, indirect communication, the leap, and the impossibility of forming a philosophical system for human existence. The Postscript sums up the aims of the preceding pseudonymous works and opens the way to the (...) next part of Kierkegaard's increasingly tempestuous life: it can thus be seen as a cornerstone of his philosophical thought. This volume offers the work in a new and accessible translation by Alastair Hannay, together with an introduction that sets the work in its philosophical and historical contexts. (shrink)

In Alfonso de Cartagena's 'Memoriale virtutum' (1422) María Morrás and Jeremy Lawrance offer a new edition from the manuscripts of a compilation of Aristotle's Nicomachean Ethics addressed by the major Castilian intellectual of the day, bishop Alfonso de Cartagena, to the heir to the throne of Portugal, crown prince Duarte. The work was a speculum principis, an education for the future king in the virtues suitable to a statesman; Cartagena's choice of Aristotle was thus a significant index of the advent (...) of new Renaissance ideas. This edition shows how the "memorial" throws light on the ideological transformation of society those ideas would bring, setting new ethical guidelines for the ruling class at the crossroads between medieval feudalism and Renaissance absolutism. (shrink)

Abstract:During the early 19th century, a peculiarly systematic way of organizing books emerged in Germany. This systematization, which purported to be a rational organization of subject matter, was an outgrowth of the philosophy of Hegel. This article attempts to outline Hegel's organizational practice. It argues that Hegel's encyclopedia was a reaction against the Enlightenment encyclopedia, and that it attempted to restore the systematic mindset of pre-modern reference books. Yet it did this, not in a straightforward fashion, but by developing a (...) method for organizing material that both stresses the interconnectedness of knowledge and promises to be highly scalable. In its attempt to trace the Hegelian organizational method, this article revisits and calls attention to a forgotten work in Hegel scholarship by Michael John Petry, who was the first writer to seriously stress the importance of classification in Hegel's work. This article is an attempt to demonstrate that Hegelianism and information organization can be brought into fruitful and mutually beneficial dialogue. (shrink)

Vizantiĭsʹkyĭ neoplatonizm i︠a︡k predmet relihii︠e︡znavchoho ta istoryko-filosofsʹkoho doslidz︠h︡enni︠a︡ -- Formuvanni︠a︡ vizantiĭsʹkoho neoplatonizmu u tvorakh Ĭoana Filopona (Dionisii︠a︡ Areopahita) -- Filosofii︠a︡ butti︠a︡ Maksyma Spovidnyka--kulʹminat︠s︡ii︠a︡ rozvytku vizantiĭsʹkoho neoplatonizmu -- Vizantiĭsʹkyĭ neoplatonichnyĭ esent︠s︡ializm kint︠s︡i︠a︡ VII-pochatku XIV stolitʹ -- Palamizm i︠a︡k osoblyva forma vizantiĭsʹkoho neoplatonizmu.

Attempts to think anew about philosophical questions from the perspective of breath and breathing. As a physiological or biological matter, breath is mostly considered to be mechanical and thoughtless. By expanding on the insights of many religions and therapeutic practices, which emphasize the cultivation of breath, the contributors argue that breath should be understood as fundamentally and comprehensively intertwined with human life and experience. Various dimensions of the respiratory world are referred to as “atmospheres” that encircle and connect human existence, (...) coexistence, and the world. Drawing from a number of traditions of breathing, including from Indian and East Asian religion and philosophy, the book considers breath in relation to ontological, hermeneutical, phenomenological, ethical, and aesthetic concerns in philosophy. The wide-ranging topics include poetry, theater, environmental issues and health, feminism, and media studies. “Atmospheres of Breathing, the first collection of its kind, explores an emerging ‘respiratory philosophy’ of great consequence for philosophy and other fields. Its rich and diverse essays, many written by the pioneers of this radically new direction, show the deep historical and intercultural roots of such a philosophy, ranging from treatments of forerunners like Zhuangzi and Heraclitus to contemporary theorists of breathing such as Abram and Kleinberg-Levin. Presented here is the vision of innovative ways in which philosophy, on its own or inspired by spiritual practices, can bring breathing into the center of its concern. This is a landmark book that scintillates with brilliant and original insights. If taken as seriously as it deserves, this book has the potential to revolutionize contemporary and future thought.” — Edward S. Casey, author of The World at a Glance and The World on Edge “Air, the misunderstood element, finds ways and means of advancing to places where no one reckons with its presence; and, more significantly, it makes space on its own strength for strange places where there were previously none.” — Peter Sloterdijk. (shrink)

Contributors to this volume consider the implications of 'the Age of Breath': a spiritual shift in human awareness to the needs of the other figured through breathing.

Journalen NB26 -- Journalen NB27 -- Journalen NB28 -- Journalen NB29 -- Journalen NB30.

1. Ḥāshīyat al-Ṣabbān ʻalá al-Sharḥ al-Ṣaghīr lil-Mullawī ʻalá al-Sullam al-murawnaq -- 2. Taqrīrāt Ḥasan ibn Riḍwān al-Ḥusaynī.