We investigate computability theoretic and topological properties of spaces of orders on computable orderable groups. A left order on a group G is a linear order of the domain of G, which is left-invariant under the group operation. Right orders and bi-orders are defined similarly. In particular, we study groups for which the spaces of left orders are homeomorphic to the Cantor set, and their Turing degree spectra contain certain upper cones of degrees. Our approach unifies and extends Sikora’s [28] (...) investigation of orders on groups in topology and Solomon’s [31] investigation of these orders in computable algebra. Furthermore, we establish that a computable free group Fn of rank n>1 has a bi-order in every Turing degree. (shrink)

C'est un fait que nous distinguons entre la connaissance quantitative et la connaissance qualitative. L'analyse de cette distinction remonte à l'Antiquité. Depuis Aristote, elle semble être acceptée comme définitive. L'épistémologie réaliste du Stagirite Justine la distinction par la différence objective entre les catégories de qualité et de quantité, irréductibles l'une à l'autre. Selon cette optique, les deux modes de connaissance nous offrent deux perspectives différentes sur le monde matériel. Ces deux perspectives se complètent l'une l'autre. Il faut tout de même (...) se demander si les deux sont jugées également nécessaires pour la connaissance sensible du monde perceptible. La question est d'autant plus importante qu'on considère la connaissance sensible comme point de départ du processus intellectuel qui mène, ou doit en principe mener, à la connaissance substantielle de la réalité matérielle. (shrink)

Based on formal arguments from Zermelo–Fraenkel set theory we develop the environment for explaining and resolving certain fundamental problems in physics. By these formal tools we show that any quantum system defined by an infinite dimensional Hilbert space of states interferes with the spacetime structure M. M and the quantum system both gain additional degrees of freedom, given by models of Zermelo–Fraenkel set theory. In particular, M develops the ground state where classical gravity vanishes. Quantum mechanics distinguishes set-theoretic random forcing (...) such that M and gravitational degrees of freedom are parameterized by extended real line. The large scale smooth geometry compatible with the forcing extensions is one of exotic smoothness structures of \. The amoeba forcing makes the old real line to have Lebesgue measure zero in the extended one. We apply the entire procedure to the cosmological constant problem, especially to discard the zero-modes contributions to the gravitational vacuum density. Moreover, there exists certain exotic smooth \ from which one determines the realistic, agreeing with observation, small value of the vacuum energy density. (shrink)

This paper attempts to demonstrate that the conviction about the harmony and order of the world was a fundamental metaphysical principle of the Pythagoreans. This harmony and order were primarily sought in the structures of arithmetics, yet following the discovery of incommensurable magnitudes (irrational numbers, as we now call them), the Pythagoreans began to see geometrical structure as a fundamental part of the world. On the example of the Pythagoreans’ metaphysics and science, the paper shows the mutual relations between metaphysics (...) and science. It demonstrates— on the one hand—the necessity of the first as a guide for the latter, and—on the other—how our scientific research can change its basic metaphysical principles when these are found to be inappropriate. The paper also tries to show the need for a realistic approach in our scientific research by means of the same example of the Pythagoreans, that is, the need to discern something which is below the surface appearance. (shrink)

Z recenzji prof. Barbary Stawickiej-Pireckiej: Układ artykułów, przebieg granic tematycznych, zasięg problemowy proponowanych tekstów składają się na logiczną, ciekawą i różnorodną mapę tez i koncepcji, stanowiących niejako osnowę wiążącą Stary Kontynent z Nowym Światem, myśl głównych przedstawicieli filozofii hiszpańskiej – Unamuna i Ortegi y Gasseta – z „wędrującą”, wielokulturową świadomością bytu Marii Zambrano, złożone konteksty problematyki socjologicznej Peru w świetle nowelistyki Alfreda Bryce`a Echeniquego z polityczną utopią wybitnego meksykańskiego poety i eseisty – Octavio Paza. Filozoficzny wymiar dzieła literackiego w poszukiwaniu (...) nowych dróg dla słowa (Cervantes, Machado, Goytisolo, Cortázar) spotyka się w przedstawionym tomie z próbą odnalezienia nowych dróg dla koncepcji jednostki i społeczeństwa (teologia wyzwolenia, twórczość Santayany, koncepcje Manuela Castellsa i Nicolasa Gomeza Dávili). [...] -/- Wszyscy autorzy tekstów, piszący zarówno po polsku jak i po hiszpańsku, mają wypracowany własny, indywidualny sposób wypowiedzi, obrazowania, argumentacji. Czytelnik tomu obcuje zatem z dojrzałymi formami nie tylko opisu zjawisk i problemów, lecz także z ich wnikliwą i ciekawą interpretacją. (shrink)

S. Jakowski introduced the discussive prepositional calculus D 2as a basis for a logic which could be used as underlying logic of inconsistent but nontrivial theories (see, for example, N. C. A. da Costa and L. Dubikajtis, On Jakowski's discussive logic, in Non-Classical Logic, Model Theory and Computability, A. I. Arruda, N. C. A da Costa and R. Chuaqui edts., North-Holland, Amsterdam, 1977, 37–56). D 2has afterwards been extended to a first-order predicate calculus and to a higher-order logic (cf. the (...) quoted paper). In this paper we present a natural version of D 2, in the sense of Jakowski and Gentzen; as a consequence, we suggest a new formulation of the discussive predicate calculus (with equality). A semantics for the new calculus is also presented. (shrink)

In philosophy /ontology/ as well as in physics one deals with various kinds of ESSE. Quantum objects do not obey the Bell inequalities, which are natural for macroscopic objects. Some beings may be real but not actual. Actual beings are those which show up NOW. For a physicist this seems to correspond to a reduction of the wave packet. Existence in an atractor.

From the Preface: This book represents the implementation of a decision adopted by the Council of the National Academy of Sciences relating to the celebration of the 500th anniversary of the birth of Nicholas Copernicus. From the outset it was intended that this Copernican volume would describe a number of Copernican-type intellectual revolutions that have taken place in recent centuries. Such revolutions are characterized by the abandonment of widely held concepts and replacement by dramatically new conceptualizations that resulted in deepened (...) understanding of natural processes.It was the original intention of the Academy's Council that the essays would be addressed to the general educated public, including teaching staffs of colleges and high schools and college students. The combination of the intended broad coverage and the contemplated readership presented considerable difficulties and affected the choice of incidents in the history of modern science which could be discussed. As it has turned out, the material presented is quite rich and, while there is an unavoidable variation in the amount of specialized knowledge expected from the reader, we hope that the summaries preceding particular chapters are sufficient to create a broad perspective and make the whole understandable. To the extent that our goals have been approached, the help of numerous scientists is gratefully acknowledged.The introductory chapter describes the circumstances and the essence of the initial intellectual revolution due to Copernicus himself. The subsequent six parts present in turn: several revolutions in astronomy-cosmology, all in the twentieth century and one of them still in progress; a number of deep revolutionary changes in the biological sciences, one of them made twenty years ago by an inspired contribution of a graduate student; several revolutionary changes in the physical sciences; revolutions in the thinking of mathematicians; the emergence of a "pluralistic" point of view in scientific research; and revolutions in technology.The epoch when it was possible for individuals to acquire a reasonably detailed view of practically all of science is now far behind us. It was followed by a prolonged period of compartmentalization of research, with specialists in one domain becoming increasingly ignorant of developments in another. In the present epoch the pendulum appears to be moving in the opposite direction. The many problems faced by modern society depend for their solution on interdisciplinary studies and on participation of individuals with wide horizons. It is hoped that the publication of the present volume will serve not only to commemorate the achievements of Nicholas Copernicus but also to stimulate and accelerate this trend. (shrink)

Gdyby nastał zwyczaj umieszczania słów kluczowych w życiorysach, Jej osobę i życie mogłyby określić: „buntownicza niezależność”, „bojowość”, „odwaga”, „zracjonalizowany radykalizm” i „lakonizm”. Klemens Szaniawski żartował, że Barbara pisze wyłącznie zwięzłe streszczenia swych własnych rozpraw: traktowała to jako komplement; i słusznie. Wspominała te słowa z nie ukrywaną satysfakcją. Niekiedy zwięzłość Jej wypowiedzi działa nieomal hipnotycznie...

We prove a 0-1 law for the fragment of second order logic SO over parametric classes of finite structures which allow only one unary atomic type. This completes the investigation of 0-1 laws for fragments of second order logic defined in terms of first order quantifier prefixes over, e.g., simple graphs and tournaments. We also prove a low oscillation law, and establish the 0-1 law for Σ14 without any restriction on the number of unary types.

By now many formulations have been proposed to provide a definition of the realm of research topics in the methodology of science, which is sometimes also called, in the tradition of Anglo-Saxon terminology, the philosophy of science. There are various situations in which fundamental discrepancies exist among some of these formulations. Without resorting in this article to citation and detailed analysis of such definitions, let us emphasize from the outset that one of the principal sources of significant differences among them (...) lies in the following circumstance: the methodology of science may be treated either as a theoretical discipline or as a practical discipline . Inasmuch as closer examination of this question shows that practical interpretation of the methodology of science leads us to expect from it statements which — albeit in a different, nonindependent role — are also formulated in the framework of methodological investigations of a theoretical nature, to that degree, in this case one can speak of their being a single discipline, existing however, in two variants, the theoretical and the practical. Such a concept has the advantage that it creates the possibility of demonstrating the connections that exist within a very broad set of the most diverse intuitive versions of the tasks and character of methodological studies — versions that usually elevate to absolutes either the theoretical or the practical method whereby such researches are conducted. (shrink)

The author presents Leszek Kołakowski from the perspective of his private acquaintanceship, lasting for about 47 years, as a witty man and a workaholic. L. Kołakowski never formed a classic “school”, but there is something all his disciples share: a thesis, key to understanding his ideas, which holds that “THERE IS MORE THAN ONE CORRECT OPINION IN THE HUMANITIES”, i.e. we will ALWAYS have opinions for and against, which goes against any dogmatism, wherever it may appear; this also bears consequences (...) in diagnosing the socio-political reality past and present. (shrink)

Zainteresowanie społecznym nauczaniem Kościoła wynika między innymi z faktu, że stawia ono siebie w ciągłym dialogu ze współczesną myślą społeczną. Dialog z ideologią liberalną zajmuje tu niewątpliwie znaczycie miejsce. Wynika to z faktu, ze współczesne próby rozwiązania kwestii społecznej w krajach o ustabilizowanej demokracji nawiązują czysto do liberalnych rozwiązań zarówno w sferze życia społeczno-politycznego, jak i społeczno-ekonomicznego. Katolicka nauka społeczna wychodzi naprzeciw wyzwaniom społecznym, politycznym, ekonomicznym i kulturowym współczesnych społeczeństw, państw i narodów z dziedzictwem własnej myśli społecznej, który Kościół reprezentował (...) w całej swojej historii, szczególnie od encykliki „Rerum Novarum" Leona XIII do „Centesimus Annus" Jana Pawła II, Uwzględniając wyniki analizy trudnych spraw społecznych, Kocioł w swoim nauczaniu poszukuje wciąż aktualnych rozwiązań, nawiązując do własnej historii i tradycji. (shrink)

Coreference resolution is the task of finding all expressions that refer to the same entity in a text. It is one of the higher level NLP (Natural Language Processing) tasks. It allows, for example, to extract more information about medical products from larger texts. A product such as ‘ambidextrous gloves’ may appear in a text in many different forms. For example, they could be referred to by the pronoun ‘they’, such as in this sentence. The algorithm presented in this paper (...) finds pronouns and for each of them (except the pleonastic ‘it’) it creates a coreference candidate with entities that appeared earlier in the same sentence or in the previous sentence. Each candidate (pair of mentions) is described by 48 binary features which represent their grammatical and location properties. In the training set, each pair is marked as a coreference or not, based on which a decision tree classifier is trained. A classifier with a high precision of 0.94 and a decent recall of 0.61 were obtained on the training set, still with a good precision out of a sample of 0.64. (shrink)

Recently the cosmological evolution of the universe has been considered where 3-dimensional spatial topology undergone drastic changes. The process can explain, among others, the observed smallness of the neutrino masses and the speed of inflation. However, the entire evolution is perfectly smooth from 4-dimensional point of view. Thus the raison d’être for such topology changes is the existence of certain non-standard 4-smoothness on R4 already at very early stages of the universe. We show that the existence of such smoothness can (...) be understood as a byproduct of the quantumness of the origins of the universe. Our analysis is based on certain formal aspects of the quantum mechanical lattice of projections of infinite dimensional Hilbert spaces where formalization reaches the level of models of axiomatic set theory. (shrink)

Der Lebenslauf Edith Steins ist vielen Menschen bekannt. Viele wissen, daß sie bei Edmund Husserl, einem der bedeutendsten Philosophen des 20. Jahrhunderts, studierte und mit einer ausgezeichneten Arbeit promovierte, daß sie vom Judentum zum Christentum konvertierte, daß sie im KZ-Lager Auschwitz umgebracht wurde. Vom Papst Johannes Paul II. wurde sie zuerst selig, dann heilig gesprochen und auf der Schwelle in das dritte Jahrtausend zur Patronin Europas erhoben.

Książka o filozofii i życiu Stein została wydana w serii: Orbis Phaenomenologicus, publikującej prace: a) z zakresu fenomenologii, b) określające pozycje fenomenologii w kontekście innych kierunków filozoficznych, c) podejmujące aporie myślenia fenomenologicznego, oraz d) pogłębiające badania fenomenologiczne. Seria obejmuje trzy obszary badawcze: 1) perspektywy - dział poświęcony tematom fenomenologicznym, analizie dzieł ważnych myślicieli, zarysowaniu barwnego obrazu różnych ośrodków fenomenologicznych, 2) źródła - poświęcony gromadzeniu tekstów źródłowych oraz udostępnianiu materiału dokumentarnego międzynarodowym ośrodkom fenomenologicznym, 3) studia - zawierający aktualne wyniki badan fenomenologicznych.