Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the most important notions (...) of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

By the end of his life Plato had rearranged the theory of ideas into his teaching about ideal numbers, but no written records have been left. The Ideal mathematics of Plato is present in all his dialogues. It can be clearly grasped in relation to the effective use of mathematical modelling. Many problems of mathematical modelling were laid in the foundation of the method by cutting the three-level idealism of Plato to the single-level “ideism” of Aristotle. For a long time, (...) the real, ideal numbers of Plato’s Ideal mathematics eliminates many mathematical problems, extends the capabilities of modelling, and improves mathematics. (shrink)

Among the main theorems obtained in mathematical logic in this century are the so called limitation theorems, i.e., the Löwenheim-Skolem theorem on the cardinality of models of first-order theories, Gödel’s incompleteness theorems and Tarski’s theorem on the undefinability of truth. Problems connected with the latter are the subject of this paper. In Section 1 we shall consider Tarski’s theorem. In particular the original formulation of it as well as some specifications will be provided. Next various meanings of the notion of (...) a satisfaction predicate will be studied. In Section 2 the problem of definability of the notion of truth, in particular of the notion of truth for the language of Peano arithmetic PA, will be discussed. It will be explicitly shown that the notion of satisfaction for the language of PA can be defined in a certain weak fragment of the second order arithmetic. Finally the axiomatic characterization of satisfaction and truth as well and its mathematical and philosophical meaning will be discussed. (shrink)

Russian translation of the XVIII and XIX sections of the third volume of Ingarden R. Spór o istnienie Świata . Translated by Maxim Lebedev and Yanina Kubka from Polish, the translation is compared with German translation by Alexander Nesterow.

Consider a gas that is adiabatically isolated from its environment and confined to the left half of a container. Then remove the wall separating the two parts. The gas will immediately start spreading and soon be evenly distributed over the entire available space. The gas has approached equilibrium. Thermodynamics (TD) characterizes this process in terms of an increase of thermodynamic entropy, which attains its maximum value at equilibrium. The second law of thermodynamics captures the irreversibility of this process by positing (...) that in an isolated system such as the gas entropy cannot decrease. The aim of statistical mechanics (SM) is to explain the behavior of the gas and, in particular, its conformity with the second law in terms of the dynamical laws governing the individual molecules of which the gas is made up. In what follows these laws are assumed to be the ones of Hamiltonian classical mechanics. We should not, however, ask for an explanation of the second law literally construed. This law is a universal law and as such cannot be explained by a statistical theory. But this is not a problem because we.. (shrink)

It is said that Europe finds itself today in a post-christian situa-tion. Further, there are many who advocate abandoning monotheism in order to get back to prechristian polytheism in the hope that the plurality of gods would favour a democratic tolerance in a pluralistic world. In this article the author firstly asks if European Christians have not gone back to adoring idols and to attempting to distinguish between them in the new forms of devotion to possessiveness, to power and to (...) pleasure. He then goes on to ask about the possibilities of pro-claiming the God of Jesus Christ. The third and the fourth part of the article point out several forms of necessary witness to God in contemporary society, with special reference made to European society in the conclusion. (shrink)

It is said that Europe finds itself today in a post-christian situa-tion. Further, there are many who advocate abandoning monotheism in order to get back to prechristian polytheism in the hope that the plurality of gods would favour a democratic tolerance in a pluralistic world. In this article the author firstly asks if European Christians have not gone back to adoring idols and to attempting to distinguish between them in the new forms of devotion to possessiveness, to power and to (...) pleasure. He then goes on to ask about the possibilities of pro-claiming the God of Jesus Christ. The third and the fourth part of the article point out several forms of necessary witness to God in contemporary society, with special reference made to European society in the conclusion. (shrink)

Some initial considerations on film in documentary form are discussed, along with its relationships with reality and fiction in cinema language. Found footage genre is explained, pointing its most important technical and aesthetical characteristics. The text points the importance of the movie camera in documentary and found footage, not only as a technical device that objectivizes the information in a static manner, but also as an axis that configures dynamism and subjectivity on films. Redacted (2007) by Brian De Palma is (...) analyzed as an example of hybrid forms of fiction and reality in cinema. Beyond a traditional analysis of narrative of films, this text emphasizes the forms in which they are developed, which affect and determine the substance of films. (shrink)

The effects of time and the longitudinal course of the children’s internalizing symptoms following Intimate Partner Violence Exposure are still of great interest today. This study aimed to analyze the effect of the frequency of IPVE, adverse experiences after the cessation of the IPVE and the time elapsed since the termination of the violent relation on the prevalence of anxiety and depression among children. Participants were 107 children and their mothers who had been victims of IPV and had existing judicial (...) protection and restraining orders. Hierarchical logistic regression models were estimated to analyze children’s adjustment, considering the effect of the time elapsed since the termination, frequency of IPVE, experiences of revictimization, maternal pathology, and anxious anticipation of the mother at the prospect of future harm. Exposure to multiple events of violence at the hands of multiple ex-partners and higher scores in the mother’s anxious anticipation were significant predictors of children’s pathological depression and anxiety. Our results emphasize the need for early psychological evaluation of women and children’s victims of IPV to provide timely interventions that avoid symptoms from becoming chronic. Strategies to bring support and emotional security to the victims after the end of the violent relationship are desirable. (shrink)

Some environmentalists have argued that an effective ecological conscience may be rooted in a perspective that is either anthropocentric or sentiocentric. But, neither seems to have had any substantial effect on the ways in which our species treats nature. In looking to successfully awaken the ecological conscience, the focus should be on extending moral consideration to the land (wherein doing so includes all of the soils, waters, plants, animals, and the collectivity of which these things comprise) by means of coming (...) to love the land. Coming to love the land involves coming to view the land’s interests as our own—and, conferring upon the land a kind of moral patient-hood. In order to perceive the land’s “subjectivity,” and so, to come to love the land, we must relearn the way to look at the land by viewing its personality through the lens of he or she who can already do so, i.e., the nature writer. (shrink)