We present the first effectively presentable fully abstract model for Starkʼs Reduced ML, a call-by-value higher-order programming language featuring integer-valued references. The model is constructed using techniques of nominal game semantics. Its distinctive feature is the presence of carefully restricted information about the store in plays, combined with conditions concerning the participantsʼ ability to distinguish reference names. We show how it leads to an explicit characterization of program equivalence.

We introduce a game model for an Algol-like programming language with primitives for parallel composition and synchronization on semaphores. The semantics is based on a simplified version of Hyland–Ong-style games and it emphasizes the intuitive connection between the concurrent nature of games and that of computation. The model is fully abstract for may-equivalence.

The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s. It was a remarkable period in the history of Polish science, in particular in the history of Polish logic and mathematics. Therefore, it is justified to ask whether and to what extent the development of logic and mathematics was accompanied by a philosophical reflection. We try to answer those questions by analyzing (...) both works of Polish logicians and mathematicians who have a philosophical temperament as well as their research practice. Works and philosophical views of the following Polish scientists will be analyzed: Wacław Sierpiński, Zygmunt Janiszewski, Stefan Mazurkiewicz, Stefan Banach Hugo Steinhaus, Eustachy Żylińsk and Leon Chwistek, Jan Łukasiewicz, Zygmunt Zawirski, Stanisław Leśniewski, Tadeusz Kotarbiński, Kazimierz Ajdukiewicz, Alfred Tarski, Andrzej Mostowski and Henryk Mehlberg, Jan Sleszyński, Stanisław Zaremba and Witold Wilkosz. To indicate the background of scientists being active in the 1920s and 1930s we consider in Chapter 1 some predecessors, in particular: Jan Śniadecki, Józef Maria Hoene-Wroński, Samuel Dickstein and Edward Stamm. (shrink)

Contents: Preface. SCIENTIFIC WORKS OF MARIA STEFFEN-BATÓG AND TADEUSZ BATÓG. List of Publications of Maria Steffen-Batóg. List of Publications of Tadeusz Batóg. Jerzy POGONOWSKI: On the Scientific Works of Maria Steffen-Batóg. Jerzy POGONOWSKI: On the Scientific Works of Tadeusz Batóg. W??l??odzimierz LAPIS: How Should Sounds Be Phonemicized? Pawe??l?? NOWAKOWSKI: On Applications of Algorithms for Phonetic Transcription in Linguistic Research. Jerzy POGONOWSKI: Tadeusz Batóg's Phonological Systems. MATHEMATICAL LOGIC. Wojciech BUSZKOWSKI: Incomplete Information Systems and Kleene 3-valued Logic. Maciej KANDULSKI: Categorial Grammars with (...) Structural Rules. Miros??l??awa KO??L??OWSKA-GAWIEJNOWICZ: Labelled Deductive Systems for the Lambek Calculus. Roman MURAWSKI: Satisfaction Classes - a Survey. Kazimierz _WIRYDOWICZ: A New Approach to Dyadic Deontic Logic and the Normative Consequence Relation. Wojciech ZIELONKA: More about the Axiomatics of the Lambek Calculus. THEORETICAL LINGUISTICS. Jacek Juliusz JADACKI: Troubles with Categorial Interpretation of Natural Language. Maciej KARPI??N??SKI: Conversational Devices in Human-Computer Communication Using WIMP UI. Witold MACIEJEWSKI: Qualitative Orientation and Grammatical Categories. Zygmunt VETULANI: A System of Computer Understanding of Texts. Andrzej WÓJCIK: The Formal Development of van Sandt's Presupposition Theory. W??l??adys??l??aw ZABROCKI: Psychologism in Noam Chomsky's Theory . Ryszard ZUBER: Defining Presupposition without Negation. PHILOSOPHY OF LANGUAGE AND METHODOLOGY OF SCIENCES. Jerzy KMITA: Philosophical Antifundamentalism. Anna LUCHOWSKA: Peirce and Quine: Two Views on Meaning. Stefan WIERTLEWSKI: Method According to Feyerabend. Jan WOLE??N??SKI: Wittgenstein and Ordinary Language. Krystyna ZAMIARA: Context of Discovery - Context of Justification and the Problem of Psychologism. (shrink)

Les décrets en l'honneur de Diodoros Pasparos de Pergame, riches en informations sur les relations entre un grand bienfaiteur et sa cité, ont souvent attiré l'attention des chercheurs. En évoquant les honneurs exceptionnels accordés à Diodoros, on a souligné, à juste titre, que ces textes accusent les traits significatifs de la « basse » époque hellénistique. On pourrait aussi remarquer que leur nombre même témoigne de l'ostentation avec laquelle les Pergaméniens voulaient louer Diodoros. Cependant, la chronologie relative de ces décrets (...) et leurs rapports réciproques n'ont pas été établis de façon convaincante. Le classement proposé dans le présent article, d'une part, permet de mieux comprendre l'activité de gymnasiarque de Diodoros, d'autre part, jette quelque lumière sur la procédure législative en vigueur dans la cité de Pergame, dans la première moitié du Ier s. avant J.-C. On constate que la cité fonctionne comme une cité démocratique et la procédure législative en vigueur est la même qu'à l'époque attalide. Le rôle joué par les stratèges ne prive pas les citoyens particuliers du droit d'initiative législative, seulement cette initiative doit passer toujours par l'intermédiaire des stratèges, chargés de la mise en délibération (sans doute aussi de la rédaction) des projets de décrets. (shrink)

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)

The paper is devoted to the discussion of some philosophical and historical problems connected with the theorem on the undefinability of the notion of truth. In particular the problem of the priority of proving this theorem will be considered. It is claimed that Tarski obtained this theorem independently though he made clear his indebtedness to Gödel’s methods. On the other hand, Gödel was aware of the formal undefinability of truth in 1931, but he did not publish this result. Reasons for (...) that are also considered. (shrink)

The Athenian ephebeia prior to the reform of Epikrates : REINMUTH, Eph. Inscr. 1 and the chronology of the first ephebic inscriptions This study reexamines two inscriptions (EM 13354 and EM 13354) which have been sometimes wrongly considered as belonging to one stele and often quoted in the discussions about of the Athenian ephêbeia. The inscription EM 13354 has definitely to be excluded from these discussions. As for the inscription EM 13354, it bears two decrees of the Akamantis tribe. The (...) first honoring an unknown person with ateleia was voted not under the archon Nikophemos (361/ 0), but under the archon Molon (362/ 1). The date of the second decree, which honors Autolykos, kosmêtês of the ephebes, is uncertain but, whatever its date, Autolykos took office before the reform of the ephêbeia implemented by Epikrates in 335/ 4. Thus this decree proves that the office of the kosmêtês predates this reform. In addition, new dates have been proposed for some ephebic inscriptions posterior to the reform of Epikrates. (shrink)

This volume is written jointly by Witold Marciszewski, who contributed the introductory and the three subsequent chapters, and Roman Murawski who is the author of the next ones - those concerned with the 19th century and the modern inquiries into formalization, algebraization and mechanization of reasonings. Besides the authors there are other persons, as well as institutions, to whom the book owes its coming into being. The study which resulted in this volume was carried out in the Historical Section (...) of the research project _Logical Systems and Algorithms for Automatic Testing of Reasoning,_ 1986-1990, in which participated nine Polish universities; the project was coordinated by the Department of Logic, Methodology and Philosophy of Science of the Bia??l??ystok Branch of the University of Warsaw, and supported by the Ministry of Education 1987). The major part of the project was focussed on the software for computer-aided theorem proving called Mizar MSE ) due to Dr. Andrzej Trybulec. He and other colleagues deserve a grateful mention for a hands-on experience and theoretical stimulants owed to their collaboration. (shrink)

Recent years have seen the appearance of many English-language hand books of logic and numerous monographs on topical discoveries in the foundations of mathematics. These publications on the foundations of mathematics as a whole are rather difficult for the beginners or refer the reader to other handbooks and various piecemeal contribu tions and also sometimes to largely conceived "mathematical fol klore" of unpublished results. As distinct from these, the present book is as easy as possible systematic exposition of the now (...) classical results in the foundations of mathematics. Hence the book may be useful especially for those readers who want to have all the proofs carried out in full and all the concepts explained in detail. In this sense the book is self-contained. The reader's ability to guess is not assumed, and the author's ambition was to reduce the use of such words as evident and obvious in proofs to a minimum. This is why the book, it is believed, may be helpful in teaching or learning the foundation of mathematics in those situations in which the student cannot refer to a parallel lecture on the subject. This is also the reason that I do not insert in the book the last results and the most modem and fashionable approaches to the subject, which does not enrich the essential knowledge in founda tions but can discourage the beginner by their abstract form. A. G. (shrink)

In this article, the author notes that Thomas Aquinas, in his brief work entitled De Ente et Essentia, proved that at the base of understanding the world, the human being, and God in particular, there is our understanding of being and its essence. When we make a small mistake at the beginning in our understanding of being and its essence, it will turn to be a big one in the end. And what is “at the end” of our knowledge is (...) the discovery of the First and Ultimate Cause of all things, known as: Ipsum Esse, God, the Absolute, The Most Perfect Substance, on whom everything depends, and who depends not on anything else. These present inquiries about the proper understanding of being and its essence are aimed at formulating proof of the necessity of existence of a Being that is the First Cause, and which, existing as Ipsum Esse, is the source and reason of existence of all beings. Without these inquiries, the proof itself would be incomprehensible, and more importantly it would be a purely a priori one. Furthermore, without the existential conception of being, which Thomas first formulated, one could not discover the First Cause which, as Ipsum Esse, is the source of the existence of every being. This issue seems to have escaped the attention of the author of the book Aquinas’s Way to God. The Proof in “De Ente et Essentia.”. (shrink)

Natural Deduction Natural Deduction is a common name for the class of proof systems composed of simple and self-evident inference rules based upon methods of proof and traditional ways of reasoning that have been applied since antiquity in deductive practice. The first formal ND systems were independently constructed in the 1930s by G. Gentzen and S. Jaśkowski and … Continue reading Natural Deduction →.

The paper is devoted to phenomenological ideas in conceptions of modern philosophy of mathematics. Views of Husserl, Weyl, Becker andGödel will be discussed and analysed. The aim of the paper is to show the influence of phenomenological ideas on the philosophical conceptions concerning mathematics. We shall start by indicating the attachment of Edmund Husserl to mathematics and by presenting the main points of his philosophy of mathematics. Next, works of two philosophers who attempted to apply Husserl’s phenomenological ideas to the (...) philosophy of mathematics, namely Hermann Weyl and Oskar Becker, will be briefly discussed. Lastly, the connections between Husserl’s ideas and the philosophy of mathematics of Kurt Gödel will be studied. (shrink)

The paper consists of two parts, outlined in the title.I. In the historical science time appears as an element of the historian’s workshop. The historian collects source information, evaluates them and assigns respective dates. Only on the ground of thus “processed” sources may he reproduce the past: events and longer development processes, setting them in time. This dated time is understood colloquially as something objective, which runs one way and may be measured.II. A historian who studies the past reality depends (...) on the extent to which those sources are preserved. As a result of their interpretation, with the use of increasingly excellent research methods, he reproduces that reality. He must carry out an ongoing selection of historical facts found. This exposes him to temptations of such selection of those facts so as to adjust the historical knowledge to serve well the national interests, his own political opinions, etc. In this way the historian exerts influence on social awareness, which may consists of various myths and stereotypes, which sometimes lead to negative social behaviors: aggression, chauvinism, etc. Therefore, for researcher honesty’s sake and in the sense of moral responsibility, he must be careful to be as impartial as possible in his work. (shrink)

The objective of Working Group 4 of the COST Action NET4Age-Friendly is to examine existing policies, advocacy, and funding opportunities and to build up relations with policy makers and funding organisations. Also, to synthesize and improve existing knowledge and models to develop from effective business and evaluation models, as well as to guarantee quality and education, proper dissemination and ensure the future of the Action. The Working Group further aims to enable capacity building to improve interdisciplinary participation, to promote knowledge (...) exchange and to foster a cross-European interdisciplinary research capacity, to improve cooperation and co-creation with cross-sectors stakeholders and to introduce and educate students SHAFE implementation and sustainability. To enable the achievement of the objectives of Working Group 4, the Leader of the Working Group, the Chair and Vice-Chair, in close cooperation with the Science Communication Coordinator, developed a template to map the current state of SHAFE policies, funding opportunities and networking in the COST member countries of the Action. On invitation, the Working Group lead received contributions from 37 countries, in a total of 85 Action members. The contributions provide an overview of the diversity of SHAFE policies and opportunities in Europe and beyond. These were not edited or revised and are a result of the main areas of expertise and knowledge of the contributors; thus, gaps in areas or content are possible and these shall be further explored in the following works and reports of this WG. But this preliminary mapping is of huge importance to proceed with the WG activities. In the following chapters, an introduction on the need of SHAFE policies is presented, followed by a summary of the main approaches to be pursued for the next period of work. The deliverable finishes with the opportunities of capacity building, networking and funding that will be relevant to undertake within the frame of Working Group 4 and the total COST Action. The total of country contributions is presented in the annex of this deliverable. (shrink)

This summary was delivered at the closing session of the “Korczak: A New Anthropology of Education” conference on September 21, 2002 in the Polish Culture Institute of Warsaw University’s Polish Studies Faculty. Author points that the primary goal of the conference was to set Korczak’s work against modern-day thought trends and cultural dilemmas. Summing up the result of the conference author notices that the deepest roots of the Korczak’s work lies in the Judaic and Christian traditions but it also draws (...) on European enlightenment, Polish romanticism, and positivism. (shrink)

A new type of formalization of classical first-order logic with equality is introduced on the basis of the sequent calculus. It serves to justify the claim that equality is a logical constant characterised by well-behaved rules satisfying properties usually regarded as essential. The main feature of this approach is the application of sequents built not only from formulae but also from terms. Two variants of sequent calculus are examined, a structural and a logical one. The former is defined in accordance (...) with Dos̆en’s criteria for logical constants. The latter is a standard Gentzen’s sequent calculus and satisfies Hacking’s criteria for logicality, including cut elimination. It is also shown that provided rules are harmonious in the sense advocated by Gratzl and Orlandelli. (shrink)

DARWIN’s (1859, 1871) discoveries have profound ethical implications that continue to be misrepresented and/or ignored. In contrast to socialdarwinistic misuses of his theory, Darwin was a great humanitarian who paved the way for an integrated scientific and ethical world view. As an ethical doctrine, socialdarwinism is long dead ever since its defeat by E. G. Moore although the socialdarwinistic thought is a hard-die in the biological community. The accusations of sociobiology for being socialdarwinistic are unfounded and stem from the moralistic (...) fallacy that is, a false assumption that morality is good by definition. Both social and developmental psychology demonstrate that the moral agency is a motivational device for executing reciprocity that remains at the core of any morality across all studied societies and throughout the ontogeny of moral judgment. The level of true universalizing ethical reflection (KOHLBERG’s postconvential stages or GIBBS’s existential phase) is achieved by a small minority of humans, thus showing that Homo sapiens is a moral but not an ethical animal. While the origin of reciprocity has been perfectly explained by sociobiology, the evolutionary assembly of affective and cognitive elements that make up the moral agency is being successfully studied by the social/personality/developmental psychology as extended to non-human primates. As DARWIN (1871) expected, the key innovation for the evolution of moral agency was the emergence of empathy that evolved independently at least three times: in elephants, dolphins and primates. Empathy has a motivational power of its own; it is also necessary for moral agency that requires two cognitive abilities: reflective self-consciousness and understanding of causality; the two make possible the attribution of responsibility. All these requirements are met by the chimpanzees whose moral agency operates in dyads. In contrast, the human moral agency allows for a third party intervention that opens up vast opportunities for ideologies, especially religions, to use and misuse the moral agency to enforce a reciprocation that may be harmful to both individuals and the entire group. Also, the moral agency is known to enforce enhanced intragroup cohesion and loyalty in response to conflict and war, which suggests that the two prima facie opposed human universals, morality and warfare, may have coevolved. The most important ethical consequence that follows from the increasing understanding of the primate moral agency is that every received morality is ethically flawed, none can be taken as a paragon of goodness, and each needs corrections by science-informed ethics. In fact, Darwin pioneered the integration of science and ethics, an approach that has come to be appreciated only recently under the heading of consilience. (shrink)

Most Enlightenment thinkers believed that the World’s order (as ultimately based on divine laws) is good and thus every gain of knowledge will have good consequences. Scientific process was assumed to entail moral progress. In fact some moral progress did occur in the Western civilization and science contributed to it, but it is widely incommensurate with the progress of science. The Enlightenment’s concept of a concerted scientific and moral progress proved largely wrong for several reasons. (1) Public morality and science (...) evolve largely independently and may either enhance or inhibit each other. (2) There are no objective values to be read in the World’s order and simply followed. Instead, our real, subjective values and the moral systems they fuel have all been generated and shaped by evolution rather than designed to be universally good, and thus ought to be managed rather than simply followed. (3) Our evolved morality is flawed, deficient, prone to doctrinal manipulation and refractory to progress. (4) The majority of people show metaethical incompetence in failing to take a reasoned critical stand toward the principles and assumptions of received morals. This makes moral progress largely dependent on those who reach metaethical competence by transcending the conventional stages of moral development. (shrink)

True Darwinian Ethics -/- Darwin’s model for the evolution of morality as presented in Descent of Man (1871) is shown to comprise three major stages that are here referred to as empathic premorality, tribal morality, and universalizing morality. Empathy, the key component of Darwin’s “social instincts” that started moral evolution, is here recognized as the principal cognitive device that conveys epistemic credibility to moral agency. The two constitutive elements of the tribal morality are conscience that Darwin conceived of as a (...) conflict between a lasting social motive and an immediate selfish impulse, and true altruism that evolved as a result of group (community) selection. Darwin’s genius recognized the uniqueness of group selection in human evolution as being dependent on mental faculties and speech that facilitated habit formation through praise and blame form other group members, with empathy as a gauge of others’ emotional reactions. Contrary to repeated claims, Darwin did not derive morality from reciprocity that he (and his contemporaries) considered to be “a low motive”, and adduced it only as a mechanism of habit formation. The universalizing morality was brought about by the increasing powers of intellect that led to respecting individual lives (rather than group interests only) and extending humane concerns beyond one’s group, ultimately to all sentient beings, which places Darwin among the spiritual fathers of modern humanitarianism. In terms of substantive ethics, Darwin’s views support moral individualism that requires to treat each subject according to his/her individual characteristics rather than any group membership. Darwin’s moral individualism and universalism have been elaborated by Peter Singer as the principle of equal consideration of interests and the expanding circle of ethics, respectively. Darwin’s model of moral evolution, which starts with intuitive but epistemically reliable moral agency and then allows for its rational improvement, provides a way out of the moral subjectivism of evolutionary ethics that reduces morality to an adaptation to social life. The primary or core morality that relies on empathy and implements reciprocity supports welfare (wellbeing) of a group and its members. Welfare (which has been defined by Darwin) is a basic “terminal” (ultimate) value that constitutes an objective, measurable fact. Since the primary morality supports welfare, it is objectively good, which justifies an ethical reasoning that such morality ought to be extended (with appropriate adjustments) to all sentient beings. Confusion over the status of morality is largely due to the lack of appreciation of its complexity: not only had its motivational apparatus (known as the moral agency) evolved by superposition of many emotional and pure cognitive mechanisms, but it has subsequently been co-opted to implement prudential, religious and possibly other norms that are accidental and sometimes contrary to its original social function. Those secondary morality norms are now enforced by the moral agency but lack moral objectivity and thus may support the perception of moral subjectivism and relativism. In short, true Darwinian ethics is based on the scientific axiology that recognizes evolutionary origins of all values, requires respecting all values that are experienced by each and every subject according to its individual characteristics, and calls for a critical assessment of each and every received morality. (shrink)

In the evolution of the vertebrates and probably a few other animals (Metazoa), biological values have been translated (subjectivized) into affective experience that necessarily involves the consciousness of external objects/events (as different from one’s body), which is tantamount to the origins of subjectivity. Mammals, birds and other vertebrates are experiencing subjects even though their negative and positive experience greatly vary in scope. Some mammals are capable of vicarious experience and may act as empathic agents, and some of them, at least (...) the great apes, use true reflective self-consciousness and thus perceive themselves as agents, which generates attributive feelings. The balance of positive and negative experience determines the intrinsic value of (an individual) life. Every subjective life is autotelic in striving to maximize this balance. A subjective life may also have a social value that is measured in terms of the impact on intrinsic values of other lives. The social value of life is contingent upon an agency, that is, conscious intentional actions that impact intrinsic value of other lives. The difference between the social value of a subjective life and an instrumental value of an individual comes down to the difference between agent causation and event causation. The moral agency refers to a subcategory of agent causation that involves the awareness of impact on another subject’s wellbeing (interests). The moral agency is at present known only in the hominids (including the chimpanzees) which understand causality and use reflective self-consciousness, which in turn enables them to perceive themselves as agents and attribute to themselves responsibility. The moral agency originated as a motivational mechanism of reciprocity execution , and thus as an adaptation for group life, which is why it favors ingroup members and often promotes norms that harm other groups. The human moral agency is frequently used by third parties to implement group norms that are based on ideologies (religious or secular) and may actually harm both group members and the entire groups. Any received, bioculturally evolved morality is unlikely to be good in either absolute or universal sense. Therefore, the moral capacity alone does not make a human life categorically more valuable, even if human motivation were dominated by moral agency (which is true only of some people). The life of a vertebrate has, therefore, two values, intrinsic and social. Each can be negative or positive, and may vary to a large extent independently of the other, whereby a joint value of a subjective life cannot be sensibly assessed and compared without prior assessments of the intrinsic and social component separately. In the absence of objective reasons to rate the intrinsic value of a human life as categorically higher than that of other mentally advanced mammals, and in consideration of the observed range of social values of human lives, some of which approach zero and some are highly negative (lower than any thinkable negative values of non-human lives), the doctrine of extraordinary and inalienable (innate) human „dignity” is groundless and unethical, as it leads to a depreciation of the lives of non-human subjects, and often preempts the need to impart a real social value to one’s own life. (shrink)

Having positive experience is, by defintion, in the interest of every subject. Whether being alive per se, in addition to having positive experiences, is in a subject's interest depends of her/his cognitive development. Only a reflectively self-conscious subject can take and thus have an interest in one's own individual existence and may not want to die regardless of the expected experience. Since most non-human subjects (except for a few mammalian and avian species) are not aware of their subjective existence they (...) cannot take and thus have interest in their lives per se. However, they do have interest in maximizing rewarding experience and minimizing suffering. (shrink)

There are many religions in the human world, and people manifest their religiousness in many different ways. The main problem this paper addresses concerns the possibility of sorting out this complex world of human religiousness by showing that it can be phenomenologically reduced to a few very basic existential attitudes. These attitudes express the main types of ways in which a human being relates to his or herself and the world, independently of the worldview or religion professed by the individual. (...) I use Kierkegaard’s theories of the stages of existence and subjective truth as a model. The theory of the stages of existence provides five basic existential attitudes on the basis of which religious attitudes can develop: spiritlessness, the aesthetic, the ethical, religiousness A, and religiousness B. The theory of subjective truth shows how the concept of truth functions in an ethical and existential sense as the personal truth of an individual engaged in building their religious identity. In turn, I discuss the problem of the relation of Kierkegaard’s philosophy to phenomenology, briefly introduce his concept of subjective truth and the stages of existence, and show how existential attitudes can be transformed into religious ones. I also consider the problem of the demonic as the inverted order of this anthropological and existential model. Finally, I argue that the model developed herein may be useful for further research into the phenomenology of religious attitudes. (shrink)

In the paper some applications of Gödel's incompleteness theorems to discussions of problems of computer science are presented. In particular the problem of relations between the mind and machine (arguments by J.J.C. Smart and J.R. Lucas) is discussed. Next Gödel's opinion on this issue is studied. Finally some interpretations of Gödel's incompleteness theorems from the point of view of the information theory are presented.

In this paper† we will treat mereology as a theory of some structures that are not axiomatizable in an elementary langauge and we will use a variable rangingover the power set of the universe of the structure). A mereological structure is an ordered pair M = hM,⊑i, where M is a non-empty set and ⊑is a binary relation in M, i.e., ⊑ is a subset of M × M. The relation ⊑ isa relation of being a mereological part . We (...) formulate an axiomatization of mereological structures, different from Tarski’s axiomatization aspresented in [10] . We prove that these axiomatizations are equivalent . Of course, these axiomatizations are definitionally equivalent to thevery first axiomatization of mereology from [5], where the relation of being aproper part ⊏ is a primitive one.Moreover, we will show that Simons’ “Classical Extensional Mereology”from [9] is essentially weaker than Leśniewski’s mereology. (shrink)

The paper contains an exposition of some non standard approach to gentzenization of modal logics. The first section is devoted to short discussion of desirable properties of Gentzen systems and the short review of various sequential systems for modal logics. Two non standard, cut-free sequent systems are then presented, both based on the idea of using special modal sequents, in addition to usual ones. First of them, GSC I is well suited for nonsymmetric modal logics The second one, GSC II (...) is devised specially for symmetric, i.e. Blogics. GSC I and GSC II are not different formalizations, from the theoretical point of view GSC I may be seen as a simplification of the more general approach present in GSC II. They are considered separately, mainly because Blogics demand different, and more complicated, strategy in completeness proof, whereas non symmetric logics are easily and uniformly characterised by means of Fitting's Consistency Properties. The weakest modal logic captured by this formalization is minimal regular logic C, but many stronger logics are obtainable by addition of suitable structural rules, which conforms to Do en's methodology. Both variants of GSC satisfy also other, besides cut-freedom, desirable properties. (shrink)

We classify two of Bertrand Russell's theories of events within the point-free ontology. The first of such approaches was presented informally by Russell in ‘The World of Physics and the World of Sense’ (Lecture IV in Our Knowledge of the External World of 1914). Based on this theory, Russell sketched ways to construct instants as collections of events. This paper formalizes Russell's approach from 1914. We will also show that in such a reconstructed theory, we obtain all axioms of Russell's (...) second theory from 1936 and all axioms of Thomason's theory of events from 1989. Russell's work certainly influenced the works of Stanisław Leśniewski, his student Alfred Tarski, and Czesław Lejewski – prominent members of the Lvov-Warsaw School (LWS). We see our work in the tradition of the research of Leśniewski and Tarski. Building on the technical tools developed in this environment and in the spirit of the traditional research of the LWS, we engage here, in particular, with two classic works by Russell on fundamental ontology. (shrink)

The paper is a brief survey of some sequent calculi which do not follow strictly the shape of sequent calculus introduced by Gentzen. We propose the following rough classification of all SC: Systems which are based on some deviations from the ordinary notion of a sequent are called generalised; remaining ones are called ordinary. Among the latter we distinguish three types according to the proportion between the number of primitive sequents and rules. In particular, in one of these types, called (...) Gentzen’s type, we have a subtype of standard SC due to Gentzen. Hence by nonstandard ones we mean all these ordinary SC where other kinds of rules are applied than those admitted in standard Gentzen’s sequent calculi. We describe briefly some of the most interesting or important nonstandard SC belonging to the three abovementioned types. (shrink)

This paper is an attempt to clash the problem of forgiveness as formulated in contemporary secular and Christian ethics with Kierkegaard’s considerations concerning this issue. Kierkegaard’s thought is increasingly used in the modern debate on forgiveness. It is therefore worth investigating whether Kierkegaard’s considerations are really able to overcome in any way contemporary disputes concerning this problem or enrich our thinking in this area. The main thesis of this paper states that there is a fundamental, ontological difference between Kierkegaard’s understanding (...) of forgiveness and that of modern thinkers. While the Danish philosopher refers to the transcendent reality of spirit, where the act of forgiveness is always performed by God, in contemporary ethical and Christian thought, forgiveness is first and foremost formulated from an immanent point of view that appeals to the world of human values. This difference is demonstrated by analyzing the four main themes corresponding to the most important issues taken up in the contemporary debate on forgiveness. These are: the victim-offender relation, the conditionality and unconditionality of forgiveness, the issue of condonation, and the problem of the unforgivable. As a result of the analyses presented herein, the impossibility of directly applying Kierkegaard’s transcendent theses to ethical thought of the immanent variety will be shown. (shrink)

Spouses exhibit two kinds of behaviours: protective and transgressive. Protective acts are those aiming to overcome current problems, leading to preserving some balance. Transgressive acts are deliberately overstepping everyday marital reality and doing new things in new ways. They lead to changing the relation with the hope of improving it, but also create the risk of deterioration. The more transgressive behaviours spouses exhibit, the more chances they have to get to know each other and experience the joy of being part (...) of a union. Transgressive tendencies stem from a network personality structure and consist of five psychons: cognitive, instrumental, motivational, emotional, and personal. The success of a marriage is the effect of a specific form of transgressive behaviours in marriage exhibited by both spouses, which is recognizing difficulties as they appear, finding their sources, and taking steps together to overcome them. (shrink)

The aim of the paper is to examine the nature of moral and legal norms in a broader context: first, taking into account logical and methodological assumptions, second, in the perspective of psychology of emotions and legal policy. The basic subject of the research carried out by Leon Petrażycki was represented by law. Originally, it had a psychological character, not an objective, eternal, and unchanging one. To fully understand the genesis and nature of morality and law, Petrażycki addressed the study (...) of mental phenomena, especially emotional experiences. First, however, he developed appropriate rules of logic and scientific methodology. Then he developed a new classification of mental phenomena, among which the fundamental role is played by bilateral emotions. At some stage, emotions begin to cooperate with cognitive processes, first of all with imaginations. Imaginations of acts, such as theft, betrayal, murder, can cause repulsive emotions, and type imaginations, such as truthfulness, charity, justice can evoke apulsive emotions. On the basis of such associations, judgments are created over time, the content of which becomes a basis for fundamental rules of conduct, that is, for norms. There are two fundamentally different types of norms: moral norms and legal norms. The norms of the first type are imperative and represent the nature of validity, while the norms of the second type are imperative-attributive and they also always entitle someone to something, i.e. they give someone a right. This division determines a fundamental difference between morality and law. (shrink)

Listening and polyphony lead us directly to reflection on the musical form of the fugue. Starting with M. Heidegger’s considerations about the juncture of beyng, we will phe-nomenologically ask about the essence of the fugue, and the musical work put under analysis will be The Art of Fugue by J.S. Bach. The article aims to show the convergence between Heidegger’s philosophy and the essence of the musical form of fugue as an artis-tic mode of the essential occurrence of beyng as (...) an event. (shrink)

The main goal of this paper is to present the Marian Smoluchowski’s work on thermal and primordial fluctuations which are the main cause of Brownian motion and one of the first empirical evidences for molecular structure of matter.

All physical processes are deterministic de iure. Physicists speak about different types of determinism of physical processes, depending on the degree with which their course can be anticipated. Usually, the course of ergodic processes can be predicted with less certainty than the non-ergodic ones, the latter being integrable. Recent measurements of motions of single particles in composite systems, especially in living biological cells, show that such motions are, in most cases, breaking the Boltzmann’s ergodic hypothesis. On the other hand, their (...) trajectories are random, i.e., one cannot know a priori where the particle will be even in near future. This leads to conclusion that many existing in nature processes are nonergodic but not integrable, therefore predictable only in the mean, representing still other type of determinism. (shrink)

The time of mechanics is the eternal and unchangeable time of Parmenides, it is Plato’s idea of time, whereas the time of thermodynamics is Heraclitus’ flowing time, Thomas Aquinas’ time measured by various phenomena. I once wrote [2] that people who are not used to a physicist’s way of thinking are (at best) confused by the idea of a symmetrical time of mechanics. Physicists on the other hand often believe that the time of thermodynamics (irreversibility) does not really exist, and (...) is merely an illusion. It seems therefore that both of these aspects of time, the time of mechanics and the time of thermodynamics, should be treated as complementary, in anticipation of a future “theory of everything” which will somehow reconcile them. (shrink)

The spontaneity of natural life is the only property which differs this type of life from artificial life. However, it may be the main basis to understand life. Artificial life is constructed by living beings; it is a part of the natural life process, and its properties are not an effect of its own restrictions but of external assumptions. Therefore the investigation of artificial life is not a safe way of searching for basic properties of natural life. The purposefulness appears (...) only in the area of a life process. We generalize the notion of information and encoding to apply them to the physical phenomena description. We use them to define the purposeful information—its example is a biological information, its quantity is an Eigen’s information value. Next we investigate properties of the spontaneous process of purposeful information collecting. In effect we get such properties of this process as: a goal “to exist”, reproduction and the Darwinian mechanism of randomchangeability and elimination. In this process a natural identity criterion of the evolving object connected with the “small change tendency” appears. (shrink)

This review pertains to the book _Evolutionary Theology (Teologia ewolucyjna)_ written by Wojciech P. Grygiel and Damian Wąsek. The book presents a distinct and modern viewpoint on theology by offering a comprehensive analysis of the characteristics of theological language and utilizing it to reevaluate certain theological beliefs, such as the concept of original sin, within the framework of the ever-changing understanding of the Universe. This approach contributes significantly to the restoration of theology’s credibility in modern culture by bridging the gap (...) between science and theology. (shrink)