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)

Transformácia politického systému -- Aktuálne problémy a riešenia -- Alternatívy súčasného kapitalizmu -- Cynizmus ako princíp -- Appendix o školstve.

Between the zone of certainty beyond all doubt and the zone of incomprehensible uncertainty, the sources of which are nothing but chance, we need to use solid results from a vast interdisciplinarity. We wish to give here a sense of the factors in play and the state of the debate and advance in the territory of how interdisciplinarity may help to solve problems which are common in many areas of knowledge. Chaos and complexity certainly put limits on what we can (...) know. High complexity, asymmetry and/or non-linearity are universal types of imprecision. Can hazard have purpose and direction?The idea is that the more effort we put into project design to cover as many details and possible consequences as possible we can grasp in our in-depth analysis aiming to create the project (in art or science or society), the greater the chances that the random occurrence of the unpredictable event will settle on the project's purpose and direction and not on contrary to them. There is no vicious circle here. This kind of method can explain many good results already obtained in such circumstances. Simplicity, beauty, rationalistic optimism, are features of unshakeable scientific results We may call this feature of scientific theory or art _uniqueness. _Uniqueness is strongly correlated with _essentialization. _Science is working in that sense: to simplify a phenomenon to its essence in order to study it easily without losing anything important in the analysis. That is _essentialization. _Why and how complex systems move to the edge of chaos? And what do they do to stay there? They are in constant struggle to create or keep order in complexity. That is the pattern of self-organization, the specific feature of human nature. That is why our action is meant to build resilience to deal better with unpredictable events and prevent the emergence of a critical threshold. Uncertainty, indeterminacy, randomness, and contradictions appear, not as non-essential substances of debate to be eliminated by explanation, but as everlasting ingredients of our conception of reality. There are compelling reasons to believe that it is impossible to make accurate, nontrivial predictions concerning human behavior. Logic and reason are and remain priority, but unpredictability forces us to imagination and creative thinking. Indeed we are confronted with a new human landscape. The anomalies become the new normal. (shrink)

Translated excerpts from works by various authors; original titles and names of the translators given in captions.

The earliest writer who deserves to be called a psychologist is Hobbes; and if we consider the time when he wrote, we cannot fail to be surprised at what I may term his prevision of the most important results which have now been established by science. He was the first clearly to sound the note which has ever since constituted the bass, or fundamental tone, of scientific thought. Let us listen to it through the clear instrumentality of his own language:-.

Il est commun, aujourd'hui, d'associer la démocratie au consensus, et ce d'une double manière : d'une part en admettant qu'elle est le meilleur régime politique possible, d'autre part en considérant que l'accord vaut intrinsèquement mieux que le désaccord, et l'entente que le conflit: La qualité de la démocratie tiendrait à ses débats publics, qui à la fois rendent possible la confrontation des points de vue, tout en y mettant fin par l'obtention de consensus éclairés et légitimés par la règle de (...) la majorité. Et si le conflit, au contraire, dans certaines conditions, devait servir de principe à la vie politique? Il ne suffit pas de vivre en démocratie pour rendre la démocratie vivante. La démocratie n'est pas un régime mais un questionnement. Elle exige des citoyens une interrogation continue sur le bien commun à suivre. Machiavel n'était pas un démocrate. Mais c'est étrangement en actualisant sa pensée, dans le sillage des travaux de Lefort, qu'il est possible d'associer le conflit civil avec l'imaginaire social pour redynamiser la démocratie par la tension conflictuelle entre l'idéologie et l'utopie. Penser la démocratie à partir de ce que donne à penser Machiavel : voilà ce que s'efforce de faire Sébastien Roman, pour proposer dans une perspective républicaine le modèle d'un espace public dissensuel."--Page 4 of cover. (shrink)

The volume consists of thirteen papers devoted to various problems of the philosophy of logic and mathematics. They can be divided into two groups. The first group contains papers devoted to some general problems of the philosophy of mathematics whereas the second group - papers devoted to the history of logic in Poland and to the work of Polish logicians and math-ematicians in the philosophy of mathematics and logic. Among considered problems are: meaning of reverse mathematics, proof in mathematics, the (...) status of Church's Thesis, phenomenology in the philosophy of mathematics, mathematics vs. theology, the problem of truth, philosophy of logic and mathematics in the interwar Poland. (shrink)

The volume contains twenty essays devoted to the philosophy of mathematics and the history of logic. They have been divided into four parts: general philosophical problems of mathematics, Hilbert's program vs. the incompleteness phenomenon, philosophy of mathematics in Poland, mathematical logic in Poland. Among considered problems are: epistemology of mathematics, the meaning of the axiomatic method, existence of mathematical objects, distinction between proof and truth, undefinability of truth, Goedel's theorems and computer science, philosophy of mathematics in Polish mathematical and logical (...) schools, beginnings of mathematical logic in Poland, contribution of Polish logicians to recursion theory. (shrink)

Models are of central importance in many scientific contexts. The centrality of models such as inflationary models in cosmology, general-circulation models of the global climate, the double-helix model of DNA, evolutionary models in biology, agent-based models in the social sciences, and general-equilibrium models of markets in their respective domains is a case in point (the Other Internet Resources section at the end of this entry contains links to online resources that discuss these models). Scientists spend significant amounts of time building, (...) testing, comparing, and revising models, and much journal space is dedicated to interpreting and discussing the implications of models. In short, models are one of the principal instruments of modern science. (shrink)

The problem of how the brain produces consciousness, subjectivity and "something it is like to be" remains one of the greatest challenges to a complete science of the natural world. While various scientists and philosophers approach the problem from their own unique perspectives and in the terms of their own respective fields, Biophysics of Consciousness: A Foundational Approach attempts a consilience across disparate disciplines to explain how it is possible that an objective brain produces subjective experience. This volume unites the (...) cr me de la cr me of physicists, neuroscientists, and psychiatrists in the attempt to understand consciousness through a foundational approach encompassing ontological, evolutionary, neurobiological, and Freudian interpretations with the focus on conscious phenomena occurring in the brain. By integrating the perspectives of these diverse disciplines with the latest research and theories on the biophysics of the brain, the book tries to explain how what John Searle calls a "conscious field" can be an adaptive and causal element in the natural world. (shrink)

This textbook is a second edition of the successful, Mathematical Logic: On Numbers, Sets, Structures, and Symmetry. It retains the original two parts found in the first edition, while presenting new material in the form of an added third part to the textbook. The textbook offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Part I, Logic Sets, and Numbers, shows how mathematical logic is used to (...) develop the number structures of classical mathematics. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. The added Part III to the book is closer to what one finds in standard introductory mathematical textbooks. Definitions, theorems, and proofs that are introduced are still preceded by remarks that motivate the material, but the exposition is more formal, and includes more advanced topics. The focus is on the notion of countable categoricity, which analyzed in detail using examples from the first two parts of the book. This textbook is suitable for graduate students in mathematical logic and set theory and will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background. (shrink)

The book is a collection of the author’s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the (...) history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered.This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields. (shrink)

The article is devoted to the analysis of the phenomenon of historical experience in Gadamer's hermeneutics and Ankersmit's philosophical-historical concept. The interest of the philosophy of history in experience was actualized against the background of exhaustion of the heuristic potential of historical narrativism and constructivism, closely related to the so-called "linguistic turn". At first glance, Gadamer and Ankersmit are representing antinomic interpretations of historical experience: as mediated by the effects of involvement in a tradition or heritage and direct, extracontextual encounter (...) with the past. However, the investigation proves that, despite the apparent antinomy of these approaches, the Gadamerian hermeneutic experience as an experience of the prevailing historical reality is not so far from the sublime historical experience of Ankersmit. And, on the contrary, the sublime historical experience, despite its claims to immediacy, turns out to be an experience of the finitude of human existence, that is, it is close to what Gadamer considered the essence of hermeneutic experience. In both cases, historical experience is considered as a condition for the possibility of understanding the past, and therefore, the question of the universal structure of such experience and understanding necessarily arises. The differences in the positions of the two authors stem from fundamentally different ontological prejudices that they share. For Gadamer, this is the reduction of history to a linguistically structured heritage, as a result of which most of the past falls out of hermeneutic experience. For Ankersmit, this is an uncritical understanding of time, as a result of which his concept of the sublime does not receive a reliable methodological foundation. Clarification of the temporality of the sublime historical, as well as rejection of the rigid connection between historical experience and language, open the prospect of removing the abstract antinomy of contextuality and immediacy of historical experience. The temporality of human existence turns out to be a universal prerequisite of historical experience, the two opposite forms of which are heredity and discontinuity. Contrary to the widespread criticism of Ankersmit's theory as far from historiographical practice, the development of the potential of the concept of sublime historical experience reveals its relevance to the dynamic and tragic modern history that Ukraine is currently experiencing. (shrink)

Most scientific models are not physical objects, and this raises important questions. What sort of entity are models, what is truth in a model, and how do we learn about models? In this paper I argue that models share important aspects in common with literary fiction, and that therefore theories of fiction can be brought to bear on these questions. In particular, I argue that the pretence theory as developed by Walton (1990, Mimesis as make-believe: on the foundations of the (...) representational arts. Harvard University Press, Cambridge/MA) has the resources to answer these questions. I introduce this account, outline the answers that it offers, and develop a general picture of scientific modelling based on it. (shrink)