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.

The present article deals with different Marxist theories on the Soviet experience, which emerged in post-Soviet Russophone Marxist or neo-Marxist scholarship (concurrently with some reference to Marxist traditions in other former Eastern Bloc countries). The article demonstrates that these theories – if we leave the remaining ‘Marxist-Leninists’ of the classical Soviet type aside and focus on critical, post-Soviet Marxism – may be classified as either ‘fundamentally rejectionist’ or ‘Thermidorian’. The former, in line with the seminal criticisms of K. Kautsky and (...) other early opponents of Lenin, reject the socialist nature of the October 1917 Revolution outright. The latter mostly define the Revolution as at least socialist-oriented, but further bifurcate into different varieties of the ‘state capitalism’ thesis with a number of theorists defining Stalinist societies as special varieties of post-revolutionary industrialism essentially different from orthodox capitalism. Most critical post-Soviet Marxists agree, however, that the main vector of Soviet-type regimes’ evolution indeed pointed towards increased class stratification. However, it should be remembered that Soviet-type bureaucracy was a class-in-the-making rather than a class-in-itself or a class-for-itself, and this point is further elaborated in the works of those theorists who prioritise the differences rather than similarities between Soviet-type industrialism and orthodox capitalism. (shrink)

The book deals with the influences exerted by Social Darwinism upon Korea’s modern ideologies and discourses in the 1880s-1900s. It argues that Social Darwinism constituted the main keystone for many pivotal discourses in early modern Korea, especially nationalism.

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)

In this article we are offering a method of analysis and formalization of the Epicurean objection to the Skeptics from the Adversus mathematicos VIII, 337, 6-9. We emphasize the importance of this objection for understanding Sextus Empiricus’ response to it, continuously discussed by the historians of philosophy. The Epicureans argue that the Skeptics cannot criticize their proof, because when the Skeptics are criticizing their proof, they think something different from the original proof, so that the original proof remains untouchable by (...) any criticism. We explain in which sense the holistic assumption used by Sextus Empiricus and some philosophers before him can be used in the Epicurean objection to the Skeptics. In the final formalization we show that Epicureans’ argument can be interpreted as logically correct and deduced from sound premises. In the course of arguing for this thesis we are using the technical means of contemporary epistemic logic. (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)