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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.

Mathematics --- Logic --- History --- Philosophy. --- Logic of mathematics --- Mathematics, Logic of --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Psychology --- Science --- Reasoning --- Thought and thinking --- Math --- Methodology --- Logic, Symbolic and mathematical. --- Philosophy (General). --- Logic. --- Mathematical Logic and Foundations. --- History of Mathematical Sciences. --- History of Philosophy. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Mathematical logic. --- Mathematics. --- History. --- Mental philosophy --- Humanities --- Annals --- Auxiliary sciences of history

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Logique mathématique --- Logique mathématique --- Histoire des mathematiques

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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.

Philosophy --- Mathematical logic --- Logic --- History of philosophy --- Mathematics --- filosofie --- geschiedenis --- wiskunde --- logica --- anno 1920-1929 --- anno 1930-1939 --- Poland

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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 Bialystok Branch of the University of Warsaw, and supported by the Ministry of Education some of its results are reported in Srzednicki Ed. 1987. The major part of the project was focussed on the software for computer-aided theorem proving called Mizar MSE Multi-Sorted first-order logic with Equality, reported in Marciszewski 1994a 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.

Reasoning.

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Dieses Werk gibt eine Einführung in philosophische Probleme und Hintergründe des mathematischen Denkens und Sprechens, Lehrens und Lernens. Es wendet sich an Lehrende und Studierende der Mathematik und Philosophie. Ausgangspunkt und immer wieder Bezugspunkt sind die reellen Zahlen. In pointierterWeise werden mathematische und philosophische Probleme und Fragen vermerkt, die sich auf dem Weg zu ihnen stellen. Ein umfangreicher Abriss von Auffassungen aus der Geschichte der Mathematik und Philosophie bis hin zu aktuellen Strömungen bildet den Hintergrund für ihre Diskussion. Kapitel über Mengenlehre, Logik und Axiomatik, über ungelöste und unlösbare Probleme und fundamentale Ergebnisse schließen sich an. Ein Rückblick schließt den Text ab. Die Erweiterung der zweiten Auflage betrifft im Kern drei Themen: Die Differenz zwischen Wahrheit und Beweisbarkeit, das philosophische Problem der Anwendbarkeit der Mathematik und den Begriff des Kontinuums. Sie führte zu einer Überarbeitung weiter Teile des Buches. Der Rückblick ist neu geschrieben. Die Autoren Thomas Bedürftig (Leibniz Universität Hannover) und Roman Murawski (Adam Mickiewicz Universität Poznan) sind Mathematiker mit den Forschungsgebieten Philosophie, Geschichte und Grundlagen der Mathematik, Mathematikdidaktik und mathematische Logik. This elementary introduction to philosophical problems and issues in mathematical thought, speech, teaching, and learning is now available in a revised and expanded second edition. It is designed for teachers and students of mathematics and philosophy alike. Real numbers form the basis for discussion and remain a continuous touchstone throughout the work, which incisively addresses a range of mathematical and philosophical problems and questions. The work provides an overview and engages in an in-depth discussion of viewpoints held throughout the history of mathematics and philosophy up to the present day.

Mathematics --- Logic of mathematics --- Mathematics, Logic of --- Philosophy. --- Axiomatics. --- Logic. --- Mathematics. --- Set Theory.