Leśniewski's Systems of Logic and Foundations of Mathematics
Leśniewski's Systems of Logic and Foundations of Mathematics

Author: Rafal Urbaniak

Publisher: Springer Science & Business Media

Published: 2013-09-24

Total Pages: 240

ISBN-13: 3319004824

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This meticulous critical assessment of the ground-breaking work of philosopher Stanislaw Leśniewski focuses exclusively on primary texts and explores the full range of output by one of the master logicians of the Lvov-Warsaw school. The author’s nuanced survey eschews secondary commentary, analyzing Leśniewski's core philosophical views and evaluating the formulations that were to have such a profound influence on the evolution of mathematical logic. One of the undisputed leaders of the cohort of brilliant logicians that congregated in Poland in the early twentieth century, Leśniewski was a guide and mentor to a generation of celebrated analytical philosophers (Alfred Tarski was his PhD student). His primary achievement was a system of foundational mathematical logic intended as an alternative to the Principia Mathematica of Alfred North Whitehead and Bertrand Russell. Its three strands—‘protothetic’, ‘ontology’, and ‘mereology’, are detailed in discrete sections of this volume, alongside a wealth other chapters grouped to provide the fullest possible coverage of Leśniewski’s academic output. With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great pioneers.​

Leśniewski’s Systems Protothetic
Leśniewski’s Systems Protothetic

Author: Jan J.T. Srzednicki

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 322

ISBN-13: 9401157367

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Between the two world wars, Stanislaw Lesniewski (1886-1939), created the famous and important system of foundations of mathematics that comprises three deductive theories: Protothetic, Ontology, and Mereology. His research started in 1914 with studies on the general theory of sets (later named `Mereology'). Ontology followed between 1919 and 1921, and was the next step towards an integrated system. In order to combine these two systematically he constructed Protothetic - the system of `first principles'. Together they amount to what Z. Jordan called `... most thorough, original, and philosophically significant attempt to provide a logically secure foundation for the whole of mathematics'. The volume collects many of the most significant commentaries on, and contributions to, Protothetic. A Protothetic Bibliography is included.

S. Leśniewski’s Lecture Notes in Logic
S. Leśniewski’s Lecture Notes in Logic

Author: Jan J.T. Srzednicki

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 191

ISBN-13: 940092741X

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Stanislaw Lesniewski (1886-1939) was one of the leading Polish logicians and founders of the Warsaw School of Logic whose membership included, beside himself, Jan Lukasiewicz, Tadeusz Kotarbinski, Alfred Tarski, and many others. In his lifetime LeSniewski published only a few hundred pages. He produced many important results in many areas of mathematics; these stood in various relations to each other, and to materials produced by others, and, in time, created more and more editorial problems. Very many were left unpublished at the time of his death. Then in 1944 in the fire of Warsaw the whole of this material was burned and lost -a considerable loss since a great deal of what is important could have been reconstructed from these notes. The present publication aims at presenting unique Lesniewski's materials from alternative sources comprising lecture notes taken during some of Lesniewski's lectures and seminars delivered at the University of Warsaw be tween the two world wars. The editors are aware of the limitations of student notes which cannot compensate for the loss of the original materials. However, they are unique in reflecting Lesniewski's ideas as he himself presented them. Already at the time of his death it was realized that these notes would provide a unique access to Lesniewski's own thought as well as a valuable record of some of the activities of the Warsaw School of Logic.

Polish Scientific Philosophy: The Lvov-Warsaw School
Polish Scientific Philosophy: The Lvov-Warsaw School

Author:

Publisher: BRILL

Published: 2023-03-13

Total Pages: 368

ISBN-13: 9004457275

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One can often encounter an opinion that Polish scientific (or analytic) philosophy (or the Lvov-Warsaw School) deserves to be much better known than actually is. This book is thought as a response to such a claim. The papers collected in this volume are divided into two parts: Background and Influence and History and Systematics. However, there is no sharp borderline between themes which are touched in both parts. Generally speaking, all papers of the first part relate the Lvov-Warsaw School to some philosophical movements (Brentanism, phenomenology and Marxism) external to it whereas the papers collected in the second one focus on internal issues connected with the school (only Roberto Poli takes into account Brentano's views in his discussion of reism). Since the Polish school of mathematical logic is much better known than the Polish analytic philosophy we decided to omit here any treatment of the former. Thus, this collection centers on purely philosophical matters. We projected this volume not as an exhaustive panorama of Polish analytic philosophy but rather as a series of essays on particular persons or topic. As a result one can find here papers on Twardowski. Ajdukiewicz, Kotarbinski, Tarski and Lukasiewicz as well as on ethics on science, nominalism, and the methodology of psychology. We hope that this book will contribute to a better knowledge and evaluation of Polish achievements in analytic philosophy. We would like to express our gratitude to Professor Leszek Nowak, the editor-in-chief of Poznan Studies in the Philosophy of the Sciences and the Humanities, who initiated the idea of the collection and helped in its preparation.

Formal and Informal Methods in Philosophy
Formal and Informal Methods in Philosophy

Author:

Publisher: BRILL

Published: 2020-03-31

Total Pages: 328

ISBN-13: 9004420509

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This book examines the tension between formal and informal methods in philosophy. The rise of analytic philosophy was accompanied by the development of formal logic and many successful applications of formal methods. But analytical philosophy does not rely on formal methods alone. Elements of broadly understood informal logic and logical semiotics, procedures used in natural sciences and humanities, and various kinds of intuition also belong to the philosopher’s toolkit. Papers gathered in the book concern the opposition formality–informality as well as other pairs, such as methodology versus metaphilosophy, interdisciplinarity versus intradisciplinarity, and methodological uniformity versus diversity of sciences. Problems of the nature of logic and the explanatory role of mathematical theories are also discussed.

Alfred Tarski: Philosophy of Language and Logic
Alfred Tarski: Philosophy of Language and Logic

Author: Douglas Patterson

Publisher: Springer

Published: 2012-02-10

Total Pages: 273

ISBN-13: 0230367224

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This study looks to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all of the major issues in Tarski scholarship in light of the conception of Intuitionistic Formalism developed: semantics, truth, paradox, logical consequence.

New Essays on Tarski and Philosophy
New Essays on Tarski and Philosophy

Author: Douglas Patterson

Publisher: OUP Oxford

Published: 2008-09-18

Total Pages: 442

ISBN-13: 0191608831

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New Essays on Tarski and Philosophy aims to show the way to a proper understanding of the philosophical legacy of the great logician, mathematician, and philosopher Alfred Tarski (1902-1983). The contributors are an international group of scholars, some expert in the historical background and context of Tarski's work, others specializing in aspects of his philosophical development, others more interested in understanding Tarski in the light of contemporary thought. The essays can be seen as addressing Tarski's seminal treatment of four basic questions about logical consequence. (1) How are we to understand truth, one of the notions in terms of which logical consequence is explained? What is it that is preserved in valid inference, or that such inference allows us to discover new claims to have on the basis of old? (2) Among what kinds of things does the relation of logical consequence hold? (3) Given answers to the first two questions, what is involved in the consequence relationship itself? What is the preservation at work in 'truth preservation'? (4) Finally, what do truth and consequence so construed have to do with meaning?

Tradition of the Lvov-Warsaw School
Tradition of the Lvov-Warsaw School

Author: Anna Brożek

Publisher: BRILL

Published: 2016-04-08

Total Pages: 366

ISBN-13: 9004311769

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The volume aims to show the variety of research currents of the Lvov-Warsaw School and the ways in which these currents are developed today. The content of the book is divided into three parts. The first part provides an overview of the logico-semiotical achievements of the Lvov-Warsaw School. It also includes analyses of specific problems: categorial grammar, theory of truth, theory of reasoning and semiotic defects. The second part presents some metaphysical and ontological views of Twardowski, Kotarbiński, Ajdukiewicz, Bocheński and Lejewski. In the third part, specific features of psychological and sociological branches of the Lvov-Warsaw School are discussed. Contributors include: Anna Brożek, Wojciech Buszkowski, Alicja Chybińska, Mariusz Grygianiec, Aleksandra Horecka, Stepan Ivanyk, Jacek Jadacki, Ryszard Kleszcz, Natalia Miklaszewska, Wioletta Miśkiewicz, Teresa Rzepa, Piotr Surma, Jan Woleński, and Marta Zaręba.