Leśniewski’s Systems Protothetic


Book Description

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.




Leśniewski's Systems of Logic and Foundations of Mathematics


Book Description

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


Book Description




The Golden Age of Polish Philosophy


Book Description

Jan Wolenski ́ and Sandra Lapointe Polish philosophy goes back to the 13th century, when Witelo, famous for his works in optics and the metaphysics of light, lived and worked in Silesia. Yet, Poland’s academic life only really began after the University of Cracow was founded in 1364 – its development was interrupted by the sudden death of King Kazimierz III, but it was re-established in 1400. The main currents of classical scholastic thought like Thomism, Scottism or Ockhamism had been late – about a century – to come to Poland and they had a considerable impact on the budding Polish philosophical scene. The controversy between the via antiqua and the via moderna was hotly 1 debated. Intellectuals deliberated on the issues of concilliarism (whether the C- mon Council has priority over the Pope) and curialism (whether the Bishop of Rome has priority over the Common Council). On the whole, the situation had at least two remarkable features. Firstly, Polish philosophy was pluralistic, and remained so, since its very beginning. But it was also eclectic, which might explain why it aimed to a large extent at achieving a compromise between rival views. Secondly, given the shortcomings of the political system of the time as well as external pr- sure by an increasingly hegemonic Germany, thinkers were very much interested in political matters. Poland was a stronghold of political thought (mostly inclined towards concilliarism) and Polish political thought distinguished itself in Europe J.




Tradition of the Lvov-Warsaw School


Book Description

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.




Logic in Question


Book Description

This contributed volume collects papers related to the Logic in Question workshop, which has taken place annually at Sorbonne University in Paris since 2011. Each year, the workshop brings together historians, philosophers, mathematicians, linguists, and computer scientists to explore questions related to the nature of logic and how it has developed over the years. As a result, chapter authors provide a thorough, interdisciplinary exploration of topics that have been studied in the workshop. Organized into three sections, the first part of the book focuses on historical questions related to logic, the second explores philosophical questions, and the third section is dedicated to mathematical discussions. Specific topics include: • logic and analogy• Chinese logic• nineteenth century British logic (in particular Boole and Lewis Carroll)• logical diagrams • the place and value of logic in Louis Couturat’s philosophical thinking• contributions of logical analysis for mathematics education• the exceptionality of logic• the logical expressive power of natural languages• the unification of mathematics via topos theory Logic in Question will appeal to pure logicians, historians of logic, philosophers, linguists, and other researchers interested in the history of logic, making this volume a unique and valuable contribution to the field.




S. Leśniewski’s Lecture Notes in Logic


Book Description

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.




The Reconstruction of A. N. Prior's Ontology


Book Description

Although the first analytic philosophers were primarily focused on the logical analysis of language, some of their initial works also contained ontological discussions. One of the most distinct ontological positions of the twentieth century was defended by Arthur Norman Prior. The unusual nature of the position could be demonstrated by the fact that he was ascribed to such divergent positions as nominalism and platonism. This might have been caused by his atypical combination of ontological views. He was, on the one hand, a nominalist in his mature works. On the other hand, he advocated intensional logic and presentism. The aim of this study is to reconstruct the ideas which influenced him as he formulated his ontological positions. Not only are Prior’s ideas introduced, but also the ideas of his precursors and contemporaries who influenced him. In contrast, the ideas of logicians and philosophers who Prior opposed are also presented. The dissertation consists of four parts which deal with Prior’s concepts of possible worlds, theories of quantifications, propositions and individuals. It is a historical study and therefore the polemics which arose after Prior’s death are not discussed.




Formal and Informal Methods in Philosophy


Book Description

The title of this book refers to the tension between formal and informal elements in the ways analytical philosophy is practiced. The authors examine questions of the scopes and limits of both kinds of research methods.




Polish Logic, 1920-1939


Book Description

Polish Logic 1920-1939