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 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


Book Description




Spatial Information Theory


Book Description

This book constitutes the proceedings of the 12th International Conference on Spatial Information Theory, COSIT 2015, held in Santa Fee, NM, USA, in October 2015. The 22 papers presented in this book were carefully reviewed and selected from 52 full paper submissions. The following topics are addressed: formalizing and modeling space-time, qualitative spatio-temporal reasoning and representation, language and space, signs, images, maps, and other representations of space, navigations by humans and machines.




Relational Methods for Computer Science Applications


Book Description

This volume addresses all current aspects of relational methods and their applications in computer science. It presents a broad variety of fields and issues in which theories of relations provide conceptual or technical tools. The contributions address such subjects as relational methods in programming, relational constraints, relational methods in linguistics and spatial reasoning, relational modelling of uncertainty. All contributions provide the readers with new and original developments in the respective fields. The reader thus gets an interdisciplinary spectrum of the state of the art of relational methods and implementation-oriented solutions of problems related to these areas.




Who Gave You the Epsilon?


Book Description

Follows on from Sherlock Holmes in Babylon to take the history of mathematics through the nineteenth and twentieth centuries.




Alfred Tarski: Philosophy of Language and Logic


Book Description

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.




Aspects of Natural Language Processing


Book Description

For many years Leonard Bolc has played an important role in the Polish computer science community. He is especially known for his clear vision in the development of artificial intelligence, inspiring research, organizational and editorial achievements in areas such as e.g.: logic, automatic reasoning, natural language processing, and computer applications of natural language or human-like reasoning. This Festschrift volume, published to honor Leonard Bolc on his 75th birthday includes 17 refereed papers by leading researchers, his friends, former students and colleagues to celebrate his scientific career. The essays present research in the areas which Leonard Bolc and his colleagues investigated during his long scientific career. The volume is organized in three parts; the first is devoted to logic - the domain which was one of the most explored by Leonard Bolc himself. The second part contains papers focusing on different aspects of computational linguistics; the third part comprises papers describing different applications in which natural language processing or automatic reasoning plays an important role.




Philosophy and Ideology


Book Description

The purpose of this study is to describe the development of philosophy in Poland since the end of the Second World War and the development of Marxist-Leninist philosophy which, owing to international political events, has assumed an impor tant role in the intellectual life of contemporary Poland. This task could not have been accomplished without relating post-war developments to those of the inter war period. Consequently, the period studied covers the years 1918-1958. Yet another extension was necessary. Marxism-Leninism regards sociology as a part of philosophy. Moreover, Marxism-Leninism often resorts to sociology to support or justify some of its philosophical views. Finally, its criticism of 'bourgeois philosophy' is often concerned with social philosophy and socio logical theories which supposedly are implicit or explicit in 'bourgeois philoso phy'. For this reason it was desirable to consider in this study some theoretical and methodological problems of the social sciences. They are taken into ac count when they illuminate philosophical controversies or the evolution of Marxist-Leninist philosophy. Marxism-Leninism is not only a new line of development but also a new point of departure in Polish philosophy. It provides a striking contrast with the established philosophical tradition which originated roughly at the time when G. E. Moore and Bertrand Russell initiated the analytical trend in English philosophy. The contrast can be epitomised by the contradistinction of philoso phy and ideology, chosen as the title of this study.




Logic and Philosophy in the Lvov—Warsaw School


Book Description

The Lvov-Warsaw School was active in all spheres of philosophy. Its members worked in the border area between philosophy and disci plines such as psychology, linguistics, and literary theory. But its most important achievements were without doubt in logic and philosophical analysis based on logic. The present book is concerned with fields to which the Lvov-Warsaw School made its most important and famous contributions. Data on the School as a whole are included only in the first and last part of the book. This work is based on my monograph (1985), which appeared in Polish. But it is not merely a translation, because some fragments of the Polish version have been omitted (e. g., the chapter on ethics), and some have been revised. Many persons helped me in my work on the book in Polish as well as on the present edition. I must first mention the late Izydora D~mbska, to whom this book is dedicated. On various detailed issues I have availed myself of advice and information given to me by Stefan Amsterdamski, Zdzislaw Augustynek, Kazimierz Czarnota, Henryk Hii, Boleslaw Iwanus, Jacek Jadacki, Jacek KabziIiski, Stanislaw Kiczuk, Tomasz Komendzinski, Janina Kotarbinska, Czeslaw Lejewski, Jerzy Perzanowski, Marian Przet~cki, the late Jerzy Slupecki, Klemens Szaniawski, Stefan Zamecki, Zbigniew Zwinogrodzki i Jan Zygmunt. I am indebted to Jaakko Hintikka for suggesting that my book be trans lated into English and published by Reidel. Olgierd Wojtasiewicz helped me to prepare the English text.