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.​

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.

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.

Volume five of a ten volume set which provides full and detailed coverage of all aspects of philosophy, including information on how philosophy is practiced in different countries, who the most influential philosophers were, and what the basic concepts are.

1. STRUCTURE AND REFERENCES 1.1. The main part of the dictionary consists of alphabetically arranged articles concerned with basic logical theories and some other selected topics. Within each article a set of concepts is defined in their mutual relations. This way of defining concepts in the context of a theory provides better understand ing of ideas than that provided by isolated short defmitions. A disadvantage of this method is that it takes more time to look something up inside an extensive article. To reduce this disadvantage the following measures have been adopted. Each article is divided into numbered sections, the numbers, in boldface type, being addresses to which we refer. Those sections of larger articles which are divided at the first level, i.e. numbered with single numerals, have titles. Main sections are further subdivided, the subsections being numbered by numerals added to the main section number, e.g. I, 1.1, 1.2, ... , 1.1.1, 1.1.2, and so on. A comprehensive subject index is supplied together with a glossary. The aim of the latter is to provide, if possible, short defmitions which sometimes may prove sufficient. As to the use of the glossary, see the comment preceding it.