A Precis of Mathematical Logic

by Józef Maria Bocheński (Editor)

The work of which this is an English translation appeared originally in French as Precis de logique mathematique. In 1954 Dr. Albert Menne brought out a revised and somewhat enlarged edition in German (Grund­ riss der Logistik, F. Schoningh, Paderborn). In making my translation I have used both editions. For the most part I have followed the original French edition, since I thought there was some advantage in keeping the work as short as possible. However, I have included the more extensive historical notes of Dr. Menne, his bibliography, and the two sections on modal logic and the syntactical categories (§ 25 and 27), which were not in the original. I have endeavored to correct the typo­ graphical errors that appeared in the original editions and have made a few additions to the bibliography. In making the translation I have profited more than words can tell from the ever-generous help of Fr. Bochenski while he was teaching at the University of Notre Dame during 1955-56. OTTO BIRD Notre Dame, 1959 I GENERAL PRINCIPLES § O. INTRODUCTION 0. 1. Notion and history. Mathematical logic, also called 'logistic', ·symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the last century with the aid of an artificial notation and a rigorously deductive method.

109 pages, Hardcover

First published July 31, 1960

About the author

Józef Maria Bocheński (born 30 august 1902 in Czuszw, Poland - 1995) was a Polish dominican, logician and philosopher. After taking part in the 1920 campaign against Bolshevik Russia, he took up legal studies in Lww, then he studied economy in Poznań. Having received his doctorate in philosophy (studied in Freiburg, 1928-1931) and theology (Rome, 1931-1934), he lectured in logic at the Collegium Angelicum in Rome (until 1940). During World War II he served as a chaplain for Polish forces fighting in the September campaign (1939) taken prisoner of war, he escaped the Germans and reached Rome. He joined the Polish army and served as chaplain first in France, and then in England. Fought as a soldier in 1944, in the Italian campaign of the II Corps at Monte Cassino. In 1945 he received the chair of history of twentieth-century philosophy at the Freiburg University (of which he was Rector in 1964-1966); he founded and ran the Institute of Eastern Europe in Freiburg, published the journal Studies in Soviet Thought and a book series concerned with the foundations of the Marxists philosophy (Sovietica). Bocheski served as consultant to several governments: West Germany (under K. Adenauer), South Africa, USA, Argentina, and Switzerland. Before 1989 none of his works had been published officially in Poland.

Reviews

[Sathyan · Rating 5 out of 5]

This book does exactly what it sets out to do; it provides the reader with a definition of the terms used in formal logic, and demonstrates methods of their use in constructing statements and arguments, giving axiomatic systems where these are useful and deriving most of the useful theorems. There is a minimum of fuss, consisting of extremely brief and generally necessary historical discussion, a welcome relief to anyone who has tried to read a modern textbook.

This Precis thoroughly covers systems from the propositional calculus to the logic of functions, using wherever possible the notation of Lukasiewicz along with that of Whitehead and Russell. Where one system is omitted it is generally inapplicable.

[Charls · Rating 5 out of 5]

Basically the definitive summary of logical notations and the thinking behind them of the (mid-)twentieth century.