UNILOG 2018
FROM ARISTOTLE TO LWS
Prof. Dr. Angel Garrido
Dep. of Fundamental Mathematics
Faculty of Sciences UNED
Paseo Senda del Rey, 9
28040 - Madrid, Spain
Abstract
The roots of the Lvov-Warsaw School (LWS, by acronym) can be traced back to Aristotle himself. But in later times we better put them into thinking GW Leibniz and who somehow inherited many of these ways of thinking, such as the philosopher and mathematician Bernhard Bolzano. Since he would pass the key figure of Franz Brentano, who had as one of his disciples to Kazimierz Twardowski, which starts with the brilliant Polish school of mathematics and philosophy dealt with. Among them, one of the most interesting thinkers must be Jan Lukasiewicz, the father of many-valued logic.
Jan Lukasiewicz (1878-1956) began teaching at the University of Lvóv (now Lwiw; former Lemberg, but also Leópolis), and then at Warsaw, but after World War II must to continue in Dublin. Some questions may be very astonishing in the CV of Lukasiewicz. For instance, that a firstly Polish Minister of Education in Paderewski cabinet, into the new Polish Republic, and also Rector for two times at Warsaw University, was awarded with a Doctorate `Honoris Causa´ in spring 1936, at University of Münster, into the maximum of effervescency of Nazism in Germany. The explanation must be their good relation with a very good friend, the former theologian, and then logician, Heinrich Schölz, which was the first Chairman of Mathematical Logic in German universities.
Lukasiewicz firstly studied Law, and then Mathematics and Philosophy in Lvov (then Lemberg). His doctoral supervisor was Kazimierz Twardowski, and in 1902 he obtain his Ph. D. title with a very special mention: `sub auspiciis Imperatoris´ (i.e., under the auspices of the Kaiser). Also he received a doctorate ring with diamonds from the Kaiser of the Austro-Hungarian Empire, Franz Joseph I.
From 1902, Lukasiewicz was employed as a private teacher, and also as a desk in the Universitary Library of Lvov. So it was until 1904 when he obtained a scholarship to study abroad. He defends his `Habilitationschrift´ in 1906, entitled “Analysis and construction of the concept of cause”. This permits to give university courses. His first lectures were on the Algebra of Logic, according to the recent translation to Polish of this book of the French logician Louis Couturat.
Between 1902 and 1906, Lukasiewicz continued his studies in the universities of Berlin and Leuwen (Lovaina). In 1906, by his `Habilitationschrift´, he obtain the qualification as university professor at Lvov. And the, in 1911, he was appointed as associate professor in his `alma mater´ (Lemberg).
Jan Lukasiewicz was also very active in historical research on logic, giving a new and up-to-date interpretation of Aristotle´s syllogism and of the Stoics´ propositional calculus. According to Scholz, the better pages on history of logic are due to him. And also, as Arianna Betti says, “Jan Lukasiewicz is first and foremost associated with the rejection of the Principle of Bivalence and the discovery of Many-Valued Logic.”
The discovery of MVL by Lukasiewicz was in 1918, a little earlier than Emil Leon Post. According to Jan Wolenski, “although Post´s remarks were parenthetical and extremely condensed, Lukasiewicz explained his intuitions and motivations carefully and at length. He was guided by considerations about future contingents and the concept of possibility”. So, he introduces, firstly, three-valued logic, then four-valued logic, generalized to logics with an arbitrary finite number of veritative values, and finally, to logics with a countably infinite-valued number of such values.
Very noteworthy is his treatment of the history of logic in the light of the new formal logic (then called Logistics). Thus, not only he addressed the issue of future contingents departing from Aristotle, but also put in value logic of the Stoics, at least so far taken. In fact, Heinrich Scholz said, rightly, that Lukasiewicz had written the most lucid pages on the history of logic.
Acknowledgements
This work was supported by the MICINN´s Research Project FFI2016-77574-P, and the Investigation Group of our Spanish University (UNED) that we belong to, into a section about `Science and Technique´, that belongs to the Project entitled “Estudio sistemático de las lecturas heideggerianas de Jacques Derrida. Confluencias y divergencias”. Being Principal Researcher (IP), Prof. Dr. Cristina De Peretti.