Józef Maria Bocheński


Józef Maria Bocheński was a Polish Dominican, logician and philosopher.

Life

After taking part in the 1920 campaign against Soviet Russia, he took up legal studies in Lwów, then studied economics in Poznań. Bocheński earned a doctorate in philosophy. He was also an alumnus of the Pontifical University of Saint Thomas Aquinas, Angelicum in Rome where he studied Sacred Theology from 1931 to 1934 earning a doctorate in Sacred Theology. Bocheński was a professor of logic at the Angelicum until 1940.
During World War II he served as chaplain to Polish forces during the 1939 invasion of Poland, was taken prisoner of war, escaped the Germans and reached Rome. He joined the Polish Army and served as chaplain first in France, then in England. He fought as a soldier in 1944 in the Italian campaign of the Polish II Corps at Monte Cassino.
In 1945 he received the chair in the history of twentieth-century philosophy at the University of Fribourg ; he founded and ran the Institute of Eastern Europe there, and published the journal Studies in Soviet Thought and a book series concerned with the foundations of Marxist philosophy.
Bocheński served as consultant to several governments: West Germany, South Africa, the United States, Argentina, and Switzerland.
Before 1989 none of his works were published officially in Poland.

Cracow Circle

Bocheński is perhaps the most famous exponent of the Cracow Circle Thomism, which has been called "the most significant expression of Catholic thought between the two World Wars." The Circle was founded by a group of philosophers and theologians that, in distinction from traditional neo-Thomism, embraced modern formal logic and applied it to traditional Thomist philosophy and theology. Inspired by the logical clarity of Aquinas, members of the Circle held both philosophy and theology to contain "propositions with truth-values…a structured body of propositions connected in meaning and subject matter, and linked by logical relations of compatibility and incompatibility, entailment etc." "The Cracow Circle set about investigating and where possible improving this logical structure with the most advanced logical tools available at the time, namely those of modern mathematical logic, then called ‘logistic’." Other members of the Circle included :pl:Jan Salamucha|Jan Salamucha and Jan F. Drewnowski.

''Précis de logique mathématique''

Bochenski said "that once when he went to visit Lukasiewicz before the war , Lukasiewicz conveyed him inside excitedly, indicated a complex formula, beginning something like 'CCC...', and said, 'Look at this beautiful and self-evidently true formula.' Clearly the formula's truth was not immediately evident to the bemused Bochenski."
In Bocheński's Précis de logique mathématique, he uses this notation, in the style of Łukasiewicz:
Tautology VpqOpqContradiction
Logical disjunction ApqXpqLogical NOR
Converse conditional BpqMpqConverse nonimplication
Material conditional CpqLpqMaterial nonimplication
Logical NAND DpqKpqLogical conjunction
Logical biconditional EpqJpqExclusive disjunction
Negation Np; Fpqp; IpqProjection function to first argument
Negation Nq; Gpqq; HpqProjection function to second argument

The logical hexagon for the square of opposition

quoted a passage of Bochenski’s Formale Logik in Structure intellectuelles : "Hindu logic knows of three logical propositions and not the four of western logic. For it Some S are P does not signify Some S at least are P but Some S are P but not all." This passage shows that Indian tradition explicitly speaks of the existence of partial quantity, the third quantity to be considered along with totality apprehended by A the universal affirmative of the square, and zero quantity apprehended by E the universal negative of the square. To the two universals A and E entertaining a relationship of contrariety, one should add the third contrary constituted by the double negation of the first two. As the subcontrary I contradicts E and the subcontrary O contradicts A, the logical proposition apprehending partial quantity can be represented by the conjunction of I and O : I & O. In Blanché’s logical hexagon this conjunction is symbolized by the letter Y. Many scholars think that the logical square of opposition, representing four values, should be replaced by the logical hexagon, which has the power to express more relations of opposition.

Works