# Józef Maria Bocheński

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**Józef Maria Bocheński** (Czuszów, Congress Poland, Russian Empire, 30 August 1902 – 8 February 1995, Fribourg, Switzerland) was a Polish Dominican, logician and philosopher.

## LifeEdit

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 studied in Fribourg in Switzerland, 1928–31). 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 (of which he was rector in 1964-66); 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 (*Sovietica*).

Bocheński served as consultant to several governments: West Germany (under Konrad Adenauer), South Africa, the United States, Argentina, and Switzerland.

Before 1989 none of his works were published officially in Poland.

## Cracow CircleEdit

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."^{[1]} 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.^{[2]} 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’." ^{[3]} Other members of the Circle included Jan Salamucha and Jan F. Drewnowski.

*Précis de logique mathématique*Edit

Bochenski said "that once when he went to visit Lukasiewicz before the war [World War II], 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."^{[4]}

In Bocheński's *Précis de logique mathématique*, he uses this notation, in the style of Łukasiewicz:^{[5]}

Tautology (Truth) | (T T T T)(p,q) |
Vpq |
Opq |
(F F F F)(p,q) |
Contradiction (Falsity) |

Logical disjunction (Disjunction) | (T T T F)(p,q) |
Apq |
Xpq |
(F F F T)(p,q) |
Logical NOR (Joint denial) |

Converse conditional (Converse implication) | (T T F T)(p,q) |
Bpq |
Mpq |
(F F T F)(p,q) |
Converse nonimplication |

Material conditional (Material implication) | (T F T T)(p,q) |
Cpq |
Lpq |
(F T F F)(p,q) |
Material nonimplication |

Logical NAND (Alternative denial) | (F T T T)(p,q) |
Dpq |
Kpq |
(T F F F)(p,q) |
Logical conjunction (Conjunction) |

Logical biconditional (Equivalence) | (T F F T)(p,q) |
Epq |
Jpq |
(F T T F)(p,q) |
Exclusive disjunction (Nonequivalence) |

Negation (of first argument) | (F F T T)(p,q) |
Np; Fpq |
p; Ipq |
(T T F F)(p,q) |
Projection function to first argument |

Negation (of second argument) | (F T F T)(p,q) |
Nq; Gpq |
q; Hpq |
(T F T F)(p,q) |
Projection function to second argument |

## The logical hexagon for the square of oppositionEdit

Robert Blanché quoted a passage of Bochenski’s *Formale Logik* in *Structure intellectuelles* (1966, 39): "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^{[who?]} 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.

## WorksEdit

*Elementa logicae graecae*(1937), Rome: Anonima Libraria Catolica Italiana.*Manuale di filosofia bolscevica*(1946)*La logique de Théophraste*(1947), 1987 reprint, New York, Garland Publishing.*Europäische Philosophie der Gegenwart*(1947), Bern: A. Francke.*Précis de logique mathématique*(1948), Bussum, North Holland: F. G. Kroonder.*ABC tomizmu*(1950), London: Veritas.*Der sowjetrussische Dialektische Materialismus*(1950)*Ancient formal logic*(1951)*Szkice etyczne: Zebrał i ułożył Adam Bocheński*(1953), London: Veritas.*Die zeitgenössischen Denkmethoden*(1954)*Die kommunistische Ideologie und die Würde, Freiheit und Gleichheit der Menschen im Sinne des Grundgesetzes für die Bundesrepublik Deutschland vom 23.5.1949*(1956), [Bonn]: Bundeszentrale für Heimatdienst.*Bibliographie der Sowietischen Philosophie*(1959), Fribourg: Ost-Europa Institut.*Formale Logik*(1956) translated into English as*A history of formal logic*(1961)*Der sowjetrussische dialektische Materialismus*(Diamat) (1962)- (co-edited with Gerhart Niemayer)
*Handbook on Communism*(1962), New York: Praeger. *The Logic of Religion*(1965)*Wege zum philosophischen Denken*(1967)*Guide to Marxist philosophy: an introductory bibliography*(1972), Chicago: Swallow Press.*Philosophy, an introduction*(1972), New York: Harper & Row.*Marxismus-Leninismus. Wissenschaft oder Glaube?*(1973), München: Olzog.*Was ist Autorität?: Einf. in d. Logik d. Autorität*(1974), Fribourg: Herder.*Logic and Ontology*(1974)*Sto zabobonów. Krótki filozoficzny słownik zabobonów*("One Hundred Superstitions. A Short Philosophical Dictionary of Superstitions", 1987).*Logika i filosofia*(1993)*Miedzy logika a wiara*(1994)*Szkice o nacionalizmie i katolicyzmie polskim*(1994), Komorów: Wydawn. Antyk, Marcin Dybowski.*Wspomnienia*(1994), Kraków: Philed.*Lewica, religia, sowietologica*(1996), Warsaw: Zakon Ojców Dominikanów.*The Road to Understanding. More than Dreamt of in Your Philosophy*(1996), ISBN 1-886670-06-4

## See alsoEdit

## NotesEdit

**^**http://segr-did2.fmag.unict.it/~polphil/polphil/Cracow/Cracow.html Archived 2013-03-13 at the Wayback Machine Accessed 15 March 2013**^**http://segr-did2.fmag.unict.it/~polphil/polphil/Cracow/Cracow.html Archived 2013-03-13 at the Wayback Machine Accessed 15 March 2013**^**" Bocheński and Balance: System and History in Analytic Philosophy", Peter Simons, Studies in East European Thought 55 (2003), 281–297, Reprinted in: Edgar Morscher, Otto Neumaier and Peter Simons, Ein Philosoph mit "Bodenhaftung": Zu Leben und Werk von Joseph M. Bocheński. St.Augustin: Academia, 2011, 61–79**^**Simons, Peter (2014), "Lukasiewicz's Parenthesis-Free or Polish Notation," in*Stanford Encyclopedia of Philosophy*, [emphasis as in Simons]. http://plato.stanford.edu . Accessed 2020 May 26.**^**Józef Maria Bocheński (1948/1959),*A Précis of Mathematical Logic*, trans., Otto Bird, from French and German editions, Dordrecht, South Holland: Reidel, passim.